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 |
|
|