Difference between Standard Deviation and Variance.
In: Mathematics
Variance is defined as the average of squared mean deviations for a population — e.g. for data *x_i* with mean *mu*, the difference between each *x_i* and *mu* is squared and added, and the result is then divided by the numbee of data (or that number minus one for samples).
This gives an idea of how much variation there is in the data, with the square eliminating negatives to give an idea of the variance in absolute terms.
Standard Deviation is the square root of the variance. This works out to give us a measure of *about how far from the mean* we can go and still contain a certain proportion of the data based on the underlying probability distribution (the *normal* or Gaussian distribution, here). For normally-distributed data, we can expect around 64% of observations to be within one standard deviation of the mean in both directions.
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