Question

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. Estimate the mean and the standard deviation.

Number of Clients

Frequency

20 up to 30

1

30 up to 40

15

40 up to 50

22

50 up to 60

8

60 up to 70

4

Answer 1

44.80

9.27

Explanation:

From the data:

Midpoint (x) : __ 25 _ 35 _ 45 _ 55 _ 65

Frequency (f) : _ 1 __ 15 __ 22 _ 8 __ 4

The mean (m):

Σfx / Σf

[(25 * 1) + (35* 15) + (45 * 22) + (55 * 8) + (65 * 4)] / (1 + 15 + 22 + 8 + 4)

= 2240 / 50

= 44.80

Standard deviation :

Sqrt[(Σ(X² * f) / Σf) - m²)]

[(25^2 * 1) + (35^2 * 15) + (45^2 * 22) + (55^2 * 8) + (65^2 * 4)] / (1 + 15 + 22 + 8 + 4)

(104650 / 50) - (44.80²)

1908.51 - 44.80^2

2093 - 2007.04

Sqrt(85.96)

= 9.27