Standard deviation is a measure of how close the numbers are to the mean. It is calculated as the square root of the variance and denoted by σ (the Greek letter sigma).
Formula to calculate standard deviation.
To calculate standard deviation;
- Find the mean of the (μ) numbers given.
- Subtract the mean from each of the numbers (x), square the difference and find their sum.
- Divide the result by the total number of observations (N) and finally find the square root of the result.
Formula to determine standard deviation.
![Calculate Standard Deviation.](https://www.learntocalculate.com/wp-content/uploads/2020/04/standard-deviation-1.png)
Example:
Find the standard deviation of the following numbers.
2, 4, 5, 8, 1.
We start by finding the mean of the list of data.
![Calculate Standard Deviation.](https://www.learntocalculate.com/wp-content/uploads/2020/04/MEAN.png)
Then subtract the mean from each of the numbers, square the difference and find their sum.
![Calculate Standard Deviation.](https://www.learntocalculate.com/wp-content/uploads/2020/04/SUBTRACT-SUMMING-AND-SQUARE..png)
Divide the result by the total number of observations and finally find the square root of the result.
![Calculate Standard Deviation.](https://www.learntocalculate.com/wp-content/uploads/2020/04/DIVIDESQUARE-ROOT.png)
Therefore, the standard deviation of the list of data is 2.45.