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Q. 2.7

Expert-verified
Found in: Page 79

### Introductory Statistics

Book edition OER 2018
Author(s) Barbara Illowsky, Susan Dean
Pages 902 pages
ISBN 9781938168208

# The following data are the shoe sizes of $50$ male students. The sizes are continuous data since shoe size is measured. Construct a histogram and calculate the width of each bar or class interval. Suppose you choose six bars.$9;9;9.5;9.5;10;10;10;10;10;10;10.5;10.5;10.5;10.5;10.5;10.5;10.5;10.5\phantom{\rule{0ex}{0ex}}11;11;11;11;11;11;11;11;11;11;11;11;11;11.5;11.5;11.5;11.5;11.5;11.5;11.5\phantom{\rule{0ex}{0ex}}12;12;12;12;12;12;12;12.5;12.5;12.5;12.5;14$

The histogram of the given $50$ sampled student is

See the step by step solution

## Step 1: Given

Here we have

$9;9;9.5;9.5;10;10;10;10;10;10;10.5;10.5;10.5;10.5;10.5;10.5;10.5;10.5\phantom{\rule{0ex}{0ex}}11;11;11;11;11;11;11;11;11;11;11;11;11;11.5;11.5;11.5;11.5;11.5;11.5;11.5\phantom{\rule{0ex}{0ex}}12;12;12;12;12;12;12;12.5;12.5;12.5;12.5;14$

## Step 2: Explanation

The density of all intervals is defined by the histogram for each interval.
It indicates which intervals have the lowest frequency and which have the highest frequency.
As a result, we can simply determine the maximum and lowest shoe size intervals.
As we can see, the maximum bar height does not equal the highest frequency since bars indicate area.
The interval $11$ to $12$ has the highest frequency.