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

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

Step-by-step explanation:

Step(i):-

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

Mean of the data

          $x^{-} = \frac{12+7+6+3+5+12+9+10+11+2}{10} = 7.7$

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

$S^{2} = \frac{sum (x-x^{-})^{2} }{n-1} = \frac{120.1}{10-1} = 13.344$

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