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#
