Advertising expenses are a significant component of the cost of goods sold. Listed below is a frequency distribution showing the advertising expenditures for 40 manufacturing companies. Estimate the mean, median, and standard deviation of advertising expense. Advertising Expenditure ($millions) Number of companies

$20 to under $30 9

30 to under 40 13

40 to under 50 21

50 to under 60 18

60 to under 70 14

Total 75

Mean = 47

Median = 47.38

Standard Deviation = 12.73

Explanation:

Note: You wrote " 40 manufacturing companies, but the total number of companies you actually listed is 75, definitely you meant 75.

Let y represent the range of advertising expenditure, f represent the number of companies, x represent the midpoint of the range of advertising expenditure.

y                                       f                      x                  fx                    fx²

$20 to under $30            9                     25               225               5625

$30 to under $40            13                    35               455               15925

$40 to under $50            21                    45               945              42525

$50 to under $60            18                    55               990              54450

$60 to under $70            14                     65               910               59150

                                       n = 75                                

Mean,

Standard Deviation:

Median:

Get the cumulative frequencies(cf)

         y                                        f                                cf

$20 to under $30                     9                                9

$30 to under $40                     13                               22

$40 to under $50                     21                               43

$50 to under $60                     18                               61

$60 to under $70                      14                              75

                                                N = 75

Median = Size of (N/2)th item

Median = Size of (75/2)th item

Median = Size of (37.5)th item

The median class = 40 to under 50

Lower limit, L₁ = 40

Cumulative frequency, cf = 22

f = 21

Class Width, h = 10

Median =

Median =

Median = 47.38

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