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Author's title

Author

*The author of this computation has been verified*

R Software Module

rwasp_smp.wasp

Title produced by software

Standard Deviation-Mean Plot

Date of computation

Mon, 19 Dec 2016 13:15:19 +0100

Cite this page as follows

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2016/Dec/19/t14821497554n5g74e9zz2yugx.htm/, Retrieved Sat, 26 Apr 2025 04:19:01 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=301321, Retrieved Sat, 26 Apr 2025 04:19:01 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

134

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)

-       [Standard Deviation-Mean Plot] [standard deviatio...] [2016-12-19 12:15:19] [1e2c9196efc58119c3757b6c78ac7c5f] [Current]

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Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	1 seconds
R Server	Big Analytics Cloud Computing Center

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input view raw input (R code)  \tabularnewline
Raw Outputview raw output of R engine  \tabularnewline
Computing time1 seconds \tabularnewline
R ServerBig Analytics Cloud Computing Center \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=301321&T=0

[TABLE]
[ROW]

Summary of computational transaction[/C][/ROW] [ROW]

Raw Input[/C]

view raw input (R code) [/C][/ROW] [ROW]

Raw Output[/C]

view raw output of R engine [/C][/ROW] [ROW]

Computing time[/C]

1 seconds[/C][/ROW] [ROW]

R Server[/C]

Big Analytics Cloud Computing Center[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=301321&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=301321&T=0

As an alternative you can also use a QR Code:

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

Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	1 seconds
R Server	Big Analytics Cloud Computing Center

Standard Deviation-Mean Plot
Section	Mean	Standard Deviation	Range
1	3375.25	1202.49029795116	2906
2	3362.25	911.076789665211	1917
3	3829	1277.51320932505	2946
4	2984.25	921.741964977184	2244
5	3421.75	685.060277153283	1648
6	2954.75	418.280906409397	848
7	3446.25	991.931911305744	2140
8	3764.5	948.740393012405	2039
9	3001.75	663.252277292233	1561
10	4090.75	1144.24600356159	2372
11	6789	1954.01484129471	4740
12	3186.5	788.741402488801	1924
13	2991	760.137268305315	1613
14	2357.75	1556.70386286752	3632
15	3974.5	2113.29923736954	5035
16	2531.5	1201.06078114307	2613
17	3256.5	1087.72928617372	2532
18	5391.75	1767.69650015682	4155
19	5134.75	1764.55705017813	4124
20	4052.25	2728.67151742382	5791
21	3184.25	790.040241591106	1841
22	5305.5	1742.11413709512	4026
23	4385.5	1964.70362480791	4442
24	5179.75	1483.26899673211	3185
25	4679	1234.40782023878	2730
26	7332.25	1163.89672365435	2790
27	9762.5	4346.95008022867	9673
28	14340.5	4646.91385043163	10689
29	13041.5	5600.56726293566	12478
30	12919	4913.45696361872	11633
31	17771	2673.18199904159	5949

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 3375.25 & 1202.49029795116 & 2906 \tabularnewline
2 & 3362.25 & 911.076789665211 & 1917 \tabularnewline
3 & 3829 & 1277.51320932505 & 2946 \tabularnewline
4 & 2984.25 & 921.741964977184 & 2244 \tabularnewline
5 & 3421.75 & 685.060277153283 & 1648 \tabularnewline
6 & 2954.75 & 418.280906409397 & 848 \tabularnewline
7 & 3446.25 & 991.931911305744 & 2140 \tabularnewline
8 & 3764.5 & 948.740393012405 & 2039 \tabularnewline
9 & 3001.75 & 663.252277292233 & 1561 \tabularnewline
10 & 4090.75 & 1144.24600356159 & 2372 \tabularnewline
11 & 6789 & 1954.01484129471 & 4740 \tabularnewline
12 & 3186.5 & 788.741402488801 & 1924 \tabularnewline
13 & 2991 & 760.137268305315 & 1613 \tabularnewline
14 & 2357.75 & 1556.70386286752 & 3632 \tabularnewline
15 & 3974.5 & 2113.29923736954 & 5035 \tabularnewline
16 & 2531.5 & 1201.06078114307 & 2613 \tabularnewline
17 & 3256.5 & 1087.72928617372 & 2532 \tabularnewline
18 & 5391.75 & 1767.69650015682 & 4155 \tabularnewline
19 & 5134.75 & 1764.55705017813 & 4124 \tabularnewline
20 & 4052.25 & 2728.67151742382 & 5791 \tabularnewline
21 & 3184.25 & 790.040241591106 & 1841 \tabularnewline
22 & 5305.5 & 1742.11413709512 & 4026 \tabularnewline
23 & 4385.5 & 1964.70362480791 & 4442 \tabularnewline
24 & 5179.75 & 1483.26899673211 & 3185 \tabularnewline
25 & 4679 & 1234.40782023878 & 2730 \tabularnewline
26 & 7332.25 & 1163.89672365435 & 2790 \tabularnewline
27 & 9762.5 & 4346.95008022867 & 9673 \tabularnewline
28 & 14340.5 & 4646.91385043163 & 10689 \tabularnewline
29 & 13041.5 & 5600.56726293566 & 12478 \tabularnewline
30 & 12919 & 4913.45696361872 & 11633 \tabularnewline
31 & 17771 & 2673.18199904159 & 5949 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=301321&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]3375.25[/C][C]1202.49029795116[/C][C]2906[/C][/ROW]
[ROW][C]2[/C][C]3362.25[/C][C]911.076789665211[/C][C]1917[/C][/ROW]
[ROW][C]3[/C][C]3829[/C][C]1277.51320932505[/C][C]2946[/C][/ROW]
[ROW][C]4[/C][C]2984.25[/C][C]921.741964977184[/C][C]2244[/C][/ROW]
[ROW][C]5[/C][C]3421.75[/C][C]685.060277153283[/C][C]1648[/C][/ROW]
[ROW][C]6[/C][C]2954.75[/C][C]418.280906409397[/C][C]848[/C][/ROW]
[ROW][C]7[/C][C]3446.25[/C][C]991.931911305744[/C][C]2140[/C][/ROW]
[ROW][C]8[/C][C]3764.5[/C][C]948.740393012405[/C][C]2039[/C][/ROW]
[ROW][C]9[/C][C]3001.75[/C][C]663.252277292233[/C][C]1561[/C][/ROW]
[ROW][C]10[/C][C]4090.75[/C][C]1144.24600356159[/C][C]2372[/C][/ROW]
[ROW][C]11[/C][C]6789[/C][C]1954.01484129471[/C][C]4740[/C][/ROW]
[ROW][C]12[/C][C]3186.5[/C][C]788.741402488801[/C][C]1924[/C][/ROW]
[ROW][C]13[/C][C]2991[/C][C]760.137268305315[/C][C]1613[/C][/ROW]
[ROW][C]14[/C][C]2357.75[/C][C]1556.70386286752[/C][C]3632[/C][/ROW]
[ROW][C]15[/C][C]3974.5[/C][C]2113.29923736954[/C][C]5035[/C][/ROW]
[ROW][C]16[/C][C]2531.5[/C][C]1201.06078114307[/C][C]2613[/C][/ROW]
[ROW][C]17[/C][C]3256.5[/C][C]1087.72928617372[/C][C]2532[/C][/ROW]
[ROW][C]18[/C][C]5391.75[/C][C]1767.69650015682[/C][C]4155[/C][/ROW]
[ROW][C]19[/C][C]5134.75[/C][C]1764.55705017813[/C][C]4124[/C][/ROW]
[ROW][C]20[/C][C]4052.25[/C][C]2728.67151742382[/C][C]5791[/C][/ROW]
[ROW][C]21[/C][C]3184.25[/C][C]790.040241591106[/C][C]1841[/C][/ROW]
[ROW][C]22[/C][C]5305.5[/C][C]1742.11413709512[/C][C]4026[/C][/ROW]
[ROW][C]23[/C][C]4385.5[/C][C]1964.70362480791[/C][C]4442[/C][/ROW]
[ROW][C]24[/C][C]5179.75[/C][C]1483.26899673211[/C][C]3185[/C][/ROW]
[ROW][C]25[/C][C]4679[/C][C]1234.40782023878[/C][C]2730[/C][/ROW]
[ROW][C]26[/C][C]7332.25[/C][C]1163.89672365435[/C][C]2790[/C][/ROW]
[ROW][C]27[/C][C]9762.5[/C][C]4346.95008022867[/C][C]9673[/C][/ROW]
[ROW][C]28[/C][C]14340.5[/C][C]4646.91385043163[/C][C]10689[/C][/ROW]
[ROW][C]29[/C][C]13041.5[/C][C]5600.56726293566[/C][C]12478[/C][/ROW]
[ROW][C]30[/C][C]12919[/C][C]4913.45696361872[/C][C]11633[/C][/ROW]
[ROW][C]31[/C][C]17771[/C][C]2673.18199904159[/C][C]5949[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=301321&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=301321&T=1

As an alternative you can also use a QR Code:

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

Standard Deviation-Mean Plot
Section	Mean	Standard Deviation	Range
1	3375.25	1202.49029795116	2906
2	3362.25	911.076789665211	1917
3	3829	1277.51320932505	2946
4	2984.25	921.741964977184	2244
5	3421.75	685.060277153283	1648
6	2954.75	418.280906409397	848
7	3446.25	991.931911305744	2140
8	3764.5	948.740393012405	2039
9	3001.75	663.252277292233	1561
10	4090.75	1144.24600356159	2372
11	6789	1954.01484129471	4740
12	3186.5	788.741402488801	1924
13	2991	760.137268305315	1613
14	2357.75	1556.70386286752	3632
15	3974.5	2113.29923736954	5035
16	2531.5	1201.06078114307	2613
17	3256.5	1087.72928617372	2532
18	5391.75	1767.69650015682	4155
19	5134.75	1764.55705017813	4124
20	4052.25	2728.67151742382	5791
21	3184.25	790.040241591106	1841
22	5305.5	1742.11413709512	4026
23	4385.5	1964.70362480791	4442
24	5179.75	1483.26899673211	3185
25	4679	1234.40782023878	2730
26	7332.25	1163.89672365435	2790
27	9762.5	4346.95008022867	9673
28	14340.5	4646.91385043163	10689
29	13041.5	5600.56726293566	12478
30	12919	4913.45696361872	11633
31	17771	2673.18199904159	5949

Regression: S.E.(k) = alpha + beta * Mean(k)
alpha	249.243381870882
beta	0.277769530799814
S.D.	0.0375920881192717
T-STAT	7.38904234099768
p-value	3.84836833591426e-08

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 249.243381870882 \tabularnewline
beta & 0.277769530799814 \tabularnewline
S.D. & 0.0375920881192717 \tabularnewline
T-STAT & 7.38904234099768 \tabularnewline
p-value & 3.84836833591426e-08 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=301321&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]249.243381870882[/C][/ROW]
[ROW][C]beta[/C][C]0.277769530799814[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0375920881192717[/C][/ROW]
[ROW][C]T-STAT[/C][C]7.38904234099768[/C][/ROW]
[ROW][C]p-value[/C][C]3.84836833591426e-08[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=301321&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=301321&T=2

As an alternative you can also use a QR Code:

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

Regression: S.E.(k) = alpha + beta * Mean(k)
alpha	249.243381870882
beta	0.277769530799814
S.D.	0.0375920881192717
T-STAT	7.38904234099768
p-value	3.84836833591426e-08

Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha	-0.716208461381068
beta	0.94568307659901
S.D.	0.129449602607105
T-STAT	7.30541506156083
p-value	4.78740110747504e-08
Lambda	0.0543169234009898

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -0.716208461381068 \tabularnewline
beta & 0.94568307659901 \tabularnewline
S.D. & 0.129449602607105 \tabularnewline
T-STAT & 7.30541506156083 \tabularnewline
p-value & 4.78740110747504e-08 \tabularnewline
Lambda & 0.0543169234009898 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=301321&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-0.716208461381068[/C][/ROW]
[ROW][C]beta[/C][C]0.94568307659901[/C][/ROW]
[ROW][C]S.D.[/C][C]0.129449602607105[/C][/ROW]
[ROW][C]T-STAT[/C][C]7.30541506156083[/C][/ROW]
[ROW][C]p-value[/C][C]4.78740110747504e-08[/C][/ROW]
[ROW][C]Lambda[/C][C]0.0543169234009898[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=301321&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=301321&T=3

As an alternative you can also use a QR Code:

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

Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha	-0.716208461381068
beta	0.94568307659901
S.D.	0.129449602607105
T-STAT	7.30541506156083
p-value	4.78740110747504e-08
Lambda	0.0543169234009898

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Parameters (Session):

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')

Free Statistics

Description of Statistical Computation

Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code