I’ve been looking at Statistics in my free time and what exactly does standard deviation is useful for and/or how can I extract meaningful data by using SD and what conclusion can I derive from said data?
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Lots of great responses on what standard deviation is, so I thought I would add another way it is useful… if you have a normal distribution (also called Gaussian distribution, which lots of random things tend towards a normal distribution) then the standard deviation can tell you the probability of where values lie. So for example, if you know something has a normal distribution and a mean of 4 with a standard deviation of 1, then there is a 68% chance a random value in that distribution would be between 3 and 5 (mean +/- stdev). 95% would be between 2 and 6 and 99.7% would be between 1 and 7.
Working backwards from this, you could also figure out how likely something is if you know it is a normal distribution and you know the mean and standard deviation. So take the SAT for example, the test is made to have a scores of 200-800 on each section with a normal distribution having a mean of 500 and a standard deviation of 100. You happened to get a 710 and wonder how many others did as well. Well as above, 95% would be between 2 standard deviations of the mean, so 300-700. And being a normal distribution it would also mean that exactly half of the ones not in that 95% would be higher than 700 and half will be lower than 300. So by getting higher than 700, you are in the top 2.5% of test takers.
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