Free Statistics

of Irreproducible Research!

Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_percentiles.wasp
Title produced by softwarePercentiles
Date of computationMon, 17 Oct 2011 14:54:08 -0400
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2011/Oct/17/t1318877658dea2l0a6ztprj6x.htm/, Retrieved Thu, 16 May 2024 01:32:40 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=131004, Retrieved Thu, 16 May 2024 01:32:40 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact54
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Percentiles] [Intrinsic Motivat...] [2010-10-12 12:10:58] [b98453cac15ba1066b407e146608df68]
- R PD    [Percentiles] [] [2011-10-17 18:54:08] [2e63149daec6ba44c7d6fab36a0b0c34] [Current]
Feedback Forum

Post a new message
Dataseries X:
26
20
19
19
20
25
25
22
26
22
17
22
19
24
26
21
13
26
20
22
14
21
7
23
17
25
25
19
20
23
22
10




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Herman Ole Andreas Wold' @ wold.wessa.net

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 1 seconds \tabularnewline
R Server & 'Herman Ole Andreas Wold' @ wold.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=131004&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Herman Ole Andreas Wold' @ wold.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=131004&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=131004&T=0

As an alternative you can also use a QR Code:  

The GUIDs for individual cells are displayed in the table below:

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Herman Ole Andreas Wold' @ wold.wessa.net







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)
0.058.88.95101011.65108.0510
0.113.213.3141414.31313.713
0.1516.416.851717171714.1517
0.217.818.21919191717.819
0.251919191919191919
0.31919191919.3191919
0.352020202020202020
0.42020202020202020
0.4520.420.85212120.952020.1521
0.52121.52121.521.52121.521.5
0.552222222222222222
0.62222222222222222
0.652222.45222222.152222.5522
0.72323.12323232323.923
0.752424.752424.524.252424.2525
0.82525252525252525
0.852525.052525252525.9525
0.925.826262625.9262626
0.952626262626262626

\begin{tabular}{lllllllll}
\hline
Percentiles - Ungrouped Data \tabularnewline
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) \tabularnewline
0.05 & 8.8 & 8.95 & 10 & 10 & 11.65 & 10 & 8.05 & 10 \tabularnewline
0.1 & 13.2 & 13.3 & 14 & 14 & 14.3 & 13 & 13.7 & 13 \tabularnewline
0.15 & 16.4 & 16.85 & 17 & 17 & 17 & 17 & 14.15 & 17 \tabularnewline
0.2 & 17.8 & 18.2 & 19 & 19 & 19 & 17 & 17.8 & 19 \tabularnewline
0.25 & 19 & 19 & 19 & 19 & 19 & 19 & 19 & 19 \tabularnewline
0.3 & 19 & 19 & 19 & 19 & 19.3 & 19 & 19 & 19 \tabularnewline
0.35 & 20 & 20 & 20 & 20 & 20 & 20 & 20 & 20 \tabularnewline
0.4 & 20 & 20 & 20 & 20 & 20 & 20 & 20 & 20 \tabularnewline
0.45 & 20.4 & 20.85 & 21 & 21 & 20.95 & 20 & 20.15 & 21 \tabularnewline
0.5 & 21 & 21.5 & 21 & 21.5 & 21.5 & 21 & 21.5 & 21.5 \tabularnewline
0.55 & 22 & 22 & 22 & 22 & 22 & 22 & 22 & 22 \tabularnewline
0.6 & 22 & 22 & 22 & 22 & 22 & 22 & 22 & 22 \tabularnewline
0.65 & 22 & 22.45 & 22 & 22 & 22.15 & 22 & 22.55 & 22 \tabularnewline
0.7 & 23 & 23.1 & 23 & 23 & 23 & 23 & 23.9 & 23 \tabularnewline
0.75 & 24 & 24.75 & 24 & 24.5 & 24.25 & 24 & 24.25 & 25 \tabularnewline
0.8 & 25 & 25 & 25 & 25 & 25 & 25 & 25 & 25 \tabularnewline
0.85 & 25 & 25.05 & 25 & 25 & 25 & 25 & 25.95 & 25 \tabularnewline
0.9 & 25.8 & 26 & 26 & 26 & 25.9 & 26 & 26 & 26 \tabularnewline
0.95 & 26 & 26 & 26 & 26 & 26 & 26 & 26 & 26 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=131004&T=1

[TABLE]
[ROW][C]Percentiles - Ungrouped Data[/C][/ROW]
[ROW][C]p[/C][C]Weighted Average at Xnp[/C][C]Weighted Average at X(n+1)p[/C][C]Empirical Distribution Function[/C][C]Empirical Distribution Function - Averaging[/C][C]Empirical Distribution Function - Interpolation[/C][C]Closest Observation[/C][C]True Basic - Statistics Graphics Toolkit[/C][C]MS Excel (old versions)[/C][/ROW]
[ROW][C]0.05[/C][C]8.8[/C][C]8.95[/C][C]10[/C][C]10[/C][C]11.65[/C][C]10[/C][C]8.05[/C][C]10[/C][/ROW]
[ROW][C]0.1[/C][C]13.2[/C][C]13.3[/C][C]14[/C][C]14[/C][C]14.3[/C][C]13[/C][C]13.7[/C][C]13[/C][/ROW]
[ROW][C]0.15[/C][C]16.4[/C][C]16.85[/C][C]17[/C][C]17[/C][C]17[/C][C]17[/C][C]14.15[/C][C]17[/C][/ROW]
[ROW][C]0.2[/C][C]17.8[/C][C]18.2[/C][C]19[/C][C]19[/C][C]19[/C][C]17[/C][C]17.8[/C][C]19[/C][/ROW]
[ROW][C]0.25[/C][C]19[/C][C]19[/C][C]19[/C][C]19[/C][C]19[/C][C]19[/C][C]19[/C][C]19[/C][/ROW]
[ROW][C]0.3[/C][C]19[/C][C]19[/C][C]19[/C][C]19[/C][C]19.3[/C][C]19[/C][C]19[/C][C]19[/C][/ROW]
[ROW][C]0.35[/C][C]20[/C][C]20[/C][C]20[/C][C]20[/C][C]20[/C][C]20[/C][C]20[/C][C]20[/C][/ROW]
[ROW][C]0.4[/C][C]20[/C][C]20[/C][C]20[/C][C]20[/C][C]20[/C][C]20[/C][C]20[/C][C]20[/C][/ROW]
[ROW][C]0.45[/C][C]20.4[/C][C]20.85[/C][C]21[/C][C]21[/C][C]20.95[/C][C]20[/C][C]20.15[/C][C]21[/C][/ROW]
[ROW][C]0.5[/C][C]21[/C][C]21.5[/C][C]21[/C][C]21.5[/C][C]21.5[/C][C]21[/C][C]21.5[/C][C]21.5[/C][/ROW]
[ROW][C]0.55[/C][C]22[/C][C]22[/C][C]22[/C][C]22[/C][C]22[/C][C]22[/C][C]22[/C][C]22[/C][/ROW]
[ROW][C]0.6[/C][C]22[/C][C]22[/C][C]22[/C][C]22[/C][C]22[/C][C]22[/C][C]22[/C][C]22[/C][/ROW]
[ROW][C]0.65[/C][C]22[/C][C]22.45[/C][C]22[/C][C]22[/C][C]22.15[/C][C]22[/C][C]22.55[/C][C]22[/C][/ROW]
[ROW][C]0.7[/C][C]23[/C][C]23.1[/C][C]23[/C][C]23[/C][C]23[/C][C]23[/C][C]23.9[/C][C]23[/C][/ROW]
[ROW][C]0.75[/C][C]24[/C][C]24.75[/C][C]24[/C][C]24.5[/C][C]24.25[/C][C]24[/C][C]24.25[/C][C]25[/C][/ROW]
[ROW][C]0.8[/C][C]25[/C][C]25[/C][C]25[/C][C]25[/C][C]25[/C][C]25[/C][C]25[/C][C]25[/C][/ROW]
[ROW][C]0.85[/C][C]25[/C][C]25.05[/C][C]25[/C][C]25[/C][C]25[/C][C]25[/C][C]25.95[/C][C]25[/C][/ROW]
[ROW][C]0.9[/C][C]25.8[/C][C]26[/C][C]26[/C][C]26[/C][C]25.9[/C][C]26[/C][C]26[/C][C]26[/C][/ROW]
[ROW][C]0.95[/C][C]26[/C][C]26[/C][C]26[/C][C]26[/C][C]26[/C][C]26[/C][C]26[/C][C]26[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=131004&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=131004&T=1

As an alternative you can also use a QR Code:  

The GUIDs for individual cells are displayed in the table below:

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)
0.058.88.95101011.65108.0510
0.113.213.3141414.31313.713
0.1516.416.851717171714.1517
0.217.818.21919191717.819
0.251919191919191919
0.31919191919.3191919
0.352020202020202020
0.42020202020202020
0.4520.420.85212120.952020.1521
0.52121.52121.521.52121.521.5
0.552222222222222222
0.62222222222222222
0.652222.45222222.152222.5522
0.72323.12323232323.923
0.752424.752424.524.252424.2525
0.82525252525252525
0.852525.052525252525.9525
0.925.826262625.9262626
0.952626262626262626



Parameters (Session):
par1 = 8 ; par2 = 0 ;
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('method_1.htm', 'Weighted Average at Xnp',''),1,TRUE)
a<-table.element(a,hyperlink('method_2.htm','Weighted Average at X(n+1)p',''),1,TRUE)
a<-table.element(a,hyperlink('method_3.htm','Empirical Distribution Function',''),1,TRUE)
a<-table.element(a,hyperlink('method_4.htm','Empirical Distribution Function - Averaging',''),1,TRUE)
a<-table.element(a,hyperlink('method_5.htm','Empirical Distribution Function - Interpolation',''),1,TRUE)
a<-table.element(a,hyperlink('method_6.htm','Closest Observation',''),1,TRUE)
a<-table.element(a,hyperlink('method_7.htm','True Basic - Statistics Graphics Toolkit',''),1,TRUE)
a<-table.element(a,hyperlink('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')