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of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationWed, 25 Mar 2009 11:22:12 -0600
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2009/Mar/25/t12380017640z5zgji7qca5u79.htm/, Retrieved Thu, 28 Mar 2024 17:32:07 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=39186, Retrieved Thu, 28 Mar 2024 17:32:07 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact236
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [central tendancy ...] [2009-03-25 17:22:12] [d41d8cd98f00b204e9800998ecf8427e] [Current]
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Dataseries X:
517
540
454
292
445
483
545
355
370
372
422
445
471
413
307
308
389
377
521
420
413
384
466
434
263
334
334
416
309
334
350
337
277
439
433
455
372
409
471
382
417
405
410
357
360
329
359
393
448
593
535
449
742
631
513
526
677
631
547
533
433
427
470
418
485
464
439
452
423
537
384
380




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'Sir Ronald Aylmer Fisher' @ 193.190.124.24

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 3 seconds \tabularnewline
R Server & 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=39186&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]3 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Sir Ronald Aylmer Fisher' @ 193.190.124.24[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=39186&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=39186&T=0

As an alternative you can also use a QR Code:  

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

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'Sir Ronald Aylmer Fisher' @ 193.190.124.24







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean433.68055555555610.850488879117039.9687572041316
Geometric Mean424.591298494787
Harmonic Mean415.906568163138
Quadratic Mean443.213125933788
Winsorized Mean ( 1 / 24 )432.97222222222210.479280776634841.3169788510295
Winsorized Mean ( 2 / 24 )432.11111111111110.005330260862743.1880907321348
Winsorized Mean ( 3 / 24 )432.7361111111119.8876907924936643.7651338611465
Winsorized Mean ( 4 / 24 )430.6805555555569.3193604827723846.2135311056702
Winsorized Mean ( 5 / 24 )427.5555555555568.5986835457657449.7233737327264
Winsorized Mean ( 6 / 24 )429.0555555555568.2615426174385351.9340727783576
Winsorized Mean ( 7 / 24 )429.0555555555568.0847885745118653.0694837102108
Winsorized Mean ( 8 / 24 )428.7222222222228.0208848628848353.450738858758
Winsorized Mean ( 9 / 24 )428.4722222222227.9735962020703553.7363833537205
Winsorized Mean ( 10 / 24 )428.6111111111117.8524528317952754.5830863670556
Winsorized Mean ( 11 / 24 )429.5277777777787.3381325584452358.5336629390059
Winsorized Mean ( 12 / 24 )429.5277777777787.0593275131751560.8454242951797
Winsorized Mean ( 13 / 24 )429.1666666666676.8748879632356462.4252597222953
Winsorized Mean ( 14 / 24 )428.7777777777786.6784585333107464.2031054979416
Winsorized Mean ( 15 / 24 )423.1527777777785.6754509283673774.5584418081656
Winsorized Mean ( 16 / 24 )424.9305555555565.2691756662902980.6445984092088
Winsorized Mean ( 17 / 24 )422.5694444444444.7762464222553288.4731245179157
Winsorized Mean ( 18 / 24 )422.5694444444444.7762464222553288.4731245179157
Winsorized Mean ( 19 / 24 )423.6254.5446591769272293.2138106528872
Winsorized Mean ( 20 / 24 )423.3472222222224.2666941626453399.2213657891403
Winsorized Mean ( 21 / 24 )423.3472222222224.10175540316715103.211230463751
Winsorized Mean ( 22 / 24 )421.2083333333333.64209315193702115.650071473135
Winsorized Mean ( 23 / 24 )420.8888888888893.60053223523661116.896297933361
Winsorized Mean ( 24 / 24 )421.8888888888893.27600678927779128.781445224628
Trimmed Mean ( 1 / 24 )431.7142857142869.9417379965573343.4244279887261
Trimmed Mean ( 2 / 24 )430.3823529411769.289581554951546.3295736622039
Trimmed Mean ( 3 / 24 )429.4393939393948.8197470955151548.6906698444635
Trimmed Mean ( 4 / 24 )428.2031258.3034338519602251.5694028078411
Trimmed Mean ( 5 / 24 )427.4838709677427.9053677797558254.075140193028
Trimmed Mean ( 6 / 24 )427.4666666666677.6659223416624355.7619354351516
Trimmed Mean ( 7 / 24 )427.1379310344837.4707920182017457.1743839199123
Trimmed Mean ( 8 / 24 )426.7857142857147.2769300240650358.6491436463345
Trimmed Mean ( 9 / 24 )426.4629629629637.0521523823293860.4727379447378
Trimmed Mean ( 10 / 24 )426.1538461538466.7825737480769862.8306984903291
Trimmed Mean ( 11 / 24 )425.86.4722326841954165.7887348580288
Trimmed Mean ( 12 / 24 )425.2916666666676.2039765282916268.5514628766299
Trimmed Mean ( 13 / 24 )424.7391304347835.9269657072800871.6621541968897
Trimmed Mean ( 14 / 24 )424.1818181818185.6127001042385375.5753577251509
Trimmed Mean ( 15 / 24 )423.6190476190485.2494070657872780.6984564752013
Trimmed Mean ( 16 / 24 )423.6755.0406536384246984.051599334329
Trimmed Mean ( 17 / 24 )423.5263157894744.8619252346521687.1108244879817
Trimmed Mean ( 18 / 24 )423.6388888888894.7414338427696789.3482653005707
Trimmed Mean ( 19 / 24 )423.7647058823534.5683673317272392.7606462245965
Trimmed Mean ( 20 / 24 )423.781254.3869616145643896.6001727922758
Trimmed Mean ( 21 / 24 )423.8333333333334.2062032278374100.763874300778
Trimmed Mean ( 22 / 24 )423.8928571428573.98885328024329106.269352959757
Trimmed Mean ( 23 / 24 )424.2307692307693.81628401309953111.163311686075
Trimmed Mean ( 24 / 24 )424.6666666666673.550192210895119.617936562260
Median422.5
Midrange502.5
Midmean - Weighted Average at Xnp423.526315789474
Midmean - Weighted Average at X(n+1)p423.526315789474
Midmean - Empirical Distribution Function423.526315789474
Midmean - Empirical Distribution Function - Averaging423.526315789474
Midmean - Empirical Distribution Function - Interpolation423.526315789474
Midmean - Closest Observation423.526315789474
Midmean - True Basic - Statistics Graphics Toolkit423.526315789474
Midmean - MS Excel (old versions)423.526315789474
Number of observations72

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 433.680555555556 & 10.8504888791170 & 39.9687572041316 \tabularnewline
Geometric Mean & 424.591298494787 &  &  \tabularnewline
Harmonic Mean & 415.906568163138 &  &  \tabularnewline
Quadratic Mean & 443.213125933788 &  &  \tabularnewline
Winsorized Mean ( 1 / 24 ) & 432.972222222222 & 10.4792807766348 & 41.3169788510295 \tabularnewline
Winsorized Mean ( 2 / 24 ) & 432.111111111111 & 10.0053302608627 & 43.1880907321348 \tabularnewline
Winsorized Mean ( 3 / 24 ) & 432.736111111111 & 9.88769079249366 & 43.7651338611465 \tabularnewline
Winsorized Mean ( 4 / 24 ) & 430.680555555556 & 9.31936048277238 & 46.2135311056702 \tabularnewline
Winsorized Mean ( 5 / 24 ) & 427.555555555556 & 8.59868354576574 & 49.7233737327264 \tabularnewline
Winsorized Mean ( 6 / 24 ) & 429.055555555556 & 8.26154261743853 & 51.9340727783576 \tabularnewline
Winsorized Mean ( 7 / 24 ) & 429.055555555556 & 8.08478857451186 & 53.0694837102108 \tabularnewline
Winsorized Mean ( 8 / 24 ) & 428.722222222222 & 8.02088486288483 & 53.450738858758 \tabularnewline
Winsorized Mean ( 9 / 24 ) & 428.472222222222 & 7.97359620207035 & 53.7363833537205 \tabularnewline
Winsorized Mean ( 10 / 24 ) & 428.611111111111 & 7.85245283179527 & 54.5830863670556 \tabularnewline
Winsorized Mean ( 11 / 24 ) & 429.527777777778 & 7.33813255844523 & 58.5336629390059 \tabularnewline
Winsorized Mean ( 12 / 24 ) & 429.527777777778 & 7.05932751317515 & 60.8454242951797 \tabularnewline
Winsorized Mean ( 13 / 24 ) & 429.166666666667 & 6.87488796323564 & 62.4252597222953 \tabularnewline
Winsorized Mean ( 14 / 24 ) & 428.777777777778 & 6.67845853331074 & 64.2031054979416 \tabularnewline
Winsorized Mean ( 15 / 24 ) & 423.152777777778 & 5.67545092836737 & 74.5584418081656 \tabularnewline
Winsorized Mean ( 16 / 24 ) & 424.930555555556 & 5.26917566629029 & 80.6445984092088 \tabularnewline
Winsorized Mean ( 17 / 24 ) & 422.569444444444 & 4.77624642225532 & 88.4731245179157 \tabularnewline
Winsorized Mean ( 18 / 24 ) & 422.569444444444 & 4.77624642225532 & 88.4731245179157 \tabularnewline
Winsorized Mean ( 19 / 24 ) & 423.625 & 4.54465917692722 & 93.2138106528872 \tabularnewline
Winsorized Mean ( 20 / 24 ) & 423.347222222222 & 4.26669416264533 & 99.2213657891403 \tabularnewline
Winsorized Mean ( 21 / 24 ) & 423.347222222222 & 4.10175540316715 & 103.211230463751 \tabularnewline
Winsorized Mean ( 22 / 24 ) & 421.208333333333 & 3.64209315193702 & 115.650071473135 \tabularnewline
Winsorized Mean ( 23 / 24 ) & 420.888888888889 & 3.60053223523661 & 116.896297933361 \tabularnewline
Winsorized Mean ( 24 / 24 ) & 421.888888888889 & 3.27600678927779 & 128.781445224628 \tabularnewline
Trimmed Mean ( 1 / 24 ) & 431.714285714286 & 9.94173799655733 & 43.4244279887261 \tabularnewline
Trimmed Mean ( 2 / 24 ) & 430.382352941176 & 9.2895815549515 & 46.3295736622039 \tabularnewline
Trimmed Mean ( 3 / 24 ) & 429.439393939394 & 8.81974709551515 & 48.6906698444635 \tabularnewline
Trimmed Mean ( 4 / 24 ) & 428.203125 & 8.30343385196022 & 51.5694028078411 \tabularnewline
Trimmed Mean ( 5 / 24 ) & 427.483870967742 & 7.90536777975582 & 54.075140193028 \tabularnewline
Trimmed Mean ( 6 / 24 ) & 427.466666666667 & 7.66592234166243 & 55.7619354351516 \tabularnewline
Trimmed Mean ( 7 / 24 ) & 427.137931034483 & 7.47079201820174 & 57.1743839199123 \tabularnewline
Trimmed Mean ( 8 / 24 ) & 426.785714285714 & 7.27693002406503 & 58.6491436463345 \tabularnewline
Trimmed Mean ( 9 / 24 ) & 426.462962962963 & 7.05215238232938 & 60.4727379447378 \tabularnewline
Trimmed Mean ( 10 / 24 ) & 426.153846153846 & 6.78257374807698 & 62.8306984903291 \tabularnewline
Trimmed Mean ( 11 / 24 ) & 425.8 & 6.47223268419541 & 65.7887348580288 \tabularnewline
Trimmed Mean ( 12 / 24 ) & 425.291666666667 & 6.20397652829162 & 68.5514628766299 \tabularnewline
Trimmed Mean ( 13 / 24 ) & 424.739130434783 & 5.92696570728008 & 71.6621541968897 \tabularnewline
Trimmed Mean ( 14 / 24 ) & 424.181818181818 & 5.61270010423853 & 75.5753577251509 \tabularnewline
Trimmed Mean ( 15 / 24 ) & 423.619047619048 & 5.24940706578727 & 80.6984564752013 \tabularnewline
Trimmed Mean ( 16 / 24 ) & 423.675 & 5.04065363842469 & 84.051599334329 \tabularnewline
Trimmed Mean ( 17 / 24 ) & 423.526315789474 & 4.86192523465216 & 87.1108244879817 \tabularnewline
Trimmed Mean ( 18 / 24 ) & 423.638888888889 & 4.74143384276967 & 89.3482653005707 \tabularnewline
Trimmed Mean ( 19 / 24 ) & 423.764705882353 & 4.56836733172723 & 92.7606462245965 \tabularnewline
Trimmed Mean ( 20 / 24 ) & 423.78125 & 4.38696161456438 & 96.6001727922758 \tabularnewline
Trimmed Mean ( 21 / 24 ) & 423.833333333333 & 4.2062032278374 & 100.763874300778 \tabularnewline
Trimmed Mean ( 22 / 24 ) & 423.892857142857 & 3.98885328024329 & 106.269352959757 \tabularnewline
Trimmed Mean ( 23 / 24 ) & 424.230769230769 & 3.81628401309953 & 111.163311686075 \tabularnewline
Trimmed Mean ( 24 / 24 ) & 424.666666666667 & 3.550192210895 & 119.617936562260 \tabularnewline
Median & 422.5 &  &  \tabularnewline
Midrange & 502.5 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 423.526315789474 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 423.526315789474 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 423.526315789474 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 423.526315789474 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 423.526315789474 &  &  \tabularnewline
Midmean - Closest Observation & 423.526315789474 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 423.526315789474 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 423.526315789474 &  &  \tabularnewline
Number of observations & 72 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=39186&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]433.680555555556[/C][C]10.8504888791170[/C][C]39.9687572041316[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]424.591298494787[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]415.906568163138[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]443.213125933788[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 24 )[/C][C]432.972222222222[/C][C]10.4792807766348[/C][C]41.3169788510295[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 24 )[/C][C]432.111111111111[/C][C]10.0053302608627[/C][C]43.1880907321348[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 24 )[/C][C]432.736111111111[/C][C]9.88769079249366[/C][C]43.7651338611465[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 24 )[/C][C]430.680555555556[/C][C]9.31936048277238[/C][C]46.2135311056702[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 24 )[/C][C]427.555555555556[/C][C]8.59868354576574[/C][C]49.7233737327264[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 24 )[/C][C]429.055555555556[/C][C]8.26154261743853[/C][C]51.9340727783576[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 24 )[/C][C]429.055555555556[/C][C]8.08478857451186[/C][C]53.0694837102108[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 24 )[/C][C]428.722222222222[/C][C]8.02088486288483[/C][C]53.450738858758[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 24 )[/C][C]428.472222222222[/C][C]7.97359620207035[/C][C]53.7363833537205[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 24 )[/C][C]428.611111111111[/C][C]7.85245283179527[/C][C]54.5830863670556[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 24 )[/C][C]429.527777777778[/C][C]7.33813255844523[/C][C]58.5336629390059[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 24 )[/C][C]429.527777777778[/C][C]7.05932751317515[/C][C]60.8454242951797[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 24 )[/C][C]429.166666666667[/C][C]6.87488796323564[/C][C]62.4252597222953[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 24 )[/C][C]428.777777777778[/C][C]6.67845853331074[/C][C]64.2031054979416[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 24 )[/C][C]423.152777777778[/C][C]5.67545092836737[/C][C]74.5584418081656[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 24 )[/C][C]424.930555555556[/C][C]5.26917566629029[/C][C]80.6445984092088[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 24 )[/C][C]422.569444444444[/C][C]4.77624642225532[/C][C]88.4731245179157[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 24 )[/C][C]422.569444444444[/C][C]4.77624642225532[/C][C]88.4731245179157[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 24 )[/C][C]423.625[/C][C]4.54465917692722[/C][C]93.2138106528872[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 24 )[/C][C]423.347222222222[/C][C]4.26669416264533[/C][C]99.2213657891403[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 24 )[/C][C]423.347222222222[/C][C]4.10175540316715[/C][C]103.211230463751[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 24 )[/C][C]421.208333333333[/C][C]3.64209315193702[/C][C]115.650071473135[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 24 )[/C][C]420.888888888889[/C][C]3.60053223523661[/C][C]116.896297933361[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 24 )[/C][C]421.888888888889[/C][C]3.27600678927779[/C][C]128.781445224628[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 24 )[/C][C]431.714285714286[/C][C]9.94173799655733[/C][C]43.4244279887261[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 24 )[/C][C]430.382352941176[/C][C]9.2895815549515[/C][C]46.3295736622039[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 24 )[/C][C]429.439393939394[/C][C]8.81974709551515[/C][C]48.6906698444635[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 24 )[/C][C]428.203125[/C][C]8.30343385196022[/C][C]51.5694028078411[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 24 )[/C][C]427.483870967742[/C][C]7.90536777975582[/C][C]54.075140193028[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 24 )[/C][C]427.466666666667[/C][C]7.66592234166243[/C][C]55.7619354351516[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 24 )[/C][C]427.137931034483[/C][C]7.47079201820174[/C][C]57.1743839199123[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 24 )[/C][C]426.785714285714[/C][C]7.27693002406503[/C][C]58.6491436463345[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 24 )[/C][C]426.462962962963[/C][C]7.05215238232938[/C][C]60.4727379447378[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 24 )[/C][C]426.153846153846[/C][C]6.78257374807698[/C][C]62.8306984903291[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 24 )[/C][C]425.8[/C][C]6.47223268419541[/C][C]65.7887348580288[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 24 )[/C][C]425.291666666667[/C][C]6.20397652829162[/C][C]68.5514628766299[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 24 )[/C][C]424.739130434783[/C][C]5.92696570728008[/C][C]71.6621541968897[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 24 )[/C][C]424.181818181818[/C][C]5.61270010423853[/C][C]75.5753577251509[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 24 )[/C][C]423.619047619048[/C][C]5.24940706578727[/C][C]80.6984564752013[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 24 )[/C][C]423.675[/C][C]5.04065363842469[/C][C]84.051599334329[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 24 )[/C][C]423.526315789474[/C][C]4.86192523465216[/C][C]87.1108244879817[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 24 )[/C][C]423.638888888889[/C][C]4.74143384276967[/C][C]89.3482653005707[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 24 )[/C][C]423.764705882353[/C][C]4.56836733172723[/C][C]92.7606462245965[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 24 )[/C][C]423.78125[/C][C]4.38696161456438[/C][C]96.6001727922758[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 24 )[/C][C]423.833333333333[/C][C]4.2062032278374[/C][C]100.763874300778[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 24 )[/C][C]423.892857142857[/C][C]3.98885328024329[/C][C]106.269352959757[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 24 )[/C][C]424.230769230769[/C][C]3.81628401309953[/C][C]111.163311686075[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 24 )[/C][C]424.666666666667[/C][C]3.550192210895[/C][C]119.617936562260[/C][/ROW]
[ROW][C]Median[/C][C]422.5[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]502.5[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]423.526315789474[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]423.526315789474[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]423.526315789474[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]423.526315789474[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]423.526315789474[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]423.526315789474[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]423.526315789474[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]423.526315789474[/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=39186&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=39186&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 Mean433.68055555555610.850488879117039.9687572041316
Geometric Mean424.591298494787
Harmonic Mean415.906568163138
Quadratic Mean443.213125933788
Winsorized Mean ( 1 / 24 )432.97222222222210.479280776634841.3169788510295
Winsorized Mean ( 2 / 24 )432.11111111111110.005330260862743.1880907321348
Winsorized Mean ( 3 / 24 )432.7361111111119.8876907924936643.7651338611465
Winsorized Mean ( 4 / 24 )430.6805555555569.3193604827723846.2135311056702
Winsorized Mean ( 5 / 24 )427.5555555555568.5986835457657449.7233737327264
Winsorized Mean ( 6 / 24 )429.0555555555568.2615426174385351.9340727783576
Winsorized Mean ( 7 / 24 )429.0555555555568.0847885745118653.0694837102108
Winsorized Mean ( 8 / 24 )428.7222222222228.0208848628848353.450738858758
Winsorized Mean ( 9 / 24 )428.4722222222227.9735962020703553.7363833537205
Winsorized Mean ( 10 / 24 )428.6111111111117.8524528317952754.5830863670556
Winsorized Mean ( 11 / 24 )429.5277777777787.3381325584452358.5336629390059
Winsorized Mean ( 12 / 24 )429.5277777777787.0593275131751560.8454242951797
Winsorized Mean ( 13 / 24 )429.1666666666676.8748879632356462.4252597222953
Winsorized Mean ( 14 / 24 )428.7777777777786.6784585333107464.2031054979416
Winsorized Mean ( 15 / 24 )423.1527777777785.6754509283673774.5584418081656
Winsorized Mean ( 16 / 24 )424.9305555555565.2691756662902980.6445984092088
Winsorized Mean ( 17 / 24 )422.5694444444444.7762464222553288.4731245179157
Winsorized Mean ( 18 / 24 )422.5694444444444.7762464222553288.4731245179157
Winsorized Mean ( 19 / 24 )423.6254.5446591769272293.2138106528872
Winsorized Mean ( 20 / 24 )423.3472222222224.2666941626453399.2213657891403
Winsorized Mean ( 21 / 24 )423.3472222222224.10175540316715103.211230463751
Winsorized Mean ( 22 / 24 )421.2083333333333.64209315193702115.650071473135
Winsorized Mean ( 23 / 24 )420.8888888888893.60053223523661116.896297933361
Winsorized Mean ( 24 / 24 )421.8888888888893.27600678927779128.781445224628
Trimmed Mean ( 1 / 24 )431.7142857142869.9417379965573343.4244279887261
Trimmed Mean ( 2 / 24 )430.3823529411769.289581554951546.3295736622039
Trimmed Mean ( 3 / 24 )429.4393939393948.8197470955151548.6906698444635
Trimmed Mean ( 4 / 24 )428.2031258.3034338519602251.5694028078411
Trimmed Mean ( 5 / 24 )427.4838709677427.9053677797558254.075140193028
Trimmed Mean ( 6 / 24 )427.4666666666677.6659223416624355.7619354351516
Trimmed Mean ( 7 / 24 )427.1379310344837.4707920182017457.1743839199123
Trimmed Mean ( 8 / 24 )426.7857142857147.2769300240650358.6491436463345
Trimmed Mean ( 9 / 24 )426.4629629629637.0521523823293860.4727379447378
Trimmed Mean ( 10 / 24 )426.1538461538466.7825737480769862.8306984903291
Trimmed Mean ( 11 / 24 )425.86.4722326841954165.7887348580288
Trimmed Mean ( 12 / 24 )425.2916666666676.2039765282916268.5514628766299
Trimmed Mean ( 13 / 24 )424.7391304347835.9269657072800871.6621541968897
Trimmed Mean ( 14 / 24 )424.1818181818185.6127001042385375.5753577251509
Trimmed Mean ( 15 / 24 )423.6190476190485.2494070657872780.6984564752013
Trimmed Mean ( 16 / 24 )423.6755.0406536384246984.051599334329
Trimmed Mean ( 17 / 24 )423.5263157894744.8619252346521687.1108244879817
Trimmed Mean ( 18 / 24 )423.6388888888894.7414338427696789.3482653005707
Trimmed Mean ( 19 / 24 )423.7647058823534.5683673317272392.7606462245965
Trimmed Mean ( 20 / 24 )423.781254.3869616145643896.6001727922758
Trimmed Mean ( 21 / 24 )423.8333333333334.2062032278374100.763874300778
Trimmed Mean ( 22 / 24 )423.8928571428573.98885328024329106.269352959757
Trimmed Mean ( 23 / 24 )424.2307692307693.81628401309953111.163311686075
Trimmed Mean ( 24 / 24 )424.6666666666673.550192210895119.617936562260
Median422.5
Midrange502.5
Midmean - Weighted Average at Xnp423.526315789474
Midmean - Weighted Average at X(n+1)p423.526315789474
Midmean - Empirical Distribution Function423.526315789474
Midmean - Empirical Distribution Function - Averaging423.526315789474
Midmean - Empirical Distribution Function - Interpolation423.526315789474
Midmean - Closest Observation423.526315789474
Midmean - True Basic - Statistics Graphics Toolkit423.526315789474
Midmean - MS Excel (old versions)423.526315789474
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')