Question

A small dataset has 10 numbers: 10,12,13,13, 14,15, 15, 17, 18, 19 (a) find the mean and standard deviation. use N-1 formula for calculating the standard deviation (b) convert all the score to Z score (3) does the rank order of the subject change when you convert their scores to Z scores

Answer 1

Arranging the data to calculate the mean and SD

	X	X2
	10	100
	12	144
	13	169
	13	169
	14	196
	15	225
	15	225
	17	289
	18	324
	19	361
Sum =	146	2202

a)

Mean is given by

Variance is given by

Standard deviation is given by

Mean = 14.6, Standard Deviation = 2.797

b)

Z score is given by

X	X - Mean	Z-score = (X-Mean)/Sigma
10	-4.6	-1.645
12	-2.6	-0.930
13	-1.6	-0.572
13	-1.6	-0.572
14	-0.6	-0.215
15	0.4	0.143
15	0.4	0.143
17	2.4	0.858
18	3.4	1.216
19	4.4	1.573

c)

No, the rank order does not change after converting to Z scores

Please let me know if you have any doubts. Happy to help. Please thumbs up if you like the solution. Thanks