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CH1 - Categorical Variable

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CH 1 Continued - Categorical Variables in Statistics

Continuing from the previous chapter, we will now look at how to represent categorical data in statistics with an example.

1000 ball bearings classified as:

  • conforming (910)
  • too thick (53)
  • too thin (37)

Here, the data is classified into three categories, which are mutually exclusive and exhaustive. The data is categorical because it is classified into categories and not measured.

Lets make a table of counts for the data.

Table of Counts

Classificationfrequencyf/n - relative frequency proportion
Conforming910.910
too thick53.053
too thin37.037

Bar Chart with MatPlotLib

import micropip
await micropip.install("matplotlib")
import matplotlib.pyplot as plt
 
# Data
labels = ['Conforming', 'Too Thick', 'Too Thin']
values = [0.910, 0.053, 0.037]
 
# Create the bar chart
plt.figure(figsize=(6, 4))
plt.bar(labels, values, color=['green', 'red', 'blue'])
 
# Add title and labels
plt.title('Bar Chart of Measurements')
plt.xlabel('Measurement Type')
plt.ylabel('Proportion')
 
# Show the values on top of the bars
for i, value in enumerate(values):
    plt.text(i, value + 0.01, f'{value:.3f}', ha='center', va='bottom')
 
# Display the chart
plt.show()

This will create a bar chart with the proportion of each category, where the height of the bar represents the proportion of the category.

Variable Statistics and Boxplots

Now, lets look at another example

Chromium VS Nickel Simple Dataset

Chromium: 31, 1, 511, 2, 574, 496, 322, 424, 269, 140, 244, 252, 76, 108, 24, 38, 18, 43, 30, 191

Nickel: 23, 22, 55, 39, 283, 34, 159, 37, 61, 34, 163, 140, 32, 23, 54, 837, 64, 354, 376, 471

We are going to find:

  • Mean
  • Median
  • Standard Deviation
  • Quartiles

Lets find these with python.

This will yield the 1-Variable Statistics we would normally get from a Ti-84 Graphing Calculator. And lets include a graph to go along with it.

import micropip
await micropip.install("numpy")
await micropip.install("scipy")
await micropip.install("matplotlib")
 
import numpy as np
import matplotlib.pyplot as plt
import scipy as stats
 
# Data
chromium = [31, 1, 511, 2, 574, 496, 322, 424, 269, 140, 244, 252, 76, 108, 24, 38, 18, 43, 30, 191]
nickel = [23, 22, 55, 39, 283, 34, 159, 37, 61, 34, 163, 140, 32, 23, 54, 837, 64, 354, 376, 471]
 
# Mean
mean_chromium = np.mean(chromium)
mean_nickel = np.mean(nickel)
 
# standard deviation
std_chromium = np.std(chromium)
std_nickel = np.std(nickel)
 
# Median
median_chromium = np.median(chromium)
median_nickel = np.median(nickel)
 
# Quartiles
first_quartile_chromium = np.percentile(chromium, 25)
second_quartile_chromium = np.percentile(chromium, 50)
third_quartile_chromium = np.percentile(chromium, 75)
fourth_quartile_chromium = np.percentile(chromium, 100)
 
firsst_quartile_nickel = np.percentile(nickel, 25)
second_quartile_nickel = np.percentile(nickel, 50)
third_quartile_nickel = np.percentile(nickel, 75)
fourth_quartile_nickel = np.percentile(nickel, 100)
 
# print the results as f string
print(f"Chromium Mean: {mean_chromium}, Median: {median_chromium}, Standard Deviation: {std_chromium}")
print(f"Chromium Quartiles: {first_quartile_chromium}, {second_quartile_chromium}, {third_quartile_chromium}, {fourth_quartile_chromium}")
 
print(f"Nickel Mean: {mean_nickel}, Median: {median_nickel}, Standard Deviation: {std_nickel}")
print(f"Nickel Quartiles: {firsst_quartile_nickel}, {second_quartile_nickel}, {third_quartile_nickel}, {fourth_quartile_nickel}")
 
# Boxplot
plt.figure(figsize=(6, 4))
plt.boxplot([chromium, nickel], labels=['Chromium', 'Nickel'])
plt.title('Boxplot of Chromium and Nickel')
 
# Display the chart
plt.show()

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