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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, 10 Oct 2012 06:14:06 -0400
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2012/Oct/10/t1349864276jzl3nsp8fgob9k9.htm/, Retrieved Wed, 01 May 2024 03:30:18 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=174816, Retrieved Wed, 01 May 2024 03:30:18 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact128
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [Robuustheid van h...] [2012-10-10 10:14:06] [5f6947d5d5479fbcf21e52ac422c0dd8] [Current]
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Dataseries X:
530,3
527,76
521,41
1601,93
1577,49
1551,43
1551,43
1516,88
1485,95
1438,22
1385,06
1329,49
1329,49
1276,16
1242,34
1181,59
1160,21
1135,18
1135,18
1084,96
1077,35
1061,13
1029,98
1013,08
1013,08
996,04
975,02
951,89
944,4
932,47
932,47
920,44
900,18
886,9
867,74
859,03
859,03
844,99
834,82
825,62
816,92
813,21
813,21
811,03
804,16
788,62
778,76
765,91
765,91
753,85
742,22
732,11
729,94
731,22
731,22
729,11
726,94
720,52
709,36
703,21
703,21
695,88
681,63
672,1
665,49
658,93
658,93
656
650,66
645,93
638,74
634,67
634,67
627,03
623,13
615,35
610,71




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

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 1 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=174816&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' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=174816&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=174816&T=0

As an alternative you can also use a QR Code:  

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

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







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean902.96896103896132.066151517719828.1595675907656
Geometric Mean864.923071946864
Harmonic Mean831.957392145064
Quadratic Mean945.250780565528
Winsorized Mean ( 1 / 25 )902.73402597402631.963730021465928.2424493439213
Winsorized Mean ( 2 / 25 )902.12311688311731.768525013281228.3967580020154
Winsorized Mean ( 3 / 25 )905.25597402597431.333213131143428.8912589410181
Winsorized Mean ( 4 / 25 )903.70220779220830.825004006434429.3171805461426
Winsorized Mean ( 5 / 25 )902.19896103896130.245296815303529.8293968331124
Winsorized Mean ( 6 / 25 )898.78363636363629.28497721346830.6909453885554
Winsorized Mean ( 7 / 25 )894.64545454545528.058222613069431.8853217070397
Winsorized Mean ( 8 / 25 )888.87194805194826.768188682202733.2062792370755
Winsorized Mean ( 9 / 25 )889.34766233766226.709101834577833.2975503199552
Winsorized Mean ( 10 / 25 )883.35545454545525.129116017543335.1526672855806
Winsorized Mean ( 11 / 25 )879.1997402597424.068092874161236.529680388745
Winsorized Mean ( 12 / 25 )870.56441558441522.145842380456839.3105125841891
Winsorized Mean ( 13 / 25 )867.44948051948121.424466978214940.4887310102759
Winsorized Mean ( 14 / 25 )862.89857142857120.619720103999241.8482194266649
Winsorized Mean ( 15 / 25 )864.17649350649320.454884678316342.247927920248
Winsorized Mean ( 16 / 25 )855.11467532467518.513077222591646.1897644050864
Winsorized Mean ( 17 / 25 )855.53857142857117.968528174976547.6131691531652
Winsorized Mean ( 18 / 25 )855.07805194805216.938747777889250.4805941478284
Winsorized Mean ( 19 / 25 )849.20038961038915.509202125251754.7546148894237
Winsorized Mean ( 20 / 25 )844.81077922077914.845032071248156.908653020495
Winsorized Mean ( 21 / 25 )846.48805194805214.63637951354457.834524662656
Winsorized Mean ( 22 / 25 )844.80805194805213.523907554071262.4677482133284
Winsorized Mean ( 23 / 25 )840.44701298701312.38080394639367.8830725876948
Winsorized Mean ( 24 / 25 )833.91402597402611.286482144383273.8860891556926
Winsorized Mean ( 25 / 25 )831.75168831168810.92120124108576.1593592088275
Trimmed Mean ( 1 / 25 )898.73693333333331.139824665197128.8613357010257
Trimmed Mean ( 2 / 25 )894.52082191780830.163635868937429.6556033829791
Trimmed Mean ( 3 / 25 )890.39845070422529.128011024845130.5684603711784
Trimmed Mean ( 4 / 25 )884.87173913043528.079536243049831.5130467779523
Trimmed Mean ( 5 / 25 )884.87173913043527.007455113664232.7639807381459
Trimmed Mean ( 6 / 25 )874.07446153846125.897347219943733.7515056702538
Trimmed Mean ( 7 / 25 )869.04111111111124.834891298577134.9927487365689
Trimmed Mean ( 8 / 25 )864.42393442622923.876990219200536.2032201919281
Trimmed Mean ( 9 / 25 )860.43559322033923.040337673256337.3447475216076
Trimmed Mean ( 10 / 25 )860.43559322033922.01018492863539.0926108076867
Trimmed Mean ( 11 / 25 )852.27963636363621.121216753995740.3518247215754
Trimmed Mean ( 12 / 25 )848.72415094339620.261951572501941.8875816530538
Trimmed Mean ( 13 / 25 )845.97627450980419.6352952552743.0844692433513
Trimmed Mean ( 14 / 25 )843.38061224489819.000089639978744.388243857035
Trimmed Mean ( 15 / 25 )841.09659574468118.371058693714445.7837846891458
Trimmed Mean ( 16 / 25 )838.46377777777817.581430476640447.6903047730847
Trimmed Mean ( 17 / 25 )836.6002325581417.024583825409449.1407156343818
Trimmed Mean ( 18 / 25 )834.50804878048816.403616247717450.873419383766
Trimmed Mean ( 19 / 25 )832.25179487179515.811711894862252.6351479463919
Trimmed Mean ( 20 / 25 )832.25179487179515.369313170292254.150226861177
Trimmed Mean ( 21 / 25 )828.80971428571414.922816428733155.5397647785766
Trimmed Mean ( 22 / 25 )826.84545454545514.323459606288457.7266580332622
Trimmed Mean ( 23 / 25 )824.81741935483913.779802173835959.856985532125
Trimmed Mean ( 24 / 25 )823.01310344827613.333350442241761.7259035539085
Trimmed Mean ( 25 / 25 )821.71777777777813.013447803779463.1437410106746
Median813.21
Midrange1061.67
Midmean - Weighted Average at Xnp827.048421052632
Midmean - Weighted Average at X(n+1)p832.251794871795
Midmean - Empirical Distribution Function832.251794871795
Midmean - Empirical Distribution Function - Averaging832.251794871795
Midmean - Empirical Distribution Function - Interpolation832.251794871795
Midmean - Closest Observation828.8425
Midmean - True Basic - Statistics Graphics Toolkit832.251794871795
Midmean - MS Excel (old versions)832.251794871795
Number of observations77

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 902.968961038961 & 32.0661515177198 & 28.1595675907656 \tabularnewline
Geometric Mean & 864.923071946864 &  &  \tabularnewline
Harmonic Mean & 831.957392145064 &  &  \tabularnewline
Quadratic Mean & 945.250780565528 &  &  \tabularnewline
Winsorized Mean ( 1 / 25 ) & 902.734025974026 & 31.9637300214659 & 28.2424493439213 \tabularnewline
Winsorized Mean ( 2 / 25 ) & 902.123116883117 & 31.7685250132812 & 28.3967580020154 \tabularnewline
Winsorized Mean ( 3 / 25 ) & 905.255974025974 & 31.3332131311434 & 28.8912589410181 \tabularnewline
Winsorized Mean ( 4 / 25 ) & 903.702207792208 & 30.8250040064344 & 29.3171805461426 \tabularnewline
Winsorized Mean ( 5 / 25 ) & 902.198961038961 & 30.2452968153035 & 29.8293968331124 \tabularnewline
Winsorized Mean ( 6 / 25 ) & 898.783636363636 & 29.284977213468 & 30.6909453885554 \tabularnewline
Winsorized Mean ( 7 / 25 ) & 894.645454545455 & 28.0582226130694 & 31.8853217070397 \tabularnewline
Winsorized Mean ( 8 / 25 ) & 888.871948051948 & 26.7681886822027 & 33.2062792370755 \tabularnewline
Winsorized Mean ( 9 / 25 ) & 889.347662337662 & 26.7091018345778 & 33.2975503199552 \tabularnewline
Winsorized Mean ( 10 / 25 ) & 883.355454545455 & 25.1291160175433 & 35.1526672855806 \tabularnewline
Winsorized Mean ( 11 / 25 ) & 879.19974025974 & 24.0680928741612 & 36.529680388745 \tabularnewline
Winsorized Mean ( 12 / 25 ) & 870.564415584415 & 22.1458423804568 & 39.3105125841891 \tabularnewline
Winsorized Mean ( 13 / 25 ) & 867.449480519481 & 21.4244669782149 & 40.4887310102759 \tabularnewline
Winsorized Mean ( 14 / 25 ) & 862.898571428571 & 20.6197201039992 & 41.8482194266649 \tabularnewline
Winsorized Mean ( 15 / 25 ) & 864.176493506493 & 20.4548846783163 & 42.247927920248 \tabularnewline
Winsorized Mean ( 16 / 25 ) & 855.114675324675 & 18.5130772225916 & 46.1897644050864 \tabularnewline
Winsorized Mean ( 17 / 25 ) & 855.538571428571 & 17.9685281749765 & 47.6131691531652 \tabularnewline
Winsorized Mean ( 18 / 25 ) & 855.078051948052 & 16.9387477778892 & 50.4805941478284 \tabularnewline
Winsorized Mean ( 19 / 25 ) & 849.200389610389 & 15.5092021252517 & 54.7546148894237 \tabularnewline
Winsorized Mean ( 20 / 25 ) & 844.810779220779 & 14.8450320712481 & 56.908653020495 \tabularnewline
Winsorized Mean ( 21 / 25 ) & 846.488051948052 & 14.636379513544 & 57.834524662656 \tabularnewline
Winsorized Mean ( 22 / 25 ) & 844.808051948052 & 13.5239075540712 & 62.4677482133284 \tabularnewline
Winsorized Mean ( 23 / 25 ) & 840.447012987013 & 12.380803946393 & 67.8830725876948 \tabularnewline
Winsorized Mean ( 24 / 25 ) & 833.914025974026 & 11.2864821443832 & 73.8860891556926 \tabularnewline
Winsorized Mean ( 25 / 25 ) & 831.751688311688 & 10.921201241085 & 76.1593592088275 \tabularnewline
Trimmed Mean ( 1 / 25 ) & 898.736933333333 & 31.1398246651971 & 28.8613357010257 \tabularnewline
Trimmed Mean ( 2 / 25 ) & 894.520821917808 & 30.1636358689374 & 29.6556033829791 \tabularnewline
Trimmed Mean ( 3 / 25 ) & 890.398450704225 & 29.1280110248451 & 30.5684603711784 \tabularnewline
Trimmed Mean ( 4 / 25 ) & 884.871739130435 & 28.0795362430498 & 31.5130467779523 \tabularnewline
Trimmed Mean ( 5 / 25 ) & 884.871739130435 & 27.0074551136642 & 32.7639807381459 \tabularnewline
Trimmed Mean ( 6 / 25 ) & 874.074461538461 & 25.8973472199437 & 33.7515056702538 \tabularnewline
Trimmed Mean ( 7 / 25 ) & 869.041111111111 & 24.8348912985771 & 34.9927487365689 \tabularnewline
Trimmed Mean ( 8 / 25 ) & 864.423934426229 & 23.8769902192005 & 36.2032201919281 \tabularnewline
Trimmed Mean ( 9 / 25 ) & 860.435593220339 & 23.0403376732563 & 37.3447475216076 \tabularnewline
Trimmed Mean ( 10 / 25 ) & 860.435593220339 & 22.010184928635 & 39.0926108076867 \tabularnewline
Trimmed Mean ( 11 / 25 ) & 852.279636363636 & 21.1212167539957 & 40.3518247215754 \tabularnewline
Trimmed Mean ( 12 / 25 ) & 848.724150943396 & 20.2619515725019 & 41.8875816530538 \tabularnewline
Trimmed Mean ( 13 / 25 ) & 845.976274509804 & 19.63529525527 & 43.0844692433513 \tabularnewline
Trimmed Mean ( 14 / 25 ) & 843.380612244898 & 19.0000896399787 & 44.388243857035 \tabularnewline
Trimmed Mean ( 15 / 25 ) & 841.096595744681 & 18.3710586937144 & 45.7837846891458 \tabularnewline
Trimmed Mean ( 16 / 25 ) & 838.463777777778 & 17.5814304766404 & 47.6903047730847 \tabularnewline
Trimmed Mean ( 17 / 25 ) & 836.60023255814 & 17.0245838254094 & 49.1407156343818 \tabularnewline
Trimmed Mean ( 18 / 25 ) & 834.508048780488 & 16.4036162477174 & 50.873419383766 \tabularnewline
Trimmed Mean ( 19 / 25 ) & 832.251794871795 & 15.8117118948622 & 52.6351479463919 \tabularnewline
Trimmed Mean ( 20 / 25 ) & 832.251794871795 & 15.3693131702922 & 54.150226861177 \tabularnewline
Trimmed Mean ( 21 / 25 ) & 828.809714285714 & 14.9228164287331 & 55.5397647785766 \tabularnewline
Trimmed Mean ( 22 / 25 ) & 826.845454545455 & 14.3234596062884 & 57.7266580332622 \tabularnewline
Trimmed Mean ( 23 / 25 ) & 824.817419354839 & 13.7798021738359 & 59.856985532125 \tabularnewline
Trimmed Mean ( 24 / 25 ) & 823.013103448276 & 13.3333504422417 & 61.7259035539085 \tabularnewline
Trimmed Mean ( 25 / 25 ) & 821.717777777778 & 13.0134478037794 & 63.1437410106746 \tabularnewline
Median & 813.21 &  &  \tabularnewline
Midrange & 1061.67 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 827.048421052632 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 832.251794871795 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 832.251794871795 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 832.251794871795 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 832.251794871795 &  &  \tabularnewline
Midmean - Closest Observation & 828.8425 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 832.251794871795 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 832.251794871795 &  &  \tabularnewline
Number of observations & 77 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=174816&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]902.968961038961[/C][C]32.0661515177198[/C][C]28.1595675907656[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]864.923071946864[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]831.957392145064[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]945.250780565528[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 25 )[/C][C]902.734025974026[/C][C]31.9637300214659[/C][C]28.2424493439213[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 25 )[/C][C]902.123116883117[/C][C]31.7685250132812[/C][C]28.3967580020154[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 25 )[/C][C]905.255974025974[/C][C]31.3332131311434[/C][C]28.8912589410181[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 25 )[/C][C]903.702207792208[/C][C]30.8250040064344[/C][C]29.3171805461426[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 25 )[/C][C]902.198961038961[/C][C]30.2452968153035[/C][C]29.8293968331124[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 25 )[/C][C]898.783636363636[/C][C]29.284977213468[/C][C]30.6909453885554[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 25 )[/C][C]894.645454545455[/C][C]28.0582226130694[/C][C]31.8853217070397[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 25 )[/C][C]888.871948051948[/C][C]26.7681886822027[/C][C]33.2062792370755[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 25 )[/C][C]889.347662337662[/C][C]26.7091018345778[/C][C]33.2975503199552[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 25 )[/C][C]883.355454545455[/C][C]25.1291160175433[/C][C]35.1526672855806[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 25 )[/C][C]879.19974025974[/C][C]24.0680928741612[/C][C]36.529680388745[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 25 )[/C][C]870.564415584415[/C][C]22.1458423804568[/C][C]39.3105125841891[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 25 )[/C][C]867.449480519481[/C][C]21.4244669782149[/C][C]40.4887310102759[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 25 )[/C][C]862.898571428571[/C][C]20.6197201039992[/C][C]41.8482194266649[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 25 )[/C][C]864.176493506493[/C][C]20.4548846783163[/C][C]42.247927920248[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 25 )[/C][C]855.114675324675[/C][C]18.5130772225916[/C][C]46.1897644050864[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 25 )[/C][C]855.538571428571[/C][C]17.9685281749765[/C][C]47.6131691531652[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 25 )[/C][C]855.078051948052[/C][C]16.9387477778892[/C][C]50.4805941478284[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 25 )[/C][C]849.200389610389[/C][C]15.5092021252517[/C][C]54.7546148894237[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 25 )[/C][C]844.810779220779[/C][C]14.8450320712481[/C][C]56.908653020495[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 25 )[/C][C]846.488051948052[/C][C]14.636379513544[/C][C]57.834524662656[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 25 )[/C][C]844.808051948052[/C][C]13.5239075540712[/C][C]62.4677482133284[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 25 )[/C][C]840.447012987013[/C][C]12.380803946393[/C][C]67.8830725876948[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 25 )[/C][C]833.914025974026[/C][C]11.2864821443832[/C][C]73.8860891556926[/C][/ROW]
[ROW][C]Winsorized Mean ( 25 / 25 )[/C][C]831.751688311688[/C][C]10.921201241085[/C][C]76.1593592088275[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 25 )[/C][C]898.736933333333[/C][C]31.1398246651971[/C][C]28.8613357010257[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 25 )[/C][C]894.520821917808[/C][C]30.1636358689374[/C][C]29.6556033829791[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 25 )[/C][C]890.398450704225[/C][C]29.1280110248451[/C][C]30.5684603711784[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 25 )[/C][C]884.871739130435[/C][C]28.0795362430498[/C][C]31.5130467779523[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 25 )[/C][C]884.871739130435[/C][C]27.0074551136642[/C][C]32.7639807381459[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 25 )[/C][C]874.074461538461[/C][C]25.8973472199437[/C][C]33.7515056702538[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 25 )[/C][C]869.041111111111[/C][C]24.8348912985771[/C][C]34.9927487365689[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 25 )[/C][C]864.423934426229[/C][C]23.8769902192005[/C][C]36.2032201919281[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 25 )[/C][C]860.435593220339[/C][C]23.0403376732563[/C][C]37.3447475216076[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 25 )[/C][C]860.435593220339[/C][C]22.010184928635[/C][C]39.0926108076867[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 25 )[/C][C]852.279636363636[/C][C]21.1212167539957[/C][C]40.3518247215754[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 25 )[/C][C]848.724150943396[/C][C]20.2619515725019[/C][C]41.8875816530538[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 25 )[/C][C]845.976274509804[/C][C]19.63529525527[/C][C]43.0844692433513[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 25 )[/C][C]843.380612244898[/C][C]19.0000896399787[/C][C]44.388243857035[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 25 )[/C][C]841.096595744681[/C][C]18.3710586937144[/C][C]45.7837846891458[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 25 )[/C][C]838.463777777778[/C][C]17.5814304766404[/C][C]47.6903047730847[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 25 )[/C][C]836.60023255814[/C][C]17.0245838254094[/C][C]49.1407156343818[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 25 )[/C][C]834.508048780488[/C][C]16.4036162477174[/C][C]50.873419383766[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 25 )[/C][C]832.251794871795[/C][C]15.8117118948622[/C][C]52.6351479463919[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 25 )[/C][C]832.251794871795[/C][C]15.3693131702922[/C][C]54.150226861177[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 25 )[/C][C]828.809714285714[/C][C]14.9228164287331[/C][C]55.5397647785766[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 25 )[/C][C]826.845454545455[/C][C]14.3234596062884[/C][C]57.7266580332622[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 25 )[/C][C]824.817419354839[/C][C]13.7798021738359[/C][C]59.856985532125[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 25 )[/C][C]823.013103448276[/C][C]13.3333504422417[/C][C]61.7259035539085[/C][/ROW]
[ROW][C]Trimmed Mean ( 25 / 25 )[/C][C]821.717777777778[/C][C]13.0134478037794[/C][C]63.1437410106746[/C][/ROW]
[ROW][C]Median[/C][C]813.21[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]1061.67[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]827.048421052632[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]832.251794871795[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]832.251794871795[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]832.251794871795[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]832.251794871795[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]828.8425[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]832.251794871795[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]832.251794871795[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]77[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=174816&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=174816&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 Mean902.96896103896132.066151517719828.1595675907656
Geometric Mean864.923071946864
Harmonic Mean831.957392145064
Quadratic Mean945.250780565528
Winsorized Mean ( 1 / 25 )902.73402597402631.963730021465928.2424493439213
Winsorized Mean ( 2 / 25 )902.12311688311731.768525013281228.3967580020154
Winsorized Mean ( 3 / 25 )905.25597402597431.333213131143428.8912589410181
Winsorized Mean ( 4 / 25 )903.70220779220830.825004006434429.3171805461426
Winsorized Mean ( 5 / 25 )902.19896103896130.245296815303529.8293968331124
Winsorized Mean ( 6 / 25 )898.78363636363629.28497721346830.6909453885554
Winsorized Mean ( 7 / 25 )894.64545454545528.058222613069431.8853217070397
Winsorized Mean ( 8 / 25 )888.87194805194826.768188682202733.2062792370755
Winsorized Mean ( 9 / 25 )889.34766233766226.709101834577833.2975503199552
Winsorized Mean ( 10 / 25 )883.35545454545525.129116017543335.1526672855806
Winsorized Mean ( 11 / 25 )879.1997402597424.068092874161236.529680388745
Winsorized Mean ( 12 / 25 )870.56441558441522.145842380456839.3105125841891
Winsorized Mean ( 13 / 25 )867.44948051948121.424466978214940.4887310102759
Winsorized Mean ( 14 / 25 )862.89857142857120.619720103999241.8482194266649
Winsorized Mean ( 15 / 25 )864.17649350649320.454884678316342.247927920248
Winsorized Mean ( 16 / 25 )855.11467532467518.513077222591646.1897644050864
Winsorized Mean ( 17 / 25 )855.53857142857117.968528174976547.6131691531652
Winsorized Mean ( 18 / 25 )855.07805194805216.938747777889250.4805941478284
Winsorized Mean ( 19 / 25 )849.20038961038915.509202125251754.7546148894237
Winsorized Mean ( 20 / 25 )844.81077922077914.845032071248156.908653020495
Winsorized Mean ( 21 / 25 )846.48805194805214.63637951354457.834524662656
Winsorized Mean ( 22 / 25 )844.80805194805213.523907554071262.4677482133284
Winsorized Mean ( 23 / 25 )840.44701298701312.38080394639367.8830725876948
Winsorized Mean ( 24 / 25 )833.91402597402611.286482144383273.8860891556926
Winsorized Mean ( 25 / 25 )831.75168831168810.92120124108576.1593592088275
Trimmed Mean ( 1 / 25 )898.73693333333331.139824665197128.8613357010257
Trimmed Mean ( 2 / 25 )894.52082191780830.163635868937429.6556033829791
Trimmed Mean ( 3 / 25 )890.39845070422529.128011024845130.5684603711784
Trimmed Mean ( 4 / 25 )884.87173913043528.079536243049831.5130467779523
Trimmed Mean ( 5 / 25 )884.87173913043527.007455113664232.7639807381459
Trimmed Mean ( 6 / 25 )874.07446153846125.897347219943733.7515056702538
Trimmed Mean ( 7 / 25 )869.04111111111124.834891298577134.9927487365689
Trimmed Mean ( 8 / 25 )864.42393442622923.876990219200536.2032201919281
Trimmed Mean ( 9 / 25 )860.43559322033923.040337673256337.3447475216076
Trimmed Mean ( 10 / 25 )860.43559322033922.01018492863539.0926108076867
Trimmed Mean ( 11 / 25 )852.27963636363621.121216753995740.3518247215754
Trimmed Mean ( 12 / 25 )848.72415094339620.261951572501941.8875816530538
Trimmed Mean ( 13 / 25 )845.97627450980419.6352952552743.0844692433513
Trimmed Mean ( 14 / 25 )843.38061224489819.000089639978744.388243857035
Trimmed Mean ( 15 / 25 )841.09659574468118.371058693714445.7837846891458
Trimmed Mean ( 16 / 25 )838.46377777777817.581430476640447.6903047730847
Trimmed Mean ( 17 / 25 )836.6002325581417.024583825409449.1407156343818
Trimmed Mean ( 18 / 25 )834.50804878048816.403616247717450.873419383766
Trimmed Mean ( 19 / 25 )832.25179487179515.811711894862252.6351479463919
Trimmed Mean ( 20 / 25 )832.25179487179515.369313170292254.150226861177
Trimmed Mean ( 21 / 25 )828.80971428571414.922816428733155.5397647785766
Trimmed Mean ( 22 / 25 )826.84545454545514.323459606288457.7266580332622
Trimmed Mean ( 23 / 25 )824.81741935483913.779802173835959.856985532125
Trimmed Mean ( 24 / 25 )823.01310344827613.333350442241761.7259035539085
Trimmed Mean ( 25 / 25 )821.71777777777813.013447803779463.1437410106746
Median813.21
Midrange1061.67
Midmean - Weighted Average at Xnp827.048421052632
Midmean - Weighted Average at X(n+1)p832.251794871795
Midmean - Empirical Distribution Function832.251794871795
Midmean - Empirical Distribution Function - Averaging832.251794871795
Midmean - Empirical Distribution Function - Interpolation832.251794871795
Midmean - Closest Observation828.8425
Midmean - True Basic - Statistics Graphics Toolkit832.251794871795
Midmean - MS Excel (old versions)832.251794871795
Number of observations77



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')