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Used cars, cheap! Refer to Exercise 24Suppose each car’s price is reduced by 10% instead of $500What effect will this discount have on each of the following characteristics of the resulting price distribution?

a. Shape

b. Median

c. Interquartile range (IQR)

Short Answer

Expert verified

Part (a) Shape will remain unaffected.

Part (b) Median is reduced by 10%

Part (c) Interquartile range decreases by 10%

Step by step solution

01

Part (a) Step 1: Given information

Each car’s price is reduced by 10% instead of a $500

Every car’s price gets reduced by 10%

02

Part (a) Step 2: Explanation

90Instead of the prior price of 100percent, the new price is 90 percent (or 0.90). As a result, each price must be multiplied by 0.90When every value in the data is multiplied by 0.90, the structure of the distribution remains unchanged since the associations between each data pair remain unchanged. As a result, the new price's distribution shape is identical to the previous price's distribution shape.

03

Part (b) Step 1: Explanation

As a result, the new price is 90 percent (or 0.90) lower than the prior price of 100 percent. As a result, each price must be multiplied by 0.90 The Median is a measure of the center, as we all know. When every value in the data is multiplied by 0.90 the distribution's center is multiplied by 0.90 as well. As a result, the Median is also multiplied by 0.90 We can also state that the median has been reduced by 10%

04

Part (c) Step 1: Explanation

0.90As a result, the new price is 90percent (or 0.90) lower than the prior price of 100percent. As a result, each price must be multiplied by 0.90The interquartile range is a measure of variability, as we all know. When every value in the data is multiplied by 0.90 the distribution's variability is multiplied by 0.90as well. As a result, the interquartile range is multiplied by 0.90

We can also argue that the interquartile range (IQR) has shrunk by 10%

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