The standard deviation is found by calculating the square root of the variance of a data set. The steps to find the standard deviation are:
- Calculate the mean (average) of the data points.
- Subtract the mean from each data point to find the deviation for each point.
- Square each deviation to make all values positive.
- Sum up all the squared deviations.
- Divide this sum by the number of data points minus one for a sample (or by the total number of points for a population) to find the variance.
- Take the square root of the variance. This value is the standard deviation.
This process shows how spread out the data points are from the mean on average. The formula for sample standard deviation is:
s=1n−1∑i=1n(xi−xˉ)2s=\sqrt{\frac{1}{n-1}\sum_{i=1}^n(x_i-\bar{x})^2}s=n−11i=1∑n(xi−xˉ)2
Where xix_ixi are the data points, xˉ\bar{x}xˉ is the mean, and nnn is the number of data points.
