Standard deviation is something that not a lot of people will be able to use in their everyday conversation. This wiki is going to attempt to explain standard deviation in the simplest of terms. If we know the standard deviation of a set of numbers, we know the story of that set of numbers. To find the standard deviation, we need to have a set of numbers/scores, the average of those scores, and the number of numbers/scores in a data set. It may be thought of as the average difference of the scores from the mean of distribution, how far they are away from the mean (wikipedia.org)



To get a standard deviation we need to have the set of numbers and the mean of that set. We then subtract the mean from each value, and then square each individual value. We add those squared values up, and then divide by one less than the number of values in a given set (N-1). We then take the square root of that number. This doesn’t make much sense without an example, but we are just getting an idea of what this standard deviation is.



The number that we come up with is the standard deviation. Ok, what is that you may ask? The standard deviation is the amount of variance around the mean of a set of scores/numbers. A good way to phrase it is by posing the question, “How close are all the scores to the mean?” The standard deviation goes above and below the average of a set of numbers, meaning that it is labeled either +1 or -1, or +2 or -2 standard deviations from the mean. +/-1 standard deviation from the mean contains roughly 68% of the data, while +/-2 standard deviations contains almost 95% of the data. This also has to fall within a normal distribution, which means the average is in the middle of a bell curve. When the examples are pretty tightly bunched together and the bell-shaped curve is steep, the standard deviation is small. When the examples are spread apart and the bell curve is relatively flat, that tells you that you have a relatively large standard deviation (robertniles.com)



After a brief explanation of what standard deviation is, I will give an example with some numbers. Let’s say we have a set of numbers with the mean being 50. Te standard deviation has been calculated to be 3.5. To sum it up, we can say with just these few numbers that 68% of the data set will fall between 46.5 and 53.5. We can also say that 95% of all data in that set will fall between 43 and 57. So that is the most basic explanation of standard deviation.