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Author's title

Author

*The author of this computation has been verified*

R Software Module

rwasp_centraltendency.wasp

Title produced by software

Central Tendency

Date of computation

Thu, 03 Sep 2015 04:46:47 +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/2015/Sep/03/t1441252014j9bg22e5my2jpgz.htm/, Retrieved Thu, 16 May 2024 09:19:03 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=280434, Retrieved Thu, 16 May 2024 09:19:03 +0000

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Original text written by user:

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User-defined keywords

Estimated Impact

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

-     [Multiple Regression] [Regressie analyse] [2015-01-14 11:00:58] [46c7ebd23dbdec306a09830d8b7528e7]
- RMPD    [Central Tendency] [] [2015-09-03 03:46:47] [8145b3fe416df466b077d26de89041cd] [Current]

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14910.50.670.6700.5201110
1390.890.50.830.330.51201111
1480.890.410.6701201110
1580.890.50.83000201111
1280.890.70.67011201111
2240.780.3000.50.5201111
1590.890.40.830.670.50201110
10510.40.50.6711201111
1590.890.70.8300.50201111
1670.780.60.330.670.50.5201111
16510.60.5100.5201111
1590.780.20.6700.50.5201111
1190.890.4100.50.5201111
1760.890.40.50.6701201110
540.890.50.670.3300201110
910.890.30.170.6700.5201100
1630.890.40.830.330.50.5201111
1240.670.70.670.330.51201110
13710.50.670.3301201101
1210.780.20.67001201110
1530.780.30.50.6700.5201111
1480.890.610.3301201111
2210.780.60.830.3301201110
1880.890.20.830.3301201111
1490.890.710.6710201111
2440.330.20.67000201111
1481110.3311201101
920.890.40.830.6700.5201100
1500.890.41101201111
1530.670.20.830.6700.5201110
940.560.40.670.3301201110
1560.890.40.6700.51201110
1320.890.710.670.50.5201111
16110.20.670.6700.5201111
1050.780.61100.5201111
970.780.3110.50.5201111
1510.330.30.50.3300201110
1310.780.20.6700.50201101
1660.890.50.830.670.50.5201111
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1110.780.610.670.50.5201111
1450.890.410.670.51201111
1620.890.610.330.51201111
16310.41101201111
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18710.50.830.670.50.5201110
1090.890.20.5001201111
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1050.890.50.17001201110
830.780.70.8310.51201101
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15510.51000.5201101
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1620.780.80.8300.51201110
990.670.3110.51201110
20210.20.830.6700.5201111
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1830.780.20.670.670.51201110
21410.10.830.6701201111
1880.560.40.6710.50201111
1040.670.5100.50.5201100
1770.890.80.830.330.51201110
1260.890.40.670.6700.5201110
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1390.780.30.67000201110
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10810.60.830.670.50.5201101
1590.890.410.3300.5201110
740.440.30.83000201100
1100.780.80.83011201111
960.890.60.50.3311201100
1160.670.30.5000201100
870.780.50.830.670.51201100
970.780.410.3301201101
1270.330.30.330.6700201100
1060.890.710.3300.5201101
800.890.20.670.330.50.5201101
740.890.40.83101201100
910.890.610.670.50.5201100
1330.560.60.83001201100
740.670.60.830.670.50.5201101
1140.670.410.330.51201101
1400.780.60.83001201101
950.780.510.330.51201100
980.780.50.83001201101
1210.890.60.67001201100
12610.80.830.330.51201101
980.890.50.830.6710.5201101
950.890.60.830.670.51201101
1100.780.40.830.670.51201101
7010.30.670.670.51201101
1020.780.30.83100.5201100
860.670.20000201101
1300.780.40.83000.5201101
960.890.51000.5201101
1020.670.30.1700.50201100
1000.220.40.1700.50201100
940.440.50.5100201100
520.890.30.50.6701201100
980.670.51000.5201100
1180.890.40.670.6700.5201100
990.670.40.830.6701201101
480.780.61011201211
500.780.310.6711201211
1500.780.410.3310.5201211
15410.31111201211
1090.7811111201200
680.670.41000.5201201
1940.890.80.8310.51201211
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15910.50.830.6701201211
670.780.41000.5201210
1470.670.30.830.6701201210
390.890.50.83101201211
1000.670.310.6701201211
1110.670.30.67001201211
13810.40.83001201211
1010.670.31000.5201211
13110.610.330.50.5201201
1010.890.60.830.6711201211
1140.890.41111201211
16510.41000201210
1140.670.410.6700.5201211
1110.440.30.670.670.51201211
750.890.210.3310201211
820.560.50.830.6701201211
1210.780.410.6711201211
3210.410.6700201211
15010.40.830.6701201210
1170.890.30.670.670.50.5201211
710.670.40.830.6710.5201201
1650.890.210.330.51201211
1540.3300000201211
1260.890.410.670.51201211
1490.780.61011201210
14510.40.670.6700.5201210
1200.440.41000.5201211
1090.670.40.8300.50201210
1320.330.20.1700.50201210
1720.890.40.83111201211
1690.890.30.83000.5201210
11410.60.830.6710201211
1560.890.60.83101201211
1720.890.40.83001201210
6810.510.6710.5201201
890.890.40.8300.51201201
16710.61111201211
1130.780.60.830.670.51201210
1150.780.910.670.51201200
780.670.40.830.670.50201200
1180.890.8110.51201200
870.670.50.83101201201
1730.780.40.83100201210
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1000.890.810.6711201201
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1100.890.310.3301201201
1180.890.30.830.330.51201211
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14610.40.670.330.50.5201201
490.670.510.3301201210
9010.50.670.670.51201200
1210.890.41000201200
1550.890.7110.50201211
1040.890.50.50.3300.5201200
1470.890.40.670.3310201201
11010.70.67101201200
10810.70.67101201200
11310.70.67101201200
1150.890.70.67101201200
610.890.70.67000201201
600.890.710.670.51201201
1090.330.10.670.330.50201201
680.670.20.670.670.51201201
1110.560.30.330.3301201200
770.440.60.830.3300.5201200
7310.81111201201
1510.890.810.330.50.5201210
890.3300.17000201200
780.670.30.670.3301201200
1100.670.60.830.330.51201200
22010.50.830.6701201211
650.780.710.3300.5201201
1410.670.30.8300.51201210
11710.310.6700201200
1220.780.410.6700.5201211
630.890.40.83101201200
440.890.10.83001201211
520.890.510.6701201201
131000000201200
1010.670.410.330.50201201
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15210.410.330.51201211
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770.890.30.83001201200
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1030.560.30.17001201211
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17510.30.830.6711201211
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1490.780.40.830.6700.5201210
1680.4400000201210
1400.890.210.330.51201210
880.890.510.670.51201201
1680.890.310.6700.5201211
940.4400000201211
5110.50.83101201211
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1450.670.30.8300.50.5201211
660.3300000201211
850.780.30.6700.50201201
1090.890.510.670.51201210
630.780.40.67001201200
1020.780.50.830.6700.5201201
1620.890.71110.5201200
860.780.810.670.51201201
1140.780.610.330.51201201
1640.670.40.830.3300.5201210
1190.890.50.830.330.50201211
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14210.6100.51201211
8310.30.670.6700.5201210
940.780.60.8310.50.5201201
810.780.30.330.3301201200
1660.890.710.6711201211
1100.890.71101201200
640.670.60.6710.51201201
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1040.670.50.830.3300.5201200
1050.560.40.67001201201
490.780.410.3311201201
8810.71101201200
950.670.20.1700.50201201
1020.780.50.830.6700.5201201
990.560.40.830.670.50201200
6310.210.6711201201
760.890.50.670.6700201200
1090.440.40.5001201200
11710.70.67111201201
570.890.60.830.6710201201
1200.780.40.83000201200
730.890.510.6711201201
910.1100.17000201200
1080.890.710.670.51201200
1050.890.40.670.6701201201
11710.50.67101201210
1190.890.60.830.6700.5201200
3110.80.50.670.50.5201201

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	'George Udny Yule' @ yule.wessa.net

\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' @ yule.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=280434&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' @ yule.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=280434&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=280434&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	'George Udny Yule' @ yule.wessa.net

Parameters (Session):

par2 = grey ; par3 = FALSE ; par4 = Unknown ;

Parameters (R input):

R code (references can be found in the software module):

geomean <- function(x) {
return(exp(mean(log(x))))
}
harmean <- function(x) {
return(1/mean(1/x))
}
quamean <- function(x) {
return(sqrt(mean(x*x)))
}
winmean <- function(x) {
x <-sort(x[!is.na(x)])
n<-length(x)
denom <- 3
nodenom <- n/denom
if (nodenom>40) denom <- n/40
sqrtn = sqrt(n)
roundnodenom = floor(nodenom)
win <- array(NA,dim=c(roundnodenom,2))
for (j in 1:roundnodenom) {
win[j,1] <- (j*x[j+1]+sum(x[(j+1):(n-j)])+j*x[n-j])/n
win[j,2] <- sd(c(rep(x[j+1],j),x[(j+1):(n-j)],rep(x[n-j],j)))/sqrtn
}
return(win)
}
trimean <- function(x) {
x <-sort(x[!is.na(x)])
n<-length(x)
denom <- 3
nodenom <- n/denom
if (nodenom>40) denom <- n/40
sqrtn = sqrt(n)
roundnodenom = floor(nodenom)
tri <- array(NA,dim=c(roundnodenom,2))
for (j in 1:roundnodenom) {
tri[j,1] <- mean(x,trim=j/n)
tri[j,2] <- sd(x[(j+1):(n-j)]) / sqrt(n-j*2)
}
return(tri)
}
midrange <- function(x) {
return((max(x)+min(x))/2)
}
q1 <- function(data,n,p,i,f) {
np <- n*p;
i <<- floor(np)
f <<- np - i
qvalue <- (1-f)*data[i] + f*data[i+1]
}
q2 <- function(data,n,p,i,f) {
np <- (n+1)*p
i <<- floor(np)
f <<- np - i
qvalue <- (1-f)*data[i] + f*data[i+1]
}
q3 <- function(data,n,p,i,f) {
np <- n*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- data[i]
} else {
qvalue <- data[i+1]
}
}
q4 <- function(data,n,p,i,f) {
np <- n*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- (data[i]+data[i+1])/2
} else {
qvalue <- data[i+1]
}
}
q5 <- function(data,n,p,i,f) {
np <- (n-1)*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- data[i+1]
} else {
qvalue <- data[i+1] + f*(data[i+2]-data[i+1])
}
}
q6 <- function(data,n,p,i,f) {
np <- n*p+0.5
i <<- floor(np)
f <<- np - i
qvalue <- data[i]
}
q7 <- function(data,n,p,i,f) {
np <- (n+1)*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- data[i]
} else {
qvalue <- f*data[i] + (1-f)*data[i+1]
}
}
q8 <- function(data,n,p,i,f) {
np <- (n+1)*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- data[i]
} else {
if (f == 0.5) {
qvalue <- (data[i]+data[i+1])/2
} else {
if (f < 0.5) {
qvalue <- data[i]
} else {
qvalue <- data[i+1]
}
}
}
}
midmean <- function(x,def) {
x <-sort(x[!is.na(x)])
n<-length(x)
if (def==1) {
qvalue1 <- q1(x,n,0.25,i,f)
qvalue3 <- q1(x,n,0.75,i,f)
}
if (def==2) {
qvalue1 <- q2(x,n,0.25,i,f)
qvalue3 <- q2(x,n,0.75,i,f)
}
if (def==3) {
qvalue1 <- q3(x,n,0.25,i,f)
qvalue3 <- q3(x,n,0.75,i,f)
}
if (def==4) {
qvalue1 <- q4(x,n,0.25,i,f)
qvalue3 <- q4(x,n,0.75,i,f)
}
if (def==5) {
qvalue1 <- q5(x,n,0.25,i,f)
qvalue3 <- q5(x,n,0.75,i,f)
}
if (def==6) {
qvalue1 <- q6(x,n,0.25,i,f)
qvalue3 <- q6(x,n,0.75,i,f)
}
if (def==7) {
qvalue1 <- q7(x,n,0.25,i,f)
qvalue3 <- q7(x,n,0.75,i,f)
}
if (def==8) {
qvalue1 <- q8(x,n,0.25,i,f)
qvalue3 <- q8(x,n,0.75,i,f)
}
midm <- 0
myn <- 0
roundno4 <- round(n/4)
round3no4 <- round(3*n/4)
for (i in 1:n) {
if ((x[i]>=qvalue1) & (x[i]<=qvalue3)){
midm = midm + x[i]
myn = myn + 1
}
}
midm = midm / myn
return(midm)
}
(arm <- mean(x))
sqrtn <- sqrt(length(x))
(armse <- sd(x) / sqrtn)
(armose <- arm / armse)
(geo <- geomean(x))
(har <- harmean(x))
(qua <- quamean(x))
(win <- winmean(x))
(tri <- trimean(x))
(midr <- midrange(x))
midm <- array(NA,dim=8)
for (j in 1:8) midm[j] <- midmean(x,j)
midm
bitmap(file='test1.png')
lb <- win[,1] - 2*win[,2]
ub <- win[,1] + 2*win[,2]
if ((ylimmin == '') | (ylimmax == '')) plot(win[,1],type='b',main=main, xlab='j', pch=19, ylab='Winsorized Mean(j/n)', ylim=c(min(lb),max(ub))) else plot(win[,1],type='l',main=main, xlab='j', pch=19, ylab='Winsorized Mean(j/n)', ylim=c(ylimmin,ylimmax))
lines(ub,lty=3)
lines(lb,lty=3)
grid()
dev.off()
bitmap(file='test2.png')
lb <- tri[,1] - 2*tri[,2]
ub <- tri[,1] + 2*tri[,2]
if ((ylimmin == '') | (ylimmax == '')) plot(tri[,1],type='b',main=main, xlab='j', pch=19, ylab='Trimmed Mean(j/n)', ylim=c(min(lb),max(ub))) else plot(tri[,1],type='l',main=main, xlab='j', pch=19, ylab='Trimmed Mean(j/n)', ylim=c(ylimmin,ylimmax))
lines(ub,lty=3)
lines(lb,lty=3)
grid()
dev.off()
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Central Tendency - Ungrouped Data',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Measure',header=TRUE)
a<-table.element(a,'Value',header=TRUE)
a<-table.element(a,'S.E.',header=TRUE)
a<-table.element(a,'Value/S.E.',header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('arithmetic_mean.htm', 'Arithmetic Mean', 'click to view the definition of the Arithmetic Mean'),header=TRUE)
a<-table.element(a,arm)
a<-table.element(a,hyperlink('arithmetic_mean_standard_error.htm', armse, 'click to view the definition of the Standard Error of the Arithmetic Mean'))
a<-table.element(a,armose)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('geometric_mean.htm', 'Geometric Mean', 'click to view the definition of the Geometric Mean'),header=TRUE)
a<-table.element(a,geo)
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('harmonic_mean.htm', 'Harmonic Mean', 'click to view the definition of the Harmonic Mean'),header=TRUE)
a<-table.element(a,har)
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('quadratic_mean.htm', 'Quadratic Mean', 'click to view the definition of the Quadratic Mean'),header=TRUE)
a<-table.element(a,qua)
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
for (j in 1:length(win[,1])) {
a<-table.row.start(a)
mylabel <- paste('Winsorized Mean (',j)
mylabel <- paste(mylabel,'/')
mylabel <- paste(mylabel,length(win[,1]))
mylabel <- paste(mylabel,')')
a<-table.element(a,hyperlink('winsorized_mean.htm', mylabel, 'click to view the definition of the Winsorized Mean'),header=TRUE)
a<-table.element(a,win[j,1])
a<-table.element(a,win[j,2])
a<-table.element(a,win[j,1]/win[j,2])
a<-table.row.end(a)
}
for (j in 1:length(tri[,1])) {
a<-table.row.start(a)
mylabel <- paste('Trimmed Mean (',j)
mylabel <- paste(mylabel,'/')
mylabel <- paste(mylabel,length(tri[,1]))
mylabel <- paste(mylabel,')')
a<-table.element(a,hyperlink('arithmetic_mean.htm', mylabel, 'click to view the definition of the Trimmed Mean'),header=TRUE)
a<-table.element(a,tri[j,1])
a<-table.element(a,tri[j,2])
a<-table.element(a,tri[j,1]/tri[j,2])
a<-table.row.end(a)
}
a<-table.row.start(a)
a<-table.element(a,hyperlink('median_1.htm', 'Median', 'click to view the definition of the Median'),header=TRUE)
a<-table.element(a,median(x))
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('midrange.htm', 'Midrange', 'click to view the definition of the Midrange'),header=TRUE)
a<-table.element(a,midr)
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_1.htm','Weighted Average at Xnp',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[1])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_2.htm','Weighted Average at X(n+1)p',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[2])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_3.htm','Empirical Distribution Function',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[3])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_4.htm','Empirical Distribution Function - Averaging',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[4])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_5.htm','Empirical Distribution Function - Interpolation',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[5])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_6.htm','Closest Observation',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[6])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_7.htm','True Basic - Statistics Graphics Toolkit',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[7])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_8.htm','MS Excel (old versions)',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[8])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Number of observations',header=TRUE)
a<-table.element(a,length(x))
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable.tab')

Free Statistics

Description of Statistical Computation

Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code