Question

In: Statistics and Probability

Find the sample variance and standard deviation. 23​, 16​, 3​, 8​, 11

Find the sample variance and standard deviation. 23​, 16​, 3​, 8​, 11

Solutions

Expert Solution

Sample standard deviation =

Sample variance =

As per data, sample size = n = 5.

Step 1: Find the sample mean =

The mean of a data set is the sum of the terms divided by the total number of terms.

Mean=Sum of terms / Number of terms

Step 2: Create the following table.
23 10.8 116.64
16 3.8 14.44
3 -9.2 84.64
8 -4.2 17.64
11 -1.2 1.44

Step 3: Find the sum of numbers in the last column to get.

Step 4: Calculate sample variance using the below formula.

Step 5: Calculate sample standard deviation () using below formula.

ANS : Sample variance = 58.7 and sample standard deviation = 7.66159

orchestra answered 3 years ago
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