a.       Find the population variance

x	(x-u)	abs(x-u)	variance
6	1.71	1.71	2.92
2	-2.29	2.29	5.22
4	-0.29	0.29	0.08
9	4.71	4.71	22.22
1	-3.29	3.29	10.8
3	-1.29	1.29	1.65
5	0.71	0.71	0.51
4.29
	SSx = ∑(x - u)2 =		43.41
Population Variance =			6.2

                                                  i.      α² = ∑ ( x – µ )² / N

b.      Find the population standard deviation
Pop. Standard Deviation = 2.49

c.       Find the interquartile range
Range: 1    2    3    4    5    6    9
Q3 – Q1
i = (P/100) * n
Q1 = P25/100 * 7
i = 25/100 * 7 = 1.75
i = 1.75 + 1 = 2.75 = 2
Q1 = P25 = 2

Q3
i = P75/100 * 7 = 5.25
i = 5.25 + 1 = 6.25 = 6
Q3 = P75 = 6
Interquartile range = Q3 – Q1 = 6 – 2 = 4

d.      Find the z-score for each value

x	(x-u)	abs(x-u)	variance	z-Score
6	1.71	1.71	2.92	0.69
2	-2.29	2.29	5.22	-0.92
4	-0.29	0.29	0.08	-0.11
9	4.71	4.71	22.22	1.89
1	-3.29	3.29	10.8	-1.32
3	-1.29	1.29	1.65	-0.52
5	0.71	0.71	0.51	0.29

 

 

Descriptive statistics
	# 1
mean	4.29
range	8
population variance	6.20
population standard deviation	2.49
1st quartile	2.50
median	4.00
3rd quartile	5.50
interquartile range	3.00