What is Standard Deviation? – Simplified

Standard deviation is simply defined as a measure of statistical dispersion. In simpler terms, standard deviation is a way to describe how a set of values spread out around the mean or midpoint of that same set. To explain it clearly, take for example five bamboo sticks for height measurement. To compute for the mean, all you have to do is to sum up the different height measurements of the five sticks. Afterwards, you just have to divide the result by five.

Getting the mean is simple. However, that does not give you anything about the spreads of the five heights. To give you more information over and above the mean value you have to get the spreads. The mean alone does not give you information if there is an overly towering bamboo stick. Nor mean alone does not tell you if the bamboo sticks are almost exactly the same in height.

The question is how do you calculate standard deviation? Again, the fundamental thought of standard deviation is to measure discrepancies around the mean value. For the result, you could expect the possibilities below:
There may be values that will be below the mean.
There may be values that will be above the mean.
There may be values that will be equal to the mean.

In short, differences may be positive, which means the result is more than the mean, and vice versa. Moreover, the difference may also be zero, which means it is equal to the mean. Adding the differences is not just the right thing to do because the negative and positive results will just cancel out each other.

To do it right, you have to square each variations around the mean. Squaring a negative value will give you a positive value. After squaring all the values, you can now perform the calculation for standard deviation. Simply add up all the squared values and divide by one less than the number of values in your set. The result is called the variance. For the final step to get the standard deviation, you have to take the square root of the variance. To take the square root, you have to reverse the process of squaring a value.

For a simpler step-by-step instructions on how to do it, refer below:
Calculate for the average, which is the mean, of your set of values.
Calculate the difference between each number and the mean or average.
Square the results you get.
Take the sum of the square of all the differences.
Divide the result by one less than the values of values in your set. The result will be the variance.
Finally, take the square root of the variance and you end up with the standard deviation.

That explains about the standard deviation. A low standard deviation will mean that a set of values are closely collected near the average or mean. A high standard deviation is the exact opposite of low standard deviation. It means that the set of numbers are widely apart. Finally, the zero standard deviation would mean the values are equal to the mean.