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Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationFri, 05 Jun 2009 06:09:43 -0600
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2009/Jun/05/t12442038994ejr5ettwh08xbo.htm/, Retrieved Fri, 10 May 2024 05:03:18 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=41809, Retrieved Fri, 10 May 2024 05:03:18 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact147
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Central Tendency] [Trimmed Mean Plot...] [2008-04-19 09:45:15] [74be16979710d4c4e7c6647856088456]
-    D  [Central Tendency] [opgave 5 dennis gys] [2009-06-05 11:53:39] [74be16979710d4c4e7c6647856088456]
-    D      [Central Tendency] [opgave 5(3) denni...] [2009-06-05 12:09:43] [d41d8cd98f00b204e9800998ecf8427e] [Current]
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Dataseries X:
10.738
10.171
9.721
9.897
9.828
9.924
10.371
10.846
10.413
10.709
10.662
10.570
10.297
10.635
10.872
10.296
10.383
10.431
10.574
10.653
10.805
10.872
10.625
10.407
10.463
10.556
10.646
10.702
11.353
11.346
11.451
11.964
12.574
13.031
13.812
14.544
14.931
14.886
16.005
17.064
15.168
16.050
15.839
15.137
14.954
15.648
15.305
15.579
16.348
15.928
16.171
15.937
15.713
15.594
15.683
16.438
17.032
17.696
17.745
19.394
20.148
20.108
18.584
18.441
18.391
19.178
18.079
18.483
19.644
19.195
19.650
20.830




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'George Udny Yule' @ 72.249.76.132

\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 & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=41809&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]'George Udny Yule' @ 72.249.76.132[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=41809&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=41809&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'George Udny Yule' @ 72.249.76.132







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean14.02941666666670.40713021796218334.4592861146205
Geometric Mean13.6173601744972
Harmonic Mean13.2245850741038
Quadratic Mean14.4427538242462
Winsorized Mean ( 1 / 24 )14.02143055555560.40478689346161634.6390428693194
Winsorized Mean ( 2 / 24 )14.02223611111110.40427311046554134.685057571511
Winsorized Mean ( 3 / 24 )14.00427777777780.40019189118965534.9939068883858
Winsorized Mean ( 4 / 24 )14.01766666666670.39820670881101135.2019851913632
Winsorized Mean ( 5 / 24 )14.00898611111110.39363918168447235.5883935414241
Winsorized Mean ( 6 / 24 )13.99248611111110.39047432884119435.8345864954463
Winsorized Mean ( 7 / 24 )13.99802777777780.38921269292434535.9649827260354
Winsorized Mean ( 8 / 24 )13.93336111111110.37711194509539136.9475464575556
Winsorized Mean ( 9 / 24 )13.92373611111110.37453589015957837.1759729225913
Winsorized Mean ( 10 / 24 )13.91873611111110.37342813863368437.27286369484
Winsorized Mean ( 11 / 24 )13.91384722222220.37176557540923537.426400244041
Winsorized Mean ( 12 / 24 )13.86718055555560.36239281634137438.2656055259458
Winsorized Mean ( 13 / 24 )13.82366666666670.35048902567769639.4410827555516
Winsorized Mean ( 14 / 24 )13.81686111111110.34863448710196939.6313664375663
Winsorized Mean ( 15 / 24 )13.68602777777780.32865384190392341.6426830688888
Winsorized Mean ( 16 / 24 )13.690250.32612003869150741.9791744626593
Winsorized Mean ( 17 / 24 )13.55236111111110.30635606994246644.2372860888843
Winsorized Mean ( 18 / 24 )13.53261111111110.30302240200552344.6587810721151
Winsorized Mean ( 19 / 24 )13.487750.29674292997577945.4526414533310
Winsorized Mean ( 20 / 24 )13.45663888888890.29216471782500846.0583981155066
Winsorized Mean ( 21 / 24 )13.45518055555560.28895993633526746.5641733113622
Winsorized Mean ( 22 / 24 )13.43654166666670.28610277814547546.9640377271506
Winsorized Mean ( 23 / 24 )13.44293055555560.28450677767668547.2499483679513
Winsorized Mean ( 24 / 24 )13.43559722222220.27789061502699148.3485101535986
Trimmed Mean ( 1 / 24 )13.99381428571430.40248722536360534.7683439469969
Trimmed Mean ( 2 / 24 )13.96457352941180.39950429299475234.9547521122513
Trimmed Mean ( 3 / 24 )13.93312121212120.3960181275519135.1830389640304
Trimmed Mean ( 4 / 24 )13.90643750.39339818237799935.3495214846669
Trimmed Mean ( 5 / 24 )13.87414516129030.39061678765765635.5185583407385
Trimmed Mean ( 6 / 24 )13.84178333333330.38829206644657135.647865432857
Trimmed Mean ( 7 / 24 )13.81060344827590.38594859054418935.7835312438966
Trimmed Mean ( 8 / 24 )13.77617857142860.38297510778960135.9714725349642
Trimmed Mean ( 9 / 24 )13.74998148148150.3817451957430736.0187413877391
Trimmed Mean ( 10 / 24 )13.723250.38025522297074536.0895766080136
Trimmed Mean ( 11 / 24 )13.69510.37807721838432036.2230235890034
Trimmed Mean ( 12 / 24 )13.66527083333330.37512427224493236.4286500352363
Trimmed Mean ( 13 / 24 )13.63893478260870.37280297136830536.5848338937575
Trimmed Mean ( 14 / 24 )13.61568181818180.37163202544860836.6375362880686
Trimmed Mean ( 15 / 24 )13.59104761904760.36969565904450936.7628001209809
Trimmed Mean ( 16 / 24 )13.579650.3705375280312236.648514584077
Trimmed Mean ( 17 / 24 )13.56655263157890.37100626055797636.5669102488338
Trimmed Mean ( 18 / 24 )13.56822222222220.37447366896458236.2327804241572
Trimmed Mean ( 19 / 24 )13.57241176470590.37812668259261735.8938218050283
Trimmed Mean ( 20 / 24 )13.58243750.38251143757277635.5085787399908
Trimmed Mean ( 21 / 24 )13.59753333333330.38732774957891935.1060138296722
Trimmed Mean ( 22 / 24 )13.61496428571430.39227208690448434.7079609797203
Trimmed Mean ( 23 / 24 )13.63742307692310.39706948499873434.3451803579582
Trimmed Mean ( 24 / 24 )13.66279166666670.40111455219486634.0620692814683
Median14.715
Midrange15.2755
Midmean - Weighted Average at Xnp13.4889459459459
Midmean - Weighted Average at X(n+1)p13.5682222222222
Midmean - Empirical Distribution Function13.4889459459459
Midmean - Empirical Distribution Function - Averaging13.5682222222222
Midmean - Empirical Distribution Function - Interpolation13.5682222222222
Midmean - Closest Observation13.4889459459459
Midmean - True Basic - Statistics Graphics Toolkit13.5682222222222
Midmean - MS Excel (old versions)13.5665526315790
Number of observations72

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 14.0294166666667 & 0.407130217962183 & 34.4592861146205 \tabularnewline
Geometric Mean & 13.6173601744972 &  &  \tabularnewline
Harmonic Mean & 13.2245850741038 &  &  \tabularnewline
Quadratic Mean & 14.4427538242462 &  &  \tabularnewline
Winsorized Mean ( 1 / 24 ) & 14.0214305555556 & 0.404786893461616 & 34.6390428693194 \tabularnewline
Winsorized Mean ( 2 / 24 ) & 14.0222361111111 & 0.404273110465541 & 34.685057571511 \tabularnewline
Winsorized Mean ( 3 / 24 ) & 14.0042777777778 & 0.400191891189655 & 34.9939068883858 \tabularnewline
Winsorized Mean ( 4 / 24 ) & 14.0176666666667 & 0.398206708811011 & 35.2019851913632 \tabularnewline
Winsorized Mean ( 5 / 24 ) & 14.0089861111111 & 0.393639181684472 & 35.5883935414241 \tabularnewline
Winsorized Mean ( 6 / 24 ) & 13.9924861111111 & 0.390474328841194 & 35.8345864954463 \tabularnewline
Winsorized Mean ( 7 / 24 ) & 13.9980277777778 & 0.389212692924345 & 35.9649827260354 \tabularnewline
Winsorized Mean ( 8 / 24 ) & 13.9333611111111 & 0.377111945095391 & 36.9475464575556 \tabularnewline
Winsorized Mean ( 9 / 24 ) & 13.9237361111111 & 0.374535890159578 & 37.1759729225913 \tabularnewline
Winsorized Mean ( 10 / 24 ) & 13.9187361111111 & 0.373428138633684 & 37.27286369484 \tabularnewline
Winsorized Mean ( 11 / 24 ) & 13.9138472222222 & 0.371765575409235 & 37.426400244041 \tabularnewline
Winsorized Mean ( 12 / 24 ) & 13.8671805555556 & 0.362392816341374 & 38.2656055259458 \tabularnewline
Winsorized Mean ( 13 / 24 ) & 13.8236666666667 & 0.350489025677696 & 39.4410827555516 \tabularnewline
Winsorized Mean ( 14 / 24 ) & 13.8168611111111 & 0.348634487101969 & 39.6313664375663 \tabularnewline
Winsorized Mean ( 15 / 24 ) & 13.6860277777778 & 0.328653841903923 & 41.6426830688888 \tabularnewline
Winsorized Mean ( 16 / 24 ) & 13.69025 & 0.326120038691507 & 41.9791744626593 \tabularnewline
Winsorized Mean ( 17 / 24 ) & 13.5523611111111 & 0.306356069942466 & 44.2372860888843 \tabularnewline
Winsorized Mean ( 18 / 24 ) & 13.5326111111111 & 0.303022402005523 & 44.6587810721151 \tabularnewline
Winsorized Mean ( 19 / 24 ) & 13.48775 & 0.296742929975779 & 45.4526414533310 \tabularnewline
Winsorized Mean ( 20 / 24 ) & 13.4566388888889 & 0.292164717825008 & 46.0583981155066 \tabularnewline
Winsorized Mean ( 21 / 24 ) & 13.4551805555556 & 0.288959936335267 & 46.5641733113622 \tabularnewline
Winsorized Mean ( 22 / 24 ) & 13.4365416666667 & 0.286102778145475 & 46.9640377271506 \tabularnewline
Winsorized Mean ( 23 / 24 ) & 13.4429305555556 & 0.284506777676685 & 47.2499483679513 \tabularnewline
Winsorized Mean ( 24 / 24 ) & 13.4355972222222 & 0.277890615026991 & 48.3485101535986 \tabularnewline
Trimmed Mean ( 1 / 24 ) & 13.9938142857143 & 0.402487225363605 & 34.7683439469969 \tabularnewline
Trimmed Mean ( 2 / 24 ) & 13.9645735294118 & 0.399504292994752 & 34.9547521122513 \tabularnewline
Trimmed Mean ( 3 / 24 ) & 13.9331212121212 & 0.39601812755191 & 35.1830389640304 \tabularnewline
Trimmed Mean ( 4 / 24 ) & 13.9064375 & 0.393398182377999 & 35.3495214846669 \tabularnewline
Trimmed Mean ( 5 / 24 ) & 13.8741451612903 & 0.390616787657656 & 35.5185583407385 \tabularnewline
Trimmed Mean ( 6 / 24 ) & 13.8417833333333 & 0.388292066446571 & 35.647865432857 \tabularnewline
Trimmed Mean ( 7 / 24 ) & 13.8106034482759 & 0.385948590544189 & 35.7835312438966 \tabularnewline
Trimmed Mean ( 8 / 24 ) & 13.7761785714286 & 0.382975107789601 & 35.9714725349642 \tabularnewline
Trimmed Mean ( 9 / 24 ) & 13.7499814814815 & 0.38174519574307 & 36.0187413877391 \tabularnewline
Trimmed Mean ( 10 / 24 ) & 13.72325 & 0.380255222970745 & 36.0895766080136 \tabularnewline
Trimmed Mean ( 11 / 24 ) & 13.6951 & 0.378077218384320 & 36.2230235890034 \tabularnewline
Trimmed Mean ( 12 / 24 ) & 13.6652708333333 & 0.375124272244932 & 36.4286500352363 \tabularnewline
Trimmed Mean ( 13 / 24 ) & 13.6389347826087 & 0.372802971368305 & 36.5848338937575 \tabularnewline
Trimmed Mean ( 14 / 24 ) & 13.6156818181818 & 0.371632025448608 & 36.6375362880686 \tabularnewline
Trimmed Mean ( 15 / 24 ) & 13.5910476190476 & 0.369695659044509 & 36.7628001209809 \tabularnewline
Trimmed Mean ( 16 / 24 ) & 13.57965 & 0.37053752803122 & 36.648514584077 \tabularnewline
Trimmed Mean ( 17 / 24 ) & 13.5665526315789 & 0.371006260557976 & 36.5669102488338 \tabularnewline
Trimmed Mean ( 18 / 24 ) & 13.5682222222222 & 0.374473668964582 & 36.2327804241572 \tabularnewline
Trimmed Mean ( 19 / 24 ) & 13.5724117647059 & 0.378126682592617 & 35.8938218050283 \tabularnewline
Trimmed Mean ( 20 / 24 ) & 13.5824375 & 0.382511437572776 & 35.5085787399908 \tabularnewline
Trimmed Mean ( 21 / 24 ) & 13.5975333333333 & 0.387327749578919 & 35.1060138296722 \tabularnewline
Trimmed Mean ( 22 / 24 ) & 13.6149642857143 & 0.392272086904484 & 34.7079609797203 \tabularnewline
Trimmed Mean ( 23 / 24 ) & 13.6374230769231 & 0.397069484998734 & 34.3451803579582 \tabularnewline
Trimmed Mean ( 24 / 24 ) & 13.6627916666667 & 0.401114552194866 & 34.0620692814683 \tabularnewline
Median & 14.715 &  &  \tabularnewline
Midrange & 15.2755 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 13.4889459459459 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 13.5682222222222 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 13.4889459459459 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 13.5682222222222 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 13.5682222222222 &  &  \tabularnewline
Midmean - Closest Observation & 13.4889459459459 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 13.5682222222222 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 13.5665526315790 &  &  \tabularnewline
Number of observations & 72 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=41809&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]14.0294166666667[/C][C]0.407130217962183[/C][C]34.4592861146205[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]13.6173601744972[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]13.2245850741038[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]14.4427538242462[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 24 )[/C][C]14.0214305555556[/C][C]0.404786893461616[/C][C]34.6390428693194[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 24 )[/C][C]14.0222361111111[/C][C]0.404273110465541[/C][C]34.685057571511[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 24 )[/C][C]14.0042777777778[/C][C]0.400191891189655[/C][C]34.9939068883858[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 24 )[/C][C]14.0176666666667[/C][C]0.398206708811011[/C][C]35.2019851913632[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 24 )[/C][C]14.0089861111111[/C][C]0.393639181684472[/C][C]35.5883935414241[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 24 )[/C][C]13.9924861111111[/C][C]0.390474328841194[/C][C]35.8345864954463[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 24 )[/C][C]13.9980277777778[/C][C]0.389212692924345[/C][C]35.9649827260354[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 24 )[/C][C]13.9333611111111[/C][C]0.377111945095391[/C][C]36.9475464575556[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 24 )[/C][C]13.9237361111111[/C][C]0.374535890159578[/C][C]37.1759729225913[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 24 )[/C][C]13.9187361111111[/C][C]0.373428138633684[/C][C]37.27286369484[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 24 )[/C][C]13.9138472222222[/C][C]0.371765575409235[/C][C]37.426400244041[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 24 )[/C][C]13.8671805555556[/C][C]0.362392816341374[/C][C]38.2656055259458[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 24 )[/C][C]13.8236666666667[/C][C]0.350489025677696[/C][C]39.4410827555516[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 24 )[/C][C]13.8168611111111[/C][C]0.348634487101969[/C][C]39.6313664375663[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 24 )[/C][C]13.6860277777778[/C][C]0.328653841903923[/C][C]41.6426830688888[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 24 )[/C][C]13.69025[/C][C]0.326120038691507[/C][C]41.9791744626593[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 24 )[/C][C]13.5523611111111[/C][C]0.306356069942466[/C][C]44.2372860888843[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 24 )[/C][C]13.5326111111111[/C][C]0.303022402005523[/C][C]44.6587810721151[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 24 )[/C][C]13.48775[/C][C]0.296742929975779[/C][C]45.4526414533310[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 24 )[/C][C]13.4566388888889[/C][C]0.292164717825008[/C][C]46.0583981155066[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 24 )[/C][C]13.4551805555556[/C][C]0.288959936335267[/C][C]46.5641733113622[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 24 )[/C][C]13.4365416666667[/C][C]0.286102778145475[/C][C]46.9640377271506[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 24 )[/C][C]13.4429305555556[/C][C]0.284506777676685[/C][C]47.2499483679513[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 24 )[/C][C]13.4355972222222[/C][C]0.277890615026991[/C][C]48.3485101535986[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 24 )[/C][C]13.9938142857143[/C][C]0.402487225363605[/C][C]34.7683439469969[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 24 )[/C][C]13.9645735294118[/C][C]0.399504292994752[/C][C]34.9547521122513[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 24 )[/C][C]13.9331212121212[/C][C]0.39601812755191[/C][C]35.1830389640304[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 24 )[/C][C]13.9064375[/C][C]0.393398182377999[/C][C]35.3495214846669[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 24 )[/C][C]13.8741451612903[/C][C]0.390616787657656[/C][C]35.5185583407385[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 24 )[/C][C]13.8417833333333[/C][C]0.388292066446571[/C][C]35.647865432857[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 24 )[/C][C]13.8106034482759[/C][C]0.385948590544189[/C][C]35.7835312438966[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 24 )[/C][C]13.7761785714286[/C][C]0.382975107789601[/C][C]35.9714725349642[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 24 )[/C][C]13.7499814814815[/C][C]0.38174519574307[/C][C]36.0187413877391[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 24 )[/C][C]13.72325[/C][C]0.380255222970745[/C][C]36.0895766080136[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 24 )[/C][C]13.6951[/C][C]0.378077218384320[/C][C]36.2230235890034[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 24 )[/C][C]13.6652708333333[/C][C]0.375124272244932[/C][C]36.4286500352363[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 24 )[/C][C]13.6389347826087[/C][C]0.372802971368305[/C][C]36.5848338937575[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 24 )[/C][C]13.6156818181818[/C][C]0.371632025448608[/C][C]36.6375362880686[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 24 )[/C][C]13.5910476190476[/C][C]0.369695659044509[/C][C]36.7628001209809[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 24 )[/C][C]13.57965[/C][C]0.37053752803122[/C][C]36.648514584077[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 24 )[/C][C]13.5665526315789[/C][C]0.371006260557976[/C][C]36.5669102488338[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 24 )[/C][C]13.5682222222222[/C][C]0.374473668964582[/C][C]36.2327804241572[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 24 )[/C][C]13.5724117647059[/C][C]0.378126682592617[/C][C]35.8938218050283[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 24 )[/C][C]13.5824375[/C][C]0.382511437572776[/C][C]35.5085787399908[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 24 )[/C][C]13.5975333333333[/C][C]0.387327749578919[/C][C]35.1060138296722[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 24 )[/C][C]13.6149642857143[/C][C]0.392272086904484[/C][C]34.7079609797203[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 24 )[/C][C]13.6374230769231[/C][C]0.397069484998734[/C][C]34.3451803579582[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 24 )[/C][C]13.6627916666667[/C][C]0.401114552194866[/C][C]34.0620692814683[/C][/ROW]
[ROW][C]Median[/C][C]14.715[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]15.2755[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]13.4889459459459[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]13.5682222222222[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]13.4889459459459[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]13.5682222222222[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]13.5682222222222[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]13.4889459459459[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]13.5682222222222[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]13.5665526315790[/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=41809&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=41809&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 Mean14.02941666666670.40713021796218334.4592861146205
Geometric Mean13.6173601744972
Harmonic Mean13.2245850741038
Quadratic Mean14.4427538242462
Winsorized Mean ( 1 / 24 )14.02143055555560.40478689346161634.6390428693194
Winsorized Mean ( 2 / 24 )14.02223611111110.40427311046554134.685057571511
Winsorized Mean ( 3 / 24 )14.00427777777780.40019189118965534.9939068883858
Winsorized Mean ( 4 / 24 )14.01766666666670.39820670881101135.2019851913632
Winsorized Mean ( 5 / 24 )14.00898611111110.39363918168447235.5883935414241
Winsorized Mean ( 6 / 24 )13.99248611111110.39047432884119435.8345864954463
Winsorized Mean ( 7 / 24 )13.99802777777780.38921269292434535.9649827260354
Winsorized Mean ( 8 / 24 )13.93336111111110.37711194509539136.9475464575556
Winsorized Mean ( 9 / 24 )13.92373611111110.37453589015957837.1759729225913
Winsorized Mean ( 10 / 24 )13.91873611111110.37342813863368437.27286369484
Winsorized Mean ( 11 / 24 )13.91384722222220.37176557540923537.426400244041
Winsorized Mean ( 12 / 24 )13.86718055555560.36239281634137438.2656055259458
Winsorized Mean ( 13 / 24 )13.82366666666670.35048902567769639.4410827555516
Winsorized Mean ( 14 / 24 )13.81686111111110.34863448710196939.6313664375663
Winsorized Mean ( 15 / 24 )13.68602777777780.32865384190392341.6426830688888
Winsorized Mean ( 16 / 24 )13.690250.32612003869150741.9791744626593
Winsorized Mean ( 17 / 24 )13.55236111111110.30635606994246644.2372860888843
Winsorized Mean ( 18 / 24 )13.53261111111110.30302240200552344.6587810721151
Winsorized Mean ( 19 / 24 )13.487750.29674292997577945.4526414533310
Winsorized Mean ( 20 / 24 )13.45663888888890.29216471782500846.0583981155066
Winsorized Mean ( 21 / 24 )13.45518055555560.28895993633526746.5641733113622
Winsorized Mean ( 22 / 24 )13.43654166666670.28610277814547546.9640377271506
Winsorized Mean ( 23 / 24 )13.44293055555560.28450677767668547.2499483679513
Winsorized Mean ( 24 / 24 )13.43559722222220.27789061502699148.3485101535986
Trimmed Mean ( 1 / 24 )13.99381428571430.40248722536360534.7683439469969
Trimmed Mean ( 2 / 24 )13.96457352941180.39950429299475234.9547521122513
Trimmed Mean ( 3 / 24 )13.93312121212120.3960181275519135.1830389640304
Trimmed Mean ( 4 / 24 )13.90643750.39339818237799935.3495214846669
Trimmed Mean ( 5 / 24 )13.87414516129030.39061678765765635.5185583407385
Trimmed Mean ( 6 / 24 )13.84178333333330.38829206644657135.647865432857
Trimmed Mean ( 7 / 24 )13.81060344827590.38594859054418935.7835312438966
Trimmed Mean ( 8 / 24 )13.77617857142860.38297510778960135.9714725349642
Trimmed Mean ( 9 / 24 )13.74998148148150.3817451957430736.0187413877391
Trimmed Mean ( 10 / 24 )13.723250.38025522297074536.0895766080136
Trimmed Mean ( 11 / 24 )13.69510.37807721838432036.2230235890034
Trimmed Mean ( 12 / 24 )13.66527083333330.37512427224493236.4286500352363
Trimmed Mean ( 13 / 24 )13.63893478260870.37280297136830536.5848338937575
Trimmed Mean ( 14 / 24 )13.61568181818180.37163202544860836.6375362880686
Trimmed Mean ( 15 / 24 )13.59104761904760.36969565904450936.7628001209809
Trimmed Mean ( 16 / 24 )13.579650.3705375280312236.648514584077
Trimmed Mean ( 17 / 24 )13.56655263157890.37100626055797636.5669102488338
Trimmed Mean ( 18 / 24 )13.56822222222220.37447366896458236.2327804241572
Trimmed Mean ( 19 / 24 )13.57241176470590.37812668259261735.8938218050283
Trimmed Mean ( 20 / 24 )13.58243750.38251143757277635.5085787399908
Trimmed Mean ( 21 / 24 )13.59753333333330.38732774957891935.1060138296722
Trimmed Mean ( 22 / 24 )13.61496428571430.39227208690448434.7079609797203
Trimmed Mean ( 23 / 24 )13.63742307692310.39706948499873434.3451803579582
Trimmed Mean ( 24 / 24 )13.66279166666670.40111455219486634.0620692814683
Median14.715
Midrange15.2755
Midmean - Weighted Average at Xnp13.4889459459459
Midmean - Weighted Average at X(n+1)p13.5682222222222
Midmean - Empirical Distribution Function13.4889459459459
Midmean - Empirical Distribution Function - Averaging13.5682222222222
Midmean - Empirical Distribution Function - Interpolation13.5682222222222
Midmean - Closest Observation13.4889459459459
Midmean - True Basic - Statistics Graphics Toolkit13.5682222222222
Midmean - MS Excel (old versions)13.5665526315790
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')