Consider a data set containing the following values: 70 65 71 78 89 68 50 75

The mean of the preceding values is:

70.75.

The deviations for the mean have been calculated as follows:

-0.75, -5.75, 0.25,7.25,18.25,-2.75,-20.75, and 4.25

a. If this is the sample data, the sample variance is and the sample standard deviation is ___
b. If this is a population data, the population variance is and the population standard deviation is

a. 125.0714; 11.1835.

b. 109.4375; 10.4612.

Step-by-step explanation:

Given the following data;

70, 65, 71, 78, 89, 68, 50, 75.

Mean = 70.75

The deviation for the mean of the data is -0.75, -5.75, 0.25,7.25,18.25,-2.75,-20.75, and 4.25.

We would then find the square of this deviation;

= 875.5

Next is to find the population variance;

Variance, V = 109.4375

The population standard deviation is the square root of the population variance;

Standard deviation, Sd = 10.4612

To find the sample variance;

Variance, V = 125.0714

The sample variance is;

Standard deviation, Sd = 11.1835

Therefore,

a. The sample variance is 125.0714 and the sample standard deviation is 11.1835.

b. If this is a population data, the population variance is 109.4375 and the population standard deviation is 10.4612.