Chapter 6, Problem 3E

a)

To determine

To explain the shape of the distribution.

Answer to Problem 3E

The distribution is left skewed.

Explanation of Solution

Given:

Lowest salary = $300

Mean salary = $700

Median = $500

Range = $1200

IQR = $600

First quartile = $350

Standard deviation = $400

If the median is less than the mean then the distribution is left skewed. If the median is greater than mean then the distribution is right skewed. If the both equals then it is symmetric.

Here, Median < mean, the distribution is left skewed.

b)

To determine

To explain between what values the middle 50% salary found.

Answer to Problem 3E

The middle 50% of salaries fall between $350 and $950

Explanation of Solution

Given:

Lowest salary = $300

Mean salary = $700

Median = $500

Range = $1200

IQR = $600

First quartile = $350

Standard deviation = $400

Formula:

Third quartile:

  $Q_3=Q_1+IQR$

First need to find third quartile.

  $Q_3=350+600=950$

Therefore, middle 50% salary is between 350 and 950

c)

To determine

To explain the change in summary statistics when each employee’s salary raises by $50

Explanation of Solution

Given:

Lowest salary = $300

Mean salary = $700

Median = $500

Range = $1200

IQR = $600

First quartile = $350

Standard deviation = $400

The change in salary will affect on only lowest salary, mean salary, median and first quartile. Other things will remain unchanged.

Therefore, the summary statistics becomes,

Lowest salary = $350

Mean salary = $750

Median = $550

Range = $1200

IQR = $600

First quartile = $400

Standard deviation = $400

d)

To determine

To explain the change in summary statistics when each employee’s salary raises by 10%

Explanation of Solution

Given:

Lowest salary = $300

Mean salary = $700

Median = $500

Range = $1200

IQR = $600

First quartile = $350

Standard deviation = $400

We need to multiply by 0.10 to each value.

Therefore, the summary statistics becomes,

Lowest salary = $330

Mean salary = $770

Median = $550

Range = $1320

IQR = $660

First quartile = $385

Standard deviation = $440