Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_percentiles.wasp
Title produced by softwarePercentiles
Date of computationWed, 01 Feb 2017 04:50:11 +0000
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2017/Feb/01/t1485924666q5rhkuo396lx1aw.htm/, Retrieved Sun, 12 May 2024 21:39:11 +0200
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=, Retrieved Sun, 12 May 2024 21:39:11 +0200
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact0
Dataseries X:
73
19
16
64
28
28
31
90
60
56
31
56
22
18
45
48
17
17
17
91
92
63
50
51
69
16
17




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time0 seconds
R Server'Sir Ronald Aylmer Fisher' @ fisher.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 & 0 seconds \tabularnewline
R Server & 'Sir Ronald Aylmer Fisher' @ fisher.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&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]0 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Sir Ronald Aylmer Fisher' @ fisher.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&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 time0 seconds
R Server'Sir Ronald Aylmer Fisher' @ fisher.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)
0.051616161616.3161616
0.116.716.81717171716.217
0.151717171717171717
0.21717171717.2171717
0.2517.7518181818.5181818
0.319.320.2222221.41920.819
0.3524.726.82828282223.228
0.42828.6282829.22830.428
0.453131313131313131
0.53845454545454545
0.5547.5548.8484848.64849.248
0.650.250.8515150.65050.251
0.6553.7556565655.5565656
0.75658.4565656.85657.660
0.7560.7563636361.5606363
0.863.666646463.8646764
0.8568.7572.2696969.46969.873
0.978.190.2909079.87390.890
0.9590.6591.6919190.79191.492

\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 & 16 & 16 & 16 & 16 & 16.3 & 16 & 16 & 16 \tabularnewline
0.1 & 16.7 & 16.8 & 17 & 17 & 17 & 17 & 16.2 & 17 \tabularnewline
0.15 & 17 & 17 & 17 & 17 & 17 & 17 & 17 & 17 \tabularnewline
0.2 & 17 & 17 & 17 & 17 & 17.2 & 17 & 17 & 17 \tabularnewline
0.25 & 17.75 & 18 & 18 & 18 & 18.5 & 18 & 18 & 18 \tabularnewline
0.3 & 19.3 & 20.2 & 22 & 22 & 21.4 & 19 & 20.8 & 19 \tabularnewline
0.35 & 24.7 & 26.8 & 28 & 28 & 28 & 22 & 23.2 & 28 \tabularnewline
0.4 & 28 & 28.6 & 28 & 28 & 29.2 & 28 & 30.4 & 28 \tabularnewline
0.45 & 31 & 31 & 31 & 31 & 31 & 31 & 31 & 31 \tabularnewline
0.5 & 38 & 45 & 45 & 45 & 45 & 45 & 45 & 45 \tabularnewline
0.55 & 47.55 & 48.8 & 48 & 48 & 48.6 & 48 & 49.2 & 48 \tabularnewline
0.6 & 50.2 & 50.8 & 51 & 51 & 50.6 & 50 & 50.2 & 51 \tabularnewline
0.65 & 53.75 & 56 & 56 & 56 & 55.5 & 56 & 56 & 56 \tabularnewline
0.7 & 56 & 58.4 & 56 & 56 & 56.8 & 56 & 57.6 & 60 \tabularnewline
0.75 & 60.75 & 63 & 63 & 63 & 61.5 & 60 & 63 & 63 \tabularnewline
0.8 & 63.6 & 66 & 64 & 64 & 63.8 & 64 & 67 & 64 \tabularnewline
0.85 & 68.75 & 72.2 & 69 & 69 & 69.4 & 69 & 69.8 & 73 \tabularnewline
0.9 & 78.1 & 90.2 & 90 & 90 & 79.8 & 73 & 90.8 & 90 \tabularnewline
0.95 & 90.65 & 91.6 & 91 & 91 & 90.7 & 91 & 91.4 & 92 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&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]16[/C][C]16[/C][C]16[/C][C]16[/C][C]16.3[/C][C]16[/C][C]16[/C][C]16[/C][/ROW]
[ROW][C]0.1[/C][C]16.7[/C][C]16.8[/C][C]17[/C][C]17[/C][C]17[/C][C]17[/C][C]16.2[/C][C]17[/C][/ROW]
[ROW][C]0.15[/C][C]17[/C][C]17[/C][C]17[/C][C]17[/C][C]17[/C][C]17[/C][C]17[/C][C]17[/C][/ROW]
[ROW][C]0.2[/C][C]17[/C][C]17[/C][C]17[/C][C]17[/C][C]17.2[/C][C]17[/C][C]17[/C][C]17[/C][/ROW]
[ROW][C]0.25[/C][C]17.75[/C][C]18[/C][C]18[/C][C]18[/C][C]18.5[/C][C]18[/C][C]18[/C][C]18[/C][/ROW]
[ROW][C]0.3[/C][C]19.3[/C][C]20.2[/C][C]22[/C][C]22[/C][C]21.4[/C][C]19[/C][C]20.8[/C][C]19[/C][/ROW]
[ROW][C]0.35[/C][C]24.7[/C][C]26.8[/C][C]28[/C][C]28[/C][C]28[/C][C]22[/C][C]23.2[/C][C]28[/C][/ROW]
[ROW][C]0.4[/C][C]28[/C][C]28.6[/C][C]28[/C][C]28[/C][C]29.2[/C][C]28[/C][C]30.4[/C][C]28[/C][/ROW]
[ROW][C]0.45[/C][C]31[/C][C]31[/C][C]31[/C][C]31[/C][C]31[/C][C]31[/C][C]31[/C][C]31[/C][/ROW]
[ROW][C]0.5[/C][C]38[/C][C]45[/C][C]45[/C][C]45[/C][C]45[/C][C]45[/C][C]45[/C][C]45[/C][/ROW]
[ROW][C]0.55[/C][C]47.55[/C][C]48.8[/C][C]48[/C][C]48[/C][C]48.6[/C][C]48[/C][C]49.2[/C][C]48[/C][/ROW]
[ROW][C]0.6[/C][C]50.2[/C][C]50.8[/C][C]51[/C][C]51[/C][C]50.6[/C][C]50[/C][C]50.2[/C][C]51[/C][/ROW]
[ROW][C]0.65[/C][C]53.75[/C][C]56[/C][C]56[/C][C]56[/C][C]55.5[/C][C]56[/C][C]56[/C][C]56[/C][/ROW]
[ROW][C]0.7[/C][C]56[/C][C]58.4[/C][C]56[/C][C]56[/C][C]56.8[/C][C]56[/C][C]57.6[/C][C]60[/C][/ROW]
[ROW][C]0.75[/C][C]60.75[/C][C]63[/C][C]63[/C][C]63[/C][C]61.5[/C][C]60[/C][C]63[/C][C]63[/C][/ROW]
[ROW][C]0.8[/C][C]63.6[/C][C]66[/C][C]64[/C][C]64[/C][C]63.8[/C][C]64[/C][C]67[/C][C]64[/C][/ROW]
[ROW][C]0.85[/C][C]68.75[/C][C]72.2[/C][C]69[/C][C]69[/C][C]69.4[/C][C]69[/C][C]69.8[/C][C]73[/C][/ROW]
[ROW][C]0.9[/C][C]78.1[/C][C]90.2[/C][C]90[/C][C]90[/C][C]79.8[/C][C]73[/C][C]90.8[/C][C]90[/C][/ROW]
[ROW][C]0.95[/C][C]90.65[/C][C]91.6[/C][C]91[/C][C]91[/C][C]90.7[/C][C]91[/C][C]91.4[/C][C]92[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&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)
0.051616161616.3161616
0.116.716.81717171716.217
0.151717171717171717
0.21717171717.2171717
0.2517.7518181818.5181818
0.319.320.2222221.41920.819
0.3524.726.82828282223.228
0.42828.6282829.22830.428
0.453131313131313131
0.53845454545454545
0.5547.5548.8484848.64849.248
0.650.250.8515150.65050.251
0.6553.7556565655.5565656
0.75658.4565656.85657.660
0.7560.7563636361.5606363
0.863.666646463.8646764
0.8568.7572.2696969.46969.873
0.978.190.2909079.87390.890
0.9590.6591.6919190.79191.492



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('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')