Question

A set if n=5 measurements consists of the values 33, 27,45,38, 42. 1) Calculate the mean for the population. 2) calculate the deviation 3) calculate the variance and standard deviation for the population

Answer 1

1)

Mean = $\sum$ X / n

= ( 33 + 27 + 45 + 38 + 42) / 5

= 37

Mean for the population = 37

b)

Deviation = $\sum$ | X - $\mu$ | / n . Where $\mu$ is mean

= [ |(33 - 37) | + |(27-37)| + |(45-37)| + |(38-37)| + |(42-37)| ] / 5

= [ 4 + 10 + 8 + 1 + 5 ] / 5

= 5.6

Deviation = 5.6

3)

Variance = $\sum$ (X² - n $\mu$ ² ) / n

= [ ( 33² + 27² + 45² + 38² + 42²) - 5 * 37² ] / 5

= 41.2

Variance for population = 41.2

Standard deviation = Sqrt(Variance)

= Sqrt( 41.2)

= 6.4187

Standard deviation for the population = 6.4187