Question

Used cars, cheap! Refer to Exercise $24$Suppose each car’s price is reduced by 10% instead of $\$500$What 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

Part (a) Shape will remain unaffected.

Part (b) Median is reduced by $10\%$

Part (c) Interquartile range decreases by $10\%$

Step-by-step solution

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 $10\%$

Part (a) Step 2: Explanation

$90$Instead of the prior price of $100$percent, the new price is 90 percent (or $0.90$). As a result, each price must be multiplied by $0.90$When 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.

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 $10\%$

Part (c) Step 1: Explanation

$0.90$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 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 $0.90$as well. As a result, the interquartile range is multiplied by $0.90$

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