Real-Life Math
You have the preliminary results of a survey. While you will still be getting more surveys in, you are curious about these results and want to do a few calculations.
You decide to see what the standard deviation is.
The standard deviation reveals how numbers are set out in relation to their average (or mean). They might all be clustered close to that mean. Another set of numbers with the same average might have numbers that aren't anywhere close to that mean.
A large standard deviation means that the numbers tend to be widespread, or quite different from each other. A small standard deviation means that the numbers in the set are close together.
There's a formula for finding out the standard deviation.
s = standard deviation
n = number of survey results (also called number of elements in a set)
(x - xavg)2 = the sum of all the deviations from the mean squared
The survey results you have received are:
12
1
10
9
9
9
8
7
6
They're interesting results. Now you want to figure out what the standard deviation is. So you start by determining the average or mean of the survey results (the set).
To find the average, you add up all the results and then divide by the total number of results.
| xavg= | (12 + 1 + 10 + 9 + 9 + 9 + 8 + 7 + 6)
9 |
| xavg = 7.89 |
Now you have to figure out the sum of the deviations from the mean squared.
| (x - xavg)2 |
| (x - xavg)2 = (12 - 7.88)2 + (1 - 7.88)2 + (10 - 7.88)2 + (9 - 7.88)2 + (9 - 7.88)2 + (9 - 7.88)2 + (8 - 7.88)2 + (7 - 7.88)2 + (6 - 7.88)2 |
| (x - xavg)2 = (4.12)2 + (-6.88)2 + (2.12)2 + (1.12)2 + (1.12)2 + (1.12)2 + (0.12)2 + (-0.88)2 + (-1.88)2 |
| (x - xavg)2 = 16.97 + 47.33 + 4.49 + 1.25 + 1.25 + 1.25 + 0.014 + 0.77 + 3.53 |
| (x - xavg)2 = 76.9 |