Question

ceo age salary
1 53 145
2 43 621
3 33 262
4 45 208
5 46 362
6 55 424
7 37 300
8 41 339
9 55 736
10 36 291
11 45 58
12 55 498
13 50 643
14 49 390
15 47 332
16 69 750
(a) find the mean ceo age.
(b) find the median ceo age.
(c) find the mean ceo salary.
(d) find the median ceo salary.
(e) are the salaries skewed right, skewed left, or approximately symmetric?

Explanation:

Step1: Calculate sum of ages

Sum of ages = \(53 + 43+33 + 45+46+55+37+41+55+36+45+55+50+49+47+69\) = \(751\)

Step2: Calculate number of data - points

Number of CEOs \(n = 16\)

Step3: Calculate mean age

Mean age \(\bar{x}=\frac{751}{16}=46.9375\)

Step4: Arrange ages in ascending order

\(33,36,37,41,43,45,45,46,47,49,50,53,55,55,55,69\)

Step5: Calculate median age

Since \(n = 16\) (even), median is the average of \(\frac{n}{2}\)th and \((\frac{n}{2}+ 1)\)th ordered values. \(\frac{n}{2}=8\) and \(\frac{n}{2}+1 = 9\). Median age=\(\frac{46 + 47}{2}=46.5\)

Step6: Calculate sum of salaries

Sum of salaries = \(145+621+262+208+362+424+300+339+736+291+58+498+643+390+332+750\) = \(5427\)

Step7: Calculate mean salary

Mean salary \(\bar{y}=\frac{5427}{16}=339.1875\)

Step8: Arrange salaries in ascending order

\(58,145,208,262,291,300,332,339,362,390,424,498,621,643,736,750\)

Step9: Calculate median salary

Since \(n = 16\) (even), median is the average of \(\frac{n}{2}\)th and \((\frac{n}{2}+1)\)th ordered values. \(\frac{n}{2}=8\) and \(\frac{n}{2}+1 = 9\). Median salary=\(\frac{339+362}{2}=350.5\)

Step10: Analyze skewness of salaries

The mean (\(339.1875\)) is less than the median (\(350.5\)). So the data is skewed left.

Answer:

(a) \(46.9375\)
(b) \(46.5\)
(c) \(339.1875\)
(d) \(350.5\)
(e) Skewed left