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Byju's Answer
Standard X
Mathematics
Addition of Rational Expressions
The variance ...
Question
The variance of first n natural numbers is
n
2
−
1
12
.
A
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B
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Solution
The correct option is
A
W
e
h
a
v
e
,
σ
2
=
1
n
∑
n
i
=
1
x
2
i
−
[
1
n
∑
n
i
=
1
x
i
]
2
=
1
n
(
1
2
+
2
2
+
.
.
.
.
.
.
+
n
2
)
−
[
1
n
(
1
+
2
+
.
.
.
.
+
n
)
]
2
=
1
n
n
(
n
+
1
)
(
2
n
+
1
)
6
−
[
n
+
1
2
]
2
=
n
2
−
1
12
Suggest Corrections
20
Similar questions
Q.
Assertion :The variance of first
n
natural numbers is
n
2
−
1
6
. Reason: The sum of the first
n
odd natural numbers is
n
2
and the sum of squares of first
n
odd natural numbers is
n
3
(
4
n
2
−
1
)
.
Q.
Statement-1 : The variance of first n even natural numbers is
n
2
−
1
4
Statement-2 : The sum of first n natural numbers is
n
(
n
+
1
)
2
and The sum of squares first n natural numbers is
n
(
n
+
1
)
(
2
n
+
1
)
6
Q.
Assertion :The variance of first
n
even natural numbers is
n
2
−
1
4
. Reason: The sum of first
n
natural even numbers is
n
(
n
+
1
)
and the sum of squares of first
n
natural numbers is
n
(
n
+
1
)
(
2
n
+
1
)
6
Q.
The variance of first
n
natural numbers is
Q.
State the following statement is True or False
The variance of first
n
even natural numbers is
n
2
−
1
4
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