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## The Standard Deviation (and Variance) Explained in One Minute: From Concept to Definition & Formulas

July 24, 2017 at 14:08 by K. Prabhu

Practically, nobody calculates the standard deviation by hand as there are tons of applications that do it for you. However, it is crucial to understand what exactly this term means and you know why we care about it. To understand what the standard deviation tells us, think about the huge room in which one on the left side, there are all of the male members of your family. On the right side, there are all of the female members of your family. For each side, we will measure only one thing, the average length of their hair. If you have, let's say a standard western family, will reveal that most men will have short hair, whereas when it comes to women, there are a lot of variation from very short to very long hair. The statistics enthusiasts will quickly tell you that the male group has a low standard deviation. In other words, the more guys have hair lengths close to the average than with the female group.

Next, we will get scientific by

1. Calculating the average hair size for the male well as female group. In other words, the mean.
2. Subtracting the mean from each individual value, then multiplying the result by itself. In other words, squaring it.
3. We once again calculate the mean, but this time the mean for the previously calculated square differences and the mean is called the variance.
4. We calculate the square root of that variance and there we have it. That is the standard deviation.

The bottom line is this. Whether you choose to calculate the standard deviation or not, the most important thing is realizing that its role is helping you better understand the nature of your data by knowing how close to the average, individual values tend to be.

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