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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: Tue, 20 Oct 2009 08:30:10 -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/Oct/20/t12560490559kbnhxrkrxj5g28.htm/, Retrieved Tue, 20 Oct 2009 16:30:56 +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/Oct/20/t12560490559kbnhxrkrxj5g28.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:
KDGP1W51
 
Dataseries X:
» Textbox « » Textfile « » CSV «
8,55 8,56 8,57 8,59 8,61 8,62 8,62 8,63 8,71 8,72 8,74 8,75 8,79 8,82 8,82 8,84 8,86 8,86 8,85 8,86 8,86 8,87 8,88 8,9 8,91 8,96 8,98 8,99 9 9 9 9,01 9,01 8,99 8,99 8,99 9 9 9,02 9,05 9,05 9,05 9,06 9,06 9,08 9,07 9,06 9,08 9,07 9,11 9,15 9,15 9,17 9,2 9,23 9,26 9,27 9,28 9,29 9,29 9,11 9,06 9,11 9,13 9,13 9,19 9,2 9,23 9,24 9,28 9,32 9,32 9,32 9,36 9,37 9,38 9,41 9,44 9,44 9,44 9,47 9,48 9,56 9,58 9,56 9,58 9,7 9,74 9,76 9,78 9,84 9,88 9,96 9,97 9,96 9,96
 
Output produced by software:


Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'RServer@AstonUniversity' @ vre.aston.ac.uk
R Framework
error message
Warning: there are blank lines in the 'Data' field.
Please, use NA for missing data - blank lines are simply
 deleted and are NOT treated as missing values.


Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean9.146041666666670.0353877268243571258.452364348295
Geometric Mean9.1396214484026
Harmonic Mean9.13328310587145
Quadratic Mean9.15254313474312
Winsorized Mean ( 1 / 32 )9.146041666666670.0353440108721713258.7720363641
Winsorized Mean ( 2 / 32 )9.146250.0353079342258684259.042342763259
Winsorized Mean ( 3 / 32 )9.1468750.0352022080211086259.838104317638
Winsorized Mean ( 4 / 32 )9.1443750.0342823712114141266.736946041686
Winsorized Mean ( 5 / 32 )9.14281250.0337351991993812271.017000550799
Winsorized Mean ( 6 / 32 )9.13906250.0329430256858370277.420252382254
Winsorized Mean ( 7 / 32 )9.138333333333330.0325265298825256280.950146429324
Winsorized Mean ( 8 / 32 )9.143333333333330.0311531540272884293.496232366209
Winsorized Mean ( 9 / 32 )9.140520833333330.0302730156721696301.936250168045
Winsorized Mean ( 10 / 32 )9.130104166666670.0276742861489206329.912906065068
Winsorized Mean ( 11 / 32 )9.131250.0275056812313384331.976871367083
Winsorized Mean ( 12 / 32 )9.133750.0263700263457147346.368633851756
Winsorized Mean ( 13 / 32 )9.13781250.0258280426635266353.794231295122
Winsorized Mean ( 14 / 32 )9.126145833333330.0239120142450578381.655252451999
Winsorized Mean ( 15 / 32 )9.127708333333330.0232551065730765392.50339724957
Winsorized Mean ( 16 / 32 )9.1243750.0222780537218039409.567869524879
Winsorized Mean ( 17 / 32 )9.126145833333330.0220507636974734413.869830475713
Winsorized Mean ( 18 / 32 )9.126145833333330.0220507636974734413.869830475713
Winsorized Mean ( 19 / 32 )9.120208333333330.0211780148989106430.645099499031
Winsorized Mean ( 20 / 32 )9.113958333333330.0202963132761184449.045016666019
Winsorized Mean ( 21 / 32 )9.113958333333330.0197092234879276462.420974571417
Winsorized Mean ( 22 / 32 )9.113958333333330.0191000821888253477.168540073904
Winsorized Mean ( 23 / 32 )9.109166666666670.0172155240700319529.125144817609
Winsorized Mean ( 24 / 32 )9.111666666666670.01689860543054539.196367659997
Winsorized Mean ( 25 / 32 )9.12468750.0153411162968167594.786410809843
Winsorized Mean ( 26 / 32 )9.121979166666670.0136671104375426667.44021776609
Winsorized Mean ( 27 / 32 )9.124791666666670.0133639827280914682.789842842746
Winsorized Mean ( 28 / 32 )9.1218750.0129872681412193702.370575613881
Winsorized Mean ( 29 / 32 )9.1218750.0129872681412193702.370575613881
Winsorized Mean ( 30 / 32 )9.118750.0125893734777154724.321191689264
Winsorized Mean ( 31 / 32 )9.118750.0118379500507270770.298063509734
Winsorized Mean ( 32 / 32 )9.112083333333330.0110112747906235827.523016780275
Trimmed Mean ( 1 / 32 )9.14361702127660.0344684946494674265.27462583626
Trimmed Mean ( 2 / 32 )9.141086956521740.0334697046667031273.115255947138
Trimmed Mean ( 3 / 32 )9.138333333333330.0323469217363527282.510138300527
Trimmed Mean ( 4 / 32 )9.135227272727270.0310988149676317293.748404311721
Trimmed Mean ( 5 / 32 )9.132674418604650.0299869668080584304.554791321889
Trimmed Mean ( 6 / 32 )9.130357142857140.0288667415430657316.293306926788
Trimmed Mean ( 7 / 32 )9.128658536585370.0277830684366062328.569126819617
Trimmed Mean ( 8 / 32 )9.1270.0266228939263307342.82524000793
Trimmed Mean ( 9 / 32 )9.124487179487180.0255779986286926356.731866005014
Trimmed Mean ( 10 / 32 )9.122236842105260.0245454098929801371.647362251392
Trimmed Mean ( 11 / 32 )9.121216216216220.0238717670605977382.092209305760
Trimmed Mean ( 12 / 32 )9.120.0231092526639320394.647119603056
Trimmed Mean ( 13 / 32 )9.118428571428570.0224176761393792406.75173085452
Trimmed Mean ( 14 / 32 )9.116323529411770.0216878894400870420.341663701103
Trimmed Mean ( 15 / 32 )9.115303030303030.0211710975267721430.554108910800
Trimmed Mean ( 16 / 32 )9.11406250.0206608559779614441.127052515241
Trimmed Mean ( 17 / 32 )9.113064516129030.0202124997448970450.862814156857
Trimmed Mean ( 18 / 32 )9.111833333333330.0197018621200666462.485894876546
Trimmed Mean ( 19 / 32 )9.110517241379310.0190748238748252477.61999278029
Trimmed Mean ( 20 / 32 )9.109642857142860.0184671774218341493.288316295286
Trimmed Mean ( 21 / 32 )9.109259259259260.0178800488305016509.465010169311
Trimmed Mean ( 22 / 32 )9.108846153846150.0172565021434177527.850086775588
Trimmed Mean ( 23 / 32 )9.10840.0165895467456012549.044536277949
Trimmed Mean ( 24 / 32 )9.108333333333330.0161177332114993565.112551114504
Trimmed Mean ( 25 / 32 )9.108043478260870.0155716190651730584.913067815257
Trimmed Mean ( 26 / 32 )9.106590909090910.0151627644990452600.589088464991
Trimmed Mean ( 27 / 32 )9.10523809523810.0149573070145898608.748492382791
Trimmed Mean ( 28 / 32 )9.10350.0147132854669094618.726525796975
Trimmed Mean ( 29 / 32 )9.101842105263160.0144498704909753629.890912236738
Trimmed Mean ( 30 / 32 )9.10.0140633487398193647.07205718607
Trimmed Mean ( 31 / 32 )9.098235294117650.0136186316503414668.072646923345
Trimmed Mean ( 32 / 32 )9.096250.0131733938850857690.501633773994
Median9.075
Midrange9.26
Midmean - Weighted Average at Xnp9.1084
Midmean - Weighted Average at X(n+1)p9.11265306122449
Midmean - Empirical Distribution Function9.1084
Midmean - Empirical Distribution Function - Averaging9.11265306122449
Midmean - Empirical Distribution Function - Interpolation9.11265306122449
Midmean - Closest Observation9.1084
Midmean - True Basic - Statistics Graphics Toolkit9.11265306122449
Midmean - MS Excel (old versions)9.1084
Number of observations96
 
Charts produced by software:
http://www.freestatistics.org/blog/date/2009/Oct/20/t12560490559kbnhxrkrxj5g28/1x5tx1256049005.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Oct/20/t12560490559kbnhxrkrxj5g28/1x5tx1256049005.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Oct/20/t12560490559kbnhxrkrxj5g28/2yw8d1256049005.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Oct/20/t12560490559kbnhxrkrxj5g28/2yw8d1256049005.ps (open in new window)


 
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,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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