Q 12. Shopping spree The figure is a c... [FREE SOLUTION]

91影视

The Practice of Statistics for AP Examination

Daren Starnes, Josh Tabor

$Math Studyset 91影视 Explanations$ Math

6th Edition 路 837 pages

ISBN: 9781319113339

Chapter 2: Q 12. (page 105)

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 $$19.50 ?$
c. Explain why the graph is steepest between $$ 10$ and $$ 30$

Short Answer

Expert verified

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:

$I Q R = Q_{3} 鈭� Q_{1} = 47 鈭� 19 = 28$

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 $25 t h$ 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$