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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 computationFri, 09 Oct 2015 19:55:02 +0100
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2015/Oct/09/t1444416923j3xq1r1rrjh8g6i.htm/, Retrieved Tue, 14 May 2024 01:48:24 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=282034, Retrieved Tue, 14 May 2024 01:48:24 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact56
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [] [2015-10-09 18:55:02] [baf7db162d56d42e62a4d339fc25c05c] [Current]
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Dataseries X:
79,21
79,08
79,88
80,57
80,9
80,89
80,61
80,98
81,68
83,28
83,94
89,25
95,3
97,68
98,53
98,32
97,02
90,13
88,49
88,07
87,17
86,1
86,59
85,89
85,82
86,68
86,3
86,32
85,61
85,52
85,97
86,6
86,78
84,98
85,21
86,39
88,39
88,83
95,76
100,98
102,56
102,92
104,35
105,07
105,41
105,06
104,33
104,61
104,78
104,38
104,08
103,4
101,72
100,1
100,37
96,27
95,28
95,85
96,76
97
96,71
96,97
96,97
98,01
99,18
99,51
99,16
99,4
97,59
96,71
96,56
96,42




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'George Udny Yule' @ yule.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 & 2 seconds \tabularnewline
R Server & 'George Udny Yule' @ yule.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=282034&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]'George Udny Yule' @ yule.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=282034&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=282034&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'George Udny Yule' @ yule.wessa.net







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean92.96097222222220.95865381780867596.9703249445308
Geometric Mean92.6065586393592
Harmonic Mean92.249795912489
Quadratic Mean93.3112671310979
Winsorized Mean ( 1 / 24 )92.95805555555550.95743457833290997.0907649036602
Winsorized Mean ( 2 / 24 )92.97638888888890.95370310931554497.4898665850177
Winsorized Mean ( 3 / 24 )92.99347222222220.94619953014670998.2810382581817
Winsorized Mean ( 4 / 24 )92.986250.94414156962902898.4876135011576
Winsorized Mean ( 5 / 24 )92.98972222222220.9378288358548299.1542578635505
Winsorized Mean ( 6 / 24 )92.98805555555550.93725017827159999.2136973791102
Winsorized Mean ( 7 / 24 )92.99388888888890.93550841782750399.4046521835102
Winsorized Mean ( 8 / 24 )93.04388888888890.916958949466161101.470070108436
Winsorized Mean ( 9 / 24 )93.15888888888890.86919628021238107.178195546495
Winsorized Mean ( 10 / 24 )93.18388888888890.843833624629049110.42921989492
Winsorized Mean ( 11 / 24 )93.28777777777780.811204069962013114.999149082359
Winsorized Mean ( 12 / 24 )93.18611111111110.783676993728312118.908825774994
Winsorized Mean ( 13 / 24 )93.10847222222220.755650018655037123.216396378768
Winsorized Mean ( 14 / 24 )93.00736111111110.736113700463453126.349178194285
Winsorized Mean ( 15 / 24 )92.99486111111110.722095471414864128.784717246458
Winsorized Mean ( 16 / 24 )92.87930555555550.702106497545977132.286634406874
Winsorized Mean ( 17 / 24 )92.87222222222220.696020383962513133.433192995716
Winsorized Mean ( 18 / 24 )92.84972222222220.684276829814441135.690291087893
Winsorized Mean ( 19 / 24 )92.89722222222220.676296709101182137.361635761448
Winsorized Mean ( 20 / 24 )92.72777777777780.653163040175229141.967276275922
Winsorized Mean ( 21 / 24 )92.68694444444440.642731408516268144.207896512184
Winsorized Mean ( 22 / 24 )92.65333333333330.622738600563863148.7836682188
Winsorized Mean ( 23 / 24 )92.55111111111110.609667504611977151.805878468158
Winsorized Mean ( 24 / 24 )92.54777777777780.602459786456029153.616523224214
Trimmed Mean ( 1 / 24 )92.98142857142860.94904623116624997.9735502001489
Trimmed Mean ( 2 / 24 )93.00617647058820.938693542950799.0804476807537
Trimmed Mean ( 3 / 24 )93.02242424242420.92830278650423100.206985904593
Trimmed Mean ( 4 / 24 )93.033281250.91877188060241101.258302756285
Trimmed Mean ( 5 / 24 )93.0469354838710.907575747894083102.522500959038
Trimmed Mean ( 6 / 24 )93.06066666666670.895527016083178103.91720740452
Trimmed Mean ( 7 / 24 )93.07568965517240.880594211472815105.696458644102
Trimmed Mean ( 8 / 24 )93.09071428571430.862390059138083107.945022440024
Trimmed Mean ( 9 / 24 )93.09851851851850.844200646454983110.280084372671
Trimmed Mean ( 10 / 24 )93.08923076923080.832310103904414111.844407910638
Trimmed Mean ( 11 / 24 )93.07560.822337393392413113.184199998534
Trimmed Mean ( 12 / 24 )93.04666666666670.815750390599719114.062668849305
Trimmed Mean ( 13 / 24 )93.02847826086960.811927090762549114.577379322937
Trimmed Mean ( 14 / 24 )93.01840909090910.811189124225879114.669201438908
Trimmed Mean ( 15 / 24 )93.01976190476190.812238735844589114.522686249428
Trimmed Mean ( 16 / 24 )93.022750.814173876368886114.254157127799
Trimmed Mean ( 17 / 24 )93.03973684210530.818144127404554113.720472622911
Trimmed Mean ( 18 / 24 )93.05944444444440.821666806186064113.256911127272
Trimmed Mean ( 19 / 24 )93.08411764705880.825591142142061112.748445199575
Trimmed Mean ( 20 / 24 )93.106250.829034459525444112.306851579241
Trimmed Mean ( 21 / 24 )93.15166666666670.834781006912541111.588148143416
Trimmed Mean ( 22 / 24 )93.20857142857140.84024525808027110.930196311405
Trimmed Mean ( 23 / 24 )93.27846153846150.847402309742081110.075769756696
Trimmed Mean ( 24 / 24 )93.37333333333330.853984197548079109.338479097649
Median95.805
Midrange92.245
Midmean - Weighted Average at Xnp92.8678378378378
Midmean - Weighted Average at X(n+1)p93.0594444444444
Midmean - Empirical Distribution Function92.8678378378378
Midmean - Empirical Distribution Function - Averaging93.0594444444444
Midmean - Empirical Distribution Function - Interpolation93.0594444444444
Midmean - Closest Observation92.8678378378378
Midmean - True Basic - Statistics Graphics Toolkit93.0594444444444
Midmean - MS Excel (old versions)93.0397368421053
Number of observations72

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 92.9609722222222 & 0.958653817808675 & 96.9703249445308 \tabularnewline
Geometric Mean & 92.6065586393592 &  &  \tabularnewline
Harmonic Mean & 92.249795912489 &  &  \tabularnewline
Quadratic Mean & 93.3112671310979 &  &  \tabularnewline
Winsorized Mean ( 1 / 24 ) & 92.9580555555555 & 0.957434578332909 & 97.0907649036602 \tabularnewline
Winsorized Mean ( 2 / 24 ) & 92.9763888888889 & 0.953703109315544 & 97.4898665850177 \tabularnewline
Winsorized Mean ( 3 / 24 ) & 92.9934722222222 & 0.946199530146709 & 98.2810382581817 \tabularnewline
Winsorized Mean ( 4 / 24 ) & 92.98625 & 0.944141569629028 & 98.4876135011576 \tabularnewline
Winsorized Mean ( 5 / 24 ) & 92.9897222222222 & 0.93782883585482 & 99.1542578635505 \tabularnewline
Winsorized Mean ( 6 / 24 ) & 92.9880555555555 & 0.937250178271599 & 99.2136973791102 \tabularnewline
Winsorized Mean ( 7 / 24 ) & 92.9938888888889 & 0.935508417827503 & 99.4046521835102 \tabularnewline
Winsorized Mean ( 8 / 24 ) & 93.0438888888889 & 0.916958949466161 & 101.470070108436 \tabularnewline
Winsorized Mean ( 9 / 24 ) & 93.1588888888889 & 0.86919628021238 & 107.178195546495 \tabularnewline
Winsorized Mean ( 10 / 24 ) & 93.1838888888889 & 0.843833624629049 & 110.42921989492 \tabularnewline
Winsorized Mean ( 11 / 24 ) & 93.2877777777778 & 0.811204069962013 & 114.999149082359 \tabularnewline
Winsorized Mean ( 12 / 24 ) & 93.1861111111111 & 0.783676993728312 & 118.908825774994 \tabularnewline
Winsorized Mean ( 13 / 24 ) & 93.1084722222222 & 0.755650018655037 & 123.216396378768 \tabularnewline
Winsorized Mean ( 14 / 24 ) & 93.0073611111111 & 0.736113700463453 & 126.349178194285 \tabularnewline
Winsorized Mean ( 15 / 24 ) & 92.9948611111111 & 0.722095471414864 & 128.784717246458 \tabularnewline
Winsorized Mean ( 16 / 24 ) & 92.8793055555555 & 0.702106497545977 & 132.286634406874 \tabularnewline
Winsorized Mean ( 17 / 24 ) & 92.8722222222222 & 0.696020383962513 & 133.433192995716 \tabularnewline
Winsorized Mean ( 18 / 24 ) & 92.8497222222222 & 0.684276829814441 & 135.690291087893 \tabularnewline
Winsorized Mean ( 19 / 24 ) & 92.8972222222222 & 0.676296709101182 & 137.361635761448 \tabularnewline
Winsorized Mean ( 20 / 24 ) & 92.7277777777778 & 0.653163040175229 & 141.967276275922 \tabularnewline
Winsorized Mean ( 21 / 24 ) & 92.6869444444444 & 0.642731408516268 & 144.207896512184 \tabularnewline
Winsorized Mean ( 22 / 24 ) & 92.6533333333333 & 0.622738600563863 & 148.7836682188 \tabularnewline
Winsorized Mean ( 23 / 24 ) & 92.5511111111111 & 0.609667504611977 & 151.805878468158 \tabularnewline
Winsorized Mean ( 24 / 24 ) & 92.5477777777778 & 0.602459786456029 & 153.616523224214 \tabularnewline
Trimmed Mean ( 1 / 24 ) & 92.9814285714286 & 0.949046231166249 & 97.9735502001489 \tabularnewline
Trimmed Mean ( 2 / 24 ) & 93.0061764705882 & 0.9386935429507 & 99.0804476807537 \tabularnewline
Trimmed Mean ( 3 / 24 ) & 93.0224242424242 & 0.92830278650423 & 100.206985904593 \tabularnewline
Trimmed Mean ( 4 / 24 ) & 93.03328125 & 0.91877188060241 & 101.258302756285 \tabularnewline
Trimmed Mean ( 5 / 24 ) & 93.046935483871 & 0.907575747894083 & 102.522500959038 \tabularnewline
Trimmed Mean ( 6 / 24 ) & 93.0606666666667 & 0.895527016083178 & 103.91720740452 \tabularnewline
Trimmed Mean ( 7 / 24 ) & 93.0756896551724 & 0.880594211472815 & 105.696458644102 \tabularnewline
Trimmed Mean ( 8 / 24 ) & 93.0907142857143 & 0.862390059138083 & 107.945022440024 \tabularnewline
Trimmed Mean ( 9 / 24 ) & 93.0985185185185 & 0.844200646454983 & 110.280084372671 \tabularnewline
Trimmed Mean ( 10 / 24 ) & 93.0892307692308 & 0.832310103904414 & 111.844407910638 \tabularnewline
Trimmed Mean ( 11 / 24 ) & 93.0756 & 0.822337393392413 & 113.184199998534 \tabularnewline
Trimmed Mean ( 12 / 24 ) & 93.0466666666667 & 0.815750390599719 & 114.062668849305 \tabularnewline
Trimmed Mean ( 13 / 24 ) & 93.0284782608696 & 0.811927090762549 & 114.577379322937 \tabularnewline
Trimmed Mean ( 14 / 24 ) & 93.0184090909091 & 0.811189124225879 & 114.669201438908 \tabularnewline
Trimmed Mean ( 15 / 24 ) & 93.0197619047619 & 0.812238735844589 & 114.522686249428 \tabularnewline
Trimmed Mean ( 16 / 24 ) & 93.02275 & 0.814173876368886 & 114.254157127799 \tabularnewline
Trimmed Mean ( 17 / 24 ) & 93.0397368421053 & 0.818144127404554 & 113.720472622911 \tabularnewline
Trimmed Mean ( 18 / 24 ) & 93.0594444444444 & 0.821666806186064 & 113.256911127272 \tabularnewline
Trimmed Mean ( 19 / 24 ) & 93.0841176470588 & 0.825591142142061 & 112.748445199575 \tabularnewline
Trimmed Mean ( 20 / 24 ) & 93.10625 & 0.829034459525444 & 112.306851579241 \tabularnewline
Trimmed Mean ( 21 / 24 ) & 93.1516666666667 & 0.834781006912541 & 111.588148143416 \tabularnewline
Trimmed Mean ( 22 / 24 ) & 93.2085714285714 & 0.84024525808027 & 110.930196311405 \tabularnewline
Trimmed Mean ( 23 / 24 ) & 93.2784615384615 & 0.847402309742081 & 110.075769756696 \tabularnewline
Trimmed Mean ( 24 / 24 ) & 93.3733333333333 & 0.853984197548079 & 109.338479097649 \tabularnewline
Median & 95.805 &  &  \tabularnewline
Midrange & 92.245 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 92.8678378378378 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 93.0594444444444 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 92.8678378378378 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 93.0594444444444 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 93.0594444444444 &  &  \tabularnewline
Midmean - Closest Observation & 92.8678378378378 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 93.0594444444444 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 93.0397368421053 &  &  \tabularnewline
Number of observations & 72 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=282034&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]92.9609722222222[/C][C]0.958653817808675[/C][C]96.9703249445308[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]92.6065586393592[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]92.249795912489[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]93.3112671310979[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 24 )[/C][C]92.9580555555555[/C][C]0.957434578332909[/C][C]97.0907649036602[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 24 )[/C][C]92.9763888888889[/C][C]0.953703109315544[/C][C]97.4898665850177[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 24 )[/C][C]92.9934722222222[/C][C]0.946199530146709[/C][C]98.2810382581817[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 24 )[/C][C]92.98625[/C][C]0.944141569629028[/C][C]98.4876135011576[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 24 )[/C][C]92.9897222222222[/C][C]0.93782883585482[/C][C]99.1542578635505[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 24 )[/C][C]92.9880555555555[/C][C]0.937250178271599[/C][C]99.2136973791102[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 24 )[/C][C]92.9938888888889[/C][C]0.935508417827503[/C][C]99.4046521835102[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 24 )[/C][C]93.0438888888889[/C][C]0.916958949466161[/C][C]101.470070108436[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 24 )[/C][C]93.1588888888889[/C][C]0.86919628021238[/C][C]107.178195546495[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 24 )[/C][C]93.1838888888889[/C][C]0.843833624629049[/C][C]110.42921989492[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 24 )[/C][C]93.2877777777778[/C][C]0.811204069962013[/C][C]114.999149082359[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 24 )[/C][C]93.1861111111111[/C][C]0.783676993728312[/C][C]118.908825774994[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 24 )[/C][C]93.1084722222222[/C][C]0.755650018655037[/C][C]123.216396378768[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 24 )[/C][C]93.0073611111111[/C][C]0.736113700463453[/C][C]126.349178194285[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 24 )[/C][C]92.9948611111111[/C][C]0.722095471414864[/C][C]128.784717246458[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 24 )[/C][C]92.8793055555555[/C][C]0.702106497545977[/C][C]132.286634406874[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 24 )[/C][C]92.8722222222222[/C][C]0.696020383962513[/C][C]133.433192995716[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 24 )[/C][C]92.8497222222222[/C][C]0.684276829814441[/C][C]135.690291087893[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 24 )[/C][C]92.8972222222222[/C][C]0.676296709101182[/C][C]137.361635761448[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 24 )[/C][C]92.7277777777778[/C][C]0.653163040175229[/C][C]141.967276275922[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 24 )[/C][C]92.6869444444444[/C][C]0.642731408516268[/C][C]144.207896512184[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 24 )[/C][C]92.6533333333333[/C][C]0.622738600563863[/C][C]148.7836682188[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 24 )[/C][C]92.5511111111111[/C][C]0.609667504611977[/C][C]151.805878468158[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 24 )[/C][C]92.5477777777778[/C][C]0.602459786456029[/C][C]153.616523224214[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 24 )[/C][C]92.9814285714286[/C][C]0.949046231166249[/C][C]97.9735502001489[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 24 )[/C][C]93.0061764705882[/C][C]0.9386935429507[/C][C]99.0804476807537[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 24 )[/C][C]93.0224242424242[/C][C]0.92830278650423[/C][C]100.206985904593[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 24 )[/C][C]93.03328125[/C][C]0.91877188060241[/C][C]101.258302756285[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 24 )[/C][C]93.046935483871[/C][C]0.907575747894083[/C][C]102.522500959038[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 24 )[/C][C]93.0606666666667[/C][C]0.895527016083178[/C][C]103.91720740452[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 24 )[/C][C]93.0756896551724[/C][C]0.880594211472815[/C][C]105.696458644102[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 24 )[/C][C]93.0907142857143[/C][C]0.862390059138083[/C][C]107.945022440024[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 24 )[/C][C]93.0985185185185[/C][C]0.844200646454983[/C][C]110.280084372671[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 24 )[/C][C]93.0892307692308[/C][C]0.832310103904414[/C][C]111.844407910638[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 24 )[/C][C]93.0756[/C][C]0.822337393392413[/C][C]113.184199998534[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 24 )[/C][C]93.0466666666667[/C][C]0.815750390599719[/C][C]114.062668849305[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 24 )[/C][C]93.0284782608696[/C][C]0.811927090762549[/C][C]114.577379322937[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 24 )[/C][C]93.0184090909091[/C][C]0.811189124225879[/C][C]114.669201438908[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 24 )[/C][C]93.0197619047619[/C][C]0.812238735844589[/C][C]114.522686249428[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 24 )[/C][C]93.02275[/C][C]0.814173876368886[/C][C]114.254157127799[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 24 )[/C][C]93.0397368421053[/C][C]0.818144127404554[/C][C]113.720472622911[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 24 )[/C][C]93.0594444444444[/C][C]0.821666806186064[/C][C]113.256911127272[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 24 )[/C][C]93.0841176470588[/C][C]0.825591142142061[/C][C]112.748445199575[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 24 )[/C][C]93.10625[/C][C]0.829034459525444[/C][C]112.306851579241[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 24 )[/C][C]93.1516666666667[/C][C]0.834781006912541[/C][C]111.588148143416[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 24 )[/C][C]93.2085714285714[/C][C]0.84024525808027[/C][C]110.930196311405[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 24 )[/C][C]93.2784615384615[/C][C]0.847402309742081[/C][C]110.075769756696[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 24 )[/C][C]93.3733333333333[/C][C]0.853984197548079[/C][C]109.338479097649[/C][/ROW]
[ROW][C]Median[/C][C]95.805[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]92.245[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]92.8678378378378[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]93.0594444444444[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]92.8678378378378[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]93.0594444444444[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]93.0594444444444[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]92.8678378378378[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]93.0594444444444[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]93.0397368421053[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]72[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=282034&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=282034&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 Mean92.96097222222220.95865381780867596.9703249445308
Geometric Mean92.6065586393592
Harmonic Mean92.249795912489
Quadratic Mean93.3112671310979
Winsorized Mean ( 1 / 24 )92.95805555555550.95743457833290997.0907649036602
Winsorized Mean ( 2 / 24 )92.97638888888890.95370310931554497.4898665850177
Winsorized Mean ( 3 / 24 )92.99347222222220.94619953014670998.2810382581817
Winsorized Mean ( 4 / 24 )92.986250.94414156962902898.4876135011576
Winsorized Mean ( 5 / 24 )92.98972222222220.9378288358548299.1542578635505
Winsorized Mean ( 6 / 24 )92.98805555555550.93725017827159999.2136973791102
Winsorized Mean ( 7 / 24 )92.99388888888890.93550841782750399.4046521835102
Winsorized Mean ( 8 / 24 )93.04388888888890.916958949466161101.470070108436
Winsorized Mean ( 9 / 24 )93.15888888888890.86919628021238107.178195546495
Winsorized Mean ( 10 / 24 )93.18388888888890.843833624629049110.42921989492
Winsorized Mean ( 11 / 24 )93.28777777777780.811204069962013114.999149082359
Winsorized Mean ( 12 / 24 )93.18611111111110.783676993728312118.908825774994
Winsorized Mean ( 13 / 24 )93.10847222222220.755650018655037123.216396378768
Winsorized Mean ( 14 / 24 )93.00736111111110.736113700463453126.349178194285
Winsorized Mean ( 15 / 24 )92.99486111111110.722095471414864128.784717246458
Winsorized Mean ( 16 / 24 )92.87930555555550.702106497545977132.286634406874
Winsorized Mean ( 17 / 24 )92.87222222222220.696020383962513133.433192995716
Winsorized Mean ( 18 / 24 )92.84972222222220.684276829814441135.690291087893
Winsorized Mean ( 19 / 24 )92.89722222222220.676296709101182137.361635761448
Winsorized Mean ( 20 / 24 )92.72777777777780.653163040175229141.967276275922
Winsorized Mean ( 21 / 24 )92.68694444444440.642731408516268144.207896512184
Winsorized Mean ( 22 / 24 )92.65333333333330.622738600563863148.7836682188
Winsorized Mean ( 23 / 24 )92.55111111111110.609667504611977151.805878468158
Winsorized Mean ( 24 / 24 )92.54777777777780.602459786456029153.616523224214
Trimmed Mean ( 1 / 24 )92.98142857142860.94904623116624997.9735502001489
Trimmed Mean ( 2 / 24 )93.00617647058820.938693542950799.0804476807537
Trimmed Mean ( 3 / 24 )93.02242424242420.92830278650423100.206985904593
Trimmed Mean ( 4 / 24 )93.033281250.91877188060241101.258302756285
Trimmed Mean ( 5 / 24 )93.0469354838710.907575747894083102.522500959038
Trimmed Mean ( 6 / 24 )93.06066666666670.895527016083178103.91720740452
Trimmed Mean ( 7 / 24 )93.07568965517240.880594211472815105.696458644102
Trimmed Mean ( 8 / 24 )93.09071428571430.862390059138083107.945022440024
Trimmed Mean ( 9 / 24 )93.09851851851850.844200646454983110.280084372671
Trimmed Mean ( 10 / 24 )93.08923076923080.832310103904414111.844407910638
Trimmed Mean ( 11 / 24 )93.07560.822337393392413113.184199998534
Trimmed Mean ( 12 / 24 )93.04666666666670.815750390599719114.062668849305
Trimmed Mean ( 13 / 24 )93.02847826086960.811927090762549114.577379322937
Trimmed Mean ( 14 / 24 )93.01840909090910.811189124225879114.669201438908
Trimmed Mean ( 15 / 24 )93.01976190476190.812238735844589114.522686249428
Trimmed Mean ( 16 / 24 )93.022750.814173876368886114.254157127799
Trimmed Mean ( 17 / 24 )93.03973684210530.818144127404554113.720472622911
Trimmed Mean ( 18 / 24 )93.05944444444440.821666806186064113.256911127272
Trimmed Mean ( 19 / 24 )93.08411764705880.825591142142061112.748445199575
Trimmed Mean ( 20 / 24 )93.106250.829034459525444112.306851579241
Trimmed Mean ( 21 / 24 )93.15166666666670.834781006912541111.588148143416
Trimmed Mean ( 22 / 24 )93.20857142857140.84024525808027110.930196311405
Trimmed Mean ( 23 / 24 )93.27846153846150.847402309742081110.075769756696
Trimmed Mean ( 24 / 24 )93.37333333333330.853984197548079109.338479097649
Median95.805
Midrange92.245
Midmean - Weighted Average at Xnp92.8678378378378
Midmean - Weighted Average at X(n+1)p93.0594444444444
Midmean - Empirical Distribution Function92.8678378378378
Midmean - Empirical Distribution Function - Averaging93.0594444444444
Midmean - Empirical Distribution Function - Interpolation93.0594444444444
Midmean - Closest Observation92.8678378378378
Midmean - True Basic - Statistics Graphics Toolkit93.0594444444444
Midmean - MS Excel (old versions)93.0397368421053
Number of observations72



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')