Question

Consider a sample with six observations of 15, 16, 12, 8, 6, and 9. Compute the z-scores for each sample observation.
Sample observation. z-scores
15
16
12
8
6
9

Answer 1

Answer:

1 ; 1.25 ; 0.25 ; - 0.75 ; - 1.25 ;- 0.5

Step-by-step explanation:

Given the sample observations : 15, 16, 12, 8, 6, 9

Zscore for each sample Observation :

Zscore = (x - mean) / standard deviation

(15 + 16 + 12 + 8 + 6 + 9) / 6 = 11

Mean value (m) = 11

Standard deviation (s) = 5

Sqrt[(x - m)^2 / (n - 1)]

[(15-11)^2 + (16-11)^2 + (12-11)^2 + (8-11)^2 + (6-11)^2 + (9-11)^2] / (6 - 1)

= 80/5 = 16

Sqrt(16) = 4

Zscore = (x - mean) / standard deviation

x = 15

Zscore = (15 - 11) / 4 = 1

x = 16

Zscore = (16 - 11) / 4 = 1.25

x = 12

Zscore = (12 - 11) / 4 = 0.25

x = 8

Zscore = (8 - 11) / 4 = - 0.75

x = 6

Zscore = (6 - 11) / 4 = - 1.25

x = 9

Zscore = (9 - 11) / 4 = - 0.5