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Q. 2.23

Expert-verified
Found in: Page 98

### Introductory Statistics

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

# The following data are the number of pages in 40 books on a shelf. Construct a box plot using a graphingcalculator, and state the interquartile range.$136;140;178;190;205;215;217;218;232;234;240;255;270;275;290;301;303;315;317;318;326;333;343;$$349;360;369;377;388;391;392;398;400;402;405;408;422;429;450;475;512$

We may deduce from the box plot that the distribution is more or less symmetrical, and that there are no outliers in the data.

See the step by step solution

## Step 1: Given

Here we have$136;140;178;190;205;215;217;218;232;234;240;255;270;275;290;301;303;315;317;318;326;333;343;$

$349;360;369;377;388;391;392;398;400;402;405;408;422;429;450;475;512$

## Step 2: Solution

The box plot of the given number of pages is

By calculation we get the IQR as$161.$

## Step 3: Explanation of Solution

The shape of the distribution is defined by the box plot.
It provides an overview of the quartiles.
As a result, we can quickly grasp the concepts of skewness and median.
The fundamental aspect of a boxplot is that it is primarily used to find outliers.
An outlier is a star that is outside of the acceptable range and is indicated on the plot.
There is no outlier in our situation.
The 1st quartile is represented by the end point of the boxplot below, while the $3rd$ quartile is represented by the end point of the boxplot above.
So the data in the boxplot is $50%$ of the data, and the data outside of the interval is $50%$ of the data.
We must also calculate $IQR=3rd$quartile $-1st$ quartile as a result of this.
1st quartile $=235.5,3rd$ quartile $=396.5$, according to the graph.
As a result, the IQR is $=396.5-235.5=161.$