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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: Wed, 25 May 2011 18:15:14 +0000
 
Cite this page as follows:
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2011/May/25/t1306347102kpcxiavpqpw7utd.htm/, Retrieved Wed, 25 May 2011 20:11:45 +0200
 
Original text written by user:
 
IsPrivate?
No (this computation is public)
 
User-defined keywords:
KDGP1W52
 
Dataseries X:
» Textbox « » Textfile « » CSV «
505,7 55,7 735,7 575,9 545,8 905,8 765,8 945,7 15,7 645,7 155,9 416 825,8 725,9 925,9 556 116,1 876,3 336,2 186,1 286,1 26 915,8 405,7 965,7 395,6 425,8 545,6 65,6 445,6 895,5 175,4 715,4 865,5 57,4 145,4 315,3 635,4 5,2 515,2 515,1 955 955 634,9 205 275 425 84,9 534,7 4,8 704,7 684,7 884,6 994,6 294,7 524,7 914,5 564,4 984,5 934,4 514,6 474,5 784,4 504,5 824,4 414,6 964,7 64,6 244,7 344,7 34,7 685 425 484,8 785,1 704,9 245,4 285,6 218,8 706,1 856,2 456,6 606,8 527,3 657,8 948,2 486,6 238,9 289,4 969,5 589,5 189,7 639,8 9710,1 969,9 939,9 859,7 679,9 879,9 329,8 349,6 39,5 849,5 449,6 749,6 249,7 649,8 619,4 939 778,9
 
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'Herman Ole Andreas Wold' @ www.yougetit.org


Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean626.4387.88638455267947.1277252237463
Geometric Mean411.061295838867
Harmonic Mean129.61987255576
Quadratic Mean1111.00510943101
Winsorized Mean ( 1 / 36 )547.20181818181828.211149405190819.3966509596072
Winsorized Mean ( 2 / 36 )547.20909090909128.151345813922219.438114771709
Winsorized Mean ( 3 / 36 )547.09181818181828.047167115516319.5061346455612
Winsorized Mean ( 4 / 36 )547.39363636363627.991612239358219.5556308683771
Winsorized Mean ( 5 / 36 )547.43909090909127.931267364244419.5995077405576
Winsorized Mean ( 6 / 36 )548.26818181818227.778177300982819.7373706661014
Winsorized Mean ( 7 / 36 )547.75909090909127.676471651235519.7915073066996
Winsorized Mean ( 8 / 36 )548.28272727272727.591806445348619.8712153319398
Winsorized Mean ( 9 / 36 )547.80818181818227.503873747388619.9174918722202
Winsorized Mean ( 10 / 36 )549.33545454545527.194924052522320.1999260407754
Winsorized Mean ( 11 / 36 )551.87545454545526.638742008406320.7170238884141
Winsorized Mean ( 12 / 36 )554.97363636363626.156027302816421.2178107148511
Winsorized Mean ( 13 / 36 )555.67090909090925.905975312138921.4495266978246
Winsorized Mean ( 14 / 36 )557.07090909090925.41470952275221.919231797326
Winsorized Mean ( 15 / 36 )557.15272727272725.032765241342722.256938931883
Winsorized Mean ( 16 / 36 )557.48727272727324.936889017612422.3559270899242
Winsorized Mean ( 17 / 36 )558.50727272727324.444089894917622.8483561927744
Winsorized Mean ( 18 / 36 )559.0823.928392855640723.3647116784196
Winsorized Mean ( 19 / 36 )560.66909090909123.239505985307124.1256888706484
Winsorized Mean ( 20 / 36 )560.86909090909122.997000339093224.3887934356227
Winsorized Mean ( 21 / 36 )560.31545454545422.892889011292224.4755240052521
Winsorized Mean ( 22 / 36 )559.01545454545522.51275361597124.8310563905819
Winsorized Mean ( 23 / 36 )563.09272727272721.705313482562225.942621272211
Winsorized Mean ( 24 / 36 )564.64181818181821.329949865640926.471783653433
Winsorized Mean ( 25 / 36 )563.23272727272721.126162037874426.6604377199691
Winsorized Mean ( 26 / 36 )558.41090909090920.345824454164827.4459710565625
Winsorized Mean ( 27 / 36 )559.36818181818220.147074652843627.7642383053974
Winsorized Mean ( 28 / 36 )554.60818181818218.335281126779330.2481417101458
Winsorized Mean ( 29 / 36 )558.24636363636417.860706270633831.2555592806662
Winsorized Mean ( 30 / 36 )558.49181818181817.482610119778931.9455627252117
Winsorized Mean ( 31 / 36 )557.19545454545516.779626799789833.2066655113233
Winsorized Mean ( 32 / 36 )553.90818181818216.081819838795334.4431281640123
Winsorized Mean ( 33 / 36 )563.53818181818214.050749372707640.107339962437
Winsorized Mean ( 34 / 36 )563.63090909090913.371488953732542.1516938795045
Winsorized Mean ( 35 / 36 )563.12181818181812.696221314473344.3534973307277
Winsorized Mean ( 36 / 36 )560.53636363636412.314440605171845.5186217229349
Trimmed Mean ( 1 / 36 )548.07777777777827.982302216526519.5865863193372
Trimmed Mean ( 2 / 36 )548.9867924528327.723232286325619.802409285573
Trimmed Mean ( 3 / 36 )549.92692307692327.464605344589820.0231139744104
Trimmed Mean ( 4 / 36 )550.94607843137327.213015263139120.2456829242898
Trimmed Mean ( 5 / 36 )551.92326.944264802879220.4838767744378
Trimmed Mean ( 6 / 36 )552.92959183673526.654088343720320.7446446753826
Trimmed Mean ( 7 / 36 )552.92959183673526.359064306155420.9768292764328
Trimmed Mean ( 8 / 36 )554.83297872340426.042886966273321.3045880605302
Trimmed Mean ( 9 / 36 )555.81195652173925.697516469596621.629014507271
Trimmed Mean ( 10 / 36 )556.89888888888925.317388905845921.9966952737491
Trimmed Mean ( 11 / 36 )557.84431818181824.934981379372222.3719564773087
Trimmed Mean ( 12 / 36 )558.53837209302324.586866088329122.7169404220308
Trimmed Mean ( 13 / 36 )558.92738095238124.260580219466523.0385001469957
Trimmed Mean ( 14 / 36 )558.92738095238123.919373409571623.3671414121877
Trimmed Mean ( 15 / 36 )559.26341463414623.594520771214223.703105481865
Trimmed Mean ( 16 / 36 )559.69743589743623.269163914043124.0531820552287
Trimmed Mean ( 17 / 36 )559.89736842105322.900190221663324.4494636508039
Trimmed Mean ( 18 / 36 )560.01891891891922.536263070582724.8496796991126
Trimmed Mean ( 19 / 36 )560.09861111111122.178878832083925.2536936312972
Trimmed Mean ( 20 / 36 )560.05142857142921.850880727862225.6306112118082
Trimmed Mean ( 21 / 36 )559.98529411764721.491706984703626.0558779493974
Trimmed Mean ( 22 / 36 )559.95909090909121.074668559806626.5702442399042
Trimmed Mean ( 23 / 36 )560.032812520.628465323927427.1485446787167
Trimmed Mean ( 24 / 36 )559.79677419354820.209792193807427.6992840314844
Trimmed Mean ( 25 / 36 )559.42666666666719.755974976429428.3168341392471
Trimmed Mean ( 26 / 36 )559.13793103448319.232097343372729.0731645671064
Trimmed Mean ( 27 / 36 )559.19285714285718.716395315813629.8771663938082
Trimmed Mean ( 28 / 36 )559.19285714285718.10987630283330.8777844636841
Trimmed Mean ( 29 / 36 )559.1796296296317.670947404267931.6440096185547
Trimmed Mean ( 30 / 36 )559.52517.199632480648832.531218363504
Trimmed Mean ( 31 / 36 )559.62216.668126310196733.5743796024423
Trimmed Mean ( 32 / 36 )559.90217391304316.122603177784734.7277773780683
Trimmed Mean ( 33 / 36 )560.37045454545515.556118684826936.0225108781169
Trimmed Mean ( 34 / 36 )560.11904761904815.240198860314136.7527387767632
Trimmed Mean ( 35 / 36 )559.83514.949192393073637.4491802152061
Trimmed Mean ( 36 / 36 )559.56315789473714.688073669582538.0964291494219
Median545.7
Midrange4857.45
Midmean - Weighted Average at Xnp554.370909090909
Midmean - Weighted Average at X(n+1)p559.192857142857
Midmean - Empirical Distribution Function559.192857142857
Midmean - Empirical Distribution Function - Averaging559.192857142857
Midmean - Empirical Distribution Function - Interpolation559.17962962963
Midmean - Closest Observation559.192857142857
Midmean - True Basic - Statistics Graphics Toolkit559.192857142857
Midmean - MS Excel (old versions)559.192857142857
Number of observations110
 
Charts produced by software:
http://www.freestatistics.org/blog/date/2011/May/25/t1306347102kpcxiavpqpw7utd/1btif1306347312.png (open in new window)
http://www.freestatistics.org/blog/date/2011/May/25/t1306347102kpcxiavpqpw7utd/1btif1306347312.ps (open in new window)


http://www.freestatistics.org/blog/date/2011/May/25/t1306347102kpcxiavpqpw7utd/2sw661306347312.png (open in new window)
http://www.freestatistics.org/blog/date/2011/May/25/t1306347102kpcxiavpqpw7utd/2sw661306347312.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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