Answer:
Explanation:
The question is incomplete. The complete question is:
Health issues are a concern of managers, especially as they evaluate the cost of medical insurance. A recent survey of 150 executives at Elvers Industries, a large insurance and financial firm located in the Southwest, reported the number of pounds by which the executives were overweight. Compute the mean and the standard deviation.
Pounds Overweight Frequency
0 up to 6 14
6 up to 12 42
12 up to 18 58
18 up to 24. 28
24 up to 30. 8
Solution:
This is grouped data. We would determine the midpoint or class mark, x of each class by taking their averages.
The table would become
Class. x f fx
0 up to 6 (0+6)/2 = 3 14 42
6 up to 12 (6+12)/2 = 9 42 378
12 up to 18 (12+18)/2 = 15 58 870
18 up to 24 (18+24)/2= 21 28 588
24 up to 30 (24+30)/2 = 27 8 216
Summation f = 14 + 42 + 58 + 28 + 8 = 150
Summation fx = 42 + 378 + 870 + 588 + 216 = 2094
Mean = Summation fx/Summation f
Mean, m = 2094/150 = 13.96
Standard deviation = √summation of f(x - m)²)/(n - 1)
We would create another column on the table
f x x - m f(x - m)²
14 3 - 10.96 1681.7024
42 9 - 4.96 1033.2672
58 15 1.04 62.7328
28 21 7.04 1387.7248
8 27 12.04 1159.6928
Total = 5325.12
Standard deviation = √5325.12/150 - 1)
Standard deviation = 5.98