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© 2014 Pacific Crest
307
Step
Explanation
60 65.25 70.5 75.75 81 86.25 91.5
3.
Calculate mean
Add the numbers in the data set and divide by the number of elements in
the data set.
68 + 72 + 75 + 78 + 79 + 82 + 85 + 88 + 91 + 92 = 810
mean =
x
= 810/10 = 81
4.
Calculate squared
difference
For each element in the set of data, calculate the deviation from the mean,
x
i
– x
, and the squares of the deviations from the mean, (
x
i
– x
)
2
x
x
i
–
x
(
x
i
–
x
)
2
68
68-81
169
72
72-81
81
75
75-81
36
78
78-81
9
79
79-81
4
82
82-81
1
85
85-81
16
88
88-81
49
91
91-81
100
92
92-81
121
5.
Compute variance
Sum the numbers of the
(x
i
– x )
2
column. The variance,
σ
2
of the sample is
(
)
2
1
1
n
i
i
x x
n
σ
=
−
=
−
∑
Σ
(
x
i
–
x
)
2
= 169 + 81 + 36 + 9 + 4 + 1 + 16 + 49 + 100 + 121 = 586
(
)
2
1
586 586 65.1
1 10 1 9
n
i
i
x x
n
σ
=
−
=
=
= =
−
−
∑
7.2 Variation