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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 computationWed, 28 Oct 2009 15:51:32 -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/Oct/28/t1256766816yo1ofdjhaiyz387.htm/, Retrieved Mon, 06 May 2024 04:36:21 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=51869, Retrieved Mon, 06 May 2024 04:36:21 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsKDGP1W52
Estimated Impact81
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [Centrummaten eige...] [2009-10-28 21:51:32] [9b42eb3f67be7a3fb50ab98e0efd6cc3] [Current]
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Dataseries X:
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
23.595
22.937
21.814
21.928
21.777
21.383
21.467




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

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 2 seconds \tabularnewline
R Server & 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=51869&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Sir Ronald Aylmer Fisher' @ 193.190.124.24[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=51869&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=51869&T=0

As an alternative you can also use a QR Code:  

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

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







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean15.19956944444440.46445511971156832.7255934951983
Geometric Mean14.6973193567844
Harmonic Mean14.2101396397802
Quadratic Mean15.6953155091115
Winsorized Mean ( 1 / 24 )15.19044444444440.46221088027420332.8647487385689
Winsorized Mean ( 2 / 24 )15.16480555555560.45561555020947233.2842141770259
Winsorized Mean ( 3 / 24 )15.16105555555560.45448175222121933.3589973226822
Winsorized Mean ( 4 / 24 )15.15933333333330.45400975365764533.3898847132798
Winsorized Mean ( 5 / 24 )15.13905555555560.44948102437264633.6811894933397
Winsorized Mean ( 6 / 24 )15.13472222222220.4477063657295933.8050190498373
Winsorized Mean ( 7 / 24 )15.090.43610857250340234.6014753009293
Winsorized Mean ( 8 / 24 )15.01577777777780.42236252693130735.5518703017419
Winsorized Mean ( 9 / 24 )15.01127777777780.42143469153146635.6194638918495
Winsorized Mean ( 10 / 24 )14.954750.40982877104552136.4902394769617
Winsorized Mean ( 11 / 24 )14.95536111111110.40945370314337536.5251577804739
Winsorized Mean ( 12 / 24 )14.91552777777780.40255530096301137.0521211423528
Winsorized Mean ( 13 / 24 )14.88086111111110.39679954736928737.5022129177533
Winsorized Mean ( 14 / 24 )14.87930555555560.39603123179452137.5710407690159
Winsorized Mean ( 15 / 24 )14.76388888888890.37645486460442139.2182178450603
Winsorized Mean ( 16 / 24 )14.7430.37302948420686139.5223450804343
Winsorized Mean ( 17 / 24 )14.755750.36819122646379540.076321594401
Winsorized Mean ( 18 / 24 )14.75350.36488504631815840.4332820675141
Winsorized Mean ( 19 / 24 )14.67802777777780.35246803147650141.6435718050542
Winsorized Mean ( 20 / 24 )14.585250.34008914344484142.886549838853
Winsorized Mean ( 21 / 24 )14.70920833333330.31724473425936946.365492457024
Winsorized Mean ( 22 / 24 )14.51823611111110.2922322574424849.6804707261611
Winsorized Mean ( 23 / 24 )14.53931944444440.28621136243218150.7992391388361
Winsorized Mean ( 24 / 24 )14.51231944444440.23668491781969061.3149311672667
Trimmed Mean ( 1 / 24 )15.14968571428570.45684371182755733.1616378250692
Trimmed Mean ( 2 / 24 )15.10652941176470.45027875595496333.5492829985425
Trimmed Mean ( 3 / 24 )15.07474242424240.44638472295848733.7707400117372
Trimmed Mean ( 4 / 24 )15.0423750.4419557749300834.0359281477424
Trimmed Mean ( 5 / 24 )15.00841935483870.43653006953937434.3811810505416
Trimmed Mean ( 6 / 24 )14.97706666666670.43112231729179034.7397155423294
Trimmed Mean ( 7 / 24 )14.94444827586210.42476738317327635.1826643661238
Trimmed Mean ( 8 / 24 )14.91771428571430.41970712246236735.5431525636115
Trimmed Mean ( 9 / 24 )14.90137037037040.41641778671563635.7846634936039
Trimmed Mean ( 10 / 24 )14.88446153846150.41212377372939236.1164836567641
Trimmed Mean ( 11 / 24 )14.874340.40886758158781636.3793576938438
Trimmed Mean ( 12 / 24 )14.86329166666670.40434562860801336.7588780861427
Trimmed Mean ( 13 / 24 )14.85647826086960.39959556333961737.1787868131134
Trimmed Mean ( 14 / 24 )14.85340909090910.39422239717397637.6777402739857
Trimmed Mean ( 15 / 24 )14.85023809523810.38689910332679738.3827152028696
Trimmed Mean ( 16 / 24 )14.86060.38113747233841138.9901310643245
Trimmed Mean ( 17 / 24 )14.87452631578950.37360425075643239.8135896089865
Trimmed Mean ( 18 / 24 )14.88850.36401842684040740.9004020187346
Trimmed Mean ( 19 / 24 )14.90438235294120.35114274109704242.4453665377699
Trimmed Mean ( 20 / 24 )14.93118750.33598476599219644.4400729179097
Trimmed Mean ( 21 / 24 )14.97270.31720118402904147.2025350278302
Trimmed Mean ( 22 / 24 )15.00496428571430.29756056465079350.4265889645814
Trimmed Mean ( 23 / 24 )15.06623076923080.27530097268649554.7263986109769
Trimmed Mean ( 24 / 24 )15.13495833333330.24158444737683862.6487280024485
Median15.5865
Midrange16.9455
Midmean - Weighted Average at Xnp14.7781351351351
Midmean - Weighted Average at X(n+1)p14.8885
Midmean - Empirical Distribution Function14.7781351351351
Midmean - Empirical Distribution Function - Averaging14.8885
Midmean - Empirical Distribution Function - Interpolation14.8885
Midmean - Closest Observation14.7781351351351
Midmean - True Basic - Statistics Graphics Toolkit14.8885
Midmean - MS Excel (old versions)14.8745263157895
Number of observations72

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 15.1995694444444 & 0.464455119711568 & 32.7255934951983 \tabularnewline
Geometric Mean & 14.6973193567844 &  &  \tabularnewline
Harmonic Mean & 14.2101396397802 &  &  \tabularnewline
Quadratic Mean & 15.6953155091115 &  &  \tabularnewline
Winsorized Mean ( 1 / 24 ) & 15.1904444444444 & 0.462210880274203 & 32.8647487385689 \tabularnewline
Winsorized Mean ( 2 / 24 ) & 15.1648055555556 & 0.455615550209472 & 33.2842141770259 \tabularnewline
Winsorized Mean ( 3 / 24 ) & 15.1610555555556 & 0.454481752221219 & 33.3589973226822 \tabularnewline
Winsorized Mean ( 4 / 24 ) & 15.1593333333333 & 0.454009753657645 & 33.3898847132798 \tabularnewline
Winsorized Mean ( 5 / 24 ) & 15.1390555555556 & 0.449481024372646 & 33.6811894933397 \tabularnewline
Winsorized Mean ( 6 / 24 ) & 15.1347222222222 & 0.44770636572959 & 33.8050190498373 \tabularnewline
Winsorized Mean ( 7 / 24 ) & 15.09 & 0.436108572503402 & 34.6014753009293 \tabularnewline
Winsorized Mean ( 8 / 24 ) & 15.0157777777778 & 0.422362526931307 & 35.5518703017419 \tabularnewline
Winsorized Mean ( 9 / 24 ) & 15.0112777777778 & 0.421434691531466 & 35.6194638918495 \tabularnewline
Winsorized Mean ( 10 / 24 ) & 14.95475 & 0.409828771045521 & 36.4902394769617 \tabularnewline
Winsorized Mean ( 11 / 24 ) & 14.9553611111111 & 0.409453703143375 & 36.5251577804739 \tabularnewline
Winsorized Mean ( 12 / 24 ) & 14.9155277777778 & 0.402555300963011 & 37.0521211423528 \tabularnewline
Winsorized Mean ( 13 / 24 ) & 14.8808611111111 & 0.396799547369287 & 37.5022129177533 \tabularnewline
Winsorized Mean ( 14 / 24 ) & 14.8793055555556 & 0.396031231794521 & 37.5710407690159 \tabularnewline
Winsorized Mean ( 15 / 24 ) & 14.7638888888889 & 0.376454864604421 & 39.2182178450603 \tabularnewline
Winsorized Mean ( 16 / 24 ) & 14.743 & 0.373029484206861 & 39.5223450804343 \tabularnewline
Winsorized Mean ( 17 / 24 ) & 14.75575 & 0.368191226463795 & 40.076321594401 \tabularnewline
Winsorized Mean ( 18 / 24 ) & 14.7535 & 0.364885046318158 & 40.4332820675141 \tabularnewline
Winsorized Mean ( 19 / 24 ) & 14.6780277777778 & 0.352468031476501 & 41.6435718050542 \tabularnewline
Winsorized Mean ( 20 / 24 ) & 14.58525 & 0.340089143444841 & 42.886549838853 \tabularnewline
Winsorized Mean ( 21 / 24 ) & 14.7092083333333 & 0.317244734259369 & 46.365492457024 \tabularnewline
Winsorized Mean ( 22 / 24 ) & 14.5182361111111 & 0.29223225744248 & 49.6804707261611 \tabularnewline
Winsorized Mean ( 23 / 24 ) & 14.5393194444444 & 0.286211362432181 & 50.7992391388361 \tabularnewline
Winsorized Mean ( 24 / 24 ) & 14.5123194444444 & 0.236684917819690 & 61.3149311672667 \tabularnewline
Trimmed Mean ( 1 / 24 ) & 15.1496857142857 & 0.456843711827557 & 33.1616378250692 \tabularnewline
Trimmed Mean ( 2 / 24 ) & 15.1065294117647 & 0.450278755954963 & 33.5492829985425 \tabularnewline
Trimmed Mean ( 3 / 24 ) & 15.0747424242424 & 0.446384722958487 & 33.7707400117372 \tabularnewline
Trimmed Mean ( 4 / 24 ) & 15.042375 & 0.44195577493008 & 34.0359281477424 \tabularnewline
Trimmed Mean ( 5 / 24 ) & 15.0084193548387 & 0.436530069539374 & 34.3811810505416 \tabularnewline
Trimmed Mean ( 6 / 24 ) & 14.9770666666667 & 0.431122317291790 & 34.7397155423294 \tabularnewline
Trimmed Mean ( 7 / 24 ) & 14.9444482758621 & 0.424767383173276 & 35.1826643661238 \tabularnewline
Trimmed Mean ( 8 / 24 ) & 14.9177142857143 & 0.419707122462367 & 35.5431525636115 \tabularnewline
Trimmed Mean ( 9 / 24 ) & 14.9013703703704 & 0.416417786715636 & 35.7846634936039 \tabularnewline
Trimmed Mean ( 10 / 24 ) & 14.8844615384615 & 0.412123773729392 & 36.1164836567641 \tabularnewline
Trimmed Mean ( 11 / 24 ) & 14.87434 & 0.408867581587816 & 36.3793576938438 \tabularnewline
Trimmed Mean ( 12 / 24 ) & 14.8632916666667 & 0.404345628608013 & 36.7588780861427 \tabularnewline
Trimmed Mean ( 13 / 24 ) & 14.8564782608696 & 0.399595563339617 & 37.1787868131134 \tabularnewline
Trimmed Mean ( 14 / 24 ) & 14.8534090909091 & 0.394222397173976 & 37.6777402739857 \tabularnewline
Trimmed Mean ( 15 / 24 ) & 14.8502380952381 & 0.386899103326797 & 38.3827152028696 \tabularnewline
Trimmed Mean ( 16 / 24 ) & 14.8606 & 0.381137472338411 & 38.9901310643245 \tabularnewline
Trimmed Mean ( 17 / 24 ) & 14.8745263157895 & 0.373604250756432 & 39.8135896089865 \tabularnewline
Trimmed Mean ( 18 / 24 ) & 14.8885 & 0.364018426840407 & 40.9004020187346 \tabularnewline
Trimmed Mean ( 19 / 24 ) & 14.9043823529412 & 0.351142741097042 & 42.4453665377699 \tabularnewline
Trimmed Mean ( 20 / 24 ) & 14.9311875 & 0.335984765992196 & 44.4400729179097 \tabularnewline
Trimmed Mean ( 21 / 24 ) & 14.9727 & 0.317201184029041 & 47.2025350278302 \tabularnewline
Trimmed Mean ( 22 / 24 ) & 15.0049642857143 & 0.297560564650793 & 50.4265889645814 \tabularnewline
Trimmed Mean ( 23 / 24 ) & 15.0662307692308 & 0.275300972686495 & 54.7263986109769 \tabularnewline
Trimmed Mean ( 24 / 24 ) & 15.1349583333333 & 0.241584447376838 & 62.6487280024485 \tabularnewline
Median & 15.5865 &  &  \tabularnewline
Midrange & 16.9455 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 14.7781351351351 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 14.8885 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 14.7781351351351 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 14.8885 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 14.8885 &  &  \tabularnewline
Midmean - Closest Observation & 14.7781351351351 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 14.8885 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 14.8745263157895 &  &  \tabularnewline
Number of observations & 72 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=51869&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]15.1995694444444[/C][C]0.464455119711568[/C][C]32.7255934951983[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]14.6973193567844[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]14.2101396397802[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]15.6953155091115[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 24 )[/C][C]15.1904444444444[/C][C]0.462210880274203[/C][C]32.8647487385689[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 24 )[/C][C]15.1648055555556[/C][C]0.455615550209472[/C][C]33.2842141770259[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 24 )[/C][C]15.1610555555556[/C][C]0.454481752221219[/C][C]33.3589973226822[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 24 )[/C][C]15.1593333333333[/C][C]0.454009753657645[/C][C]33.3898847132798[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 24 )[/C][C]15.1390555555556[/C][C]0.449481024372646[/C][C]33.6811894933397[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 24 )[/C][C]15.1347222222222[/C][C]0.44770636572959[/C][C]33.8050190498373[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 24 )[/C][C]15.09[/C][C]0.436108572503402[/C][C]34.6014753009293[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 24 )[/C][C]15.0157777777778[/C][C]0.422362526931307[/C][C]35.5518703017419[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 24 )[/C][C]15.0112777777778[/C][C]0.421434691531466[/C][C]35.6194638918495[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 24 )[/C][C]14.95475[/C][C]0.409828771045521[/C][C]36.4902394769617[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 24 )[/C][C]14.9553611111111[/C][C]0.409453703143375[/C][C]36.5251577804739[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 24 )[/C][C]14.9155277777778[/C][C]0.402555300963011[/C][C]37.0521211423528[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 24 )[/C][C]14.8808611111111[/C][C]0.396799547369287[/C][C]37.5022129177533[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 24 )[/C][C]14.8793055555556[/C][C]0.396031231794521[/C][C]37.5710407690159[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 24 )[/C][C]14.7638888888889[/C][C]0.376454864604421[/C][C]39.2182178450603[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 24 )[/C][C]14.743[/C][C]0.373029484206861[/C][C]39.5223450804343[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 24 )[/C][C]14.75575[/C][C]0.368191226463795[/C][C]40.076321594401[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 24 )[/C][C]14.7535[/C][C]0.364885046318158[/C][C]40.4332820675141[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 24 )[/C][C]14.6780277777778[/C][C]0.352468031476501[/C][C]41.6435718050542[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 24 )[/C][C]14.58525[/C][C]0.340089143444841[/C][C]42.886549838853[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 24 )[/C][C]14.7092083333333[/C][C]0.317244734259369[/C][C]46.365492457024[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 24 )[/C][C]14.5182361111111[/C][C]0.29223225744248[/C][C]49.6804707261611[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 24 )[/C][C]14.5393194444444[/C][C]0.286211362432181[/C][C]50.7992391388361[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 24 )[/C][C]14.5123194444444[/C][C]0.236684917819690[/C][C]61.3149311672667[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 24 )[/C][C]15.1496857142857[/C][C]0.456843711827557[/C][C]33.1616378250692[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 24 )[/C][C]15.1065294117647[/C][C]0.450278755954963[/C][C]33.5492829985425[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 24 )[/C][C]15.0747424242424[/C][C]0.446384722958487[/C][C]33.7707400117372[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 24 )[/C][C]15.042375[/C][C]0.44195577493008[/C][C]34.0359281477424[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 24 )[/C][C]15.0084193548387[/C][C]0.436530069539374[/C][C]34.3811810505416[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 24 )[/C][C]14.9770666666667[/C][C]0.431122317291790[/C][C]34.7397155423294[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 24 )[/C][C]14.9444482758621[/C][C]0.424767383173276[/C][C]35.1826643661238[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 24 )[/C][C]14.9177142857143[/C][C]0.419707122462367[/C][C]35.5431525636115[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 24 )[/C][C]14.9013703703704[/C][C]0.416417786715636[/C][C]35.7846634936039[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 24 )[/C][C]14.8844615384615[/C][C]0.412123773729392[/C][C]36.1164836567641[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 24 )[/C][C]14.87434[/C][C]0.408867581587816[/C][C]36.3793576938438[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 24 )[/C][C]14.8632916666667[/C][C]0.404345628608013[/C][C]36.7588780861427[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 24 )[/C][C]14.8564782608696[/C][C]0.399595563339617[/C][C]37.1787868131134[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 24 )[/C][C]14.8534090909091[/C][C]0.394222397173976[/C][C]37.6777402739857[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 24 )[/C][C]14.8502380952381[/C][C]0.386899103326797[/C][C]38.3827152028696[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 24 )[/C][C]14.8606[/C][C]0.381137472338411[/C][C]38.9901310643245[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 24 )[/C][C]14.8745263157895[/C][C]0.373604250756432[/C][C]39.8135896089865[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 24 )[/C][C]14.8885[/C][C]0.364018426840407[/C][C]40.9004020187346[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 24 )[/C][C]14.9043823529412[/C][C]0.351142741097042[/C][C]42.4453665377699[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 24 )[/C][C]14.9311875[/C][C]0.335984765992196[/C][C]44.4400729179097[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 24 )[/C][C]14.9727[/C][C]0.317201184029041[/C][C]47.2025350278302[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 24 )[/C][C]15.0049642857143[/C][C]0.297560564650793[/C][C]50.4265889645814[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 24 )[/C][C]15.0662307692308[/C][C]0.275300972686495[/C][C]54.7263986109769[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 24 )[/C][C]15.1349583333333[/C][C]0.241584447376838[/C][C]62.6487280024485[/C][/ROW]
[ROW][C]Median[/C][C]15.5865[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]16.9455[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]14.7781351351351[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]14.8885[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]14.7781351351351[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]14.8885[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]14.8885[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]14.7781351351351[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]14.8885[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]14.8745263157895[/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=51869&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=51869&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 Mean15.19956944444440.46445511971156832.7255934951983
Geometric Mean14.6973193567844
Harmonic Mean14.2101396397802
Quadratic Mean15.6953155091115
Winsorized Mean ( 1 / 24 )15.19044444444440.46221088027420332.8647487385689
Winsorized Mean ( 2 / 24 )15.16480555555560.45561555020947233.2842141770259
Winsorized Mean ( 3 / 24 )15.16105555555560.45448175222121933.3589973226822
Winsorized Mean ( 4 / 24 )15.15933333333330.45400975365764533.3898847132798
Winsorized Mean ( 5 / 24 )15.13905555555560.44948102437264633.6811894933397
Winsorized Mean ( 6 / 24 )15.13472222222220.4477063657295933.8050190498373
Winsorized Mean ( 7 / 24 )15.090.43610857250340234.6014753009293
Winsorized Mean ( 8 / 24 )15.01577777777780.42236252693130735.5518703017419
Winsorized Mean ( 9 / 24 )15.01127777777780.42143469153146635.6194638918495
Winsorized Mean ( 10 / 24 )14.954750.40982877104552136.4902394769617
Winsorized Mean ( 11 / 24 )14.95536111111110.40945370314337536.5251577804739
Winsorized Mean ( 12 / 24 )14.91552777777780.40255530096301137.0521211423528
Winsorized Mean ( 13 / 24 )14.88086111111110.39679954736928737.5022129177533
Winsorized Mean ( 14 / 24 )14.87930555555560.39603123179452137.5710407690159
Winsorized Mean ( 15 / 24 )14.76388888888890.37645486460442139.2182178450603
Winsorized Mean ( 16 / 24 )14.7430.37302948420686139.5223450804343
Winsorized Mean ( 17 / 24 )14.755750.36819122646379540.076321594401
Winsorized Mean ( 18 / 24 )14.75350.36488504631815840.4332820675141
Winsorized Mean ( 19 / 24 )14.67802777777780.35246803147650141.6435718050542
Winsorized Mean ( 20 / 24 )14.585250.34008914344484142.886549838853
Winsorized Mean ( 21 / 24 )14.70920833333330.31724473425936946.365492457024
Winsorized Mean ( 22 / 24 )14.51823611111110.2922322574424849.6804707261611
Winsorized Mean ( 23 / 24 )14.53931944444440.28621136243218150.7992391388361
Winsorized Mean ( 24 / 24 )14.51231944444440.23668491781969061.3149311672667
Trimmed Mean ( 1 / 24 )15.14968571428570.45684371182755733.1616378250692
Trimmed Mean ( 2 / 24 )15.10652941176470.45027875595496333.5492829985425
Trimmed Mean ( 3 / 24 )15.07474242424240.44638472295848733.7707400117372
Trimmed Mean ( 4 / 24 )15.0423750.4419557749300834.0359281477424
Trimmed Mean ( 5 / 24 )15.00841935483870.43653006953937434.3811810505416
Trimmed Mean ( 6 / 24 )14.97706666666670.43112231729179034.7397155423294
Trimmed Mean ( 7 / 24 )14.94444827586210.42476738317327635.1826643661238
Trimmed Mean ( 8 / 24 )14.91771428571430.41970712246236735.5431525636115
Trimmed Mean ( 9 / 24 )14.90137037037040.41641778671563635.7846634936039
Trimmed Mean ( 10 / 24 )14.88446153846150.41212377372939236.1164836567641
Trimmed Mean ( 11 / 24 )14.874340.40886758158781636.3793576938438
Trimmed Mean ( 12 / 24 )14.86329166666670.40434562860801336.7588780861427
Trimmed Mean ( 13 / 24 )14.85647826086960.39959556333961737.1787868131134
Trimmed Mean ( 14 / 24 )14.85340909090910.39422239717397637.6777402739857
Trimmed Mean ( 15 / 24 )14.85023809523810.38689910332679738.3827152028696
Trimmed Mean ( 16 / 24 )14.86060.38113747233841138.9901310643245
Trimmed Mean ( 17 / 24 )14.87452631578950.37360425075643239.8135896089865
Trimmed Mean ( 18 / 24 )14.88850.36401842684040740.9004020187346
Trimmed Mean ( 19 / 24 )14.90438235294120.35114274109704242.4453665377699
Trimmed Mean ( 20 / 24 )14.93118750.33598476599219644.4400729179097
Trimmed Mean ( 21 / 24 )14.97270.31720118402904147.2025350278302
Trimmed Mean ( 22 / 24 )15.00496428571430.29756056465079350.4265889645814
Trimmed Mean ( 23 / 24 )15.06623076923080.27530097268649554.7263986109769
Trimmed Mean ( 24 / 24 )15.13495833333330.24158444737683862.6487280024485
Median15.5865
Midrange16.9455
Midmean - Weighted Average at Xnp14.7781351351351
Midmean - Weighted Average at X(n+1)p14.8885
Midmean - Empirical Distribution Function14.7781351351351
Midmean - Empirical Distribution Function - Averaging14.8885
Midmean - Empirical Distribution Function - Interpolation14.8885
Midmean - Closest Observation14.7781351351351
Midmean - True Basic - Statistics Graphics Toolkit14.8885
Midmean - MS Excel (old versions)14.8745263157895
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')