Chapter 2.1, Problem 12E

a.

To determine

To find: The interquartile range of the provided distribution.

Explanation of Solution

Given:

The plot is:

  

From the provided plot, the third quartile and first quartile are $47 and $19 respectively.

Thus, the interquartile range is:

  $\begin{array}{c}IQR=Q_3-Q_1\\ =47-19\\ =28\end{array}$

Thus, the required value is 28.

b.

To determine

To find: The percentile for the shopper.

Answer to Problem 12E

The percentile is 25.

Explanation of Solution

It has been provided that the amount spent by the shopper is $19.50. To find the percentile, construct a vertical line that cuts the x -axis at 19.50. Now, construct a horizontal line for the intersection of the vertical line.

It could be seen that both the line intersecting at 25^th percentile.

Thus, the required percentile is 25.

c.

To determine

To explain: The reason of curve being flat between $10 and $30.

Explanation of Solution

Here, the cumulative relative frequency is increasing between the values $10\%$ and $30\%$ because of the slight increase in the frequency for these values. So, it could be said that the mostly shoppers are spending the amount between $10 and $30.