*Unverified author*

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

Title produced by software: Central Tendency

Date of computation: Sun, 03 Apr 2011 11:32:44 +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/Apr/03/t1301830169dfp083opilg9ftd.htm/, Retrieved Sun, 03 Apr 2011 13:29:30 +0200

Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords:

KDGP1W52

Dataseries X:

» Textbox « » Textfile « » CSV «

814 1150 1225 1691 1759 1754 2100 2062 2012 1897 1964 2186 966 1549 1538 1612 2078 2137 2907 2249 1883 1739 1828 1868 1138 1430 1809 1763 2200 2067 2503 2141 2103 1972 2181 2344 970 1199 1718 1683 2025 2051 2439 2353 2230 1852 2147 2286 1007 1665 1642 1518 1831 2207 2822 2393 2306 1785 2047 2171 1212 1335 2011 1860 1954 2152 2835 2224 2182 1992 2389 2724 891 1247 2017 2257 2255 2255 3057 3330 1896 2096 2374 2535 1041 1728 2201 2455 2204 2660 3670 2665 2639 2226 2586 2684 1185 1749 2459 2618 2585 3310 3923

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 'RServer@AstonUniversity' @ vre.aston.ac.uk Central Tendency - Ungrouped Data Measure Value S.E. Value/S.E. Arithmetic Mean 2044.99029126214 56.2231800310618 36.3727254511811 Geometric Mean 1961.14084298547 Harmonic Mean 1868.80974441796 Quadratic Mean 2122.36000258734 Winsorized Mean ( 1 / 34 ) 2043.28155339806 55.3098508038175 36.94245281271 Winsorized Mean ( 2 / 34 ) 2038.1359223301 53.2777189246834 38.254939653316 Winsorized Mean ( 3 / 34 ) 2037.66990291262 53.1171071127532 38.3618388438813 Winsorized Mean ( 4 / 34 ) 2029.28155339806 50.6994207230752 40.0257345045849 Winsorized Mean ( 5 / 34 ) 2023.65048543689 49.0057353736504 41.2941560820854 Winsorized Mean ( 6 / 34 ) 2025.1067961165 47.2054896683625 42.8998154736598 Winsorized Mean ( 7 / 34 ) 2025.03883495146 46.9078993637166 43.1705291095988 Winsorized Mean ( 8 / 34 ) 2020.14563106796 45.1970712957753 44.6963834857324 Winsorized Mean ( 9 / 34 ) 2017.87378640777 44.4521587592058 45.3942810143023 Winsorized Mean ( 10 / 34 ) 2017.29126213592 43.9560759573361 45.8933428018896 Winsorized Mean ( 11 / 34 ) 2018.14563106796 43.6305954712722 46.2552850647379 Winsorized Mean ( 12 / 34 ) 2018.26213592233 42.8256084113402 47.1274597324318 Winsorized Mean ( 13 / 34 ) 2026.71844660194 40.5368232724218 49.9969727026136 Winsorized Mean ( 14 / 34 ) 2035.28155339806 37.8198848841082 53.8151176196011 Winsorized Mean ( 15 / 34 ) 2047.95145631068 35.8630328499051 57.1048038486265 Winsorized Mean ( 16 / 34 ) 2043.29126213592 34.2970573960032 59.5762848848378 Winsorized Mean ( 17 / 34 ) 2039.82524271845 33.3033648660319 61.24982418215 Winsorized Mean ( 18 / 34 ) 2043.14563106796 30.7137115697047 66.5222640523612 Winsorized Mean ( 19 / 34 ) 2047.94174757282 29.8657533945145 68.5715749581247 Winsorized Mean ( 20 / 34 ) 2049.30097087379 28.8633778546874 71.0000396069714 Winsorized Mean ( 21 / 34 ) 2043.59223300971 27.1723158577885 75.2086146688872 Winsorized Mean ( 22 / 34 ) 2044.44660194175 26.8432524023192 76.1624028005306 Winsorized Mean ( 23 / 34 ) 2047.12621359223 25.6547338377736 79.795262213092 Winsorized Mean ( 24 / 34 ) 2044.56310679612 24.7575783754691 82.5833236105982 Winsorized Mean ( 25 / 34 ) 2045.04854368932 24.1584865547056 84.6513517748066 Winsorized Mean ( 26 / 34 ) 2037.98058252427 22.7065638358219 89.752927711112 Winsorized Mean ( 27 / 34 ) 2034.04854368932 21.9442485295294 92.691647241973 Winsorized Mean ( 28 / 34 ) 2027.52427184466 20.9052818672372 96.9862202634157 Winsorized Mean ( 29 / 34 ) 2028.08737864078 20.703127200491 97.9604365563034 Winsorized Mean ( 30 / 34 ) 2034.49514563107 19.9071032811969 102.199456992456 Winsorized Mean ( 31 / 34 ) 2039.91262135922 18.832586287134 108.318241066701 Winsorized Mean ( 32 / 34 ) 2039.91262135922 17.4910931988241 116.625793377875 Winsorized Mean ( 33 / 34 ) 2039.59223300971 17.2408081817691 118.300268265059 Winsorized Mean ( 34 / 34 ) 2045.8640776699 16.3564837580052 125.079699765459 Trimmed Mean ( 1 / 34 ) 2044.99029126214 52.8059651358261 38.7265015609896 Trimmed Mean ( 2 / 34 ) 2038.58415841584 49.9254390563072 40.8325734725472 Trimmed Mean ( 3 / 34 ) 2031.34020618557 47.8957982794526 42.4116577895522 Trimmed Mean ( 4 / 34 ) 2031.34020618557 45.6382959572009 44.5095541711404 Trimmed Mean ( 5 / 34 ) 2028.98924731183 43.9125248623952 46.2052513188411 Trimmed Mean ( 6 / 34 ) 2030.1978021978 42.4400179173554 47.836874295182 Trimmed Mean ( 7 / 34 ) 2031.1797752809 41.220605219196 49.2758358223959 Trimmed Mean ( 8 / 34 ) 2031.1797752809 39.8903918776262 50.9190228441989 Trimmed Mean ( 9 / 34 ) 2034.04705882353 38.7281298394772 52.5211794954824 Trimmed Mean ( 10 / 34 ) 2036.27710843373 37.5351781840523 54.2498319429557 Trimmed Mean ( 11 / 34 ) 2038.69135802469 36.2469779156424 56.2444505792824 Trimmed Mean ( 12 / 34 ) 2041.12658227848 34.8062722483309 58.6424931608803 Trimmed Mean ( 13 / 34 ) 2043.67532467532 33.2674103044682 61.4317527565659 Trimmed Mean ( 14 / 34 ) 2045.46666666667 31.8900664210085 64.1411855235007 Trimmed Mean ( 15 / 34 ) 2045.46666666667 30.760175602189 66.4972363331082 Trimmed Mean ( 16 / 34 ) 2046.49315068493 29.7672736899808 68.7497676810674 Trimmed Mean ( 17 / 34 ) 2046.63768115942 28.8552031667263 70.9278555182538 Trimmed Mean ( 18 / 34 ) 2047.25373134328 27.9348384321203 73.2867575489282 Trimmed Mean ( 19 / 34 ) 2047.61538461538 27.2618242898282 75.1092576507941 Trimmed Mean ( 20 / 34 ) 2047.5873015873 26.5880911759622 77.0114442603721 Trimmed Mean ( 21 / 34 ) 2047.44262295082 25.9343277857658 78.9472023282813 Trimmed Mean ( 22 / 34 ) 2047.76271186441 25.409807020151 80.5894633611522 Trimmed Mean ( 23 / 34 ) 2048.0350877193 24.815837534759 82.5293558942212 Trimmed Mean ( 24 / 34 ) 2048.10909090909 24.277709674138 84.3617095022293 Trimmed Mean ( 25 / 34 ) 2048.39622641509 23.7542042665237 86.2329970489415 Trimmed Mean ( 26 / 34 ) 2048.66666666667 23.1956328997705 88.3212230301738 Trimmed Mean ( 27 / 34 ) 2049.5306122449 22.7372058297908 90.1399506864453 Trimmed Mean ( 28 / 34 ) 2050.78723404255 22.2737143250443 92.0720812036577 Trimmed Mean ( 29 / 34 ) 2052.68888888889 21.8440483127353 93.9701679606775 Trimmed Mean ( 30 / 34 ) 2052.68888888889 21.3050752141298 96.3474133866243 Trimmed Mean ( 31 / 34 ) 2054.72093023256 20.7595988849871 98.9769090248893 Trimmed Mean ( 32 / 34 ) 2056.41463414634 20.2613781297763 101.494312034196 Trimmed Mean ( 33 / 34 ) 2059.37837837838 19.8689910118974 103.647858975085 Trimmed Mean ( 34 / 34 ) 2061.14285714286 19.3554605613356 106.48895956835 Median 2067 Midrange 2368.5 Midmean - Weighted Average at Xnp 2042.71153846154 Midmean - Weighted Average at X(n+1)p 2048.39622641509 Midmean - Empirical Distribution Function 2048.39622641509 Midmean - Empirical Distribution Function - Averaging 2048.39622641509 Midmean - Empirical Distribution Function - Interpolation 2048.66666666667 Midmean - Closest Observation 2042.71153846154 Midmean - True Basic - Statistics Graphics Toolkit 2048.39622641509 Midmean - MS Excel (old versions) 2048.39622641509 Number of observations 103

Charts produced by software:

http://www.freestatistics.org/blog/date/2011/Apr/03/t1301830169dfp083opilg9ftd/1y0k21301830360.png (open in new window) http://www.freestatistics.org/blog/date/2011/Apr/03/t1301830169dfp083opilg9ftd/1y0k21301830360.ps (open in new window) http://www.freestatistics.org/blog/date/2011/Apr/03/t1301830169dfp083opilg9ftd/2e1q51301830360.png (open in new window) http://www.freestatistics.org/blog/date/2011/Apr/03/t1301830169dfp083opilg9ftd/2e1q51301830360.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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