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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 computationFri, 12 Dec 2008 08:57:50 -0700
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2008/Dec/12/t1229097545dyb7thmtiz8hadr.htm/, Retrieved Mon, 10 Nov 2025 00:49:28 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=32853, Retrieved Mon, 10 Nov 2025 00:49:28 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact440

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
F     [Univariate Data Series] [Airline data] [2007-10-18 09:58:47] [42daae401fd3def69a25014f2252b4c2]
F RMPD  [Standard Deviation-Mean Plot] [Q5 Standard DMP] [2008-11-29 16:26:32] [aa5573c1db401b164e448aef050955a1]
-   PD    [Standard Deviation-Mean Plot] [Q8 SDMN bouwprod] [2008-11-30 00:14:02] [aa5573c1db401b164e448aef050955a1]
-           [Standard Deviation-Mean Plot] [Q8 SDMN bouwprod] [2008-11-30 00:31:28] [aa5573c1db401b164e448aef050955a1]
-   P         [Standard Deviation-Mean Plot] [Standard Deviatio...] [2008-12-12 12:06:26] [aa5573c1db401b164e448aef050955a1]
-    D            [Standard Deviation-Mean Plot] [SDMP Totale Produ...] [2008-12-12 15:57:50] [8a1195ff8db4df756ce44b463a631c76] [Current]
- RM                [Variance Reduction Matrix] [VRM Totale Productie] [2008-12-12 16:00:44] [aa5573c1db401b164e448aef050955a1]
- RMPD              [Cross Correlation Function] [CCF Bouwproductie...] [2008-12-12 16:06:05] [aa5573c1db401b164e448aef050955a1]
-   P                 [Cross Correlation Function] [CCF Bouwproductie...] [2008-12-12 16:12:34] [aa5573c1db401b164e448aef050955a1]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
97.4
97
105.4
102.7
98.1
104.5
87.4
89.9
109.8
111.7
98.6
96.9
95.1
97
112.7
102.9
97.4
111.4
87.4
96.8
114.1
110.3
103.9
101.6
94.6
95.9
104.7
102.8
98.1
113.9
80.9
95.7
113.2
105.9
108.8
102.3
99
100.7
115.5
100.7
109.9
114.6
85.4
100.5
114.8
116.5
112.9
102
106
105.3
118.8
106.1
109.3
117.2
92.5
104.2
112.5
122.4
113.3
100
110.7
112.8
109.8
117.3
109.1

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 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 & 1 seconds \tabularnewline
R Server & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=32853&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]1 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=32853&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=32853&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 time1 seconds
R Server'George Udny Yule' @ 72.249.76.132






Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
199.957.2695504425214424.3
2102.558.2741107734250926.7
3101.49.1665399440276633
4106.0416666666679.4891764498806631.1
5108.9666666666678.4264015109797929.9

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 99.95 & 7.26955044252144 & 24.3 \tabularnewline
2 & 102.55 & 8.27411077342509 & 26.7 \tabularnewline
3 & 101.4 & 9.16653994402766 & 33 \tabularnewline
4 & 106.041666666667 & 9.48917644988066 & 31.1 \tabularnewline
5 & 108.966666666667 & 8.42640151097979 & 29.9 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=32853&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]99.95[/C][C]7.26955044252144[/C][C]24.3[/C][/ROW]
[ROW][C]2[/C][C]102.55[/C][C]8.27411077342509[/C][C]26.7[/C][/ROW]
[ROW][C]3[/C][C]101.4[/C][C]9.16653994402766[/C][C]33[/C][/ROW]
[ROW][C]4[/C][C]106.041666666667[/C][C]9.48917644988066[/C][C]31.1[/C][/ROW]
[ROW][C]5[/C][C]108.966666666667[/C][C]8.42640151097979[/C][C]29.9[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=32853&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=32853&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
199.957.2695504425214424.3
2102.558.2741107734250926.7
3101.49.1665399440276633
4106.0416666666679.4891764498806631.1
5108.9666666666678.4264015109797929.9






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha-1.60843366685685
beta0.097643348931479
S.D.0.123797838387940
T-STAT0.788732260619112
p-value0.487853165292207

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & -1.60843366685685 \tabularnewline
beta & 0.097643348931479 \tabularnewline
S.D. & 0.123797838387940 \tabularnewline
T-STAT & 0.788732260619112 \tabularnewline
p-value & 0.487853165292207 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=32853&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-1.60843366685685[/C][/ROW]
[ROW][C]beta[/C][C]0.097643348931479[/C][/ROW]
[ROW][C]S.D.[/C][C]0.123797838387940[/C][/ROW]
[ROW][C]T-STAT[/C][C]0.788732260619112[/C][/ROW]
[ROW][C]p-value[/C][C]0.487853165292207[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=32853&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=32853&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-1.60843366685685
beta0.097643348931479
S.D.0.123797838387940
T-STAT0.788732260619112
p-value0.487853165292207






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha-3.87535127649888
beta1.29564848100560
S.D.1.53240951828272
T-STAT0.845497541973999
p-value0.459934249914382
Lambda-0.295648481005603

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -3.87535127649888 \tabularnewline
beta & 1.29564848100560 \tabularnewline
S.D. & 1.53240951828272 \tabularnewline
T-STAT & 0.845497541973999 \tabularnewline
p-value & 0.459934249914382 \tabularnewline
Lambda & -0.295648481005603 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=32853&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-3.87535127649888[/C][/ROW]
[ROW][C]beta[/C][C]1.29564848100560[/C][/ROW]
[ROW][C]S.D.[/C][C]1.53240951828272[/C][/ROW]
[ROW][C]T-STAT[/C][C]0.845497541973999[/C][/ROW]
[ROW][C]p-value[/C][C]0.459934249914382[/C][/ROW]
[ROW][C]Lambda[/C][C]-0.295648481005603[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=32853&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=32853&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-3.87535127649888
beta1.29564848100560
S.D.1.53240951828272
T-STAT0.845497541973999
p-value0.459934249914382
Lambda-0.295648481005603


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')