Question

The following sample data are from a normal population: 12 7 6 3 5 12 9 10 11 2 Calculate the point estimate of the population mean.

Answer 1

The sample mean (x⁻ ) is the point of estimate of the Population mean

x⁻ = 7.7

The sample standard deviation (S) is the point of estimate of the Population standard deviation

S = 3.65

Explanation:

Step(i):-

Given data 12 7 6 3 5 12 9 10 11 2

Mean of the data

`x^(-) = (12+7+6+3+5+12+9+10+11+2)/(10) = 7.7`

x : 12 7 6 3 5 12 9 10 11 2

x-x⁻ : 4.3 -0.7 -1.7 -4.7 -2.7 4.3 1.3 2.3 3.3 -5.7

(x-x⁻ )² : 18.49 0.49 2.89 22.09 7.29 18.49 1.69 5.29 10.89 32.49

Step(ii):-

Standard deviation of the sample

`S^(2) = (sum (x-x^(-))^(2) )/(n-1) = (120.1)/(10-1) = 13.344`

Standard deviation of the sample

S = √13.344 =3.65

Final answer:-

The sample mean (x⁻ ) is the point of estimate of the Population mean

x⁻ = 7.7

The sample standard deviation (S) is the point of estimate of the Population standard deviation

S = 3.65