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Paper Analyse (3)

*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: Sat, 13 Dec 2008 07:48:04 -0700
 
Cite this page as follows:
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2008/Dec/13/t12291797278v5x0qao87ten1i.htm/, Retrieved Sat, 13 Dec 2008 15:48:49 +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/2008/Dec/13/t12291797278v5x0qao87ten1i.htm/},
    year = {2008},
}
@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 = {2008},
    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:
» Textbox « » Textfile « » CSV «
1593 1477.9 1733.7 1569.7 1843.7 1950.3 1657.5 1772.1 1568.3 1809.8 1646.7 1808.5 1763.9 1625.5 1538.8 1342.4 1645.1 1619.9 1338.1 1505.5 1529.1 1511.9 1656.7 1694.4 1662.3 1588.7 1483.3 1585.6 1658.9 1584.4 1470.6 1618.7 1407.6 1473.9 1515.3 1485.4 1496.1 1493.5 1298.4 1375.3 1507.9 1455.3 1363.3 1392.8 1348.8 1880.3 1669.2 1543.6 1701.2 1516.5 1466.8 1484.1 1577.2 1684.5 1414.7 1674.5 1598.7 1739.1 1674.6 1671.8 1802 1526.8 1580.9 1634.8 1610.3 1712 1678.8 1708.1 1680.6 2056 1624 2021.4 1861.1 1750.8 1767.5 1710.3 2151.5 2047.9 1915.4 1984.7 1896.5 2170.8 2139.9 2330.5 2121.8 2226.8 1857.9 2155.9 2341.7 2290.2 2006.5 2111.9 1731.3 1762.2 1863.2 1943.5 1975.2
 
Output produced by software:


Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135


Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean1706.3515463917524.486637868281569.685007618055
Geometric Mean1690.32657469611
Harmonic Mean1675.10774399296
Quadratic Mean1723.13573509065
Winsorized Mean ( 1 / 32 )1706.6453608247424.387916615578569.9791371163938
Winsorized Mean ( 2 / 32 )1705.9030927835024.15858537948470.6127062486115
Winsorized Mean ( 3 / 32 )1704.1402061855723.654708209767672.0423262495322
Winsorized Mean ( 4 / 32 )1702.4288659793823.051691313654773.8526662887831
Winsorized Mean ( 5 / 32 )1702.279381443322.797197366582874.6705550717643
Winsorized Mean ( 6 / 32 )1703.0896907216522.582497693381975.4163562350662
Winsorized Mean ( 7 / 32 )1703.320618556722.260054532460476.519157492308
Winsorized Mean ( 8 / 32 )1702.4134020618621.877869111248977.814406577034
Winsorized Mean ( 9 / 32 )1705.2618556701021.204699817186380.4190519258374
Winsorized Mean ( 10 / 32 )1700.6845360824719.948028228324785.2557714785882
Winsorized Mean ( 11 / 32 )1700.1969072164919.726039853731886.190483230462
Winsorized Mean ( 12 / 32 )1697.3268041237119.085316763670488.9336459615192
Winsorized Mean ( 13 / 32 )1695.8659793814418.670347472836190.8320523680019
Winsorized Mean ( 14 / 32 )1693.4989690721618.038312039507393.883450145617
Winsorized Mean ( 15 / 32 )1692.1536082474217.777910517452095.182929770419
Winsorized Mean ( 16 / 32 )1688.2608247422717.082610488229698.8292056360783
Winsorized Mean ( 17 / 32 )1688.4886597938116.7186638764387100.994234483856
Winsorized Mean ( 18 / 32 )1683.7567010309315.8479338704525106.244556217526
Winsorized Mean ( 19 / 32 )1681.8958762886615.0653887569073111.639726224624
Winsorized Mean ( 20 / 32 )1679.0505154639214.5156925041126115.671402861986
Winsorized Mean ( 21 / 32 )1676.2144329896913.881918570864120.748038135579
Winsorized Mean ( 22 / 32 )1676.5092783505213.7203983205315122.191006353056
Winsorized Mean ( 23 / 32 )1676.0350515463913.5794803034555123.424093860197
Winsorized Mean ( 24 / 32 )1675.0701030927812.7829488156293131.039412521524
Winsorized Mean ( 25 / 32 )1666.9257731958811.5449859021565144.385258442325
Winsorized Mean ( 26 / 32 )1669.1773195876311.1802758697993149.296612983986
Winsorized Mean ( 27 / 32 )1668.7041237113410.7844773898416154.732034144108
Winsorized Mean ( 28 / 32 )1667.203092783508.8460810305849188.467987916822
Winsorized Mean ( 29 / 32 )1666.246391752588.62831191229638193.113833701118
Winsorized Mean ( 30 / 32 )1667.452577319598.2244353064469202.743716156721
Winsorized Mean ( 31 / 32 )1668.091752577328.02354362475405207.899630212137
Winsorized Mean ( 32 / 32 )1665.485567010317.43803526037347223.914717893752
Trimmed Mean ( 1 / 32 )1703.9578947368423.692685901737871.919152678754
Trimmed Mean ( 2 / 32 )1701.1548387096822.896954283604574.2961189352508
Trimmed Mean ( 3 / 32 )1698.6241758241822.125727175161876.771450826305
Trimmed Mean ( 4 / 32 )1696.620224719121.462406391165279.0507920592492
Trimmed Mean ( 5 / 32 )1695.0011494252920.910558980153581.0595810008732
Trimmed Mean ( 6 / 32 )1693.3420.349345387581483.2134875961854
Trimmed Mean ( 7 / 32 )1693.3419.755001824334885.7170257465676
Trimmed Mean ( 8 / 32 )1689.4086419753119.140862113852588.2618887240538
Trimmed Mean ( 9 / 32 )1687.4126582278518.510559138867891.1594644747752
Trimmed Mean ( 10 / 32 )1684.9142857142917.908431717201694.0849713878562
Trimmed Mean ( 11 / 32 )1682.8746666666717.456332864983296.404822231733
Trimmed Mean ( 12 / 32 )1680.7821917808216.964194132987399.0782219659051
Trimmed Mean ( 13 / 32 )1678.8985915493016.5026639509108101.735004514628
Trimmed Mean ( 14 / 32 )1678.8985915493016.0293584512065104.738976089397
Trimmed Mean ( 15 / 32 )1675.3641791044815.5785897652851107.542736816770
Trimmed Mean ( 16 / 32 )1673.6938461538515.0840688815607110.957716999014
Trimmed Mean ( 17 / 32 )1672.2920634920614.6160264747585114.414958564838
Trimmed Mean ( 18 / 32 )1670.7770491803314.1109141562417118.403175774497
Trimmed Mean ( 19 / 32 )1669.5915254237313.6579245462615122.243428697279
Trimmed Mean ( 20 / 32 )1668.4894736842113.2435899007771125.984682868072
Trimmed Mean ( 21 / 32 )1667.5581818181812.8334715172697129.938199463348
Trimmed Mean ( 22 / 32 )1666.8037735849112.4417026524935133.969105366045
Trimmed Mean ( 23 / 32 )1665.9647058823511.9783686812093139.081101126549
Trimmed Mean ( 24 / 32 )1665.0979591836711.4185538275156145.823891916264
Trimmed Mean ( 25 / 32 )1665.0979591836710.8731248596887153.138861244655
Trimmed Mean ( 26 / 32 )1664.0088888888910.4482654411877159.261735668512
Trimmed Mean ( 27 / 32 )1663.560465116289.97187581115395166.825228935916
Trimmed Mean ( 28 / 32 )1663.560465116289.43595989202363176.300078015647
Trimmed Mean ( 29 / 32 )1662.746153846159.18942642267648180.941233692567
Trimmed Mean ( 30 / 32 )1662.429729729738.90025041391552186.784601827666
Trimmed Mean ( 31 / 32 )1662.429729729738.59674546866785193.378963677442
Trimmed Mean ( 32 / 32 )1661.384848484858.2179187086357202.166133225314
Median1662.3
Midrange1820.05
Midmean - Weighted Average at Xnp1661.37708333333
Midmean - Weighted Average at X(n+1)p1665.09795918367
Midmean - Empirical Distribution Function1665.09795918367
Midmean - Empirical Distribution Function - Averaging1665.09795918367
Midmean - Empirical Distribution Function - Interpolation1665.09795918367
Midmean - Closest Observation1662.126
Midmean - True Basic - Statistics Graphics Toolkit1665.09795918367
Midmean - MS Excel (old versions)1665.09795918367
Number of observations97
 
Charts produced by software:
http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/13/t12291797278v5x0qao87ten1i/10aiw1229179682.png (open in new window)
http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/13/t12291797278v5x0qao87ten1i/10aiw1229179682.ps (open in new window)


http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/13/t12291797278v5x0qao87ten1i/2rp7r1229179682.png (open in new window)
http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/13/t12291797278v5x0qao87ten1i/2rp7r1229179682.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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