Question

A social psychologist records the age (in years) that a sample of eight participants first experienced peer pressure. The recorded ages for the participants are 14, 20, 17, 16, 12, 16, 15, and 16. Compute the SS, the variance, and the standard deviation for this sample using the definitional and computational formula. Please show step by step.

Answer 1

solution

14, 20, 17, 16, 12, 16, 15 , 16

The mean of sample is   $\bar x$

$\sum$x/n =  (14+ 20+ 17+ 16+12 +16+15 +16/ 8)

= 15.75

The sample mean is 15.75

Sample standard deviation is s

s = $\sqrt$ 1/(n-1)$\sum$(x - $\bar x$ )²

⁼  $\sqrt$1/4 (14 - 15.75 )²+ (20 - 15.75 )²+ (17- 15.75)²+ (16- 15.75 )² +( 12 - 15.75 )²+( 16 - 15.75 )²+( 15- 15.75 )²+( 16 - 15.75 )²

= $\sqrt$ 5.3571428571429

=2.3145502494314

The sample standard deviation is 2.3146

variance = ( s)²

⁼( 2.3146)²

⁼5.357