Standard Deviation

The standard deviation is a statistical measure that calculates the amount of variation or dispersion within a set of data values. It quantifies the average distance between each data point and the mean of the data set, providing an understanding of how spread out the values are.


The standard deviation is calculated using the following steps:

  1. Compute the mean of the data set.
  2. Subtract the mean from each data point and square the result.
  3. Calculate the average of the squared differences.
  4. Take the square root of the average to obtain the standard deviation.


A higher standard deviation indicates a greater degree of variability in the data points, while a lower standard deviation implies that the data values cluster around the mean. It provides insight into the spread of the data set and is commonly used to assess the reliability and consistency of data.


The standard deviation possesses the following properties:

  • The standard deviation is always non-negative.
  • If all data values are identical, the standard deviation is zero.
  • The standard deviation is affected by outliers, as it incorporates the squared differences of data points.
  • Adding or subtracting a constant value from each data point does not change the standard deviation. Scaling the data set also scales the standard deviation accordingly.
  • The standard deviation is more sensitive to extreme values than the mean, making it useful in detecting outliers.