# 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, 20, 23, 13, 18, 17, 22, 17, 15, 16The range is 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.)Can you please explain me this math problem having trouble understanding. Thank you.

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, 20, 23, 13, 18, 17, 22, 17, 15, 16

The range is

The mean is

The variance is

The standard deviation is

Can you please explain me this math problem having trouble understanding. Thank you.

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Step 1

The range of the ages of shoppers at the gaming store:

The range is the difference between the largest and the smallest values in the data set. That is,

Range=Maximum value –Minimum value.

Here, the maximum value is 23 and the minimum value is 12. Thus, the range is,

Range=23 –12=11.

The mean of the ages of shoppers at the gaming store:

Mean:

Mean of a data set is the sum of the data set divided by the number of elements in the data set.

The general formula for mean is,

x-bar=Sum of observations xi/Total number of observations.

Let the random variable X represents the ages of a random sample of shoppers at a gaming store.

The data points of the variable are X: 12, 20, 23, 13, 18, 17, 22, 17, 15 and 16.

The mean of the ages of shoppers at the gaming store is obtained as 17.3 years from the calculation given below:

Step 2

The variance of the ages of shoppers at the gaming store:

Variance:

The formula for sample variance is,

Step 3

The variance is obtained as 12.9 years from...

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