Question

218, 211, 215, 211, 215

a. Find the mean and the standard deviation (using either formula)

b. Now change the score of 218 to 88 and find the new mean and standard deviation (using either formula).

c. Describe how one extreme score influenced the mean and standard deviation.

Answer 1

Mean = Sum of observations/ Number of observations

= (218 + 211 + 215 + 211 + 215)/5

= 214

Standard deviation = {Sum of (X - mean)²/n}^1/2

= {[(218 - 214)² + (211 - 214)² + (215 - 214)² + (211 - 214)² + 215 - 214)²]/5}^1/2

= [(16 + 9 + 1 + 9 + 1)/5}^1/2

= 2.683

b) When 218 is replaced by 88,

Mean = Sum of observations/ Number of observations

= (88 + 211 + 215 + 211 + 215)/5

= 188

Standard deviation = {Sum of (X - mean)²/n}^1/2

= {[(88 - 188)² + (211 - 188)² + (215 - 188)² + (211 - 188)² + 215 - 188)²]/5}^1/2

= [(10,000 + 529 + 729 + 529 + 729)/5}^1/2

= 50.03

c) One extreme score have significance impact on both mean and standard deviation. More impact is there on standard deviation, compared to mean, because the deviation of each score from the mean score have increased, resulting in higher standard deviation.