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)"Mean=Sum of X valuesN (Number of Values)
= ( 9 + 4 + (-5) + 7 + 12 + (-8) ) / 6=9+4+(−5)+7+12+(−8)6
= 19 / 6=196
Step 2:
In order to find the variance, subtract the mean from each of the values,
9 - 19 / 6 = 54/6 - 19/6 = 35/69−196=546−196=356
4 - 19 / 6 = 24/6 - 19/6 = 5/64−196=246−196=56
-5 - 19 / 6 = -30/6 - 19/6 = -49/6−5−196=−306−196=−496
7 - 19 / 6 = 42/6 - 19/6 = 23/67−196=426−196=236
12 - 19 / 6 = 72/6 - 19/6 = 53/612−196=726−196=536
-8 - 19 / 6 = -48/6 - 19/6 = -67/6−8−196=−486−196=−676
Step 3:
Now square all of the answers that you had gotten from subtraction.
(35/6)^2 = 1225/36(356)2=122536
(5/6)^2 = 25/36(56)2=2536
(-49/6)^2 = 2401/36(−496)2=240136
(23/6)^2 = 529/36(236)2=52936
(53/6)^2 = 2809/36(536)2=280936
(-67/6)^2 = 4489/36(−676)2=448936
Step 4:
Add all of the squared numbers,
1225/36 + 25/36 + 2401/36 + 529/36 + 2809/36 + 4489/36 = 1913/6122536+2536+240136+52936+280936+448936=19136
Step 5:
Divide the sum of squares by
(1913/6) / (6 - 1) = (1913/6) / 5 = 1913/30 = 63.7(6)191366−1=191365=191330=63.7(6)
Therefore
"sample variance" = 1913/30sample variance=191330
