Question 617183: find the variance, and standard deviation for the following set of scores:
X
4
2
2
3
5
6
Round off all answers to the nearest hundredth.
show all of your work
Add them.
X
4
2
2
3
5
6
---
22
Out beside that column square every number, that is, multiply
it by itself, then add that column and you have:
X X²
4 16
2 4
2 4
3 9
5 25
6 36
--- ---
∑x=22 ∑x²=94
The variance is s². The short-cut formula is:
n(∑X²) − (∑X)²
s² = --------------
n(n − 1)
We substitute ∑x=22, ∑x²=94, and n=6 (the number of numbers)
6(94) − (22)²
s² = --------------
6(6 − 1)
564 − 484
s² = --------------
6(5)
80
s² = --------------
30
s² = = 2.66666666667
That's the variance.
To get the standard deviation, take the square root:
s = = = 1.632993162
Round off all answers to the nearest hundredth.
s² = 2.67
s = 1.63
Edwin
