Question

# The National Sporting Goods Association (NSGA) conducted a survey of the ages of people that purchased...

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.)

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

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