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The coefficients of variations for the two distributions are 60 and 70 and its standard deviations are 21 and 16 respectively. Determine its arithmetic mean.
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The coefficient of variation C.V with standard deviation σ and with arithmetic mean
x
_
is defined as:
C.V=
x
_
σ
×100
Let us find the mean
x
_
of the first distribution with coefficient of variation C.V=60 with standard deviation σ=21:
60=
x
_
21
×100
⇒60
x
_
=2100
⇒
x
_
=
60
2100
=35
Now we find the mean
y
_
of the first distribution with coefficient of variation C.V=70 with standard deviation σ=16:
70=
y
_
16
×100
⇒70
y
_
=1600
⇒
y
_
=
70
1600
=22.85
Hence, the mean of the given distributions is 35 and 22.85.
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