The applet below calculates the standard deviation for the data set on the number line. Move the points around to change the data.
As shown, finding the standard deviation involves calculating the average of the squared differences between each data point and the mean, and then taking the square root of that average. The sum of squares can also be written in sigma notation.
σ=ni=1∑n(xi−x)2
Standard deviation is sensitive to outliers because of the squaring of differences. It is commonly used when analyzing a data set that exhibits a normal distribution.
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