The lower-case sigma represents the standard deviation and the is equal to the square root of a complex fraction. Below is the full equation for standard deviation – if it seems very daunting do not worry, I will go over each variable and what it means. Now that we understand the definition of standard deviation and can visualize – how can we find it? Well before we know how to solve it, we must go over some Greek mathematical letters. There is no need to know why we do this (I promise there is a reason), but it is important to know how we got these numbers and how we use standard deviation in building a bell curve. Therefore, you might be thinking 108.4 or 75.4 was not in our dataset but that does not matter this is how you build a bell curve (by adding and subtracting to the mean by the standard deviation).
This means that I added 5.5 to 91.9 to get 97.4 and I subtracted 5.5 from 91.9 to get 86.4. Additionally, the red lines I drew on the curve show one standard deviation away from the mean in each direction. This image is a bell curve of our test scores data as you can see the middle of the curve is the value 91.9 which is our mean. If this is confusing for you, let’s take a look at the image below. This tells us that the data is fairly central to the mean and there are few if not no outliers in our dataset. So, what does this 5.5 really tell us about the test scores? The number 5.5 shows us how the numbers are spread out from the mean and 5.5 is a relatively low standard deviation score. The average of these test scores is 91.9, while the standard deviation is roughly 5.5. Sample Python Code for Standard Deviation
This is very different than the mean, median which gives us the “middle” of our data, also known as the average. The standard deviation is more commonly used, and it is a measure of the dispersion of the data. The standard deviation or variance, the standard deviation is just the variance square rooted or raised to ½. Now that we discussed mean, median, and mode – let’s discuss a topic that is a bit more complex but is frequently used in finance, health, and many other sectors.
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