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Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationSat, 05 Mar 2016 11:59:25 +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/05/t1457179249h4na49y6iiem69e.htm/, Retrieved Sat, 27 Apr 2024 10:59:35 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=293452, Retrieved Sat, 27 Apr 2024 10:59:35 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact104
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Central Tendency] [Studio 100 - Cent...] [2016-03-05 11:36:02] [e6773be784e85f51fb44487d8478f111]
-    D    [Central Tendency] [Centrumaten - Con...] [2016-03-05 11:59:25] [268d33ec1c95cc32f8abd6e0112b4a36] [Current]
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Dataseries X:
98,72
98,67
98,82
99,39
99,33
99,22
99,05
98,83
98,84
98,89
98,8
99,4
98,89
98,85
98,69
98,48
98,39
98,35
98,26
98,06
98,14
98,17
98,41
98,64
99,25
99,61
100,28
100,31
100,55
100,45
100,78
100,68
101,69
98,09
99,13
99,18
96,22
96,11
96
95,96
97,95
98,43
98,32
97,45
96,42
95,36
95,1
95,54
94,07
93,48
92,86
90,98
91,45
91,16
90,71
90,31
89,78
91,02
90,77
90,69




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Sir Ronald Aylmer Fisher' @ fisher.wessa.net

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 1 seconds \tabularnewline
R Server & 'Sir Ronald Aylmer Fisher' @ fisher.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=293452&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 Ronald Aylmer Fisher' @ fisher.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=293452&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=293452&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 Ronald Aylmer Fisher' @ fisher.wessa.net







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean97.09050.411570536478469235.90245509491
Geometric Mean97.037798672437
Harmonic Mean96.9838523293867
Quadratic Mean97.1419539557103
Winsorized Mean ( 1 / 20 )97.08416666666670.406385493122867238.896733051724
Winsorized Mean ( 2 / 20 )97.09350.402378719840887241.298794425296
Winsorized Mean ( 3 / 20 )97.0880.401142703942816242.028582461368
Winsorized Mean ( 4 / 20 )97.08533333333330.399103406638188243.258593433524
Winsorized Mean ( 5 / 20 )97.09116666666670.392805143659197247.173867842485
Winsorized Mean ( 6 / 20 )97.09216666666670.391336338042729248.104142723555
Winsorized Mean ( 7 / 20 )97.03033333333330.377090030061958257.313441348186
Winsorized Mean ( 8 / 20 )97.0410.363788035074378266.751488899737
Winsorized Mean ( 9 / 20 )97.2510.31055506166811313.152197480304
Winsorized Mean ( 10 / 20 )97.34433333333330.28510850017813341.429081463774
Winsorized Mean ( 11 / 20 )97.43783333333330.259005386989619376.200026052889
Winsorized Mean ( 12 / 20 )97.63783333333330.214752924865367454.651937311422
Winsorized Mean ( 13 / 20 )97.68550.202542235952487482.296936935738
Winsorized Mean ( 14 / 20 )97.71583333333330.192986679038353506.334602057762
Winsorized Mean ( 15 / 20 )97.80083333333330.170858796503866572.407364060534
Winsorized Mean ( 16 / 20 )97.76883333333330.16378642764122596.928785500464
Winsorized Mean ( 17 / 20 )97.80.158110309772947618.555489142011
Winsorized Mean ( 18 / 20 )97.8210.150755292418178648.872742249444
Winsorized Mean ( 19 / 20 )97.88116666666670.139044579216222703.955286990772
Winsorized Mean ( 20 / 20 )98.22116666666670.07908484025759111241.97211939413
Trimmed Mean ( 1 / 20 )97.13724137931030.398468088420669243.77671437709
Trimmed Mean ( 2 / 20 )97.19410714285710.388492823379344250.182503494928
Trimmed Mean ( 3 / 20 )97.250.378598781082345256.868233230915
Trimmed Mean ( 4 / 20 )97.31230769230770.366574335219578265.464050106011
Trimmed Mean ( 5 / 20 )97.38040.351955697583126276.683686806918
Trimmed Mean ( 6 / 20 )97.45270833333330.335337336715859290.61096890594
Trimmed Mean ( 7 / 20 )97.53108695652170.313953938013663310.654128352667
Trimmed Mean ( 8 / 20 )97.62863636363640.289621863061698337.090008784449
Trimmed Mean ( 9 / 20 )97.73357142857140.260579587497324375.062269332878
Trimmed Mean ( 10 / 20 )97.8140.24042238472514406.842316749436
Trimmed Mean ( 11 / 20 )97.88815789473680.221339789268432442.25287382027
Trimmed Mean ( 12 / 20 )97.95638888888890.203698404813236480.889327428469
Trimmed Mean ( 13 / 20 )98.00323529411760.194512380219124503.840604817617
Trimmed Mean ( 14 / 20 )98.04906250.185166315484542529.518893560235
Trimmed Mean ( 15 / 20 )98.09666666666670.174462941645677562.277958524251
Trimmed Mean ( 16 / 20 )98.13892857142860.166493035974382589.447648648375
Trimmed Mean ( 17 / 20 )98.19230769230770.155628065189272630.942160547252
Trimmed Mean ( 18 / 20 )98.250.140137096434532701.099155753518
Trimmed Mean ( 19 / 20 )98.3150.116464419626601844.163396127417
Trimmed Mean ( 20 / 20 )98.38350.07790099992601911262.9298737299
Median98.4
Midrange95.735
Midmean - Weighted Average at Xnp98.0141935483871
Midmean - Weighted Average at X(n+1)p98.0966666666667
Midmean - Empirical Distribution Function98.0141935483871
Midmean - Empirical Distribution Function - Averaging98.0966666666667
Midmean - Empirical Distribution Function - Interpolation98.0966666666667
Midmean - Closest Observation98.0141935483871
Midmean - True Basic - Statistics Graphics Toolkit98.0966666666667
Midmean - MS Excel (old versions)98.0490625
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 97.0905 & 0.411570536478469 & 235.90245509491 \tabularnewline
Geometric Mean & 97.037798672437 &  &  \tabularnewline
Harmonic Mean & 96.9838523293867 &  &  \tabularnewline
Quadratic Mean & 97.1419539557103 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 97.0841666666667 & 0.406385493122867 & 238.896733051724 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 97.0935 & 0.402378719840887 & 241.298794425296 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 97.088 & 0.401142703942816 & 242.028582461368 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 97.0853333333333 & 0.399103406638188 & 243.258593433524 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 97.0911666666667 & 0.392805143659197 & 247.173867842485 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 97.0921666666667 & 0.391336338042729 & 248.104142723555 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 97.0303333333333 & 0.377090030061958 & 257.313441348186 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 97.041 & 0.363788035074378 & 266.751488899737 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 97.251 & 0.31055506166811 & 313.152197480304 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 97.3443333333333 & 0.28510850017813 & 341.429081463774 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 97.4378333333333 & 0.259005386989619 & 376.200026052889 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 97.6378333333333 & 0.214752924865367 & 454.651937311422 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 97.6855 & 0.202542235952487 & 482.296936935738 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 97.7158333333333 & 0.192986679038353 & 506.334602057762 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 97.8008333333333 & 0.170858796503866 & 572.407364060534 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 97.7688333333333 & 0.16378642764122 & 596.928785500464 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 97.8 & 0.158110309772947 & 618.555489142011 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 97.821 & 0.150755292418178 & 648.872742249444 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 97.8811666666667 & 0.139044579216222 & 703.955286990772 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 98.2211666666667 & 0.0790848402575911 & 1241.97211939413 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 97.1372413793103 & 0.398468088420669 & 243.77671437709 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 97.1941071428571 & 0.388492823379344 & 250.182503494928 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 97.25 & 0.378598781082345 & 256.868233230915 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 97.3123076923077 & 0.366574335219578 & 265.464050106011 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 97.3804 & 0.351955697583126 & 276.683686806918 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 97.4527083333333 & 0.335337336715859 & 290.61096890594 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 97.5310869565217 & 0.313953938013663 & 310.654128352667 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 97.6286363636364 & 0.289621863061698 & 337.090008784449 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 97.7335714285714 & 0.260579587497324 & 375.062269332878 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 97.814 & 0.24042238472514 & 406.842316749436 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 97.8881578947368 & 0.221339789268432 & 442.25287382027 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 97.9563888888889 & 0.203698404813236 & 480.889327428469 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 98.0032352941176 & 0.194512380219124 & 503.840604817617 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 98.0490625 & 0.185166315484542 & 529.518893560235 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 98.0966666666667 & 0.174462941645677 & 562.277958524251 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 98.1389285714286 & 0.166493035974382 & 589.447648648375 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 98.1923076923077 & 0.155628065189272 & 630.942160547252 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 98.25 & 0.140137096434532 & 701.099155753518 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 98.315 & 0.116464419626601 & 844.163396127417 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 98.3835 & 0.0779009999260191 & 1262.9298737299 \tabularnewline
Median & 98.4 &  &  \tabularnewline
Midrange & 95.735 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 98.0141935483871 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 98.0966666666667 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 98.0141935483871 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 98.0966666666667 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 98.0966666666667 &  &  \tabularnewline
Midmean - Closest Observation & 98.0141935483871 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 98.0966666666667 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 98.0490625 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=293452&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]97.0905[/C][C]0.411570536478469[/C][C]235.90245509491[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]97.037798672437[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]96.9838523293867[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]97.1419539557103[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]97.0841666666667[/C][C]0.406385493122867[/C][C]238.896733051724[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]97.0935[/C][C]0.402378719840887[/C][C]241.298794425296[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]97.088[/C][C]0.401142703942816[/C][C]242.028582461368[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]97.0853333333333[/C][C]0.399103406638188[/C][C]243.258593433524[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]97.0911666666667[/C][C]0.392805143659197[/C][C]247.173867842485[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]97.0921666666667[/C][C]0.391336338042729[/C][C]248.104142723555[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]97.0303333333333[/C][C]0.377090030061958[/C][C]257.313441348186[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]97.041[/C][C]0.363788035074378[/C][C]266.751488899737[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]97.251[/C][C]0.31055506166811[/C][C]313.152197480304[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]97.3443333333333[/C][C]0.28510850017813[/C][C]341.429081463774[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]97.4378333333333[/C][C]0.259005386989619[/C][C]376.200026052889[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]97.6378333333333[/C][C]0.214752924865367[/C][C]454.651937311422[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]97.6855[/C][C]0.202542235952487[/C][C]482.296936935738[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]97.7158333333333[/C][C]0.192986679038353[/C][C]506.334602057762[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]97.8008333333333[/C][C]0.170858796503866[/C][C]572.407364060534[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]97.7688333333333[/C][C]0.16378642764122[/C][C]596.928785500464[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]97.8[/C][C]0.158110309772947[/C][C]618.555489142011[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]97.821[/C][C]0.150755292418178[/C][C]648.872742249444[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]97.8811666666667[/C][C]0.139044579216222[/C][C]703.955286990772[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]98.2211666666667[/C][C]0.0790848402575911[/C][C]1241.97211939413[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]97.1372413793103[/C][C]0.398468088420669[/C][C]243.77671437709[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]97.1941071428571[/C][C]0.388492823379344[/C][C]250.182503494928[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]97.25[/C][C]0.378598781082345[/C][C]256.868233230915[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]97.3123076923077[/C][C]0.366574335219578[/C][C]265.464050106011[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]97.3804[/C][C]0.351955697583126[/C][C]276.683686806918[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]97.4527083333333[/C][C]0.335337336715859[/C][C]290.61096890594[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]97.5310869565217[/C][C]0.313953938013663[/C][C]310.654128352667[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]97.6286363636364[/C][C]0.289621863061698[/C][C]337.090008784449[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]97.7335714285714[/C][C]0.260579587497324[/C][C]375.062269332878[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]97.814[/C][C]0.24042238472514[/C][C]406.842316749436[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]97.8881578947368[/C][C]0.221339789268432[/C][C]442.25287382027[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]97.9563888888889[/C][C]0.203698404813236[/C][C]480.889327428469[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]98.0032352941176[/C][C]0.194512380219124[/C][C]503.840604817617[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]98.0490625[/C][C]0.185166315484542[/C][C]529.518893560235[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]98.0966666666667[/C][C]0.174462941645677[/C][C]562.277958524251[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]98.1389285714286[/C][C]0.166493035974382[/C][C]589.447648648375[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]98.1923076923077[/C][C]0.155628065189272[/C][C]630.942160547252[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]98.25[/C][C]0.140137096434532[/C][C]701.099155753518[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]98.315[/C][C]0.116464419626601[/C][C]844.163396127417[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]98.3835[/C][C]0.0779009999260191[/C][C]1262.9298737299[/C][/ROW]
[ROW][C]Median[/C][C]98.4[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]95.735[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]98.0141935483871[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]98.0966666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]98.0141935483871[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]98.0966666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]98.0966666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]98.0141935483871[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]98.0966666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]98.0490625[/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=293452&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=293452&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 Mean97.09050.411570536478469235.90245509491
Geometric Mean97.037798672437
Harmonic Mean96.9838523293867
Quadratic Mean97.1419539557103
Winsorized Mean ( 1 / 20 )97.08416666666670.406385493122867238.896733051724
Winsorized Mean ( 2 / 20 )97.09350.402378719840887241.298794425296
Winsorized Mean ( 3 / 20 )97.0880.401142703942816242.028582461368
Winsorized Mean ( 4 / 20 )97.08533333333330.399103406638188243.258593433524
Winsorized Mean ( 5 / 20 )97.09116666666670.392805143659197247.173867842485
Winsorized Mean ( 6 / 20 )97.09216666666670.391336338042729248.104142723555
Winsorized Mean ( 7 / 20 )97.03033333333330.377090030061958257.313441348186
Winsorized Mean ( 8 / 20 )97.0410.363788035074378266.751488899737
Winsorized Mean ( 9 / 20 )97.2510.31055506166811313.152197480304
Winsorized Mean ( 10 / 20 )97.34433333333330.28510850017813341.429081463774
Winsorized Mean ( 11 / 20 )97.43783333333330.259005386989619376.200026052889
Winsorized Mean ( 12 / 20 )97.63783333333330.214752924865367454.651937311422
Winsorized Mean ( 13 / 20 )97.68550.202542235952487482.296936935738
Winsorized Mean ( 14 / 20 )97.71583333333330.192986679038353506.334602057762
Winsorized Mean ( 15 / 20 )97.80083333333330.170858796503866572.407364060534
Winsorized Mean ( 16 / 20 )97.76883333333330.16378642764122596.928785500464
Winsorized Mean ( 17 / 20 )97.80.158110309772947618.555489142011
Winsorized Mean ( 18 / 20 )97.8210.150755292418178648.872742249444
Winsorized Mean ( 19 / 20 )97.88116666666670.139044579216222703.955286990772
Winsorized Mean ( 20 / 20 )98.22116666666670.07908484025759111241.97211939413
Trimmed Mean ( 1 / 20 )97.13724137931030.398468088420669243.77671437709
Trimmed Mean ( 2 / 20 )97.19410714285710.388492823379344250.182503494928
Trimmed Mean ( 3 / 20 )97.250.378598781082345256.868233230915
Trimmed Mean ( 4 / 20 )97.31230769230770.366574335219578265.464050106011
Trimmed Mean ( 5 / 20 )97.38040.351955697583126276.683686806918
Trimmed Mean ( 6 / 20 )97.45270833333330.335337336715859290.61096890594
Trimmed Mean ( 7 / 20 )97.53108695652170.313953938013663310.654128352667
Trimmed Mean ( 8 / 20 )97.62863636363640.289621863061698337.090008784449
Trimmed Mean ( 9 / 20 )97.73357142857140.260579587497324375.062269332878
Trimmed Mean ( 10 / 20 )97.8140.24042238472514406.842316749436
Trimmed Mean ( 11 / 20 )97.88815789473680.221339789268432442.25287382027
Trimmed Mean ( 12 / 20 )97.95638888888890.203698404813236480.889327428469
Trimmed Mean ( 13 / 20 )98.00323529411760.194512380219124503.840604817617
Trimmed Mean ( 14 / 20 )98.04906250.185166315484542529.518893560235
Trimmed Mean ( 15 / 20 )98.09666666666670.174462941645677562.277958524251
Trimmed Mean ( 16 / 20 )98.13892857142860.166493035974382589.447648648375
Trimmed Mean ( 17 / 20 )98.19230769230770.155628065189272630.942160547252
Trimmed Mean ( 18 / 20 )98.250.140137096434532701.099155753518
Trimmed Mean ( 19 / 20 )98.3150.116464419626601844.163396127417
Trimmed Mean ( 20 / 20 )98.38350.07790099992601911262.9298737299
Median98.4
Midrange95.735
Midmean - Weighted Average at Xnp98.0141935483871
Midmean - Weighted Average at X(n+1)p98.0966666666667
Midmean - Empirical Distribution Function98.0141935483871
Midmean - Empirical Distribution Function - Averaging98.0966666666667
Midmean - Empirical Distribution Function - Interpolation98.0966666666667
Midmean - Closest Observation98.0141935483871
Midmean - True Basic - Statistics Graphics Toolkit98.0966666666667
Midmean - MS Excel (old versions)98.0490625
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')