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JEE Main Math Class 12 Statistics Part 1 Questions
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© examsnet.com
Question : 42
Total: 115
Consider the statistics of two sets of observations as follows Size Mean Variance
Size
Mean
Varience
Observation I
10
2
2
Observation II
n
3
1
If the variance of the combined set of these two observations is 17 then the value of nis equal to
17
9
, then the value of
n
is equal to
[2021, 16 March Shift-11]
Your Answer:
Validate
Solution:
Size
Mean
Varience
Observation I
10
2
2
Observation II
n
3
1
Variance of combined set is
17
∕
9
.
Let the observations for group I be set
A
:
{
x
1
,
x
2
,
x
3
,
.
.
.
,
x
10
}
⇒
∑
x
i
10
=
2
⇒
∑
x
i
=
20
and
Σ
(
x
i
2
10
)
−
(
∑
x
i
10
)
2
=
2
⇒
∑
x
i
2
10
−
400
100
=
2
⇒
∑
x
i
2
10
=
6
⇒
∑
x
i
2
=
60
Let the observation for group II be set
B
:
{
y
1
,
y
2
,
y
3
,
.
.
.
,
y
10
}
∑
y
i
n
=
3
⇒
∑
y
i
=
3
n
and
∑
y
i
2
n
−
(
∑
y
i
n
)
2
=
1
∑
y
i
2
n
−
9
=
1
⇒
∑
y
i
2
=
10
n
Combined variance
=
17
∕
9
⇒
σ
2
=
∑
(
x
i
2
+
y
i
2
)
n
+
10
−
[
∑
(
x
i
+
y
i
n
+
10
)
]
2
⇒
17
9
=
60
+
10
n
n
+
10
−
[
20
+
3
n
n
+
10
]
2
⇒
17
9
=
−
(
10
n
+
60
)
(
n
+
10
)
−
(
3
n
+
20
)
2
(
n
+
10
)
2
⇒
17
9
=
n
2
+
40
n
+
200
n
2
+
20
n
+
100
⇒
n
2
+
340
n
+
1700
=
9
n
2
+
360
n
+
1800
⇒
8
n
2
−
20
n
−
100
=
0
⇒
2
n
2
−
5
n
−
25
=
0
⇒
2
n
2
−
10
n
+
5
n
−
25
=
0
⇒
2
n
(
n
−
5
)
+
5
(
n
−
5
)
=
0
⇒
(
2
n
+
5
)
(
n
−
5
)
=
0
∴
n
=
5
© examsnet.com
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