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Author's title

Author

*Unverified author*

R Software Module

rwasp_percentiles.wasp

Title produced by software

Percentiles

Date of computation

Tue, 24 Sep 2019 15:25:27 +0200

Cite this page as follows

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2019/Sep/24/t15693315820xl2re66qpruxb5.htm/, Retrieved Thu, 02 May 2024 21:08:32 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=318913, Retrieved Thu, 02 May 2024 21:08:32 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

131

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)

-       [Percentiles] [Upvotes (Measured...] [2019-09-24 13:25:27] [d41d8cd98f00b204e9800998ecf8427e] [Current]

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Dataseries X:

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Histogram

Boxplots

12.3
13.6
15.9
22.1
24.9
25.2
26.8
27.1
28.5
32.5
33.9
36.2
38.8
39.7
40.3
40.5
42.3
46.3
46.4
49.3
49.9
50.4
50.5
56.2
59.2
59.7
59.8
60.4
63.4
64.5
67.3
72.3
74.7
78.3
83.2
83.7

Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	0 seconds
R Server	Big Analytics Cloud Computing Center

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input view raw input (R code)  \tabularnewline
Raw Outputview raw output of R engine  \tabularnewline
Computing time0 seconds \tabularnewline
R ServerBig Analytics Cloud Computing Center \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=318913&T=0

[TABLE]
[ROW]

Summary of computational transaction[/C][/ROW] [ROW]

Raw Input[/C]

view raw input (R code) [/C][/ROW] [ROW]

Raw Output[/C]

view raw output of R engine [/C][/ROW] [ROW]

Computing time[/C]

0 seconds[/C][/ROW] [ROW]

R Server[/C]

Big Analytics Cloud Computing Center[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=318913&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=318913&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 Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	0 seconds
R Server	Big Analytics Cloud Computing Center

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)
0.05	38.98	39.025	39.7	39.7	39.79	38.8	39.475	38.8
0.1	39.94	40	40.3	40.3	40.36	39.7	40	40
0.15	40.42	40.45	40.5	40.5	41.31	40.5	40.35	40.5
0.2	41.94	42.3	42.3	42.3	44.7	42.3	42.3	42.3
0.25	46.3	46.325	46.3	46.35	46.375	46.3	46.375	46.3
0.3	46.98	47.85	49.3	49.3	49.01	46.4	47.85	47.85
0.35	49.54	49.75	49.9	49.9	49.925	49.3	49.45	49.9
0.4	50.2	50.4	50.4	50.4	50.42	50.4	50.4	50.4
0.45	50.48	51.925	50.5	50.5	52.495	50.5	54.775	50.5
0.5	56.2	57.7	56.2	57.7	57.7	56.2	57.7	57.7
0.55	59.3	59.575	59.7	59.7	59.525	59.2	59.325	59.7
0.6	59.74	59.8	59.8	59.8	59.78	59.7	59.8	59.8
0.65	60.16	61.15	60.4	60.4	60.37	60.4	62.65	60.4
0.7	62.8	63.95	63.4	63.4	63.51	63.4	63.95	63.95
0.75	64.5	66.6	64.5	65.9	65.2	64.5	65.2	67.3
0.8	68.3	72.3	72.3	72.3	69.3	67.3	72.3	72.3
0.85	73.26	75.6	74.7	74.7	73.62	72.3	77.4	74.7
0.9	76.86	80.75	78.3	78.3	77.22	78.3	80.75	80.75
0.95	82.22	83.575	83.2	83.2	82.465	83.2	83.325	83.7

\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 & 38.98 & 39.025 & 39.7 & 39.7 & 39.79 & 38.8 & 39.475 & 38.8 \tabularnewline
0.1 & 39.94 & 40 & 40.3 & 40.3 & 40.36 & 39.7 & 40 & 40 \tabularnewline
0.15 & 40.42 & 40.45 & 40.5 & 40.5 & 41.31 & 40.5 & 40.35 & 40.5 \tabularnewline
0.2 & 41.94 & 42.3 & 42.3 & 42.3 & 44.7 & 42.3 & 42.3 & 42.3 \tabularnewline
0.25 & 46.3 & 46.325 & 46.3 & 46.35 & 46.375 & 46.3 & 46.375 & 46.3 \tabularnewline
0.3 & 46.98 & 47.85 & 49.3 & 49.3 & 49.01 & 46.4 & 47.85 & 47.85 \tabularnewline
0.35 & 49.54 & 49.75 & 49.9 & 49.9 & 49.925 & 49.3 & 49.45 & 49.9 \tabularnewline
0.4 & 50.2 & 50.4 & 50.4 & 50.4 & 50.42 & 50.4 & 50.4 & 50.4 \tabularnewline
0.45 & 50.48 & 51.925 & 50.5 & 50.5 & 52.495 & 50.5 & 54.775 & 50.5 \tabularnewline
0.5 & 56.2 & 57.7 & 56.2 & 57.7 & 57.7 & 56.2 & 57.7 & 57.7 \tabularnewline
0.55 & 59.3 & 59.575 & 59.7 & 59.7 & 59.525 & 59.2 & 59.325 & 59.7 \tabularnewline
0.6 & 59.74 & 59.8 & 59.8 & 59.8 & 59.78 & 59.7 & 59.8 & 59.8 \tabularnewline
0.65 & 60.16 & 61.15 & 60.4 & 60.4 & 60.37 & 60.4 & 62.65 & 60.4 \tabularnewline
0.7 & 62.8 & 63.95 & 63.4 & 63.4 & 63.51 & 63.4 & 63.95 & 63.95 \tabularnewline
0.75 & 64.5 & 66.6 & 64.5 & 65.9 & 65.2 & 64.5 & 65.2 & 67.3 \tabularnewline
0.8 & 68.3 & 72.3 & 72.3 & 72.3 & 69.3 & 67.3 & 72.3 & 72.3 \tabularnewline
0.85 & 73.26 & 75.6 & 74.7 & 74.7 & 73.62 & 72.3 & 77.4 & 74.7 \tabularnewline
0.9 & 76.86 & 80.75 & 78.3 & 78.3 & 77.22 & 78.3 & 80.75 & 80.75 \tabularnewline
0.95 & 82.22 & 83.575 & 83.2 & 83.2 & 82.465 & 83.2 & 83.325 & 83.7 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=318913&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]38.98[/C][C]39.025[/C][C]39.7[/C][C]39.7[/C][C]39.79[/C][C]38.8[/C][C]39.475[/C][C]38.8[/C][/ROW]
[ROW][C]0.1[/C][C]39.94[/C][C]40[/C][C]40.3[/C][C]40.3[/C][C]40.36[/C][C]39.7[/C][C]40[/C][C]40[/C][/ROW]
[ROW][C]0.15[/C][C]40.42[/C][C]40.45[/C][C]40.5[/C][C]40.5[/C][C]41.31[/C][C]40.5[/C][C]40.35[/C][C]40.5[/C][/ROW]
[ROW][C]0.2[/C][C]41.94[/C][C]42.3[/C][C]42.3[/C][C]42.3[/C][C]44.7[/C][C]42.3[/C][C]42.3[/C][C]42.3[/C][/ROW]
[ROW][C]0.25[/C][C]46.3[/C][C]46.325[/C][C]46.3[/C][C]46.35[/C][C]46.375[/C][C]46.3[/C][C]46.375[/C][C]46.3[/C][/ROW]
[ROW][C]0.3[/C][C]46.98[/C][C]47.85[/C][C]49.3[/C][C]49.3[/C][C]49.01[/C][C]46.4[/C][C]47.85[/C][C]47.85[/C][/ROW]
[ROW][C]0.35[/C][C]49.54[/C][C]49.75[/C][C]49.9[/C][C]49.9[/C][C]49.925[/C][C]49.3[/C][C]49.45[/C][C]49.9[/C][/ROW]
[ROW][C]0.4[/C][C]50.2[/C][C]50.4[/C][C]50.4[/C][C]50.4[/C][C]50.42[/C][C]50.4[/C][C]50.4[/C][C]50.4[/C][/ROW]
[ROW][C]0.45[/C][C]50.48[/C][C]51.925[/C][C]50.5[/C][C]50.5[/C][C]52.495[/C][C]50.5[/C][C]54.775[/C][C]50.5[/C][/ROW]
[ROW][C]0.5[/C][C]56.2[/C][C]57.7[/C][C]56.2[/C][C]57.7[/C][C]57.7[/C][C]56.2[/C][C]57.7[/C][C]57.7[/C][/ROW]
[ROW][C]0.55[/C][C]59.3[/C][C]59.575[/C][C]59.7[/C][C]59.7[/C][C]59.525[/C][C]59.2[/C][C]59.325[/C][C]59.7[/C][/ROW]
[ROW][C]0.6[/C][C]59.74[/C][C]59.8[/C][C]59.8[/C][C]59.8[/C][C]59.78[/C][C]59.7[/C][C]59.8[/C][C]59.8[/C][/ROW]
[ROW][C]0.65[/C][C]60.16[/C][C]61.15[/C][C]60.4[/C][C]60.4[/C][C]60.37[/C][C]60.4[/C][C]62.65[/C][C]60.4[/C][/ROW]
[ROW][C]0.7[/C][C]62.8[/C][C]63.95[/C][C]63.4[/C][C]63.4[/C][C]63.51[/C][C]63.4[/C][C]63.95[/C][C]63.95[/C][/ROW]
[ROW][C]0.75[/C][C]64.5[/C][C]66.6[/C][C]64.5[/C][C]65.9[/C][C]65.2[/C][C]64.5[/C][C]65.2[/C][C]67.3[/C][/ROW]
[ROW][C]0.8[/C][C]68.3[/C][C]72.3[/C][C]72.3[/C][C]72.3[/C][C]69.3[/C][C]67.3[/C][C]72.3[/C][C]72.3[/C][/ROW]
[ROW][C]0.85[/C][C]73.26[/C][C]75.6[/C][C]74.7[/C][C]74.7[/C][C]73.62[/C][C]72.3[/C][C]77.4[/C][C]74.7[/C][/ROW]
[ROW][C]0.9[/C][C]76.86[/C][C]80.75[/C][C]78.3[/C][C]78.3[/C][C]77.22[/C][C]78.3[/C][C]80.75[/C][C]80.75[/C][/ROW]
[ROW][C]0.95[/C][C]82.22[/C][C]83.575[/C][C]83.2[/C][C]83.2[/C][C]82.465[/C][C]83.2[/C][C]83.325[/C][C]83.7[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=318913&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=318913&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
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)
0.05	38.98	39.025	39.7	39.7	39.79	38.8	39.475	38.8
0.1	39.94	40	40.3	40.3	40.36	39.7	40	40
0.15	40.42	40.45	40.5	40.5	41.31	40.5	40.35	40.5
0.2	41.94	42.3	42.3	42.3	44.7	42.3	42.3	42.3
0.25	46.3	46.325	46.3	46.35	46.375	46.3	46.375	46.3
0.3	46.98	47.85	49.3	49.3	49.01	46.4	47.85	47.85
0.35	49.54	49.75	49.9	49.9	49.925	49.3	49.45	49.9
0.4	50.2	50.4	50.4	50.4	50.42	50.4	50.4	50.4
0.45	50.48	51.925	50.5	50.5	52.495	50.5	54.775	50.5
0.5	56.2	57.7	56.2	57.7	57.7	56.2	57.7	57.7
0.55	59.3	59.575	59.7	59.7	59.525	59.2	59.325	59.7
0.6	59.74	59.8	59.8	59.8	59.78	59.7	59.8	59.8
0.65	60.16	61.15	60.4	60.4	60.37	60.4	62.65	60.4
0.7	62.8	63.95	63.4	63.4	63.51	63.4	63.95	63.95
0.75	64.5	66.6	64.5	65.9	65.2	64.5	65.2	67.3
0.8	68.3	72.3	72.3	72.3	69.3	67.3	72.3	72.3
0.85	73.26	75.6	74.7	74.7	73.62	72.3	77.4	74.7
0.9	76.86	80.75	78.3	78.3	77.22	78.3	80.75	80.75
0.95	82.22	83.575	83.2	83.2	82.465	83.2	83.325	83.7

Figure 1

PNG link

Postscript link

PDF link

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, 'Weighted Average at Xnp',1,TRUE)
a<-table.element(a, 'Weighted Average at X(n+1)p',1,TRUE)
a<-table.element(a, 'Empirical Distribution Function',1,TRUE)
a<-table.element(a, 'Empirical Distribution Function - Averaging',1,TRUE)
a<-table.element(a, 'Empirical Distribution Function - Interpolation',1,TRUE)
a<-table.element(a, 'Closest Observation',1,TRUE)
a<-table.element(a, 'True Basic - Statistics Graphics Toolkit',1,TRUE)
a<-table.element(a, '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,signif(qval[perc,j],6))
}
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable.tab')

Free Statistics

Description of Statistical Computation

Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code