Finding Variance Cara computes the mean and variance for the set 87, 46, 90, 78, and 89. She finds the mean to be 78. Her steps for
finding the variance are shown below.
o?
(87 - 78)2 + (46-78)2 + (90 - 78)2 + (78 - 78)2 + (89-78)
5
(9)2-(32)2 + (12)? + 0 + (11)3
5
o2 = 81-1024 + 144 +0+121
5
-678
= - 135.6
What is the first error Cara made in computing the variance?

Her first step shows subtracting the mean from each data value, then squaring those differences, and finally adding the squares. This first step is correctly done.

The second step however is where an error shows up. The 9^2-32^2 portion should be 9^2+(-32)^2. The negative sign should be inside the parenthesis. When you square -32, you end up with 1024, which is the same result when you square 32. In other words (-32)^2 = 32^2 = 1024. So ultimately the result is positive. When adding a bunch of squares like this, the final result should be positive. This is useful for when you apply the square root to go from the variance to the standard deviation.

Side note: because Cara divided by 5, and there are n = 5 items in the set, this means she is computing the population variance. If you wanted the sample variance, then you'd divide by n-1 = 5-1 = 4

4

step-by-step explanation: