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AP EAMCET Engineering 21 Apr 2019 Shift 2 Paper
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© examsnet.com
Question : 35
Total: 160
The standard deviations of
x
i
(i = 1 , 2 , ... , 10) and
y
i
(i = 1 , ... , 10) are respectively 'a' and 'b'
→
x
,
→
y
are the means of these two sets of observations respectively. If
z
i
=
(
x
i
−
−
x
)
(
y
i
−
−
y
)
and
10
Σ
i
=
1
z
i
= c , then the standard deviation of the observations
(
x
i
−
y
i
)
, (i = 1 , 2 , .. , 10) is
√
a
2
+
b
2
+
c
5
√
a
2
+
b
2
−
c
5
√
a
2
+
b
2
−
c
2
5
√
a
2
+
b
2
+
c
2
5
Validate
Solution:
It is given that,
z
i
=
(
x
i
−
x
)
(
y
i
−
y
)
And
10
∑
i
=
1
z
i
=
c
Rewrite the above equation.
10
∑
i
=
1
{
(
x
i
−
x
)
(
y
i
−
y
)
}
=
c
10
∑
i
=
1
{
x
i
y
i
−
x
i
y
−
x
y
i
+
x
⋅
y
}
=
c
10
∑
i
=
1
x
i
y
i
−
10
∑
i
=
1
x
i
y
−
10
∑
i
=
1
x
y
i
+
10
∑
i
=
1
x
⋅
y
=
c
10
∑
i
=
1
x
i
y
i
−
10
x
⋅
y
−
10
x
⋅
y
+
10
x
⋅
y
=
c
10
∑
i
=
1
x
i
y
i
−
10
x
⋅
y
=
c
Now,
σ
(
x
i
−
y
i
)
=
√
1
10
∑
(
x
i
−
y
i
)
2
−
(
x
−
y
)
2
=
√
(
1
10
∑
x
i
2
+
1
10
∑
y
i
2
−
1
5
∑
x
i
y
i
−
x
2
−
y
2
+
2
x
y
)
=
√
(
1
10
∑
x
i
2
−
x
2
)
+
(
1
10
∑
y
i
2
−
y
2
)
−
1
5
(
∑
x
i
y
i
−
10
x
y
)
=
√
a
2
+
b
2
−
c
5
© examsnet.com
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