Tutorial Mean2

*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 10:00:41 +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/t128912408324zrfnxrvwpjoks.htm/, Retrieved Sun, 07 Nov 2010 11:01:25 +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/t128912408324zrfnxrvwpjoks.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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56,3 62,3 63,3 59 62,5 62,5 59 56,5 62 53,8 61,5 61,5 64,5 58,3 51,3 58,8 65,3 59,5 61,3 63,3 61,8 53,5 58 61,3 63,3 61,5 60,8 59 65,5 56,3 64,3 58 64,3 57,5 57,8 61,5 62,3 61,8 65,3 58,3 62,8 59,3 61,5 62 61,3 62,3 52,8 59,8 59,5 61,3 63,5 64,8 60 59 55,8 57,8 61,3 62,3 64,3 55,5 64,5 60 56,3 58,3 60 54,5 55,8 62,8 60,5 63,3 66,8 60 60,5 64,3 58,3 66,5 65,3 60,5 59,5 59 61,3 61,5 64,8 56,8 66,5 61,5 63 57 65,5 62 56 61,3 55,5 61 54,5 66 56,5 56 51,5 62 63 61 64 61 59,8 61,3 63,3 63,5 61,5 60,3 61,3 64,8 60,5 57,3 59,5 60,8 60,5 67 64,8 50,5 57,5 60,5 61,8 61,3 66,3 53,3 59 57,8 60 68,3 67,5 63,8 65 59,5 66 61,8 57,3 66 56,5 58,3 61 62,8 59,3 67,3 66,3 64,5 60,5 66 57,5 64 68 63,5 69 63,8 66 63,5 59,5 66,3 57 60 57 67,3 62 65 59,5 67,8 58 60 58,5 58,3 61,5 65 66,5 68,5 57 61,5 66,5 52,5 55 71 66,5 58,8 66,3 65,8 71 59,5 69,8 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 2 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Central Tendency - Ungrouped Data Measure Value S.E. Value/S.E. Arithmetic Mean 61.3645569620253 0.256281392810069 239.442108103037 Geometric Mean 61.2372724731216 Harmonic Mean 61.1088975575365 Quadratic Mean 61.4907258624307 Winsorized Mean ( 1 / 79 ) 61.3637130801688 0.254987015853283 240.654265766523 Winsorized Mean ( 2 / 79 ) 61.3654008438819 0.254707389714766 240.925090208815 Winsorized Mean ( 3 / 79 ) 61.3628691983122 0.250415989775183 245.043734041913 Winsorized Mean ( 4 / 79 ) 61.3628691983122 0.248955238420601 246.481534542534 Winsorized Mean ( 5 / 79 ) 61.3628691983122 0.246029517848452 249.412630382466 Winsorized Mean ( 6 / 79 ) 61.3552742616034 0.243713269976746 251.751881493599 Winsorized Mean ( 7 / 79 ) 61.3582278481013 0.241795075058484 253.761280428314 Winsorized Mean ( 8 / 79 ) 61.3717299578059 0.237566470510858 258.334982313932 Winsorized Mean ( 9 / 79 ) 61.364135021097 0.236679950068022 259.270525464708 Winsorized Mean ( 10 / 79 ) 61.3725738396624 0.232723572526047 263.714471093354 Winsorized Mean ( 11 / 79 ) 61.3632911392405 0.231701827441175 264.837320520571 Winsorized Mean ( 12 / 79 ) 61.3632911392405 0.231701827441175 264.837320520571 Winsorized Mean ( 13 / 79 ) 61.3632911392405 0.231701827441175 264.837320520571 Winsorized Mean ( 14 / 79 ) 61.3751054852321 0.226463910865101 271.014950023501 Winsorized Mean ( 15 / 79 ) 61.3751054852321 0.226463910865101 271.014950023501 Winsorized Mean ( 16 / 79 ) 61.3818565400844 0.222869660955 275.415937176295 Winsorized Mean ( 17 / 79 ) 61.3603375527426 0.220699348288351 278.026818060982 Winsorized Mean ( 18 / 79 ) 61.3755274261603 0.219098899446197 280.127045737315 Winsorized Mean ( 19 / 79 ) 61.3755274261603 0.219098899446197 280.127045737315 Winsorized Mean ( 20 / 79 ) 61.3755274261603 0.219098899446197 280.127045737315 Winsorized Mean ( 21 / 79 ) 61.4021097046413 0.21638891030065 283.758116898548 Winsorized Mean ( 22 / 79 ) 61.4021097046413 0.21638891030065 283.758116898548 Winsorized Mean ( 23 / 79 ) 61.4021097046413 0.21638891030065 283.758116898548 Winsorized Mean ( 24 / 79 ) 61.3818565400844 0.214393562332267 286.304569373939 Winsorized Mean ( 25 / 79 ) 61.4029535864979 0.212301707040808 289.224964049372 Winsorized Mean ( 26 / 79 ) 61.4029535864979 0.212301707040808 289.224964049372 Winsorized Mean ( 27 / 79 ) 61.4029535864979 0.212301707040808 289.224964049372 Winsorized Mean ( 28 / 79 ) 61.3675105485232 0.208903917113973 293.759501479537 Winsorized Mean ( 29 / 79 ) 61.4042194092827 0.205347404869224 299.026030781290 Winsorized Mean ( 30 / 79 ) 61.4042194092827 0.205347404869224 299.026030781290 Winsorized Mean ( 31 / 79 ) 61.4042194092827 0.205347404869224 299.026030781290 Winsorized Mean ( 32 / 79 ) 61.431223628692 0.202814395944624 302.893802693695 Winsorized Mean ( 33 / 79 ) 61.431223628692 0.202814395944624 302.893802693695 Winsorized Mean ( 34 / 79 ) 61.431223628692 0.202814395944624 302.893802693695 Winsorized Mean ( 35 / 79 ) 61.4016877637131 0.200028573948173 306.964582868156 Winsorized Mean ( 36 / 79 ) 61.4016877637131 0.191647783719567 320.388196367355 Winsorized Mean ( 37 / 79 ) 61.4016877637131 0.191647783719567 320.388196367355 Winsorized Mean ( 38 / 79 ) 61.4016877637131 0.191647783719567 320.388196367355 Winsorized Mean ( 39 / 79 ) 61.4016877637131 0.185735274419268 330.587110906615 Winsorized Mean ( 40 / 79 ) 61.4016877637131 0.185735274419268 330.587110906615 Winsorized Mean ( 41 / 79 ) 61.4016877637131 0.185735274419268 330.587110906615 Winsorized Mean ( 42 / 79 ) 61.4016877637131 0.185735274419268 330.587110906615 Winsorized Mean ( 43 / 79 ) 61.4016877637131 0.185735274419268 330.587110906615 Winsorized Mean ( 44 / 79 ) 61.4016877637131 0.175947660657443 348.977005629292 Winsorized Mean ( 45 / 79 ) 61.4016877637131 0.175947660657443 348.977005629292 Winsorized Mean ( 46 / 79 ) 61.4016877637131 0.175947660657443 348.977005629291 Winsorized Mean ( 47 / 79 ) 61.4016877637131 0.175947660657443 348.977005629292 Winsorized Mean ( 48 / 79 ) 61.4016877637131 0.168981245888514 363.363919119303 Winsorized Mean ( 49 / 79 ) 61.4016877637131 0.168981245888514 363.363919119303 Winsorized Mean ( 50 / 79 ) 61.4016877637131 0.168981245888514 363.363919119303 Winsorized Mean ( 51 / 79 ) 61.4016877637131 0.168981245888514 363.363919119303 Winsorized Mean ( 52 / 79 ) 61.4675105485232 0.163470014590335 376.017037146319 Winsorized Mean ( 53 / 79 ) 61.4004219409283 0.157778254673969 389.156427593938 Winsorized Mean ( 54 / 79 ) 61.4004219409283 0.157778254673969 389.156427593938 Winsorized Mean ( 55 / 79 ) 61.4004219409283 0.157778254673969 389.156427593938 Winsorized Mean ( 56 / 79 ) 61.4004219409283 0.157778254673969 389.156427593938 Winsorized Mean ( 57 / 79 ) 61.3523206751055 0.153822729663056 398.850812292149 Winsorized Mean ( 58 / 79 ) 61.4012658227848 0.149755433670040 410.010270198755 Winsorized Mean ( 59 / 79 ) 61.4759493670886 0.143741950723924 427.682726284699 Winsorized Mean ( 60 / 79 ) 61.4759493670886 0.143741950723924 427.682726284699 Winsorized Mean ( 61 / 79 ) 61.4502109704641 0.133361879863422 460.777930195617 Winsorized Mean ( 62 / 79 ) 61.4502109704641 0.133361879863422 460.777930195617 Winsorized Mean ( 63 / 79 ) 61.4502109704641 0.133361879863422 460.777930195617 Winsorized Mean ( 64 / 79 ) 61.3962025316456 0.129041722376235 475.785671494978 Winsorized Mean ( 65 / 79 ) 61.3962025316456 0.129041722376235 475.785671494978 Winsorized Mean ( 66 / 79 ) 61.3962025316456 0.129041722376235 475.785671494978 Winsorized Mean ( 67 / 79 ) 61.3113924050633 0.122480270775974 500.581783634418 Winsorized Mean ( 68 / 79 ) 61.3974683544304 0.115729767654229 530.524424259367 Winsorized Mean ( 69 / 79 ) 61.3974683544304 0.115729767654229 530.524424259367 Winsorized Mean ( 70 / 79 ) 61.3974683544304 0.115729767654229 530.524424259367 Winsorized Mean ( 71 / 79 ) 61.4573839662447 0.111193229945289 552.707966091854 Winsorized Mean ( 72 / 79 ) 61.3966244725738 0.106527072745243 576.34761652939 Winsorized Mean ( 73 / 79 ) 61.3966244725738 0.106527072745243 576.34761652939 Winsorized Mean ( 74 / 79 ) 61.3966244725738 0.106527072745243 576.34761652939 Winsorized Mean ( 75 / 79 ) 61.3966244725738 0.106527072745243 576.34761652939 Winsorized Mean ( 76 / 79 ) 61.3966244725738 0.106527072745243 576.34761652939 Winsorized Mean ( 77 / 79 ) 61.3966244725738 0.106527072745243 576.34761652939 Winsorized Mean ( 78 / 79 ) 61.3966244725738 0.106527072745243 576.34761652939 Winsorized Mean ( 79 / 79 ) 61.3966244725738 0.0915528018836951 670.61436907818 Trimmed Mean ( 1 / 79 ) 61.3645569620253 0.250203438175468 245.258647960666 Trimmed Mean ( 2 / 79 ) 61.3655319148936 0.245136656977854 250.331927796655 Trimmed Mean ( 3 / 79 ) 61.3683982683983 0.239917299704547 255.789800668698 Trimmed Mean ( 4 / 79 ) 61.3683982683983 0.236017793740164 260.015981405028 Trimmed Mean ( 5 / 79 ) 61.3722466960352 0.232319737042685 264.171471082368 Trimmed Mean ( 6 / 79 ) 61.3742222222222 0.229109321348451 267.881821049430 Trimmed Mean ( 7 / 79 ) 61.3775784753363 0.226187592092229 271.356964843188 Trimmed Mean ( 8 / 79 ) 61.3775784753363 0.223442381930587 274.690852939455 Trimmed Mean ( 9 / 79 ) 61.3817351598174 0.221213143653825 277.477794248398 Trimmed Mean ( 10 / 79 ) 61.383870967742 0.218984683117892 280.311253251879 Trimmed Mean ( 11 / 79 ) 61.3851162790698 0.217149559399564 282.685889157705 Trimmed Mean ( 12 / 79 ) 61.387323943662 0.215332423035839 285.081656901455 Trimmed Mean ( 13 / 79 ) 61.3895734597156 0.213409473281288 287.660957668923 Trimmed Mean ( 14 / 79 ) 61.3918660287081 0.211373569082949 290.44249143854 Trimmed Mean ( 15 / 79 ) 61.3932367149758 0.209754085099576 292.691494832298 Trimmed Mean ( 16 / 79 ) 61.3932367149758 0.20803699234891 295.107307704247 Trimmed Mean ( 17 / 79 ) 61.3955665024631 0.206549470466504 297.243882367733 Trimmed Mean ( 18 / 79 ) 61.3980099502488 0.205160973322485 299.267492037774 Trimmed Mean ( 19 / 79 ) 61.3994974874372 0.203821788331444 301.241089041926 Trimmed Mean ( 20 / 79 ) 61.4010152284264 0.202396792826517 303.369506853085 Trimmed Mean ( 21 / 79 ) 61.4025641025641 0.20088021465129 305.667555210220 Trimmed Mean ( 22 / 79 ) 61.4025906735751 0.199479075524983 307.814694408312 Trimmed Mean ( 23 / 79 ) 61.4026178010471 0.197985771447772 310.136518155017 Trimmed Mean ( 24 / 79 ) 61.4026455026455 0.196393856917750 312.650540430910 Trimmed Mean ( 25 / 79 ) 61.403743315508 0.194843787526193 315.143449504406 Trimmed Mean ( 26 / 79 ) 61.4037837837838 0.193341523002134 317.592324868084 Trimmed Mean ( 27 / 79 ) 61.403825136612 0.191736708284252 320.250752639293 Trimmed Mean ( 28 / 79 ) 61.4038674033149 0.190021750299254 323.141257811875 Trimmed Mean ( 29 / 79 ) 61.4055865921788 0.188425548231678 325.887795834766 Trimmed Mean ( 30 / 79 ) 61.4056497175141 0.186962236041196 328.438785381148 Trimmed Mean ( 31 / 79 ) 61.4057142857143 0.18539393868984 331.217485963469 Trimmed Mean ( 32 / 79 ) 61.4057142857143 0.183712573989424 334.248837476141 Trimmed Mean ( 33 / 79 ) 61.4046783625731 0.182079515673405 337.241002292176 Trimmed Mean ( 34 / 79 ) 61.403550295858 0.180326192127346 340.513763261272 Trimmed Mean ( 35 / 79 ) 61.4023952095808 0.178442774836517 344.101324729094 Trimmed Mean ( 36 / 79 ) 61.4024242424242 0.176606660202977 347.678984313804 Trimmed Mean ( 37 / 79 ) 61.40245398773 0.175183332886923 350.503971901049 Trimmed Mean ( 38 / 79 ) 61.4024844720497 0.173648173411977 353.602823833761 Trimmed Mean ( 39 / 79 ) 61.4025157232704 0.171991870376095 357.008244569941 Trimmed Mean ( 40 / 79 ) 61.4025477707006 0.170587434218353 359.947659990623 Trimmed Mean ( 41 / 79 ) 61.4025806451613 0.169067895839264 363.182970606896 Trimmed Mean ( 42 / 79 ) 61.402614379085 0.167423328088153 366.750649866156 Trimmed Mean ( 43 / 79 ) 61.4026490066225 0.165642629815652 370.693516970596 Trimmed Mean ( 44 / 79 ) 61.4026845637584 0.163713333062362 375.062210359915 Trimmed Mean ( 45 / 79 ) 61.4027210884354 0.162268725562613 378.401450282806 Trimmed Mean ( 46 / 79 ) 61.4027586206897 0.160697548027754 382.101403377261 Trimmed Mean ( 47 / 79 ) 61.4027972027972 0.158988058835574 386.210119505266 Trimmed Mean ( 48 / 79 ) 61.4028368794326 0.157127015337099 390.784721186865 Trimmed Mean ( 49 / 79 ) 61.4028776978417 0.155569263989655 394.698002183291 Trimmed Mean ( 50 / 79 ) 61.4029197080292 0.153867912459307 399.062538294124 Trimmed Mean ( 51 / 79 ) 61.402962962963 0.15200862890734 403.943930054079 Trimmed Mean ( 52 / 79 ) 61.403007518797 0.149975086598288 409.421383988037 Trimmed Mean ( 53 / 79 ) 61.4007633587786 0.148135787731455 414.48973471615 Trimmed Mean ( 54 / 79 ) 61.4007751937984 0.146521753269742 419.055695305267 Trimmed Mean ( 55 / 79 ) 61.4007874015748 0.144747197243509 424.193273312780 Trimmed Mean ( 56 / 79 ) 61.4008 0.142794668735758 429.993644325913 Trimmed Mean ( 57 / 79 ) 61.4008130081301 0.140644050521285 436.568861466614 Trimmed Mean ( 58 / 79 ) 61.402479338843 0.138570341009899 443.114153370357 Trimmed Mean ( 59 / 79 ) 61.4025210084034 0.136592623419586 449.530285539555 Trimmed Mean ( 60 / 79 ) 61.4 0.134855371109221 455.302591917319 Trimmed Mean ( 61 / 79 ) 61.3973913043478 0.132927266116248 461.887113894708 Trimmed Mean ( 62 / 79 ) 61.395575221239 0.131583215154216 466.591237714347 Trimmed Mean ( 63 / 79 ) 61.395575221239 0.130080799430484 471.980303703846 Trimmed Mean ( 64 / 79 ) 61.3936936936937 0.128400921082258 478.140601922651 Trimmed Mean ( 65 / 79 ) 61.3915887850467 0.126870567445798 483.89149683022 Trimmed Mean ( 66 / 79 ) 61.3914285714286 0.125152758569273 490.531964882325 Trimmed Mean ( 67 / 79 ) 61.3912621359223 0.123223000510380 498.212686605947 Trimmed Mean ( 68 / 79 ) 61.3940594059406 0.121604958391109 504.86477046835 Trimmed Mean ( 69 / 79 ) 61.3939393939394 0.120354884618498 510.10758382218 Trimmed Mean ( 70 / 79 ) 61.3938144329897 0.118931873141143 516.209934406146 Trimmed Mean ( 71 / 79 ) 61.3936842105263 0.117312291049005 523.335480549779 Trimmed Mean ( 72 / 79 ) 61.3913978494624 0.11587074977949 529.826534878685 Trimmed Mean ( 73 / 79 ) 61.3912087912088 0.114649205924706 535.46998687044 Trimmed Mean ( 74 / 79 ) 61.3910112359551 0.113240418416850 542.129851639795 Trimmed Mean ( 75 / 79 ) 61.3908045977011 0.111616541318622 550.015292289465 Trimmed Mean ( 76 / 79 ) 61.3905882352941 0.109744081333382 559.397714112717 Trimmed Mean ( 77 / 79 ) 61.3903614457831 0.107582284151035 570.636345288942 Trimmed Mean ( 78 / 79 ) 61.3901234567901 0.105080876234551 584.217848733592 Trimmed Mean ( 79 / 79 ) 61.3898734177215 0.102176809557056 600.820026421369 Median 61.5 Midrange 61.25 Midmean - Weighted Average at Xnp 61.4504132231406 Midmean - Weighted Average at X(n+1)p 61.4504132231406 Midmean - Empirical Distribution Function 61.4504132231406 Midmean - Empirical Distribution Function - Averaging 61.4504132231406 Midmean - Empirical Distribution Function - Interpolation 61.4504132231406 Midmean - Closest Observation 61.4262295081968 Midmean - True Basic - Statistics Graphics Toolkit 61.4504132231406 Midmean - MS Excel (old versions) 61.4504132231406 Number of observations 237

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Nov/07/t128912408324zrfnxrvwpjoks/1ydwv1289124038.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/07/t128912408324zrfnxrvwpjoks/1ydwv1289124038.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/07/t128912408324zrfnxrvwpjoks/2ydwv1289124038.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/07/t128912408324zrfnxrvwpjoks/2ydwv1289124038.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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