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Description of Statistical Computation

Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_smp.wasp
Title produced by softwareStandard Deviation-Mean Plot
Date of computationMon, 13 Dec 2010 13:46:39 +0000
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2010/Dec/13/t1292247884u5cl2no3rdyruqp.htm/, Retrieved Thu, 12 Feb 2026 05:36:19 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=108918, Retrieved Thu, 12 Feb 2026 05:36:19 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsPaper DMA
Estimated Impact384

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Variance Reduction Matrix] [Unemployment] [2010-11-29 09:29:57] [b98453cac15ba1066b407e146608df68]
-   PD  [Variance Reduction Matrix] [VRM WS9] [2010-12-06 11:58:32] [f4dc4aa51d65be851b8508203d9f6001]
- R PD    [Variance Reduction Matrix] [] [2010-12-06 17:10:58] [d39e5c40c631ed6c22677d2e41dbfc7d]
- RMPD        [Standard Deviation-Mean Plot] [Paper DMA SMP2] [2010-12-13 13:46:39] [f92ba2b01007f169e2985fcc57236bd0] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
25,64
27,97
27,62
23,31
29,07
29,58
28,63
29,92
32,68
31,54
32,43
26,54
25,85
27,6
25,71
25,38
28,57
27,64
25,36
25,9
26,29
21,74
19,2
19,32
19,82
20,36
24,31
25,97
25,61
24,67
25,59
26,09
28,37
27,34
24,46
27,46
30,23
32,33
29,87
24,87
25,48
27,28
28,24
29,58
26,95
29,08
28,76
29,59
30,7
30,52
32,67
33,19
37,13
35,54
37,75
41,84
42,94
49,14
44,61
40,22
44,23
45,85
53,38
53,26
51,8
55,3
57,81
63,96
63,77
59,15
56,12
57,42
63,52
61,71
63,01
68,18
72,03
69,75
74,41
74,33
64,24
60,03
59,44
62,5
55,04
58,34
61,92
67,65
67,68
70,3
75,26
71,44
76,36
81,71
92,6
90,6
92,23
94,09
102,79
109,65
124,05
132,69
135,81
116,07
101,42
75,73
55,48
43,8
45,29

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'George Udny Yule' @ 72.249.76.132

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 2 seconds \tabularnewline
R Server & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=108918&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'George Udny Yule' @ 72.249.76.132[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=108918&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=108918&T=0

As an alternative you can also use a QR Code:  
QR Code


The GUIDs for individual cells are displayed in the table below:

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'George Udny Yule' @ 72.249.76.132






Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
128.74416666666672.779481502770339.37
224.883.116034776325959.37
325.00416666666672.61067200799598.55
428.52166666666672.10080864661617.46
538.02083333333335.8738286388681718.62
655.17083333333336.0660837423907219.73
766.09583333333335.4162994047988414.97
872.408333333333311.711969660707537.56
998.650833333333328.752112794567292.01

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 28.7441666666667 & 2.77948150277033 & 9.37 \tabularnewline
2 & 24.88 & 3.11603477632595 & 9.37 \tabularnewline
3 & 25.0041666666667 & 2.6106720079959 & 8.55 \tabularnewline
4 & 28.5216666666667 & 2.1008086466161 & 7.46 \tabularnewline
5 & 38.0208333333333 & 5.87382863886817 & 18.62 \tabularnewline
6 & 55.1708333333333 & 6.06608374239072 & 19.73 \tabularnewline
7 & 66.0958333333333 & 5.41629940479884 & 14.97 \tabularnewline
8 & 72.4083333333333 & 11.7119696607075 & 37.56 \tabularnewline
9 & 98.6508333333333 & 28.7521127945672 & 92.01 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=108918&T=1

[TABLE]
[ROW][C]Standard Deviation-Mean Plot[/C][/ROW]
[ROW][C]Section[/C][C]Mean[/C][C]Standard Deviation[/C][C]Range[/C][/ROW]
[ROW][C]1[/C][C]28.7441666666667[/C][C]2.77948150277033[/C][C]9.37[/C][/ROW]
[ROW][C]2[/C][C]24.88[/C][C]3.11603477632595[/C][C]9.37[/C][/ROW]
[ROW][C]3[/C][C]25.0041666666667[/C][C]2.6106720079959[/C][C]8.55[/C][/ROW]
[ROW][C]4[/C][C]28.5216666666667[/C][C]2.1008086466161[/C][C]7.46[/C][/ROW]
[ROW][C]5[/C][C]38.0208333333333[/C][C]5.87382863886817[/C][C]18.62[/C][/ROW]
[ROW][C]6[/C][C]55.1708333333333[/C][C]6.06608374239072[/C][C]19.73[/C][/ROW]
[ROW][C]7[/C][C]66.0958333333333[/C][C]5.41629940479884[/C][C]14.97[/C][/ROW]
[ROW][C]8[/C][C]72.4083333333333[/C][C]11.7119696607075[/C][C]37.56[/C][/ROW]
[ROW][C]9[/C][C]98.6508333333333[/C][C]28.7521127945672[/C][C]92.01[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=108918&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=108918&T=1

As an alternative you can also use a QR Code:  
QR Code


The GUIDs for individual cells are displayed in the table below:

Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
128.74416666666672.779481502770339.37
224.883.116034776325959.37
325.00416666666672.61067200799598.55
428.52166666666672.10080864661617.46
538.02083333333335.8738286388681718.62
655.17083333333336.0660837423907219.73
766.09583333333335.4162994047988414.97
872.408333333333311.711969660707537.56
998.650833333333328.752112794567292.01






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha-6.28267023528712
beta0.285650915342497
S.D.0.0579707687681435
T-STAT4.92749917609287
p-value0.0016990911240378

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & -6.28267023528712 \tabularnewline
beta & 0.285650915342497 \tabularnewline
S.D. & 0.0579707687681435 \tabularnewline
T-STAT & 4.92749917609287 \tabularnewline
p-value & 0.0016990911240378 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=108918&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-6.28267023528712[/C][/ROW]
[ROW][C]beta[/C][C]0.285650915342497[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0579707687681435[/C][/ROW]
[ROW][C]T-STAT[/C][C]4.92749917609287[/C][/ROW]
[ROW][C]p-value[/C][C]0.0016990911240378[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=108918&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=108918&T=2

As an alternative you can also use a QR Code:  
QR Code


The GUIDs for individual cells are displayed in the table below:

Regression: S.E.(k) = alpha + beta * Mean(k)
alpha-6.28267023528712
beta0.285650915342497
S.D.0.0579707687681435
T-STAT4.92749917609287
p-value0.0016990911240378






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha-3.87943602128262
beta1.47264730779450
S.D.0.246961188936811
T-STAT5.96307182571632
p-value0.000562645270986705
Lambda-0.472647307794503

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -3.87943602128262 \tabularnewline
beta & 1.47264730779450 \tabularnewline
S.D. & 0.246961188936811 \tabularnewline
T-STAT & 5.96307182571632 \tabularnewline
p-value & 0.000562645270986705 \tabularnewline
Lambda & -0.472647307794503 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=108918&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-3.87943602128262[/C][/ROW]
[ROW][C]beta[/C][C]1.47264730779450[/C][/ROW]
[ROW][C]S.D.[/C][C]0.246961188936811[/C][/ROW]
[ROW][C]T-STAT[/C][C]5.96307182571632[/C][/ROW]
[ROW][C]p-value[/C][C]0.000562645270986705[/C][/ROW]
[ROW][C]Lambda[/C][C]-0.472647307794503[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=108918&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=108918&T=3

As an alternative you can also use a QR Code:  
QR Code


The GUIDs for individual cells are displayed in the table below:

Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha-3.87943602128262
beta1.47264730779450
S.D.0.246961188936811
T-STAT5.96307182571632
p-value0.000562645270986705
Lambda-0.472647307794503


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
par1 = 12 ;
Parameters (R input):
par1 = 12 ;
R code (references can be found in the software module):
par1 <- as.numeric(par1)
(n <- length(x))
(np <- floor(n / par1))
arr <- array(NA,dim=c(par1,np))
j <- 0
k <- 1
for (i in 1:(np*par1))
{
j = j + 1
arr[j,k] <- x[i]
if (j == par1) {
j = 0
k=k+1
}
}
arr
arr.mean <- array(NA,dim=np)
arr.sd <- array(NA,dim=np)
arr.range <- array(NA,dim=np)
for (j in 1:np)
{
arr.mean[j] <- mean(arr[,j],na.rm=TRUE)
arr.sd[j] <- sd(arr[,j],na.rm=TRUE)
arr.range[j] <- max(arr[,j],na.rm=TRUE) - min(arr[,j],na.rm=TRUE)
}
arr.mean
arr.sd
arr.range
(lm1 <- lm(arr.sd~arr.mean))
(lnlm1 <- lm(log(arr.sd)~log(arr.mean)))
(lm2 <- lm(arr.range~arr.mean))
bitmap(file='test1.png')
plot(arr.mean,arr.sd,main='Standard Deviation-Mean Plot',xlab='mean',ylab='standard deviation')
dev.off()
bitmap(file='test2.png')
plot(arr.mean,arr.range,main='Range-Mean Plot',xlab='mean',ylab='range')
dev.off()
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Standard Deviation-Mean Plot',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Section',header=TRUE)
a<-table.element(a,'Mean',header=TRUE)
a<-table.element(a,'Standard Deviation',header=TRUE)
a<-table.element(a,'Range',header=TRUE)
a<-table.row.end(a)
for (j in 1:np) {
a<-table.row.start(a)
a<-table.element(a,j,header=TRUE)
a<-table.element(a,arr.mean[j])
a<-table.element(a,arr.sd[j] )
a<-table.element(a,arr.range[j] )
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Regression: S.E.(k) = alpha + beta * Mean(k)',2,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'alpha',header=TRUE)
a<-table.element(a,lm1$coefficients[[1]])
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'beta',header=TRUE)
a<-table.element(a,lm1$coefficients[[2]])
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'S.D.',header=TRUE)
a<-table.element(a,summary(lm1)$coefficients[2,2])
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'T-STAT',header=TRUE)
a<-table.element(a,summary(lm1)$coefficients[2,3])
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'p-value',header=TRUE)
a<-table.element(a,summary(lm1)$coefficients[2,4])
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable1.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Regression: ln S.E.(k) = alpha + beta * ln Mean(k)',2,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'alpha',header=TRUE)
a<-table.element(a,lnlm1$coefficients[[1]])
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'beta',header=TRUE)
a<-table.element(a,lnlm1$coefficients[[2]])
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'S.D.',header=TRUE)
a<-table.element(a,summary(lnlm1)$coefficients[2,2])
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'T-STAT',header=TRUE)
a<-table.element(a,summary(lnlm1)$coefficients[2,3])
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'p-value',header=TRUE)
a<-table.element(a,summary(lnlm1)$coefficients[2,4])
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Lambda',header=TRUE)
a<-table.element(a,1-lnlm1$coefficients[[2]])
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable2.tab')