Question

The National Sporting Goods Association (NSGA) conducted a survey of the ages of people that purchased athletic footwear in 2009. The ages are summarized in the following relative frequency distribution. Assume the survey was based on 100 individuals.

Age of Purchaser	Percent
Under 14 years old	20
14 to 17 years old	9
18 to 24 years old	10
25 to 34 years old	12
35 to 44 years old	13
46 to 64 years old	25
65 years old and over	11

a.	Calculate the average age of this distribution. Use 10 as the midpoint of the first class and 75 as the midpoint of the last class. (Round your intermediate calculations to 4 decimal places and final answer to 2 decimal places.)

Average Age

b.	Calculate the sample standard deviation. (Round your intermediate calculations to 4 decimal places and final answer to 2 decimal places.)

Standard Deviation

Answer 1

Following table shows the calculations:

Age of purchaser	Mid Point, X	Percent, p	Frequency, f=( p*100)/100	xf	f(x-mean)^2
Under 14 years old	10	20	20	200	13566.8405
14 to 17 years old	15.5	9	9	139.5	3798.873225
18 to 24 years old	21	10	10	210	2263.52025
25 to 34 years old	29.5	12	12	354	514.0443
35 to 44 years old	39.5	13	13	513.5	155.181325
45 to 64 years old	54.5	25	25	1362.5	8514.675625
65 years old and over	75	11	11	825	16692.41228
Total		1	100	3604.5	45505.5475

(a)

The sample mean is

(b)

The sample standard deviation is