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KEAM 2015 Math Paper
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© examsnet.com
Question : 104
Total: 120
The mean of five observations is 4 and their variance is 5.2 .If three of these observations are 2,4 and 6, then the other two observations are
3 and 5
2 and 6
4 and 4
8 and 10
1 and 7
Validate
Solution:
Let the observations be
2
,
4
,
6
,
x
,
y
Now,
x
=
Σ
x
i
N
⇒
4
=
2
+
4
+
6
+
x
+
y
5
⇒
x
+
y
=
8
.....(i)
Also,
σ
2
=
Σ
x
i
2
N
−
(
x
)
2
⇒
(
5.2
)
2
=
4
+
16
+
36
+
x
2
+
y
2
5
−
(
4
)
2
⇒
x
2
+
y
2
=
50
.....(ii)
From Eqs. (i) and (ii), we get
x
2
+
(
8
−
x
)
2
=
50
⇒
2
x
2
−
16
x
+
64
=
50
⇒
2
x
2
−
16
x
+
14
=
0
⇒
x
2
−
8
x
+
7
=
0
⇒
(
x
−
1
)
(
x
−
7
)
=
0
⇒
x
=
1
,
7
⇒
y
=
7
,
1
Hence, remaining two observations are 1 and 7 .
© examsnet.com
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