Chapter 2.1, Problem 27E

(a)

To determine

Effect of raise on shape of the resulting salary distribution.

Answer to Problem 27E

Shape will remain unaffected.

Explanation of Solution

Given information:

Each teacher receives a 5% raise instead of a $1000 raise.

Every teacher gets a 5% raise.

That means

New salary becomes 105% (or 1.05) instead of previous salary which was 100%.

Thus,

Every salary needs to be multiplied by 1.05.

When every value in the data is multiplied by 1.05, 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 salaries remains the same as that of the old salaries distribution shape.

(b)

To determine

Effect of raise on Median of the resulting salary distribution.

Answer to Problem 27E

Median is increased by 5%.

Explanation of Solution

Given information:

Each teacher receives a 5% raise instead of a $1000 raise.

Every teacher gets a 5% raise.

That means

New salary becomes 105% (or 1.05) instead of previous salary which was 100%.

Thus,

Every salary needs to be multiplied by 1.05.

We know that

Median is a measure of the center.

When every value in the data is multiplied by 1.05, then the center of the distribution is also multiplied by 1.05.

Thus,

Median also gets multiplied by 1.05.

We can also say

The median is increased by 5%.

(c)

To determine

Effect of raise on Interquartile range ( IQR ) of the resulting salary distribution.

Answer to Problem 27E

Interquartile range increases by 5%.

Explanation of Solution

Given information:

Each teacher receives a 5% raise instead of a $1000 raise.

Every teacher gets a 5% raise.

That means

New salary becomes 105% (or 1.05) instead of previous salary which was 100%.

Thus,

Every salary needs to be multiplied by 1.05.

We know that

Interquartile rangeis a measure of the variability.

When every value in the data is multiplied by 1.05, then the variability of the distribution is also multiplied by 1.05.

Thus,

Interquartile range also gets multiplied by 1.05.

We can also say

Interquartile range equivalently increased by 5%.