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Byju's Answer
Standard XII
Mathematics
Standard Deviation about Mean for Continuous Frequency Distributions
The S.D.is no...
Question
The S.D.is not less than the mean deviation. If this is true enter 1, else enter 0.
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Solution
We take
1
N
∑
i
f
i
(
x
i
−
¯
x
)
2
≥
{
1
N
∑
f
i
|
x
i
−
¯
x
|
}
2
Put
|
x
i
−
¯
x
|
=
z
i
∴
1
N
∑
i
f
i
z
2
i
−
¯
z
2
≥
{
1
N
∑
i
f
i
z
i
}
2
to
1
N
∑
f
i
z
2
i
≥
{
1
N
∑
i
z
i
}
2
⇒
σ
2
z
≥
0
which is always true.
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Standard Deviation about Mean for Continuous Frequency Distributions
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