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	15
14 to 17 years old	4
18 to 24 years old	6
25 to 34 years old	15
35 to 44 years old	16
45 to 64 years old	28
65 years old and over	16

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 intermediate calculations to at least 4 decimal places and final answer to 2 decimal places.)

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

Answer 1

Here we have the ages are summarized in the relative frequency distribution

We first find mid points of ages as

Age of Purchaser	Age mid point (m)	Percent (f)	m*f	m^2*f
					<14	10	15	150	1500
14 to 17	15.5	4	62	961
18 to 24	21	6	126	2646
25 to 34	29.5	15	442.5	13053.75
35 to 44	39.5	16	632	24964
45 to 64	54.5	28	1526	83167
>65	75	16	1200	90000
Total		N=100	4138.5	216291.75

a) Average is

Thus Average age for this distribution is 41.38

b) Sample standard deviation is

first find variance

variance is,

Now Standard deviation is

Standard deviation is 21.32