The IRS was interested in the number of individual tax forms prepared by small accounting firms. The IRS randomly sampled 50 public accounting firms with 10 or fewer employees in the Dallas-Fort Worth area. The following frequency table reports the results of the study.
Number of Clients Frequency
25 up to 40 3
40 up to 55 11
55 up to 70 24
70 up to 85 8
85 up to 100 4
Estimate the mean and the standard deviation. Round squared deviations to the nearest whole number and the final answer to 2 decimal places.

Answer:

Estimates of the number of individual tax forms prepared by small accounting firms:

1. Mean = 10

2. Standard deviation = 7.56

Step-by-step explanation:

a) Data and Calculations:

Number of Clients     Frequency    Mean Diff   Squared Deviation

25 up to 40                       3                  -7                    49

40 up to 55                      11                     1                       1

55 up to 70                     24                  14                   196

70 up to 85                       8                    -2                     4

85 up to 100                     4                   -6                   36

Sum                               50                                       286

Mean of frequencies = 10 (50/5)                            57.2 (286/5)

Standard deviation = square root of 57.2 = 7.56

b) The IRS can obtain the mean value of the number of individual tax forms prepared by small accounting firms by dividing the sum of the frequencies by the numbers (50/5).  Similarly, the IRS can calculate the standard deviation of the number of individual tax forms prepared by small accounting firms, which measures how spread out the data is about the mean value, by working out the mean of the frequency numbers.  Then subtract the mean for each number and square each result.  Add up the squared differences and divide by the number to get the mean.  Finally, take the square root of the mean differences.

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