WS6 - Mini Tutorial - Hyp 1 - Central tend.

*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 Nov 2010 14:21:40 +0000

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2010/Nov/11/t1289485807jlmi129evn19ag3.htm/, Retrieved Thu, 11 Nov 2010 15:30:08 +0100

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/2010/Nov/11/t1289485807jlmi129evn19ag3.htm/}, year = {2010}, } @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 = {2010}, note = {{ISBN} 3-900051-07-0}, url = {http://www.R-project.org}, }

Original text written by user:

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Dataseries X:

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2,4 2,4 2,5 2,6 2,4 2,6 2,4 2,3 2,4 2,4 2,4 2,4 2,4 2,4 2,4 2,4 2,5 2,1 2,1 2 2 2 1,9 1,9 2 1,8 1,6 1,3 1,4 1,4 1,5 1,7 1,6 1,5 1,6 1,5 1,1 1,1 1,1 1,4 1,3 1,4 1,3 1,1 1 0,9 0,8 0,8 0,8 0,8 1 1,1 1 0,9 1,1 1,2 1,2 1,4 1,5 1,7 1,9 1,9 1,9 1,7 1,7 2,1 2 2 2,5 2,4 2,5 2,5 2 1,9 2,2 2,7 3,1 2,8 2,6 2,3 2,2 2,2 2 2 2,6 2,5 2,5 2,3 2 1,9 2 2,1 2,1 2,3 2,3 2,3 2,1 2,4 2,5 2,1 1,8 1,9 1,9 2,1 2,2 2 2,2 2 1,9 1,6 1,7 2 2,5 2,4 2,3 2,3 2,1 2,4 2,2 2,4 1,9 2,1 2,1 2,1 2 2,1 2,2 2,2 2,6 2,5 2,3 2,2 2,4 2,3 2,2 2,5 2,5 2,5 2,4 2,3 1,7 1,6 1,9 1,9 1,8 1,8 1,9 1,9 1,9 1,9 1,8 1,7 2,1 2,6 3,1 3,1 3,2 3,3 3,6 3,3 3,7 4 4 3,8 3,6 3,2 2,1 1,6 1,1 1,2 0,6 0,6 0 -0,1 -0,6 -0,2 -0,3 -0,1 0,5 0,9 1 0,9 1,4 1,5 1,6 1,4 1,7 1,6 1,8

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 1.93756613756614 0.0544236119733445 35.6015719521725 Geometric Mean NaN Harmonic Mean 0 Quadratic Mean 2.07629605090538 Winsorized Mean ( 1 / 63 ) 1.93915343915344 0.0540518200431706 35.8758213433823 Winsorized Mean ( 2 / 63 ) 1.93809523809524 0.0534116157286595 36.286025271003 Winsorized Mean ( 3 / 63 ) 1.93809523809524 0.0527915198214644 36.7122455396185 Winsorized Mean ( 4 / 63 ) 1.93597883597884 0.052424968742116 36.9285644308559 Winsorized Mean ( 5 / 63 ) 1.93862433862434 0.05188879876142 37.3611335181984 Winsorized Mean ( 6 / 63 ) 1.94497354497355 0.0474758939962496 40.9676023189198 Winsorized Mean ( 7 / 63 ) 1.94867724867725 0.046892686520259 41.5561016713206 Winsorized Mean ( 8 / 63 ) 1.94444444444444 0.0462626242515678 42.0305695126784 Winsorized Mean ( 9 / 63 ) 1.95396825396825 0.044873872240028 43.5435623544271 Winsorized Mean ( 10 / 63 ) 1.94867724867725 0.0441156901284145 44.1719769770104 Winsorized Mean ( 11 / 63 ) 1.94867724867725 0.0441156901284145 44.1719769770104 Winsorized Mean ( 12 / 63 ) 1.94867724867725 0.0441156901284145 44.1719769770104 Winsorized Mean ( 13 / 63 ) 1.93492063492063 0.0405583857932473 47.7070425037179 Winsorized Mean ( 14 / 63 ) 1.92751322751323 0.039755009064522 48.4847890333741 Winsorized Mean ( 15 / 63 ) 1.91957671957672 0.0389759601323913 49.2502740934774 Winsorized Mean ( 16 / 63 ) 1.91957671957672 0.0389759601323913 49.2502740934774 Winsorized Mean ( 17 / 63 ) 1.92857142857143 0.037761327901498 51.0726591395882 Winsorized Mean ( 18 / 63 ) 1.92857142857143 0.037761327901498 51.0726591395882 Winsorized Mean ( 19 / 63 ) 1.92857142857143 0.037761327901498 51.0726591395882 Winsorized Mean ( 20 / 63 ) 1.92857142857143 0.037761327901498 51.0726591395882 Winsorized Mean ( 21 / 63 ) 1.92857142857143 0.0353357173458449 54.5785277173157 Winsorized Mean ( 22 / 63 ) 1.92857142857143 0.0353357173458449 54.5785277173157 Winsorized Mean ( 23 / 63 ) 1.92857142857143 0.0353357173458449 54.5785277173157 Winsorized Mean ( 24 / 63 ) 1.92857142857143 0.0353357173458449 54.5785277173157 Winsorized Mean ( 25 / 63 ) 1.92857142857143 0.0353357173458449 54.5785277173157 Winsorized Mean ( 26 / 63 ) 1.92857142857143 0.0353357173458449 54.5785277173157 Winsorized Mean ( 27 / 63 ) 1.92857142857143 0.0353357173458449 54.5785277173157 Winsorized Mean ( 28 / 63 ) 1.94338624338624 0.0335371314714102 57.9473007416554 Winsorized Mean ( 29 / 63 ) 1.94338624338624 0.0335371314714102 57.9473007416554 Winsorized Mean ( 30 / 63 ) 1.94338624338624 0.0335371314714102 57.9473007416554 Winsorized Mean ( 31 / 63 ) 1.95978835978836 0.031659418789809 61.9022216674176 Winsorized Mean ( 32 / 63 ) 1.95978835978836 0.031659418789809 61.9022216674176 Winsorized Mean ( 33 / 63 ) 1.95978835978836 0.031659418789809 61.9022216674176 Winsorized Mean ( 34 / 63 ) 1.95978835978836 0.0281390179692699 69.6466508507372 Winsorized Mean ( 35 / 63 ) 1.95978835978836 0.0281390179692699 69.6466508507372 Winsorized Mean ( 36 / 63 ) 1.95978835978836 0.0281390179692699 69.6466508507372 Winsorized Mean ( 37 / 63 ) 1.95978835978836 0.0281390179692699 69.6466508507372 Winsorized Mean ( 38 / 63 ) 1.95978835978836 0.0281390179692699 69.6466508507372 Winsorized Mean ( 39 / 63 ) 1.95978835978836 0.0281390179692699 69.6466508507372 Winsorized Mean ( 40 / 63 ) 1.95978835978836 0.0281390179692699 69.6466508507372 Winsorized Mean ( 41 / 63 ) 1.98148148148148 0.0259162748798318 76.4570329134564 Winsorized Mean ( 42 / 63 ) 1.98148148148148 0.0259162748798318 76.4570329134564 Winsorized Mean ( 43 / 63 ) 1.98148148148148 0.0259162748798318 76.4570329134564 Winsorized Mean ( 44 / 63 ) 1.98148148148148 0.0259162748798318 76.4570329134564 Winsorized Mean ( 45 / 63 ) 1.98148148148148 0.0259162748798318 76.4570329134564 Winsorized Mean ( 46 / 63 ) 2.00582010582011 0.0235962403556472 85.0059194002089 Winsorized Mean ( 47 / 63 ) 2.00582010582011 0.0235962403556472 85.0059194002089 Winsorized Mean ( 48 / 63 ) 2.00582010582011 0.0235962403556472 85.0059194002089 Winsorized Mean ( 49 / 63 ) 2.00582010582011 0.0235962403556472 85.0059194002089 Winsorized Mean ( 50 / 63 ) 2.00582010582011 0.0235962403556472 85.0059194002089 Winsorized Mean ( 51 / 63 ) 2.00582010582011 0.0235962403556472 85.0059194002089 Winsorized Mean ( 52 / 63 ) 2.00582010582011 0.0235962403556472 85.0059194002089 Winsorized Mean ( 53 / 63 ) 1.97777777777778 0.0212113901957545 93.241308538732 Winsorized Mean ( 54 / 63 ) 2.00634920634921 0.0185997959062957 107.869420527894 Winsorized Mean ( 55 / 63 ) 2.00634920634921 0.0185997959062957 107.869420527894 Winsorized Mean ( 56 / 63 ) 2.00634920634921 0.0185997959062957 107.869420527894 Winsorized Mean ( 57 / 63 ) 2.00634920634921 0.0185997959062957 107.869420527894 Winsorized Mean ( 58 / 63 ) 2.00634920634921 0.0185997959062957 107.869420527894 Winsorized Mean ( 59 / 63 ) 2.00634920634921 0.0185997959062957 107.869420527894 Winsorized Mean ( 60 / 63 ) 2.00634920634921 0.0185997959062957 107.869420527894 Winsorized Mean ( 61 / 63 ) 2.00634920634921 0.0185997959062957 107.869420527894 Winsorized Mean ( 62 / 63 ) 2.03915343915344 0.0158356346203184 128.769922269932 Winsorized Mean ( 63 / 63 ) 2.03915343915344 0.0158356346203184 128.769922269932 Trimmed Mean ( 1 / 63 ) 1.94010695187166 0.0521376736094001 37.2112297607745 Trimmed Mean ( 2 / 63 ) 1.94108108108108 0.050055135224978 38.7788599982138 Trimmed Mean ( 3 / 63 ) 1.94262295081967 0.0481594028049829 40.3373554835417 Trimmed Mean ( 4 / 63 ) 1.94419889502762 0.046348033771595 41.947818209694 Trimmed Mean ( 5 / 63 ) 1.9463687150838 0.0444895654982997 43.7488811878414 Trimmed Mean ( 6 / 63 ) 1.94802259887006 0.0426031663907492 45.7248313658922 Trimmed Mean ( 7 / 63 ) 1.94857142857143 0.0415690388041182 46.8755469125349 Trimmed Mean ( 8 / 63 ) 1.9485549132948 0.0405683421658351 48.0314158594281 Trimmed Mean ( 9 / 63 ) 1.94912280701754 0.0396004157571708 49.2197561502772 Trimmed Mean ( 10 / 63 ) 1.94852071005917 0.0387816941424757 50.2433107460628 Trimmed Mean ( 11 / 63 ) 1.94850299401198 0.0380126032075595 51.2593937166735 Trimmed Mean ( 12 / 63 ) 1.94848484848485 0.0371828153789071 52.4028325620059 Trimmed Mean ( 13 / 63 ) 1.94846625766871 0.036285492938905 53.6982165558396 Trimmed Mean ( 14 / 63 ) 1.94968944099379 0.0357606369486181 54.5205456993161 Trimmed Mean ( 15 / 63 ) 1.95157232704403 0.0352846798850825 55.3093391636267 Trimmed Mean ( 16 / 63 ) 1.95414012738854 0.034852181329294 56.0693779515613 Trimmed Mean ( 17 / 63 ) 1.95677419354839 0.0343839109845673 56.9095875808502 Trimmed Mean ( 18 / 63 ) 1.95882352941176 0.034004206266715 57.6053301773187 Trimmed Mean ( 19 / 63 ) 1.96092715231788 0.0335924609161803 58.3740249697923 Trimmed Mean ( 20 / 63 ) 1.96308724832215 0.0331455818574697 59.226211709412 Trimmed Mean ( 21 / 63 ) 1.96530612244898 0.0326600495736815 60.1746215361744 Trimmed Mean ( 22 / 63 ) 1.96758620689655 0.0323546374686633 60.8131124572864 Trimmed Mean ( 23 / 63 ) 1.96993006993007 0.032021042356318 61.5198608467968 Trimmed Mean ( 24 / 63 ) 1.97234042553191 0.0316565021223894 62.3044333169379 Trimmed Mean ( 25 / 63 ) 1.97482014388489 0.0312578802522582 63.1783130509057 Trimmed Mean ( 26 / 63 ) 1.97737226277372 0.0308215946433831 64.1554171889102 Trimmed Mean ( 27 / 63 ) 1.98 0.0303435278916079 65.2527948323242 Trimmed Mean ( 28 / 63 ) 1.98270676691729 0.0298189126762873 66.4915850031645 Trimmed Mean ( 29 / 63 ) 1.98473282442748 0.0294094005216057 67.4863407354867 Trimmed Mean ( 30 / 63 ) 1.98682170542636 0.0289592537559634 68.6074897567837 Trimmed Mean ( 31 / 63 ) 1.98897637795276 0.0284637341199439 69.8775631324888 Trimmed Mean ( 32 / 63 ) 1.9904 0.028087972400093 70.8630716253982 Trimmed Mean ( 33 / 63 ) 1.99186991869919 0.0276734228803205 71.9777212711793 Trimmed Mean ( 34 / 63 ) 1.99338842975207 0.027215483793478 73.2446442943546 Trimmed Mean ( 35 / 63 ) 1.99495798319328 0.0270004705286351 73.8860450997526 Trimmed Mean ( 36 / 63 ) 1.9965811965812 0.0267596638779897 74.6115947376835 Trimmed Mean ( 37 / 63 ) 1.99826086956522 0.0264901463681907 75.434119607762 Trimmed Mean ( 38 / 63 ) 2 0.0261885606317835 76.3692219713945 Trimmed Mean ( 39 / 63 ) 2.0018018018018 0.0258510184472806 77.4360904149362 Trimmed Mean ( 40 / 63 ) 2.00366972477064 0.0254729842802595 78.6586174091663 Trimmed Mean ( 41 / 63 ) 2.00560747663551 0.0250491238653225 80.0669711012143 Trimmed Mean ( 42 / 63 ) 2.00666666666667 0.0247798610577524 80.979738425082 Trimmed Mean ( 43 / 63 ) 2.00776699029126 0.0244758228857851 82.030622613196 Trimmed Mean ( 44 / 63 ) 2.00891089108911 0.0241324320579519 83.2452728454757 Trimmed Mean ( 45 / 63 ) 2.01010101010101 0.023744280718126 84.656218226334 Trimmed Mean ( 46 / 63 ) 2.01134020618557 0.0233049174354859 86.3053993541699 Trimmed Mean ( 47 / 63 ) 2.01157894736842 0.0230323380382654 87.3371580438958 Trimmed Mean ( 48 / 63 ) 2.01182795698925 0.0227210178592639 88.5447988928443 Trimmed Mean ( 49 / 63 ) 2.01208791208791 0.0223653297032582 89.9645987241935 Trimmed Mean ( 50 / 63 ) 2.0123595505618 0.0219585123204563 91.6437107028923 Trimmed Mean ( 51 / 63 ) 2.01264367816092 0.021492344465551 93.6446780567325 Trimmed Mean ( 52 / 63 ) 2.01294117647059 0.0209566870453394 96.0524519985257 Trimmed Mean ( 53 / 63 ) 2.01325301204819 0.0203388200289133 98.9857331539483 Trimmed Mean ( 54 / 63 ) 2.01481481481481 0.0198847847341424 101.324446895085 Trimmed Mean ( 55 / 63 ) 2.01518987341772 0.0196602601193752 102.500671973905 Trimmed Mean ( 56 / 63 ) 2.01558441558442 0.0193948904089321 103.923475363189 Trimmed Mean ( 57 / 63 ) 2.016 0.0190816170202661 105.651423454252 Trimmed Mean ( 58 / 63 ) 2.01643835616438 0.0187117136891898 107.763425074707 Trimmed Mean ( 59 / 63 ) 2.0169014084507 0.0182742262776874 110.368634917984 Trimmed Mean ( 60 / 63 ) 2.01739130434783 0.0177551454712115 113.622910475099 Trimmed Mean ( 61 / 63 ) 2.01791044776119 0.0171361342473746 117.757623664179 Trimmed Mean ( 62 / 63 ) 2.01846153846154 0.0163924683239432 123.133471944145 Trimmed Mean ( 63 / 63 ) 2.01746031746032 0.0159266885699865 126.671674943289 Median 2 Midrange 1.7 Midmean - Weighted Average at Xnp 2.05412844036697 Midmean - Weighted Average at X(n+1)p 2.05412844036697 Midmean - Empirical Distribution Function 2.05412844036697 Midmean - Empirical Distribution Function - Averaging 2.05412844036697 Midmean - Empirical Distribution Function - Interpolation 2.05412844036697 Midmean - Closest Observation 2.05412844036697 Midmean - True Basic - Statistics Graphics Toolkit 2.05412844036697 Midmean - MS Excel (old versions) 2.05412844036697 Number of observations 189

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Nov/11/t1289485807jlmi129evn19ag3/1wufi1289485295.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/11/t1289485807jlmi129evn19ag3/1wufi1289485295.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/11/t1289485807jlmi129evn19ag3/2ole31289485295.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/11/t1289485807jlmi129evn19ag3/2ole31289485295.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')

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