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Description of Statistical Computation

Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationThu, 24 Nov 2016 20:04:18 +0100
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2016/Nov/24/t1480014296jch1wd8pu35q9ax.htm/, Retrieved Tue, 07 May 2024 10:47:12 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=297045, Retrieved Tue, 07 May 2024 10:47:12 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact61

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [Geel] [2016-11-24 19:04:18] [f0fcaf0884a2ab8e55345d70fdb8db2d] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
5
5
1
7
2
4
1
2
2
5
3
7
6
9
4

Tables (Output of Computation)





Summary of computational transaction
Raw Input view raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R ServerBig 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=297045&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=297045&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=297045&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 Input view raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R ServerBig Analytics Cloud Computing Center






Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean4.20.6187556.78783
Geometric Mean3.46941
Harmonic Mean2.72885
Quadratic Mean4.79583
Winsorized Mean ( 1 / 5 )4.066670.5560637.31332
Winsorized Mean ( 2 / 5 )4.20.5089678.25201
Winsorized Mean ( 3 / 5 )40.4364369.16515
Winsorized Mean ( 4 / 5 )3.733330.35812610.4246
Winsorized Mean ( 5 / 5 )4.066670.24816816.3868
Trimmed Mean ( 1 / 5 )4.076920.5484427.43364
Trimmed Mean ( 2 / 5 )4.090910.512657.97993
Trimmed Mean ( 3 / 5 )40.4714058.48528
Trimmed Mean ( 4 / 5 )40.4364369.16515
Trimmed Mean ( 5 / 5 )4.20.37416611.225
Median4
Midrange5
Midmean - Weighted Average at Xnp3.55556
Midmean - Weighted Average at X(n+1)p3.8
Midmean - Empirical Distribution Function3.8
Midmean - Empirical Distribution Function - Averaging3.8
Midmean - Empirical Distribution Function - Interpolation3.55556
Midmean - Closest Observation3.55556
Midmean - True Basic - Statistics Graphics Toolkit3.8
Midmean - MS Excel (old versions)3.8
Number of observations15

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 4.2 & 0.618755 & 6.78783 \tabularnewline
Geometric Mean & 3.46941 &  &  \tabularnewline
Harmonic Mean & 2.72885 &  &  \tabularnewline
Quadratic Mean & 4.79583 &  &  \tabularnewline
Winsorized Mean ( 1 / 5 ) & 4.06667 & 0.556063 & 7.31332 \tabularnewline
Winsorized Mean ( 2 / 5 ) & 4.2 & 0.508967 & 8.25201 \tabularnewline
Winsorized Mean ( 3 / 5 ) & 4 & 0.436436 & 9.16515 \tabularnewline
Winsorized Mean ( 4 / 5 ) & 3.73333 & 0.358126 & 10.4246 \tabularnewline
Winsorized Mean ( 5 / 5 ) & 4.06667 & 0.248168 & 16.3868 \tabularnewline
Trimmed Mean ( 1 / 5 ) & 4.07692 & 0.548442 & 7.43364 \tabularnewline
Trimmed Mean ( 2 / 5 ) & 4.09091 & 0.51265 & 7.97993 \tabularnewline
Trimmed Mean ( 3 / 5 ) & 4 & 0.471405 & 8.48528 \tabularnewline
Trimmed Mean ( 4 / 5 ) & 4 & 0.436436 & 9.16515 \tabularnewline
Trimmed Mean ( 5 / 5 ) & 4.2 & 0.374166 & 11.225 \tabularnewline
Median & 4 &  &  \tabularnewline
Midrange & 5 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 3.55556 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 3.8 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 3.8 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 3.8 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 3.55556 &  &  \tabularnewline
Midmean - Closest Observation & 3.55556 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 3.8 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 3.8 &  &  \tabularnewline
Number of observations & 15 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=297045&T=1

[TABLE]
[ROW][C]Central Tendency - Ungrouped Data[/C][/ROW]
[ROW][C]Measure[/C][C]Value[/C][C]S.E.[/C][C]Value/S.E.[/C][/ROW]
[ROW][C]Arithmetic Mean[/C][C]4.2[/C][C]0.618755[/C][C]6.78783[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]3.46941[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]2.72885[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]4.79583[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 5 )[/C][C]4.06667[/C][C]0.556063[/C][C]7.31332[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 5 )[/C][C]4.2[/C][C]0.508967[/C][C]8.25201[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 5 )[/C][C]4[/C][C]0.436436[/C][C]9.16515[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 5 )[/C][C]3.73333[/C][C]0.358126[/C][C]10.4246[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 5 )[/C][C]4.06667[/C][C]0.248168[/C][C]16.3868[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 5 )[/C][C]4.07692[/C][C]0.548442[/C][C]7.43364[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 5 )[/C][C]4.09091[/C][C]0.51265[/C][C]7.97993[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 5 )[/C][C]4[/C][C]0.471405[/C][C]8.48528[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 5 )[/C][C]4[/C][C]0.436436[/C][C]9.16515[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 5 )[/C][C]4.2[/C][C]0.374166[/C][C]11.225[/C][/ROW]
[ROW][C]Median[/C][C]4[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]5[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]3.55556[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]3.8[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]3.8[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]3.8[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]3.55556[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]3.55556[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]3.8[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]3.8[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]15[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=297045&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=297045&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:

Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean4.20.6187556.78783
Geometric Mean3.46941
Harmonic Mean2.72885
Quadratic Mean4.79583
Winsorized Mean ( 1 / 5 )4.066670.5560637.31332
Winsorized Mean ( 2 / 5 )4.20.5089678.25201
Winsorized Mean ( 3 / 5 )40.4364369.16515
Winsorized Mean ( 4 / 5 )3.733330.35812610.4246
Winsorized Mean ( 5 / 5 )4.066670.24816816.3868
Trimmed Mean ( 1 / 5 )4.076920.5484427.43364
Trimmed Mean ( 2 / 5 )4.090910.512657.97993
Trimmed Mean ( 3 / 5 )40.4714058.48528
Trimmed Mean ( 4 / 5 )40.4364369.16515
Trimmed Mean ( 5 / 5 )4.20.37416611.225
Median4
Midrange5
Midmean - Weighted Average at Xnp3.55556
Midmean - Weighted Average at X(n+1)p3.8
Midmean - Empirical Distribution Function3.8
Midmean - Empirical Distribution Function - Averaging3.8
Midmean - Empirical Distribution Function - Interpolation3.55556
Midmean - Closest Observation3.55556
Midmean - True Basic - Statistics Graphics Toolkit3.8
Midmean - MS Excel (old versions)3.8
Number of observations15


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
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,'Arithmetic Mean',header=TRUE)
a<-table.element(a,signif(arm,6))
a<-table.element(a, signif(armse,6))
a<-table.element(a,signif(armose,6))
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Geometric Mean',header=TRUE)
a<-table.element(a,signif(geo,6))
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Harmonic Mean',header=TRUE)
a<-table.element(a,signif(har,6))
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Quadratic Mean',header=TRUE)
a<-table.element(a,signif(qua,6))
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, mylabel,header=TRUE)
a<-table.element(a,signif(win[j,1],6))
a<-table.element(a,signif(win[j,2],6))
a<-table.element(a,signif(win[j,1]/win[j,2],6))
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, mylabel,header=TRUE)
a<-table.element(a,signif(tri[j,1],6))
a<-table.element(a,signif(tri[j,2],6))
a<-table.element(a,signif(tri[j,1]/tri[j,2],6))
a<-table.row.end(a)
}
a<-table.row.start(a)
a<-table.element(a, 'Median',header=TRUE)
a<-table.element(a,signif(median(x),6))
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Midrange',header=TRUE)
a<-table.element(a,signif(midr,6))
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <-  'Midmean'
mylabel <- paste(mymid,'Weighted Average at Xnp',sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,signif(midm[1],6))
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <-  'Midmean'
mylabel <- paste(mymid,'Weighted Average at X(n+1)p',sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,signif(midm[2],6))
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <-  'Midmean'
mylabel <- paste(mymid,'Empirical Distribution Function',sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,signif(midm[3],6))
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <-  'Midmean'
mylabel <- paste(mymid,'Empirical Distribution Function - Averaging',sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,signif(midm[4],6))
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <-  'Midmean'
mylabel <- paste(mymid,'Empirical Distribution Function - Interpolation',sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,signif(midm[5],6))
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <-  'Midmean'
mylabel <- paste(mymid,'Closest Observation',sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,signif(midm[6],6))
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <-  'Midmean'
mylabel <- paste(mymid,'True Basic - Statistics Graphics Toolkit',sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,signif(midm[7],6))
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <-  'Midmean'
mylabel <- paste(mymid,'MS Excel (old versions)',sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,signif(midm[8],6))
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,signif(length(x),6))
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable.tab')