Q 57. - The Practice of Statistics for AP

Question

The statistics of writing style Numerical data can distinguish different types of writing, and sometimes even individual authors. Here are data on the percent of words of $1$ to $15$ letters used in articles in Popular science magazine: 

(a) Make a histogram of this distribution. Describe its shape, center, and spread.

(b) How does the distribution of lengths of words used in Popular science compare with the similar distribution for Shakespeare’s plays in Exercise $52$? Look in particular at short words ($2, 3,$ and $4$ letters) and very long words (more than $10$ letters).

Step-by-Step Solution

Answer

Part (b) Short words ($2,3$ and $4$ letters) are used maximum times.

Part (a) 

Part (a) Step 1: Given information

Length	1	2	3	4	5	6	7	8	9	10	11	12	13	14	15
Percent	3.6	14.8	18.7	16.0	12.5	8.2	8.1	5.9	4.4	3.6	2.1	0.9	0.6	0.4	0.2

Part (a) Step 2: Concept

A histogram is an often used graphing tool. It's used to summarise discrete or continuous data that's measured on an interval scale. It's a popular method for displaying key characteristics of data distribution in a user-friendly manner.

Part (a) Step 3: Explanation

The following is a histogram of the percentage of words with $1$ to $15$ letters: 

The form is regular and slightly tilted to the right. Because of the skewness to the right, the majority of words contain letters between $7$ and $15$, although a few have letters between $7$ and $15$. It's unimodal, having only one peak at $3$ o'clock. The data is centered on $4$ letters. There are $14$ letters in the spread, ranging from$1$ to $15$. The data has no outliers or extreme values. As a result, a distribution histogram is created.

Shape: regular and skewed towards the right.

Center: $4$ letters.

Spread $14$ from $1$ letter to $15$ letters.

Part (b) Step 1: Explanation

The percentage of words with $1$ to $15$ letters as compared to the distribution of word lengths used in Shakespeare's plays, particularly in short words ($2,3,$ and $4$ letters are used most often). Long words (more than $10$ letters) are used at rates ranging from $1\%$ to $4\%$

Length	1	2	3	4	5	6	7	8	9	10	11	12	13	14	15
Percent	3.6	14.8	18.7	16	12.5	8.2	8.1	5.9	4.4	3.6	2.1	0.9	0.6	0.4	0.2