http://www.ck12.org Chapter 6. Normal Distribution Curves
TABLE6.2:
x (x−μ) (x−μ)^2
15 − 25 625
65 25 625
55 15 225
35 − 5 25
45 5 25
25 − 15 225μ=15 + 65 + 55 + 35 + 45 + 25
6
=
240
6
= 40
σ^2 =
∑(x−μ)^2
n
σ^2 =625 + 625 + 225 + 25 + 25 + 225
6
=
1 , 750
6
≈ 291. 66
Brand B
TABLE6.3:
x (x−μ) (x−μ)^2
40 0 0
50 10 100
35 − 5 25
40 0 0
45 5 25
30 − 10 100μ=40 + 50 + 35 + 40 + 45 + 30
6
=
240
6
= 40
σ^2 =
∑(x−μ)^2
n
σ^2 =0 + 100 + 25 + 0 + 25 + 100
6
=
250
6
≈ 41. 66
The variance is simply the average of the squares of the distance of each data value from the mean. If these data
values are close to the value of the mean, the variance will be small. This was the case for Brand B. If these data
values are far from the mean, the variance will be large, as was the case for Brand A.
The variance of a data set is always a positive value.
Example B
What would the variances of the 2 data sets in Example A have been had they been samples instead of small
populations?
First, let’s calculate the variance of the data set for Brand A had it been a sample: