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