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Chapter 2: Q. 2.23 (page 98)

The following data are the number of pages in 40 books on a shelf. Construct a box plot using a graphing

calculator, 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

Short Answer

Expert verified

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

Step by step solution

01

Given

Here we have136;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

02

Solution

The box plot of the given number of pages is

By calculation we get the IQR as161.

03

Explanation of Solution

Theshapeofthedistributionisdefinedbytheboxplot.
Itprovidesanoverviewofthequartiles.
Asaresult,wecanquicklygrasptheconceptsofskewnessandmedian.
Thefundamentalaspectofaboxplotisthatitisprimarilyusedtofindoutliers.
Anoutlierisastarthatisoutsideoftheacceptablerangeandisindicatedontheplot.
Thereisnooutlierinoursituation.
The 1st quartile is represented by the end point of the boxplot below, while the 3rdquartile 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=3rdquartile -1stquartile as a result of this.
1st quartile =235.5,3rdquartile =396.5, according to the graph.
As a result, the IQR is=396.5-235.5=161.

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