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


Let x's be random variables 
selected independently from an 
unknown population with equal
probability. Statistics are 
estimates for the population 
characteristics.
For further information, click
[Explanations] below.
..............................

.. ..


Total frequency(F)=
Total of x(weighted)=
-Estimates by sample-
Mean(unbiased)=
Variance(unbiased)
  =(F>1)
Standard deviation
  =(F>1)
Coefficient of variation
  =(F>1)
Variance of sample mean(unbiased)
  =(F>1)
Standard error of sample mean
  =(F>1)
Variance of variance(unbiased)
  =(F>3)
Standard error of sample 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)
Kurtosis(minus 3, Excel)
  =(F>3)

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