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 $\$30$

The plot is:

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

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 $28$

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 $25$

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 $\$30$