Chapter 13.3, Problem 4GP

To determine

To Describe: The data using measures of variation.

Explanation of Solution

Given: Use measures of variation to describe the data below.

  

First we finding the range of the data

Highest cost of the video game = $\$59.99$

Lowest cost of the video game = $\$22.79$

Then

Range = Highest cost − lowest cost

  $\begin{array}{l}=\$59.99-\$22.79\\ =\$37.2\end{array}$

Thus

The range of the data is $\$37.2$

Now

Finding median, upper quartile, lower quartile

Arranging the data in ascending order. After arranging the data we can find the median, upper quartile, lower quartile

Thus

  $22.79,24.95,29.25,32.5,34,44.76,49.99,59.99$

Median

  $\begin{array}{l}22.79,24.95,29.25,\underset{\_}{32.5,34},44.76,49.99,59.99\\ =\frac{32.5+34}{2}=33.25\\ Median=\$33.25\end{array}$

Lower quartile

  $\begin{array}{l}22.79,\underset{\_}{24.95,29.25},32.5,34,44.76,49.99,59.99\\ =\frac{24.95+29.25}{2}=27.1\\ \text{Lower quartile=\$}27.1\end{array}$

Upper quartile

  $\begin{array}{l}22.79,24.95,29.25,32.5,34,\underset{\_}{44.76,49.99},59.99\\ =\frac{44.76+49.99}{2}=47.375\\ \text{Upper quartile}\approx \text{\$}47.4\end{array}$

Now finding interquartile range

Interquartile range = Upper quartile − Lower quartile

  $\begin{array}{l}\text{=\$}47.4-\$27.1\\ =\$20.3\end{array}$

Now, from the data it is concluded that

One fourth of the given data the cost of the video games is less than $\text{\$27}\text{.1}$

In one fourth of the given data the cost of the video games is greater than $\text{\$}47.4$

And

Cost of half of the video games is between $\text{\$27}\text{.1}$ and $\text{\$}47.4$