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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 computationTue, 29 Nov 2016 14:14:51 +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/29/t14804253953jaootrpufr4qqt.htm/, Retrieved Tue, 07 May 2024 10:48:21 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=297262, Retrieved Tue, 07 May 2024 10:48:21 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact85

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [Central Tendency ...] [2016-11-29 13:14:51] [7b02c9ca65294818d9c418453f92ae83] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
0,0500
0,2222
0,3158
0,0500
0,3810
0,1500
0,4211
0,3500
0,3684
0,1905
0,3158
0,1000
0,2941
0,1053
0,2778

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=297262&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=297262&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=297262&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 Mean0.2394670.03221357.43374
Geometric Mean0.197996
Harmonic Mean0.150275
Quadratic Mean0.26809
Winsorized Mean ( 1 / 5 )0.2367930.03123287.58156
Winsorized Mean ( 2 / 5 )0.241780.02804518.62113
Winsorized Mean ( 3 / 5 )0.239160.02651869.01857
Winsorized Mean ( 4 / 5 )0.241960.019765212.2417
Winsorized Mean ( 5 / 5 )0.255460.015470816.5124
Trimmed Mean ( 1 / 5 )0.2400690.03090787.76727
Trimmed Mean ( 2 / 5 )0.2445360.02904838.41827
Trimmed Mean ( 3 / 5 )0.2468330.02802238.80847
Trimmed Mean ( 4 / 5 )0.2523140.024713910.2094
Trimmed Mean ( 5 / 5 )0.260080.023294111.165
Median0.2778
Midrange0.23555
Midmean - Weighted Average at Xnp0.233938
Midmean - Weighted Average at X(n+1)p0.246833
Midmean - Empirical Distribution Function0.246833
Midmean - Empirical Distribution Function - Averaging0.246833
Midmean - Empirical Distribution Function - Interpolation0.252314
Midmean - Closest Observation0.233938
Midmean - True Basic - Statistics Graphics Toolkit0.246833
Midmean - MS Excel (old versions)0.246833
Number of observations15

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 0.239467 & 0.0322135 & 7.43374 \tabularnewline
Geometric Mean & 0.197996 &  &  \tabularnewline
Harmonic Mean & 0.150275 &  &  \tabularnewline
Quadratic Mean & 0.26809 &  &  \tabularnewline
Winsorized Mean ( 1 / 5 ) & 0.236793 & 0.0312328 & 7.58156 \tabularnewline
Winsorized Mean ( 2 / 5 ) & 0.24178 & 0.0280451 & 8.62113 \tabularnewline
Winsorized Mean ( 3 / 5 ) & 0.23916 & 0.0265186 & 9.01857 \tabularnewline
Winsorized Mean ( 4 / 5 ) & 0.24196 & 0.0197652 & 12.2417 \tabularnewline
Winsorized Mean ( 5 / 5 ) & 0.25546 & 0.0154708 & 16.5124 \tabularnewline
Trimmed Mean ( 1 / 5 ) & 0.240069 & 0.0309078 & 7.76727 \tabularnewline
Trimmed Mean ( 2 / 5 ) & 0.244536 & 0.0290483 & 8.41827 \tabularnewline
Trimmed Mean ( 3 / 5 ) & 0.246833 & 0.0280223 & 8.80847 \tabularnewline
Trimmed Mean ( 4 / 5 ) & 0.252314 & 0.0247139 & 10.2094 \tabularnewline
Trimmed Mean ( 5 / 5 ) & 0.26008 & 0.0232941 & 11.165 \tabularnewline
Median & 0.2778 &  &  \tabularnewline
Midrange & 0.23555 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 0.233938 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 0.246833 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 0.246833 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 0.246833 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 0.252314 &  &  \tabularnewline
Midmean - Closest Observation & 0.233938 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 0.246833 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 0.246833 &  &  \tabularnewline
Number of observations & 15 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=297262&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]0.239467[/C][C]0.0322135[/C][C]7.43374[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]0.197996[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]0.150275[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]0.26809[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 5 )[/C][C]0.236793[/C][C]0.0312328[/C][C]7.58156[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 5 )[/C][C]0.24178[/C][C]0.0280451[/C][C]8.62113[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 5 )[/C][C]0.23916[/C][C]0.0265186[/C][C]9.01857[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 5 )[/C][C]0.24196[/C][C]0.0197652[/C][C]12.2417[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 5 )[/C][C]0.25546[/C][C]0.0154708[/C][C]16.5124[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 5 )[/C][C]0.240069[/C][C]0.0309078[/C][C]7.76727[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 5 )[/C][C]0.244536[/C][C]0.0290483[/C][C]8.41827[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 5 )[/C][C]0.246833[/C][C]0.0280223[/C][C]8.80847[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 5 )[/C][C]0.252314[/C][C]0.0247139[/C][C]10.2094[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 5 )[/C][C]0.26008[/C][C]0.0232941[/C][C]11.165[/C][/ROW]
[ROW][C]Median[/C][C]0.2778[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]0.23555[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]0.233938[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]0.246833[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]0.246833[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]0.246833[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]0.252314[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]0.233938[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]0.246833[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]0.246833[/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=297262&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=297262&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 Mean0.2394670.03221357.43374
Geometric Mean0.197996
Harmonic Mean0.150275
Quadratic Mean0.26809
Winsorized Mean ( 1 / 5 )0.2367930.03123287.58156
Winsorized Mean ( 2 / 5 )0.241780.02804518.62113
Winsorized Mean ( 3 / 5 )0.239160.02651869.01857
Winsorized Mean ( 4 / 5 )0.241960.019765212.2417
Winsorized Mean ( 5 / 5 )0.255460.015470816.5124
Trimmed Mean ( 1 / 5 )0.2400690.03090787.76727
Trimmed Mean ( 2 / 5 )0.2445360.02904838.41827
Trimmed Mean ( 3 / 5 )0.2468330.02802238.80847
Trimmed Mean ( 4 / 5 )0.2523140.024713910.2094
Trimmed Mean ( 5 / 5 )0.260080.023294111.165
Median0.2778
Midrange0.23555
Midmean - Weighted Average at Xnp0.233938
Midmean - Weighted Average at X(n+1)p0.246833
Midmean - Empirical Distribution Function0.246833
Midmean - Empirical Distribution Function - Averaging0.246833
Midmean - Empirical Distribution Function - Interpolation0.252314
Midmean - Closest Observation0.233938
Midmean - True Basic - Statistics Graphics Toolkit0.246833
Midmean - MS Excel (old versions)0.246833
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')