Normally distributed data, is when if you were to graph a histogram with itty bitty little bin widths, the result would be a bell curve. Once we have recognized that we have data that behaves this way there are a few pieces of information that we can collect. The first that we will be looking at is the standard deviation. This is a measure of how spread out the data is. It’s more helpful than just the mean because it let’s us know if most of our values were close to the mean or very far away.
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Check out this video below on how we can calculate the standard deviation for a sample set of data.
Given that you know the mean and the standard deviation of a set of data, a z-score is used to determine where a single measurement stands in relation to the rest of the data. It is going to give this measurement a value based on how many standard deviations above or below the mean it is. Anything between -1 and 1 is pretty well average, and keep in mind that anything between -2 and 2 is also pretty normal. It is only once we start looking at values above 2 or below -2 that we are looking at samples abnormally off of the mean. That doesn’t mean a bad thing or a good thing necessarily because according to the normal curve 5% of the data points measure should exist outside of the -2 to 2 range. 1 in 20 isn’t so rare when you stop and think about it.
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