Chapter 2.1, Problem 28E

(a)

To determine

Effect of discounton the shape of the resulting price distribution.

Answer to Problem 28E

Shape will remain unaffected.

Explanation of Solution

Given information:

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

Every car’s price gets reduced by 10%.

That means

New price becomes 90% (or 0.90) instead of previous price which was 100%.

Thus,

Every price needs to be multiplied by 0.90.

When every value in the data is multiplied by 0.90, then the shape of the distribution will not be affected because there will be no change in the relationships between every data pair.

Thus,

The distribution shape of the new price remains the same as that of the old price distribution shape.

(b)

To determine

Effect of discounton the Median of the resulting price distribution.

Answer to Problem 28E

Median is reduced by 10%.

Explanation of Solution

Given information:

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

Every car’s price gets reduced by 10%.

That means

New price becomes 90% (or 0.90) instead of previous price which was 100%.

Thus,

Every price needs to be multiplied by 0.90.

We know that

Median is a measure of the center.

When every value in the data is multiplied by 0.90, then the center of the distribution is also multiplied by 0.90.

Thus,

Median also gets multiplied by 0.90.

We can also say

The median is reduced by 10%.

(c)

To determine

Effect of discount on the Interquartile range ( IQR ) of the resulting price distribution.

Answer to Problem 28E

Interquartile range decreases by 10%.

Explanation of Solution

Given information:

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

Every car’s price gets reduced by 10%.

That means

New price becomes 90% (or 0.90) instead of previous price which was 100%.

Thus,

Every price needs to be multiplied by 0.90.

We know that

Interquartile range is a measure of the variability.

When every value in the data is multiplied by 0.90, then the variability of the distribution is also multiplied by 0.90.

Thus,

Interquartile range also gets multiplied by 0.90.

We can also say

Interquartile range equivalently decreased by 10%.