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JEE Main Math Class 12 Statistics Part 2 Questions
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© examsnet.com
Question : 11
Total: 28
If the mean and variance of five observations are
24
5
and
194
25
respectively and the mean of first four observations is
7
2
, then the variance of the first four observations in equal to
[29-Jan-2024 Shift 2]
4
5
77
12
5
4
105
4
Validate
Solution:
👈: Video Solution
X
=
24
5
;
σ
2
=
194
25
Let first four observation be
x
1
,
x
2
,
x
3
,
x
4
Here,
x
1
+
x
2
+
x
3
+
x
4
+
x
5
5
=
24
5
.
.
.
.
(1)
Also,
x
1
+
x
2
+
x
3
+
x
4
4
=
7
2
⇒
x
1
+
x
2
+
x
3
+
x
4
=
14
Now from eqn -1
x
5
=
10
Now,
σ
2
=
194
25
x
1
2
+
x
2
2
+
x
3
2
+
x
4
2
+
x
5
2
5
−
576
25
=
194
25
⇒
x
1
2
+
x
2
2
+
x
3
2
+
x
4
2
=
54
Now, variance of first 4 observations
Var
=
4
Σ
i
=
1
x
i
2
4
−
(
4
Σ
i
=
1
x
i
4
)
2
=
54
4
−
49
4
=
5
4
© examsnet.com
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