Tutorial Mean

*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: Sun, 07 Nov 2010 09:33:08 +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/07/t12891236229nx4wfwegjnk2r4.htm/, Retrieved Sun, 07 Nov 2010 10:53:44 +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/07/t12891236229nx4wfwegjnk2r4.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:

IsPrivate?

No (this computation is public)

User-defined keywords:

Dataseries X:

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85 105 108 92 112,5 112 104 69 94,5 68,5 104 103,5 123,5 93 50,5 89 107 78,5 115 114 85 81 83,5 112 101 103,5 93,5 112 140 83,5 90 84 110,5 96 95 121 99,5 142,5 118 104,5 102,5 89,5 95 98,5 94 108 63,5 84,5 93,5 112 148,5 112 109 91,5 75 84 107 92,5 109,5 84 102,5 106 77 111,5 114 75 73,5 93,5 105 113,5 140 77 84,5 113,5 77,5 117,5 98 112 101 95 81 91 142 98,5 112 116,5 98,5 83,5 133 91,5 72,5 106,5 67 122,5 74 144,5 84 72,5 64 116 84 93,5 111,5 92 115 85 108 108 85 86 110,5 98 105 76,5 84 128 87 128 111 79 90 84 112 93 117 84 99,5 95 84 134 171,5 98,5 118,5 94,5 105 104 83 105,5 84 86 81 94 78,5 119,5 133 119 95 112 75 92 112 98,5 112,5 112,5 108 108 88 106 92 117,5 84 112 100 112 84 127,5 80,5 93,5 86,5 92,5 108,5 121 112 114 84 81 111,5 81 70 140 117 84 112 150,5 147 105 119,5 84 91 101 117,5 121 133 112 91,5 105 etc...

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 12 seconds R Server 'George Udny Yule' @ 72.249.76.132 Central Tendency - Ungrouped Data Measure Value S.E. Value/S.E. Arithmetic Mean 101.308016877637 1.26280903898965 80.2243361820502 Geometric Mean 99.495165034419 Harmonic Mean 97.7029259587095 Quadratic Mean 103.148729209587 Winsorized Mean ( 1 / 79 ) 101.362869198312 1.25462238561633 80.7915356527916 Winsorized Mean ( 2 / 79 ) 101.189873417722 1.21780175559493 83.0922380862287 Winsorized Mean ( 3 / 79 ) 101.221518987342 1.21199000170567 83.5167937399564 Winsorized Mean ( 4 / 79 ) 101.221518987342 1.20475484896528 84.0183536711036 Winsorized Mean ( 5 / 79 ) 101.200421940928 1.19835364337254 84.4495466764875 Winsorized Mean ( 6 / 79 ) 101.162447257384 1.18547428371404 85.334999372948 Winsorized Mean ( 7 / 79 ) 101.147679324895 1.17163787391034 86.3301550566252 Winsorized Mean ( 8 / 79 ) 101.147679324895 1.16732670429045 86.6489894843759 Winsorized Mean ( 9 / 79 ) 101.090717299578 1.15426923795247 87.579841839067 Winsorized Mean ( 10 / 79 ) 101.090717299578 1.15426923795247 87.579841839067 Winsorized Mean ( 11 / 79 ) 101.137130801688 1.14946913399703 87.9859474347127 Winsorized Mean ( 12 / 79 ) 101.137130801688 1.14946913399703 87.9859474347127 Winsorized Mean ( 13 / 79 ) 100.862869198312 1.10556148752187 91.2322564929405 Winsorized Mean ( 14 / 79 ) 100.892405063291 1.09576827647630 92.074581121963 Winsorized Mean ( 15 / 79 ) 100.829113924051 1.08775068390946 92.695059093563 Winsorized Mean ( 16 / 79 ) 100.829113924051 1.08775068390946 92.695059093563 Winsorized Mean ( 17 / 79 ) 100.829113924051 1.08775068390946 92.695059093563 Winsorized Mean ( 18 / 79 ) 100.525316455696 1.03490145779273 97.1351578440132 Winsorized Mean ( 19 / 79 ) 100.565400843882 1.03090636704758 97.5504702060299 Winsorized Mean ( 20 / 79 ) 100.607594936709 1.02676411742622 97.9851099480383 Winsorized Mean ( 21 / 79 ) 100.563291139241 1.02178542725945 98.4191870977872 Winsorized Mean ( 22 / 79 ) 100.238396624473 0.977732306175238 102.521309760738 Winsorized Mean ( 23 / 79 ) 100.238396624473 0.95861944328845 104.565369841253 Winsorized Mean ( 24 / 79 ) 100.086497890295 0.944013807158032 106.022281804974 Winsorized Mean ( 25 / 79 ) 100.139240506329 0.938942744905611 106.651061579261 Winsorized Mean ( 26 / 79 ) 100.194092827004 0.933750695874448 107.302830690984 Winsorized Mean ( 27 / 79 ) 100.137130801688 0.907378288308996 110.358746833479 Winsorized Mean ( 28 / 79 ) 100.137130801688 0.907378288308996 110.358746833479 Winsorized Mean ( 29 / 79 ) 100.137130801688 0.896311117213077 111.721397714051 Winsorized Mean ( 30 / 79 ) 100.073839662447 0.890715073823246 112.352246642573 Winsorized Mean ( 31 / 79 ) 100.008438818565 0.885031741186243 112.999832847261 Winsorized Mean ( 32 / 79 ) 100.008438818565 0.885031741186243 112.999832847261 Winsorized Mean ( 33 / 79 ) 100.008438818565 0.885031741186243 112.999832847261 Winsorized Mean ( 34 / 79 ) 100.223628691983 0.853529296017296 117.422599504953 Winsorized Mean ( 35 / 79 ) 100.297468354430 0.847270760056225 118.377115183079 Winsorized Mean ( 36 / 79 ) 100.297468354430 0.847270760056225 118.377115183079 Winsorized Mean ( 37 / 79 ) 100.219409282700 0.840611399401248 119.222044043282 Winsorized Mean ( 38 / 79 ) 100.219409282700 0.840611399401248 119.222044043282 Winsorized Mean ( 39 / 79 ) 100.219409282700 0.826811611632477 121.211903500998 Winsorized Mean ( 40 / 79 ) 100.135021097046 0.819831033154015 122.141047420237 Winsorized Mean ( 41 / 79 ) 100.135021097046 0.819831033154015 122.141047420237 Winsorized Mean ( 42 / 79 ) 100.046413502110 0.812627948341958 123.114659920618 Winsorized Mean ( 43 / 79 ) 99.9556962025316 0.805382477834374 124.109598797464 Winsorized Mean ( 44 / 79 ) 99.9556962025316 0.805382477834374 124.109598797464 Winsorized Mean ( 45 / 79 ) 99.7658227848101 0.79062316000095 126.186314583411 Winsorized Mean ( 46 / 79 ) 99.7658227848101 0.79062316000095 126.186314583411 Winsorized Mean ( 47 / 79 ) 99.7658227848101 0.79062316000095 126.186314583411 Winsorized Mean ( 48 / 79 ) 99.7658227848101 0.79062316000095 126.186314583411 Winsorized Mean ( 49 / 79 ) 99.7658227848101 0.79062316000095 126.186314583411 Winsorized Mean ( 50 / 79 ) 99.6603375527426 0.782647289584118 127.337485070318 Winsorized Mean ( 51 / 79 ) 99.6603375527426 0.782647289584118 127.337485070318 Winsorized Mean ( 52 / 79 ) 99.4409282700422 0.766504414405297 129.733014450014 Winsorized Mean ( 53 / 79 ) 99.4409282700422 0.766504414405297 129.733014450014 Winsorized Mean ( 54 / 79 ) 99.4409282700422 0.766504414405297 129.733014450014 Winsorized Mean ( 55 / 79 ) 99.4409282700422 0.748328526683232 132.884053893799 Winsorized Mean ( 56 / 79 ) 99.4409282700422 0.748328526683232 132.884053893799 Winsorized Mean ( 57 / 79 ) 99.5611814345991 0.738216000425321 134.86727648444 Winsorized Mean ( 58 / 79 ) 99.5611814345991 0.738216000425321 134.86727648444 Winsorized Mean ( 59 / 79 ) 99.5611814345991 0.738216000425321 134.86727648444 Winsorized Mean ( 60 / 79 ) 99.5611814345991 0.738216000425321 134.86727648444 Winsorized Mean ( 61 / 79 ) 99.5611814345991 0.738216000425321 134.86727648444 Winsorized Mean ( 62 / 79 ) 99.8227848101266 0.71658883074587 139.302736139809 Winsorized Mean ( 63 / 79 ) 99.8227848101266 0.71658883074587 139.302736139809 Winsorized Mean ( 64 / 79 ) 99.957805907173 0.705614406716097 141.660664742338 Winsorized Mean ( 65 / 79 ) 100.094936708861 0.69459548094089 144.105367016315 Winsorized Mean ( 66 / 79 ) 100.094936708861 0.69459548094089 144.105367016315 Winsorized Mean ( 67 / 79 ) 100.236286919831 0.683367754916057 146.679860439338 Winsorized Mean ( 68 / 79 ) 100.379746835443 0.672104105615443 149.351485873644 Winsorized Mean ( 69 / 79 ) 100.670886075949 0.649656898344682 154.96008174847 Winsorized Mean ( 70 / 79 ) 100.670886075949 0.649656898344682 154.96008174847 Winsorized Mean ( 71 / 79 ) 100.820675105485 0.638326999500969 157.945183556868 Winsorized Mean ( 72 / 79 ) 100.972573839662 0.626986890157815 161.044154869406 Winsorized Mean ( 73 / 79 ) 100.972573839662 0.626986890157815 161.044154869406 Winsorized Mean ( 74 / 79 ) 101.284810126582 0.604142611482769 167.650498742334 Winsorized Mean ( 75 / 79 ) 101.284810126582 0.604142611482769 167.650498742334 Winsorized Mean ( 76 / 79 ) 101.284810126582 0.604142611482769 167.650498742334 Winsorized Mean ( 77 / 79 ) 101.284810126582 0.604142611482769 167.650498742334 Winsorized Mean ( 78 / 79 ) 101.284810126582 0.58000000796003 174.628980580225 Winsorized Mean ( 79 / 79 ) 101.284810126582 0.58000000796003 174.628980580225 Trimmed Mean ( 1 / 79 ) 101.308016877637 1.21878405242256 83.1222041971004 Trimmed Mean ( 2 / 79 ) 101.225531914894 1.18039350663474 85.755751235437 Trimmed Mean ( 3 / 79 ) 101.032467532468 1.16006716003902 87.0919124450256 Trimmed Mean ( 4 / 79 ) 101.032467532468 1.14074141444023 88.5673705307218 Trimmed Mean ( 5 / 79 ) 100.900881057269 1.12239301831213 89.8979942061691 Trimmed Mean ( 6 / 79 ) 100.837777777778 1.10450761931675 91.2965886465831 Trimmed Mean ( 7 / 79 ) 100.780269058296 1.08822557612561 92.6097229005605 Trimmed Mean ( 8 / 79 ) 100.780269058296 1.07348434183566 93.881452323712 Trimmed Mean ( 9 / 79 ) 100.666666666667 1.05857388305431 95.0964956515007 Trimmed Mean ( 10 / 79 ) 100.615207373272 1.04471642455821 96.3086297947506 Trimmed Mean ( 11 / 79 ) 100.562790697674 1.03003580127799 97.630383888505 Trimmed Mean ( 12 / 79 ) 100.504694835681 1.01506714546199 99.0128537653906 Trimmed Mean ( 13 / 79 ) 100.445497630332 0.999177310233844 100.528201152630 Trimmed Mean ( 14 / 79 ) 100.409090909091 0.987334364906136 101.697149899808 Trimmed Mean ( 15 / 79 ) 100.369565217391 0.975804544562975 102.858267853572 Trimmed Mean ( 16 / 79 ) 100.369565217391 0.964393106807297 104.075365645938 Trimmed Mean ( 17 / 79 ) 100.298029556650 0.95227939888922 105.324161872705 Trimmed Mean ( 18 / 79 ) 100.261194029851 0.939408585432293 106.727994170623 Trimmed Mean ( 19 / 79 ) 100.243718592965 0.930533904132348 107.727099622914 Trimmed Mean ( 20 / 79 ) 100.223350253807 0.92144125591823 108.768030094260 Trimmed Mean ( 21 / 79 ) 100.2 0.912113388056815 109.854762918751 Trimmed Mean ( 22 / 79 ) 100.178756476684 0.90260075228505 110.989001751958 Trimmed Mean ( 23 / 79 ) 100.175392670157 0.895948972732344 111.809261150951 Trimmed Mean ( 24 / 79 ) 100.171957671958 0.890280825726614 112.517258349579 Trimmed Mean ( 25 / 79 ) 100.176470588235 0.885276814641944 113.158357850761 Trimmed Mean ( 26 / 79 ) 100.178378378378 0.88027599416115 113.803374217699 Trimmed Mean ( 27 / 79 ) 100.177595628415 0.87527570082535 114.452618225265 Trimmed Mean ( 28 / 79 ) 100.179558011050 0.871684974659593 114.926333392601 Trimmed Mean ( 29 / 79 ) 100.18156424581 0.867805694153331 115.442390987710 Trimmed Mean ( 30 / 79 ) 100.183615819209 0.864333186272073 115.908560969766 Trimmed Mean ( 31 / 79 ) 100.188571428571 0.860924716558606 116.373208367228 Trimmed Mean ( 32 / 79 ) 100.188571428571 0.857579263865549 116.827185136182 Trimmed Mean ( 33 / 79 ) 100.204678362573 0.853941996575876 117.343658895302 Trimmed Mean ( 34 / 79 ) 100.213017751479 0.84999194800329 117.898784790714 Trimmed Mean ( 35 / 79 ) 100.212574850299 0.847632017597334 118.226509581785 Trimmed Mean ( 36 / 79 ) 100.209090909091 0.845393945169387 118.535378070413 Trimmed Mean ( 37 / 79 ) 100.205521472393 0.842909419738516 118.880533454565 Trimmed Mean ( 38 / 79 ) 100.204968944099 0.84055392544773 119.213016453078 Trimmed Mean ( 39 / 79 ) 100.204402515723 0.837936658734175 119.584698283873 Trimmed Mean ( 40 / 79 ) 100.203821656051 0.835844111772823 119.883385244551 Trimmed Mean ( 41 / 79 ) 100.206451612903 0.83389882205749 120.166198778963 Trimmed Mean ( 42 / 79 ) 100.209150326797 0.83170137389145 120.486936143833 Trimmed Mean ( 43 / 79 ) 100.215231788079 0.829645392662897 120.792850384452 Trimmed Mean ( 44 / 79 ) 100.224832214765 0.827732137591571 121.083654558087 Trimmed Mean ( 45 / 79 ) 100.234693877551 0.825552710634965 121.415256211147 Trimmed Mean ( 46 / 79 ) 100.251724137931 0.82391406728865 121.677403163950 Trimmed Mean ( 47 / 79 ) 100.269230769231 0.822013339331926 121.980053086149 Trimmed Mean ( 48 / 79 ) 100.287234042553 0.819828268685334 122.327123707716 Trimmed Mean ( 49 / 79 ) 100.305755395683 0.817334336973918 122.723041059371 Trimmed Mean ( 50 / 79 ) 100.324817518248 0.814504475625238 123.172825344190 Trimmed Mean ( 51 / 79 ) 100.348148148148 0.811765236489504 123.617203148666 Trimmed Mean ( 52 / 79 ) 100.372180451128 0.808656989073838 124.122071295130 Trimmed Mean ( 53 / 79 ) 100.404580152672 0.806063969080287 124.561553430099 Trimmed Mean ( 54 / 79 ) 100.437984496124 0.803091164716075 125.064237920776 Trimmed Mean ( 55 / 79 ) 100.472440944882 0.799702073294136 125.637339579495 Trimmed Mean ( 56 / 79 ) 100.508 0.79698998253307 126.10948970846 Trimmed Mean ( 57 / 79 ) 100.544715447154 0.793860725649459 126.652839973786 Trimmed Mean ( 58 / 79 ) 100.578512396694 0.790961515688142 127.159805378382 Trimmed Mean ( 59 / 79 ) 100.613445378151 0.787612327313799 127.744883985374 Trimmed Mean ( 60 / 79 ) 100.649572649573 0.783766010959015 128.417883963121 Trimmed Mean ( 61 / 79 ) 100.686956521739 0.779369302151898 129.190303292335 Trimmed Mean ( 62 / 79 ) 100.725663716814 0.774361792969724 130.075714777359 Trimmed Mean ( 63 / 79 ) 100.725663716814 0.770299006605082 130.761772835122 Trimmed Mean ( 64 / 79 ) 100.756756756757 0.765631463767306 131.599550860908 Trimmed Mean ( 65 / 79 ) 100.817757009346 0.761133565482309 132.457378811642 Trimmed Mean ( 66 / 79 ) 100.842857142857 0.756816226456558 133.246161508729 Trimmed Mean ( 67 / 79 ) 100.868932038835 0.751828824428541 134.164757670078 Trimmed Mean ( 68 / 79 ) 100.891089108911 0.746994107111435 135.062764415972 Trimmed Mean ( 69 / 79 ) 100.909090909091 0.742320111839728 135.937433594522 Trimmed Mean ( 70 / 79 ) 100.917525773196 0.738699240918571 136.615174597587 Trimmed Mean ( 71 / 79 ) 100.926315789474 0.734411283947564 137.424789073202 Trimmed Mean ( 72 / 79 ) 100.930107526882 0.730304401151259 138.202792380512 Trimmed Mean ( 73 / 79 ) 100.928571428571 0.726381107507484 138.947131726621 Trimmed Mean ( 74 / 79 ) 100.926966292135 0.721697444460288 139.846644971303 Trimmed Mean ( 75 / 79 ) 100.913793103448 0.718088682795314 140.531100853198 Trimmed Mean ( 76 / 79 ) 100.9 0.713701441710159 141.375642675213 Trimmed Mean ( 77 / 79 ) 100.885542168675 0.708421140898089 142.408994232977 Trimmed Mean ( 78 / 79 ) 100.870370370370 0.702111991270141 143.667066827748 Trimmed Mean ( 79 / 79 ) 100.854430379747 0.69700243210116 144.697386601241 Median 101 Midrange 111 Midmean - Weighted Average at Xnp 100.728 Midmean - Weighted Average at X(n+1)p 100.728 Midmean - Empirical Distribution Function 100.728 Midmean - Empirical Distribution Function - Averaging 100.728 Midmean - Empirical Distribution Function - Interpolation 100.728 Midmean - Closest Observation 100.728 Midmean - True Basic - Statistics Graphics Toolkit 100.728 Midmean - MS Excel (old versions) 100.728 Number of observations 237

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Nov/07/t12891236229nx4wfwegjnk2r4/1ehy01289122375.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/07/t12891236229nx4wfwegjnk2r4/1ehy01289122375.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/07/t12891236229nx4wfwegjnk2r4/278fl1289122375.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/07/t12891236229nx4wfwegjnk2r4/278fl1289122375.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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