Eigenmaten

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 02:45:25 -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/t1208767575u0x3de4qsj2zpss.htm/, Retrieved Mon, 21 Apr 2008 10:46:17 +0200

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Dataseries X:

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2434 2637 1831 1851 1839 2609 2417 2394 2372 2717 2998 2538 3007 2475 2175 2465 2279 2323 2746 2601 2486 2718 2646 2551 2712 2606 2365 3533 3509 2912 3599 2719 2869 4085 2686 2545 3071 3388 2652 3190 2884 3295 3818 3226 3953 3810 2877 3515 3708 3450 3360 4098 4374 3703 4257 3487 3659 3904 2957 3320 3420 3500 2791 2919 3179 3016 3492 3034 2612 3525 2846 3212 2591

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 'Gwilym Jenkins' @ 72.249.127.135 Central Tendency - Ungrouped Data Measure Value S.E. Value/S.E. Arithmetic Mean 3004.68493150685 67.9453398495627 44.2220899646613 Geometric Mean 2949.16068961325 Harmonic Mean 2893.28767625999 Quadratic Mean 3059.49742940698 Winsorized Mean ( 1 / 24 ) 3003.19178082192 67.487920046346 44.4996938527597 Winsorized Mean ( 2 / 24 ) 2999.16438356164 66.3454619762895 45.205267914684 Winsorized Mean ( 3 / 24 ) 3011.94520547945 63.3916034825544 47.5133146980317 Winsorized Mean ( 4 / 24 ) 3010.41095890411 60.7608338725117 49.545254188258 Winsorized Mean ( 5 / 24 ) 3010.06849315068 59.5558501573367 50.5419448332714 Winsorized Mean ( 6 / 24 ) 3006.45205479452 57.5827246929616 52.2110072217893 Winsorized Mean ( 7 / 24 ) 3006.35616438356 57.3294617794683 52.439985847909 Winsorized Mean ( 8 / 24 ) 2997.58904109589 54.864881195449 54.6358431073125 Winsorized Mean ( 9 / 24 ) 2999.80821917808 54.3261251680448 55.2185198171027 Winsorized Mean ( 10 / 24 ) 2996.10958904110 52.9144277800694 56.6217894577631 Winsorized Mean ( 11 / 24 ) 2991.7397260274 50.6931971642709 59.0165918384017 Winsorized Mean ( 12 / 24 ) 2982.53424657534 48.7004600653347 61.2424244570603 Winsorized Mean ( 13 / 24 ) 2983.06849315068 48.1953049146597 61.8954169588274 Winsorized Mean ( 14 / 24 ) 2991.12328767123 46.5057931008075 64.3172191728367 Winsorized Mean ( 15 / 24 ) 2991.32876712329 46.1192536928464 64.8607366252172 Winsorized Mean ( 16 / 24 ) 2990.67123287671 45.6362347973837 65.5328215869414 Winsorized Mean ( 17 / 24 ) 2998.12328767123 44.1265560313317 67.9437408517094 Winsorized Mean ( 18 / 24 ) 2999.35616438356 43.6206507946289 68.7600049459344 Winsorized Mean ( 19 / 24 ) 2991.02739726027 41.9760657532333 71.2555439293375 Winsorized Mean ( 20 / 24 ) 2983.6301369863 40.6338548801813 73.4271987185132 Winsorized Mean ( 21 / 24 ) 2975.28767123288 39.1625689076249 75.9727401501896 Winsorized Mean ( 22 / 24 ) 2974.38356164384 36.9705734218295 80.452730005199 Winsorized Mean ( 23 / 24 ) 2964.61643835616 34.803512557693 85.1815296930672 Winsorized Mean ( 24 / 24 ) 2958.3698630137 33.3940799607757 88.5896502161032 Trimmed Mean ( 1 / 24 ) 3001.92957746479 65.020641588444 46.1688704406496 Trimmed Mean ( 2 / 24 ) 3000.59420289855 62.0821215848625 48.3326620659527 Trimmed Mean ( 3 / 24 ) 3001.37313432836 59.3153148379044 50.6003068942725 Trimmed Mean ( 4 / 24 ) 2997.41538461538 57.3865808335304 52.2319911916416 Trimmed Mean ( 5 / 24 ) 2993.65079365079 56.0466631289545 53.4135419759581 Trimmed Mean ( 6 / 24 ) 2989.72131147541 54.7976612477458 54.5592867177046 Trimmed Mean ( 7 / 24 ) 2986.27118644068 53.822781208666 55.4834053421204 Trimmed Mean ( 8 / 24 ) 2982.59649122807 52.6745092249175 56.6231472322321 Trimmed Mean ( 9 / 24 ) 2980.10909090909 51.846507940988 57.4794563657222 Trimmed Mean ( 10 / 24 ) 2977.09433962264 50.9111270964271 58.4762999645233 Trimmed Mean ( 11 / 24 ) 2974.37254901961 50.0316367424148 59.4498349980634 Trimmed Mean ( 12 / 24 ) 2972.02040816327 49.3718148012126 60.1967017037881 Trimmed Mean ( 13 / 24 ) 2970.65957446808 48.9074176481813 60.7404708185109 Trimmed Mean ( 14 / 24 ) 2969.11111111111 48.3519736492733 61.4062030362588 Trimmed Mean ( 15 / 24 ) 2966.44186046512 47.9069708307794 61.9208814296233 Trimmed Mean ( 16 / 24 ) 2963.48780487805 47.3220043947899 62.623885923233 Trimmed Mean ( 17 / 24 ) 2960.30769230769 46.5705413574879 63.5661000713644 Trimmed Mean ( 18 / 24 ) 2955.91891891892 45.802706858035 64.5359002052162 Trimmed Mean ( 19 / 24 ) 2950.88571428571 44.7728678987615 65.9079003149436 Trimmed Mean ( 20 / 24 ) 2946.21212121212 43.7007679179755 67.4178569754664 Trimmed Mean ( 21 / 24 ) 2941.80645161290 42.4759873809768 69.25810635612 Trimmed Mean ( 22 / 24 ) 2937.79310344828 41.0692488398776 71.5326719244918 Trimmed Mean ( 23 / 24 ) 2933.29629629630 39.590237897673 74.0914036404087 Trimmed Mean ( 24 / 24 ) 2929.32 38.0313782728595 77.0237665062604 Median 2912 Midrange 3102.5 Midmean - Weighted Average at Xnp 2941.16666666667 Midmean - Weighted Average at X(n+1)p 2955.91891891892 Midmean - Empirical Distribution Function 2955.91891891892 Midmean - Empirical Distribution Function - Averaging 2955.91891891892 Midmean - Empirical Distribution Function - Interpolation 2955.91891891892 Midmean - Closest Observation 2946.31578947368 Midmean - True Basic - Statistics Graphics Toolkit 2955.91891891892 Midmean - MS Excel (old versions) 2955.91891891892 Number of observations 73

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Apr/21/t1208767575u0x3de4qsj2zpss/10vkx1208767523.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Apr/21/t1208767575u0x3de4qsj2zpss/10vkx1208767523.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Apr/21/t1208767575u0x3de4qsj2zpss/2wos61208767523.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Apr/21/t1208767575u0x3de4qsj2zpss/2wos61208767523.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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