CH1 - Categorical Variable

CH 1 Continued - Categorical Variables in Statistics

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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.

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Table of Counts

Classification	frequency	f/n - relative frequency proportion
Conforming	910	.910
too thick	53	.053
too thin	37	.037

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Bar Chart with MatPlotLib

Python

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()

Output

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

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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.

Python

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()

Output