Question

How do I calculate the variance of {3,6,7,8,9}?

Answer 1

`s^2` = `sum((x_i - barx)^2)/ (n - 1)`

Explanation:

Where:

`s^2` = variance

`sum` = sum of all values in the sample

`n` = sample size

`barx` = mean

`x_i` = Sample observation for each term

Step 1 - Find the mean of your terms.

`(3 + 6 + 7 + 8 + 9)/5 = 6.6`

Step 2 - Subtract the sample mean from each term (`barx-x_i`).

`(3 - 6.6) = -3.6`

`(6 - 6.6)^2` `= -0.6`

`(7 - 6.6)^2` `= 0.4`

`(8 - 6.6)^2` `= 1.4`

`(9 - 6.6)^2` `= 2.4`

Note: The sum of these answers should be `0`

Step 3 - Square each of the results. (Squaring makes negative numbers positive.)

-`3.6^2 = 12.96`

-`0.6^2 = 0.36`

`0.4^2 = 0.16`

`1.4^2 = 1.96`

`2.4^2 = 5.76`

Step 4 - Find the sum of the squared terms.

`(12.96 + 0.36 + 0.16 + 1.96 + 5.76) = 21.2`

Step 5 - Finally, we'll find the variance. (Make sure to -1 from the sample size.)

`s^2 = (21.2)/(5-1)`

`s^2 = 5.3`

An extra, if you'd care to expand - from this point, if you take the square root of the variance, you'll get the standard deviation (a measure of how spread out your terms are from the mean).

I hope this helps. I'm sure that I didn't need to write out every step, but I wanted to make sure you knew exactly where each number was coming from.