Question

The ages​ (in years) of a random sample of shoppers at a gaming store are shown. Determine the​ range, mean,​ variance, and standard deviation of the sample data set.

12​,17​,23​,15​,13​,18​,22​,18​,13​,17

The range is _ ​(Simplify your​ answer.)

The mean is _ (Simplify your answer. Round to the nearest tenth as​ needed.)

The variance is _ ​(Simplify your answer. Round to the nearest hundredth as​ needed.)

The standard deviation is _ ​(Simplify your answer. Round to the nearest tenth as​ needed.)

Answer 1

Arranging the numbers in ascending order we have 12 13 13 15 17 17 18 18 22 23 (10 observations)

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Range = Largest Value - Smallest Value = 23 - 12 = 11

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Mean = Sum of observations/Number of Observations.

= (12 + 13 + 13 + 15 + 17 + 17 + 18 + 18 + 22 + 23)/10

= 168 /10

= 16.8 (Rounding to the nearest tenth, which is 1 decimal place)

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Variance = Sum Of Squares (SS) / n - 1, where

SS = SUM(X - Mean)². We take n - 1 observations as this is a sample and not a population.

#	X	Mean	(x - mean)2
1	12	16.8	23.04
2	13	16.8	14.44
3	13	16.8	14.44
4	15	16.8	3.24
5	17	16.8	0.04
6	17	16.8	0.04
7	18	16.8	1.44
8	18	16.8	1.44
9	22	16.8	27.04
10	23	16.8	38.44
Total	168.00		123.6

Therefore Variance = 123.6/(10-1) = 123.6/9 = 13.73 (Rounding to the nearest hundredth, which is 2 decimal places)

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Standard Deviation = SQRT(Variance) = SQRT(13.73) = 3.7 (Rounding to the nearest tenth, which is 1 decimal place)

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