Question

Consider the following raw scores, x: 2, 7,4,9, 1, 10. a. Assuming the scores represent a population, calculate the SS, the variance and the standard deviation of the scores. b. Assuming the scores represent a sample, calculate the SS, the variance and the standard deviation of the scores.

Answer 1

Solution:

x	x2
2	4
7	49
4	16
9	81
1	1
10	100
$\sum$x=33	$\sum$x2=251

Population Variance σ²=( $\sum$ x² ) - (( $\sum$ x)² / n ) n

=251-(33)²6 /6

=251-181.5 / 6

=69.5/ 6

=11.5833

Population Variance = 11.58

Population Standard deviation σ=$\sqrt{}$( $\sum$ x² ) - (( $\sum$ x)² / n ) n -1

=$\sqrt{}$251-(33)266

=$\sqrt{}$251-181.56

=$\sqrt{}$69.56

=$\sqrt{}$11.5833

=3.4034

Population Standard deviation σ = 3.40

Sample Variance S²=( $\sum$ x² ) - (( $\sum$ x)² / n ) n -1

=251-(33⁾²65

=251-181.55

=69.55

=13.9

Sample Variance = 13.9

The sample standard is S

  S =$\sqrt{}$( $\sum$ x² ) - (( $\sum$ x)² / n ) n -1

=$\sqrt{}$251-(33)²6 /5

=$\sqrt{}$251-181.5/5

=$\sqrt{}$69.5/5

=$\sqrt{}$13.9

=3.7283

The sample standard is = 3.72