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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, 25 Mar 2009 10:10:19 -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/Mar/25/t1237997482mxaau034dqasbku.htm/, Retrieved Tue, 30 Apr 2024 08:21:52 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=39179, Retrieved Tue, 30 Apr 2024 08:21:52 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact197
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [Centrummaten - Go...] [2009-03-25 16:10:19] [80b98812df2028d0ae657015c109b08c] [Current]
- RM      [Mean versus Median] [Gemiddelde vs Med...] [2009-03-25 16:22:40] [e43857445179f9bbfaf3355c08c250c8]
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Dataseries X:
10.812
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 time3 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 & 3 seconds \tabularnewline
R Server & 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=39179&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]3 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=39179&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=39179&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 time3 seconds
R Server'Sir Ronald Aylmer Fisher' @ 193.190.124.24







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean13.98534246575340.40392612727260834.6235153447125
Geometric Mean13.5743955909049
Harmonic Mean13.1842845858026
Quadratic Mean14.3992034035753
Winsorized Mean ( 1 / 24 )13.97746575342470.40161701320740634.802972219223
Winsorized Mean ( 2 / 24 )13.97826027397260.40111457587385434.8485473097557
Winsorized Mean ( 3 / 24 )13.96054794520550.39708699241324435.1574043268506
Winsorized Mean ( 4 / 24 )13.97375342465750.3951614999309935.362132766218
Winsorized Mean ( 5 / 24 )13.96519178082190.39067184923079135.7466037246311
Winsorized Mean ( 6 / 24 )13.94891780821920.38754500733048135.9930267307615
Winsorized Mean ( 7 / 24 )13.95438356164380.386317256034236.1215641902584
Winsorized Mean ( 8 / 24 )13.89060273972600.37436003979949337.1049291136036
Winsorized Mean ( 9 / 24 )13.88110958904110.37182111865471337.3327626985373
Winsorized Mean ( 10 / 24 )13.87617808219180.37072800225014637.4295386320155
Winsorized Mean ( 11 / 24 )13.87135616438360.36909154351236237.5824274714627
Winsorized Mean ( 12 / 24 )13.82532876712330.35983618908284738.421173819013
Winsorized Mean ( 13 / 24 )13.78241095890410.34810780087975639.5923645608415
Winsorized Mean ( 14 / 24 )13.7756986301370.34628070677731939.7818831962697
Winsorized Mean ( 15 / 24 )13.64665753424660.326502823986641.7964456405641
Winsorized Mean ( 16 / 24 )13.65082191780820.32402937740431742.1283465936331
Winsorized Mean ( 17 / 24 )13.51482191780820.30445342668329944.3904411424697
Winsorized Mean ( 18 / 24 )13.49534246575340.30115750202690444.8115765834312
Winsorized Mean ( 19 / 24 )13.45109589041100.29493624234544745.6067921101953
Winsorized Mean ( 20 / 24 )13.42041095890410.29040325243393446.213018781383
Winsorized Mean ( 21 / 24 )13.41897260273970.28726511877968246.7128506925737
Winsorized Mean ( 22 / 24 )13.40058904109590.28443767981222647.1125662744206
Winsorized Mean ( 23 / 24 )13.40689041095890.28288752501990847.3930068496849
Winsorized Mean ( 24 / 24 )13.39965753424660.27640396369960148.4785288709155
Trimmed Mean ( 1 / 24 )13.9490.39930066381202634.9335757843033
Trimmed Mean ( 2 / 24 )13.91888405797100.39631428727093535.1208233087382
Trimmed Mean ( 3 / 24 )13.88653731343280.39283446101667435.3495904547015
Trimmed Mean ( 4 / 24 )13.85883076923080.3902135556636535.5160156998148
Trimmed Mean ( 5 / 24 )13.82553968253970.38742755583684135.6854835807345
Trimmed Mean ( 6 / 24 )13.79211475409840.3850901115879535.8152918994088
Trimmed Mean ( 7 / 24 )13.75977966101690.3827401276319335.9507108547796
Trimmed Mean ( 8 / 24 )13.72417543859650.37977354511033136.1377868872077
Trimmed Mean ( 9 / 24 )13.69656363636360.37852821551615236.1837323478973
Trimmed Mean ( 10 / 24 )13.66832075471700.37703431928655136.2521925870862
Trimmed Mean ( 11 / 24 )13.63856862745100.37487677374577536.3814714130571
Trimmed Mean ( 12 / 24 )13.60704081632650.37197493693364536.5805312812079
Trimmed Mean ( 13 / 24 )13.57878723404260.36971022847621536.7281892362253
Trimmed Mean ( 14 / 24 )13.55337777777780.36858366413003736.7715096917483
Trimmed Mean ( 15 / 24 )13.52641860465120.36673535231922636.8833234077664
Trimmed Mean ( 16 / 24 )13.51214634146340.36763750797420336.7539928554068
Trimmed Mean ( 17 / 24 )13.49592307692310.36820568751625636.6532173035139
Trimmed Mean ( 18 / 24 )13.49372972972970.37175211042383836.2976546773209
Trimmed Mean ( 19 / 24 )13.49354285714290.37553937085693935.9311004498732
Trimmed Mean ( 20 / 24 )13.49848484848480.38012560005934535.5105913581654
Trimmed Mean ( 21 / 24 )13.50767741935480.38525054377330535.0620593213315
Trimmed Mean ( 22 / 24 )13.51831034482760.39064963925349734.6046917403024
Trimmed Mean ( 23 / 24 )13.53277777777780.39615146939605534.1606148739241
Trimmed Mean ( 24 / 24 )13.548760.40127879867576733.7639567420740
Median14.544
Midrange15.2755
Midmean - Weighted Average at Xnp13.4144444444444
Midmean - Weighted Average at X(n+1)p13.4937297297297
Midmean - Empirical Distribution Function13.4937297297297
Midmean - Empirical Distribution Function - Averaging13.4937297297297
Midmean - Empirical Distribution Function - Interpolation13.4937297297297
Midmean - Closest Observation13.4185
Midmean - True Basic - Statistics Graphics Toolkit13.4937297297297
Midmean - MS Excel (old versions)13.4937297297297
Number of observations73

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 13.9853424657534 & 0.403926127272608 & 34.6235153447125 \tabularnewline
Geometric Mean & 13.5743955909049 &  &  \tabularnewline
Harmonic Mean & 13.1842845858026 &  &  \tabularnewline
Quadratic Mean & 14.3992034035753 &  &  \tabularnewline
Winsorized Mean ( 1 / 24 ) & 13.9774657534247 & 0.401617013207406 & 34.802972219223 \tabularnewline
Winsorized Mean ( 2 / 24 ) & 13.9782602739726 & 0.401114575873854 & 34.8485473097557 \tabularnewline
Winsorized Mean ( 3 / 24 ) & 13.9605479452055 & 0.397086992413244 & 35.1574043268506 \tabularnewline
Winsorized Mean ( 4 / 24 ) & 13.9737534246575 & 0.39516149993099 & 35.362132766218 \tabularnewline
Winsorized Mean ( 5 / 24 ) & 13.9651917808219 & 0.390671849230791 & 35.7466037246311 \tabularnewline
Winsorized Mean ( 6 / 24 ) & 13.9489178082192 & 0.387545007330481 & 35.9930267307615 \tabularnewline
Winsorized Mean ( 7 / 24 ) & 13.9543835616438 & 0.3863172560342 & 36.1215641902584 \tabularnewline
Winsorized Mean ( 8 / 24 ) & 13.8906027397260 & 0.374360039799493 & 37.1049291136036 \tabularnewline
Winsorized Mean ( 9 / 24 ) & 13.8811095890411 & 0.371821118654713 & 37.3327626985373 \tabularnewline
Winsorized Mean ( 10 / 24 ) & 13.8761780821918 & 0.370728002250146 & 37.4295386320155 \tabularnewline
Winsorized Mean ( 11 / 24 ) & 13.8713561643836 & 0.369091543512362 & 37.5824274714627 \tabularnewline
Winsorized Mean ( 12 / 24 ) & 13.8253287671233 & 0.359836189082847 & 38.421173819013 \tabularnewline
Winsorized Mean ( 13 / 24 ) & 13.7824109589041 & 0.348107800879756 & 39.5923645608415 \tabularnewline
Winsorized Mean ( 14 / 24 ) & 13.775698630137 & 0.346280706777319 & 39.7818831962697 \tabularnewline
Winsorized Mean ( 15 / 24 ) & 13.6466575342466 & 0.3265028239866 & 41.7964456405641 \tabularnewline
Winsorized Mean ( 16 / 24 ) & 13.6508219178082 & 0.324029377404317 & 42.1283465936331 \tabularnewline
Winsorized Mean ( 17 / 24 ) & 13.5148219178082 & 0.304453426683299 & 44.3904411424697 \tabularnewline
Winsorized Mean ( 18 / 24 ) & 13.4953424657534 & 0.301157502026904 & 44.8115765834312 \tabularnewline
Winsorized Mean ( 19 / 24 ) & 13.4510958904110 & 0.294936242345447 & 45.6067921101953 \tabularnewline
Winsorized Mean ( 20 / 24 ) & 13.4204109589041 & 0.290403252433934 & 46.213018781383 \tabularnewline
Winsorized Mean ( 21 / 24 ) & 13.4189726027397 & 0.287265118779682 & 46.7128506925737 \tabularnewline
Winsorized Mean ( 22 / 24 ) & 13.4005890410959 & 0.284437679812226 & 47.1125662744206 \tabularnewline
Winsorized Mean ( 23 / 24 ) & 13.4068904109589 & 0.282887525019908 & 47.3930068496849 \tabularnewline
Winsorized Mean ( 24 / 24 ) & 13.3996575342466 & 0.276403963699601 & 48.4785288709155 \tabularnewline
Trimmed Mean ( 1 / 24 ) & 13.949 & 0.399300663812026 & 34.9335757843033 \tabularnewline
Trimmed Mean ( 2 / 24 ) & 13.9188840579710 & 0.396314287270935 & 35.1208233087382 \tabularnewline
Trimmed Mean ( 3 / 24 ) & 13.8865373134328 & 0.392834461016674 & 35.3495904547015 \tabularnewline
Trimmed Mean ( 4 / 24 ) & 13.8588307692308 & 0.39021355566365 & 35.5160156998148 \tabularnewline
Trimmed Mean ( 5 / 24 ) & 13.8255396825397 & 0.387427555836841 & 35.6854835807345 \tabularnewline
Trimmed Mean ( 6 / 24 ) & 13.7921147540984 & 0.38509011158795 & 35.8152918994088 \tabularnewline
Trimmed Mean ( 7 / 24 ) & 13.7597796610169 & 0.38274012763193 & 35.9507108547796 \tabularnewline
Trimmed Mean ( 8 / 24 ) & 13.7241754385965 & 0.379773545110331 & 36.1377868872077 \tabularnewline
Trimmed Mean ( 9 / 24 ) & 13.6965636363636 & 0.378528215516152 & 36.1837323478973 \tabularnewline
Trimmed Mean ( 10 / 24 ) & 13.6683207547170 & 0.377034319286551 & 36.2521925870862 \tabularnewline
Trimmed Mean ( 11 / 24 ) & 13.6385686274510 & 0.374876773745775 & 36.3814714130571 \tabularnewline
Trimmed Mean ( 12 / 24 ) & 13.6070408163265 & 0.371974936933645 & 36.5805312812079 \tabularnewline
Trimmed Mean ( 13 / 24 ) & 13.5787872340426 & 0.369710228476215 & 36.7281892362253 \tabularnewline
Trimmed Mean ( 14 / 24 ) & 13.5533777777778 & 0.368583664130037 & 36.7715096917483 \tabularnewline
Trimmed Mean ( 15 / 24 ) & 13.5264186046512 & 0.366735352319226 & 36.8833234077664 \tabularnewline
Trimmed Mean ( 16 / 24 ) & 13.5121463414634 & 0.367637507974203 & 36.7539928554068 \tabularnewline
Trimmed Mean ( 17 / 24 ) & 13.4959230769231 & 0.368205687516256 & 36.6532173035139 \tabularnewline
Trimmed Mean ( 18 / 24 ) & 13.4937297297297 & 0.371752110423838 & 36.2976546773209 \tabularnewline
Trimmed Mean ( 19 / 24 ) & 13.4935428571429 & 0.375539370856939 & 35.9311004498732 \tabularnewline
Trimmed Mean ( 20 / 24 ) & 13.4984848484848 & 0.380125600059345 & 35.5105913581654 \tabularnewline
Trimmed Mean ( 21 / 24 ) & 13.5076774193548 & 0.385250543773305 & 35.0620593213315 \tabularnewline
Trimmed Mean ( 22 / 24 ) & 13.5183103448276 & 0.390649639253497 & 34.6046917403024 \tabularnewline
Trimmed Mean ( 23 / 24 ) & 13.5327777777778 & 0.396151469396055 & 34.1606148739241 \tabularnewline
Trimmed Mean ( 24 / 24 ) & 13.54876 & 0.401278798675767 & 33.7639567420740 \tabularnewline
Median & 14.544 &  &  \tabularnewline
Midrange & 15.2755 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 13.4144444444444 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 13.4937297297297 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 13.4937297297297 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 13.4937297297297 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 13.4937297297297 &  &  \tabularnewline
Midmean - Closest Observation & 13.4185 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 13.4937297297297 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 13.4937297297297 &  &  \tabularnewline
Number of observations & 73 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=39179&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]13.9853424657534[/C][C]0.403926127272608[/C][C]34.6235153447125[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]13.5743955909049[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]13.1842845858026[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]14.3992034035753[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 24 )[/C][C]13.9774657534247[/C][C]0.401617013207406[/C][C]34.802972219223[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 24 )[/C][C]13.9782602739726[/C][C]0.401114575873854[/C][C]34.8485473097557[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 24 )[/C][C]13.9605479452055[/C][C]0.397086992413244[/C][C]35.1574043268506[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 24 )[/C][C]13.9737534246575[/C][C]0.39516149993099[/C][C]35.362132766218[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 24 )[/C][C]13.9651917808219[/C][C]0.390671849230791[/C][C]35.7466037246311[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 24 )[/C][C]13.9489178082192[/C][C]0.387545007330481[/C][C]35.9930267307615[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 24 )[/C][C]13.9543835616438[/C][C]0.3863172560342[/C][C]36.1215641902584[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 24 )[/C][C]13.8906027397260[/C][C]0.374360039799493[/C][C]37.1049291136036[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 24 )[/C][C]13.8811095890411[/C][C]0.371821118654713[/C][C]37.3327626985373[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 24 )[/C][C]13.8761780821918[/C][C]0.370728002250146[/C][C]37.4295386320155[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 24 )[/C][C]13.8713561643836[/C][C]0.369091543512362[/C][C]37.5824274714627[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 24 )[/C][C]13.8253287671233[/C][C]0.359836189082847[/C][C]38.421173819013[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 24 )[/C][C]13.7824109589041[/C][C]0.348107800879756[/C][C]39.5923645608415[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 24 )[/C][C]13.775698630137[/C][C]0.346280706777319[/C][C]39.7818831962697[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 24 )[/C][C]13.6466575342466[/C][C]0.3265028239866[/C][C]41.7964456405641[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 24 )[/C][C]13.6508219178082[/C][C]0.324029377404317[/C][C]42.1283465936331[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 24 )[/C][C]13.5148219178082[/C][C]0.304453426683299[/C][C]44.3904411424697[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 24 )[/C][C]13.4953424657534[/C][C]0.301157502026904[/C][C]44.8115765834312[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 24 )[/C][C]13.4510958904110[/C][C]0.294936242345447[/C][C]45.6067921101953[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 24 )[/C][C]13.4204109589041[/C][C]0.290403252433934[/C][C]46.213018781383[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 24 )[/C][C]13.4189726027397[/C][C]0.287265118779682[/C][C]46.7128506925737[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 24 )[/C][C]13.4005890410959[/C][C]0.284437679812226[/C][C]47.1125662744206[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 24 )[/C][C]13.4068904109589[/C][C]0.282887525019908[/C][C]47.3930068496849[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 24 )[/C][C]13.3996575342466[/C][C]0.276403963699601[/C][C]48.4785288709155[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 24 )[/C][C]13.949[/C][C]0.399300663812026[/C][C]34.9335757843033[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 24 )[/C][C]13.9188840579710[/C][C]0.396314287270935[/C][C]35.1208233087382[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 24 )[/C][C]13.8865373134328[/C][C]0.392834461016674[/C][C]35.3495904547015[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 24 )[/C][C]13.8588307692308[/C][C]0.39021355566365[/C][C]35.5160156998148[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 24 )[/C][C]13.8255396825397[/C][C]0.387427555836841[/C][C]35.6854835807345[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 24 )[/C][C]13.7921147540984[/C][C]0.38509011158795[/C][C]35.8152918994088[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 24 )[/C][C]13.7597796610169[/C][C]0.38274012763193[/C][C]35.9507108547796[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 24 )[/C][C]13.7241754385965[/C][C]0.379773545110331[/C][C]36.1377868872077[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 24 )[/C][C]13.6965636363636[/C][C]0.378528215516152[/C][C]36.1837323478973[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 24 )[/C][C]13.6683207547170[/C][C]0.377034319286551[/C][C]36.2521925870862[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 24 )[/C][C]13.6385686274510[/C][C]0.374876773745775[/C][C]36.3814714130571[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 24 )[/C][C]13.6070408163265[/C][C]0.371974936933645[/C][C]36.5805312812079[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 24 )[/C][C]13.5787872340426[/C][C]0.369710228476215[/C][C]36.7281892362253[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 24 )[/C][C]13.5533777777778[/C][C]0.368583664130037[/C][C]36.7715096917483[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 24 )[/C][C]13.5264186046512[/C][C]0.366735352319226[/C][C]36.8833234077664[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 24 )[/C][C]13.5121463414634[/C][C]0.367637507974203[/C][C]36.7539928554068[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 24 )[/C][C]13.4959230769231[/C][C]0.368205687516256[/C][C]36.6532173035139[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 24 )[/C][C]13.4937297297297[/C][C]0.371752110423838[/C][C]36.2976546773209[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 24 )[/C][C]13.4935428571429[/C][C]0.375539370856939[/C][C]35.9311004498732[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 24 )[/C][C]13.4984848484848[/C][C]0.380125600059345[/C][C]35.5105913581654[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 24 )[/C][C]13.5076774193548[/C][C]0.385250543773305[/C][C]35.0620593213315[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 24 )[/C][C]13.5183103448276[/C][C]0.390649639253497[/C][C]34.6046917403024[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 24 )[/C][C]13.5327777777778[/C][C]0.396151469396055[/C][C]34.1606148739241[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 24 )[/C][C]13.54876[/C][C]0.401278798675767[/C][C]33.7639567420740[/C][/ROW]
[ROW][C]Median[/C][C]14.544[/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]13.4144444444444[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]13.4937297297297[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]13.4937297297297[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]13.4937297297297[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]13.4937297297297[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]13.4185[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]13.4937297297297[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]13.4937297297297[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]73[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=39179&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=39179&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 Mean13.98534246575340.40392612727260834.6235153447125
Geometric Mean13.5743955909049
Harmonic Mean13.1842845858026
Quadratic Mean14.3992034035753
Winsorized Mean ( 1 / 24 )13.97746575342470.40161701320740634.802972219223
Winsorized Mean ( 2 / 24 )13.97826027397260.40111457587385434.8485473097557
Winsorized Mean ( 3 / 24 )13.96054794520550.39708699241324435.1574043268506
Winsorized Mean ( 4 / 24 )13.97375342465750.3951614999309935.362132766218
Winsorized Mean ( 5 / 24 )13.96519178082190.39067184923079135.7466037246311
Winsorized Mean ( 6 / 24 )13.94891780821920.38754500733048135.9930267307615
Winsorized Mean ( 7 / 24 )13.95438356164380.386317256034236.1215641902584
Winsorized Mean ( 8 / 24 )13.89060273972600.37436003979949337.1049291136036
Winsorized Mean ( 9 / 24 )13.88110958904110.37182111865471337.3327626985373
Winsorized Mean ( 10 / 24 )13.87617808219180.37072800225014637.4295386320155
Winsorized Mean ( 11 / 24 )13.87135616438360.36909154351236237.5824274714627
Winsorized Mean ( 12 / 24 )13.82532876712330.35983618908284738.421173819013
Winsorized Mean ( 13 / 24 )13.78241095890410.34810780087975639.5923645608415
Winsorized Mean ( 14 / 24 )13.7756986301370.34628070677731939.7818831962697
Winsorized Mean ( 15 / 24 )13.64665753424660.326502823986641.7964456405641
Winsorized Mean ( 16 / 24 )13.65082191780820.32402937740431742.1283465936331
Winsorized Mean ( 17 / 24 )13.51482191780820.30445342668329944.3904411424697
Winsorized Mean ( 18 / 24 )13.49534246575340.30115750202690444.8115765834312
Winsorized Mean ( 19 / 24 )13.45109589041100.29493624234544745.6067921101953
Winsorized Mean ( 20 / 24 )13.42041095890410.29040325243393446.213018781383
Winsorized Mean ( 21 / 24 )13.41897260273970.28726511877968246.7128506925737
Winsorized Mean ( 22 / 24 )13.40058904109590.28443767981222647.1125662744206
Winsorized Mean ( 23 / 24 )13.40689041095890.28288752501990847.3930068496849
Winsorized Mean ( 24 / 24 )13.39965753424660.27640396369960148.4785288709155
Trimmed Mean ( 1 / 24 )13.9490.39930066381202634.9335757843033
Trimmed Mean ( 2 / 24 )13.91888405797100.39631428727093535.1208233087382
Trimmed Mean ( 3 / 24 )13.88653731343280.39283446101667435.3495904547015
Trimmed Mean ( 4 / 24 )13.85883076923080.3902135556636535.5160156998148
Trimmed Mean ( 5 / 24 )13.82553968253970.38742755583684135.6854835807345
Trimmed Mean ( 6 / 24 )13.79211475409840.3850901115879535.8152918994088
Trimmed Mean ( 7 / 24 )13.75977966101690.3827401276319335.9507108547796
Trimmed Mean ( 8 / 24 )13.72417543859650.37977354511033136.1377868872077
Trimmed Mean ( 9 / 24 )13.69656363636360.37852821551615236.1837323478973
Trimmed Mean ( 10 / 24 )13.66832075471700.37703431928655136.2521925870862
Trimmed Mean ( 11 / 24 )13.63856862745100.37487677374577536.3814714130571
Trimmed Mean ( 12 / 24 )13.60704081632650.37197493693364536.5805312812079
Trimmed Mean ( 13 / 24 )13.57878723404260.36971022847621536.7281892362253
Trimmed Mean ( 14 / 24 )13.55337777777780.36858366413003736.7715096917483
Trimmed Mean ( 15 / 24 )13.52641860465120.36673535231922636.8833234077664
Trimmed Mean ( 16 / 24 )13.51214634146340.36763750797420336.7539928554068
Trimmed Mean ( 17 / 24 )13.49592307692310.36820568751625636.6532173035139
Trimmed Mean ( 18 / 24 )13.49372972972970.37175211042383836.2976546773209
Trimmed Mean ( 19 / 24 )13.49354285714290.37553937085693935.9311004498732
Trimmed Mean ( 20 / 24 )13.49848484848480.38012560005934535.5105913581654
Trimmed Mean ( 21 / 24 )13.50767741935480.38525054377330535.0620593213315
Trimmed Mean ( 22 / 24 )13.51831034482760.39064963925349734.6046917403024
Trimmed Mean ( 23 / 24 )13.53277777777780.39615146939605534.1606148739241
Trimmed Mean ( 24 / 24 )13.548760.40127879867576733.7639567420740
Median14.544
Midrange15.2755
Midmean - Weighted Average at Xnp13.4144444444444
Midmean - Weighted Average at X(n+1)p13.4937297297297
Midmean - Empirical Distribution Function13.4937297297297
Midmean - Empirical Distribution Function - Averaging13.4937297297297
Midmean - Empirical Distribution Function - Interpolation13.4937297297297
Midmean - Closest Observation13.4185
Midmean - True Basic - Statistics Graphics Toolkit13.4937297297297
Midmean - MS Excel (old versions)13.4937297297297
Number of observations73



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')