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Summary univariate

*The author of this computation has been verified*
R Software Module: /rwasp_summary1.wasp (opens new window with default values)
Title produced by software: Univariate Summary Statistics
Date of computation: Sun, 13 Dec 2009 05:04:55 -0700
 
Cite this page as follows:
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2009/Dec/13/t1260705973xaxq6rcevpvc4ta.htm/, Retrieved Sun, 13 Dec 2009 13:06:18 +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/2009/Dec/13/t1260705973xaxq6rcevpvc4ta.htm/},
    year = {2009},
}
@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 = {2009},
    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:
paper
 
Dataseries X:
» Textbox « » Textfile « » CSV «
125.9 133.1 147 145.8 164.4 149.8 137.7 151.7 156.8 180 180.4 170.4 191.6 199.5 218.2 217.5 205 194 199.3 219.3 211.1 215.2 240.2 242.2 240.7 255.4 253 218.2 203.7 205.6 215.6 188.5 202.9 214 230.3 230 241 259.6 247.8 270.3 289.7 322.7 315 320.2 329.5 360.6 382.2 435.4 464 468.8 403 351.6 252 188 146.5 152.9 148.1 165.1 177 206.1
 
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 Mean232.51833333333310.549208739884922.0413055677074
Geometric Mean220.520661596011
Harmonic Mean210.326474891660
Quadratic Mean246.232893483656
Winsorized Mean ( 1 / 20 )232.55833333333310.499164963208822.1501742422627
Winsorized Mean ( 2 / 20 )231.75833333333310.134070267119122.8692250225749
Winsorized Mean ( 3 / 20 )230.5433333333339.547001885902024.1482442434389
Winsorized Mean ( 4 / 20 )229.2033333333339.1303739586741725.103389452694
Winsorized Mean ( 5 / 20 )227.4458.6324075453055726.3478060791613
Winsorized Mean ( 6 / 20 )226.6558.383609050177327.0354925478314
Winsorized Mean ( 7 / 20 )224.2757.7273487552530429.0235379692858
Winsorized Mean ( 8 / 20 )223.6216666666677.4795552194366929.8977225391095
Winsorized Mean ( 9 / 20 )223.4266666666677.3664332094817230.3303729651797
Winsorized Mean ( 10 / 20 )223.217.0700676844105931.5711263262975
Winsorized Mean ( 11 / 20 )219.9655.865739281316937.4999619742076
Winsorized Mean ( 12 / 20 )216.2255.1001620806193642.3957114660446
Winsorized Mean ( 13 / 20 )215.0554.5024779273057847.7636988947298
Winsorized Mean ( 14 / 20 )215.6154.0863288850828152.7649648531974
Winsorized Mean ( 15 / 20 )215.7653.8690206829632955.7673420951436
Winsorized Mean ( 16 / 20 )215.6053.8089660985775456.604599363727
Winsorized Mean ( 17 / 20 )216.5683333333333.2888722601948965.8488126627635
Winsorized Mean ( 18 / 20 )215.0383333333333.0023080496903471.6243402656542
Winsorized Mean ( 19 / 20 )215.642.7989346237896677.0436001495564
Winsorized Mean ( 20 / 20 )216.342.6684981704838681.0718187454379
Trimmed Mean ( 1 / 20 )230.2827586206909.937271233900723.1736412542597
Trimmed Mean ( 2 / 20 )227.8446428571439.2241963432864524.7007581341189
Trimmed Mean ( 3 / 20 )225.6703703703708.5782396722416726.3073053438478
Trimmed Mean ( 4 / 20 )223.7961538461548.0673064024361827.7411248168994
Trimmed Mean ( 5 / 20 )222.1747.5969359075665229.2452118463597
Trimmed Mean ( 6 / 20 )220.856257.1861543798974930.7335799266743
Trimmed Mean ( 7 / 20 )219.5956521739136.7402167115791332.5799097522586
Trimmed Mean ( 8 / 20 )218.6840909090916.381718524290734.2672730043976
Trimmed Mean ( 9 / 20 )217.8023809523815.9865989407034836.3816556127589
Trimmed Mean ( 10 / 20 )216.8655.4879034224700939.5169126176768
Trimmed Mean ( 11 / 20 )215.8631578947374.8962368646342744.0875643606881
Trimmed Mean ( 12 / 20 )215.2416666666674.5067839076747647.7594823883444
Trimmed Mean ( 13 / 20 )215.0970588235294.2268210017274050.8886131529167
Trimmed Mean ( 14 / 20 )215.1031254.0245378525882153.4479070340128
Trimmed Mean ( 15 / 20 )215.033.8642902427819555.6454061393684
Trimmed Mean ( 16 / 20 )214.9253.6951191351944858.1645657789293
Trimmed Mean ( 17 / 20 )214.8269230769233.4542217544613662.1925684995354
Trimmed Mean ( 18 / 20 )214.5708333333333.2823334707620865.3714301866822
Trimmed Mean ( 19 / 20 )214.53.1222979660411368.699400996623
Trimmed Mean ( 20 / 20 )214.322.9364371537451272.9864079422429
Median214.6
Midrange297.35
Midmean - Weighted Average at Xnp213.803225806452
Midmean - Weighted Average at X(n+1)p215.03
Midmean - Empirical Distribution Function213.803225806452
Midmean - Empirical Distribution Function - Averaging215.03
Midmean - Empirical Distribution Function - Interpolation215.03
Midmean - Closest Observation213.803225806452
Midmean - True Basic - Statistics Graphics Toolkit215.03
Midmean - MS Excel (old versions)215.103125
Number of observations60


Variability - Ungrouped Data
Absolute range342.9
Relative range (unbiased)4.19635261171575
Relative range (biased)4.23176549787481
Variance (unbiased)6677.14830225989
Variance (biased)6565.86249722222
Standard Deviation (unbiased)81.7138195304802
Standard Deviation (biased)81.0300098557455
Coefficient of Variation (unbiased)0.35142957701033
Coefficient of Variation (biased)0.348488692027491
Mean Squared Error (MSE versus 0)60630.6378333333
Mean Squared Error (MSE versus Mean)6565.86249722222
Mean Absolute Deviation from Mean (MAD Mean)60.9832222222222
Mean Absolute Deviation from Median (MAD Median)57.7883333333333
Median Absolute Deviation from Mean44.2683333333333
Median Absolute Deviation from Median38
Mean Squared Deviation from Mean6565.86249722222
Mean Squared Deviation from Median6886.92916666667
Interquartile Difference (Weighted Average at Xnp)76
Interquartile Difference (Weighted Average at X(n+1)p)77.05
Interquartile Difference (Empirical Distribution Function)76
Interquartile Difference (Empirical Distribution Function - Averaging)75.7
Interquartile Difference (Empirical Distribution Function - Interpolation)74.35
Interquartile Difference (Closest Observation)76
Interquartile Difference (True Basic - Statistics Graphics Toolkit)74.35
Interquartile Difference (MS Excel (old versions))78.4
Semi Interquartile Difference (Weighted Average at Xnp)38
Semi Interquartile Difference (Weighted Average at X(n+1)p)38.525
Semi Interquartile Difference (Empirical Distribution Function)38
Semi Interquartile Difference (Empirical Distribution Function - Averaging)37.85
Semi Interquartile Difference (Empirical Distribution Function - Interpolation)37.175
Semi Interquartile Difference (Closest Observation)38
Semi Interquartile Difference (True Basic - Statistics Graphics Toolkit)37.175
Semi Interquartile Difference (MS Excel (old versions))39.2
Coefficient of Quartile Variation (Weighted Average at Xnp)0.176744186046512
Coefficient of Quartile Variation (Weighted Average at X(n+1)p)0.178129695988903
Coefficient of Quartile Variation (Empirical Distribution Function)0.176744186046512
Coefficient of Quartile Variation (Empirical Distribution Function - Averaging)0.174948000924428
Coefficient of Quartile Variation (Empirical Distribution Function - Interpolation)0.171768511031535
Coefficient of Quartile Variation (Closest Observation)0.176744186046512
Coefficient of Quartile Variation (True Basic - Statistics Graphics Toolkit)0.171768511031535
Coefficient of Quartile Variation (MS Excel (old versions))0.181313598519889
Number of all Pairs of Observations1770
Squared Differences between all Pairs of Observations13354.2966045198
Mean Absolute Differences between all Pairs of Observations86.9913559322034
Gini Mean Difference86.9913559322036
Leik Measure of Dispersion0.502911804901114
Index of Diversity0.981309260525483
Index of Qualitative Variation0.997941620873372
Coefficient of Dispersion0.284171585378482
Observations60


Percentiles - Ungrouped Data
pWeighted Average at XnpWeighted Average at X(n+1)pEmpirical Distribution FunctionEmpirical Distribution Function - AveragingEmpirical Distribution Function - InterpolationClosest ObservationTrue Basic - Statistics Graphics ToolkitMS Excel (old versions)
0.02127.34127.484133.1133.1133.928125.9131.516125.9
0.04134.94135.124137.7137.7140.616133.1135.676133.1
0.06142.56143.046145.8145.8146.178145.8140.454145.8
0.08146.36146.416146.5146.5146.86146.5145.884146.5
0.1147147.11147147.55147.99147147.99147
0.12148.44148.644149.8149.8149.952148.1149.256148.1
0.14150.56150.826151.7151.7152.012149.8150.674151.7
0.16152.42152.612152.9152.9154.616152.9151.988152.9
0.18156.02156.722156.8156.8161.512156.8152.978156.8
0.2164.4164.54164.4164.75164.96164.4164.96164.4
0.22166.16167.326170.4170.4170.294165.1168.174165.1
0.24173.04174.624177177177.48170.4172.776177
0.26178.8179.58180180180.136180177.42180
0.28180.32181.008180.4180.4184.352180.4187.392180.4
0.3188188.15188188.25188.35188188.35188
0.32189.12190.112191.6191.6191.228188.5189.988191.6
0.34192.56193.376194194194.318191.6192.224194
0.36197.18199.088199.3199.3199.348199.3194.212199.3
0.38199.46200.112199.5199.5200.928199.5202.288199.5
0.4202.9203.22202.9203.3203.38202.9203.38202.9
0.42203.96204.506205205204.714203.7204.194205
0.44205.24205.504205.6205.6205.576205205.096205.6
0.46205.9206.4206.1206.1206.8206.1210.8206.1
0.48210.1211.912211.1211.1212.028211.1213.188211.1
0.5214214.6214214.6214.6214214.6214.6
0.52215.28215.488215.6215.6215.472215.2215.312215.6
0.54216.36217.386217.5217.5217.234215.6215.714217.5
0.56217.92218.2218.2218.2218.2218.2218.2218.2
0.58218.2218.618218.2218.2218.442218.2218.882218.2
0.6219.3225.72219.3224.65223.58219.3223.58230
0.62230.06230.246230.3230.3230.174230230.054230.3
0.64234.26240.22240.2240.2237.824230.3240.68240.2
0.66240.5240.778240.7240.7240.67240.7240.922240.7
0.68240.94241.576241241241.144241241.624241
0.7242.2246.12242.2245243.88242.2243.88247.8
0.72248.64251.664252252249.816247.8248.136252
0.74252.4253.336253253252.66252255.064253
0.76254.44256.912255.4255.4255.016255.4258.088255.4
0.78258.76265.806259.6259.6259.814259.6264.094270.3
0.8270.3285.82270.3280274.18270.3274.18289.7
0.82294.76315.104315315299.314289.7320.096315
0.84317.08320.8320.2320.2317.912315322.1320.2
0.86321.7325.828322.7322.7322.05322.7326.372322.7
0.88328.14344.528329.5329.5328.956329.5336.572351.6
0.9351.6359.7351.6356.1352.5351.6352.5360.6
0.92364.92384.696382.2382.2366.648360.6400.504382.2
0.94390.52414.016403403391.768382.2424.384403
0.96422.44451.416435.4435.4423.736435.4447.984464
0.98458.28467.744464464458.852464465.056468.8


Frequency Table (Histogram)
BinsMidpointAbs. FrequencyRel. FrequencyCumul. Rel. Freq.Density
[100,150[12580.1333330.1333330.002667
[150,200[175150.250.3833330.005
[200,250[225200.3333330.7166670.006667
[250,300[27560.10.8166670.002
[300,350[32540.0666670.8833330.001333
[350,400[37530.050.9333330.001
[400,450[42520.0333330.9666670.000667
[450,500]47520.03333310.000667


Properties of Density Trace
Bandwidth22.0185357087039
#Observations60
 
Charts produced by software:
http://www.freestatistics.org/blog/date/2009/Dec/13/t1260705973xaxq6rcevpvc4ta/1hrug1260705892.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Dec/13/t1260705973xaxq6rcevpvc4ta/1hrug1260705892.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Dec/13/t1260705973xaxq6rcevpvc4ta/2lac11260705892.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Dec/13/t1260705973xaxq6rcevpvc4ta/2lac11260705892.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Dec/13/t1260705973xaxq6rcevpvc4ta/59mrt1260705892.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Dec/13/t1260705973xaxq6rcevpvc4ta/59mrt1260705892.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Dec/13/t1260705973xaxq6rcevpvc4ta/73wda1260705893.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Dec/13/t1260705973xaxq6rcevpvc4ta/73wda1260705893.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Dec/13/t1260705973xaxq6rcevpvc4ta/93tsy1260705893.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Dec/13/t1260705973xaxq6rcevpvc4ta/93tsy1260705893.ps (open in new window)


 
Parameters (Session):
 
Parameters (R input):
 
R code (references can be found in the software module):
load(file='createtable')
x <-sort(x[!is.na(x)])
num <- 50
res <- array(NA,dim=c(num,3))
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]
}
}
}
}
iqd <- 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)
}
iqdiff <- qvalue3 - qvalue1
return(c(iqdiff,iqdiff/2,iqdiff/(qvalue3 + qvalue1)))
}
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)
}
range <- max(x) - min(x)
lx <- length(x)
biasf <- (lx-1)/lx
varx <- var(x)
bvarx <- varx*biasf
sdx <- sqrt(varx)
mx <- mean(x)
bsdx <- sqrt(bvarx)
x2 <- x*x
mse0 <- sum(x2)/lx
xmm <- x-mx
xmm2 <- xmm*xmm
msem <- sum(xmm2)/lx
axmm <- abs(x - mx)
medx <- median(x)
axmmed <- abs(x - medx)
xmmed <- x - medx
xmmed2 <- xmmed*xmmed
msemed <- sum(xmmed2)/lx
qarr <- array(NA,dim=c(8,3))
for (j in 1:8) {
qarr[j,] <- iqd(x,j)
}
sdpo <- 0
adpo <- 0
for (i in 1:(lx-1)) {
for (j in (i+1):lx) {
ldi <- x[i]-x[j]
aldi <- abs(ldi)
sdpo = sdpo + ldi * ldi
adpo = adpo + aldi
}
}
denom <- (lx*(lx-1)/2)
sdpo = sdpo / denom
adpo = adpo / denom
gmd <- 0
for (i in 1:lx) {
for (j in 1:lx) {
ldi <- abs(x[i]-x[j])
gmd = gmd + ldi
}
}
gmd <- gmd / (lx*(lx-1))
sumx <- sum(x)
pk <- x / sumx
ck <- cumsum(pk)
dk <- array(NA,dim=lx)
for (i in 1:lx) {
if (ck[i] <= 0.5) dk[i] <- ck[i] else dk[i] <- 1 - ck[i]
}
bigd <- sum(dk) * 2 / (lx-1)
iod <- 1 - sum(pk*pk)
res[1,] <- c('Absolute range','http://www.xycoon.com/absolute.htm', range)
res[2,] <- c('Relative range (unbiased)','http://www.xycoon.com/relative.htm', range/sd(x))
res[3,] <- c('Relative range (biased)','http://www.xycoon.com/relative.htm', range/sqrt(varx*biasf))
res[4,] <- c('Variance (unbiased)','http://www.xycoon.com/unbiased.htm', varx)
res[5,] <- c('Variance (biased)','http://www.xycoon.com/biased.htm', bvarx)
res[6,] <- c('Standard Deviation (unbiased)','http://www.xycoon.com/unbiased1.htm', sdx)
res[7,] <- c('Standard Deviation (biased)','http://www.xycoon.com/biased1.htm', bsdx)
res[8,] <- c('Coefficient of Variation (unbiased)','http://www.xycoon.com/variation.htm', sdx/mx)
res[9,] <- c('Coefficient of Variation (biased)','http://www.xycoon.com/variation.htm', bsdx/mx)
res[10,] <- c('Mean Squared Error (MSE versus 0)','http://www.xycoon.com/mse.htm', mse0)
res[11,] <- c('Mean Squared Error (MSE versus Mean)','http://www.xycoon.com/mse.htm', msem)
res[12,] <- c('Mean Absolute Deviation from Mean (MAD Mean)', 'http://www.xycoon.com/mean2.htm', sum(axmm)/lx)
res[13,] <- c('Mean Absolute Deviation from Median (MAD Median)', 'http://www.xycoon.com/median1.htm', sum(axmmed)/lx)
res[14,] <- c('Median Absolute Deviation from Mean', 'http://www.xycoon.com/mean3.htm', median(axmm))
res[15,] <- c('Median Absolute Deviation from Median', 'http://www.xycoon.com/median2.htm', median(axmmed))
res[16,] <- c('Mean Squared Deviation from Mean', 'http://www.xycoon.com/mean1.htm', msem)
res[17,] <- c('Mean Squared Deviation from Median', 'http://www.xycoon.com/median.htm', msemed)
mylink1 <- hyperlink('http://www.xycoon.com/difference.htm','Interquartile Difference','')
mylink2 <- paste(mylink1,hyperlink('http://www.xycoon.com/method_1.htm','(Weighted Average at Xnp)',''),sep=' ')
res[18,] <- c('', mylink2, qarr[1,1])
mylink2 <- paste(mylink1,hyperlink('http://www.xycoon.com/method_2.htm','(Weighted Average at X(n+1)p)',''),sep=' ')
res[19,] <- c('', mylink2, qarr[2,1])
mylink2 <- paste(mylink1,hyperlink('http://www.xycoon.com/method_3.htm','(Empirical Distribution Function)',''),sep=' ')
res[20,] <- c('', mylink2, qarr[3,1])
mylink2 <- paste(mylink1,hyperlink('http://www.xycoon.com/method_4.htm','(Empirical Distribution Function - Averaging)',''),sep=' ')
res[21,] <- c('', mylink2, qarr[4,1])
mylink2 <- paste(mylink1,hyperlink('http://www.xycoon.com/method_5.htm','(Empirical Distribution Function - Interpolation)',''),sep=' ')
res[22,] <- c('', mylink2, qarr[5,1])
mylink2 <- paste(mylink1,hyperlink('http://www.xycoon.com/method_6.htm','(Closest Observation)',''),sep=' ')
res[23,] <- c('', mylink2, qarr[6,1])
mylink2 <- paste(mylink1,hyperlink('http://www.xycoon.com/method_7.htm','(True Basic - Statistics Graphics Toolkit)',''),sep=' ')
res[24,] <- c('', mylink2, qarr[7,1])
mylink2 <- paste(mylink1,hyperlink('http://www.xycoon.com/method_8.htm','(MS Excel (old versions))',''),sep=' ')
res[25,] <- c('', mylink2, qarr[8,1])
mylink1 <- hyperlink('http://www.xycoon.com/deviation.htm','Semi Interquartile Difference','')
mylink2 <- paste(mylink1,hyperlink('http://www.xycoon.com/method_1.htm','(Weighted Average at Xnp)',''),sep=' ')
res[26,] <- c('', mylink2, qarr[1,2])
mylink2 <- paste(mylink1,hyperlink('http://www.xycoon.com/method_2.htm','(Weighted Average at X(n+1)p)',''),sep=' ')
res[27,] <- c('', mylink2, qarr[2,2])
mylink2 <- paste(mylink1,hyperlink('http://www.xycoon.com/method_3.htm','(Empirical Distribution Function)',''),sep=' ')
res[28,] <- c('', mylink2, qarr[3,2])
mylink2 <- paste(mylink1,hyperlink('http://www.xycoon.com/method_4.htm','(Empirical Distribution Function - Averaging)',''),sep=' ')
res[29,] <- c('', mylink2, qarr[4,2])
mylink2 <- paste(mylink1,hyperlink('http://www.xycoon.com/method_5.htm','(Empirical Distribution Function - Interpolation)',''),sep=' ')
res[30,] <- c('', mylink2, qarr[5,2])
mylink2 <- paste(mylink1,hyperlink('http://www.xycoon.com/method_6.htm','(Closest Observation)',''),sep=' ')
res[31,] <- c('', mylink2, qarr[6,2])
mylink2 <- paste(mylink1,hyperlink('http://www.xycoon.com/method_7.htm','(True Basic - Statistics Graphics Toolkit)',''),sep=' ')
res[32,] <- c('', mylink2, qarr[7,2])
mylink2 <- paste(mylink1,hyperlink('http://www.xycoon.com/method_8.htm','(MS Excel (old versions))',''),sep=' ')
res[33,] <- c('', mylink2, qarr[8,2])
mylink1 <- hyperlink('http://www.xycoon.com/variation1.htm','Coefficient of Quartile Variation','')
mylink2 <- paste(mylink1,hyperlink('http://www.xycoon.com/method_1.htm','(Weighted Average at Xnp)',''),sep=' ')
res[34,] <- c('', mylink2, qarr[1,3])
mylink2 <- paste(mylink1,hyperlink('http://www.xycoon.com/method_2.htm','(Weighted Average at X(n+1)p)',''),sep=' ')
res[35,] <- c('', mylink2, qarr[2,3])
mylink2 <- paste(mylink1,hyperlink('http://www.xycoon.com/method_3.htm','(Empirical Distribution Function)',''),sep=' ')
res[36,] <- c('', mylink2, qarr[3,3])
mylink2 <- paste(mylink1,hyperlink('http://www.xycoon.com/method_4.htm','(Empirical Distribution Function - Averaging)',''),sep=' ')
res[37,] <- c('', mylink2, qarr[4,3])
mylink2 <- paste(mylink1,hyperlink('http://www.xycoon.com/method_5.htm','(Empirical Distribution Function - Interpolation)',''),sep=' ')
res[38,] <- c('', mylink2, qarr[5,3])
mylink2 <- paste(mylink1,hyperlink('http://www.xycoon.com/method_6.htm','(Closest Observation)',''),sep=' ')
res[39,] <- c('', mylink2, qarr[6,3])
mylink2 <- paste(mylink1,hyperlink('http://www.xycoon.com/method_7.htm','(True Basic - Statistics Graphics Toolkit)',''),sep=' ')
res[40,] <- c('', mylink2, qarr[7,3])
mylink2 <- paste(mylink1,hyperlink('http://www.xycoon.com/method_8.htm','(MS Excel (old versions))',''),sep=' ')
res[41,] <- c('', mylink2, qarr[8,3])
res[42,] <- c('Number of all Pairs of Observations', 'http://www.xycoon.com/pair_numbers.htm', lx*(lx-1)/2)
res[43,] <- c('Squared Differences between all Pairs of Observations', 'http://www.xycoon.com/squared_differences.htm', sdpo)
res[44,] <- c('Mean Absolute Differences between all Pairs of Observations', 'http://www.xycoon.com/mean_abs_differences.htm', adpo)
res[45,] <- c('Gini Mean Difference', 'http://www.xycoon.com/gini_mean_difference.htm', gmd)
res[46,] <- c('Leik Measure of Dispersion', 'http://www.xycoon.com/leiks_d.htm', bigd)
res[47,] <- c('Index of Diversity', 'http://www.xycoon.com/diversity.htm', iod)
res[48,] <- c('Index of Qualitative Variation', 'http://www.xycoon.com/qualitative_variation.htm', iod*lx/(lx-1))
res[49,] <- c('Coefficient of Dispersion', 'http://www.xycoon.com/dispersion.htm', sum(axmm)/lx/medx)
res[50,] <- c('Observations', '', lx)
res
(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='Robustness of Central Tendency', xlab='j', pch=19, ylab='Winsorized Mean(j/n)', ylim=c(min(lb),max(ub))) else plot(win[,1],type='l',main='Robustness of Central Tendency', 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='Robustness of Central Tendency', xlab='j', pch=19, ylab='Trimmed Mean(j/n)', ylim=c(min(lb),max(ub))) else plot(tri[,1],type='l',main='Robustness of Central Tendency', xlab='j', pch=19, ylab='Trimmed Mean(j/n)', ylim=c(ylimmin,ylimmax))
lines(ub,lty=3)
lines(lb,lty=3)
grid()
dev.off()
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')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Variability - Ungrouped Data',2,TRUE)
a<-table.row.end(a)
for (i in 1:num) {
a<-table.row.start(a)
if (res[i,1] != '') {
a<-table.element(a,hyperlink(res[i,2],res[i,1],''),header=TRUE)
} else {
a<-table.element(a,res[i,2],header=TRUE)
}
a<-table.element(a,res[i,3])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable1.tab')
lx <- length(x)
qval <- array(NA,dim=c(99,8))
mystep <- 25
mystart <- 25
if (lx>10){
mystep=10
mystart=10
}
if (lx>20){
mystep=5
mystart=5
}
if (lx>50){
mystep=2
mystart=2
}
if (lx>=100){
mystep=1
mystart=1
}
for (perc in seq(mystart,99,mystep)) {
qval[perc,1] <- q1(x,lx,perc/100,i,f)
qval[perc,2] <- q2(x,lx,perc/100,i,f)
qval[perc,3] <- q3(x,lx,perc/100,i,f)
qval[perc,4] <- q4(x,lx,perc/100,i,f)
qval[perc,5] <- q5(x,lx,perc/100,i,f)
qval[perc,6] <- q6(x,lx,perc/100,i,f)
qval[perc,7] <- q7(x,lx,perc/100,i,f)
qval[perc,8] <- q8(x,lx,perc/100,i,f)
}
bitmap(file='test3.png')
myqqnorm <- qqnorm(x,col=2)
qqline(x)
grid()
dev.off()
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Percentiles - Ungrouped Data',9,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'p',1,TRUE)
a<-table.element(a,hyperlink('http://www.xycoon.com/method_1.htm', 'Weighted Average at Xnp',''),1,TRUE)
a<-table.element(a,hyperlink('http://www.xycoon.com/method_2.htm','Weighted Average at X(n+1)p',''),1,TRUE)
a<-table.element(a,hyperlink('http://www.xycoon.com/method_3.htm','Empirical Distribution Function',''),1,TRUE)
a<-table.element(a,hyperlink('http://www.xycoon.com/method_4.htm','Empirical Distribution Function - Averaging',''),1,TRUE)
a<-table.element(a,hyperlink('http://www.xycoon.com/method_5.htm','Empirical Distribution Function - Interpolation',''),1,TRUE)
a<-table.element(a,hyperlink('http://www.xycoon.com/method_6.htm','Closest Observation',''),1,TRUE)
a<-table.element(a,hyperlink('http://www.xycoon.com/method_7.htm','True Basic - Statistics Graphics Toolkit',''),1,TRUE)
a<-table.element(a,hyperlink('http://www.xycoon.com/method_8.htm','MS Excel (old versions)',''),1,TRUE)
a<-table.row.end(a)
for (perc in seq(mystart,99,mystep)) {
a<-table.row.start(a)
a<-table.element(a,round(perc/100,2),1,TRUE)
for (j in 1:8) {
a<-table.element(a,round(qval[perc,j],6))
}
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable2.tab')
bitmap(file='histogram1.png')
myhist<-hist(x)
dev.off()
myhist
n <- length(x)
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,hyperlink('http://www.xycoon.com/histogram.htm','Frequency Table (Histogram)',''),6,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Bins',header=TRUE)
a<-table.element(a,'Midpoint',header=TRUE)
a<-table.element(a,'Abs. Frequency',header=TRUE)
a<-table.element(a,'Rel. Frequency',header=TRUE)
a<-table.element(a,'Cumul. Rel. Freq.',header=TRUE)
a<-table.element(a,'Density',header=TRUE)
a<-table.row.end(a)
crf <- 0
mybracket <- '['
mynumrows <- (length(myhist$breaks)-1)
for (i in 1:mynumrows) {
a<-table.row.start(a)
if (i == 1)
dum <- paste('[',myhist$breaks[i],sep='')
else
dum <- paste(mybracket,myhist$breaks[i],sep='')
dum <- paste(dum,myhist$breaks[i+1],sep=',')
if (i==mynumrows)
dum <- paste(dum,']',sep='')
else
dum <- paste(dum,mybracket,sep='')
a<-table.element(a,dum,header=TRUE)
a<-table.element(a,myhist$mids[i])
a<-table.element(a,myhist$counts[i])
rf <- myhist$counts[i]/n
crf <- crf + rf
a<-table.element(a,round(rf,6))
a<-table.element(a,round(crf,6))
a<-table.element(a,round(myhist$density[i],6))
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable5.tab')
bitmap(file='density1.png')
mydensity1<-density(x,kernel='gaussian',na.rm=TRUE)
plot(mydensity1,main='Gaussian Kernel')
grid()
dev.off()
mydensity1
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Properties of Density Trace',2,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Bandwidth',header=TRUE)
a<-table.element(a,mydensity1$bw)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'#Observations',header=TRUE)
a<-table.element(a,mydensity1$n)
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable4.tab')
 





Copyright

Creative Commons License

This work is licensed under a Creative Commons Attribution-Noncommercial-Share Alike 3.0 License.

Software written by Ed van Stee & Patrick Wessa


Disclaimer

Information provided on this web site is provided "AS IS" without warranty of any kind, either express or implied, including, without limitation, warranties of merchantability, fitness for a particular purpose, and noninfringement. We use reasonable efforts to include accurate and timely information and periodically update the information, and software without notice. However, we make no warranties or representations as to the accuracy or completeness of such information (or software), and we assume no liability or responsibility for errors or omissions in the content of this web site, or any software bugs in online applications. Your use of this web site is AT YOUR OWN RISK. Under no circumstances and under no legal theory shall we be liable to you or any other person for any direct, indirect, special, incidental, exemplary, or consequential damages arising from your access to, or use of, this web site.


Privacy Policy

We may request personal information to be submitted to our servers in order to be able to:

  • personalize online software applications according to your needs
  • enforce strict security rules with respect to the data that you upload (e.g. statistical data)
  • manage user sessions of online applications
  • alert you about important changes or upgrades in resources or applications

We NEVER allow other companies to directly offer registered users information about their products and services. Banner references and hyperlinks of third parties NEVER contain any personal data of the visitor.

We do NOT sell, nor transmit by any means, personal information, nor statistical data series uploaded by you to third parties.

We carefully protect your data from loss, misuse, alteration, and destruction. However, at any time, and under any circumstance you are solely responsible for managing your passwords, and keeping them secret.

We store a unique ANONYMOUS USER ID in the form of a small 'Cookie' on your computer. This allows us to track your progress when using this website which is necessary to create state-dependent features. The cookie is used for NO OTHER PURPOSE. At any time you may opt to disallow cookies from this website - this will not affect other features of this website.

We examine cookies that are used by third-parties (banner and online ads) very closely: abuse from third-parties automatically results in termination of the advertising contract without refund. We have very good reason to believe that the cookies that are produced by third parties (banner ads) do NOT cause any privacy or security risk.

FreeStatistics.org is safe. There is no need to download any software to use the applications and services contained in this website. Hence, your system's security is not compromised by their use, and your personal data - other than data you submit in the account application form, and the user-agent information that is transmitted by your browser - is never transmitted to our servers.

As a general rule, we do not log on-line behavior of individuals (other than normal logging of webserver 'hits'). However, in cases of abuse, hacking, unauthorized access, Denial of Service attacks, illegal copying, hotlinking, non-compliance with international webstandards (such as robots.txt), or any other harmful behavior, our system engineers are empowered to log, track, identify, publish, and ban misbehaving individuals - even if this leads to ban entire blocks of IP addresses, or disclosing user's identity.


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