*30*

Just a few days ago I showed you **how to calculate the mean deviation** for a set of data. I also explained the **difference** between the **mean** and mean deviation. In this article I'll be showing you something that is slightly different, but just as useful. **I'll be explaining what variance is**.

*Image by**Karolina Grabowska**from Pixabay*

Let's say we have the set of data:

**x = {1, 2, 3, 4, 3, 2, 1, 2, 2, 3, 4, 5, 4, 1, 2}**

And in this set of data there are **15 observations**. How would we go about finding the **variance**?

Well, firstly we'd have to **organise** our set of data like this:

**x = {1, 1, 1, 2, 2, 2, 2, 2, 3, 3, 3, 4, 4, 4, 5}**

We'd then have to calculate the **mean** of our set of data:

**Mean = (3*1 + 5*2 + 3*3 + 3*4 + 1*5)/15 = 2.6**

Next we'd have to write down the numbers that exist in our set of data (excluding their frequencies):

**1, 2, 3, 4, and 5**

After that, we'd have to subtract the mean from each of these numbers and square the result, like this:

**(1 - 2.6)^2 = (-1.6)^2 = 2.56**

**(2 - 2.6)^2 = (-0.6)^2 = 0.36**

**(3 - 2.6)^2 = (0.4)^2 = 0.16**

**(4 - 2.6)^2 = (1.4)^2 = 1.96**

**(5 - 2.6)^2 = (2.4)^2 = 5.76**

*Image by**Gerd Altmann**from Pixabay*

With all the main tasks completed, we'd be ready to get the **variance**. Now, when it comes to variance, the ** frequency** at which the numbers in our set of data appear are crucial. Remember, when we were calculating the mean, we discovered that

**1**appeared

**,**

__three times__**2**appeared

**,**

__five times__**3**appeared

**,**

__three times__**4**appeared

**and**

__three times__**5**appeared

**.**

__once__Because of this fact, the variance would have to be:

**[3*(2.56) + 5*(0.36) + 3*(0.16) + 3*(1.96) + 1*(5.76)]/15 = 21.6/15 = 1.44**

What the variance simply is, in words, *is the addition* of each value in your set of data minus the mean, squared, divided by the number of observations that exist. When certain numbers appear more than once, you can use their frequencies to simplify the calculation, **as shown above**.

It's not that hard to grasp, and in a visual sense variance is a bit similar to what we'd call a mean deviation. The distinction is of course, with variance you are getting the **squares of the differences**, then dividing the result by the number of observations that exist.

Also, the popular **standard deviation** is the ** square root of variance**.

*Video related to this article:*

*Article written by Tiago Hands:**https://www.instagram.com/tiago_hands**Mathematics Proofs (Instagram):**https://www.instagram.com/mathematics.proofs**Mathematics Articles:**https://read.cash/@mathematics.proofs*