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Description of Statistical Computation

Author's title

Author*Unverified author*
R Software Modulerwasp_smp.wasp
Title produced by softwareStandard Deviation-Mean Plot
Date of computationSat, 04 Dec 2010 12:31:35 +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/04/t12914658099o46eey5zh5o4x0.htm/, Retrieved Wed, 11 Feb 2026 00:46:59 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=105121, Retrieved Wed, 11 Feb 2026 00:46:59 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsKDGP2W83
Estimated Impact466

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Standard Deviation-Mean Plot] [Retail sale of wi...] [2010-12-04 12:31:35] [69fd4ebd73ea03d240a8ad2b0e9f45ec] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
57,7
63,6
78
77,4
74,1
85,9
82
78,4
68,1
70,9
85,2
149,6
57,9
63,7
85
66,1
80,2
83,4
85,7
81,8
69,4
76,4
90,3
157,3
65,3
68,4
72,7
86,6
82,6
84,8
93,4
82,2
75,2
83,9
85,4
166,3
70,4
73,9
82,4
92,3
82,7
95,8
105,8
84,2
82,7
88,4
90,2
176,6
69,5
77,3
98,6
86,4
90,8
101,5
112,2
93,6
93,8
90,8
98,1
187,6
75
83,7
99,7
104,9
98,9
117,3
115,7
102,2
101,9
96,6
110
203,7
82,3
93,3
121,9
100,9
107,7
130
123,2
116,1
105,3
107,7
123,9
205,2
90,3
106,9
122,4
111,3
122,6
124,8
139,5
118,8
111
121,2
120,6
219,1
101,3
105
113,4
133,6
123,9
136,2
151,7
121,9
120,2
132,2
125,2
233,8

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'Gwilym Jenkins' @ 72.249.127.135

\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 & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=105121&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]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=105121&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=105121&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'Gwilym Jenkins' @ 72.249.127.135






Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
169.17510.137184027135020.3
280.15.03785668712411.8
393.4538.175079131112081.5
468.17511.732966376837527.1
582.7752.347161406181235.5
698.3540.248436822647787.9
773.259.4030137012910221.3
885.755.2265348622836811.2
9102.742.637776677495791.1
1079.759.7667804316468621.9
1192.12510.834320467846623.1
12109.47544.864044623729693.9
1382.9512.511994245523029.1
1499.5259.5879698928744421.4
15117.57546.779366890400296.8
1690.82513.881252345039629.9
17108.5259.3296570140600518.4
18128.0550.7334537887313107.1
1999.616.712869292853339.6
20119.259.5653889971431222.3
21135.52547.178835297196599.9
22107.72513.322255814988732.1
23126.4259.0621465448314220.7
24142.97550.9647181881741108.1
25113.32514.433612391451632.3
26133.42513.726221864251929.8
27152.8554.190620344607113.6

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 69.175 & 10.1371840271350 & 20.3 \tabularnewline
2 & 80.1 & 5.037856687124 & 11.8 \tabularnewline
3 & 93.45 & 38.1750791311120 & 81.5 \tabularnewline
4 & 68.175 & 11.7329663768375 & 27.1 \tabularnewline
5 & 82.775 & 2.34716140618123 & 5.5 \tabularnewline
6 & 98.35 & 40.2484368226477 & 87.9 \tabularnewline
7 & 73.25 & 9.40301370129102 & 21.3 \tabularnewline
8 & 85.75 & 5.22653486228368 & 11.2 \tabularnewline
9 & 102.7 & 42.6377766774957 & 91.1 \tabularnewline
10 & 79.75 & 9.76678043164686 & 21.9 \tabularnewline
11 & 92.125 & 10.8343204678466 & 23.1 \tabularnewline
12 & 109.475 & 44.8640446237296 & 93.9 \tabularnewline
13 & 82.95 & 12.5119942455230 & 29.1 \tabularnewline
14 & 99.525 & 9.58796989287444 & 21.4 \tabularnewline
15 & 117.575 & 46.7793668904002 & 96.8 \tabularnewline
16 & 90.825 & 13.8812523450396 & 29.9 \tabularnewline
17 & 108.525 & 9.32965701406005 & 18.4 \tabularnewline
18 & 128.05 & 50.7334537887313 & 107.1 \tabularnewline
19 & 99.6 & 16.7128692928533 & 39.6 \tabularnewline
20 & 119.25 & 9.56538899714312 & 22.3 \tabularnewline
21 & 135.525 & 47.1788352971965 & 99.9 \tabularnewline
22 & 107.725 & 13.3222558149887 & 32.1 \tabularnewline
23 & 126.425 & 9.06214654483142 & 20.7 \tabularnewline
24 & 142.975 & 50.9647181881741 & 108.1 \tabularnewline
25 & 113.325 & 14.4336123914516 & 32.3 \tabularnewline
26 & 133.425 & 13.7262218642519 & 29.8 \tabularnewline
27 & 152.85 & 54.190620344607 & 113.6 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=105121&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]69.175[/C][C]10.1371840271350[/C][C]20.3[/C][/ROW]
[ROW][C]2[/C][C]80.1[/C][C]5.037856687124[/C][C]11.8[/C][/ROW]
[ROW][C]3[/C][C]93.45[/C][C]38.1750791311120[/C][C]81.5[/C][/ROW]
[ROW][C]4[/C][C]68.175[/C][C]11.7329663768375[/C][C]27.1[/C][/ROW]
[ROW][C]5[/C][C]82.775[/C][C]2.34716140618123[/C][C]5.5[/C][/ROW]
[ROW][C]6[/C][C]98.35[/C][C]40.2484368226477[/C][C]87.9[/C][/ROW]
[ROW][C]7[/C][C]73.25[/C][C]9.40301370129102[/C][C]21.3[/C][/ROW]
[ROW][C]8[/C][C]85.75[/C][C]5.22653486228368[/C][C]11.2[/C][/ROW]
[ROW][C]9[/C][C]102.7[/C][C]42.6377766774957[/C][C]91.1[/C][/ROW]
[ROW][C]10[/C][C]79.75[/C][C]9.76678043164686[/C][C]21.9[/C][/ROW]
[ROW][C]11[/C][C]92.125[/C][C]10.8343204678466[/C][C]23.1[/C][/ROW]
[ROW][C]12[/C][C]109.475[/C][C]44.8640446237296[/C][C]93.9[/C][/ROW]
[ROW][C]13[/C][C]82.95[/C][C]12.5119942455230[/C][C]29.1[/C][/ROW]
[ROW][C]14[/C][C]99.525[/C][C]9.58796989287444[/C][C]21.4[/C][/ROW]
[ROW][C]15[/C][C]117.575[/C][C]46.7793668904002[/C][C]96.8[/C][/ROW]
[ROW][C]16[/C][C]90.825[/C][C]13.8812523450396[/C][C]29.9[/C][/ROW]
[ROW][C]17[/C][C]108.525[/C][C]9.32965701406005[/C][C]18.4[/C][/ROW]
[ROW][C]18[/C][C]128.05[/C][C]50.7334537887313[/C][C]107.1[/C][/ROW]
[ROW][C]19[/C][C]99.6[/C][C]16.7128692928533[/C][C]39.6[/C][/ROW]
[ROW][C]20[/C][C]119.25[/C][C]9.56538899714312[/C][C]22.3[/C][/ROW]
[ROW][C]21[/C][C]135.525[/C][C]47.1788352971965[/C][C]99.9[/C][/ROW]
[ROW][C]22[/C][C]107.725[/C][C]13.3222558149887[/C][C]32.1[/C][/ROW]
[ROW][C]23[/C][C]126.425[/C][C]9.06214654483142[/C][C]20.7[/C][/ROW]
[ROW][C]24[/C][C]142.975[/C][C]50.9647181881741[/C][C]108.1[/C][/ROW]
[ROW][C]25[/C][C]113.325[/C][C]14.4336123914516[/C][C]32.3[/C][/ROW]
[ROW][C]26[/C][C]133.425[/C][C]13.7262218642519[/C][C]29.8[/C][/ROW]
[ROW][C]27[/C][C]152.85[/C][C]54.190620344607[/C][C]113.6[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=105121&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=105121&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
169.17510.137184027135020.3
280.15.03785668712411.8
393.4538.175079131112081.5
468.17511.732966376837527.1
582.7752.347161406181235.5
698.3540.248436822647787.9
773.259.4030137012910221.3
885.755.2265348622836811.2
9102.742.637776677495791.1
1079.759.7667804316468621.9
1192.12510.834320467846623.1
12109.47544.864044623729693.9
1382.9512.511994245523029.1
1499.5259.5879698928744421.4
15117.57546.779366890400296.8
1690.82513.881252345039629.9
17108.5259.3296570140600518.4
18128.0550.7334537887313107.1
1999.616.712869292853339.6
20119.259.5653889971431222.3
21135.52547.178835297196599.9
22107.72513.322255814988732.1
23126.4259.0621465448314220.7
24142.97550.9647181881741108.1
25113.32514.433612391451632.3
26133.42513.726221864251929.8
27152.8554.190620344607113.6






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha-27.2623733941985
beta0.479117848591281
S.D.0.120591703144172
T-STAT3.97305814661625
p-value0.000530922773705959

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & -27.2623733941985 \tabularnewline
beta & 0.479117848591281 \tabularnewline
S.D. & 0.120591703144172 \tabularnewline
T-STAT & 3.97305814661625 \tabularnewline
p-value & 0.000530922773705959 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=105121&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-27.2623733941985[/C][/ROW]
[ROW][C]beta[/C][C]0.479117848591281[/C][/ROW]
[ROW][C]S.D.[/C][C]0.120591703144172[/C][/ROW]
[ROW][C]T-STAT[/C][C]3.97305814661625[/C][/ROW]
[ROW][C]p-value[/C][C]0.000530922773705959[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=105121&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=105121&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-27.2623733941985
beta0.479117848591281
S.D.0.120591703144172
T-STAT3.97305814661625
p-value0.000530922773705959






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha-7.53492891368666
beta2.23479340352976
S.D.0.616987389923919
T-STAT3.62210547577859
p-value0.00129828314892909
Lambda-1.23479340352976

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -7.53492891368666 \tabularnewline
beta & 2.23479340352976 \tabularnewline
S.D. & 0.616987389923919 \tabularnewline
T-STAT & 3.62210547577859 \tabularnewline
p-value & 0.00129828314892909 \tabularnewline
Lambda & -1.23479340352976 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=105121&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-7.53492891368666[/C][/ROW]
[ROW][C]beta[/C][C]2.23479340352976[/C][/ROW]
[ROW][C]S.D.[/C][C]0.616987389923919[/C][/ROW]
[ROW][C]T-STAT[/C][C]3.62210547577859[/C][/ROW]
[ROW][C]p-value[/C][C]0.00129828314892909[/C][/ROW]
[ROW][C]Lambda[/C][C]-1.23479340352976[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=105121&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=105121&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-7.53492891368666
beta2.23479340352976
S.D.0.616987389923919
T-STAT3.62210547577859
p-value0.00129828314892909
Lambda-1.23479340352976


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
par1 = 4 ;
Parameters (R input):
par1 = 4 ;
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')