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Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationThu, 08 Oct 2015 19:15:25 +0100
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2015/Oct/08/t14443281556p0q1mo1sk1wrfm.htm/, Retrieved Wed, 15 May 2024 14:10:42 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=281617, Retrieved Wed, 15 May 2024 14:10:42 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact59
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [] [2015-10-08 18:15:25] [4535d628e97572fda841f25b347e529f] [Current]
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Dataseries X:
340,7
343,5
345,3
346,9
349
351,4
353
355
360,1
364,7
366,5
369
369,9
370,8
374,5
378,4
381,3
383,5
387,6
391,7
395,4
399,3
403,3
406,6
410,5
413,5
418,7
421,7
422,8
425,8
427,6
431
434,3
437,6
440,4
443,5
446,2
446,2
449,7
454,2
458,4
461,1
464
466,2
468,7
471,8
474,9
477,5
480
482,8
485,7
488,5
492
495,1
498,5
502,2
502,1
510
515
520,4
525,2
530,1
534,5
538,5
544,4
548,4
551,9
554,9
558,1
561,3
564,4
567
568,7
570,9
572,5
574,6
577,1
580,9
583,3
586,5




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Sir Maurice George Kendall' @ kendall.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 & 'Sir Maurice George Kendall' @ kendall.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=281617&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]'Sir Maurice George Kendall' @ kendall.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=281617&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=281617&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'Sir Maurice George Kendall' @ kendall.wessa.net







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean458.998.3574376789158354.9199428860764
Geometric Mean452.945687941866
Harmonic Mean446.923628289951
Quadratic Mean464.962057054121
Winsorized Mean ( 1 / 26 )458.9858.3436015619944655.0104168553183
Winsorized Mean ( 2 / 26 )458.978.3245500885762755.1345111887598
Winsorized Mean ( 3 / 26 )458.88758.2881590417072155.3666378372824
Winsorized Mean ( 4 / 26 )458.86758.2479417791211555.6341827195698
Winsorized Mean ( 5 / 26 )458.886258.1996836817173355.9638966345945
Winsorized Mean ( 6 / 26 )458.886258.1589200901334756.2435034208667
Winsorized Mean ( 7 / 26 )458.868758.0970833148776256.6708692692926
Winsorized Mean ( 8 / 26 )459.208757.9864945720786557.4981609084699
Winsorized Mean ( 9 / 26 )459.433757.8566254278241458.4772373610839
Winsorized Mean ( 10 / 26 )459.271257.7573968771318859.204299750847
Winsorized Mean ( 11 / 26 )459.1757.6329497881457660.1569527829352
Winsorized Mean ( 12 / 26 )458.837.5346584006967360.895925946367
Winsorized Mean ( 13 / 26 )458.488757.4347052229643561.6687193708525
Winsorized Mean ( 14 / 26 )458.523757.2419882060401163.3146225807953
Winsorized Mean ( 15 / 26 )458.5057.0184363679264765.3286538430868
Winsorized Mean ( 16 / 26 )457.9056.7543398847319667.7941897823478
Winsorized Mean ( 17 / 26 )457.52256.5600560488401369.7436876443904
Winsorized Mean ( 18 / 26 )457.4556.283250010639672.8054747503886
Winsorized Mean ( 19 / 26 )457.2655.9782242240834176.488432494368
Winsorized Mean ( 20 / 26 )456.995.6793671090618680.4649516793584
Winsorized Mean ( 21 / 26 )456.596255.341242519998285.4850249338901
Winsorized Mean ( 22 / 26 )456.321255.0041984568371691.1876804918749
Winsorized Mean ( 23 / 26 )455.02754.5783056726564899.3877500835323
Winsorized Mean ( 24 / 26 )456.16754.4194985736399103.217026185009
Winsorized Mean ( 25 / 26 )455.984.15045841604167109.862563190037
Winsorized Mean ( 26 / 26 )456.5653.79127792322579120.425093924935
Trimmed Mean ( 1 / 26 )458.8717948717958.2741401323555355.458547659521
Trimmed Mean ( 2 / 26 )458.7526315789478.1905489980904256.0099978262633
Trimmed Mean ( 3 / 26 )458.6351351351358.1019116023390256.6082620554299
Trimmed Mean ( 4 / 26 )458.5416666666678.0110598798823857.2385768602443
Trimmed Mean ( 5 / 26 )458.4485714285717.9152304224975357.9198010616999
Trimmed Mean ( 6 / 26 )458.3455882352947.8133385404448758.6619389218475
Trimmed Mean ( 7 / 26 )458.2363636363647.7002239050676659.5094856053198
Trimmed Mean ( 8 / 26 )458.12343757.5774459558106860.4588195246306
Trimmed Mean ( 9 / 26 )457.9483870967747.4523608608618161.4501089851701
Trimmed Mean ( 10 / 26 )457.7283333333337.3263976286307362.4765889779969
Trimmed Mean ( 11 / 26 )457.5155172413797.1911309400370663.6221925391643
Trimmed Mean ( 12 / 26 )457.37.048216132423264.8816652906441
Trimmed Mean ( 13 / 26 )457.1111111111116.8893570206803366.3503298985615
Trimmed Mean ( 14 / 26 )456.9480769230776.7099987807668868.0995767440144
Trimmed Mean ( 15 / 26 )456.7686.5228361428859170.0259810294592
Trimmed Mean ( 16 / 26 )456.5756.3308042496043572.1195889177167
Trimmed Mean ( 17 / 26 )456.4304347826096.1400489931523674.3366112048355
Trimmed Mean ( 18 / 26 )456.3136363636365.9341484896433476.8962281884292
Trimmed Mean ( 19 / 26 )456.1928571428575.7259575556106279.6710161946368
Trimmed Mean ( 20 / 26 )456.085.520166060304182.6207028951
Trimmed Mean ( 21 / 26 )455.9842105263165.3149197209683685.7932451411019
Trimmed Mean ( 22 / 26 )455.9194444444445.1192987172327689.0589648362797
Trimmed Mean ( 23 / 26 )455.8764705882354.9351878869927892.3726676728451
Trimmed Mean ( 24 / 26 )455.968754.7892277424394495.2071554166158
Trimmed Mean ( 25 / 26 )455.9466666666674.6185152944322198.7214803026261
Trimmed Mean ( 26 / 26 )455.9428571428574.44620826678475102.546446271751
Median456.3
Midrange463.6
Midmean - Weighted Average at Xnp454.509756097561
Midmean - Weighted Average at X(n+1)p456.08
Midmean - Empirical Distribution Function454.509756097561
Midmean - Empirical Distribution Function - Averaging456.08
Midmean - Empirical Distribution Function - Interpolation456.08
Midmean - Closest Observation454.509756097561
Midmean - True Basic - Statistics Graphics Toolkit456.08
Midmean - MS Excel (old versions)456.192857142857
Number of observations80

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 458.99 & 8.35743767891583 & 54.9199428860764 \tabularnewline
Geometric Mean & 452.945687941866 &  &  \tabularnewline
Harmonic Mean & 446.923628289951 &  &  \tabularnewline
Quadratic Mean & 464.962057054121 &  &  \tabularnewline
Winsorized Mean ( 1 / 26 ) & 458.985 & 8.34360156199446 & 55.0104168553183 \tabularnewline
Winsorized Mean ( 2 / 26 ) & 458.97 & 8.32455008857627 & 55.1345111887598 \tabularnewline
Winsorized Mean ( 3 / 26 ) & 458.8875 & 8.28815904170721 & 55.3666378372824 \tabularnewline
Winsorized Mean ( 4 / 26 ) & 458.8675 & 8.24794177912115 & 55.6341827195698 \tabularnewline
Winsorized Mean ( 5 / 26 ) & 458.88625 & 8.19968368171733 & 55.9638966345945 \tabularnewline
Winsorized Mean ( 6 / 26 ) & 458.88625 & 8.15892009013347 & 56.2435034208667 \tabularnewline
Winsorized Mean ( 7 / 26 ) & 458.86875 & 8.09708331487762 & 56.6708692692926 \tabularnewline
Winsorized Mean ( 8 / 26 ) & 459.20875 & 7.98649457207865 & 57.4981609084699 \tabularnewline
Winsorized Mean ( 9 / 26 ) & 459.43375 & 7.85662542782414 & 58.4772373610839 \tabularnewline
Winsorized Mean ( 10 / 26 ) & 459.27125 & 7.75739687713188 & 59.204299750847 \tabularnewline
Winsorized Mean ( 11 / 26 ) & 459.175 & 7.63294978814576 & 60.1569527829352 \tabularnewline
Winsorized Mean ( 12 / 26 ) & 458.83 & 7.53465840069673 & 60.895925946367 \tabularnewline
Winsorized Mean ( 13 / 26 ) & 458.48875 & 7.43470522296435 & 61.6687193708525 \tabularnewline
Winsorized Mean ( 14 / 26 ) & 458.52375 & 7.24198820604011 & 63.3146225807953 \tabularnewline
Winsorized Mean ( 15 / 26 ) & 458.505 & 7.01843636792647 & 65.3286538430868 \tabularnewline
Winsorized Mean ( 16 / 26 ) & 457.905 & 6.75433988473196 & 67.7941897823478 \tabularnewline
Winsorized Mean ( 17 / 26 ) & 457.5225 & 6.56005604884013 & 69.7436876443904 \tabularnewline
Winsorized Mean ( 18 / 26 ) & 457.455 & 6.2832500106396 & 72.8054747503886 \tabularnewline
Winsorized Mean ( 19 / 26 ) & 457.265 & 5.97822422408341 & 76.488432494368 \tabularnewline
Winsorized Mean ( 20 / 26 ) & 456.99 & 5.67936710906186 & 80.4649516793584 \tabularnewline
Winsorized Mean ( 21 / 26 ) & 456.59625 & 5.3412425199982 & 85.4850249338901 \tabularnewline
Winsorized Mean ( 22 / 26 ) & 456.32125 & 5.00419845683716 & 91.1876804918749 \tabularnewline
Winsorized Mean ( 23 / 26 ) & 455.0275 & 4.57830567265648 & 99.3877500835323 \tabularnewline
Winsorized Mean ( 24 / 26 ) & 456.1675 & 4.4194985736399 & 103.217026185009 \tabularnewline
Winsorized Mean ( 25 / 26 ) & 455.98 & 4.15045841604167 & 109.862563190037 \tabularnewline
Winsorized Mean ( 26 / 26 ) & 456.565 & 3.79127792322579 & 120.425093924935 \tabularnewline
Trimmed Mean ( 1 / 26 ) & 458.871794871795 & 8.27414013235553 & 55.458547659521 \tabularnewline
Trimmed Mean ( 2 / 26 ) & 458.752631578947 & 8.19054899809042 & 56.0099978262633 \tabularnewline
Trimmed Mean ( 3 / 26 ) & 458.635135135135 & 8.10191160233902 & 56.6082620554299 \tabularnewline
Trimmed Mean ( 4 / 26 ) & 458.541666666667 & 8.01105987988238 & 57.2385768602443 \tabularnewline
Trimmed Mean ( 5 / 26 ) & 458.448571428571 & 7.91523042249753 & 57.9198010616999 \tabularnewline
Trimmed Mean ( 6 / 26 ) & 458.345588235294 & 7.81333854044487 & 58.6619389218475 \tabularnewline
Trimmed Mean ( 7 / 26 ) & 458.236363636364 & 7.70022390506766 & 59.5094856053198 \tabularnewline
Trimmed Mean ( 8 / 26 ) & 458.1234375 & 7.57744595581068 & 60.4588195246306 \tabularnewline
Trimmed Mean ( 9 / 26 ) & 457.948387096774 & 7.45236086086181 & 61.4501089851701 \tabularnewline
Trimmed Mean ( 10 / 26 ) & 457.728333333333 & 7.32639762863073 & 62.4765889779969 \tabularnewline
Trimmed Mean ( 11 / 26 ) & 457.515517241379 & 7.19113094003706 & 63.6221925391643 \tabularnewline
Trimmed Mean ( 12 / 26 ) & 457.3 & 7.0482161324232 & 64.8816652906441 \tabularnewline
Trimmed Mean ( 13 / 26 ) & 457.111111111111 & 6.88935702068033 & 66.3503298985615 \tabularnewline
Trimmed Mean ( 14 / 26 ) & 456.948076923077 & 6.70999878076688 & 68.0995767440144 \tabularnewline
Trimmed Mean ( 15 / 26 ) & 456.768 & 6.52283614288591 & 70.0259810294592 \tabularnewline
Trimmed Mean ( 16 / 26 ) & 456.575 & 6.33080424960435 & 72.1195889177167 \tabularnewline
Trimmed Mean ( 17 / 26 ) & 456.430434782609 & 6.14004899315236 & 74.3366112048355 \tabularnewline
Trimmed Mean ( 18 / 26 ) & 456.313636363636 & 5.93414848964334 & 76.8962281884292 \tabularnewline
Trimmed Mean ( 19 / 26 ) & 456.192857142857 & 5.72595755561062 & 79.6710161946368 \tabularnewline
Trimmed Mean ( 20 / 26 ) & 456.08 & 5.5201660603041 & 82.6207028951 \tabularnewline
Trimmed Mean ( 21 / 26 ) & 455.984210526316 & 5.31491972096836 & 85.7932451411019 \tabularnewline
Trimmed Mean ( 22 / 26 ) & 455.919444444444 & 5.11929871723276 & 89.0589648362797 \tabularnewline
Trimmed Mean ( 23 / 26 ) & 455.876470588235 & 4.93518788699278 & 92.3726676728451 \tabularnewline
Trimmed Mean ( 24 / 26 ) & 455.96875 & 4.78922774243944 & 95.2071554166158 \tabularnewline
Trimmed Mean ( 25 / 26 ) & 455.946666666667 & 4.61851529443221 & 98.7214803026261 \tabularnewline
Trimmed Mean ( 26 / 26 ) & 455.942857142857 & 4.44620826678475 & 102.546446271751 \tabularnewline
Median & 456.3 &  &  \tabularnewline
Midrange & 463.6 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 454.509756097561 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 456.08 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 454.509756097561 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 456.08 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 456.08 &  &  \tabularnewline
Midmean - Closest Observation & 454.509756097561 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 456.08 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 456.192857142857 &  &  \tabularnewline
Number of observations & 80 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=281617&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]458.99[/C][C]8.35743767891583[/C][C]54.9199428860764[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]452.945687941866[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]446.923628289951[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]464.962057054121[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 26 )[/C][C]458.985[/C][C]8.34360156199446[/C][C]55.0104168553183[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 26 )[/C][C]458.97[/C][C]8.32455008857627[/C][C]55.1345111887598[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 26 )[/C][C]458.8875[/C][C]8.28815904170721[/C][C]55.3666378372824[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 26 )[/C][C]458.8675[/C][C]8.24794177912115[/C][C]55.6341827195698[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 26 )[/C][C]458.88625[/C][C]8.19968368171733[/C][C]55.9638966345945[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 26 )[/C][C]458.88625[/C][C]8.15892009013347[/C][C]56.2435034208667[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 26 )[/C][C]458.86875[/C][C]8.09708331487762[/C][C]56.6708692692926[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 26 )[/C][C]459.20875[/C][C]7.98649457207865[/C][C]57.4981609084699[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 26 )[/C][C]459.43375[/C][C]7.85662542782414[/C][C]58.4772373610839[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 26 )[/C][C]459.27125[/C][C]7.75739687713188[/C][C]59.204299750847[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 26 )[/C][C]459.175[/C][C]7.63294978814576[/C][C]60.1569527829352[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 26 )[/C][C]458.83[/C][C]7.53465840069673[/C][C]60.895925946367[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 26 )[/C][C]458.48875[/C][C]7.43470522296435[/C][C]61.6687193708525[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 26 )[/C][C]458.52375[/C][C]7.24198820604011[/C][C]63.3146225807953[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 26 )[/C][C]458.505[/C][C]7.01843636792647[/C][C]65.3286538430868[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 26 )[/C][C]457.905[/C][C]6.75433988473196[/C][C]67.7941897823478[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 26 )[/C][C]457.5225[/C][C]6.56005604884013[/C][C]69.7436876443904[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 26 )[/C][C]457.455[/C][C]6.2832500106396[/C][C]72.8054747503886[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 26 )[/C][C]457.265[/C][C]5.97822422408341[/C][C]76.488432494368[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 26 )[/C][C]456.99[/C][C]5.67936710906186[/C][C]80.4649516793584[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 26 )[/C][C]456.59625[/C][C]5.3412425199982[/C][C]85.4850249338901[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 26 )[/C][C]456.32125[/C][C]5.00419845683716[/C][C]91.1876804918749[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 26 )[/C][C]455.0275[/C][C]4.57830567265648[/C][C]99.3877500835323[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 26 )[/C][C]456.1675[/C][C]4.4194985736399[/C][C]103.217026185009[/C][/ROW]
[ROW][C]Winsorized Mean ( 25 / 26 )[/C][C]455.98[/C][C]4.15045841604167[/C][C]109.862563190037[/C][/ROW]
[ROW][C]Winsorized Mean ( 26 / 26 )[/C][C]456.565[/C][C]3.79127792322579[/C][C]120.425093924935[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 26 )[/C][C]458.871794871795[/C][C]8.27414013235553[/C][C]55.458547659521[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 26 )[/C][C]458.752631578947[/C][C]8.19054899809042[/C][C]56.0099978262633[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 26 )[/C][C]458.635135135135[/C][C]8.10191160233902[/C][C]56.6082620554299[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 26 )[/C][C]458.541666666667[/C][C]8.01105987988238[/C][C]57.2385768602443[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 26 )[/C][C]458.448571428571[/C][C]7.91523042249753[/C][C]57.9198010616999[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 26 )[/C][C]458.345588235294[/C][C]7.81333854044487[/C][C]58.6619389218475[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 26 )[/C][C]458.236363636364[/C][C]7.70022390506766[/C][C]59.5094856053198[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 26 )[/C][C]458.1234375[/C][C]7.57744595581068[/C][C]60.4588195246306[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 26 )[/C][C]457.948387096774[/C][C]7.45236086086181[/C][C]61.4501089851701[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 26 )[/C][C]457.728333333333[/C][C]7.32639762863073[/C][C]62.4765889779969[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 26 )[/C][C]457.515517241379[/C][C]7.19113094003706[/C][C]63.6221925391643[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 26 )[/C][C]457.3[/C][C]7.0482161324232[/C][C]64.8816652906441[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 26 )[/C][C]457.111111111111[/C][C]6.88935702068033[/C][C]66.3503298985615[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 26 )[/C][C]456.948076923077[/C][C]6.70999878076688[/C][C]68.0995767440144[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 26 )[/C][C]456.768[/C][C]6.52283614288591[/C][C]70.0259810294592[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 26 )[/C][C]456.575[/C][C]6.33080424960435[/C][C]72.1195889177167[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 26 )[/C][C]456.430434782609[/C][C]6.14004899315236[/C][C]74.3366112048355[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 26 )[/C][C]456.313636363636[/C][C]5.93414848964334[/C][C]76.8962281884292[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 26 )[/C][C]456.192857142857[/C][C]5.72595755561062[/C][C]79.6710161946368[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 26 )[/C][C]456.08[/C][C]5.5201660603041[/C][C]82.6207028951[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 26 )[/C][C]455.984210526316[/C][C]5.31491972096836[/C][C]85.7932451411019[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 26 )[/C][C]455.919444444444[/C][C]5.11929871723276[/C][C]89.0589648362797[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 26 )[/C][C]455.876470588235[/C][C]4.93518788699278[/C][C]92.3726676728451[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 26 )[/C][C]455.96875[/C][C]4.78922774243944[/C][C]95.2071554166158[/C][/ROW]
[ROW][C]Trimmed Mean ( 25 / 26 )[/C][C]455.946666666667[/C][C]4.61851529443221[/C][C]98.7214803026261[/C][/ROW]
[ROW][C]Trimmed Mean ( 26 / 26 )[/C][C]455.942857142857[/C][C]4.44620826678475[/C][C]102.546446271751[/C][/ROW]
[ROW][C]Median[/C][C]456.3[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]463.6[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]454.509756097561[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]456.08[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]454.509756097561[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]456.08[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]456.08[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]454.509756097561[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]456.08[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]456.192857142857[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]80[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=281617&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=281617&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 Mean458.998.3574376789158354.9199428860764
Geometric Mean452.945687941866
Harmonic Mean446.923628289951
Quadratic Mean464.962057054121
Winsorized Mean ( 1 / 26 )458.9858.3436015619944655.0104168553183
Winsorized Mean ( 2 / 26 )458.978.3245500885762755.1345111887598
Winsorized Mean ( 3 / 26 )458.88758.2881590417072155.3666378372824
Winsorized Mean ( 4 / 26 )458.86758.2479417791211555.6341827195698
Winsorized Mean ( 5 / 26 )458.886258.1996836817173355.9638966345945
Winsorized Mean ( 6 / 26 )458.886258.1589200901334756.2435034208667
Winsorized Mean ( 7 / 26 )458.868758.0970833148776256.6708692692926
Winsorized Mean ( 8 / 26 )459.208757.9864945720786557.4981609084699
Winsorized Mean ( 9 / 26 )459.433757.8566254278241458.4772373610839
Winsorized Mean ( 10 / 26 )459.271257.7573968771318859.204299750847
Winsorized Mean ( 11 / 26 )459.1757.6329497881457660.1569527829352
Winsorized Mean ( 12 / 26 )458.837.5346584006967360.895925946367
Winsorized Mean ( 13 / 26 )458.488757.4347052229643561.6687193708525
Winsorized Mean ( 14 / 26 )458.523757.2419882060401163.3146225807953
Winsorized Mean ( 15 / 26 )458.5057.0184363679264765.3286538430868
Winsorized Mean ( 16 / 26 )457.9056.7543398847319667.7941897823478
Winsorized Mean ( 17 / 26 )457.52256.5600560488401369.7436876443904
Winsorized Mean ( 18 / 26 )457.4556.283250010639672.8054747503886
Winsorized Mean ( 19 / 26 )457.2655.9782242240834176.488432494368
Winsorized Mean ( 20 / 26 )456.995.6793671090618680.4649516793584
Winsorized Mean ( 21 / 26 )456.596255.341242519998285.4850249338901
Winsorized Mean ( 22 / 26 )456.321255.0041984568371691.1876804918749
Winsorized Mean ( 23 / 26 )455.02754.5783056726564899.3877500835323
Winsorized Mean ( 24 / 26 )456.16754.4194985736399103.217026185009
Winsorized Mean ( 25 / 26 )455.984.15045841604167109.862563190037
Winsorized Mean ( 26 / 26 )456.5653.79127792322579120.425093924935
Trimmed Mean ( 1 / 26 )458.8717948717958.2741401323555355.458547659521
Trimmed Mean ( 2 / 26 )458.7526315789478.1905489980904256.0099978262633
Trimmed Mean ( 3 / 26 )458.6351351351358.1019116023390256.6082620554299
Trimmed Mean ( 4 / 26 )458.5416666666678.0110598798823857.2385768602443
Trimmed Mean ( 5 / 26 )458.4485714285717.9152304224975357.9198010616999
Trimmed Mean ( 6 / 26 )458.3455882352947.8133385404448758.6619389218475
Trimmed Mean ( 7 / 26 )458.2363636363647.7002239050676659.5094856053198
Trimmed Mean ( 8 / 26 )458.12343757.5774459558106860.4588195246306
Trimmed Mean ( 9 / 26 )457.9483870967747.4523608608618161.4501089851701
Trimmed Mean ( 10 / 26 )457.7283333333337.3263976286307362.4765889779969
Trimmed Mean ( 11 / 26 )457.5155172413797.1911309400370663.6221925391643
Trimmed Mean ( 12 / 26 )457.37.048216132423264.8816652906441
Trimmed Mean ( 13 / 26 )457.1111111111116.8893570206803366.3503298985615
Trimmed Mean ( 14 / 26 )456.9480769230776.7099987807668868.0995767440144
Trimmed Mean ( 15 / 26 )456.7686.5228361428859170.0259810294592
Trimmed Mean ( 16 / 26 )456.5756.3308042496043572.1195889177167
Trimmed Mean ( 17 / 26 )456.4304347826096.1400489931523674.3366112048355
Trimmed Mean ( 18 / 26 )456.3136363636365.9341484896433476.8962281884292
Trimmed Mean ( 19 / 26 )456.1928571428575.7259575556106279.6710161946368
Trimmed Mean ( 20 / 26 )456.085.520166060304182.6207028951
Trimmed Mean ( 21 / 26 )455.9842105263165.3149197209683685.7932451411019
Trimmed Mean ( 22 / 26 )455.9194444444445.1192987172327689.0589648362797
Trimmed Mean ( 23 / 26 )455.8764705882354.9351878869927892.3726676728451
Trimmed Mean ( 24 / 26 )455.968754.7892277424394495.2071554166158
Trimmed Mean ( 25 / 26 )455.9466666666674.6185152944322198.7214803026261
Trimmed Mean ( 26 / 26 )455.9428571428574.44620826678475102.546446271751
Median456.3
Midrange463.6
Midmean - Weighted Average at Xnp454.509756097561
Midmean - Weighted Average at X(n+1)p456.08
Midmean - Empirical Distribution Function454.509756097561
Midmean - Empirical Distribution Function - Averaging456.08
Midmean - Empirical Distribution Function - Interpolation456.08
Midmean - Closest Observation454.509756097561
Midmean - True Basic - Statistics Graphics Toolkit456.08
Midmean - MS Excel (old versions)456.192857142857
Number of observations80



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')