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
. 1
. 2
. 3
. 4
. 5
. 6
. 7
. 8
. 9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
......Variable.........Frequency
.......x............................f
25 26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
......Variable.........Frequency
.......x............................f
50 51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74