Descriptive statistics exercises

This notebook contains all solutions of the exercises from Section 1.3 Descriptive Statistics in the No Bullshit Guide to Statistics.

Notebooks setup

import numpy as np
import pandas as pd
import matplotlib.pyplot as plt
import seaborn as sns

# Pandas setup
pd.set_option("display.precision", 2)

# Figures setup
sns.set_theme(
    context="paper",
    style="whitegrid",
    palette="colorblind",
    rc={'figure.figsize': (7,4)},
)

%config InlineBackend.figure_format = 'retina'

Load the sdudents dataset

import os
if os.path.exists("../datasets/students.csv"):
    data_file = open("../datasets/students.csv", "r")
else:
    import io
    data_file = io.StringIO("""
student_ID,background,curriculum,effort,score
1,arts,debate,10.96,75
2,science,lecture,8.69,75
3,arts,debate,8.6,67
4,arts,lecture,7.92,70.3
5,science,debate,9.9,76.1
6,business,debate,10.8,79.8
7,science,lecture,7.81,72.7
8,business,lecture,9.13,75.4
9,business,lecture,5.21,57
10,science,lecture,7.71,69
11,business,debate,9.82,70.4
12,arts,debate,11.53,96.2
13,science,debate,7.1,62.9
14,science,lecture,6.39,57.6
15,arts,debate,12,84.3
""")

students = pd.read_csv(data_file)

Let’s look at the effort variable:

efforts = students["effort"]
# efforts

E1.1

Compute the Mean, Min, Max, and Range of the effort variable in the students dataset.

efforts = students["effort"]

# Mean(efforts)
efforts.mean()

8.904666666666666

# Min(efforts)
efforts.min()

5.21

# Max(efforts)
efforts.max()

12.0

# Range(efforts)
efforts.max() - efforts.min()

6.79

E1.14

Find Q1, Med, and Q3 of the effort variable in the students dataset.

efforts.quantile(q=0.25), efforts.median(), efforts.quantile(q=0.75)

(7.76, 8.69, 10.350000000000001)

E1.15

Make a one-way frequency table for the effort variable. Use \((5,7]\), \((7,9]\), \((9,11]\), \((11,13]\) as the bin intervals.

bins = [5, 7, 9, 11, 13]
efforts.value_counts(bins=bins).sort_index()

(4.999, 7.0]    2
(7.0, 9.0]      6
(9.0, 11.0]     5
(11.0, 13.0]    2
Name: count, dtype: int64

# # ALT. to get [5,7), [7,9), [9,11), [11,13) instead, use
# bins2 = pd.IntervalIndex.from_breaks(bins, closed="left")
# efforts.value_counts(bins=bins2).sort_index()

E1.16

Draw a scatter plot for the following dataset of (x,y) pairs: { (2,2), (3,3), (4,3), (5,5), (6,4) }.

df = pd.DataFrame([(2,2), (3,3), (4,3), (5,5),
                   (6,4), (5,4), (7,6), (8,5)],
                  columns=["x", "y"])
sns.scatterplot(x="x", y="y", data=df)

<Axes: xlabel='x', ylabel='y'>

E1.17

TODO: add simple exercise

E1.18

Make a bar chart displaying the frequencies of the curriculum variable.

sns.countplot(data=students, x="curriculum")

<Axes: xlabel='curriculum', ylabel='count'>

E1.19

Compute frequencies and relative frequencies for the curriculum variable. Display the results in a one-way table.

students["curriculum"].value_counts()

curriculum
debate     8
lecture    7
Name: count, dtype: int64

students["curriculum"].value_counts(normalize=True)

curriculum
debate     0.53
lecture    0.47
Name: proportion, dtype: float64

E1.20

What is the mode for curriculum?

mode = students["curriculum"].describe()['top']
mode_freq = students["curriculum"].describe()['freq']

print("The mode is", mode, "with frequency", mode_freq)

The mode is debate with frequency 8

E1.21

E1.22