5. Advertising expenses are a significant component of the cost of products sold. The following distribution...
5. Advertising expenses are a significant component of the cost of products sold. The following distribution of frequencies in a sample of the advertising expenses of 70 manufacturing companies. The standard deviation is:
|
Advertising expenses (in thousands of $) |
Number of companies |
|
25 to 35 36 to 46 47 to 57 58 to 68 69 to 79 |
5 10 21 16 8 |
a. $11,123
b. $12,452
c. $13,345
d. $14,467
e. $15,588
Homework Answers
| Expenditure | Mid-Point (x) | No of Companies (f) | xf | (x - x̄) | (x - x̄)^2 | f(x - x̄)^2 | |
| 25 - 35 | 30 | 5 | 150 | -24.2 | 585.64 | 2,928.2 | |
| 36 - 46 | 41 | 10 | 410 | -13.2 | 174.24 | 1742.4 | |
| 47 - 57 | 52 | 21 | 1092 | -2.2 | 4.84 | 101.64 | |
| 58 - 68 | 63 | 16 | 1008 | 8.8 | 77.44 | 1239.04 | |
| 69 - 79 | 74 | 8 | 592 | 19.8 | 392.04 | 3136.32 | |
| Total | 60 | 3252 | 9147.6 |
Mean = Σxf / Σf = 3252 / 60 = 54.2
Standard Deviation S = √Σf(x - x̄)^2 / n - 1
= √9147.6 / 60 - 1
= √155.044068
= 12.452
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