http://www.ck12.org Chapter 6. Normal Distribution Curves
x ̄=760 + 790 + 800 + 780 + 850 + 790 + 750 + 820 + 810 + 800
10
=
7 , 950
10
= 795
s^2 =
∑(x−x ̄)^2
n− 1
s^2 =1 , 225 + 25 + 25 + 225 + 3 , 025 + 25 + 2 , 025 + 625 + 225 + 25
9
=
7 , 450
9
≈ 827. 77
The variance of the burning times for Brand A is approximately 827.78 hours.
Brand B
TABLE6.8:
x (x−x ̄) (x−x ̄)^2
820 − 21 441
900 59 3,481
810 − 31 961
790 − 51 2,601
810 − 31 961
800 − 41 1,681
850 9 81
820 − 21 441
920 79 6,241
890 49 2,401x ̄=820 + 900 + 810 + 790 + 810 + 800 + 850 + 820 + 920 + 890
10
=
8 , 410
10
= 841
s^2 =
∑(x−x ̄)^2
n− 1
s^2 =441 + 3 , 481 + 961 + 2 , 601 + 961 + 1 , 681 + 81 + 441 + 6 , 241 + 2 , 401
9
=
19 , 290
9
≈ 2 , 143. 33
The variance of the burning times for Brand B is approximately 2,143.33 hours. Therefore, Brand B has the more
variable burning times.
Practice
- The following data was collected: 5 8 9 10 4 3 7 5 Fill in the chart below and
calculate the variance. The data represents a small population.
TABLE6.9:
Data(x) Mean(μ) Data−Mean(x−
μ)Square of Data −
Mean(x−μ)^2