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L8 · Statistics & estimation
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Why Divide by n − 1?
Why Divide by n − 1?
Level 8
●●●○○
Medium
~6 min
Problem
The sample variance is usually defined as
s
2
=
1
n
−
1
∑
i
(
X
i
−
X
ˉ
)
2
s^2=\frac{1}{n-1}\sum_i (X_i-\bar X)^2
s
2
=
n
−
1
1
∑
i
(
X
i
−
X
ˉ
)
2
. Why
n
−
1
n-1
n
−
1
rather than
n
n
n
? Show that dividing by
n
n
n
underestimates the true variance.
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