Author: Dr.Y.Funatsu, Professor of Meisei university, Tokyo Email　Contents of forms　Top page


Let x's be random variables
selected from an unknown finite
population of size N with equal
probability without replacement
of sampling units. Statistics
are estimates for the population
characteristics.
For further information, click
[Explanations] below.
..............................

.. ..

Total frequency(F)=
Total of x(weighted)=
Estimates are not shown when N
is smaller than F.
Mean(unbiased)=
Variance(unbiased)=(F>1)
Standard deviation=(F>1)
Coefficient of variation
  =(F>1)
Variance of mean(unbiased)
  =(F>1)
Standard error of mean
  =(F>1)
Variance of variance(unbiased)
  =(F>3)
Standard error of variance
  =(F>3)
Third moment(unbiased)
  =(F>2)
Skewness=(F>2)
Fourth moment(unbiased)
  =(F>3)
Kurtosis(ratio of moments)
  =(F>3)
Kurtosis(minus 3)=(F>3)

Size of population
N=

......Variable.........Frequency
.......x............................f
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......Variable.........Frequency
.......x............................f
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......Variable.........Frequency
.......x............................f
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