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*The author of this computation has been verified*

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

Title produced by software: Percentiles

Date of computation: Mon, 20 Dec 2010 15:15:00 +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/Dec/20/t1292857966ao9xpcl5yw9hfkk.htm/, Retrieved Thu, 23 May 2013 16:19:25 +0000

Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords:

System-generated keywords (parent):

t1290802017s02ej0wvac8kz2e (pk = 102197)

Estimated Impact

Dataseries X:

» Textfile « » CSV « » Stem and Leaf « » Histogram « » Kernel Density « » Harrell-Davis Quantiles « » Central Tendency « » Variability «

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	'George Udny Yule' @ 72.249.76.132

Percentiles - Ungrouped Data
p	Weighted Average at Xnp	Weighted Average at X(n+1)p	Empirical Distribution Function	Empirical Distribution Function - Averaging	Empirical Distribution Function - Interpolation	Closest Observation	True Basic - Statistics Graphics Toolkit	MS Excel (old versions)
0.02	245329.36	245468.12	250741	250741	251224.4	243803	249075.88	243803
0.04	251804.48	251901.16	253158	253158	254111.6	250741	251997.84	250741
0.06	254731.44	254874.48	255542	255542	255578.6	255542	253825.52	255542
0.08	255595.68	255600.56	255603	255603	256054.2	255603	255544.44	255603
0.1	256587.9	257008.8	260376	260376	260376	256167	259534.2	256167
0.12	260600	260684	261076	261076	261365.2	260376	260768	260376
0.14	261856.84	262059.28	262522	262522	262542	262522	261538.72	262522
0.16	262560	262568	262572	262572	262994.4	262572	262526	262572
0.18	263261.92	263278.24	263276	263276	263287.2	263276	263287.76	263276
0.2	263412.6	263535.2	263903	263903	263903	263290	263657.8	263290
0.22	264036.56	264106.52	264221	264221	264235	263903	264017.48	264221
0.24	264265.8	264282.6	264291	264291	264567	264291	264229.4	264291
0.26	264884.4	265154.16	264981	264981	265846.8	264981	266250.84	264981
0.28	266482.32	266686.44	267153	267153	267007.2	266424	266890.56	266424
0.3	267521.4	267889.8	268381	268381	268381	267153	267644.2	268381
0.32	269730.4	270560.8	270976	270976	271003.8	270976	268796.2	270976
0.34	271078.86	271231.08	271115	271115	271695.4	271115	272449.92	271115
0.36	272507.96	273633.52	272566	272566	274567.6	272566	274834.48	272566
0.38	275996.5	276196	276427	276427	276322	275902	276133	276427
0.4	276446.2	276465.4	276475	276475	276475	276427	276436.6	276475
0.42	277116.08	277595.88	277509	277509	277943.4	277509	279594.12	277509
0.44	279333.48	279894.92	279681	279681	279986.6	279681	280231.08	279681
0.46	280698.98	282646.16	284678	284678	282984.8	280445	282476.84	284678
0.48	284840.12	285118.04	285257	285257	285141.2	284678	284816.96	285257
0.5	286125.5	286994	286994	286994	286994	286994	286994	286994
0.52	287159.6	288229.36	287224	287224	288061.8	287224	290407.64	287224
0.54	291161.66	291474.92	291413	291413	291464.6	291413	291480.08	291413
0.56	291912.88	293210.96	293860	293860	292932.8	291542	292191.04	293860
0.58	294641.28	295833.76	295916	295916	295504.8	293860	293942.24	295916
0.6	296450	297129.4	296806	296806	296806	296806	298099.6	296806
0.62	298131.94	298672.04	298423	298423	298536.2	298423	298739.96	298423
0.64	299042.08	299891.36	300316	300316	299519.8	298989	299413.64	300316
0.66	300419.22	300681.24	300713	300713	300554.2	300316	300347.76	300713
0.68	301153.64	301842.04	301631	301631	301447.4	300713	302738.96	301631
0.7	302554.3	302955.2	302950	302950	302950	302950	302957.8	302950
0.72	302961.96	303369.4	302963	302963	303090	302963	303191.6	303598
0.74	303659.18	303982.56	304035	304035	303772.8	303598	303650.44	304035
0.76	305865.24	309151.64	309119	309119	307085.4	304035	309358.36	309119
0.78	309276.76	309489.28	309391	309391	309336.6	309391	309565.72	309391
0.8	309609.4	311231.2	309664	309664	309664	309664	310708.8	312276
0.82	312294.84	313067.28	313218	313218	312464.4	312276	312426.72	313218
0.84	313342.56	313752.2	313737	313737	313425.6	313218	313911.8	313737
0.86	313824.4	314105.56	313927	313927	313851	313737	314306.44	313927
0.88	314306.44	319774.76	314485	314485	314373.4	314485	318641.24	323931
0.9	322986.4	326879	323931	323931	323931	323931	324668	327616
0.92	327873.88	329913.44	329765	329765	328045.8	327616	333327.56	329765
0.94	331026.74	333925.96	333476	333476	331249.4	329765	334633.04	333476
0.96	334375.92	335524.48	335083	335083	334440.2	335083	335490.52	335932
0.98	335745.22	337274.16	335932	335932	335762.2	335932	336355.84	337698

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/20/t1292857966ao9xpcl5yw9hfkk/1ngwr1292858098.png (opens in new window)

http://www.freestatistics.org/blog/date/2010/Dec/20/t1292857966ao9xpcl5yw9hfkk/1ngwr1292858098.ps (opens in new window)

Click here to open pdf file.

Parameters (Session):

Parameters (R input):

R code (references can be found in the software module):

x <-sort(x[!is.na(x)])
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]
}
}
}
}
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='test1.png')
myqqnorm <- qqnorm(x,col=2)
qqline(x)
grid()
dev.off()
load(file='createtable')
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='mytable.tab')