Basic HTML Version
© 2014 Pacific Crest
311
Step
Model
4.
Calculate squared
difference
x
x
i
– x
(
x
i
– x
)
2
24 -3.304 10.916416
32
4.696 22.052416
32
4.696 22.052416
27 -0.304 0.092416
27 -0.304 0.092416
26 -1.304 1.700416
21 -6.304 39.740416
28
0.696
0.484416
24 -3.304 10.916416
32
4.696 22.052416
31
3.696 13.660416
x
x
i
– x
(
x
i
– x
)
2
25 -2.304 5.308416
19 -8.304 68.956416
29
1.696
2.876416
35
7.696 59.228416
23 -4.304 18.524416
26 -1.304 1.700416
32
4.696 22.052416
34
6.696 44.836416
31
3.696 13.660416
20 -7.304 53.348416
27 -0.304 0.092416
Sum of the third column: 452.870
5.
Compute variance
(
)
2
1
452.870 452.870 20.585
1
23 1
22
n
i
i
x x
n
σ
=
−
=
=
=
=
−
−
∑
6.
Compute standard
deviation
2
20.585 4.537
σ
σ
= =
=
7.
Validate
The mean is 27.3 and the standard deviation is about 4.5. Two standard
deviations would be 9. So, 27.3 – 9 = 18.3 and 27.3 + 9 = 36.3. The youngest
player was 19 and the oldest player was 35 so 100% of the player ages
were within two standard deviations of the mean. This result agrees with
Chebyshev’s Theorem because 100% is more than 75%.
(Use the calculator available on the companion website to validate the
calculations performed here.)
C
ritical Thinking Questions
Developing your understanding
1. In calculating variance, what are two critical transformations used in the calculation that strongly
impact the results?
7.2 Variation