# What is the variance of {9, 4, -5, 7, 12, -8}?

##### 1 Answer

#### Explanation:

Consider the set

**Step 1:**

#"Mean" = "Sum of X values" /"N (Number of Values)"#

#= ( 9 + 4 + (-5) + 7 + 12 + (-8) ) / 6#

#= 19 / 6#

**Step 2:**

In order to find the variance, subtract the mean from each of the values,

#9 - 19 / 6 = 54/6 - 19/6 = 35/6#

#4 - 19 / 6 = 24/6 - 19/6 = 5/6#

#-5 - 19 / 6 = -30/6 - 19/6 = -49/6#

#7 - 19 / 6 = 42/6 - 19/6 = 23/6#

#12 - 19 / 6 = 72/6 - 19/6 = 53/6#

#-8 - 19 / 6 = -48/6 - 19/6 = -67/6#

**Step 3:**

Now square all of the answers that you had gotten from subtraction.

#(35/6)^2 = 1225/36#

#(5/6)^2 = 25/36#

#(-49/6)^2 = 2401/36#

#(23/6)^2 = 529/36#

#(53/6)^2 = 2809/36#

#(-67/6)^2 = 4489/36#

**Step 4:**

Add all of the squared numbers,

#1225/36 + 25/36 + 2401/36 + 529/36 + 2809/36 + 4489/36 = 1913/6#

**Step 5:**

Divide the sum of squares by

#(1913/6) / (6 - 1) = (1913/6) / 5 = 1913/30 = 63.7(6)#

Therefore

#"sample variance" = 1913/30#