Knowing how the data varies leads to understanding the data.

To answer the question of what is standard deviation you must refer to the question
raised in mean average. The mean or average have
little value without some measure of the variability of the data. Standard deviation
to the rescue!

The Equation

The standard deviation is a measure of the variability of the distribution of a random variable.

The standard deviation equation is:

It must be noted that this formula is for the sample and not
for the population. If you don't know what this means, don't
worry about it. For simple applications it makes little difference.

A word description of the steps needed to calculate the standard deviation:

calculate the weighted sum of the squares of the differences of the observations in a simple random sample from the sample mean

divide the result obtained in 1 by an estimate of the population size minus 1

take the square root of the result obtained in 2.

Now that you have seen the formula, let's describe what is happening in simpler
terms. The formula is simply finding the average distance each data point is from
the dataset mean. The squared numbers is a mathematical way of making all of
the distances positive. So here is our measure of a datset: First we find the
average of the data points, then we find the average of the distance each data
point is from the mean or average of the data. This gives us a good beginning
in describing the data within a datset.

Summary

The question of explaining standard deviation has been addressed herein. It is
the average of the distance from the mean of all the data points in the dataset.
To see an example of how this parameter is calculated go to
Standard Deviation Calculation.