A sample was taken of 20 salaries of employees in a large company. The following are the annual salaries (in thousands of dollars). For convenience, the data have been ordered. 28, 31, 34, 35, 37, 41, 42, 42, 42, 47, 49, 51, 52, 52, 60, 61, 67, 72, 75, 77.

(a) What is the median salary of the 20 employees?

(b) A histogram of the 20 salaries is slightly skewed to the right. What do we know about the mean salary of these 20 salaries, based on this information?

(c) What is the first quartile of the 20 salaries? (d) What is the interquartile range of the 20 salaries?

(e) Suppose each employee in the company receives a $3000 raise for next year (each employee’s salary is increased by $3000). For each of the following summary measures, indicate how it would change after the raise: the median salary, the interquartile range of the salaries, the standard deviation of the salaries.

(a) 48

(b) The mean is on the right side of the median

(c) 39

(d) 21.5

(e) The median salary would increase to 51

The interquartile range will remain as 21.5

The standard deviation remains the same

Step-by-step explanation:

28, 31, 34, 35, 37, 41, 42, 42, 42, 47, 49, 51, 52, 52, 60, 61, 67, 72, 75, 77.

(a) From the above data, the median salary is the average salary of the 10th and 11th salary, that is (47 + 49)/2 = 48

(b) Based on the information that the histogram of the salaries is skewed right, it means that the mean is on the right side of the median

The average is calculated as 49.75

(c) The first quartile is the middle number between the median and the smallest number that is (37 + 41)/2 = 39

(d) The interquartile range is the difference between the third and first quartiles, that is Q₃ - Q₁ = (60 + 61)/2 - 39 = 21.5

(e) The median salary would increase to (50 + 52)/2 = 51

The interquartile range of the salaries will be Q₁ = (40 + 44)/2 = 42

Q₃ = (63 + 64)/2 = 63.5

Q₃ - Q₁ = 21.5 therefore, the interquartile range will remain the same

The standard deviation of the salaries is given by

Whereby we have

When ∑x increases by 3·n, increases by 3 therefore the standard deviation remains the same.

step-by-step explanation: