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Description of Statistical Computation

Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationFri, 12 Nov 2010 17:22:47 +0000
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2010/Nov/12/t1289582531q76ye9wv7sotko5.htm/, Retrieved Mon, 03 Nov 2025 04:01:05 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=94250, Retrieved Mon, 03 Nov 2025 04:01:05 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact349

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Central Tendency] [Arabica Price in ...] [2008-01-06 21:28:17] [74be16979710d4c4e7c6647856088456]
- RM D  [Central Tendency] [US car sales] [2010-11-06 13:18:47] [97ad38b1c3b35a5feca8b85f7bc7b3ff]
-    D    [Central Tendency] [Winsorized en tri...] [2010-11-12 16:09:32] [39c51da0be01189e8a44eb69e891b7a1]
-    D        [Central Tendency] [export van petroleum] [2010-11-12 17:22:47] [ecfb965f5669057f3ac5b58964283289] [Current]
- R  D          [Central Tendency] [Winsorized Mean Yt] [2010-12-18 11:28:52] [39c51da0be01189e8a44eb69e891b7a1]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
0,163174
0,201921
0,232752
0,228971
0,245583
0,254378
0,224034
0,230488
0,145256
0,151829
0,165472
0,196739
0,187848
0,204079
0,207498
0,240080
0,239256
0,228852
0,245555
0,222047
0,266542
0,267053
0,231662
0,206036
0,257087
0,216368
0,225624
0,231318
0,253926
0,227463
0,263592
0,260886
0,232007
0,233059
0,299560
0,270942
0,283427
0,301381
0,316548
0,292079
0,312963
0,361612
0,358814
0,358174
0,220870
0,288982
0,291079
0,327455
0,335642
0,284180
0,325792
0,326291
0,356246
0,335943
0,414564
0,374787
0,361182
0,393189
0,344907
0,352865

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135

\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 & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=94250&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]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=94250&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=94250&T=0

As an alternative you can also use a QR Code:  
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'Gwilym Jenkins' @ 72.249.127.135






Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean0.267965150.0081522115702637332.8702398963048
Geometric Mean0.260595398573290
Harmonic Mean0.253172469078432
Quadratic Mean0.275184258761683
Winsorized Mean ( 1 / 20 )0.267718450.008023262212513633.3677802007329
Winsorized Mean ( 2 / 20 )0.2674832166666670.0077808281153424634.3772170136024
Winsorized Mean ( 3 / 20 )0.2669393666666670.0076082472976230935.0855270898019
Winsorized Mean ( 4 / 20 )0.2684024333333330.0072932968683450536.8012488972271
Winsorized Mean ( 5 / 20 )0.2689460166666670.0071177893863801137.7850484282796
Winsorized Mean ( 6 / 20 )0.2694002166666670.0070172839161155438.3909529508954
Winsorized Mean ( 7 / 20 )0.269427050.0069286386793794238.8860009112398
Winsorized Mean ( 8 / 20 )0.2692371833333330.0067922885245580339.6386552720612
Winsorized Mean ( 9 / 20 )0.2682627833333330.0065139659064194841.1827122197495
Winsorized Mean ( 10 / 20 )0.2682471166666670.005996190904462944.7362535550716
Winsorized Mean ( 11 / 20 )0.26901730.0058676552195809645.8474961347869
Winsorized Mean ( 12 / 20 )0.26761530.0055268218531281348.4211916200143
Winsorized Mean ( 13 / 20 )0.2677936166666670.0054210794763360949.3985778728444
Winsorized Mean ( 14 / 20 )0.2680481833333330.005349464599298550.1074786752461
Winsorized Mean ( 15 / 20 )0.2661969333333330.0048734316015581854.6220723090117
Winsorized Mean ( 16 / 20 )0.2656113333333330.0046576040976364857.0274604207169
Winsorized Mean ( 17 / 20 )0.2623634833333330.0041047962054666563.9163237833648
Winsorized Mean ( 18 / 20 )0.2622722833333330.0039547531280734366.3182441077175
Winsorized Mean ( 19 / 20 )0.2601661333333330.0035484372716570873.3185099286929
Winsorized Mean ( 20 / 20 )0.2599474666666670.0034819799980820374.6550717723402
Trimmed Mean ( 1 / 20 )0.2675532586206900.0077526936767389534.5110060808222
Trimmed Mean ( 2 / 20 )0.2673762678571430.0074189666396115836.0395565643279
Trimmed Mean ( 3 / 20 )0.2673168518518520.0071699718047512337.2828316667455
Trimmed Mean ( 4 / 20 )0.2674620384615380.0069436991879321738.5186672438770
Trimmed Mean ( 5 / 20 )0.267179920.0067835414222679139.3864949542351
Trimmed Mean ( 6 / 20 )0.2667383958333330.0066368630819108840.1904322179469
Trimmed Mean ( 7 / 20 )0.2661597391304350.0064753345248063941.1036276366576
Trimmed Mean ( 8 / 20 )0.265523250.0062879979656139842.2269936237286
Trimmed Mean ( 9 / 20 )0.2648600476190480.0060783619894650743.5742471537726
Trimmed Mean ( 10 / 20 )0.2642929250.0058786370112017644.9581977074599
Trimmed Mean ( 11 / 20 )0.2636685789473680.0057487531991847945.865350244077
Trimmed Mean ( 12 / 20 )0.2628581666666670.0055940857598087746.9885836493955
Trimmed Mean ( 13 / 20 )0.2621585882352940.0054703250802192447.923767672101
Trimmed Mean ( 14 / 20 )0.261345843750.0053116248797447849.2026168388905
Trimmed Mean ( 15 / 20 )0.2603883666666670.0050889549030924651.167355896283
Trimmed Mean ( 16 / 20 )0.2595585714285710.0049164350328617952.7940610815894
Trimmed Mean ( 17 / 20 )0.2586855769230770.0047163849341085854.8482747988359
Trimmed Mean ( 18 / 20 )0.2581447083333330.0046128974603818155.9615102114077
Trimmed Mean ( 19 / 20 )0.2575193181818180.0044762929890424457.5295939770257
Trimmed Mean ( 20 / 20 )0.25710140.0044047857074347158.368651071049
Median0.2557325
Midrange0.27991
Midmean - Weighted Average at Xnp0.259266935483871
Midmean - Weighted Average at X(n+1)p0.260388366666667
Midmean - Empirical Distribution Function0.259266935483871
Midmean - Empirical Distribution Function - Averaging0.260388366666667
Midmean - Empirical Distribution Function - Interpolation0.260388366666667
Midmean - Closest Observation0.259266935483871
Midmean - True Basic - Statistics Graphics Toolkit0.260388366666667
Midmean - MS Excel (old versions)0.26134584375
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 0.26796515 & 0.00815221157026373 & 32.8702398963048 \tabularnewline
Geometric Mean & 0.260595398573290 &  &  \tabularnewline
Harmonic Mean & 0.253172469078432 &  &  \tabularnewline
Quadratic Mean & 0.275184258761683 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 0.26771845 & 0.0080232622125136 & 33.3677802007329 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 0.267483216666667 & 0.00778082811534246 & 34.3772170136024 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 0.266939366666667 & 0.00760824729762309 & 35.0855270898019 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 0.268402433333333 & 0.00729329686834505 & 36.8012488972271 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 0.268946016666667 & 0.00711778938638011 & 37.7850484282796 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 0.269400216666667 & 0.00701728391611554 & 38.3909529508954 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 0.26942705 & 0.00692863867937942 & 38.8860009112398 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 0.269237183333333 & 0.00679228852455803 & 39.6386552720612 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 0.268262783333333 & 0.00651396590641948 & 41.1827122197495 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 0.268247116666667 & 0.0059961909044629 & 44.7362535550716 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 0.2690173 & 0.00586765521958096 & 45.8474961347869 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 0.2676153 & 0.00552682185312813 & 48.4211916200143 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 0.267793616666667 & 0.00542107947633609 & 49.3985778728444 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 0.268048183333333 & 0.0053494645992985 & 50.1074786752461 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 0.266196933333333 & 0.00487343160155818 & 54.6220723090117 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 0.265611333333333 & 0.00465760409763648 & 57.0274604207169 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 0.262363483333333 & 0.00410479620546665 & 63.9163237833648 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 0.262272283333333 & 0.00395475312807343 & 66.3182441077175 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 0.260166133333333 & 0.00354843727165708 & 73.3185099286929 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 0.259947466666667 & 0.00348197999808203 & 74.6550717723402 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 0.267553258620690 & 0.00775269367673895 & 34.5110060808222 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 0.267376267857143 & 0.00741896663961158 & 36.0395565643279 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 0.267316851851852 & 0.00716997180475123 & 37.2828316667455 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 0.267462038461538 & 0.00694369918793217 & 38.5186672438770 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 0.26717992 & 0.00678354142226791 & 39.3864949542351 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 0.266738395833333 & 0.00663686308191088 & 40.1904322179469 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 0.266159739130435 & 0.00647533452480639 & 41.1036276366576 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 0.26552325 & 0.00628799796561398 & 42.2269936237286 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 0.264860047619048 & 0.00607836198946507 & 43.5742471537726 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 0.264292925 & 0.00587863701120176 & 44.9581977074599 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 0.263668578947368 & 0.00574875319918479 & 45.865350244077 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 0.262858166666667 & 0.00559408575980877 & 46.9885836493955 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 0.262158588235294 & 0.00547032508021924 & 47.923767672101 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 0.26134584375 & 0.00531162487974478 & 49.2026168388905 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 0.260388366666667 & 0.00508895490309246 & 51.167355896283 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 0.259558571428571 & 0.00491643503286179 & 52.7940610815894 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 0.258685576923077 & 0.00471638493410858 & 54.8482747988359 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 0.258144708333333 & 0.00461289746038181 & 55.9615102114077 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 0.257519318181818 & 0.00447629298904244 & 57.5295939770257 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 0.2571014 & 0.00440478570743471 & 58.368651071049 \tabularnewline
Median & 0.2557325 &  &  \tabularnewline
Midrange & 0.27991 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 0.259266935483871 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 0.260388366666667 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 0.259266935483871 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 0.260388366666667 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 0.260388366666667 &  &  \tabularnewline
Midmean - Closest Observation & 0.259266935483871 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 0.260388366666667 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 0.26134584375 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=94250&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]0.26796515[/C][C]0.00815221157026373[/C][C]32.8702398963048[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]0.260595398573290[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]0.253172469078432[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]0.275184258761683[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]0.26771845[/C][C]0.0080232622125136[/C][C]33.3677802007329[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]0.267483216666667[/C][C]0.00778082811534246[/C][C]34.3772170136024[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]0.266939366666667[/C][C]0.00760824729762309[/C][C]35.0855270898019[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]0.268402433333333[/C][C]0.00729329686834505[/C][C]36.8012488972271[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]0.268946016666667[/C][C]0.00711778938638011[/C][C]37.7850484282796[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]0.269400216666667[/C][C]0.00701728391611554[/C][C]38.3909529508954[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]0.26942705[/C][C]0.00692863867937942[/C][C]38.8860009112398[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]0.269237183333333[/C][C]0.00679228852455803[/C][C]39.6386552720612[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]0.268262783333333[/C][C]0.00651396590641948[/C][C]41.1827122197495[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]0.268247116666667[/C][C]0.0059961909044629[/C][C]44.7362535550716[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]0.2690173[/C][C]0.00586765521958096[/C][C]45.8474961347869[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]0.2676153[/C][C]0.00552682185312813[/C][C]48.4211916200143[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]0.267793616666667[/C][C]0.00542107947633609[/C][C]49.3985778728444[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]0.268048183333333[/C][C]0.0053494645992985[/C][C]50.1074786752461[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]0.266196933333333[/C][C]0.00487343160155818[/C][C]54.6220723090117[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]0.265611333333333[/C][C]0.00465760409763648[/C][C]57.0274604207169[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]0.262363483333333[/C][C]0.00410479620546665[/C][C]63.9163237833648[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]0.262272283333333[/C][C]0.00395475312807343[/C][C]66.3182441077175[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]0.260166133333333[/C][C]0.00354843727165708[/C][C]73.3185099286929[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]0.259947466666667[/C][C]0.00348197999808203[/C][C]74.6550717723402[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]0.267553258620690[/C][C]0.00775269367673895[/C][C]34.5110060808222[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]0.267376267857143[/C][C]0.00741896663961158[/C][C]36.0395565643279[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]0.267316851851852[/C][C]0.00716997180475123[/C][C]37.2828316667455[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]0.267462038461538[/C][C]0.00694369918793217[/C][C]38.5186672438770[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]0.26717992[/C][C]0.00678354142226791[/C][C]39.3864949542351[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]0.266738395833333[/C][C]0.00663686308191088[/C][C]40.1904322179469[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]0.266159739130435[/C][C]0.00647533452480639[/C][C]41.1036276366576[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]0.26552325[/C][C]0.00628799796561398[/C][C]42.2269936237286[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]0.264860047619048[/C][C]0.00607836198946507[/C][C]43.5742471537726[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]0.264292925[/C][C]0.00587863701120176[/C][C]44.9581977074599[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]0.263668578947368[/C][C]0.00574875319918479[/C][C]45.865350244077[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]0.262858166666667[/C][C]0.00559408575980877[/C][C]46.9885836493955[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]0.262158588235294[/C][C]0.00547032508021924[/C][C]47.923767672101[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]0.26134584375[/C][C]0.00531162487974478[/C][C]49.2026168388905[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]0.260388366666667[/C][C]0.00508895490309246[/C][C]51.167355896283[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]0.259558571428571[/C][C]0.00491643503286179[/C][C]52.7940610815894[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]0.258685576923077[/C][C]0.00471638493410858[/C][C]54.8482747988359[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]0.258144708333333[/C][C]0.00461289746038181[/C][C]55.9615102114077[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]0.257519318181818[/C][C]0.00447629298904244[/C][C]57.5295939770257[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]0.2571014[/C][C]0.00440478570743471[/C][C]58.368651071049[/C][/ROW]
[ROW][C]Median[/C][C]0.2557325[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]0.27991[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]0.259266935483871[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]0.260388366666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]0.259266935483871[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]0.260388366666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]0.260388366666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]0.259266935483871[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]0.260388366666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]0.26134584375[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]60[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=94250&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=94250&T=1

As an alternative you can also use a QR Code:  
QR Code


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

Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean0.267965150.0081522115702637332.8702398963048
Geometric Mean0.260595398573290
Harmonic Mean0.253172469078432
Quadratic Mean0.275184258761683
Winsorized Mean ( 1 / 20 )0.267718450.008023262212513633.3677802007329
Winsorized Mean ( 2 / 20 )0.2674832166666670.0077808281153424634.3772170136024
Winsorized Mean ( 3 / 20 )0.2669393666666670.0076082472976230935.0855270898019
Winsorized Mean ( 4 / 20 )0.2684024333333330.0072932968683450536.8012488972271
Winsorized Mean ( 5 / 20 )0.2689460166666670.0071177893863801137.7850484282796
Winsorized Mean ( 6 / 20 )0.2694002166666670.0070172839161155438.3909529508954
Winsorized Mean ( 7 / 20 )0.269427050.0069286386793794238.8860009112398
Winsorized Mean ( 8 / 20 )0.2692371833333330.0067922885245580339.6386552720612
Winsorized Mean ( 9 / 20 )0.2682627833333330.0065139659064194841.1827122197495
Winsorized Mean ( 10 / 20 )0.2682471166666670.005996190904462944.7362535550716
Winsorized Mean ( 11 / 20 )0.26901730.0058676552195809645.8474961347869
Winsorized Mean ( 12 / 20 )0.26761530.0055268218531281348.4211916200143
Winsorized Mean ( 13 / 20 )0.2677936166666670.0054210794763360949.3985778728444
Winsorized Mean ( 14 / 20 )0.2680481833333330.005349464599298550.1074786752461
Winsorized Mean ( 15 / 20 )0.2661969333333330.0048734316015581854.6220723090117
Winsorized Mean ( 16 / 20 )0.2656113333333330.0046576040976364857.0274604207169
Winsorized Mean ( 17 / 20 )0.2623634833333330.0041047962054666563.9163237833648
Winsorized Mean ( 18 / 20 )0.2622722833333330.0039547531280734366.3182441077175
Winsorized Mean ( 19 / 20 )0.2601661333333330.0035484372716570873.3185099286929
Winsorized Mean ( 20 / 20 )0.2599474666666670.0034819799980820374.6550717723402
Trimmed Mean ( 1 / 20 )0.2675532586206900.0077526936767389534.5110060808222
Trimmed Mean ( 2 / 20 )0.2673762678571430.0074189666396115836.0395565643279
Trimmed Mean ( 3 / 20 )0.2673168518518520.0071699718047512337.2828316667455
Trimmed Mean ( 4 / 20 )0.2674620384615380.0069436991879321738.5186672438770
Trimmed Mean ( 5 / 20 )0.267179920.0067835414222679139.3864949542351
Trimmed Mean ( 6 / 20 )0.2667383958333330.0066368630819108840.1904322179469
Trimmed Mean ( 7 / 20 )0.2661597391304350.0064753345248063941.1036276366576
Trimmed Mean ( 8 / 20 )0.265523250.0062879979656139842.2269936237286
Trimmed Mean ( 9 / 20 )0.2648600476190480.0060783619894650743.5742471537726
Trimmed Mean ( 10 / 20 )0.2642929250.0058786370112017644.9581977074599
Trimmed Mean ( 11 / 20 )0.2636685789473680.0057487531991847945.865350244077
Trimmed Mean ( 12 / 20 )0.2628581666666670.0055940857598087746.9885836493955
Trimmed Mean ( 13 / 20 )0.2621585882352940.0054703250802192447.923767672101
Trimmed Mean ( 14 / 20 )0.261345843750.0053116248797447849.2026168388905
Trimmed Mean ( 15 / 20 )0.2603883666666670.0050889549030924651.167355896283
Trimmed Mean ( 16 / 20 )0.2595585714285710.0049164350328617952.7940610815894
Trimmed Mean ( 17 / 20 )0.2586855769230770.0047163849341085854.8482747988359
Trimmed Mean ( 18 / 20 )0.2581447083333330.0046128974603818155.9615102114077
Trimmed Mean ( 19 / 20 )0.2575193181818180.0044762929890424457.5295939770257
Trimmed Mean ( 20 / 20 )0.25710140.0044047857074347158.368651071049
Median0.2557325
Midrange0.27991
Midmean - Weighted Average at Xnp0.259266935483871
Midmean - Weighted Average at X(n+1)p0.260388366666667
Midmean - Empirical Distribution Function0.259266935483871
Midmean - Empirical Distribution Function - Averaging0.260388366666667
Midmean - Empirical Distribution Function - Interpolation0.260388366666667
Midmean - Closest Observation0.259266935483871
Midmean - True Basic - Statistics Graphics Toolkit0.260388366666667
Midmean - MS Excel (old versions)0.26134584375
Number of observations60


Figures (Output of Computation)

Input Parameters & R Code

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')