Question

A population consists of the following N=6 scores: 2,4,1,2,7,2 a) compute mean and standard deviation for the population b)Find z-score for each score in the population c) Transform the original population into a new population of N=5 scores with a mean of M(mu)=50 and a standard deviation of sigma=10?

Answer 1

a)

Mean, = = (2 + 4 + 1 + 2 + 7 + 2) / 6 = 3

Variance = = [(2 - 3)² +  (4 - 3)² +  (1 - 3)² +  (2 - 3)² +  (7 - 3)² +  (2 - 3)² ] / 6 = 4

Standard deviation, = = 2

b)

z-score = (x - ) /

z-score for each score in the population is,

(2 - 3)/2 , (4 - 3)/2 , (1 - 3)/2 , (2 - 3)/2 , (7 - 3)/2 , (2 - 3)/2

-0.5, 0.5, -1.0, -0.5, 2.0, -0.5

c)

To transform the population, such that mean, is 50 and standard deviation, = 10, we calculate the population value as,

x = + z = 50 + 10z

50 - 0.5 * 10 , 50 + 0.5 * 10 , 50 - 1 * 10 , 50 - 0.5 * 10 , 50 + 2 * 10 , 50 - 0.5 * 10

45, 55, 40, 45, 70, 45