Central Tendency AG 2000-2006

*The author of this computation has been verified*

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

Title produced by software: Central Tendency

Date of computation: Thu, 11 Dec 2008 06:27:53 -0700

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2008/Dec/11/t1229002129omrqzwxegd1npp7.htm/, Retrieved Thu, 11 Dec 2008 13:28:51 +0000

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/2008/Dec/11/t1229002129omrqzwxegd1npp7.htm/}, year = {2008}, } @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 = {2008}, note = {{ISBN} 3-900051-07-0}, url = {http://www.R-project.org}, }

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)

Feedback Forum:

2008-11-27 13:41:43 [a2386b643d711541400692649981f2dc]  [reply]  test Post a new message

Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords:

Dataseries X:

» Textbox « » Textfile « » CSV «

9733 9259 9864 9215 10103 9380 9896 10117 9451 9700 9081 9084 9743 8587 9731 9563 9998 9437 10038 9918 9252 9737 9035 9133 9487 8700 9627 8947 9283 8829 9947 9628 9318 9605 8640 9214 9567 8547 9185 9470 9123 9278 10170 9434 9655 9429 8739 9552 9687 9019 9672 9206 9069 9788 10312 10105 9863 9656 9295 9946 9701 9049 10190 9706 9765 9893 9994 10433 10073 10112 9266 9820 10097 9115 10411 9678 10408 10153 10368 10581 10597 10680 9738 9556

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 1 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Central Tendency - Ungrouped Data Measure Value S.E. Value/S.E. Arithmetic Mean 9612.27380952381 53.2206093723043 180.611870530855 Geometric Mean 9599.99935251039 Harmonic Mean 9587.67819856305 Quadratic Mean 9624.49477894814 Winsorized Mean ( 1 / 28 ) 9611.7619047619 52.877236932476 181.775040875076 Winsorized Mean ( 2 / 28 ) 9612.64285714286 52.5039780556005 183.084086446998 Winsorized Mean ( 3 / 28 ) 9609.5 50.9309728834287 188.676937744628 Winsorized Mean ( 4 / 28 ) 9610.30952380952 50.3350534566155 190.926776944675 Winsorized Mean ( 5 / 28 ) 9615.4880952381 49.2258995205285 195.333923582812 Winsorized Mean ( 6 / 28 ) 9621.05952380952 47.1368089525606 204.109266995403 Winsorized Mean ( 7 / 28 ) 9622.39285714286 45.2632638828815 212.587251375437 Winsorized Mean ( 8 / 28 ) 9612.29761904762 43.0078805696858 223.500844303936 Winsorized Mean ( 9 / 28 ) 9611.65476190476 42.4234165183565 226.564844388377 Winsorized Mean ( 10 / 28 ) 9612.0119047619 41.7279715180727 230.349368902317 Winsorized Mean ( 11 / 28 ) 9608.86904761905 40.7597869861745 235.743848486704 Winsorized Mean ( 12 / 28 ) 9608.58333333333 40.585966249866 236.746447631145 Winsorized Mean ( 13 / 28 ) 9612.29761904762 39.6881806924768 242.195471078111 Winsorized Mean ( 14 / 28 ) 9613.29761904762 39.4378156378363 243.758369056949 Winsorized Mean ( 15 / 28 ) 9614.0119047619 39.0113790056717 246.441221761583 Winsorized Mean ( 16 / 28 ) 9619.34523809524 36.8926296151666 260.738942667853 Winsorized Mean ( 17 / 28 ) 9616.5119047619 35.2578994865567 272.747725894123 Winsorized Mean ( 18 / 28 ) 9609.65476190476 33.8058752920142 284.259900946118 Winsorized Mean ( 19 / 28 ) 9608.97619047619 33.6489972101737 285.565008979552 Winsorized Mean ( 20 / 28 ) 9606.59523809524 30.903019137447 310.862676406085 Winsorized Mean ( 21 / 28 ) 9608.09523809524 30.6286898747649 313.695926184926 Winsorized Mean ( 22 / 28 ) 9602.59523809524 29.4151107982345 326.4510986874 Winsorized Mean ( 23 / 28 ) 9599.85714285714 28.1921788960283 340.514905863114 Winsorized Mean ( 24 / 28 ) 9600.42857142857 27.887561543548 344.254859157799 Winsorized Mean ( 25 / 28 ) 9595.36904761905 26.3206145513738 364.557181174108 Winsorized Mean ( 26 / 28 ) 9602.17857142857 25.3113155862193 379.363077305095 Winsorized Mean ( 27 / 28 ) 9608.28571428571 20.9506603632970 458.614933738234 Winsorized Mean ( 28 / 28 ) 9613.95238095238 17.5509086969237 547.775191984076 Trimmed Mean ( 1 / 28 ) 9612.24390243902 51.2900090553668 187.409674505277 Trimmed Mean ( 2 / 28 ) 9612.75 49.4462804657614 194.407949585940 Trimmed Mean ( 3 / 28 ) 9612.8076923077 47.530133308514 202.246596488838 Trimmed Mean ( 4 / 28 ) 9614.02631578947 46.0018877327541 208.991995538134 Trimmed Mean ( 5 / 28 ) 9615.08108108108 44.4249728674649 216.434146392530 Trimmed Mean ( 6 / 28 ) 9614.98611111111 42.9147009124331 224.048773652888 Trimmed Mean ( 7 / 28 ) 9613.77142857143 41.7060757966452 230.512491164291 Trimmed Mean ( 8 / 28 ) 9612.25 40.7347270430223 235.971877014125 Trimmed Mean ( 9 / 28 ) 9612.24242424242 40.0839449028808 239.802805026598 Trimmed Mean ( 10 / 28 ) 9612.328125 39.4169564489467 243.862768487719 Trimmed Mean ( 11 / 28 ) 9612.37096774194 38.7433911995987 248.103500238810 Trimmed Mean ( 12 / 28 ) 9612.81666666667 38.1046543686915 252.274081104512 Trimmed Mean ( 13 / 28 ) 9613.3275862069 37.3466162411653 257.408262213876 Trimmed Mean ( 14 / 28 ) 9613.44642857143 36.5786638509219 262.815680412808 Trimmed Mean ( 15 / 28 ) 9613.46296296296 35.6669283573832 269.534367149195 Trimmed Mean ( 16 / 28 ) 9613.40384615385 34.6071603896917 277.786554513654 Trimmed Mean ( 17 / 28 ) 9612.78 33.6937260556057 285.298811539447 Trimmed Mean ( 18 / 28 ) 9612.39583333333 32.8541498018908 292.577829324322 Trimmed Mean ( 19 / 28 ) 9612.67391304348 32.0604961725301 299.829231004845 Trimmed Mean ( 20 / 28 ) 9613.04545454545 31.050510485695 309.593797466685 Trimmed Mean ( 21 / 28 ) 9613.69047619048 30.3123976218966 317.153746665222 Trimmed Mean ( 22 / 28 ) 9614.25 29.3737792981497 327.307218537099 Trimmed Mean ( 23 / 28 ) 9615.42105263158 28.3797062403021 338.813269285243 Trimmed Mean ( 24 / 28 ) 9617 27.309745920133 352.145348701697 Trimmed Mean ( 25 / 28 ) 9618.70588235294 25.8871997568474 371.562238198773 Trimmed Mean ( 26 / 28 ) 9621.15625 24.3205703031190 395.597476954155 Trimmed Mean ( 27 / 28 ) 9623.2 22.3925480215305 429.750111097105 Trimmed Mean ( 28 / 28 ) 9624.85714285714 21.1534901047794 455.000905060225 Median 9655.5 Midrange 9613.5 Midmean - Weighted Average at Xnp 9605.27906976744 Midmean - Weighted Average at X(n+1)p 9613.69047619048 Midmean - Empirical Distribution Function 9605.27906976744 Midmean - Empirical Distribution Function - Averaging 9613.69047619048 Midmean - Empirical Distribution Function - Interpolation 9613.69047619048 Midmean - Closest Observation 9605.27906976744 Midmean - True Basic - Statistics Graphics Toolkit 9613.69047619048 Midmean - MS Excel (old versions) 9613.04545454545 Number of observations 84

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/11/t1229002129omrqzwxegd1npp7/1832h1229002071.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/11/t1229002129omrqzwxegd1npp7/1832h1229002071.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/11/t1229002129omrqzwxegd1npp7/2xbwf1229002071.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/11/t1229002129omrqzwxegd1npp7/2xbwf1229002071.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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