retail sales and food services

*Unverified author*

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

Title produced by software: Central Tendency

Date of computation: Sun, 25 Apr 2010 09:19:26 +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/Apr/25/t1272187217f81bsqrs8b8mqm2.htm/, Retrieved Sun, 25 Apr 2010 11:20:19 +0200

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/Apr/25/t1272187217f81bsqrs8b8mqm2.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:

KDGP1W52

Dataseries X:

» Textbox « » Textfile « » CSV «

357704 281463 282445 319107 315278 328499 321151 328025 326280 313444 319639 324067 386918 293009 294822 338844 335407 345080 350608 351285 355147 332791 335615 343202 404868 317902 313552 361505 351436 373350 366310 361669 375078 345547 348117 356089 416856 328087 322747 373626 358275 391287 376371 371848 387261 353159 367855 376822 425283 342191 344062 373587 370144 399979 380431 385909 384798 352554 352479 338788 387964 313593 304056 334149 336155 354668 351418 354316 359483 330411 344726 347175

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 1 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Central Tendency - Ungrouped Data Measure Value S.E. Value/S.E. Arithmetic Mean 349274.527777778 3503.3744510957 99.696601848695 Geometric Mean 348020.808421584 Harmonic Mean 346758.604795102 Quadratic Mean 350519.790689564 Winsorized Mean ( 1 / 24 ) 349171.125 3465.67648360619 100.751217446780 Winsorized Mean ( 2 / 24 ) 349131.569444444 3305.19500624015 105.631156039293 Winsorized Mean ( 3 / 24 ) 349003.402777778 3240.49122700199 107.700770756496 Winsorized Mean ( 4 / 24 ) 349033.513888889 3024.93815124456 115.385338951570 Winsorized Mean ( 5 / 24 ) 349454.694444444 2853.78636489264 122.452997443483 Winsorized Mean ( 6 / 24 ) 349405.111111111 2841.1224668255 122.981362187289 Winsorized Mean ( 7 / 24 ) 349375.75 2834.17397579927 123.272513608298 Winsorized Mean ( 8 / 24 ) 349450.861111111 2780.50805999835 125.678780126003 Winsorized Mean ( 9 / 24 ) 349639.986111111 2699.38054705702 129.526007917744 Winsorized Mean ( 10 / 24 ) 349200.819444444 2563.93734751040 136.197095371117 Winsorized Mean ( 11 / 24 ) 348730.722222222 2458.72739001550 141.833829825283 Winsorized Mean ( 12 / 24 ) 348907.555555556 2405.15156495927 145.066764456262 Winsorized Mean ( 13 / 24 ) 348962.263888889 2321.53467964117 150.315335346542 Winsorized Mean ( 14 / 24 ) 348936.597222222 2236.69898511699 156.005166338452 Winsorized Mean ( 15 / 24 ) 349389.513888889 2164.64163357286 161.407555167551 Winsorized Mean ( 16 / 24 ) 349724.625 2098.92042183169 166.621193144046 Winsorized Mean ( 17 / 24 ) 349384.625 2041.17425981587 171.168445476829 Winsorized Mean ( 18 / 24 ) 349061.625 1960.71186495761 178.028006683963 Winsorized Mean ( 19 / 24 ) 348962.138888889 1796.20094832257 194.277894806133 Winsorized Mean ( 20 / 24 ) 349194.083333333 1638.04931781252 213.176782613391 Winsorized Mean ( 21 / 24 ) 348236.541666667 1389.49642719244 250.620681602111 Winsorized Mean ( 22 / 24 ) 348570.819444444 1328.36519676653 262.405865715938 Winsorized Mean ( 23 / 24 ) 347991.347222222 1232.25023628317 282.403149113501 Winsorized Mean ( 24 / 24 ) 347768.680555556 1154.49660168262 301.229713494783 Trimmed Mean ( 1 / 24 ) 349157.428571429 3292.69718847297 106.039944940505 Trimmed Mean ( 2 / 24 ) 349142.926470588 3084.00457011041 113.210897887252 Trimmed Mean ( 3 / 24 ) 349149.121212121 2939.80778548952 118.765969304345 Trimmed Mean ( 4 / 24 ) 349203.765625 2796.89860336251 124.853923987511 Trimmed Mean ( 5 / 24 ) 349253.193548387 2707.85433846995 128.977836284107 Trimmed Mean ( 6 / 24 ) 349204.833333333 2654.83546131353 131.535395854837 Trimmed Mean ( 7 / 24 ) 349163.396551724 2593.15025417692 134.648347502929 Trimmed Mean ( 8 / 24 ) 349124.392857143 2518.77439915076 138.608838082067 Trimmed Mean ( 9 / 24 ) 349069.981481481 2440.15484173356 143.052389754698 Trimmed Mean ( 10 / 24 ) 348982.288461538 2361.79300949741 147.761589207093 Trimmed Mean ( 11 / 24 ) 348950.82 2295.64163662985 152.005789767902 Trimmed Mean ( 12 / 24 ) 348980.833333333 2235.61190382306 156.100811923818 Trimmed Mean ( 13 / 24 ) 348990.391304348 2170.36184598123 160.798252121211 Trimmed Mean ( 14 / 24 ) 348993.931818182 2104.73574503922 165.813657434548 Trimmed Mean ( 15 / 24 ) 349000.952380952 2038.15261224290 171.233964662191 Trimmed Mean ( 16 / 24 ) 348954.325 1966.46555818362 177.452548582809 Trimmed Mean ( 17 / 24 ) 348863.105263158 1885.59667378823 185.014701241639 Trimmed Mean ( 18 / 24 ) 348801.75 1790.38661577006 194.819234531631 Trimmed Mean ( 19 / 24 ) 348771.176470588 1681.18058131969 207.456105754452 Trimmed Mean ( 20 / 24 ) 348748.5625 1577.90959353122 221.019356197418 Trimmed Mean ( 21 / 24 ) 348695.1 1480.42656973955 235.536910190247 Trimmed Mean ( 22 / 24 ) 348751.25 1421.09358518147 245.410473762336 Trimmed Mean ( 23 / 24 ) 348773.961538462 1350.78707367311 258.200547174369 Trimmed Mean ( 24 / 24 ) 348876.041666667 1275.40477729190 273.541426124687 Median 350946.5 Midrange 353373 Midmean - Weighted Average at Xnp 348241.891891892 Midmean - Weighted Average at X(n+1)p 348801.75 Midmean - Empirical Distribution Function 348241.891891892 Midmean - Empirical Distribution Function - Averaging 348801.75 Midmean - Empirical Distribution Function - Interpolation 348801.75 Midmean - Closest Observation 348241.891891892 Midmean - True Basic - Statistics Graphics Toolkit 348801.75 Midmean - MS Excel (old versions) 348863.105263158 Number of observations 72

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Apr/25/t1272187217f81bsqrs8b8mqm2/1nkcb1272187164.png (open in new window) http://www.freestatistics.org/blog/date/2010/Apr/25/t1272187217f81bsqrs8b8mqm2/1nkcb1272187164.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Apr/25/t1272187217f81bsqrs8b8mqm2/2nkcb1272187164.png (open in new window) http://www.freestatistics.org/blog/date/2010/Apr/25/t1272187217f81bsqrs8b8mqm2/2nkcb1272187164.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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