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Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationSat, 11 Dec 2010 13:36:47 +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/2010/Dec/11/t1292074506tipmb2pk1wtuju5.htm/, Retrieved Mon, 06 May 2024 12:17:34 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=108143, Retrieved Mon, 06 May 2024 12:17:34 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact106
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
F     [Central Tendency] [Time needed to su...] [2010-09-25 09:42:08] [b98453cac15ba1066b407e146608df68]
-    D  [Central Tendency] [Central tendency ...] [2010-12-11 13:04:54] [04d4386fa51dbd2ef12d0f1f80644886]
-    D      [Central Tendency] [Central tendency ...] [2010-12-11 13:36:47] [de8ccb310fbbdc3d90ae577a3e011cf9] [Current]
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Dataseries X:
16
29
22
30
20
39
18
9,6
10,2
20,2
50
120
19,8
18
3
11
15
27
28
14
5,6
6,5
8,5
87,9
5,8
25,2
7,5
13,7
34
17
9
9,2
5
24
40
86,5
0,54
14
4,8
28
16
5,8
16
9,1
6
17
26
99,6
41
72
23
42
40
18
45
18
2
10
13,6
160




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Sir Ronald Aylmer Fisher' @ 193.190.124.24

\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 & 2 seconds \tabularnewline
R Server & 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=108143&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]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Sir Ronald Aylmer Fisher' @ 193.190.124.24[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=108143&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=108143&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 time2 seconds
R Server'Sir Ronald Aylmer Fisher' @ 193.190.124.24







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean27.21066666666673.852387137754167.06332611278776
Geometric Mean17.3163584291602
Harmonic Mean9.109407441641
Quadratic Mean40.1999091209586
Winsorized Mean ( 1 / 20 )26.56833333333333.50194013350917.58674686614665
Winsorized Mean ( 2 / 20 )25.92166666666673.211034199581998.07268470390043
Winsorized Mean ( 3 / 20 )25.42666666666672.9823367650288.52575301516224
Winsorized Mean ( 4 / 20 )25.34666666666672.947796713037318.59851242609952
Winsorized Mean ( 5 / 20 )24.18833333333332.534735069750489.54274615205227
Winsorized Mean ( 6 / 20 )22.00833333333331.8938113480084511.6211856880452
Winsorized Mean ( 7 / 20 )21.4251.7540471764394312.2146087561288
Winsorized Mean ( 8 / 20 )21.05166666666671.6616146453841812.6694036581505
Winsorized Mean ( 9 / 20 )20.97666666666671.6184134078067712.9612536361112
Winsorized Mean ( 10 / 20 )20.97666666666671.55884457911813.4565478481090
Winsorized Mean ( 11 / 20 )21.161.5325732579424913.8068440711329
Winsorized Mean ( 12 / 20 )21.061.4772286619795914.2564252522545
Winsorized Mean ( 13 / 20 )19.99833333333331.2598706140784715.8733231094219
Winsorized Mean ( 14 / 20 )19.08833333333331.0885513404133217.5355379435623
Winsorized Mean ( 15 / 20 )18.93833333333331.0312547665814618.3643595618109
Winsorized Mean ( 16 / 20 )18.77833333333330.97137880822942219.3316275527582
Winsorized Mean ( 17 / 20 )18.8350.96273159221252719.5641237416068
Winsorized Mean ( 18 / 20 )18.7750.87845082244689621.3728526631723
Winsorized Mean ( 19 / 20 )19.28166666666670.70970866811459127.1684249227084
Winsorized Mean ( 20 / 20 )19.04833333333330.66278598631344328.7397949363477
Trimmed Mean ( 1 / 20 )25.38103448275863.206836746250047.914663729745
Trimmed Mean ( 2 / 20 )24.10892857142862.815091838120048.56417124477503
Trimmed Mean ( 3 / 20 )23.10185185185192.52236327620359.15881232088952
Trimmed Mean ( 4 / 20 )22.20769230769232.267351140144339.79455361566921
Trimmed Mean ( 5 / 20 )21.2661.9335567522795210.9983841823774
Trimmed Mean ( 6 / 20 )20.53541666666671.6730405326726912.2743091190153
Trimmed Mean ( 7 / 20 )20.21521739130431.5887100695029712.7242961314072
Trimmed Mean ( 8 / 20 )19.97954545454551.5250119728690013.1012384230387
Trimmed Mean ( 9 / 20 )19.78809523809521.4694496444650613.4663309577368
Trimmed Mean ( 10 / 20 )19.591.4074426708732713.9188617805975
Trimmed Mean ( 11 / 20 )19.37105263157891.3402718769153914.4530769952146
Trimmed Mean ( 12 / 20 )19.11.2533320668686615.2393771011697
Trimmed Mean ( 13 / 20 )18.81176470588241.1478940238299116.3880674655989
Trimmed Mean ( 14 / 20 )18.6406251.0778549802115917.2941864557147
Trimmed Mean ( 15 / 20 )18.57666666666671.0362363744603817.9270551821157
Trimmed Mean ( 16 / 20 )18.5250.99262658622592818.6626071244314
Trimmed Mean ( 17 / 20 )18.48846153846150.94657807875082219.5318927761990
Trimmed Mean ( 18 / 20 )18.43750.87557046621294221.0576997642997
Trimmed Mean ( 19 / 20 )18.38636363636360.79838298306180123.0295034168337
Trimmed Mean ( 20 / 20 )18.2450.74905115418037224.357481993288
Median18
Midrange80.27
Midmean - Weighted Average at Xnp18.2741935483871
Midmean - Weighted Average at X(n+1)p18.5766666666667
Midmean - Empirical Distribution Function18.2741935483871
Midmean - Empirical Distribution Function - Averaging18.5766666666667
Midmean - Empirical Distribution Function - Interpolation18.5766666666667
Midmean - Closest Observation18.2741935483871
Midmean - True Basic - Statistics Graphics Toolkit18.5766666666667
Midmean - MS Excel (old versions)18.640625
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 27.2106666666667 & 3.85238713775416 & 7.06332611278776 \tabularnewline
Geometric Mean & 17.3163584291602 &  &  \tabularnewline
Harmonic Mean & 9.109407441641 &  &  \tabularnewline
Quadratic Mean & 40.1999091209586 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 26.5683333333333 & 3.5019401335091 & 7.58674686614665 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 25.9216666666667 & 3.21103419958199 & 8.07268470390043 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 25.4266666666667 & 2.982336765028 & 8.52575301516224 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 25.3466666666667 & 2.94779671303731 & 8.59851242609952 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 24.1883333333333 & 2.53473506975048 & 9.54274615205227 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 22.0083333333333 & 1.89381134800845 & 11.6211856880452 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 21.425 & 1.75404717643943 & 12.2146087561288 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 21.0516666666667 & 1.66161464538418 & 12.6694036581505 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 20.9766666666667 & 1.61841340780677 & 12.9612536361112 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 20.9766666666667 & 1.558844579118 & 13.4565478481090 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 21.16 & 1.53257325794249 & 13.8068440711329 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 21.06 & 1.47722866197959 & 14.2564252522545 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 19.9983333333333 & 1.25987061407847 & 15.8733231094219 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 19.0883333333333 & 1.08855134041332 & 17.5355379435623 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 18.9383333333333 & 1.03125476658146 & 18.3643595618109 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 18.7783333333333 & 0.971378808229422 & 19.3316275527582 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 18.835 & 0.962731592212527 & 19.5641237416068 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 18.775 & 0.878450822446896 & 21.3728526631723 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 19.2816666666667 & 0.709708668114591 & 27.1684249227084 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 19.0483333333333 & 0.662785986313443 & 28.7397949363477 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 25.3810344827586 & 3.20683674625004 & 7.914663729745 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 24.1089285714286 & 2.81509183812004 & 8.56417124477503 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 23.1018518518519 & 2.5223632762035 & 9.15881232088952 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 22.2076923076923 & 2.26735114014433 & 9.79455361566921 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 21.266 & 1.93355675227952 & 10.9983841823774 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 20.5354166666667 & 1.67304053267269 & 12.2743091190153 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 20.2152173913043 & 1.58871006950297 & 12.7242961314072 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 19.9795454545455 & 1.52501197286900 & 13.1012384230387 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 19.7880952380952 & 1.46944964446506 & 13.4663309577368 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 19.59 & 1.40744267087327 & 13.9188617805975 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 19.3710526315789 & 1.34027187691539 & 14.4530769952146 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 19.1 & 1.25333206686866 & 15.2393771011697 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 18.8117647058824 & 1.14789402382991 & 16.3880674655989 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 18.640625 & 1.07785498021159 & 17.2941864557147 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 18.5766666666667 & 1.03623637446038 & 17.9270551821157 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 18.525 & 0.992626586225928 & 18.6626071244314 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 18.4884615384615 & 0.946578078750822 & 19.5318927761990 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 18.4375 & 0.875570466212942 & 21.0576997642997 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 18.3863636363636 & 0.798382983061801 & 23.0295034168337 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 18.245 & 0.749051154180372 & 24.357481993288 \tabularnewline
Median & 18 &  &  \tabularnewline
Midrange & 80.27 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 18.2741935483871 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 18.5766666666667 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 18.2741935483871 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 18.5766666666667 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 18.5766666666667 &  &  \tabularnewline
Midmean - Closest Observation & 18.2741935483871 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 18.5766666666667 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 18.640625 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=108143&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]27.2106666666667[/C][C]3.85238713775416[/C][C]7.06332611278776[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]17.3163584291602[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]9.109407441641[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]40.1999091209586[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]26.5683333333333[/C][C]3.5019401335091[/C][C]7.58674686614665[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]25.9216666666667[/C][C]3.21103419958199[/C][C]8.07268470390043[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]25.4266666666667[/C][C]2.982336765028[/C][C]8.52575301516224[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]25.3466666666667[/C][C]2.94779671303731[/C][C]8.59851242609952[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]24.1883333333333[/C][C]2.53473506975048[/C][C]9.54274615205227[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]22.0083333333333[/C][C]1.89381134800845[/C][C]11.6211856880452[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]21.425[/C][C]1.75404717643943[/C][C]12.2146087561288[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]21.0516666666667[/C][C]1.66161464538418[/C][C]12.6694036581505[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]20.9766666666667[/C][C]1.61841340780677[/C][C]12.9612536361112[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]20.9766666666667[/C][C]1.558844579118[/C][C]13.4565478481090[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]21.16[/C][C]1.53257325794249[/C][C]13.8068440711329[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]21.06[/C][C]1.47722866197959[/C][C]14.2564252522545[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]19.9983333333333[/C][C]1.25987061407847[/C][C]15.8733231094219[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]19.0883333333333[/C][C]1.08855134041332[/C][C]17.5355379435623[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]18.9383333333333[/C][C]1.03125476658146[/C][C]18.3643595618109[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]18.7783333333333[/C][C]0.971378808229422[/C][C]19.3316275527582[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]18.835[/C][C]0.962731592212527[/C][C]19.5641237416068[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]18.775[/C][C]0.878450822446896[/C][C]21.3728526631723[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]19.2816666666667[/C][C]0.709708668114591[/C][C]27.1684249227084[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]19.0483333333333[/C][C]0.662785986313443[/C][C]28.7397949363477[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]25.3810344827586[/C][C]3.20683674625004[/C][C]7.914663729745[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]24.1089285714286[/C][C]2.81509183812004[/C][C]8.56417124477503[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]23.1018518518519[/C][C]2.5223632762035[/C][C]9.15881232088952[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]22.2076923076923[/C][C]2.26735114014433[/C][C]9.79455361566921[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]21.266[/C][C]1.93355675227952[/C][C]10.9983841823774[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]20.5354166666667[/C][C]1.67304053267269[/C][C]12.2743091190153[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]20.2152173913043[/C][C]1.58871006950297[/C][C]12.7242961314072[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]19.9795454545455[/C][C]1.52501197286900[/C][C]13.1012384230387[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]19.7880952380952[/C][C]1.46944964446506[/C][C]13.4663309577368[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]19.59[/C][C]1.40744267087327[/C][C]13.9188617805975[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]19.3710526315789[/C][C]1.34027187691539[/C][C]14.4530769952146[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]19.1[/C][C]1.25333206686866[/C][C]15.2393771011697[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]18.8117647058824[/C][C]1.14789402382991[/C][C]16.3880674655989[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]18.640625[/C][C]1.07785498021159[/C][C]17.2941864557147[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]18.5766666666667[/C][C]1.03623637446038[/C][C]17.9270551821157[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]18.525[/C][C]0.992626586225928[/C][C]18.6626071244314[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]18.4884615384615[/C][C]0.946578078750822[/C][C]19.5318927761990[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]18.4375[/C][C]0.875570466212942[/C][C]21.0576997642997[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]18.3863636363636[/C][C]0.798382983061801[/C][C]23.0295034168337[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]18.245[/C][C]0.749051154180372[/C][C]24.357481993288[/C][/ROW]
[ROW][C]Median[/C][C]18[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]80.27[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]18.2741935483871[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]18.5766666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]18.2741935483871[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]18.5766666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]18.5766666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]18.2741935483871[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]18.5766666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]18.640625[/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=108143&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=108143&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 Mean27.21066666666673.852387137754167.06332611278776
Geometric Mean17.3163584291602
Harmonic Mean9.109407441641
Quadratic Mean40.1999091209586
Winsorized Mean ( 1 / 20 )26.56833333333333.50194013350917.58674686614665
Winsorized Mean ( 2 / 20 )25.92166666666673.211034199581998.07268470390043
Winsorized Mean ( 3 / 20 )25.42666666666672.9823367650288.52575301516224
Winsorized Mean ( 4 / 20 )25.34666666666672.947796713037318.59851242609952
Winsorized Mean ( 5 / 20 )24.18833333333332.534735069750489.54274615205227
Winsorized Mean ( 6 / 20 )22.00833333333331.8938113480084511.6211856880452
Winsorized Mean ( 7 / 20 )21.4251.7540471764394312.2146087561288
Winsorized Mean ( 8 / 20 )21.05166666666671.6616146453841812.6694036581505
Winsorized Mean ( 9 / 20 )20.97666666666671.6184134078067712.9612536361112
Winsorized Mean ( 10 / 20 )20.97666666666671.55884457911813.4565478481090
Winsorized Mean ( 11 / 20 )21.161.5325732579424913.8068440711329
Winsorized Mean ( 12 / 20 )21.061.4772286619795914.2564252522545
Winsorized Mean ( 13 / 20 )19.99833333333331.2598706140784715.8733231094219
Winsorized Mean ( 14 / 20 )19.08833333333331.0885513404133217.5355379435623
Winsorized Mean ( 15 / 20 )18.93833333333331.0312547665814618.3643595618109
Winsorized Mean ( 16 / 20 )18.77833333333330.97137880822942219.3316275527582
Winsorized Mean ( 17 / 20 )18.8350.96273159221252719.5641237416068
Winsorized Mean ( 18 / 20 )18.7750.87845082244689621.3728526631723
Winsorized Mean ( 19 / 20 )19.28166666666670.70970866811459127.1684249227084
Winsorized Mean ( 20 / 20 )19.04833333333330.66278598631344328.7397949363477
Trimmed Mean ( 1 / 20 )25.38103448275863.206836746250047.914663729745
Trimmed Mean ( 2 / 20 )24.10892857142862.815091838120048.56417124477503
Trimmed Mean ( 3 / 20 )23.10185185185192.52236327620359.15881232088952
Trimmed Mean ( 4 / 20 )22.20769230769232.267351140144339.79455361566921
Trimmed Mean ( 5 / 20 )21.2661.9335567522795210.9983841823774
Trimmed Mean ( 6 / 20 )20.53541666666671.6730405326726912.2743091190153
Trimmed Mean ( 7 / 20 )20.21521739130431.5887100695029712.7242961314072
Trimmed Mean ( 8 / 20 )19.97954545454551.5250119728690013.1012384230387
Trimmed Mean ( 9 / 20 )19.78809523809521.4694496444650613.4663309577368
Trimmed Mean ( 10 / 20 )19.591.4074426708732713.9188617805975
Trimmed Mean ( 11 / 20 )19.37105263157891.3402718769153914.4530769952146
Trimmed Mean ( 12 / 20 )19.11.2533320668686615.2393771011697
Trimmed Mean ( 13 / 20 )18.81176470588241.1478940238299116.3880674655989
Trimmed Mean ( 14 / 20 )18.6406251.0778549802115917.2941864557147
Trimmed Mean ( 15 / 20 )18.57666666666671.0362363744603817.9270551821157
Trimmed Mean ( 16 / 20 )18.5250.99262658622592818.6626071244314
Trimmed Mean ( 17 / 20 )18.48846153846150.94657807875082219.5318927761990
Trimmed Mean ( 18 / 20 )18.43750.87557046621294221.0576997642997
Trimmed Mean ( 19 / 20 )18.38636363636360.79838298306180123.0295034168337
Trimmed Mean ( 20 / 20 )18.2450.74905115418037224.357481993288
Median18
Midrange80.27
Midmean - Weighted Average at Xnp18.2741935483871
Midmean - Weighted Average at X(n+1)p18.5766666666667
Midmean - Empirical Distribution Function18.2741935483871
Midmean - Empirical Distribution Function - Averaging18.5766666666667
Midmean - Empirical Distribution Function - Interpolation18.5766666666667
Midmean - Closest Observation18.2741935483871
Midmean - True Basic - Statistics Graphics Toolkit18.5766666666667
Midmean - MS Excel (old versions)18.640625
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')