What is Standard Deviation?
Although standard deviation is quite a difficult concept to first grasp and understand, when used in statistics or theories of probability, the term standard deviation of a statistical population or a set of data is the square root of its variance, and its most useful purpose is as a measure of dispersion. It is also the most popular type of measure of data spread and is mostly used by investors to calculate the volatility of mutual funds.
Basically, the standard deviation of a set of data refers to how wide the dispersion of the data is from its mean (average). The more spread apart the data is from its average, the higher the deviation value. Fundamentally, standard deviation is 'the mean of the mean'.
When you are comparing the dispersal of data, it is more appropriate to use a measure of spread such as standard deviation, rather than a simple measure of central tendency such as the mean, median or mode.
In simpler terms, the standard deviation is a value that is used to verify how spread out a set of data is, and how close the individual data points are to the mean (or average) of the overall sample.
The formula for standard deviation is quite simple, when you know what it means: the square root of the variance. But this can also raise the question of 'what is the variance?' The variance is defined as the squared differences from the means. If you ever come across the equation and you find it rather complicated and it doesn't make any sense to you, don't worry, all you need to know is how to work out the final answer.
The formula's overall purpose is to find the average numerical distance between the data's average and the individual numbers and the aim of the squared numbers is to make all data positive, as they become easier to work with.
By knowing the definitions of the information you need to know, you can begin to work out the mean of your set of data. This means that you must add up all your numbers, and then divide the value you get by the total of original numbers you had. Then you must take away the mean value away from each individual point, and then square the results, i.e. times it by itself. Finally, you then have to divide the sum of all the values by the number of values you started off with, minus one, and then take away the square root (that you calculated earlier) to give you the popular standard deviation.
Although this method does sound confusing at first, it can sometimes be easier to write out your calculation in seven steps. By listing out each of your calculation steps out as you make them, it can get you used to the method so once you think you have a grasp on it, you can try and do it straight from memory. Also, if you happen to work out an incorrect answer, this kind of layout will make it easier for you to look back and discover where exactly it was that you went wrong.