find the standerd deviations and the variance of first 23 of natural number
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Answer:
Variance of first n natural numbers is given by
Variance=
n
∑n
2
−(
n
∑n
)
2
=
6n
n(n+1)(2n+1)
−(
2n
n(n+1)
)
2
=(n+1)[
6
2n+1
−
4
(n+1)
]
=
12
(n+1)
[4n+2−3n−3]
=
12
(n+1)
×(n−1).
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