Standard Deviation Problem
Here are the scores:
55
67
65
54
55
51
58
57
61
49
__
Although we wouldn't have to, it
might make it easier to arrange
them from high to low or low to
high. -----------------------------
There! This makes it easier to spot the mode, find the
median, calculate the range, and get a feel for the mean.
We'll need the mean in a moment in order to do the variance
and standard deviation, so let's find it first.
The sum of the Xs is 572. The N is 10. So the mean is 57.2.
49
51
54
55
55
57
58
61
65
67
___
Let's make a table that looks like this one. It's a good idea to set this up this
way any time we are expecting to do descriptive statistics.
Scores
49
51
54
55
55
57
58
61
65
67
- the mean
57.2
57.2
57.2
57.2
57.2
57.2
57.2
57.2
57.2
57.2
=____
-8.2
-6.2
-3.2
-2.2
-2.2
- .2
.8
3.8
7.8
9.8
____
00.0
Square it!
67.24
38.44
10.24
4.84
4.84
.04
.64
14.44
60.84
96.04
______
297.60
2
_ 2
Now for the formula: s = (X - X)
_________
N
2
Let's plug in the numbers: s = (297.60)
________
= 29.76
10
2
2
s is the variance. To get rid of the , take the square root of 29.76, 5.46.
The standard deviation is 5.46.