Question

x	f
10	3
9	6
8	4
7	5
6	2

Find the Z score when X = 9, for the for the following Data

Answer 1

Solution:

The formula for mean and SS is given as below:

Mean = ∑xf / ∑f

SS = ∑f*(x – mean)^2

Population variance = ∑f*(x – mean)^2 / ∑f

The calculation table is given as below:

No.	x	f	xf	SS
1	10	3	30	10.2675
2	9	6	54	4.335
3	8	4	32	0.09
4	7	5	35	6.6125
5	6	2	12	9.245
Total	40	20	163	30.55

Mean = 163/20

Mean = µ = 8.15

SS = ∑f*(x – mean)^2 = 30.55

SS = 30.55

∑f = 20

Population variance = 30.55/20 = 1.5275

Population variance = 1.5275

Population standard deviation = Sqrt(Variance) = Sqrt(1.5275) = 1.235921

Population standard deviation = σ = 1.235921

The formula for Z score is given as below:

Z = (X – µ)/σ

X = 9

Z = (9 - 8.15)/ 1.235921

Z = 0.687746

Required Z score = 0.687746