Questions: 12. 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. One shopper spent 19.50. Estimate this person's percentile. c. Explain why the graph is steepest between 10 and 30.

12. 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. One shopper spent 19.50. Estimate this person's percentile. c. Explain why the graph is steepest between 10 and 30.
Transcript text: E-book-STATISTICS\&PROBABI ebookshelf 12. Shopping spree The figure is a cumulative relative frequency graph of the amount spent by 50 consecutive grocery shoppers at a store. Starnes \& Tabor, The Practice of Statistics, 6 e , o 2018 Bedford, Freeman \& Worth High School Publishers a. Estimate the interquartile range (IQR) of this distribution. Show your method. b. One shopper spent $\$ 19.50$. Estimate this person's percentile. c. Explain why the graph is steepest between $\$ 10$ and $\$ 30$. Signout us Oct 14 11:51 $\nabla$
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Solution

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Solution Steps

Step 1: Identify the Quartiles for IQR Calculation

To estimate the interquartile range (IQR), we need to find the first quartile (Q1) and the third quartile (Q3) from the cumulative relative frequency graph. Q1 is the 25th percentile, and Q3 is the 75th percentile.

Step 2: Determine Q1 and Q3 from the Graph

From the graph:

  • Q1 (25th percentile) corresponds to an amount spent of approximately $15.
  • Q3 (75th percentile) corresponds to an amount spent of approximately $35.
Step 3: Calculate the IQR

The IQR is calculated as the difference between Q3 and Q1. \[ \text{IQR} = Q3 - Q1 = 35 - 15 = 20 \]

Final Answer

The estimated interquartile range (IQR) of the distribution is $20.

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