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JEE Main Math Class 12 Statistics Part 2 Questions
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© examsnet.com
Question : 23
Total: 28
Let sets
A
and
B
have 5 elements each. Let mean of the elements in sets
A
and
B
be 5 and 8 respectively and the variance of the elements in sets
A
and
B
be 12 and 20 respectively. A new set
C
of 10 elements is formed by subtracting 3 from each element of A and adding 2 to each element of B. Then the sum of the mean and variance of the elements of
C
is _______.
[11-Apr-2023 shift 1]
36
40
32
38
Validate
Solution:
ω
A
=
{
a
1
,
a
2
,
a
3
,
a
4
,
a
5
}
B
=
{
b
1
,
b
2
,
b
3
,
b
4
,
b
5
}
5
Σ
i
=
1
a
i
2
5
−
(
5
Σ
i
=
1
a
i
5
)
2
=
12
,
5
Σ
i
=
1
b
i
2
5
−
(
5
Σ
i
=
1
b
i
5
)
2
=
20
⇒
5
∑
i
=
1
a
i
2
=
185
,
5
∑
i
=
1
b
i
2
=
420
Now,
C
=
{
C
1
,
C
2
,
.
.
.
C
10
}
∴
Mean of
C
,
C
=
(
Σ
a
i
−
15
)
+
(
Σ
b
i
−
10
)
10
C
=
10
+
50
10
=
6
∴
σ
2
=
10
Σ
i
=
1
C
i
2
10
=
(
C
)
2
=
Σ
(
a
i
−
3
)
2
+
Σ
(
b
i
−
2
)
2
+
10
−
(
6
)
2
=
Σ
a
i
2
+
Σ
b
i
2
−
6
Σ
a
i
+
4
Σ
b
i
+
65
10
−
36
=
185
+
420
−
150
+
160
+
65
10
−
36
=
32
∴
Mean
+
Variance
=
C
+
σ
2
=
6
+
32
=
38
© examsnet.com
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