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

The National Sporting Goods Association (NSGA) conducted a survey of the ages of individuals that purchased skateboarding footwear. The ages of this survey are summarized in the following percent frequency distribution. Assume the survey was based on a sample of 200 individuals.

Age of User Percent Frequency
Under 14 years old 37
14 to 17 years old 27
18 to 24 years old 16
25 to 34 years old 8
35 to 44 years old 5
45 to 64 years old 7

Calculate the mean and the standard deviation of the age of individuals that purchased skateboarding shoes. Use 10 as the midpoint of the first class. (Do not round intermediate calculations. Round your answers to 2 decimal places.)

Mean-

Variance-

Standard Deviation-

Solutions

Expert Solution

From the given data, the following Table is calculated:

Age of user Mid point (x) Percent frequency Frequency (f) x f x - (x - )2 f (x - )2
Under 14 years old 10 37 200X37/100=74 740 -9.395 88.266 6531.686
14 to 17 years old 15.5 27 200X27/100=54 837 -3.895 15.171 819.235
18 to 24 years old 21 16 200X16/2=32 672 1.605 2.578 82.433
25 to 34 years old 29.5 8 200X8/100=16 472 10.105 102.111 1633.778
35 to 44 years old 39.5 5 200X5/100=10 395 20.105 404.211 4042.11
45 to 64 years old 54.5 7 200X7/100=14 763 35.105 1232.361 17253.054
Total = 200 3879 30362.295

(i)

Mean of the age of individuals that purchased skateboarding shoes is given by:

(ii)

The Variance of the age of individuals that purchased skateboarding shoes is given by:

(ii)

The Standard Deviation of the age of individuals that purchased skateboarding shoes is given by:

milcah answered 8 months ago
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