Example: The scores from 11 students on a quiz are 4, 7, 6, 3, 10, 7, 3, 7, 5, 5, and 9
- Order scores.
- Calculate the mean score.
- Calculate the deviations from the mean.
- Square the deviations from the mean.
- Calculate the mean of the squared deviations from the mean (i.e. sum the squared deviations from the mean then divide by the number of scores). This number is called the variance.
- Take the square root and you have calculated the standard deviation.
|
Score(Step 1, order) |
Deviation from the mean |
Squared deviation from the mean |
|
|
3 |
3 |
9 |
|
|
3 |
3 |
9 |
|
|
4 |
2 |
4 |
(Step 4-5, complete the calculations) |
|
5 |
1 |
1 |
Formula: |
|
5 |
1 |
1 |
|
|
6 |
0 |
0 |
|
|
7 |
1 |
1 |
|
|
7 |
1 |
1 |
|
|
7 |
1 |
1 |
|
|
9 |
3 |
9 |
|
|
10 |
4 |
4 |
|
|
TOTAL = 66 |
52 |
||
|
(Step 2, calculate mean) |
(Step 3, calculate deviations) |
(Step 6, find the standard deviation) |
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