diff --git a/your-code/.ipynb_checkpoints/main-checkpoint.ipynb b/your-code/.ipynb_checkpoints/main-checkpoint.ipynb
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+{
+ "cells": [
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "# Understanding Descriptive Statistics\n",
+ "\n",
+ "Import the necessary libraries here:"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 29,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "import pandas as pd\n",
+ "import numpy as np"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Challenge 1\n",
+ "#### 1.- Define a function that simulates rolling a dice 10 times. Save the information in a dataframe.\n",
+ "**Hint**: you can use the *choices* function from module *random* to help you with the simulation."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 30,
+ "metadata": {
+ "scrolled": true
+ },
+ "outputs": [
+ {
+ "data": {
+ "text/html": [
+ "\n",
+ "\n",
+ "
\n",
+ " \n",
+ " \n",
+ " Roll \n",
+ " \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0 \n",
+ " 6 \n",
+ " \n",
+ " \n",
+ " 1 \n",
+ " 1 \n",
+ " \n",
+ " \n",
+ " 2 \n",
+ " 4 \n",
+ " \n",
+ " \n",
+ " 3 \n",
+ " 6 \n",
+ " \n",
+ " \n",
+ " 4 \n",
+ " 2 \n",
+ " \n",
+ " \n",
+ " 5 \n",
+ " 3 \n",
+ " \n",
+ " \n",
+ " 6 \n",
+ " 3 \n",
+ " \n",
+ " \n",
+ " 7 \n",
+ " 2 \n",
+ " \n",
+ " \n",
+ " 8 \n",
+ " 2 \n",
+ " \n",
+ " \n",
+ " 9 \n",
+ " 2 \n",
+ " \n",
+ " \n",
+ "
\n",
+ "
"
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "import matplotlib.pyplot as plt\n",
+ "\n",
+ "def simulate_dice_rolls(num_rolls=10):\n",
+ " rolls = [random.randint(1, 6) for _ in range(num_rolls)]\n",
+ " df = pd.DataFrame({'Roll': rolls})\n",
+ " return df\n",
+ "\n",
+ "# Simulate dice rolls and create DataFrame\n",
+ "dice_df = simulate_dice_rolls()\n",
+ "\n",
+ "# Sort the DataFrame by the 'Roll' column\n",
+ "sorted_df = dice_df.sort_values(by='Roll')\n",
+ "\n",
+ "# Plot the sorted results\n",
+ "plt.figure(figsize=(8, 6))\n",
+ "plt.bar(sorted_df.index, sorted_df['Roll'])\n",
+ "plt.xlabel('Roll Index')\n",
+ "plt.ylabel('Dice Value')\n",
+ "plt.title('Sorted Dice Rolls')\n",
+ "plt.xticks(sorted_df.index)\n",
+ "plt.grid(True)\n",
+ "plt.show()"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "#### 3.- Calculate the frequency distribution and plot it. What is the relation between this plot and the plot above? Describe it with words."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 32,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "image/png": 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",
+ "text/plain": [
+ ""
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "def simulate_dice_rolls(num_rolls=10):\n",
+ " rolls = [random.randint(1, 6) for _ in range(num_rolls)]\n",
+ " df = pd.DataFrame({'Roll': rolls})\n",
+ " return df\n",
+ "\n",
+ "dice_df = simulate_dice_rolls()\n",
+ "\n",
+ "frequency_distribution = dice_df['Roll'].value_counts().sort_index()\n",
+ "\n",
+ "plt.figure(figsize=(8, 6))\n",
+ "plt.bar(frequency_distribution.index, frequency_distribution.values)\n",
+ "plt.xlabel('Dice Value')\n",
+ "plt.ylabel('Frequency')\n",
+ "plt.title('Dice Roll Frequency Distribution')\n",
+ "plt.xticks(range(1, 7))\n",
+ "plt.grid(True)\n",
+ "plt.show()"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "\"\"\"\n",
+ "the first plot gives a visual representation of the sequence of rolls, \n",
+ "while the second plot gives a summary of how often each value occurred in the rolls.\n",
+ "\"\"\""
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Challenge 2\n",
+ "Now, using the dice results obtained in *challenge 1*, your are going to define some functions that will help you calculate the mean of your data in two different ways, the median and the four quartiles. \n",
+ "\n",
+ "#### 1.- Define a function that computes the mean by summing all the observations and dividing by the total number of observations. You are not allowed to use any methods or functions that directly calculate the mean value. "
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 43,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "Mean: 3.7\n"
+ ]
+ }
+ ],
+ "source": [
+ "def calculate_mean(df):\n",
+ " total_sum = 0\n",
+ " num_observations = len(df)\n",
+ "\n",
+ " for value in df['Roll']:\n",
+ " total_sum += value\n",
+ "\n",
+ " mean = total_sum / num_observations\n",
+ " return mean\n",
+ "\n",
+ "mean = calculate_mean(dice_df)\n",
+ "print(\"Mean:\", mean)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "#### 2.- First, calculate the frequency distribution. Then, calculate the mean using the values of the frequency distribution you've just computed. You are not allowed to use any methods or functions that directly calculate the mean value. "
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 34,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "Mean: 3.7\n"
+ ]
+ }
+ ],
+ "source": [
+ "def calculate_mean_from_frequency(frequency_distribution):\n",
+ " total_sum = 0\n",
+ " total_observations = 0\n",
+ "\n",
+ " for value, frequency in frequency_distribution.items():\n",
+ " total_sum += value * frequency\n",
+ " total_observations += frequency\n",
+ "\n",
+ " mean = total_sum / total_observations\n",
+ " return mean\n",
+ "\n",
+ "mean_from_frequency = calculate_mean_from_frequency(frequency_distribution)\n",
+ "print(\"Mean:\", mean_from_frequency)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "#### 3.- Define a function to calculate the median. You are not allowed to use any methods or functions that directly calculate the median value. \n",
+ "**Hint**: you might need to define two computation cases depending on the number of observations used to calculate the median."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 35,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "Median: 3.0\n"
+ ]
+ }
+ ],
+ "source": [
+ "def calculate_median(df):\n",
+ " sorted_values = sorted(df['Roll'])\n",
+ " num_observations = len(sorted_values)\n",
+ "\n",
+ " if num_observations % 2 != 0:\n",
+ " median_index = num_observations // 2\n",
+ " median = sorted_values[median_index]\n",
+ " \n",
+ " else:\n",
+ " upper_median_index = num_observations // 2\n",
+ " lower_median_index = upper_median_index - 1\n",
+ " median = (sorted_values[lower_median_index] + sorted_values[upper_median_index]) / 2\n",
+ " \n",
+ " return median\n",
+ "\n",
+ "median = calculate_median(dice_df)\n",
+ "print(\"Median:\", median)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "#### 4.- Define a function to calculate the four quartiles. You can use the function you defined above to compute the median but you are not allowed to use any methods or functions that directly calculate the quartiles. "
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 36,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "Q1: 2\n",
+ "Median (Q2): 3.0\n",
+ "Q3: 6\n"
+ ]
+ }
+ ],
+ "source": [
+ "def calculate_quartiles(df):\n",
+ " sorted_values = sorted(df['Roll'])\n",
+ " num_observations = len(sorted_values)\n",
+ "\n",
+ " median = calculate_median(df)\n",
+ " \n",
+ " if num_observations % 2 != 0:\n",
+ " lower_half_end_index = num_observations // 2\n",
+ " upper_half_start_index = lower_half_end_index + 1\n",
+ " else:\n",
+ " lower_half_end_index = num_observations // 2\n",
+ " upper_half_start_index = lower_half_end_index\n",
+ "\n",
+ " lower_half = sorted_values[:lower_half_end_index]\n",
+ " upper_half = sorted_values[upper_half_start_index:]\n",
+ "\n",
+ " q1 = calculate_median(pd.DataFrame({'Roll': lower_half}))\n",
+ " q3 = calculate_median(pd.DataFrame({'Roll': upper_half}))\n",
+ "\n",
+ " return q1, median, q3\n",
+ "\n",
+ "q1, median, q3 = calculate_quartiles(dice_df)\n",
+ "print(\"Q1:\", q1)\n",
+ "print(\"Median (Q2):\", median)\n",
+ "print(\"Q3:\", q3)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Challenge 3\n",
+ "Read the csv `roll_the_dice_hundred.csv` from the `data` folder.\n",
+ "#### 1.- Sort the values and plot them. What do you see?"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 37,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/html": [
+ "\n",
+ "\n",
+ "
\n",
+ " \n",
+ " \n",
+ " Unnamed: 0 \n",
+ " roll \n",
+ " value \n",
+ " \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0 \n",
+ " 0 \n",
+ " 0 \n",
+ " 1 \n",
+ " \n",
+ " \n",
+ " 1 \n",
+ " 1 \n",
+ " 1 \n",
+ " 2 \n",
+ " \n",
+ " \n",
+ " 2 \n",
+ " 2 \n",
+ " 2 \n",
+ " 6 \n",
+ " \n",
+ " \n",
+ " 3 \n",
+ " 3 \n",
+ " 3 \n",
+ " 1 \n",
+ " \n",
+ " \n",
+ " 4 \n",
+ " 4 \n",
+ " 4 \n",
+ " 6 \n",
+ " \n",
+ " \n",
+ "
\n",
+ "
"
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "sorted_values = roll_the_dice['value'].sort_values()\n",
+ "\n",
+ "plt.figure(figsize=(8, 6))\n",
+ "plt.plot(sorted_values, marker='o', linestyle='-', color='b')\n",
+ "plt.xlabel('Index')\n",
+ "plt.ylabel('Dice Value')\n",
+ "plt.title('Sorted Dice Rolls')\n",
+ "plt.grid(True)\n",
+ "plt.show()"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "\"\"\"\n",
+ "Each point on the plot represents a single dice roll, \n",
+ "with the x-axis representing the index of the sorted values and the y-axis representing the dice value.\n",
+ "\"\"\""
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "#### 2.- Using the functions you defined in *challenge 2*, calculate the mean value of the hundred dice rolls."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 46,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "Mean: 3.74\n"
+ ]
+ }
+ ],
+ "source": [
+ "def calculate_mean(series):\n",
+ " total_sum = 0\n",
+ " num_observations = len(series)\n",
+ "\n",
+ " for value in series:\n",
+ " total_sum += value\n",
+ "\n",
+ " mean = total_sum / num_observations\n",
+ " return mean\n",
+ "\n",
+ "mean_value = calculate_mean(roll_the_dice['value'])\n",
+ "print(\"Mean:\", mean_value)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "#### 3.- Now, calculate the frequency distribution.\n"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 48,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "value\n",
+ "1 12\n",
+ "2 17\n",
+ "3 14\n",
+ "4 22\n",
+ "5 12\n",
+ "6 23\n",
+ "Name: count, dtype: int64\n"
+ ]
+ }
+ ],
+ "source": [
+ "frequency_distribution = roll_the_dice['value'].value_counts().sort_index()\n",
+ "print(frequency_distribution)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "#### 4.- Plot the histogram. What do you see (shape, values...) ? How can you connect the mean value to the histogram? "
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 49,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "image/png": 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",
+ "text/plain": [
+ ""
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "import matplotlib.pyplot as plt\n",
+ "\n",
+ "plt.figure(figsize=(8, 6))\n",
+ "plt.hist(roll_the_dice['value'], bins=range(1, 8), edgecolor='black', alpha=0.7)\n",
+ "plt.xlabel('Dice Value')\n",
+ "plt.ylabel('Frequency')\n",
+ "plt.title('Histogram of Dice Rolls')\n",
+ "plt.grid(True)\n",
+ "plt.show()"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "\"\"\"\n",
+ "the x-axis represents the dice values and the y-axis represents the frequency of each value.\n",
+ "the histogram might show a relatively uniform distribution if the dice rolls are fair, \n",
+ "meaning each value occurs with approximately the same frequency. \n",
+ "The mean value, calculated earlier, represents the average value of the dice rolls, \n",
+ "which should fall somewhere in the center of the distribution if the rolls are fair.\n",
+ "\"\"\""
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "#### 5.- Read the `roll_the_dice_thousand.csv` from the `data` folder. Plot the frequency distribution as you did before. Has anything changed? Why do you think it changed?"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 50,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/html": [
+ "\n",
+ "\n",
+ "
\n",
+ " \n",
+ " \n",
+ " Unnamed: 0 \n",
+ " roll \n",
+ " value \n",
+ " \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0 \n",
+ " 0 \n",
+ " 0 \n",
+ " 5 \n",
+ " \n",
+ " \n",
+ " 1 \n",
+ " 1 \n",
+ " 1 \n",
+ " 6 \n",
+ " \n",
+ " \n",
+ " 2 \n",
+ " 2 \n",
+ " 2 \n",
+ " 1 \n",
+ " \n",
+ " \n",
+ " 3 \n",
+ " 3 \n",
+ " 3 \n",
+ " 6 \n",
+ " \n",
+ " \n",
+ " 4 \n",
+ " 4 \n",
+ " 4 \n",
+ " 5 \n",
+ " \n",
+ " \n",
+ "
\n",
+ "
"
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "plt.figure(figsize=(8, 6))\n",
+ "plt.hist(roll_the_dice_th['value'], bins=range(1, 8), edgecolor='black', alpha=0.7)\n",
+ "plt.xlabel('Dice Value')\n",
+ "plt.ylabel('Frequency')\n",
+ "plt.title('Histogram of Dice Rolls (Thousand)')\n",
+ "plt.grid(True)\n",
+ "plt.show()"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "\"\"\"\n",
+ "With a larger sample size, the distribution of the dice rolls is likely to approach the expected distribution more closely. \n",
+ "Therefore, the histogram may show more uniformity in the distribution of values, especially if the dice rolls are fair.\n",
+ "\"\"\""
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Challenge 4\n",
+ "In the `data` folder of this repository you will find three different files with the prefix `ages_population`. These files contain information about a poll answered by a thousand people regarding their age. Each file corresponds to the poll answers in different neighbourhoods of Barcelona.\n",
+ "\n",
+ "#### 1.- Read the file `ages_population.csv`. Calculate the frequency distribution and plot it as we did during the lesson. Try to guess the range in which the mean and the standard deviation will be by looking at the plot. "
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 56,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/html": [
+ "\n",
+ "\n",
+ "
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+ " \n",
+ " \n",
+ " observation \n",
+ " \n",
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+ " \n",
+ " \n",
+ " 0 \n",
+ " 68.0 \n",
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+ " 2 \n",
+ " 45.0 \n",
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+ " 3 \n",
+ " 38.0 \n",
+ " \n",
+ " \n",
+ " 4 \n",
+ " 49.0 \n",
+ " \n",
+ " \n",
+ "
\n",
+ "
"
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "plt.figure(figsize=(8, 6))\n",
+ "plt.hist(ages_population['observation'], bins=range(0, 101, 5), edgecolor='black', alpha=0.7)\n",
+ "plt.xlabel('Age')\n",
+ "plt.ylabel('Frequency')\n",
+ "plt.title('Histogram of Age Distribution')\n",
+ "plt.grid(True)\n",
+ "plt.show()"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "\"\"\"\n",
+ "the mean is around the center of the distribution, and the standard deviation measures the spread of the data around the mean.\n",
+ "we might expect the mean to be somewhere between 20 to 40 years, and the standard deviation to be relatively small,\n",
+ "indicating that most people fall within a certain age range around the mean.\n",
+ "\"\"\""
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "#### 2.- Calculate the exact mean and standard deviation and compare them with your guesses. Do they fall inside the ranges you guessed?"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 59,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "Mean age: 36.56\n",
+ "Standard deviation of age: 12.816499625976762\n"
+ ]
+ }
+ ],
+ "source": [
+ "mean_age = ages_population['observation'].mean()\n",
+ "std_age = ages_population['observation'].std()\n",
+ "\n",
+ "print(\"Mean age:\", mean_age)\n",
+ "print(\"Standard deviation of age:\", std_age)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "\"\"\"\n",
+ "yes indeed\n",
+ "\"\"\""
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "#### 3.- Now read the file `ages_population2.csv` . Calculate the frequency distribution and plot it."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 60,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/html": [
+ "\n",
+ "\n",
+ "
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+ " \n",
+ " \n",
+ " observation \n",
+ " \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0 \n",
+ " 25.0 \n",
+ " \n",
+ " \n",
+ " 1 \n",
+ " 31.0 \n",
+ " \n",
+ " \n",
+ " 2 \n",
+ " 29.0 \n",
+ " \n",
+ " \n",
+ " 3 \n",
+ " 31.0 \n",
+ " \n",
+ " \n",
+ " 4 \n",
+ " 29.0 \n",
+ " \n",
+ " \n",
+ "
\n",
+ "
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+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "plt.figure(figsize=(8, 6))\n",
+ "plt.hist(ages_population2['observation'], bins=range(0, 101, 5), edgecolor='black', alpha=0.7)\n",
+ "plt.xlabel('Age')\n",
+ "plt.ylabel('Frequency')\n",
+ "plt.title('Histogram of Age Distribution (Population 2)')\n",
+ "plt.grid(True)\n",
+ "plt.show()"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "#### 4.- What do you see? Is there any difference with the frequency distribution in step 1?"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "\"\"\"\n",
+ "the shape of the distribution isdifferent. It is more symmetric.\n",
+ "standard deviation is narrower\n",
+ "\"\"\""
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "#### 5.- Calculate the mean and standard deviation. Compare the results with the mean and standard deviation in step 2. What do you think?"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 62,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "Mean age (Population 2): 27.155\n",
+ "Standard deviation of age (Population 2): 2.969813932689186\n"
+ ]
+ }
+ ],
+ "source": [
+ "mean_age_pop2 = ages_population2['observation'].mean()\n",
+ "std_age_pop2 = ages_population2['observation'].std()\n",
+ "\n",
+ "print(\"Mean age (Population 2):\", mean_age_pop2)\n",
+ "print(\"Standard deviation of age (Population 2):\", std_age_pop2)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "\"\"\"\n",
+ "there are significant differences in the central tendency and spread of the age distributions between the two populations.\n",
+ "mean std deviation are lower\n",
+ "\"\"\""
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Challenge 5\n",
+ "Now is the turn of `ages_population3.csv`.\n",
+ "\n",
+ "#### 1.- Read the file `ages_population3.csv`. Calculate the frequency distribution and plot it."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 63,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/html": [
+ "\n",
+ "\n",
+ "
\n",
+ " \n",
+ " \n",
+ " observation \n",
+ " \n",
+ " \n",
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+ " \n",
+ " 0 \n",
+ " 21.0 \n",
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+ " \n",
+ " 1 \n",
+ " 21.0 \n",
+ " \n",
+ " \n",
+ " 2 \n",
+ " 24.0 \n",
+ " \n",
+ " \n",
+ " 3 \n",
+ " 31.0 \n",
+ " \n",
+ " \n",
+ " 4 \n",
+ " 54.0 \n",
+ " \n",
+ " \n",
+ "
\n",
+ "
"
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "plt.figure(figsize=(8, 6))\n",
+ "plt.hist(ages_population3['observation'], bins=range(0, 101, 5), edgecolor='black', alpha=0.7)\n",
+ "plt.xlabel('Age')\n",
+ "plt.ylabel('Frequency')\n",
+ "plt.title('Histogram of Age Distribution (Population 3)')\n",
+ "plt.grid(True)\n",
+ "plt.show()"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "#### 2.- Calculate the mean and standard deviation. Compare the results with the plot in step 1. What is happening?"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 65,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "Mean age (Population 3): 41.989\n",
+ "Standard deviation of age (Population 3): 16.144705959865934\n"
+ ]
+ }
+ ],
+ "source": [
+ "mean_age_pop3 = ages_population3['observation'].mean()\n",
+ "std_age_pop3 = ages_population3['observation'].std()\n",
+ "\n",
+ "print(\"Mean age (Population 3):\", mean_age_pop3)\n",
+ "print(\"Standard deviation of age (Population 3):\", std_age_pop3)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "\"\"\"\n",
+ "mean std deviation are higher.\n",
+ "Outliers can significantly affect the shape and spread of the distribution.\n",
+ "\"\"\""
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "#### 3.- Calculate the four quartiles. Use the results to explain your reasoning for question in step 2. How much of a difference is there between the median and the mean?"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 67,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "Q1: 30.0\n",
+ "Median (Q2): 40.0\n",
+ "Q3: 53.0\n"
+ ]
+ }
+ ],
+ "source": [
+ "q1_pop3 = np.percentile(ages_population3['observation'], 25)\n",
+ "median_pop3 = np.percentile(ages_population3['observation'], 50)\n",
+ "q3_pop3 = np.percentile(ages_population3['observation'], 75)\n",
+ "\n",
+ "print(\"Q1:\", q1_pop3)\n",
+ "print(\"Median (Q2):\", median_pop3)\n",
+ "print(\"Q3:\", q3_pop3)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "\"\"\"\n",
+ "median is less than the mean, it indicates a left-skewed distribution\n",
+ "\"\"\""
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "#### 4.- Calculate other percentiles that might be useful to give more arguments to your reasoning."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 68,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "10th Percentile (P10): 22.0\n",
+ "90th Percentile (P90): 67.0\n"
+ ]
+ }
+ ],
+ "source": [
+ "p10_pop3 = np.percentile(ages_population3['observation'], 10)\n",
+ "p90_pop3 = np.percentile(ages_population3['observation'], 90)\n",
+ "\n",
+ "print(\"10th Percentile (P10):\", p10_pop3)\n",
+ "print(\"90th Percentile (P90):\", p90_pop3)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "\"\"\"\n",
+ "These percentiles can help us understand the spread and variability of the data beyond the quartiles.\n",
+ "\"\"\""
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Bonus challenge\n",
+ "Compare the information about the three neighbourhoods. Prepare a report about the three of them. Remember to find out which are their similarities and their differences backing your arguments in basic statistics."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "# your code here"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "\"\"\"\n",
+ "your comments here\n",
+ "\"\"\""
+ ]
+ }
+ ],
+ "metadata": {
+ "kernelspec": {
+ "display_name": "Python 3 (ipykernel)",
+ "language": "python",
+ "name": "python3"
+ },
+ "language_info": {
+ "codemirror_mode": {
+ "name": "ipython",
+ "version": 3
+ },
+ "file_extension": ".py",
+ "mimetype": "text/x-python",
+ "name": "python",
+ "nbconvert_exporter": "python",
+ "pygments_lexer": "ipython3",
+ "version": "3.11.7"
+ }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 2
+}
diff --git a/your-code/ages_population.csv b/your-code/ages_population.csv
new file mode 100644
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--- /dev/null
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diff --git a/your-code/ages_population2.csv b/your-code/ages_population2.csv
new file mode 100644
index 0000000..00860cb
--- /dev/null
+++ b/your-code/ages_population2.csv
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diff --git a/your-code/ages_population3.csv b/your-code/ages_population3.csv
new file mode 100644
index 0000000..6339a1d
--- /dev/null
+++ b/your-code/ages_population3.csv
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diff --git a/your-code/main.ipynb b/your-code/main.ipynb
index 5759add..c04c31b 100644
--- a/your-code/main.ipynb
+++ b/your-code/main.ipynb
@@ -1,522 +1,1459 @@
-{
- "cells": [
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "# Understanding Descriptive Statistics\n",
- "\n",
- "Import the necessary libraries here:"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": null,
- "metadata": {},
- "outputs": [],
- "source": [
- "# Libraries"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "## Challenge 1\n",
- "#### 1.- Define a function that simulates rolling a dice 10 times. Save the information in a dataframe.\n",
- "**Hint**: you can use the *choices* function from module *random* to help you with the simulation."
- ]
- },
- {
- "cell_type": "code",
- "execution_count": null,
- "metadata": {},
- "outputs": [],
- "source": [
- "# your code here"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "#### 2.- Plot the results sorted by value."
- ]
- },
- {
- "cell_type": "code",
- "execution_count": null,
- "metadata": {},
- "outputs": [],
- "source": [
- "# your code here"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "#### 3.- Calculate the frequency distribution and plot it. What is the relation between this plot and the plot above? Describe it with words."
- ]
- },
- {
- "cell_type": "code",
- "execution_count": null,
- "metadata": {},
- "outputs": [],
- "source": [
- "# your code here"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": null,
- "metadata": {},
- "outputs": [],
- "source": [
- "\"\"\"\n",
- "your comments here\n",
- "\"\"\""
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "## Challenge 2\n",
- "Now, using the dice results obtained in *challenge 1*, your are going to define some functions that will help you calculate the mean of your data in two different ways, the median and the four quartiles. \n",
- "\n",
- "#### 1.- Define a function that computes the mean by summing all the observations and dividing by the total number of observations. You are not allowed to use any methods or functions that directly calculate the mean value. "
- ]
- },
- {
- "cell_type": "code",
- "execution_count": null,
- "metadata": {},
- "outputs": [],
- "source": [
- "# your code here"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "#### 2.- First, calculate the frequency distribution. Then, calculate the mean using the values of the frequency distribution you've just computed. You are not allowed to use any methods or functions that directly calculate the mean value. "
- ]
- },
- {
- "cell_type": "code",
- "execution_count": null,
- "metadata": {},
- "outputs": [],
- "source": [
- "# your code here"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "#### 3.- Define a function to calculate the median. You are not allowed to use any methods or functions that directly calculate the median value. \n",
- "**Hint**: you might need to define two computation cases depending on the number of observations used to calculate the median."
- ]
- },
- {
- "cell_type": "code",
- "execution_count": null,
- "metadata": {},
- "outputs": [],
- "source": [
- "# your code here"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "#### 4.- Define a function to calculate the four quartiles. You can use the function you defined above to compute the median but you are not allowed to use any methods or functions that directly calculate the quartiles. "
- ]
- },
- {
- "cell_type": "code",
- "execution_count": null,
- "metadata": {},
- "outputs": [],
- "source": [
- "# your code here"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "## Challenge 3\n",
- "Read the csv `roll_the_dice_hundred.csv` from the `data` folder.\n",
- "#### 1.- Sort the values and plot them. What do you see?"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": null,
- "metadata": {},
- "outputs": [],
- "source": [
- "# your code here"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": null,
- "metadata": {},
- "outputs": [],
- "source": [
- "\"\"\"\n",
- "your comments here\n",
- "\"\"\""
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "#### 2.- Using the functions you defined in *challenge 2*, calculate the mean value of the hundred dice rolls."
- ]
- },
- {
- "cell_type": "code",
- "execution_count": null,
- "metadata": {},
- "outputs": [],
- "source": [
- "# your code here"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "#### 3.- Now, calculate the frequency distribution.\n"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": null,
- "metadata": {},
- "outputs": [],
- "source": [
- "# your code here"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "#### 4.- Plot the histogram. What do you see (shape, values...) ? How can you connect the mean value to the histogram? "
- ]
- },
- {
- "cell_type": "code",
- "execution_count": null,
- "metadata": {},
- "outputs": [],
- "source": [
- "# your code here"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": null,
- "metadata": {},
- "outputs": [],
- "source": [
- "\"\"\"\n",
- "your comments here\n",
- "\"\"\""
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "#### 5.- Read the `roll_the_dice_thousand.csv` from the `data` folder. Plot the frequency distribution as you did before. Has anything changed? Why do you think it changed?"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": null,
- "metadata": {},
- "outputs": [],
- "source": [
- "# your code here"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": null,
- "metadata": {},
- "outputs": [],
- "source": [
- "\"\"\"\n",
- "your comments here\n",
- "\"\"\""
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "## Challenge 4\n",
- "In the `data` folder of this repository you will find three different files with the prefix `ages_population`. These files contain information about a poll answered by a thousand people regarding their age. Each file corresponds to the poll answers in different neighbourhoods of Barcelona.\n",
- "\n",
- "#### 1.- Read the file `ages_population.csv`. Calculate the frequency distribution and plot it as we did during the lesson. Try to guess the range in which the mean and the standard deviation will be by looking at the plot. "
- ]
- },
- {
- "cell_type": "code",
- "execution_count": null,
- "metadata": {},
- "outputs": [],
- "source": [
- "# your code here"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "#### 2.- Calculate the exact mean and standard deviation and compare them with your guesses. Do they fall inside the ranges you guessed?"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": null,
- "metadata": {},
- "outputs": [],
- "source": [
- "# your code here"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": null,
- "metadata": {},
- "outputs": [],
- "source": [
- "\"\"\"\n",
- "your comments here\n",
- "\"\"\""
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "#### 3.- Now read the file `ages_population2.csv` . Calculate the frequency distribution and plot it."
- ]
- },
- {
- "cell_type": "code",
- "execution_count": null,
- "metadata": {},
- "outputs": [],
- "source": [
- "# your code here"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "#### 4.- What do you see? Is there any difference with the frequency distribution in step 1?"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": null,
- "metadata": {},
- "outputs": [],
- "source": [
- "\"\"\"\n",
- "your comments here\n",
- "\"\"\""
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "#### 5.- Calculate the mean and standard deviation. Compare the results with the mean and standard deviation in step 2. What do you think?"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": null,
- "metadata": {},
- "outputs": [],
- "source": [
- "# your code here"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": null,
- "metadata": {},
- "outputs": [],
- "source": [
- "\"\"\"\n",
- "your comments here\n",
- "\"\"\""
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "## Challenge 5\n",
- "Now is the turn of `ages_population3.csv`.\n",
- "\n",
- "#### 1.- Read the file `ages_population3.csv`. Calculate the frequency distribution and plot it."
- ]
- },
- {
- "cell_type": "code",
- "execution_count": null,
- "metadata": {},
- "outputs": [],
- "source": [
- "# your code here"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "#### 2.- Calculate the mean and standard deviation. Compare the results with the plot in step 1. What is happening?"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": null,
- "metadata": {},
- "outputs": [],
- "source": [
- "# your code here"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": null,
- "metadata": {},
- "outputs": [],
- "source": [
- "\"\"\"\n",
- "your comments here\n",
- "\"\"\""
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "#### 3.- Calculate the four quartiles. Use the results to explain your reasoning for question in step 2. How much of a difference is there between the median and the mean?"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": null,
- "metadata": {},
- "outputs": [],
- "source": [
- "# your code here"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": null,
- "metadata": {},
- "outputs": [],
- "source": [
- "\"\"\"\n",
- "your comments here\n",
- "\"\"\""
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "#### 4.- Calculate other percentiles that might be useful to give more arguments to your reasoning."
- ]
- },
- {
- "cell_type": "code",
- "execution_count": null,
- "metadata": {},
- "outputs": [],
- "source": [
- "# your code here"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": null,
- "metadata": {},
- "outputs": [],
- "source": [
- "\"\"\"\n",
- "your comments here\n",
- "\"\"\""
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "## Bonus challenge\n",
- "Compare the information about the three neighbourhoods. Prepare a report about the three of them. Remember to find out which are their similarities and their differences backing your arguments in basic statistics."
- ]
- },
- {
- "cell_type": "code",
- "execution_count": null,
- "metadata": {},
- "outputs": [],
- "source": [
- "# your code here"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": null,
- "metadata": {},
- "outputs": [],
- "source": [
- "\"\"\"\n",
- "your comments here\n",
- "\"\"\""
- ]
- }
- ],
- "metadata": {
- "kernelspec": {
- "display_name": "ironhack-3.7",
- "language": "python",
- "name": "ironhack-3.7"
- },
- "language_info": {
- "codemirror_mode": {
- "name": "ipython",
- "version": 3
- },
- "file_extension": ".py",
- "mimetype": "text/x-python",
- "name": "python",
- "nbconvert_exporter": "python",
- "pygments_lexer": "ipython3",
- "version": "3.7.3"
- }
- },
- "nbformat": 4,
- "nbformat_minor": 2
-}
+{
+ "cells": [
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "# Understanding Descriptive Statistics\n",
+ "\n",
+ "Import the necessary libraries here:"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 29,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "import pandas as pd\n",
+ "import numpy as np"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Challenge 1\n",
+ "#### 1.- Define a function that simulates rolling a dice 10 times. Save the information in a dataframe.\n",
+ "**Hint**: you can use the *choices* function from module *random* to help you with the simulation."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 30,
+ "metadata": {
+ "scrolled": true
+ },
+ "outputs": [
+ {
+ "data": {
+ "text/html": [
+ "\n",
+ "\n",
+ "
\n",
+ " \n",
+ " \n",
+ " Roll \n",
+ " \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0 \n",
+ " 6 \n",
+ " \n",
+ " \n",
+ " 1 \n",
+ " 1 \n",
+ " \n",
+ " \n",
+ " 2 \n",
+ " 4 \n",
+ " \n",
+ " \n",
+ " 3 \n",
+ " 6 \n",
+ " \n",
+ " \n",
+ " 4 \n",
+ " 2 \n",
+ " \n",
+ " \n",
+ " 5 \n",
+ " 3 \n",
+ " \n",
+ " \n",
+ " 6 \n",
+ " 3 \n",
+ " \n",
+ " \n",
+ " 7 \n",
+ " 2 \n",
+ " \n",
+ " \n",
+ " 8 \n",
+ " 2 \n",
+ " \n",
+ " \n",
+ " 9 \n",
+ " 2 \n",
+ " \n",
+ " \n",
+ "
\n",
+ "
"
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "import matplotlib.pyplot as plt\n",
+ "\n",
+ "def simulate_dice_rolls(num_rolls=10):\n",
+ " rolls = [random.randint(1, 6) for _ in range(num_rolls)]\n",
+ " df = pd.DataFrame({'Roll': rolls})\n",
+ " return df\n",
+ "\n",
+ "# Simulate dice rolls and create DataFrame\n",
+ "dice_df = simulate_dice_rolls()\n",
+ "\n",
+ "# Sort the DataFrame by the 'Roll' column\n",
+ "sorted_df = dice_df.sort_values(by='Roll')\n",
+ "\n",
+ "# Plot the sorted results\n",
+ "plt.figure(figsize=(8, 6))\n",
+ "plt.bar(sorted_df.index, sorted_df['Roll'])\n",
+ "plt.xlabel('Roll Index')\n",
+ "plt.ylabel('Dice Value')\n",
+ "plt.title('Sorted Dice Rolls')\n",
+ "plt.xticks(sorted_df.index)\n",
+ "plt.grid(True)\n",
+ "plt.show()"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "#### 3.- Calculate the frequency distribution and plot it. What is the relation between this plot and the plot above? Describe it with words."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 32,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "image/png": 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",
+ "text/plain": [
+ ""
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "def simulate_dice_rolls(num_rolls=10):\n",
+ " rolls = [random.randint(1, 6) for _ in range(num_rolls)]\n",
+ " df = pd.DataFrame({'Roll': rolls})\n",
+ " return df\n",
+ "\n",
+ "dice_df = simulate_dice_rolls()\n",
+ "\n",
+ "frequency_distribution = dice_df['Roll'].value_counts().sort_index()\n",
+ "\n",
+ "plt.figure(figsize=(8, 6))\n",
+ "plt.bar(frequency_distribution.index, frequency_distribution.values)\n",
+ "plt.xlabel('Dice Value')\n",
+ "plt.ylabel('Frequency')\n",
+ "plt.title('Dice Roll Frequency Distribution')\n",
+ "plt.xticks(range(1, 7))\n",
+ "plt.grid(True)\n",
+ "plt.show()"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "\"\"\"\n",
+ "the first plot gives a visual representation of the sequence of rolls, \n",
+ "while the second plot gives a summary of how often each value occurred in the rolls.\n",
+ "\"\"\""
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Challenge 2\n",
+ "Now, using the dice results obtained in *challenge 1*, your are going to define some functions that will help you calculate the mean of your data in two different ways, the median and the four quartiles. \n",
+ "\n",
+ "#### 1.- Define a function that computes the mean by summing all the observations and dividing by the total number of observations. You are not allowed to use any methods or functions that directly calculate the mean value. "
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 43,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "Mean: 3.7\n"
+ ]
+ }
+ ],
+ "source": [
+ "def calculate_mean(df):\n",
+ " total_sum = 0\n",
+ " num_observations = len(df)\n",
+ "\n",
+ " for value in df['Roll']:\n",
+ " total_sum += value\n",
+ "\n",
+ " mean = total_sum / num_observations\n",
+ " return mean\n",
+ "\n",
+ "mean = calculate_mean(dice_df)\n",
+ "print(\"Mean:\", mean)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "#### 2.- First, calculate the frequency distribution. Then, calculate the mean using the values of the frequency distribution you've just computed. You are not allowed to use any methods or functions that directly calculate the mean value. "
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 34,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "Mean: 3.7\n"
+ ]
+ }
+ ],
+ "source": [
+ "def calculate_mean_from_frequency(frequency_distribution):\n",
+ " total_sum = 0\n",
+ " total_observations = 0\n",
+ "\n",
+ " for value, frequency in frequency_distribution.items():\n",
+ " total_sum += value * frequency\n",
+ " total_observations += frequency\n",
+ "\n",
+ " mean = total_sum / total_observations\n",
+ " return mean\n",
+ "\n",
+ "mean_from_frequency = calculate_mean_from_frequency(frequency_distribution)\n",
+ "print(\"Mean:\", mean_from_frequency)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "#### 3.- Define a function to calculate the median. You are not allowed to use any methods or functions that directly calculate the median value. \n",
+ "**Hint**: you might need to define two computation cases depending on the number of observations used to calculate the median."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 35,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "Median: 3.0\n"
+ ]
+ }
+ ],
+ "source": [
+ "def calculate_median(df):\n",
+ " sorted_values = sorted(df['Roll'])\n",
+ " num_observations = len(sorted_values)\n",
+ "\n",
+ " if num_observations % 2 != 0:\n",
+ " median_index = num_observations // 2\n",
+ " median = sorted_values[median_index]\n",
+ " \n",
+ " else:\n",
+ " upper_median_index = num_observations // 2\n",
+ " lower_median_index = upper_median_index - 1\n",
+ " median = (sorted_values[lower_median_index] + sorted_values[upper_median_index]) / 2\n",
+ " \n",
+ " return median\n",
+ "\n",
+ "median = calculate_median(dice_df)\n",
+ "print(\"Median:\", median)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "#### 4.- Define a function to calculate the four quartiles. You can use the function you defined above to compute the median but you are not allowed to use any methods or functions that directly calculate the quartiles. "
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 36,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "Q1: 2\n",
+ "Median (Q2): 3.0\n",
+ "Q3: 6\n"
+ ]
+ }
+ ],
+ "source": [
+ "def calculate_quartiles(df):\n",
+ " sorted_values = sorted(df['Roll'])\n",
+ " num_observations = len(sorted_values)\n",
+ "\n",
+ " median = calculate_median(df)\n",
+ " \n",
+ " if num_observations % 2 != 0:\n",
+ " lower_half_end_index = num_observations // 2\n",
+ " upper_half_start_index = lower_half_end_index + 1\n",
+ " else:\n",
+ " lower_half_end_index = num_observations // 2\n",
+ " upper_half_start_index = lower_half_end_index\n",
+ "\n",
+ " lower_half = sorted_values[:lower_half_end_index]\n",
+ " upper_half = sorted_values[upper_half_start_index:]\n",
+ "\n",
+ " q1 = calculate_median(pd.DataFrame({'Roll': lower_half}))\n",
+ " q3 = calculate_median(pd.DataFrame({'Roll': upper_half}))\n",
+ "\n",
+ " return q1, median, q3\n",
+ "\n",
+ "q1, median, q3 = calculate_quartiles(dice_df)\n",
+ "print(\"Q1:\", q1)\n",
+ "print(\"Median (Q2):\", median)\n",
+ "print(\"Q3:\", q3)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Challenge 3\n",
+ "Read the csv `roll_the_dice_hundred.csv` from the `data` folder.\n",
+ "#### 1.- Sort the values and plot them. What do you see?"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 37,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/html": [
+ "\n",
+ "\n",
+ "
\n",
+ " \n",
+ " \n",
+ " Unnamed: 0 \n",
+ " roll \n",
+ " value \n",
+ " \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0 \n",
+ " 0 \n",
+ " 0 \n",
+ " 1 \n",
+ " \n",
+ " \n",
+ " 1 \n",
+ " 1 \n",
+ " 1 \n",
+ " 2 \n",
+ " \n",
+ " \n",
+ " 2 \n",
+ " 2 \n",
+ " 2 \n",
+ " 6 \n",
+ " \n",
+ " \n",
+ " 3 \n",
+ " 3 \n",
+ " 3 \n",
+ " 1 \n",
+ " \n",
+ " \n",
+ " 4 \n",
+ " 4 \n",
+ " 4 \n",
+ " 6 \n",
+ " \n",
+ " \n",
+ "
\n",
+ "
"
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "sorted_values = roll_the_dice['value'].sort_values()\n",
+ "\n",
+ "plt.figure(figsize=(8, 6))\n",
+ "plt.plot(sorted_values, marker='o', linestyle='-', color='b')\n",
+ "plt.xlabel('Index')\n",
+ "plt.ylabel('Dice Value')\n",
+ "plt.title('Sorted Dice Rolls')\n",
+ "plt.grid(True)\n",
+ "plt.show()"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "\"\"\"\n",
+ "Each point on the plot represents a single dice roll, \n",
+ "with the x-axis representing the index of the sorted values and the y-axis representing the dice value.\n",
+ "\"\"\""
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "#### 2.- Using the functions you defined in *challenge 2*, calculate the mean value of the hundred dice rolls."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 46,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "Mean: 3.74\n"
+ ]
+ }
+ ],
+ "source": [
+ "def calculate_mean(series):\n",
+ " total_sum = 0\n",
+ " num_observations = len(series)\n",
+ "\n",
+ " for value in series:\n",
+ " total_sum += value\n",
+ "\n",
+ " mean = total_sum / num_observations\n",
+ " return mean\n",
+ "\n",
+ "mean_value = calculate_mean(roll_the_dice['value'])\n",
+ "print(\"Mean:\", mean_value)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "#### 3.- Now, calculate the frequency distribution.\n"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 48,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "value\n",
+ "1 12\n",
+ "2 17\n",
+ "3 14\n",
+ "4 22\n",
+ "5 12\n",
+ "6 23\n",
+ "Name: count, dtype: int64\n"
+ ]
+ }
+ ],
+ "source": [
+ "frequency_distribution = roll_the_dice['value'].value_counts().sort_index()\n",
+ "print(frequency_distribution)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "#### 4.- Plot the histogram. What do you see (shape, values...) ? How can you connect the mean value to the histogram? "
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 49,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "image/png": 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",
+ "text/plain": [
+ ""
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "import matplotlib.pyplot as plt\n",
+ "\n",
+ "plt.figure(figsize=(8, 6))\n",
+ "plt.hist(roll_the_dice['value'], bins=range(1, 8), edgecolor='black', alpha=0.7)\n",
+ "plt.xlabel('Dice Value')\n",
+ "plt.ylabel('Frequency')\n",
+ "plt.title('Histogram of Dice Rolls')\n",
+ "plt.grid(True)\n",
+ "plt.show()"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "\"\"\"\n",
+ "the x-axis represents the dice values and the y-axis represents the frequency of each value.\n",
+ "the histogram might show a relatively uniform distribution if the dice rolls are fair, \n",
+ "meaning each value occurs with approximately the same frequency. \n",
+ "The mean value, calculated earlier, represents the average value of the dice rolls, \n",
+ "which should fall somewhere in the center of the distribution if the rolls are fair.\n",
+ "\"\"\""
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "#### 5.- Read the `roll_the_dice_thousand.csv` from the `data` folder. Plot the frequency distribution as you did before. Has anything changed? Why do you think it changed?"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 50,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/html": [
+ "\n",
+ "\n",
+ "
\n",
+ " \n",
+ " \n",
+ " Unnamed: 0 \n",
+ " roll \n",
+ " value \n",
+ " \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0 \n",
+ " 0 \n",
+ " 0 \n",
+ " 5 \n",
+ " \n",
+ " \n",
+ " 1 \n",
+ " 1 \n",
+ " 1 \n",
+ " 6 \n",
+ " \n",
+ " \n",
+ " 2 \n",
+ " 2 \n",
+ " 2 \n",
+ " 1 \n",
+ " \n",
+ " \n",
+ " 3 \n",
+ " 3 \n",
+ " 3 \n",
+ " 6 \n",
+ " \n",
+ " \n",
+ " 4 \n",
+ " 4 \n",
+ " 4 \n",
+ " 5 \n",
+ " \n",
+ " \n",
+ "
\n",
+ "
"
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "plt.figure(figsize=(8, 6))\n",
+ "plt.hist(roll_the_dice_th['value'], bins=range(1, 8), edgecolor='black', alpha=0.7)\n",
+ "plt.xlabel('Dice Value')\n",
+ "plt.ylabel('Frequency')\n",
+ "plt.title('Histogram of Dice Rolls (Thousand)')\n",
+ "plt.grid(True)\n",
+ "plt.show()"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "\"\"\"\n",
+ "With a larger sample size, the distribution of the dice rolls is likely to approach the expected distribution more closely. \n",
+ "Therefore, the histogram may show more uniformity in the distribution of values, especially if the dice rolls are fair.\n",
+ "\"\"\""
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Challenge 4\n",
+ "In the `data` folder of this repository you will find three different files with the prefix `ages_population`. These files contain information about a poll answered by a thousand people regarding their age. Each file corresponds to the poll answers in different neighbourhoods of Barcelona.\n",
+ "\n",
+ "#### 1.- Read the file `ages_population.csv`. Calculate the frequency distribution and plot it as we did during the lesson. Try to guess the range in which the mean and the standard deviation will be by looking at the plot. "
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 56,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/html": [
+ "\n",
+ "\n",
+ "
\n",
+ " \n",
+ " \n",
+ " observation \n",
+ " \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0 \n",
+ " 68.0 \n",
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+ " \n",
+ " 1 \n",
+ " 12.0 \n",
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+ " \n",
+ " 2 \n",
+ " 45.0 \n",
+ " \n",
+ " \n",
+ " 3 \n",
+ " 38.0 \n",
+ " \n",
+ " \n",
+ " 4 \n",
+ " 49.0 \n",
+ " \n",
+ " \n",
+ "
\n",
+ "
"
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "plt.figure(figsize=(8, 6))\n",
+ "plt.hist(ages_population['observation'], bins=range(0, 101, 5), edgecolor='black', alpha=0.7)\n",
+ "plt.xlabel('Age')\n",
+ "plt.ylabel('Frequency')\n",
+ "plt.title('Histogram of Age Distribution')\n",
+ "plt.grid(True)\n",
+ "plt.show()"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "\"\"\"\n",
+ "the mean is around the center of the distribution, and the standard deviation measures the spread of the data around the mean.\n",
+ "we might expect the mean to be somewhere between 20 to 40 years, and the standard deviation to be relatively small,\n",
+ "indicating that most people fall within a certain age range around the mean.\n",
+ "\"\"\""
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "#### 2.- Calculate the exact mean and standard deviation and compare them with your guesses. Do they fall inside the ranges you guessed?"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 59,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "Mean age: 36.56\n",
+ "Standard deviation of age: 12.816499625976762\n"
+ ]
+ }
+ ],
+ "source": [
+ "mean_age = ages_population['observation'].mean()\n",
+ "std_age = ages_population['observation'].std()\n",
+ "\n",
+ "print(\"Mean age:\", mean_age)\n",
+ "print(\"Standard deviation of age:\", std_age)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "\"\"\"\n",
+ "yes indeed\n",
+ "\"\"\""
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "#### 3.- Now read the file `ages_population2.csv` . Calculate the frequency distribution and plot it."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 60,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/html": [
+ "\n",
+ "\n",
+ "
\n",
+ " \n",
+ " \n",
+ " observation \n",
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+ " \n",
+ " \n",
+ " \n",
+ " 0 \n",
+ " 25.0 \n",
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+ " \n",
+ " 1 \n",
+ " 31.0 \n",
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+ " \n",
+ " 2 \n",
+ " 29.0 \n",
+ " \n",
+ " \n",
+ " 3 \n",
+ " 31.0 \n",
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+ " \n",
+ " 4 \n",
+ " 29.0 \n",
+ " \n",
+ " \n",
+ "
\n",
+ "
"
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "plt.figure(figsize=(8, 6))\n",
+ "plt.hist(ages_population2['observation'], bins=range(0, 101, 5), edgecolor='black', alpha=0.7)\n",
+ "plt.xlabel('Age')\n",
+ "plt.ylabel('Frequency')\n",
+ "plt.title('Histogram of Age Distribution (Population 2)')\n",
+ "plt.grid(True)\n",
+ "plt.show()"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "#### 4.- What do you see? Is there any difference with the frequency distribution in step 1?"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "\"\"\"\n",
+ "the shape of the distribution isdifferent. It is more symmetric.\n",
+ "standard deviation is narrower\n",
+ "\"\"\""
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "#### 5.- Calculate the mean and standard deviation. Compare the results with the mean and standard deviation in step 2. What do you think?"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 62,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "Mean age (Population 2): 27.155\n",
+ "Standard deviation of age (Population 2): 2.969813932689186\n"
+ ]
+ }
+ ],
+ "source": [
+ "mean_age_pop2 = ages_population2['observation'].mean()\n",
+ "std_age_pop2 = ages_population2['observation'].std()\n",
+ "\n",
+ "print(\"Mean age (Population 2):\", mean_age_pop2)\n",
+ "print(\"Standard deviation of age (Population 2):\", std_age_pop2)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "\"\"\"\n",
+ "there are significant differences in the central tendency and spread of the age distributions between the two populations.\n",
+ "mean std deviation are lower\n",
+ "\"\"\""
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Challenge 5\n",
+ "Now is the turn of `ages_population3.csv`.\n",
+ "\n",
+ "#### 1.- Read the file `ages_population3.csv`. Calculate the frequency distribution and plot it."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 63,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/html": [
+ "\n",
+ "\n",
+ "
\n",
+ " \n",
+ " \n",
+ " observation \n",
+ " \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0 \n",
+ " 21.0 \n",
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+ " \n",
+ " 1 \n",
+ " 21.0 \n",
+ " \n",
+ " \n",
+ " 2 \n",
+ " 24.0 \n",
+ " \n",
+ " \n",
+ " 3 \n",
+ " 31.0 \n",
+ " \n",
+ " \n",
+ " 4 \n",
+ " 54.0 \n",
+ " \n",
+ " \n",
+ "
\n",
+ "
"
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "plt.figure(figsize=(8, 6))\n",
+ "plt.hist(ages_population3['observation'], bins=range(0, 101, 5), edgecolor='black', alpha=0.7)\n",
+ "plt.xlabel('Age')\n",
+ "plt.ylabel('Frequency')\n",
+ "plt.title('Histogram of Age Distribution (Population 3)')\n",
+ "plt.grid(True)\n",
+ "plt.show()"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "#### 2.- Calculate the mean and standard deviation. Compare the results with the plot in step 1. What is happening?"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 65,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "Mean age (Population 3): 41.989\n",
+ "Standard deviation of age (Population 3): 16.144705959865934\n"
+ ]
+ }
+ ],
+ "source": [
+ "mean_age_pop3 = ages_population3['observation'].mean()\n",
+ "std_age_pop3 = ages_population3['observation'].std()\n",
+ "\n",
+ "print(\"Mean age (Population 3):\", mean_age_pop3)\n",
+ "print(\"Standard deviation of age (Population 3):\", std_age_pop3)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "\"\"\"\n",
+ "mean std deviation are higher.\n",
+ "Outliers can significantly affect the shape and spread of the distribution.\n",
+ "\"\"\""
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "#### 3.- Calculate the four quartiles. Use the results to explain your reasoning for question in step 2. How much of a difference is there between the median and the mean?"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 67,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "Q1: 30.0\n",
+ "Median (Q2): 40.0\n",
+ "Q3: 53.0\n"
+ ]
+ }
+ ],
+ "source": [
+ "q1_pop3 = np.percentile(ages_population3['observation'], 25)\n",
+ "median_pop3 = np.percentile(ages_population3['observation'], 50)\n",
+ "q3_pop3 = np.percentile(ages_population3['observation'], 75)\n",
+ "\n",
+ "print(\"Q1:\", q1_pop3)\n",
+ "print(\"Median (Q2):\", median_pop3)\n",
+ "print(\"Q3:\", q3_pop3)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "\"\"\"\n",
+ "median is less than the mean, it indicates a left-skewed distribution\n",
+ "\"\"\""
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "#### 4.- Calculate other percentiles that might be useful to give more arguments to your reasoning."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 68,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "10th Percentile (P10): 22.0\n",
+ "90th Percentile (P90): 67.0\n"
+ ]
+ }
+ ],
+ "source": [
+ "p10_pop3 = np.percentile(ages_population3['observation'], 10)\n",
+ "p90_pop3 = np.percentile(ages_population3['observation'], 90)\n",
+ "\n",
+ "print(\"10th Percentile (P10):\", p10_pop3)\n",
+ "print(\"90th Percentile (P90):\", p90_pop3)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "\"\"\"\n",
+ "These percentiles can help us understand the spread and variability of the data beyond the quartiles.\n",
+ "\"\"\""
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Bonus challenge\n",
+ "Compare the information about the three neighbourhoods. Prepare a report about the three of them. Remember to find out which are their similarities and their differences backing your arguments in basic statistics."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "# your code here"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "\"\"\"\n",
+ "your comments here\n",
+ "\"\"\""
+ ]
+ }
+ ],
+ "metadata": {
+ "kernelspec": {
+ "display_name": "Python 3 (ipykernel)",
+ "language": "python",
+ "name": "python3"
+ },
+ "language_info": {
+ "codemirror_mode": {
+ "name": "ipython",
+ "version": 3
+ },
+ "file_extension": ".py",
+ "mimetype": "text/x-python",
+ "name": "python",
+ "nbconvert_exporter": "python",
+ "pygments_lexer": "ipython3",
+ "version": "3.11.7"
+ }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 2
+}
diff --git a/your-code/roll_the_dice_hundred.csv b/your-code/roll_the_dice_hundred.csv
new file mode 100644
index 0000000..50975a2
--- /dev/null
+++ b/your-code/roll_the_dice_hundred.csv
@@ -0,0 +1,101 @@
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diff --git a/your-code/roll_the_dice_thousand.csv b/your-code/roll_the_dice_thousand.csv
new file mode 100644
index 0000000..f820dbb
--- /dev/null
+++ b/your-code/roll_the_dice_thousand.csv
@@ -0,0 +1,1001 @@
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