Central Tendency prijsindex schroot en ijzererts

R Software Module: rwasp_centraltendency.wasp (opens new window with default values)

Title produced by software: Central Tendency

Date of computation: Mon, 21 Apr 2008 01:11:59 -0600

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2008/Apr/21/t1208761998ihaqdik2p4n86lv.htm/, Retrieved Mon, 21 Apr 2008 09:13:20 +0200

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Dataseries X:

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229,7 231,5 226,4 242,1 228,3 209,9 209,3 220,8 239,6 241,1 241,9 240,8 179,9 190,8 174,2 170 170,3 159,3 147,9 154,2 164,5 173,9 163,6 149,7 128,2 124,7 125,1 120,9 117,5 114 113,4 118,9 121,7 121,9 120,3 115,6 105,7 105,1 104,6 105 104,9 105,1 103,9 101,9 99 97 95,8 94,7 97,6 97,9 99,3 99,7 99,7 100 99,1 98,2 98,1 98,6 100,2 101,9 97,5 97,1 98,1 98,5 98,3 99,3 100,9 100,4 101,7 102 103,2 103,1

Text written by user:

Output produced by software:

Summary of compuational transaction Raw Input view raw input (R code) Raw Output view raw output of R engine Computing time 1 seconds R Server 'George Udny Yule' @ 72.249.76.132 Central Tendency - Ungrouped Data Measure Value S.E. Value/S.E. Arithmetic Mean 136.319444444444 5.76718892275694 23.6370693365943 Geometric Mean 129.096947736812 Harmonic Mean 123.353329622673 Quadratic Mean 144.722092876888 Winsorized Mean ( 1 / 24 ) 136.331944444444 5.76493902938063 23.6484624988465 Winsorized Mean ( 2 / 24 ) 136.343055555556 5.75597016944197 23.6872415147999 Winsorized Mean ( 3 / 24 ) 136.334722222222 5.75236875741567 23.7006228167250 Winsorized Mean ( 4 / 24 ) 136.290277777778 5.73325661856438 23.7718781567299 Winsorized Mean ( 5 / 24 ) 135.734722222222 5.59334683297088 24.267174247467 Winsorized Mean ( 6 / 24 ) 135.609722222222 5.5549725217343 24.4123119766368 Winsorized Mean ( 7 / 24 ) 135.493055555556 5.52076614854643 24.542437029547 Winsorized Mean ( 8 / 24 ) 135.281944444444 5.47101243101319 24.7270402234110 Winsorized Mean ( 9 / 24 ) 134.594444444444 5.30761363289484 25.3587494783480 Winsorized Mean ( 10 / 24 ) 133.094444444444 4.96800281712461 26.7903319188287 Winsorized Mean ( 11 / 24 ) 133.033333333333 4.94505688915029 26.9022857199511 Winsorized Mean ( 12 / 24 ) 129.966666666667 4.29933075186453 30.2295110954892 Winsorized Mean ( 13 / 24 ) 128.070833333333 3.91150415811507 32.7420931069775 Winsorized Mean ( 14 / 24 ) 126.981944444444 3.70649533835229 34.2593023470235 Winsorized Mean ( 15 / 24 ) 126.961111111111 3.69088436138999 34.3985610709563 Winsorized Mean ( 16 / 24 ) 126.161111111111 3.54914058430348 35.5469466802962 Winsorized Mean ( 17 / 24 ) 126.184722222222 3.52671098539419 35.7797173470732 Winsorized Mean ( 18 / 24 ) 124.809722222222 3.28945365064276 37.9423866324532 Winsorized Mean ( 19 / 24 ) 124.651388888889 3.24067398722143 38.4646494465077 Winsorized Mean ( 20 / 24 ) 123.5125 3.03432691351395 40.7050734876039 Winsorized Mean ( 21 / 24 ) 122.083333333333 2.78343875429378 43.8606141935063 Winsorized Mean ( 22 / 24 ) 120.861111111111 2.54508221637122 47.4880969792147 Winsorized Mean ( 23 / 24 ) 120.541666666667 2.42541943358154 49.6993076734223 Winsorized Mean ( 24 / 24 ) 114.041666666667 1.41907107474572 80.363604541162 Trimmed Mean ( 1 / 24 ) 135.402857142857 5.70218438091842 23.7457872453168 Trimmed Mean ( 2 / 24 ) 134.419117647059 5.62337021842681 23.9036578467821 Trimmed Mean ( 3 / 24 ) 133.369696969697 5.53053569137315 24.1151498538803 Trimmed Mean ( 4 / 24 ) 132.2578125 5.4162453154286 24.4187264050343 Trimmed Mean ( 5 / 24 ) 131.087096774194 5.28075263646833 24.8235631922843 Trimmed Mean ( 6 / 24 ) 129.971666666667 5.15815907448237 25.1972970957104 Trimmed Mean ( 7 / 24 ) 128.805172413793 5.01462255180253 25.6859157560111 Trimmed Mean ( 8 / 24 ) 127.576785714286 4.84190312956055 26.3484795751923 Trimmed Mean ( 9 / 24 ) 126.292592592593 4.63494900555335 27.2478925747134 Trimmed Mean ( 10 / 24 ) 125.015384615385 4.414341758063 28.3202777372273 Trimmed Mean ( 11 / 24 ) 123.852 4.22292986598892 29.3284529770414 Trimmed Mean ( 12 / 24 ) 122.6 3.97642989135368 30.8316764911612 Trimmed Mean ( 13 / 24 ) 121.639130434783 3.83236595009758 31.7399569922819 Trimmed Mean ( 14 / 24 ) 120.829545454545 3.74013512823215 32.3061978543161 Trimmed Mean ( 15 / 24 ) 120.076190476190 3.6643459177488 32.7687923497025 Trimmed Mean ( 16 / 24 ) 119.25 3.55957358437273 33.5012037743882 Trimmed Mean ( 17 / 24 ) 118.431578947368 3.45016565306875 34.3263457051778 Trimmed Mean ( 18 / 24 ) 117.519444444444 3.29699194178535 35.6444439414695 Trimmed Mean ( 19 / 24 ) 116.661764705882 3.15192840473163 37.0128219063452 Trimmed Mean ( 20 / 24 ) 115.715625 2.95074180590934 39.2157744090861 Trimmed Mean ( 21 / 24 ) 114.78 2.72717866086471 42.0874516389793 Trimmed Mean ( 22 / 24 ) 113.885714285714 2.49006339715363 45.73607018034 Trimmed Mean ( 23 / 24 ) 113.007692307692 2.22440258584307 50.8036148793009 Trimmed Mean ( 24 / 24 ) 112.025 1.82954070818294 61.2312147518491 Median 109.55 Midrange 168.4 Midmean - Weighted Average at Xnp 117.037837837838 Midmean - Weighted Average at X(n+1)p 117.037837837838 Midmean - Empirical Distribution Function 117.037837837838 Midmean - Empirical Distribution Function - Averaging 117.037837837838 Midmean - Empirical Distribution Function - Interpolation 117.037837837838 Midmean - Closest Observation 117.037837837838 Midmean - True Basic - Statistics Graphics Toolkit 117.037837837838 Midmean - MS Excel (old versions) 118.431578947368 Number of observations 72

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Apr/21/t1208761998ihaqdik2p4n86lv/1g91x1208761917.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Apr/21/t1208761998ihaqdik2p4n86lv/1g91x1208761917.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Apr/21/t1208761998ihaqdik2p4n86lv/2tdfk1208761917.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Apr/21/t1208761998ihaqdik2p4n86lv/2tdfk1208761917.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')

Copyright

This work is licensed under a Creative Commons Attribution-Noncommercial-Share Alike 3.0 License.

Software written by Ed van Stee & Patrick Wessa

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