Question

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

Answer 1

`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`

http://goodcalculators.com/standard-deviation-calculator/