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AP EAMCET Engineering 22 Sep 2020 Shift 1 Paper
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© examsnet.com
Question : 13
Total: 160
The standard deviation and mean of five observations are
0
and
9
respectively. If one of the observations is changed such that the mean of the new set of five observations becomes
10
, then their standard deviation is __________
1
2
3
0
Validate
Solution:
Let the five observations are
x
1
,
x
2
,
x
3
,
x
4
,
x
5
.
s
o
, mean
=
x
1
+
x
2
+
x
3
+
x
3
+
x
2
5
=
9
(given)
⇒
x
1
+
x
2
+
x
3
+
x
4
+
x
5
=
45
.....(i)
and standard deviation
=
5
∑
i
=
1
√
(
9
−
x
i
)
2
5
=
0
(
given
)
⇒
3
∑
i
=
1
(
9
−
x
i
)
2
=
0
⇒
x
i
=
9
∀
i
Now, let observation
x
5
is changed with
y
, so
mean
=
x
1
+
x
2
+
x
3
+
x
4
+
y
5
=
10
\;emsp;(given)
⇒
x
1
+
x
2
+
x
3
+
x
4
+
y
=
50
⇒
45
−
x
5
+
y
=
50
(from Eq. (i))
⇒
x
5
+
5
=
y
⇒
y
=
14
{
∵
x
5
=
9
}
Now, the changed standard deviation is
√
(
10
−
x
1
)
2
+
(
10
−
x
2
)
2
+
(
10
−
x
3
)
2
(
10
−
x
1
)
2
+
(
10
−
x
2
)
2
+
(
10
−
x
3
)
2
+
(
10
−
x
4
)
2
+
(
10
−
y
)
2
5
{
∵
x
1
=
x
2
=
x
3
=
x
4
=
9
}
=
√
1
+
1
+
1
+
1
+
16
5
=
√
20
5
=
√
4
=
2
© examsnet.com
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