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

1 Answer
Jun 25, 2016

1913/30

Explanation:

Consider the set "X" of numbers 9, 4, -5, 7, 12, -8

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 (n-1)

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

Therefore

"sample variance" = 1913/30

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