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of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationMon, 07 Mar 2016 22:58:41 +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/2016/Mar/07/t1457391553g3hiqe8vlx716bm.htm/, Retrieved Wed, 01 May 2024 13:01:16 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=293627, Retrieved Wed, 01 May 2024 13:01:16 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact76
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Harrell-Davis Quantiles] [] [2016-02-29 17:54:08] [29ab9c45344d5c037bf74b62f65f8e78]
- RMPD  [Quartiles] [Quartielen consum...] [2016-02-29 18:00:49] [29ab9c45344d5c037bf74b62f65f8e78]
- RM D      [Central Tendency] [Centrummaten eige...] [2016-03-07 22:58:41] [0996086de175370e0a22efa864593ca4] [Current]
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Dataseries X:
91.27
91.51
91.78
91.83
92.01
92.1
92.35
92.46
93.08
93.38
93.46
93.58
93.74
94.18
94.43
94.53
94.66
94.8
95.04
95.29
95.42
95.64
95.82
96.01
96.16
96.4
96.87
97
97.26
97.42
97.64
97.93
98.1
98.29
98.42
98.49
98.67
99.1
99.37
99.54
99.58
99.77
100.06
100.26
100.57
100.94
101.03
101.12
101.26
101.94
102.26
102.51
102.61
102.76
103.04
103.22
103.47
103.64
103.76
103.85




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Sir Maurice George Kendall' @ kendall.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 & 'Sir Maurice George Kendall' @ kendall.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=293627&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]'Sir Maurice George Kendall' @ kendall.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=293627&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=293627&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'Sir Maurice George Kendall' @ kendall.wessa.net







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean97.54466666666670.487653117583095200.028797416732
Geometric Mean97.4727647046191
Harmonic Mean97.400914693868
Quadratic Mean97.6165586534033
Winsorized Mean ( 1 / 20 )97.54716666666670.486469530442518200.520609333811
Winsorized Mean ( 2 / 20 )97.55216666666670.483753280937014201.656857970475
Winsorized Mean ( 3 / 20 )97.54616666666670.481456071393572202.606577136559
Winsorized Mean ( 4 / 20 )97.54150.475641453589657205.073589073989
Winsorized Mean ( 5 / 20 )97.5340.471165953706551207.005619214893
Winsorized Mean ( 6 / 20 )97.5310.46087405904985211.621804449294
Winsorized Mean ( 7 / 20 )97.52633333333330.455101215951824214.295919050362
Winsorized Mean ( 8 / 20 )97.59566666666670.437529489993459223.060773956347
Winsorized Mean ( 9 / 20 )97.60316666666670.422709680638451230.898820484189
Winsorized Mean ( 10 / 20 )97.56316666666660.410652883211164237.580620166979
Winsorized Mean ( 11 / 20 )97.46050.385204210644569253.009954997423
Winsorized Mean ( 12 / 20 )97.46450.37512607485204259.817982630087
Winsorized Mean ( 13 / 20 )97.54033333333340.356244612738861273.801567365269
Winsorized Mean ( 14 / 20 )97.57766666666670.34356500603379284.015149834759
Winsorized Mean ( 15 / 20 )97.51016666666670.324610108735128300.391651531197
Winsorized Mean ( 16 / 20 )97.46216666666670.306213718401217318.281516502689
Winsorized Mean ( 17 / 20 )97.44516666666670.291386175862879334.419319578574
Winsorized Mean ( 18 / 20 )97.43016666666670.267310785465841364.482736814661
Winsorized Mean ( 19 / 20 )97.44916666666670.24655963760604395.235682583107
Winsorized Mean ( 20 / 20 )97.47916666666670.238214555958349409.207431823397
Trimmed Mean ( 1 / 20 )97.54413793103450.480315171437518203.083607871677
Trimmed Mean ( 2 / 20 )97.54089285714290.472508728482955206.431938665576
Trimmed Mean ( 3 / 20 )97.53462962962960.46440961468734210.018540841998
Trimmed Mean ( 4 / 20 )97.53019230769230.45519172782332214.26178541089
Trimmed Mean ( 5 / 20 )97.52680.445680441938538218.826744058581
Trimmed Mean ( 6 / 20 )97.5250.434953531389372224.219354395114
Trimmed Mean ( 7 / 20 )97.52369565217390.424272307814597229.861091228209
Trimmed Mean ( 8 / 20 )97.52318181818180.411966199265087236.726173147591
Trimmed Mean ( 9 / 20 )97.51023809523810.400700386836675243.349498274837
Trimmed Mean ( 10 / 20 )97.494750.389655499966119250.207555156997
Trimmed Mean ( 11 / 20 )97.48394736842110.377923039173612257.946558594535
Trimmed Mean ( 12 / 20 )97.48750.368731496710908264.386147832746
Trimmed Mean ( 13 / 20 )97.49088235294120.358340990088671272.061765328095
Trimmed Mean ( 14 / 20 )97.483750.348651130626442279.602563814565
Trimmed Mean ( 15 / 20 )97.47033333333330.3378578505867288.495096870098
Trimmed Mean ( 16 / 20 )97.46464285714290.327436524864852297.659654485311
Trimmed Mean ( 17 / 20 )97.4650.317136830454568307.327912246265
Trimmed Mean ( 18 / 20 )97.46791666666670.305557804943411318.983560851007
Trimmed Mean ( 19 / 20 )97.47363636363640.295502759968759329.856940672708
Trimmed Mean ( 20 / 20 )97.47750.286252441956948340.529846081315
Median97.53
Midrange97.56
Midmean - Weighted Average at Xnp97.3722580645161
Midmean - Weighted Average at X(n+1)p97.4703333333333
Midmean - Empirical Distribution Function97.3722580645161
Midmean - Empirical Distribution Function - Averaging97.4703333333333
Midmean - Empirical Distribution Function - Interpolation97.4703333333333
Midmean - Closest Observation97.3722580645161
Midmean - True Basic - Statistics Graphics Toolkit97.4703333333333
Midmean - MS Excel (old versions)97.48375
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 97.5446666666667 & 0.487653117583095 & 200.028797416732 \tabularnewline
Geometric Mean & 97.4727647046191 &  &  \tabularnewline
Harmonic Mean & 97.400914693868 &  &  \tabularnewline
Quadratic Mean & 97.6165586534033 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 97.5471666666667 & 0.486469530442518 & 200.520609333811 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 97.5521666666667 & 0.483753280937014 & 201.656857970475 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 97.5461666666667 & 0.481456071393572 & 202.606577136559 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 97.5415 & 0.475641453589657 & 205.073589073989 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 97.534 & 0.471165953706551 & 207.005619214893 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 97.531 & 0.46087405904985 & 211.621804449294 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 97.5263333333333 & 0.455101215951824 & 214.295919050362 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 97.5956666666667 & 0.437529489993459 & 223.060773956347 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 97.6031666666667 & 0.422709680638451 & 230.898820484189 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 97.5631666666666 & 0.410652883211164 & 237.580620166979 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 97.4605 & 0.385204210644569 & 253.009954997423 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 97.4645 & 0.37512607485204 & 259.817982630087 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 97.5403333333334 & 0.356244612738861 & 273.801567365269 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 97.5776666666667 & 0.34356500603379 & 284.015149834759 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 97.5101666666667 & 0.324610108735128 & 300.391651531197 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 97.4621666666667 & 0.306213718401217 & 318.281516502689 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 97.4451666666667 & 0.291386175862879 & 334.419319578574 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 97.4301666666667 & 0.267310785465841 & 364.482736814661 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 97.4491666666667 & 0.24655963760604 & 395.235682583107 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 97.4791666666667 & 0.238214555958349 & 409.207431823397 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 97.5441379310345 & 0.480315171437518 & 203.083607871677 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 97.5408928571429 & 0.472508728482955 & 206.431938665576 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 97.5346296296296 & 0.46440961468734 & 210.018540841998 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 97.5301923076923 & 0.45519172782332 & 214.26178541089 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 97.5268 & 0.445680441938538 & 218.826744058581 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 97.525 & 0.434953531389372 & 224.219354395114 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 97.5236956521739 & 0.424272307814597 & 229.861091228209 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 97.5231818181818 & 0.411966199265087 & 236.726173147591 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 97.5102380952381 & 0.400700386836675 & 243.349498274837 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 97.49475 & 0.389655499966119 & 250.207555156997 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 97.4839473684211 & 0.377923039173612 & 257.946558594535 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 97.4875 & 0.368731496710908 & 264.386147832746 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 97.4908823529412 & 0.358340990088671 & 272.061765328095 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 97.48375 & 0.348651130626442 & 279.602563814565 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 97.4703333333333 & 0.3378578505867 & 288.495096870098 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 97.4646428571429 & 0.327436524864852 & 297.659654485311 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 97.465 & 0.317136830454568 & 307.327912246265 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 97.4679166666667 & 0.305557804943411 & 318.983560851007 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 97.4736363636364 & 0.295502759968759 & 329.856940672708 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 97.4775 & 0.286252441956948 & 340.529846081315 \tabularnewline
Median & 97.53 &  &  \tabularnewline
Midrange & 97.56 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 97.3722580645161 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 97.4703333333333 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 97.3722580645161 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 97.4703333333333 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 97.4703333333333 &  &  \tabularnewline
Midmean - Closest Observation & 97.3722580645161 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 97.4703333333333 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 97.48375 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=293627&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]97.5446666666667[/C][C]0.487653117583095[/C][C]200.028797416732[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]97.4727647046191[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]97.400914693868[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]97.6165586534033[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]97.5471666666667[/C][C]0.486469530442518[/C][C]200.520609333811[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]97.5521666666667[/C][C]0.483753280937014[/C][C]201.656857970475[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]97.5461666666667[/C][C]0.481456071393572[/C][C]202.606577136559[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]97.5415[/C][C]0.475641453589657[/C][C]205.073589073989[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]97.534[/C][C]0.471165953706551[/C][C]207.005619214893[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]97.531[/C][C]0.46087405904985[/C][C]211.621804449294[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]97.5263333333333[/C][C]0.455101215951824[/C][C]214.295919050362[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]97.5956666666667[/C][C]0.437529489993459[/C][C]223.060773956347[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]97.6031666666667[/C][C]0.422709680638451[/C][C]230.898820484189[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]97.5631666666666[/C][C]0.410652883211164[/C][C]237.580620166979[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]97.4605[/C][C]0.385204210644569[/C][C]253.009954997423[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]97.4645[/C][C]0.37512607485204[/C][C]259.817982630087[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]97.5403333333334[/C][C]0.356244612738861[/C][C]273.801567365269[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]97.5776666666667[/C][C]0.34356500603379[/C][C]284.015149834759[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]97.5101666666667[/C][C]0.324610108735128[/C][C]300.391651531197[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]97.4621666666667[/C][C]0.306213718401217[/C][C]318.281516502689[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]97.4451666666667[/C][C]0.291386175862879[/C][C]334.419319578574[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]97.4301666666667[/C][C]0.267310785465841[/C][C]364.482736814661[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]97.4491666666667[/C][C]0.24655963760604[/C][C]395.235682583107[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]97.4791666666667[/C][C]0.238214555958349[/C][C]409.207431823397[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]97.5441379310345[/C][C]0.480315171437518[/C][C]203.083607871677[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]97.5408928571429[/C][C]0.472508728482955[/C][C]206.431938665576[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]97.5346296296296[/C][C]0.46440961468734[/C][C]210.018540841998[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]97.5301923076923[/C][C]0.45519172782332[/C][C]214.26178541089[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]97.5268[/C][C]0.445680441938538[/C][C]218.826744058581[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]97.525[/C][C]0.434953531389372[/C][C]224.219354395114[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]97.5236956521739[/C][C]0.424272307814597[/C][C]229.861091228209[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]97.5231818181818[/C][C]0.411966199265087[/C][C]236.726173147591[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]97.5102380952381[/C][C]0.400700386836675[/C][C]243.349498274837[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]97.49475[/C][C]0.389655499966119[/C][C]250.207555156997[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]97.4839473684211[/C][C]0.377923039173612[/C][C]257.946558594535[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]97.4875[/C][C]0.368731496710908[/C][C]264.386147832746[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]97.4908823529412[/C][C]0.358340990088671[/C][C]272.061765328095[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]97.48375[/C][C]0.348651130626442[/C][C]279.602563814565[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]97.4703333333333[/C][C]0.3378578505867[/C][C]288.495096870098[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]97.4646428571429[/C][C]0.327436524864852[/C][C]297.659654485311[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]97.465[/C][C]0.317136830454568[/C][C]307.327912246265[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]97.4679166666667[/C][C]0.305557804943411[/C][C]318.983560851007[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]97.4736363636364[/C][C]0.295502759968759[/C][C]329.856940672708[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]97.4775[/C][C]0.286252441956948[/C][C]340.529846081315[/C][/ROW]
[ROW][C]Median[/C][C]97.53[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]97.56[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]97.3722580645161[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]97.4703333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]97.3722580645161[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]97.4703333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]97.4703333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]97.3722580645161[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]97.4703333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]97.48375[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]60[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=293627&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=293627&T=1

As an alternative you can also use a QR Code:  

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

Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean97.54466666666670.487653117583095200.028797416732
Geometric Mean97.4727647046191
Harmonic Mean97.400914693868
Quadratic Mean97.6165586534033
Winsorized Mean ( 1 / 20 )97.54716666666670.486469530442518200.520609333811
Winsorized Mean ( 2 / 20 )97.55216666666670.483753280937014201.656857970475
Winsorized Mean ( 3 / 20 )97.54616666666670.481456071393572202.606577136559
Winsorized Mean ( 4 / 20 )97.54150.475641453589657205.073589073989
Winsorized Mean ( 5 / 20 )97.5340.471165953706551207.005619214893
Winsorized Mean ( 6 / 20 )97.5310.46087405904985211.621804449294
Winsorized Mean ( 7 / 20 )97.52633333333330.455101215951824214.295919050362
Winsorized Mean ( 8 / 20 )97.59566666666670.437529489993459223.060773956347
Winsorized Mean ( 9 / 20 )97.60316666666670.422709680638451230.898820484189
Winsorized Mean ( 10 / 20 )97.56316666666660.410652883211164237.580620166979
Winsorized Mean ( 11 / 20 )97.46050.385204210644569253.009954997423
Winsorized Mean ( 12 / 20 )97.46450.37512607485204259.817982630087
Winsorized Mean ( 13 / 20 )97.54033333333340.356244612738861273.801567365269
Winsorized Mean ( 14 / 20 )97.57766666666670.34356500603379284.015149834759
Winsorized Mean ( 15 / 20 )97.51016666666670.324610108735128300.391651531197
Winsorized Mean ( 16 / 20 )97.46216666666670.306213718401217318.281516502689
Winsorized Mean ( 17 / 20 )97.44516666666670.291386175862879334.419319578574
Winsorized Mean ( 18 / 20 )97.43016666666670.267310785465841364.482736814661
Winsorized Mean ( 19 / 20 )97.44916666666670.24655963760604395.235682583107
Winsorized Mean ( 20 / 20 )97.47916666666670.238214555958349409.207431823397
Trimmed Mean ( 1 / 20 )97.54413793103450.480315171437518203.083607871677
Trimmed Mean ( 2 / 20 )97.54089285714290.472508728482955206.431938665576
Trimmed Mean ( 3 / 20 )97.53462962962960.46440961468734210.018540841998
Trimmed Mean ( 4 / 20 )97.53019230769230.45519172782332214.26178541089
Trimmed Mean ( 5 / 20 )97.52680.445680441938538218.826744058581
Trimmed Mean ( 6 / 20 )97.5250.434953531389372224.219354395114
Trimmed Mean ( 7 / 20 )97.52369565217390.424272307814597229.861091228209
Trimmed Mean ( 8 / 20 )97.52318181818180.411966199265087236.726173147591
Trimmed Mean ( 9 / 20 )97.51023809523810.400700386836675243.349498274837
Trimmed Mean ( 10 / 20 )97.494750.389655499966119250.207555156997
Trimmed Mean ( 11 / 20 )97.48394736842110.377923039173612257.946558594535
Trimmed Mean ( 12 / 20 )97.48750.368731496710908264.386147832746
Trimmed Mean ( 13 / 20 )97.49088235294120.358340990088671272.061765328095
Trimmed Mean ( 14 / 20 )97.483750.348651130626442279.602563814565
Trimmed Mean ( 15 / 20 )97.47033333333330.3378578505867288.495096870098
Trimmed Mean ( 16 / 20 )97.46464285714290.327436524864852297.659654485311
Trimmed Mean ( 17 / 20 )97.4650.317136830454568307.327912246265
Trimmed Mean ( 18 / 20 )97.46791666666670.305557804943411318.983560851007
Trimmed Mean ( 19 / 20 )97.47363636363640.295502759968759329.856940672708
Trimmed Mean ( 20 / 20 )97.47750.286252441956948340.529846081315
Median97.53
Midrange97.56
Midmean - Weighted Average at Xnp97.3722580645161
Midmean - Weighted Average at X(n+1)p97.4703333333333
Midmean - Empirical Distribution Function97.3722580645161
Midmean - Empirical Distribution Function - Averaging97.4703333333333
Midmean - Empirical Distribution Function - Interpolation97.4703333333333
Midmean - Closest Observation97.3722580645161
Midmean - True Basic - Statistics Graphics Toolkit97.4703333333333
Midmean - MS Excel (old versions)97.48375
Number of observations60



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,hyperlink('arithmetic_mean.htm', 'Arithmetic Mean', 'click to view the definition of the Arithmetic Mean'),header=TRUE)
a<-table.element(a,arm)
a<-table.element(a,hyperlink('arithmetic_mean_standard_error.htm', armse, 'click to view the definition of the Standard Error of the Arithmetic Mean'))
a<-table.element(a,armose)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('geometric_mean.htm', 'Geometric Mean', 'click to view the definition of the Geometric Mean'),header=TRUE)
a<-table.element(a,geo)
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('harmonic_mean.htm', 'Harmonic Mean', 'click to view the definition of the Harmonic Mean'),header=TRUE)
a<-table.element(a,har)
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('quadratic_mean.htm', 'Quadratic Mean', 'click to view the definition of the Quadratic Mean'),header=TRUE)
a<-table.element(a,qua)
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,hyperlink('winsorized_mean.htm', mylabel, 'click to view the definition of the Winsorized Mean'),header=TRUE)
a<-table.element(a,win[j,1])
a<-table.element(a,win[j,2])
a<-table.element(a,win[j,1]/win[j,2])
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,hyperlink('arithmetic_mean.htm', mylabel, 'click to view the definition of the Trimmed Mean'),header=TRUE)
a<-table.element(a,tri[j,1])
a<-table.element(a,tri[j,2])
a<-table.element(a,tri[j,1]/tri[j,2])
a<-table.row.end(a)
}
a<-table.row.start(a)
a<-table.element(a,hyperlink('median_1.htm', 'Median', 'click to view the definition of the Median'),header=TRUE)
a<-table.element(a,median(x))
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('midrange.htm', 'Midrange', 'click to view the definition of the Midrange'),header=TRUE)
a<-table.element(a,midr)
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_1.htm','Weighted Average at Xnp',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[1])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_2.htm','Weighted Average at X(n+1)p',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[2])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_3.htm','Empirical Distribution Function',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[3])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_4.htm','Empirical Distribution Function - Averaging',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[4])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_5.htm','Empirical Distribution Function - Interpolation',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[5])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_6.htm','Closest Observation',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[6])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_7.htm','True Basic - Statistics Graphics Toolkit',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[7])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_8.htm','MS Excel (old versions)',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[8])
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,length(x))
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable.tab')