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Description of Statistical Computation

Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationTue, 12 Dec 2017 16:23:58 +0100
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/Dec/12/t15130922910tlsaqfsven3nh4.htm/, Retrieved Wed, 15 May 2024 22:58:29 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=309133, Retrieved Wed, 15 May 2024 22:58:29 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact39

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [Central Tendency ...] [2017-12-12 15:23:58] [76161aa76684ab75eda7753df0aa1ca0] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
-1.653
0.9873
0.4873
-4.053
-1.599
5.101
4.601
-1.139
2.147
3.647
-2.199
-1.113
-0.699
-2.913
-0.3127
3.987
-2.853
-2.653
-3.999
6.761
7.501
-0.1127
0.701
-4.453
0.08726
2.487
2.287
-9.999
1.901
3.801
-6.699
1.201
3.247
0.6873
-0.9127
-1.053
-2.199
1.587
-1.099
0.6474
-0.01274
-0.2526
2.447
4.087
-6.999
5.161
-0.09903
-5.953
0.7873
-1.313

Tables (Output of Computation)





Summary of computational transaction
Raw Input view raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R ServerBig 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 time1 seconds \tabularnewline
R ServerBig Analytics Cloud Computing Center \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=309133&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]1 seconds[/C][/ROW] [ROW]R Server[/C]Big Analytics Cloud Computing Center[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=309133&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=309133&T=0

As an alternative you can also use a QR Code:  
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 Outputview raw output of R engine
Computing time1 seconds
R ServerBig Analytics Cloud Computing Center






Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean-0.00013220.498053-0.000265434
Geometric MeanNaN
Harmonic Mean-0.556274
Quadratic Mean3.48637
Winsorized Mean ( 1 / 16 )0.04506780.4721160.0954592
Winsorized Mean ( 2 / 16 )-0.00693220.451672-0.0153479
Winsorized Mean ( 3 / 16 )0.03422780.4378050.0781804
Winsorized Mean ( 4 / 16 )0.1142280.3975260.287347
Winsorized Mean ( 5 / 16 )0.1028280.3768560.272857
Winsorized Mean ( 6 / 16 )0.09730780.3728280.260999
Winsorized Mean ( 7 / 16 )0.2233080.3355450.665507
Winsorized Mean ( 8 / 16 )0.2082680.3284020.634185
Winsorized Mean ( 9 / 16 )0.1722680.3065170.562018
Winsorized Mean ( 10 / 16 )0.1110680.2598620.427411
Winsorized Mean ( 11 / 16 )0.1022680.2582260.396041
Winsorized Mean ( 12 / 16 )0.1949080.228270.853846
Winsorized Mean ( 13 / 16 )0.1725480.2192020.787164
Winsorized Mean ( 14 / 16 )0.1837480.1936970.948635
Winsorized Mean ( 15 / 16 )0.1417480.168760.839937
Winsorized Mean ( 16 / 16 )0.02654780.146510.181201
Trimmed Mean ( 1 / 16 )0.0519040.4472950.11604
Trimmed Mean ( 2 / 16 )0.05933460.4150750.142949
Trimmed Mean ( 3 / 16 )0.09698610.3880270.249947
Trimmed Mean ( 4 / 16 )0.121890.3600240.338561
Trimmed Mean ( 5 / 16 )0.1242850.3417610.36366
Trimmed Mean ( 6 / 16 )0.1299310.3255970.399056
Trimmed Mean ( 7 / 16 )0.1374830.3048910.450925
Trimmed Mean ( 8 / 16 )0.1194530.2900450.411841
Trimmed Mean ( 9 / 16 )0.1021060.271460.376136
Trimmed Mean ( 10 / 16 )0.0891130.2528350.352456
Trimmed Mean ( 11 / 16 )0.08519250.2429680.350633
Trimmed Mean ( 12 / 16 )0.08220730.2281480.360325
Trimmed Mean ( 13 / 16 )0.06264130.2168290.288897
Trimmed Mean ( 14 / 16 )0.04342680.201930.215059
Trimmed Mean ( 15 / 16 )0.01836950.1887310.0973316
Trimmed Mean ( 16 / 16 )-0.004478330.178281-0.0251196
Median-0.055885
Midrange-1.249
Midmean - Weighted Average at Xnp-0.0059844
Midmean - Weighted Average at X(n+1)p0.0822073
Midmean - Empirical Distribution Function0.0822073
Midmean - Empirical Distribution Function - Averaging0.0822073
Midmean - Empirical Distribution Function - Interpolation0.0626412
Midmean - Closest Observation0.0822073
Midmean - True Basic - Statistics Graphics Toolkit0.0822073
Midmean - MS Excel (old versions)0.0822073
Number of observations50

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & -0.0001322 & 0.498053 & -0.000265434 \tabularnewline
Geometric Mean & NaN &  &  \tabularnewline
Harmonic Mean & -0.556274 &  &  \tabularnewline
Quadratic Mean & 3.48637 &  &  \tabularnewline
Winsorized Mean ( 1 / 16 ) & 0.0450678 & 0.472116 & 0.0954592 \tabularnewline
Winsorized Mean ( 2 / 16 ) & -0.0069322 & 0.451672 & -0.0153479 \tabularnewline
Winsorized Mean ( 3 / 16 ) & 0.0342278 & 0.437805 & 0.0781804 \tabularnewline
Winsorized Mean ( 4 / 16 ) & 0.114228 & 0.397526 & 0.287347 \tabularnewline
Winsorized Mean ( 5 / 16 ) & 0.102828 & 0.376856 & 0.272857 \tabularnewline
Winsorized Mean ( 6 / 16 ) & 0.0973078 & 0.372828 & 0.260999 \tabularnewline
Winsorized Mean ( 7 / 16 ) & 0.223308 & 0.335545 & 0.665507 \tabularnewline
Winsorized Mean ( 8 / 16 ) & 0.208268 & 0.328402 & 0.634185 \tabularnewline
Winsorized Mean ( 9 / 16 ) & 0.172268 & 0.306517 & 0.562018 \tabularnewline
Winsorized Mean ( 10 / 16 ) & 0.111068 & 0.259862 & 0.427411 \tabularnewline
Winsorized Mean ( 11 / 16 ) & 0.102268 & 0.258226 & 0.396041 \tabularnewline
Winsorized Mean ( 12 / 16 ) & 0.194908 & 0.22827 & 0.853846 \tabularnewline
Winsorized Mean ( 13 / 16 ) & 0.172548 & 0.219202 & 0.787164 \tabularnewline
Winsorized Mean ( 14 / 16 ) & 0.183748 & 0.193697 & 0.948635 \tabularnewline
Winsorized Mean ( 15 / 16 ) & 0.141748 & 0.16876 & 0.839937 \tabularnewline
Winsorized Mean ( 16 / 16 ) & 0.0265478 & 0.14651 & 0.181201 \tabularnewline
Trimmed Mean ( 1 / 16 ) & 0.051904 & 0.447295 & 0.11604 \tabularnewline
Trimmed Mean ( 2 / 16 ) & 0.0593346 & 0.415075 & 0.142949 \tabularnewline
Trimmed Mean ( 3 / 16 ) & 0.0969861 & 0.388027 & 0.249947 \tabularnewline
Trimmed Mean ( 4 / 16 ) & 0.12189 & 0.360024 & 0.338561 \tabularnewline
Trimmed Mean ( 5 / 16 ) & 0.124285 & 0.341761 & 0.36366 \tabularnewline
Trimmed Mean ( 6 / 16 ) & 0.129931 & 0.325597 & 0.399056 \tabularnewline
Trimmed Mean ( 7 / 16 ) & 0.137483 & 0.304891 & 0.450925 \tabularnewline
Trimmed Mean ( 8 / 16 ) & 0.119453 & 0.290045 & 0.411841 \tabularnewline
Trimmed Mean ( 9 / 16 ) & 0.102106 & 0.27146 & 0.376136 \tabularnewline
Trimmed Mean ( 10 / 16 ) & 0.089113 & 0.252835 & 0.352456 \tabularnewline
Trimmed Mean ( 11 / 16 ) & 0.0851925 & 0.242968 & 0.350633 \tabularnewline
Trimmed Mean ( 12 / 16 ) & 0.0822073 & 0.228148 & 0.360325 \tabularnewline
Trimmed Mean ( 13 / 16 ) & 0.0626413 & 0.216829 & 0.288897 \tabularnewline
Trimmed Mean ( 14 / 16 ) & 0.0434268 & 0.20193 & 0.215059 \tabularnewline
Trimmed Mean ( 15 / 16 ) & 0.0183695 & 0.188731 & 0.0973316 \tabularnewline
Trimmed Mean ( 16 / 16 ) & -0.00447833 & 0.178281 & -0.0251196 \tabularnewline
Median & -0.055885 &  &  \tabularnewline
Midrange & -1.249 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & -0.0059844 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 0.0822073 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 0.0822073 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 0.0822073 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 0.0626412 &  &  \tabularnewline
Midmean - Closest Observation & 0.0822073 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 0.0822073 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 0.0822073 &  &  \tabularnewline
Number of observations & 50 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=309133&T=1

[TABLE]
[ROW][C]Central Tendency - Ungrouped Data[/C][/ROW]
[ROW][C]Measure[/C][C]Value[/C][C]S.E.[/C][C]Value/S.E.[/C][/ROW]
[ROW][C]Arithmetic Mean[/C][C]-0.0001322[/C][C]0.498053[/C][C]-0.000265434[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]NaN[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]-0.556274[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]3.48637[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 16 )[/C][C]0.0450678[/C][C]0.472116[/C][C]0.0954592[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 16 )[/C][C]-0.0069322[/C][C]0.451672[/C][C]-0.0153479[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 16 )[/C][C]0.0342278[/C][C]0.437805[/C][C]0.0781804[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 16 )[/C][C]0.114228[/C][C]0.397526[/C][C]0.287347[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 16 )[/C][C]0.102828[/C][C]0.376856[/C][C]0.272857[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 16 )[/C][C]0.0973078[/C][C]0.372828[/C][C]0.260999[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 16 )[/C][C]0.223308[/C][C]0.335545[/C][C]0.665507[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 16 )[/C][C]0.208268[/C][C]0.328402[/C][C]0.634185[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 16 )[/C][C]0.172268[/C][C]0.306517[/C][C]0.562018[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 16 )[/C][C]0.111068[/C][C]0.259862[/C][C]0.427411[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 16 )[/C][C]0.102268[/C][C]0.258226[/C][C]0.396041[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 16 )[/C][C]0.194908[/C][C]0.22827[/C][C]0.853846[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 16 )[/C][C]0.172548[/C][C]0.219202[/C][C]0.787164[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 16 )[/C][C]0.183748[/C][C]0.193697[/C][C]0.948635[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 16 )[/C][C]0.141748[/C][C]0.16876[/C][C]0.839937[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 16 )[/C][C]0.0265478[/C][C]0.14651[/C][C]0.181201[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 16 )[/C][C]0.051904[/C][C]0.447295[/C][C]0.11604[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 16 )[/C][C]0.0593346[/C][C]0.415075[/C][C]0.142949[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 16 )[/C][C]0.0969861[/C][C]0.388027[/C][C]0.249947[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 16 )[/C][C]0.12189[/C][C]0.360024[/C][C]0.338561[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 16 )[/C][C]0.124285[/C][C]0.341761[/C][C]0.36366[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 16 )[/C][C]0.129931[/C][C]0.325597[/C][C]0.399056[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 16 )[/C][C]0.137483[/C][C]0.304891[/C][C]0.450925[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 16 )[/C][C]0.119453[/C][C]0.290045[/C][C]0.411841[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 16 )[/C][C]0.102106[/C][C]0.27146[/C][C]0.376136[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 16 )[/C][C]0.089113[/C][C]0.252835[/C][C]0.352456[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 16 )[/C][C]0.0851925[/C][C]0.242968[/C][C]0.350633[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 16 )[/C][C]0.0822073[/C][C]0.228148[/C][C]0.360325[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 16 )[/C][C]0.0626413[/C][C]0.216829[/C][C]0.288897[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 16 )[/C][C]0.0434268[/C][C]0.20193[/C][C]0.215059[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 16 )[/C][C]0.0183695[/C][C]0.188731[/C][C]0.0973316[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 16 )[/C][C]-0.00447833[/C][C]0.178281[/C][C]-0.0251196[/C][/ROW]
[ROW][C]Median[/C][C]-0.055885[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]-1.249[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]-0.0059844[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]0.0822073[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]0.0822073[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]0.0822073[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]0.0626412[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]0.0822073[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]0.0822073[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]0.0822073[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]50[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=309133&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=309133&T=1

As an alternative you can also use a QR Code:  
QR Code


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

Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean-0.00013220.498053-0.000265434
Geometric MeanNaN
Harmonic Mean-0.556274
Quadratic Mean3.48637
Winsorized Mean ( 1 / 16 )0.04506780.4721160.0954592
Winsorized Mean ( 2 / 16 )-0.00693220.451672-0.0153479
Winsorized Mean ( 3 / 16 )0.03422780.4378050.0781804
Winsorized Mean ( 4 / 16 )0.1142280.3975260.287347
Winsorized Mean ( 5 / 16 )0.1028280.3768560.272857
Winsorized Mean ( 6 / 16 )0.09730780.3728280.260999
Winsorized Mean ( 7 / 16 )0.2233080.3355450.665507
Winsorized Mean ( 8 / 16 )0.2082680.3284020.634185
Winsorized Mean ( 9 / 16 )0.1722680.3065170.562018
Winsorized Mean ( 10 / 16 )0.1110680.2598620.427411
Winsorized Mean ( 11 / 16 )0.1022680.2582260.396041
Winsorized Mean ( 12 / 16 )0.1949080.228270.853846
Winsorized Mean ( 13 / 16 )0.1725480.2192020.787164
Winsorized Mean ( 14 / 16 )0.1837480.1936970.948635
Winsorized Mean ( 15 / 16 )0.1417480.168760.839937
Winsorized Mean ( 16 / 16 )0.02654780.146510.181201
Trimmed Mean ( 1 / 16 )0.0519040.4472950.11604
Trimmed Mean ( 2 / 16 )0.05933460.4150750.142949
Trimmed Mean ( 3 / 16 )0.09698610.3880270.249947
Trimmed Mean ( 4 / 16 )0.121890.3600240.338561
Trimmed Mean ( 5 / 16 )0.1242850.3417610.36366
Trimmed Mean ( 6 / 16 )0.1299310.3255970.399056
Trimmed Mean ( 7 / 16 )0.1374830.3048910.450925
Trimmed Mean ( 8 / 16 )0.1194530.2900450.411841
Trimmed Mean ( 9 / 16 )0.1021060.271460.376136
Trimmed Mean ( 10 / 16 )0.0891130.2528350.352456
Trimmed Mean ( 11 / 16 )0.08519250.2429680.350633
Trimmed Mean ( 12 / 16 )0.08220730.2281480.360325
Trimmed Mean ( 13 / 16 )0.06264130.2168290.288897
Trimmed Mean ( 14 / 16 )0.04342680.201930.215059
Trimmed Mean ( 15 / 16 )0.01836950.1887310.0973316
Trimmed Mean ( 16 / 16 )-0.004478330.178281-0.0251196
Median-0.055885
Midrange-1.249
Midmean - Weighted Average at Xnp-0.0059844
Midmean - Weighted Average at X(n+1)p0.0822073
Midmean - Empirical Distribution Function0.0822073
Midmean - Empirical Distribution Function - Averaging0.0822073
Midmean - Empirical Distribution Function - Interpolation0.0626412
Midmean - Closest Observation0.0822073
Midmean - True Basic - Statistics Graphics Toolkit0.0822073
Midmean - MS Excel (old versions)0.0822073
Number of observations50


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
Parameters (R input):
R code (references can be found in the software module):
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]
}
}
}
}
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)
}
(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=main, xlab='j', pch=19, ylab='Winsorized Mean(j/n)', ylim=c(min(lb),max(ub))) else plot(win[,1],type='l',main=main, 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=main, xlab='j', pch=19, ylab='Trimmed Mean(j/n)', ylim=c(min(lb),max(ub))) else plot(tri[,1],type='l',main=main, xlab='j', pch=19, ylab='Trimmed Mean(j/n)', ylim=c(ylimmin,ylimmax))
lines(ub,lty=3)
lines(lb,lty=3)
grid()
dev.off()
load(file='createtable')
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,'Arithmetic Mean',header=TRUE)
a<-table.element(a,signif(arm,6))
a<-table.element(a, signif(armse,6))
a<-table.element(a,signif(armose,6))
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Geometric Mean',header=TRUE)
a<-table.element(a,signif(geo,6))
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Harmonic Mean',header=TRUE)
a<-table.element(a,signif(har,6))
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Quadratic Mean',header=TRUE)
a<-table.element(a,signif(qua,6))
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, mylabel,header=TRUE)
a<-table.element(a,signif(win[j,1],6))
a<-table.element(a,signif(win[j,2],6))
a<-table.element(a,signif(win[j,1]/win[j,2],6))
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, mylabel,header=TRUE)
a<-table.element(a,signif(tri[j,1],6))
a<-table.element(a,signif(tri[j,2],6))
a<-table.element(a,signif(tri[j,1]/tri[j,2],6))
a<-table.row.end(a)
}
a<-table.row.start(a)
a<-table.element(a, 'Median',header=TRUE)
a<-table.element(a,signif(median(x),6))
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Midrange',header=TRUE)
a<-table.element(a,signif(midr,6))
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <-  'Midmean'
mylabel <- paste(mymid,'Weighted Average at Xnp',sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,signif(midm[1],6))
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <-  'Midmean'
mylabel <- paste(mymid,'Weighted Average at X(n+1)p',sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,signif(midm[2],6))
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <-  'Midmean'
mylabel <- paste(mymid,'Empirical Distribution Function',sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,signif(midm[3],6))
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <-  'Midmean'
mylabel <- paste(mymid,'Empirical Distribution Function - Averaging',sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,signif(midm[4],6))
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <-  'Midmean'
mylabel <- paste(mymid,'Empirical Distribution Function - Interpolation',sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,signif(midm[5],6))
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <-  'Midmean'
mylabel <- paste(mymid,'Closest Observation',sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,signif(midm[6],6))
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <-  'Midmean'
mylabel <- paste(mymid,'True Basic - Statistics Graphics Toolkit',sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,signif(midm[7],6))
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <-  'Midmean'
mylabel <- paste(mymid,'MS Excel (old versions)',sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,signif(midm[8],6))
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,signif(length(x),6))
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable.tab')