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

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.