*Unverified author*

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

Title produced by software: Central Tendency

Date of computation: Fri, 20 May 2011 02:26:04 +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/20/t1305858124wpxxb3tcomm1qnu.htm/, Retrieved Fri, 20 May 2011 04:22:04 +0200

Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords:

KDGP1W52

Dataseries X:

» Textbox « » Textfile « » CSV «

1,4442 1,3999 1,3649 1,336 1,322 1,3661 1,3898 1,3067 1,2894 1,277 1,2208 1,2565 1,3406 1,3569 1,3686 1,4272 1,4614 1,4914 1,4816 1,4562 1,4268 1,4088 1,4016 1,365 1,319 1,305 1,2785 1,3239 1,3449 1,2732 1,3322 1,4369 1,4975 1,577 1,5553 1,5557 1,575 1,5527 1,4748 1,4718 1,457 1,4684 1,4227 1,3896 1,3622 1,3716 1,3419 1,3511 1,3516 1,3242 1,3074 1,2999 1,3213 1,2881 1,2611 1,2727 1,2811 1,2684 1,265 1,277 1,2271 1,202 1,1938 1,2103 1,1856 1,1786 1,2015 1,2256 1,2292 1,2037 1,2165 1,2694 1,2938 1,3201 1,3014

Output produced by software:

Summary of computational transaction Raw Input view raw input (R code) Raw Output view raw output of R engine Computing time 2 seconds R Server 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 Central Tendency - Ungrouped Data Measure Value S.E. Value/S.E. Arithmetic Mean 1.346316 0.0116549772130982 115.514254158041 Geometric Mean 1.3426498485194 Harmonic Mean 1.33905131786118 Quadratic Mean 1.3500440068383 Winsorized Mean ( 1 / 25 ) 1.34638266666667 0.011630075545808 115.767319082632 Winsorized Mean ( 2 / 25 ) 1.34608666666667 0.0114579961981525 117.480111128306 Winsorized Mean ( 3 / 25 ) 1.34637866666667 0.011399926867686 118.104149464598 Winsorized Mean ( 4 / 25 ) 1.34626666666667 0.0113611537184308 118.497355113035 Winsorized Mean ( 5 / 25 ) 1.3427 0.0105203586415077 127.62872880611 Winsorized Mean ( 6 / 25 ) 1.34274 0.0103315046914372 129.965580048845 Winsorized Mean ( 7 / 25 ) 1.342404 0.0100579213441827 133.467339230727 Winsorized Mean ( 8 / 25 ) 1.34213733333333 0.00984706180595055 136.298254218561 Winsorized Mean ( 9 / 25 ) 1.34235333333333 0.00968691145068713 138.573924224126 Winsorized Mean ( 10 / 25 ) 1.3421 0.00957304323382887 140.195752512361 Winsorized Mean ( 11 / 25 ) 1.34138133333333 0.00934238711963345 143.580148858781 Winsorized Mean ( 12 / 25 ) 1.34504533333333 0.0085571617533662 157.183581671133 Winsorized Mean ( 13 / 25 ) 1.345704 0.00842273872987353 159.770360111859 Winsorized Mean ( 14 / 25 ) 1.344192 0.00793467808119852 169.407250835432 Winsorized Mean ( 15 / 25 ) 1.343412 0.00759766297875464 176.819109212476 Winsorized Mean ( 16 / 25 ) 1.341556 0.00723124981160503 185.52201001921 Winsorized Mean ( 17 / 25 ) 1.34221333333333 0.0071169090196513 188.594982685207 Winsorized Mean ( 18 / 25 ) 1.34134933333333 0.00694410823527277 193.163655848553 Winsorized Mean ( 19 / 25 ) 1.33879066666667 0.00627117965922827 213.483066889431 Winsorized Mean ( 20 / 25 ) 1.33687066666667 0.00598596459696816 223.334208716133 Winsorized Mean ( 21 / 25 ) 1.33681466666667 0.00585993441322745 228.127923010387 Winsorized Mean ( 22 / 25 ) 1.33461466666667 0.00533396618767792 250.210559967512 Winsorized Mean ( 23 / 25 ) 1.3367 0.00503977834490424 265.229918564087 Winsorized Mean ( 24 / 25 ) 1.331356 0.00420001983693298 316.988026649943 Winsorized Mean ( 25 / 25 ) 1.33182266666667 0.00387481290374633 343.712767493627 Trimmed Mean ( 1 / 25 ) 1.34545342465753 0.0113115016158733 118.945606900632 Trimmed Mean ( 2 / 25 ) 1.34447183098592 0.0109341582038194 122.960707712852 Trimmed Mean ( 3 / 25 ) 1.34359420289855 0.0105962474425546 126.799058834986 Trimmed Mean ( 4 / 25 ) 1.3425552238806 0.0102185246694688 131.384448079077 Trimmed Mean ( 5 / 25 ) 1.34148461538462 0.00977814459324419 137.192143416601 Trimmed Mean ( 6 / 25 ) 1.34119523809524 0.00952555659858838 140.799671306766 Trimmed Mean ( 7 / 25 ) 1.34087868852459 0.00927294911700292 144.601104956561 Trimmed Mean ( 8 / 25 ) 1.34060169491525 0.00903654328287997 148.353375062682 Trimmed Mean ( 9 / 25 ) 1.34034912280702 0.00879793035115095 152.348230698561 Trimmed Mean ( 10 / 25 ) 1.34004545454545 0.00854026818043889 156.909060258174 Trimmed Mean ( 11 / 25 ) 1.33975471698113 0.00824569226764483 162.479349640318 Trimmed Mean ( 12 / 25 ) 1.33953725490196 0.0079301380749962 168.917267547401 Trimmed Mean ( 13 / 25 ) 1.33883469387755 0.00770538538096708 173.753112619724 Trimmed Mean ( 14 / 25 ) 1.3379914893617 0.00744372960005996 179.747460110712 Trimmed Mean ( 15 / 25 ) 1.33725333333333 0.00721817193343343 185.262050511624 Trimmed Mean ( 16 / 25 ) 1.33653720930233 0.00699903807918207 190.960128260728 Trimmed Mean ( 17 / 25 ) 1.33596341463415 0.00679531021573107 196.60079852446 Trimmed Mean ( 18 / 25 ) 1.33525641025641 0.00654353199708845 204.057443419018 Trimmed Mean ( 19 / 25 ) 1.33457027027027 0.00624458908702877 213.716267262874 Trimmed Mean ( 20 / 25 ) 1.33409428571429 0.00601879959954207 221.654544839105 Trimmed Mean ( 21 / 25 ) 1.33377878787879 0.00578078183210973 230.72636653925 Trimmed Mean ( 22 / 25 ) 1.33342903225806 0.0054730290674437 243.636387789344 Trimmed Mean ( 23 / 25 ) 1.33328965517241 0.00519812950639088 256.494120343326 Trimmed Mean ( 24 / 25 ) 1.33287777777778 0.00488079360850394 273.086281594753 Trimmed Mean ( 25 / 25 ) 1.333068 0.004713900437359 282.795111546069 Median 1.3322 Midrange 1.3778 Midmean - Weighted Average at Xnp 1.33295526315789 Midmean - Weighted Average at X(n+1)p 1.33525641025641 Midmean - Empirical Distribution Function 1.33525641025641 Midmean - Empirical Distribution Function - Averaging 1.33525641025641 Midmean - Empirical Distribution Function - Interpolation 1.33457027027027 Midmean - Closest Observation 1.33295526315789 Midmean - True Basic - Statistics Graphics Toolkit 1.33525641025641 Midmean - MS Excel (old versions) 1.33525641025641 Number of observations 75

Charts produced by software:

http://www.freestatistics.org/blog/date/2011/May/20/t1305858124wpxxb3tcomm1qnu/1fdkg1305858361.png (open in new window) http://www.freestatistics.org/blog/date/2011/May/20/t1305858124wpxxb3tcomm1qnu/1fdkg1305858361.ps (open in new window) http://www.freestatistics.org/blog/date/2011/May/20/t1305858124wpxxb3tcomm1qnu/2aqpa1305858361.png (open in new window) http://www.freestatistics.org/blog/date/2011/May/20/t1305858124wpxxb3tcomm1qnu/2aqpa1305858361.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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