Q 58. - The Practice of Statistics for AP

Question

Chest out, Soldier! In$1846$, a published paper provided chest measurements (in inches) of $5738$

Scottish militiamen. The table below summarizes the data

(a) Make a histogram.

(b) Describe the shape, center, and spread of the chest measurements distribution. Why might this

information be useful?

Step-by-Step Solution

Answer

Part (b) symmetric, normally distributed

Centre: roughly at $40$

Spread:$33$ to 48

Part (a) 

Part (a) Step 1: Given information

Chest Size	Count	Chest size	Count
33	3	41	934
34	18	42	658
35	81	43	370
36	185	44	92
37	420	45	50
38	749	46	21
39	1073	47	4
40	1079	48	1

Part (a) Step 2: Concept

A histogram is an often used graphing tool. It's used to summarise discrete or continuous data that are 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: 

Thus, the histogram is made for the given data.

Part (b) Step 1: Explanation

The distribution is regularly distributed and the shape is symmetric. Due to the lack of skewness, the bulk of Scottish military personnel has chest sizes ranging from to. Few people have a chest size of fewer than $45$ inches or more than $45$ inches. It has a single peak and is Unimodal. Because the center of asymmetric distribution is nearly in the middle of the tallest bar, the center is roughly at $40$ The range is $33$ to $48$, with $33$ being the smallest and $48$ being the largest chest size. Because all of the bars in the histogram are nearby, there are no outliers or extreme values in the data.