Question

Shopping spree The figure is a cumulative relative frequency graph of the amount spent by $50$ consecutive grocery shoppers at a store.

a. Estimate the interquartile range (IQR) of this distribution. Show your method.

b. What is the percentile for the shopper who spent $\backslash (19.50?$

c. Explain why the graph is steepest between $\backslash )10$ and $\$30$

Short answer

Part (a) The value is $28$

Part (b) The percentile is $25$

Part (c) It could be said that most shoppers are spending the amount between $\$10$and $\$30$

Step-by-step solution

Part (a) Step 1: Given information

The plot is:

Part (a) Step 2: Concept

The percentile of an individual is the percentage of the distribution that is less than the data value of the individual.

Part (a) Step 3: Calculation

The third quartile and first quartile, according to the plot, are$\$47$ and $\$19$ respectively.

Thus, the interquartile range is:

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

Thus, the required value is $28$

Part (b) Step 1: Explanation

The shopper spent $\$19.50$according to the information given. Construct a vertical line that cuts the $x-$axis at $19.50$to obtain the percentile. Create a horizontal line to connect the vertical and horizontal lines. Both lines overlap at the $25th$ percentile, as can be seen.

Thus, the required percentile is $25$

Part (c) Step 1: Explanation

Because of the minor rise in frequency for these values, the cumulative relative frequency for these values is growing between $10\%$ and $30\%$ As a result, it's reasonable to conclude that the majority of shoppers spend between $\$10$ and $\$30$