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*Unverified author*
R Software Module: rwasp_centraltendency.wasp (opens new window with default values)
Title produced by software: Central Tendency
Date of computation: Sun, 16 Aug 2009 08:05:26 -0600
 
Cite this page as follows:
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2009/Aug/16/t1250431547jl40q25btj7xomm.htm/, Retrieved Sun, 16 Aug 2009 16:05:49 +0200
 
BibTeX entries for LaTeX users:
@Manual{KEY,
    author = {{YOUR NAME}},
    publisher = {Office for Research Development and Education},
    title = {Statistical Computations at FreeStatistics.org, URL http://www.freestatistics.org/blog/date/2009/Aug/16/t1250431547jl40q25btj7xomm.htm/},
    year = {2009},
}
@Manual{R,
    title = {R: A Language and Environment for Statistical Computing},
    author = {{R Development Core Team}},
    organization = {R Foundation for Statistical Computing},
    address = {Vienna, Austria},
    year = {2009},
    note = {{ISBN} 3-900051-07-0},
    url = {http://www.R-project.org},
}
 
Original text written by user:
 
IsPrivate?
No (this computation is public)
 
User-defined keywords:
 
Dataseries X:
» Textbox « » Textfile « » CSV «
105,46 104,66 103,52 103,71 103,78 103,67 103,66 102,76 102 101,5 101,5 99,22 98,97 98,9 99,78 104,4 106,21 105,46 108,33 111,72 111,88 112,86 113,09 116,9 114,62 118,86 124,71 122,53 127,89 136,16 134,12 130,26 135,35 131,43 129,61 123,96 121,1 125,38 123,1 129,92 136,68 131,17 124,82 122,47 126,15 118,74 116,8 116,64 116,53 117,68 119,46 126,19 124,39 121,9 122,53 122,93 124,66 124,41 120,93 120,18 123,44 126,1 125,82 122,18 117,27 117,86 119,09 123,08 125,42 121,81 121,66 121,27 120,92 122,16 124,17 127,26 134,16 134,09 135,57 136,13 136,23 140,6 136,5 130,59 129,5 135,25 138,06 146,28 145,04 147,96 156,71 160,97 168,17 163,91 153,05 151,76
 
Output produced by software:


Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'George Udny Yule' @ 72.249.76.132


Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean123.4191666666671.5161746261813181.4016832464178
Geometric Mean122.559641456548
Harmonic Mean121.721682359690
Quadratic Mean124.300745464042
Winsorized Mean ( 1 / 32 )123.3755208333331.5028548700065682.0941018960762
Winsorized Mean ( 2 / 32 )123.3194791666671.4850941872324483.0381535574387
Winsorized Mean ( 3 / 32 )123.2038541666671.4481151494890385.0787689156758
Winsorized Mean ( 4 / 32 )123.1230208333331.4004384661111987.9174799984094
Winsorized Mean ( 5 / 32 )123.0558333333331.3855546870967188.8134077126787
Winsorized Mean ( 6 / 32 )122.8495833333331.3308930018536692.3061306673259
Winsorized Mean ( 7 / 32 )122.78251.2979813189664894.5949669736123
Winsorized Mean ( 8 / 32 )122.74251.2683769415238896.7713114151477
Winsorized Mean ( 9 / 32 )122.3393751.19408332870372102.454637845761
Winsorized Mean ( 10 / 32 )122.0758333333331.15327950259732105.851038762420
Winsorized Mean ( 11 / 32 )121.9222916666671.13009641413681107.886628204013
Winsorized Mean ( 12 / 32 )121.9085416666671.12553081024301108.312043133094
Winsorized Mean ( 13 / 32 )121.95593751.10642362427887110.225355662924
Winsorized Mean ( 14 / 32 )121.9836458333331.09872418157990111.022991828512
Winsorized Mean ( 15 / 32 )122.1039583333331.07754769991670113.31652264004
Winsorized Mean ( 16 / 32 )122.0106251.06489792168426114.574948936914
Winsorized Mean ( 17 / 32 )122.1044791666671.03810217009965117.622795408419
Winsorized Mean ( 18 / 32 )122.4832291666670.973034517954731125.877578756528
Winsorized Mean ( 19 / 32 )122.93843750.844473368646767145.580005319769
Winsorized Mean ( 20 / 32 )122.96343750.838657890700565146.619305515964
Winsorized Mean ( 21 / 32 )123.171250.808420260066486152.360419554391
Winsorized Mean ( 22 / 32 )122.6143750.71826813843799170.708358673194
Winsorized Mean ( 23 / 32 )122.9186458333330.66026298288968186.166192893887
Winsorized Mean ( 24 / 32 )123.2511458333330.580221862243449212.420720165177
Winsorized Mean ( 25 / 32 )123.1938541666670.5653527149665217.906186536960
Winsorized Mean ( 26 / 32 )123.1451041666670.548018119714033224.709913297988
Winsorized Mean ( 27 / 32 )123.0860416666670.533299899154187230.800796815977
Winsorized Mean ( 28 / 32 )123.1618750.516086154758847238.645958362418
Winsorized Mean ( 29 / 32 )122.7993750.439863111992432279.176342939421
Winsorized Mean ( 30 / 32 )122.658750.40929432879985299.683482934311
Winsorized Mean ( 31 / 32 )122.5973958333330.334406624419968366.61174414825
Winsorized Mean ( 32 / 32 )122.62406250.328054357997249373.791902197588
Trimmed Mean ( 1 / 32 )123.2039361702131.4490801539482185.0221679142642
Trimmed Mean ( 2 / 32 )123.0248913043481.3871606883530588.6882769511099
Trimmed Mean ( 3 / 32 )122.8677777777781.3268004917896292.6045615283506
Trimmed Mean ( 4 / 32 )122.7455681818181.2737372386949096.3664753238952
Trimmed Mean ( 5 / 32 )122.6402325581401.2295082372719999.7473858574965
Trimmed Mean ( 6 / 32 )122.5452380952381.18285401324231103.601320808246
Trimmed Mean ( 7 / 32 )122.4858536585371.14359844479057107.105649029601
Trimmed Mean ( 8 / 32 )122.4351.10601388276131110.699333804314
Trimmed Mean ( 9 / 32 )122.3876923076921.06889760439462114.498986436599
Trimmed Mean ( 10 / 32 )122.3944736842111.04122816136803117.548178415959
Trimmed Mean ( 11 / 32 )122.4358108108111.01666497140325120.428867183079
Trimmed Mean ( 12 / 32 )122.4980555555560.991919300263428123.495989565908
Trimmed Mean ( 13 / 32 )122.5654285714290.963406969590989127.220824054723
Trimmed Mean ( 14 / 32 )122.6316176470590.933003509735545131.437466598403
Trimmed Mean ( 15 / 32 )122.6989393939390.898027159888202136.631657565028
Trimmed Mean ( 16 / 32 )122.75843750.859973214409314142.746815183446
Trimmed Mean ( 17 / 32 )122.8308064516130.815986595917113150.530421781695
Trimmed Mean ( 18 / 32 )122.8991666666670.767438114388513160.142120077775
Trimmed Mean ( 19 / 32 )122.9374137931030.721301990448085170.438201226552
Trimmed Mean ( 20 / 32 )122.9373214285710.690439700437122178.056565042159
Trimmed Mean ( 21 / 32 )122.9350.653149267593718188.218843837807
Trimmed Mean ( 22 / 32 )122.9142307692310.612519728875715200.669831476026
Trimmed Mean ( 23 / 32 )122.94040.580608544932797211.74404178676
Trimmed Mean ( 24 / 32 )122.9422916666670.552619025366576222.472057644258
Trimmed Mean ( 25 / 32 )122.9154347826090.533567313396169230.365376020223
Trimmed Mean ( 26 / 32 )122.8911363636360.511995145646778240.024026416098
Trimmed Mean ( 27 / 32 )122.8688095238100.487616236165766251.978503607579
Trimmed Mean ( 28 / 32 )122.84950.458784619318343267.771618374061
Trimmed Mean ( 29 / 32 )122.8213157894740.424166687197513289.559080183688
Trimmed Mean ( 30 / 32 )122.8233333333330.399244325878317307.639521396148
Trimmed Mean ( 31 / 32 )122.8388235294120.373488818376171328.895585317605
Trimmed Mean ( 32 / 32 )122.86218750.359861009900451341.415669160679
Median122.73
Midrange133.535
Midmean - Weighted Average at Xnp122.772448979592
Midmean - Weighted Average at X(n+1)p122.942291666667
Midmean - Empirical Distribution Function122.772448979592
Midmean - Empirical Distribution Function - Averaging122.942291666667
Midmean - Empirical Distribution Function - Interpolation122.942291666667
Midmean - Closest Observation122.772448979592
Midmean - True Basic - Statistics Graphics Toolkit122.942291666667
Midmean - MS Excel (old versions)122.9404
Number of observations96
 
Charts produced by software:
http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Aug/16/t1250431547jl40q25btj7xomm/1ny841250431524.png (open in new window)
http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Aug/16/t1250431547jl40q25btj7xomm/1ny841250431524.ps (open in new window)


http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Aug/16/t1250431547jl40q25btj7xomm/28fdx1250431524.png (open in new window)
http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Aug/16/t1250431547jl40q25btj7xomm/28fdx1250431524.ps (open in new window)


 
Parameters (Session):
par2 = grey ; par3 = FALSE ; par4 = Unknown ;
 
Parameters (R input):
par2 = grey ; par3 = FALSE ; par4 = Unknown ;
 
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('http://www.xycoon.com/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('http://www.xycoon.com/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('http://www.xycoon.com/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('http://www.xycoon.com/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('http://www.xycoon.com/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('http://www.xycoon.com/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('http://www.xycoon.com/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('http://www.xycoon.com/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('http://www.xycoon.com/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('http://www.xycoon.com/midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('http://www.xycoon.com/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('http://www.xycoon.com/midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('http://www.xycoon.com/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('http://www.xycoon.com/midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('http://www.xycoon.com/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('http://www.xycoon.com/midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('http://www.xycoon.com/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('http://www.xycoon.com/midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('http://www.xycoon.com/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('http://www.xycoon.com/midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('http://www.xycoon.com/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('http://www.xycoon.com/midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('http://www.xycoon.com/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('http://www.xycoon.com/midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('http://www.xycoon.com/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')
 




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