Question

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

Answer 1

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