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Mathematics
Mathematics
Problem
Which of the following expressions represents the population variance
σ
2
\sigma^{2}
σ
2
for an ungrouped data set
x
1
,
x
2
,
…
,
x
n
x_{1},x_{2},\ldots ,x_{n}
x
1
,
x
2
,
…
,
x
n
having mean
x
ˉ
\bar{x}
x
ˉ
? a)
1
n
−
1
∑
i
=
1
n
(
x
i
−
x
ˉ
)
2
\displaystyle \frac{1}{n-1}\sum_{i=1}^{n}(x_{i}-\bar{x})^{2}
n
−
1
1
i
=
1
∑
n
(
x
i
−
x
ˉ
)
2
b)
1
n
∑
i
=
1
n
x
i
2
\displaystyle \frac{1}{n}\sum_{i=1}^{n}x_{i}^{2}
n
1
i
=
1
∑
n
x
i
2
c)
1
n
∑
i
=
1
n
(
x
i
−
x
ˉ
)
2
\displaystyle \frac{1}{n}\sum_{i=1}^{n}(x_{i}-\bar{x})^{2}
n
1
i
=
1
∑
n
(
x
i
−
x
ˉ
)
2
d)
1
n
∑
i
=
1
n
∣
x
i
−
x
ˉ
∣
\displaystyle \frac{1}{n}\sum_{i=1}^{n}|x_{i}-\bar{x}|
n
1
i
=
1
∑
n
∣
x
i
−
x
ˉ
∣
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