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Centrummaten Bloemen en planten

*Unverified author*
R Software Module: /rwasp_centraltendency.wasp (opens new window with default values)
Title produced by software: Central Tendency
Date of computation: Thu, 17 Dec 2009 05:33:45 -0700
 
Cite this page as follows:
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2009/Dec/17/t12610532959y6keu7oe30vklm.htm/, Retrieved Thu, 17 Dec 2009 13:34:57 +0100
 
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/Dec/17/t12610532959y6keu7oe30vklm.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:
KDGP1W52
 
Dataseries X:
» Textbox « » Textfile « » CSV «
75,9 76,9 77,9 78,9 79,9 80,9 81,9 82,9 83,9 84,9 85,9 86,9 87,9 88,9 89,9 90,9 91,9 92,9 93,9 94,9 95,9 96,9 97,9 98,9 99,9 100,9 101,9 102,9 103,9 104,9 105,9 106,9 107,9 108,9 109,9 110,9 111,9 112,9 113,9 114,9 115,9 116,9 117,9 118,9 119,9 120,9 121,9 122,9 123,9 124,9 125,9 126,9 127,9 128,9 129,9 130,9 131,9 132,9 133,9 134,9 135,9 136,9 137,9 138,9 139,9 140,9 141,9 142,9 143,9 144,9 145,9 146,9 147,9 148,9 149,9 150,9 151,9 152,9 153,9 154,9 155,9 156,9 157,9 158,9 159,9 160,9 161,9 162,9 163,9 164,9 165,9 166,9 167,9 168,9 169,9 170,9 171,9 172,9 173,9 174,9 175,9 176,9 177,9 178,9 179,9 180,9 181,9 182,9
 
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'Gwilym Jenkins' @ 72.249.127.135


Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean129.43.0138568866708542.9350181066285
Geometric Mean125.490509098969
Harmonic Mean121.504469041309
Quadratic Mean133.102504359109
Winsorized Mean ( 1 / 36 )129.43.0108118315632642.9784414434207
Winsorized Mean ( 2 / 36 )129.43.0048276605561743.0640338208445
Winsorized Mean ( 3 / 36 )129.42.9960022977437543.1908881036071
Winsorized Mean ( 4 / 36 )129.42.98442652137343.3584137767509
Winsorized Mean ( 5 / 36 )129.42.9701847132587143.5663140485394
Winsorized Mean ( 6 / 36 )129.42.9533555081221643.8145694428358
Winsorized Mean ( 7 / 36 )129.42.9340123588662544.1034270387334
Winsorized Mean ( 8 / 36 )129.42.9122240308422644.4333947627564
Winsorized Mean ( 9 / 36 )129.42.8880550358203544.8052403417042
Winsorized Mean ( 10 / 36 )129.42.8615660145071845.2199946966051
Winsorized Mean ( 11 / 36 )129.42.8328140749521145.6789597115326
Winsorized Mean ( 12 / 36 )129.42.8018530929701446.1837204543896
Winsorized Mean ( 13 / 36 )129.42.7687339797220146.7361620681927
Winsorized Mean ( 14 / 36 )129.42.7335049207849847.3384916983578
Winsorized Mean ( 15 / 36 )129.42.6962115903833847.9932659816214
Winsorized Mean ( 16 / 36 )129.42.6568973438993448.7034248037934
Winsorized Mean ( 17 / 36 )129.42.6156033913280749.4723322461734
Winsorized Mean ( 18 / 36 )129.42.5723689539617650.3038258958569
Winsorized Mean ( 19 / 36 )129.42.5272314062673051.2022760080853
Winsorized Mean ( 20 / 36 )129.42.4802264046545152.1726563982876
Winsorized Mean ( 21 / 36 )129.42.4313880046050553.2206294326188
Winsorized Mean ( 22 / 36 )129.42.3807487674397054.3526481121145
Winsorized Mean ( 23 / 36 )129.42.3283398578378555.5760790523784
Winsorized Mean ( 24 / 36 )129.42.2741911330835456.8993512100053
Winsorized Mean ( 25 / 36 )129.42.2183312248917858.3321365844781
Winsorized Mean ( 26 / 36 )129.42.1607876145666959.8855709499932
Winsorized Mean ( 27 / 36 )129.42.1015867021530861.5725251151567
Winsorized Mean ( 28 / 36 )129.42.04075387016763.4079405124004
Winsorized Mean ( 29 / 36 )129.41.9783135424233765.4092474348073
Winsorized Mean ( 30 / 36 )129.41.9142892384211667.5968904817773
Winsorized Mean ( 31 / 36 )129.41.8487036236957669.994994514759
Winsorized Mean ( 32 / 36 )129.41.7815785565037972.6322168212092
Winsorized Mean ( 33 / 36 )129.41.7129351311669775.5428490230354
Winsorized Mean ( 34 / 36 )129.41.6427937183674878.7682583353136
Winsorized Mean ( 35 / 36 )129.41.5711740026569782.3587965312403
Winsorized Mean ( 36 / 36 )129.41.4980950174153186.3763636456494
Trimmed Mean ( 1 / 36 )129.42.9860788111948243.334422224517
Trimmed Mean ( 2 / 36 )129.42.9580398915498143.745184224748
Trimmed Mean ( 3 / 36 )129.42.9297326385411644.1678528264729
Trimmed Mean ( 4 / 36 )129.42.901149197588244.6030145942075
Trimmed Mean ( 5 / 36 )129.42.8722813232690145.0512973613346
Trimmed Mean ( 6 / 36 )129.42.8431203515386645.5133740398890
Trimmed Mean ( 7 / 36 )129.42.8136571693556945.9899668692159
Trimmed Mean ( 8 / 36 )129.42.7838821814150146.4818521645293
Trimmed Mean ( 9 / 36 )129.42.7537852736430546.9898656364058
Trimmed Mean ( 10 / 36 )129.42.7233557730613647.5149083641538
Trimmed Mean ( 11 / 36 )129.42.6925824035672548.057953520221
Trimmed Mean ( 12 / 36 )129.42.6614532371118948.620053959851
Trimmed Mean ( 13 / 36 )129.42.6299556396765849.2023508107205
Trimmed Mean ( 14 / 36 )129.42.5980762113533249.8060832220917
Trimmed Mean ( 15 / 36 )129.42.5658007197234450.432599463121
Trimmed Mean ( 16 / 36 )129.42.5331140255951151.0833695966765
Trimmed Mean ( 17 / 36 )129.42.551.76
Trimmed Mean ( 18 / 36 )129.42.4664414311581252.4642500589361
Trimmed Mean ( 19 / 36 )129.42.4324199198877453.1980514310096
Trimmed Mean ( 20 / 36 )129.42.3979157616563653.963530357971
Trimmed Mean ( 21 / 36 )129.42.3629078131263054.7630336152616
Trimmed Mean ( 22 / 36 )129.42.3273733406281655.5991588204216
Trimmed Mean ( 23 / 36 )129.42.2912878474779256.4747899930748
Trimmed Mean ( 24 / 36 )129.42.2546248764114557.3931394769130
Trimmed Mean ( 25 / 36 )129.42.2173557826083558.3577976141396
Trimmed Mean ( 26 / 36 )129.42.1794494717703459.3727919257014
Trimmed Mean ( 27 / 36 )129.42.1408720964441960.4426580247006
Trimmed Mean ( 28 / 36 )129.42.1015867021530861.5725251151567
Trimmed Mean ( 29 / 36 )129.42.0615528128088362.768219759403
Trimmed Mean ( 30 / 36 )129.42.0207259421636964.0363927141179
Trimmed Mean ( 31 / 36 )129.41.9790570145063265.3846751516045
Trimmed Mean ( 32 / 36 )129.41.9364916731037166.8218726665653
Trimmed Mean ( 33 / 36 )129.41.8929694486000968.3582083671214
Trimmed Mean ( 34 / 36 )129.41.8484227510682470.0056304355795
Trimmed Mean ( 35 / 36 )129.41.8027756377319971.7782053915446
Trimmed Mean ( 36 / 36 )129.41.7559422921421273.692626790224
Median129.4
Midrange129.4
Midmean - Weighted Average at Xnp128.9
Midmean - Weighted Average at X(n+1)p129.4
Midmean - Empirical Distribution Function128.9
Midmean - Empirical Distribution Function - Averaging129.4
Midmean - Empirical Distribution Function - Interpolation129.4
Midmean - Closest Observation128.9
Midmean - True Basic - Statistics Graphics Toolkit129.4
Midmean - MS Excel (old versions)129.4
Number of observations108
 
Charts produced by software:
http://www.freestatistics.org/blog/date/2009/Dec/17/t12610532959y6keu7oe30vklm/1jt7w1261053223.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Dec/17/t12610532959y6keu7oe30vklm/1jt7w1261053223.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Dec/17/t12610532959y6keu7oe30vklm/2og151261053223.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Dec/17/t12610532959y6keu7oe30vklm/2og151261053223.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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