Question

Consider a data set containing the following values:

Answer 1

Answer:

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;

$=(-0.75)^2+(-5.75)^2+( 0.25)^2+(7.25)^2 +(18.25)^2+(-2.75)^2+(-20.75)^2 +(4.25)^2$

$=0.5625+33.0625+0.0625+52.5625+333.0625+7.5625+430.5625+18.0625$

= 875.5

Next is to find the population variance;

$V = \frac{875.5}{8}$

Variance, V = 109.4375

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

$Sd = \sqrt{109.4375}$

Standard deviation, Sd = 10.4612

To find the sample variance;

$V = \frac{875.5}{8-1}$

$V = \frac{875.5}{7}$

Variance, V = 125.0714

The sample variance is;

$Sd = \sqrt{125.0714}$

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.