Question

A company decides to investigate the amount of sick leave taken by its employees. A sample of seven employees yields the following numbers of days of sick leave taken in the past year
0 1 4 0 0 6 3
a. Find and interpret the range
The range is ______days
Choose the correct interpretation of the range below
A. The largest difference between the mean and any other value is equal to the range
B. The number of days separating the fewest and most sick days taken is equal to the range
C. The range gives the most useful value for measuring the spread of the data
D. The range represents the average distance of an observation from the mean
b. Find and interpret the standard deviations.

Answer 1

Using statistical concepts, we have that:

• a. The range is 6 days, and the interpretation is: B. The number of days separating the fewest and most sick days taken is equal to the range.

• b. The standard deviation is of 2.2, which means that the average spread about the mean is of 2.2 units.

Range and standard deviation:

• The range of a data-set is given by the difference between the highest value and the lowest value in the data-set.

• The standard deviation of a data-set is given by the square root of the  sum of the difference squared of each observation and the mean, divided by the number of observations.

Item a:

• The lowest value is of 0.

• The highest value is of 6.

Hence:

The range is 6 days, and the interpretation is: B. The number of days separating the fewest and most sick days taken is equal to the range.

Item b:

The mean is:

$M = \frac{0 + 1 + 4 + 0 + 0 + 6 + 3}{7} = 2$

Hence, the standard deviation is:

$S = \sqrt{\frac{(0-2)^2+(1-2)^2+(4-2)^2+(0-2)^2+(0-2)^2+(6-2)^2+(3-2)^2}{7}} = 2.2$

The standard deviation is of 2.2, which means that the average spread about the mean is of 2.2 units.

You can learn more about range and standard deviation at brainly.com/question/11729451