6.2. Variance of a Data Set http://www.ck12.org
x ̄=15 + 65 + 55 + 35 + 45 + 25
6
=
240
6
= 40
s^2 =
∑(x−x ̄)^2
n− 1
s^2 =625 + 625 + 225 + 25 + 25 + 225
5
=
1 , 750
5
= 350
Next, let’s calculate the variance of the data set for Brand B had it been a sample:
x ̄=40 + 50 + 35 + 40 + 45 + 30
6
=
240
6
= 40
s^2 =
∑(x−x ̄)^2
n− 1
s^2 =0 + 100 + 25 + 0 + 25 + 100
5
=
250
5
= 50
Notice that, as in Example A, the variance of the data set for Brand A is much larger than the variance of the data
set for Brand B.
Example C
The following data represents the morning temperatures(◦C)and the monthly rainfall (mm) in July for all the
Canadian cities east of Toronto:
Temperature(◦C)
11 .7 13.7 10. 5 14 .2 13.9 14.2 10.4 16.1 16. 4
4. 8 15 .2 13. 0 14 .4 12.7 8. 6 12 .9 11.5 14. 6
Precipitation (mm)
18 .6 37.1 70. 9 102 59 .9 58.0 73.0 77. 6 89. 1
86 .6 40.3 119.5 36.2 85.5 59.2 97.8 122.2 82. 6
Calculate the variance for each data set. Which data set is more variable? Both are small populations.
TABLE6.4: Temperature
x (x−μ) (x−μ)^2
11.7 − 1 1
13.7 1 1
10.5 − 2. 2 4.84
14.2 1.5 2.25
13.9 1.2 1.44
14.2 1.5 2.25
10.4 − 2. 3 5.29
16.1 3.4 11.56