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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, 19 Oct 2011 10:30:32 -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/2011/Oct/19/t1319034746nxj5ohlobkm6rva.htm/, Retrieved Wed, 15 May 2024 21:18:14 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=132803, Retrieved Wed, 15 May 2024 21:18:14 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsKDG2011W52a
Estimated Impact89
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [centrummaten aant...] [2011-10-19 14:30:32] [ce97780edec5de939908d2a0576fedc2] [Current]
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Dataseries X:
797
840
988
819
831
904
814
798
828
789
930
744
832
826
907
776
835
715
729
733
736
712
711
667
799
661
692
649
729
622
671
635
648
745
624
477
710
515
461
590
415
554
585
513
591
561
684
668
795
776
1043
964
762
1030
939
779
918
839
874
840
794
820
1003
780
607
1001
743
810
716
775
883
633




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=132803&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=132803&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=132803&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 Mean752.55555555555616.185349169366346.4960964190938
Geometric Mean739.467024199584
Harmonic Mean725.483342880463
Quadratic Mean764.813321449533
Winsorized Mean ( 1 / 24 )753.01388888888915.964253557535347.1687502441014
Winsorized Mean ( 2 / 24 )752.70833333333315.675896760345248.0169233595257
Winsorized Mean ( 3 / 24 )754.12515.304613559479649.2743575046295
Winsorized Mean ( 4 / 24 )753.51388888888915.118998415537649.8388761066681
Winsorized Mean ( 5 / 24 )754.55555555555614.192063522068753.1674308237291
Winsorized Mean ( 6 / 24 )753.05555555555613.659692610952155.1297585534076
Winsorized Mean ( 7 / 24 )754.51388888888913.048003238786757.8260041081236
Winsorized Mean ( 8 / 24 )753.73611111111112.698917939922959.3543571725518
Winsorized Mean ( 9 / 24 )752.48611111111112.430463756753660.5356425823035
Winsorized Mean ( 10 / 24 )754.29166666666711.961048504960963.0623365797588
Winsorized Mean ( 11 / 24 )753.37511.020422028321668.3617195479344
Winsorized Mean ( 12 / 24 )752.20833333333310.720045749368170.1683883557749
Winsorized Mean ( 13 / 24 )747.6944444444449.531445340005878.4450225304433
Winsorized Mean ( 14 / 24 )748.0833333333339.4657720846246679.0303555426241
Winsorized Mean ( 15 / 24 )750.5833333333338.9913832424971583.478071514709
Winsorized Mean ( 16 / 24 )749.9166666666678.8337928394966684.8918103799903
Winsorized Mean ( 17 / 24 )752.0416666666678.2902982096738190.7134638159483
Winsorized Mean ( 18 / 24 )753.2916666666678.0266681264913793.8486124996856
Winsorized Mean ( 19 / 24 )752.7638888888897.8794837958279495.5346705944704
Winsorized Mean ( 20 / 24 )753.0416666666677.6791192373439498.063546533382
Winsorized Mean ( 21 / 24 )755.0833333333336.88426428016722109.682502385715
Winsorized Mean ( 22 / 24 )757.2222222222226.492689467306116.626896455655
Winsorized Mean ( 23 / 24 )761.3755.48986965405066138.687263628969
Winsorized Mean ( 24 / 24 )760.3755.26739749119083144.354968705447
Trimmed Mean ( 1 / 24 )753.22857142857115.368721043498349.0104914583784
Trimmed Mean ( 2 / 24 )753.45588235294114.657569784440651.403874819191
Trimmed Mean ( 3 / 24 )753.86363636363613.994002817451653.8704791043427
Trimmed Mean ( 4 / 24 )753.76562513.372593652904656.3664495134254
Trimmed Mean ( 5 / 24 )753.83870967741912.691186112559459.3986017533387
Trimmed Mean ( 6 / 24 )753.66666666666712.178606477913661.8844748808881
Trimmed Mean ( 7 / 24 )753.79310344827611.713166996045464.3543376187475
Trimmed Mean ( 8 / 24 )753.66071428571411.310788918760266.6320200738325
Trimmed Mean ( 9 / 24 )753.64814814814810.903366837400369.1206816561481
Trimmed Mean ( 10 / 24 )753.82692307692310.462016377935572.0536936518995
Trimmed Mean ( 11 / 24 )753.7610.02366831706975.1980189444664
Trimmed Mean ( 12 / 24 )753.81259.6961211924706377.7437167952646
Trimmed Mean ( 13 / 24 )754.0217391304359.3457210302522680.6809594133672
Trimmed Mean ( 14 / 24 )754.8181818181829.1595138634578282.4081051757073
Trimmed Mean ( 15 / 24 )755.6428571428578.9225484912047184.6891286595665
Trimmed Mean ( 16 / 24 )756.258.7171177017200586.7545931897625
Trimmed Mean ( 17 / 24 )7578.4678288349381289.3971778074482
Trimmed Mean ( 18 / 24 )757.5833333333338.2598065813858491.7192582984462
Trimmed Mean ( 19 / 24 )758.0882352941188.0306196162427194.3997190155552
Trimmed Mean ( 20 / 24 )758.718757.7344060564707298.0965758017378
Trimmed Mean ( 21 / 24 )759.47.35841062299134103.201634008743
Trimmed Mean ( 22 / 24 )759.9285714285717.06562746391329107.552878397538
Trimmed Mean ( 23 / 24 )760.2692307692316.75222076113486112.595434548774
Trimmed Mean ( 24 / 24 )760.1256.62404286222392114.752427756
Median768.5
Midrange729
Midmean - Weighted Average at Xnp754.972972972973
Midmean - Weighted Average at X(n+1)p757.583333333333
Midmean - Empirical Distribution Function754.972972972973
Midmean - Empirical Distribution Function - Averaging757.583333333333
Midmean - Empirical Distribution Function - Interpolation757.583333333333
Midmean - Closest Observation754.972972972973
Midmean - True Basic - Statistics Graphics Toolkit757.583333333333
Midmean - MS Excel (old versions)757
Number of observations72

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 752.555555555556 & 16.1853491693663 & 46.4960964190938 \tabularnewline
Geometric Mean & 739.467024199584 &  &  \tabularnewline
Harmonic Mean & 725.483342880463 &  &  \tabularnewline
Quadratic Mean & 764.813321449533 &  &  \tabularnewline
Winsorized Mean ( 1 / 24 ) & 753.013888888889 & 15.9642535575353 & 47.1687502441014 \tabularnewline
Winsorized Mean ( 2 / 24 ) & 752.708333333333 & 15.6758967603452 & 48.0169233595257 \tabularnewline
Winsorized Mean ( 3 / 24 ) & 754.125 & 15.3046135594796 & 49.2743575046295 \tabularnewline
Winsorized Mean ( 4 / 24 ) & 753.513888888889 & 15.1189984155376 & 49.8388761066681 \tabularnewline
Winsorized Mean ( 5 / 24 ) & 754.555555555556 & 14.1920635220687 & 53.1674308237291 \tabularnewline
Winsorized Mean ( 6 / 24 ) & 753.055555555556 & 13.6596926109521 & 55.1297585534076 \tabularnewline
Winsorized Mean ( 7 / 24 ) & 754.513888888889 & 13.0480032387867 & 57.8260041081236 \tabularnewline
Winsorized Mean ( 8 / 24 ) & 753.736111111111 & 12.6989179399229 & 59.3543571725518 \tabularnewline
Winsorized Mean ( 9 / 24 ) & 752.486111111111 & 12.4304637567536 & 60.5356425823035 \tabularnewline
Winsorized Mean ( 10 / 24 ) & 754.291666666667 & 11.9610485049609 & 63.0623365797588 \tabularnewline
Winsorized Mean ( 11 / 24 ) & 753.375 & 11.0204220283216 & 68.3617195479344 \tabularnewline
Winsorized Mean ( 12 / 24 ) & 752.208333333333 & 10.7200457493681 & 70.1683883557749 \tabularnewline
Winsorized Mean ( 13 / 24 ) & 747.694444444444 & 9.5314453400058 & 78.4450225304433 \tabularnewline
Winsorized Mean ( 14 / 24 ) & 748.083333333333 & 9.46577208462466 & 79.0303555426241 \tabularnewline
Winsorized Mean ( 15 / 24 ) & 750.583333333333 & 8.99138324249715 & 83.478071514709 \tabularnewline
Winsorized Mean ( 16 / 24 ) & 749.916666666667 & 8.83379283949666 & 84.8918103799903 \tabularnewline
Winsorized Mean ( 17 / 24 ) & 752.041666666667 & 8.29029820967381 & 90.7134638159483 \tabularnewline
Winsorized Mean ( 18 / 24 ) & 753.291666666667 & 8.02666812649137 & 93.8486124996856 \tabularnewline
Winsorized Mean ( 19 / 24 ) & 752.763888888889 & 7.87948379582794 & 95.5346705944704 \tabularnewline
Winsorized Mean ( 20 / 24 ) & 753.041666666667 & 7.67911923734394 & 98.063546533382 \tabularnewline
Winsorized Mean ( 21 / 24 ) & 755.083333333333 & 6.88426428016722 & 109.682502385715 \tabularnewline
Winsorized Mean ( 22 / 24 ) & 757.222222222222 & 6.492689467306 & 116.626896455655 \tabularnewline
Winsorized Mean ( 23 / 24 ) & 761.375 & 5.48986965405066 & 138.687263628969 \tabularnewline
Winsorized Mean ( 24 / 24 ) & 760.375 & 5.26739749119083 & 144.354968705447 \tabularnewline
Trimmed Mean ( 1 / 24 ) & 753.228571428571 & 15.3687210434983 & 49.0104914583784 \tabularnewline
Trimmed Mean ( 2 / 24 ) & 753.455882352941 & 14.6575697844406 & 51.403874819191 \tabularnewline
Trimmed Mean ( 3 / 24 ) & 753.863636363636 & 13.9940028174516 & 53.8704791043427 \tabularnewline
Trimmed Mean ( 4 / 24 ) & 753.765625 & 13.3725936529046 & 56.3664495134254 \tabularnewline
Trimmed Mean ( 5 / 24 ) & 753.838709677419 & 12.6911861125594 & 59.3986017533387 \tabularnewline
Trimmed Mean ( 6 / 24 ) & 753.666666666667 & 12.1786064779136 & 61.8844748808881 \tabularnewline
Trimmed Mean ( 7 / 24 ) & 753.793103448276 & 11.7131669960454 & 64.3543376187475 \tabularnewline
Trimmed Mean ( 8 / 24 ) & 753.660714285714 & 11.3107889187602 & 66.6320200738325 \tabularnewline
Trimmed Mean ( 9 / 24 ) & 753.648148148148 & 10.9033668374003 & 69.1206816561481 \tabularnewline
Trimmed Mean ( 10 / 24 ) & 753.826923076923 & 10.4620163779355 & 72.0536936518995 \tabularnewline
Trimmed Mean ( 11 / 24 ) & 753.76 & 10.023668317069 & 75.1980189444664 \tabularnewline
Trimmed Mean ( 12 / 24 ) & 753.8125 & 9.69612119247063 & 77.7437167952646 \tabularnewline
Trimmed Mean ( 13 / 24 ) & 754.021739130435 & 9.34572103025226 & 80.6809594133672 \tabularnewline
Trimmed Mean ( 14 / 24 ) & 754.818181818182 & 9.15951386345782 & 82.4081051757073 \tabularnewline
Trimmed Mean ( 15 / 24 ) & 755.642857142857 & 8.92254849120471 & 84.6891286595665 \tabularnewline
Trimmed Mean ( 16 / 24 ) & 756.25 & 8.71711770172005 & 86.7545931897625 \tabularnewline
Trimmed Mean ( 17 / 24 ) & 757 & 8.46782883493812 & 89.3971778074482 \tabularnewline
Trimmed Mean ( 18 / 24 ) & 757.583333333333 & 8.25980658138584 & 91.7192582984462 \tabularnewline
Trimmed Mean ( 19 / 24 ) & 758.088235294118 & 8.03061961624271 & 94.3997190155552 \tabularnewline
Trimmed Mean ( 20 / 24 ) & 758.71875 & 7.73440605647072 & 98.0965758017378 \tabularnewline
Trimmed Mean ( 21 / 24 ) & 759.4 & 7.35841062299134 & 103.201634008743 \tabularnewline
Trimmed Mean ( 22 / 24 ) & 759.928571428571 & 7.06562746391329 & 107.552878397538 \tabularnewline
Trimmed Mean ( 23 / 24 ) & 760.269230769231 & 6.75222076113486 & 112.595434548774 \tabularnewline
Trimmed Mean ( 24 / 24 ) & 760.125 & 6.62404286222392 & 114.752427756 \tabularnewline
Median & 768.5 &  &  \tabularnewline
Midrange & 729 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 754.972972972973 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 757.583333333333 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 754.972972972973 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 757.583333333333 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 757.583333333333 &  &  \tabularnewline
Midmean - Closest Observation & 754.972972972973 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 757.583333333333 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 757 &  &  \tabularnewline
Number of observations & 72 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=132803&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]752.555555555556[/C][C]16.1853491693663[/C][C]46.4960964190938[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]739.467024199584[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]725.483342880463[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]764.813321449533[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 24 )[/C][C]753.013888888889[/C][C]15.9642535575353[/C][C]47.1687502441014[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 24 )[/C][C]752.708333333333[/C][C]15.6758967603452[/C][C]48.0169233595257[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 24 )[/C][C]754.125[/C][C]15.3046135594796[/C][C]49.2743575046295[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 24 )[/C][C]753.513888888889[/C][C]15.1189984155376[/C][C]49.8388761066681[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 24 )[/C][C]754.555555555556[/C][C]14.1920635220687[/C][C]53.1674308237291[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 24 )[/C][C]753.055555555556[/C][C]13.6596926109521[/C][C]55.1297585534076[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 24 )[/C][C]754.513888888889[/C][C]13.0480032387867[/C][C]57.8260041081236[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 24 )[/C][C]753.736111111111[/C][C]12.6989179399229[/C][C]59.3543571725518[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 24 )[/C][C]752.486111111111[/C][C]12.4304637567536[/C][C]60.5356425823035[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 24 )[/C][C]754.291666666667[/C][C]11.9610485049609[/C][C]63.0623365797588[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 24 )[/C][C]753.375[/C][C]11.0204220283216[/C][C]68.3617195479344[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 24 )[/C][C]752.208333333333[/C][C]10.7200457493681[/C][C]70.1683883557749[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 24 )[/C][C]747.694444444444[/C][C]9.5314453400058[/C][C]78.4450225304433[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 24 )[/C][C]748.083333333333[/C][C]9.46577208462466[/C][C]79.0303555426241[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 24 )[/C][C]750.583333333333[/C][C]8.99138324249715[/C][C]83.478071514709[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 24 )[/C][C]749.916666666667[/C][C]8.83379283949666[/C][C]84.8918103799903[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 24 )[/C][C]752.041666666667[/C][C]8.29029820967381[/C][C]90.7134638159483[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 24 )[/C][C]753.291666666667[/C][C]8.02666812649137[/C][C]93.8486124996856[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 24 )[/C][C]752.763888888889[/C][C]7.87948379582794[/C][C]95.5346705944704[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 24 )[/C][C]753.041666666667[/C][C]7.67911923734394[/C][C]98.063546533382[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 24 )[/C][C]755.083333333333[/C][C]6.88426428016722[/C][C]109.682502385715[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 24 )[/C][C]757.222222222222[/C][C]6.492689467306[/C][C]116.626896455655[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 24 )[/C][C]761.375[/C][C]5.48986965405066[/C][C]138.687263628969[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 24 )[/C][C]760.375[/C][C]5.26739749119083[/C][C]144.354968705447[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 24 )[/C][C]753.228571428571[/C][C]15.3687210434983[/C][C]49.0104914583784[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 24 )[/C][C]753.455882352941[/C][C]14.6575697844406[/C][C]51.403874819191[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 24 )[/C][C]753.863636363636[/C][C]13.9940028174516[/C][C]53.8704791043427[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 24 )[/C][C]753.765625[/C][C]13.3725936529046[/C][C]56.3664495134254[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 24 )[/C][C]753.838709677419[/C][C]12.6911861125594[/C][C]59.3986017533387[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 24 )[/C][C]753.666666666667[/C][C]12.1786064779136[/C][C]61.8844748808881[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 24 )[/C][C]753.793103448276[/C][C]11.7131669960454[/C][C]64.3543376187475[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 24 )[/C][C]753.660714285714[/C][C]11.3107889187602[/C][C]66.6320200738325[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 24 )[/C][C]753.648148148148[/C][C]10.9033668374003[/C][C]69.1206816561481[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 24 )[/C][C]753.826923076923[/C][C]10.4620163779355[/C][C]72.0536936518995[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 24 )[/C][C]753.76[/C][C]10.023668317069[/C][C]75.1980189444664[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 24 )[/C][C]753.8125[/C][C]9.69612119247063[/C][C]77.7437167952646[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 24 )[/C][C]754.021739130435[/C][C]9.34572103025226[/C][C]80.6809594133672[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 24 )[/C][C]754.818181818182[/C][C]9.15951386345782[/C][C]82.4081051757073[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 24 )[/C][C]755.642857142857[/C][C]8.92254849120471[/C][C]84.6891286595665[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 24 )[/C][C]756.25[/C][C]8.71711770172005[/C][C]86.7545931897625[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 24 )[/C][C]757[/C][C]8.46782883493812[/C][C]89.3971778074482[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 24 )[/C][C]757.583333333333[/C][C]8.25980658138584[/C][C]91.7192582984462[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 24 )[/C][C]758.088235294118[/C][C]8.03061961624271[/C][C]94.3997190155552[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 24 )[/C][C]758.71875[/C][C]7.73440605647072[/C][C]98.0965758017378[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 24 )[/C][C]759.4[/C][C]7.35841062299134[/C][C]103.201634008743[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 24 )[/C][C]759.928571428571[/C][C]7.06562746391329[/C][C]107.552878397538[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 24 )[/C][C]760.269230769231[/C][C]6.75222076113486[/C][C]112.595434548774[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 24 )[/C][C]760.125[/C][C]6.62404286222392[/C][C]114.752427756[/C][/ROW]
[ROW][C]Median[/C][C]768.5[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]729[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]754.972972972973[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]757.583333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]754.972972972973[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]757.583333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]757.583333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]754.972972972973[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]757.583333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]757[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]72[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=132803&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=132803&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 Mean752.55555555555616.185349169366346.4960964190938
Geometric Mean739.467024199584
Harmonic Mean725.483342880463
Quadratic Mean764.813321449533
Winsorized Mean ( 1 / 24 )753.01388888888915.964253557535347.1687502441014
Winsorized Mean ( 2 / 24 )752.70833333333315.675896760345248.0169233595257
Winsorized Mean ( 3 / 24 )754.12515.304613559479649.2743575046295
Winsorized Mean ( 4 / 24 )753.51388888888915.118998415537649.8388761066681
Winsorized Mean ( 5 / 24 )754.55555555555614.192063522068753.1674308237291
Winsorized Mean ( 6 / 24 )753.05555555555613.659692610952155.1297585534076
Winsorized Mean ( 7 / 24 )754.51388888888913.048003238786757.8260041081236
Winsorized Mean ( 8 / 24 )753.73611111111112.698917939922959.3543571725518
Winsorized Mean ( 9 / 24 )752.48611111111112.430463756753660.5356425823035
Winsorized Mean ( 10 / 24 )754.29166666666711.961048504960963.0623365797588
Winsorized Mean ( 11 / 24 )753.37511.020422028321668.3617195479344
Winsorized Mean ( 12 / 24 )752.20833333333310.720045749368170.1683883557749
Winsorized Mean ( 13 / 24 )747.6944444444449.531445340005878.4450225304433
Winsorized Mean ( 14 / 24 )748.0833333333339.4657720846246679.0303555426241
Winsorized Mean ( 15 / 24 )750.5833333333338.9913832424971583.478071514709
Winsorized Mean ( 16 / 24 )749.9166666666678.8337928394966684.8918103799903
Winsorized Mean ( 17 / 24 )752.0416666666678.2902982096738190.7134638159483
Winsorized Mean ( 18 / 24 )753.2916666666678.0266681264913793.8486124996856
Winsorized Mean ( 19 / 24 )752.7638888888897.8794837958279495.5346705944704
Winsorized Mean ( 20 / 24 )753.0416666666677.6791192373439498.063546533382
Winsorized Mean ( 21 / 24 )755.0833333333336.88426428016722109.682502385715
Winsorized Mean ( 22 / 24 )757.2222222222226.492689467306116.626896455655
Winsorized Mean ( 23 / 24 )761.3755.48986965405066138.687263628969
Winsorized Mean ( 24 / 24 )760.3755.26739749119083144.354968705447
Trimmed Mean ( 1 / 24 )753.22857142857115.368721043498349.0104914583784
Trimmed Mean ( 2 / 24 )753.45588235294114.657569784440651.403874819191
Trimmed Mean ( 3 / 24 )753.86363636363613.994002817451653.8704791043427
Trimmed Mean ( 4 / 24 )753.76562513.372593652904656.3664495134254
Trimmed Mean ( 5 / 24 )753.83870967741912.691186112559459.3986017533387
Trimmed Mean ( 6 / 24 )753.66666666666712.178606477913661.8844748808881
Trimmed Mean ( 7 / 24 )753.79310344827611.713166996045464.3543376187475
Trimmed Mean ( 8 / 24 )753.66071428571411.310788918760266.6320200738325
Trimmed Mean ( 9 / 24 )753.64814814814810.903366837400369.1206816561481
Trimmed Mean ( 10 / 24 )753.82692307692310.462016377935572.0536936518995
Trimmed Mean ( 11 / 24 )753.7610.02366831706975.1980189444664
Trimmed Mean ( 12 / 24 )753.81259.6961211924706377.7437167952646
Trimmed Mean ( 13 / 24 )754.0217391304359.3457210302522680.6809594133672
Trimmed Mean ( 14 / 24 )754.8181818181829.1595138634578282.4081051757073
Trimmed Mean ( 15 / 24 )755.6428571428578.9225484912047184.6891286595665
Trimmed Mean ( 16 / 24 )756.258.7171177017200586.7545931897625
Trimmed Mean ( 17 / 24 )7578.4678288349381289.3971778074482
Trimmed Mean ( 18 / 24 )757.5833333333338.2598065813858491.7192582984462
Trimmed Mean ( 19 / 24 )758.0882352941188.0306196162427194.3997190155552
Trimmed Mean ( 20 / 24 )758.718757.7344060564707298.0965758017378
Trimmed Mean ( 21 / 24 )759.47.35841062299134103.201634008743
Trimmed Mean ( 22 / 24 )759.9285714285717.06562746391329107.552878397538
Trimmed Mean ( 23 / 24 )760.2692307692316.75222076113486112.595434548774
Trimmed Mean ( 24 / 24 )760.1256.62404286222392114.752427756
Median768.5
Midrange729
Midmean - Weighted Average at Xnp754.972972972973
Midmean - Weighted Average at X(n+1)p757.583333333333
Midmean - Empirical Distribution Function754.972972972973
Midmean - Empirical Distribution Function - Averaging757.583333333333
Midmean - Empirical Distribution Function - Interpolation757.583333333333
Midmean - Closest Observation754.972972972973
Midmean - True Basic - Statistics Graphics Toolkit757.583333333333
Midmean - MS Excel (old versions)757
Number of observations72



Parameters (Session):
Parameters (R input):
R code (references can be found in the software module):
geomean <- function(x) {
return(exp(mean(log(x))))
}
harmean <- function(x) {
return(1/mean(1/x))
}
quamean <- function(x) {
return(sqrt(mean(x*x)))
}
winmean <- function(x) {
x <-sort(x[!is.na(x)])
n<-length(x)
denom <- 3
nodenom <- n/denom
if (nodenom>40) denom <- n/40
sqrtn = sqrt(n)
roundnodenom = floor(nodenom)
win <- array(NA,dim=c(roundnodenom,2))
for (j in 1:roundnodenom) {
win[j,1] <- (j*x[j+1]+sum(x[(j+1):(n-j)])+j*x[n-j])/n
win[j,2] <- sd(c(rep(x[j+1],j),x[(j+1):(n-j)],rep(x[n-j],j)))/sqrtn
}
return(win)
}
trimean <- function(x) {
x <-sort(x[!is.na(x)])
n<-length(x)
denom <- 3
nodenom <- n/denom
if (nodenom>40) denom <- n/40
sqrtn = sqrt(n)
roundnodenom = floor(nodenom)
tri <- array(NA,dim=c(roundnodenom,2))
for (j in 1:roundnodenom) {
tri[j,1] <- mean(x,trim=j/n)
tri[j,2] <- sd(x[(j+1):(n-j)]) / sqrt(n-j*2)
}
return(tri)
}
midrange <- function(x) {
return((max(x)+min(x))/2)
}
q1 <- function(data,n,p,i,f) {
np <- n*p;
i <<- floor(np)
f <<- np - i
qvalue <- (1-f)*data[i] + f*data[i+1]
}
q2 <- function(data,n,p,i,f) {
np <- (n+1)*p
i <<- floor(np)
f <<- np - i
qvalue <- (1-f)*data[i] + f*data[i+1]
}
q3 <- function(data,n,p,i,f) {
np <- n*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- data[i]
} else {
qvalue <- data[i+1]
}
}
q4 <- function(data,n,p,i,f) {
np <- n*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- (data[i]+data[i+1])/2
} else {
qvalue <- data[i+1]
}
}
q5 <- function(data,n,p,i,f) {
np <- (n-1)*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- data[i+1]
} else {
qvalue <- data[i+1] + f*(data[i+2]-data[i+1])
}
}
q6 <- function(data,n,p,i,f) {
np <- n*p+0.5
i <<- floor(np)
f <<- np - i
qvalue <- data[i]
}
q7 <- function(data,n,p,i,f) {
np <- (n+1)*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- data[i]
} else {
qvalue <- f*data[i] + (1-f)*data[i+1]
}
}
q8 <- function(data,n,p,i,f) {
np <- (n+1)*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- data[i]
} else {
if (f == 0.5) {
qvalue <- (data[i]+data[i+1])/2
} else {
if (f < 0.5) {
qvalue <- data[i]
} else {
qvalue <- data[i+1]
}
}
}
}
midmean <- function(x,def) {
x <-sort(x[!is.na(x)])
n<-length(x)
if (def==1) {
qvalue1 <- q1(x,n,0.25,i,f)
qvalue3 <- q1(x,n,0.75,i,f)
}
if (def==2) {
qvalue1 <- q2(x,n,0.25,i,f)
qvalue3 <- q2(x,n,0.75,i,f)
}
if (def==3) {
qvalue1 <- q3(x,n,0.25,i,f)
qvalue3 <- q3(x,n,0.75,i,f)
}
if (def==4) {
qvalue1 <- q4(x,n,0.25,i,f)
qvalue3 <- q4(x,n,0.75,i,f)
}
if (def==5) {
qvalue1 <- q5(x,n,0.25,i,f)
qvalue3 <- q5(x,n,0.75,i,f)
}
if (def==6) {
qvalue1 <- q6(x,n,0.25,i,f)
qvalue3 <- q6(x,n,0.75,i,f)
}
if (def==7) {
qvalue1 <- q7(x,n,0.25,i,f)
qvalue3 <- q7(x,n,0.75,i,f)
}
if (def==8) {
qvalue1 <- q8(x,n,0.25,i,f)
qvalue3 <- q8(x,n,0.75,i,f)
}
midm <- 0
myn <- 0
roundno4 <- round(n/4)
round3no4 <- round(3*n/4)
for (i in 1:n) {
if ((x[i]>=qvalue1) & (x[i]<=qvalue3)){
midm = midm + x[i]
myn = myn + 1
}
}
midm = midm / myn
return(midm)
}
(arm <- mean(x))
sqrtn <- sqrt(length(x))
(armse <- sd(x) / sqrtn)
(armose <- arm / armse)
(geo <- geomean(x))
(har <- harmean(x))
(qua <- quamean(x))
(win <- winmean(x))
(tri <- trimean(x))
(midr <- midrange(x))
midm <- array(NA,dim=8)
for (j in 1:8) midm[j] <- midmean(x,j)
midm
bitmap(file='test1.png')
lb <- win[,1] - 2*win[,2]
ub <- win[,1] + 2*win[,2]
if ((ylimmin == '') | (ylimmax == '')) plot(win[,1],type='b',main=main, xlab='j', pch=19, ylab='Winsorized Mean(j/n)', ylim=c(min(lb),max(ub))) else plot(win[,1],type='l',main=main, xlab='j', pch=19, ylab='Winsorized Mean(j/n)', ylim=c(ylimmin,ylimmax))
lines(ub,lty=3)
lines(lb,lty=3)
grid()
dev.off()
bitmap(file='test2.png')
lb <- tri[,1] - 2*tri[,2]
ub <- tri[,1] + 2*tri[,2]
if ((ylimmin == '') | (ylimmax == '')) plot(tri[,1],type='b',main=main, xlab='j', pch=19, ylab='Trimmed Mean(j/n)', ylim=c(min(lb),max(ub))) else plot(tri[,1],type='l',main=main, xlab='j', pch=19, ylab='Trimmed Mean(j/n)', ylim=c(ylimmin,ylimmax))
lines(ub,lty=3)
lines(lb,lty=3)
grid()
dev.off()
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Central Tendency - Ungrouped Data',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Measure',header=TRUE)
a<-table.element(a,'Value',header=TRUE)
a<-table.element(a,'S.E.',header=TRUE)
a<-table.element(a,'Value/S.E.',header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('arithmetic_mean.htm', 'Arithmetic Mean', 'click to view the definition of the Arithmetic Mean'),header=TRUE)
a<-table.element(a,arm)
a<-table.element(a,hyperlink('arithmetic_mean_standard_error.htm', armse, 'click to view the definition of the Standard Error of the Arithmetic Mean'))
a<-table.element(a,armose)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('geometric_mean.htm', 'Geometric Mean', 'click to view the definition of the Geometric Mean'),header=TRUE)
a<-table.element(a,geo)
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('harmonic_mean.htm', 'Harmonic Mean', 'click to view the definition of the Harmonic Mean'),header=TRUE)
a<-table.element(a,har)
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('quadratic_mean.htm', 'Quadratic Mean', 'click to view the definition of the Quadratic Mean'),header=TRUE)
a<-table.element(a,qua)
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
for (j in 1:length(win[,1])) {
a<-table.row.start(a)
mylabel <- paste('Winsorized Mean (',j)
mylabel <- paste(mylabel,'/')
mylabel <- paste(mylabel,length(win[,1]))
mylabel <- paste(mylabel,')')
a<-table.element(a,hyperlink('winsorized_mean.htm', mylabel, 'click to view the definition of the Winsorized Mean'),header=TRUE)
a<-table.element(a,win[j,1])
a<-table.element(a,win[j,2])
a<-table.element(a,win[j,1]/win[j,2])
a<-table.row.end(a)
}
for (j in 1:length(tri[,1])) {
a<-table.row.start(a)
mylabel <- paste('Trimmed Mean (',j)
mylabel <- paste(mylabel,'/')
mylabel <- paste(mylabel,length(tri[,1]))
mylabel <- paste(mylabel,')')
a<-table.element(a,hyperlink('arithmetic_mean.htm', mylabel, 'click to view the definition of the Trimmed Mean'),header=TRUE)
a<-table.element(a,tri[j,1])
a<-table.element(a,tri[j,2])
a<-table.element(a,tri[j,1]/tri[j,2])
a<-table.row.end(a)
}
a<-table.row.start(a)
a<-table.element(a,hyperlink('median_1.htm', 'Median', 'click to view the definition of the Median'),header=TRUE)
a<-table.element(a,median(x))
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('midrange.htm', 'Midrange', 'click to view the definition of the Midrange'),header=TRUE)
a<-table.element(a,midr)
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_1.htm','Weighted Average at Xnp',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[1])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_2.htm','Weighted Average at X(n+1)p',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[2])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_3.htm','Empirical Distribution Function',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[3])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_4.htm','Empirical Distribution Function - Averaging',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[4])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_5.htm','Empirical Distribution Function - Interpolation',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[5])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_6.htm','Closest Observation',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[6])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_7.htm','True Basic - Statistics Graphics Toolkit',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[7])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_8.htm','MS Excel (old versions)',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[8])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Number of observations',header=TRUE)
a<-table.element(a,length(x))
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable.tab')