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

1 Answer

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.