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Mathematics
A data consists of n observations: x1 , x2, ......., xn. If displaystyle∑ni=1 (xi +1)2 =9n and displaystyle∑ni=1 (xi - 1)2 =5n , then the standard deviation of this data is :
Q. A data consists of n observations:
x
1
,
x
2
,
.......
,
x
n
.
If
i
=
1
∑
n
(
x
i
+
1
)
2
=
9
n
and
i
=
1
∑
n
(
x
i
−
1
)
2
=
5
n
, then the standard deviation of this data is :
5292
206
JEE Main
JEE Main 2019
Statistics
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A
5
8%
B
5
63%
C
7
14%
D
2
15%
Solution:
∑
(
x
i
+
1
)
2
=
9
n
.....(1)
∑
(
x
i
−
1
)
2
=
5
n
......(2)
(
1
)
+
(
2
)
⇒
∑
(
x
1
2
+
1
)
=
7
n
⇒
n
∑
x
i
2
=
6
(
1
)
−
(
2
)
⇒
4
∑
x
i
=
4
n
⇒
∑
x
i
=
n
⇒
n
∑
x
i
=
1
⇒
variance
=
6
−
1
=
5
⇒
Standard diviation
=
5