The Standard Deviation (σ) is a measure of how spread out the numbers is.
The formula is the square root of the Variance.
The Variance (which is the square of the standard deviation, i.e.: σ2) is defined as the average of the squared differences from the Mean.[1]
In other words, follow these steps:
- Work out the Mean (the simple average of the numbers)
- Now, for each number subtract the Mean and then square the result (the squared difference).
- Then work out the average of those squared differences.
To calculate the Variance, take each difference, square it, and then average the result:
|
Variance: σ2 = |
2062 + 762 + (-224)2 + 362 + (-94)2 |
= |
108,520 |
= 21,704 |
|
|
5 |
|||||
|
5 |
So, the Variance is 21,704.
And the Standard Deviation is just the square root of Variance:
Standard Deviation: σ = 
=
147
The variance is one of several indices of variability that statisticians use to characterize the dispersion among the measures in a given population. To calculate the variance of a given population, it is necessary to first calculate the mean of the scores, then measure the amount that each score deviates from the mean and then square that deviation (by multiplying it by itself). Numerically, the variance equals the average of the several squared deviations from the mean.[2]
