Question

The following data set shows the heights in inches for the boys in a class of $40$students.

$66;66;67;67;68;68;68;68;68;69;69;69;70;71;72;72;72;73;73;74$

The following data set shows the heights in inches for the girls in a class of $40$students.

$61;61;62;62;63;63;63;65;65;65;66;66;66;67;68;68;68;69;69;69$

Construct a box plot using a graphing calculator for each data set, and state which box plot has the wider spread for the middle $50\%$of the data.

Short answer

The box plot shows that the distribution for boys is positively skewed, whereas the distribution for girls is symmetrical.

And the larger section is geared more toward females than boys.

Step-by-step solution

Introduction

The box plot of the $2$sets of data where$1^{st}$set is of$20$boys and$2^{nd}$set is of$20$girls.

Explanation

Step : 3 Explanation 

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 $1^{st}$quartiles are represented by the end point of the boxplot below, while the $3^{rd}$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 can see that the $50\%$spread area is larger for females than it is for boys.