Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationTue, 08 Mar 2016 14:43:59 +0000
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2016/Mar/08/t1457450401f5li22hdmupec03.htm/, Retrieved Sun, 28 Apr 2024 19:15:46 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=293679, Retrieved Sun, 28 Apr 2024 19:15:46 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact104
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [] [2016-03-08 14:43:59] [ac7ea8eb5659db737c8f3ddefda617c5] [Current]
Feedback Forum

Post a new message
Dataseries X:
340,4
343,2
345
346,6
348,7
351,1
352,7
354,8
359,8
364,4
366,2
368,8
369,6
370,6
374,2
378,1
381
383,2
387,3
391,4
395,1
399,1
403
406,3
410,2
413,3
418,4
421,4
422,5
425,5
427,3
430,7
433,2
437,5
439,9
443
445,6
446,2
449,3
453,9
458
461,2
463,7
466
468,3
471,7
474,7
477,3
479,8
482,6
485,6
488,5
492
494,8
498,3
502,1
505,8
511,7
516,6
521,3
526,1
530,4
534,7
538,4
544,6
547,7
551,4
554,3
557,5
560,7
563,8
566,2
567,2
569,3
570,9
573
575,1
578,1
581
584,4




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 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 & 2 seconds \tabularnewline
R Server & 'Sir Maurice George Kendall' @ kendall.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=293679&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]2 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=293679&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=293679&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 time2 seconds
R Server'Sir Maurice George Kendall' @ kendall.wessa.net







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean458.666258.3374169845277955.0129915357685
Geometric Mean452.639355957976
Harmonic Mean446.628373208702
Quadratic Mean464.614052870767
Winsorized Mean ( 1 / 26 )458.658758.3231913863396955.1061159968959
Winsorized Mean ( 2 / 26 )458.631258.3019941164358555.2435045806677
Winsorized Mean ( 3 / 26 )458.578758.2713780734159555.4416381320863
Winsorized Mean ( 4 / 26 )458.578758.2349178774639955.6871066383024
Winsorized Mean ( 5 / 26 )458.59758.1868465001542956.0163794437036
Winsorized Mean ( 6 / 26 )458.59758.1462610773985956.295458203808
Winsorized Mean ( 7 / 26 )458.59758.0847843052649456.7235293712603
Winsorized Mean ( 8 / 26 )458.99757.9878525208950657.4619397140006
Winsorized Mean ( 9 / 26 )459.2457.8619945652680158.4132940041462
Winsorized Mean ( 10 / 26 )459.08257.7630536808997859.1368447096439
Winsorized Mean ( 11 / 26 )4597.6368787944761260.1030882318052
Winsorized Mean ( 12 / 26 )458.647.5412166194365360.817772933072
Winsorized Mean ( 13 / 26 )458.331257.4418098285649161.5886807857848
Winsorized Mean ( 14 / 26 )458.313757.2467017254709163.2444617375524
Winsorized Mean ( 15 / 26 )458.463757.0498797556291165.0314283210194
Winsorized Mean ( 16 / 26 )457.803756.7771564468837567.5510080943322
Winsorized Mean ( 17 / 26 )457.4856.5928087260843769.3915171829521
Winsorized Mean ( 18 / 26 )457.446.319768712720372.382395748008
Winsorized Mean ( 19 / 26 )457.39256.0357392274809175.7806927637757
Winsorized Mean ( 20 / 26 )457.11755.7369603866375179.6793892920569
Winsorized Mean ( 21 / 26 )456.933755.4208484504973584.2919248107882
Winsorized Mean ( 22 / 26 )456.658755.0907189980326389.7041754173587
Winsorized Mean ( 23 / 26 )455.911254.7352078115111596.2811492436918
Winsorized Mean ( 24 / 26 )455.971254.43401166821789102.834923342289
Winsorized Mean ( 25 / 26 )455.75254.1527884390636109.746139657133
Winsorized Mean ( 26 / 26 )456.27253.79380740212657120.26770250494
Trimmed Mean ( 1 / 26 )458.5705128205138.257455507506955.534118519152
Trimmed Mean ( 2 / 26 )458.4776315789478.1780895977647156.0617031762848
Trimmed Mean ( 3 / 26 )458.3945945945958.0955438379963556.6230760734225
Trimmed Mean ( 4 / 26 )458.3263888888898.0091501840580157.2253458052485
Trimmed Mean ( 5 / 26 )458.2542857142867.9171236923451957.8814104113792
Trimmed Mean ( 6 / 26 )458.1735294117657.8195315044065658.5934757285099
Trimmed Mean ( 7 / 26 )458.0878787878797.7113229238657659.4045773093153
Trimmed Mean ( 8 / 26 )457.9968757.5941239844383560.3093755038123
Trimmed Mean ( 9 / 26 )457.8354838709687.4724274048569961.2699808329192
Trimmed Mean ( 10 / 26 )457.6266666666677.3495243193883462.2661612887557
Trimmed Mean ( 11 / 26 )457.4258620689667.217760812430863.3750374882419
Trimmed Mean ( 12 / 26 )457.2214285714297.0792795850576364.5858696605929
Trimmed Mean ( 13 / 26 )457.0462962962966.9251381340621565.9981486937073
Trimmed Mean ( 14 / 26 )456.8942307692316.7512829982630767.67517091
Trimmed Mean ( 15 / 26 )456.7326.5711909522256569.5052089218783
Trimmed Mean ( 16 / 26 )456.5395833333336.3820029951692171.5354699267466
Trimmed Mean ( 17 / 26 )456.4021739130436.196405759746973.655953404137
Trimmed Mean ( 18 / 26 )456.2863636363645.9945743535133676.1165575282153
Trimmed Mean ( 19 / 26 )456.1642857142865.7903909562809778.7795313232648
Trimmed Mean ( 20 / 26 )456.0355.5844456029500181.661642430378
Trimmed Mean ( 21 / 26 )455.9210526315795.3787635709190284.7631703123326
Trimmed Mean ( 22 / 26 )455.8138888888895.1767292989461988.0505551993374
Trimmed Mean ( 23 / 26 )455.7235294117654.9824380684147891.4659697028123
Trimmed Mean ( 24 / 26 )455.7031254.8049610710865694.8401284127263
Trimmed Mean ( 25 / 26 )455.6733333333334.6336746752624598.3395178271819
Trimmed Mean ( 26 / 26 )455.6642857142864.46431830675933102.068054830314
Median455.95
Midrange462.4
Midmean - Weighted Average at Xnp454.458536585366
Midmean - Weighted Average at X(n+1)p456.035
Midmean - Empirical Distribution Function454.458536585366
Midmean - Empirical Distribution Function - Averaging456.035
Midmean - Empirical Distribution Function - Interpolation456.035
Midmean - Closest Observation454.458536585366
Midmean - True Basic - Statistics Graphics Toolkit456.035
Midmean - MS Excel (old versions)456.164285714286
Number of observations80

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 458.66625 & 8.33741698452779 & 55.0129915357685 \tabularnewline
Geometric Mean & 452.639355957976 &  &  \tabularnewline
Harmonic Mean & 446.628373208702 &  &  \tabularnewline
Quadratic Mean & 464.614052870767 &  &  \tabularnewline
Winsorized Mean ( 1 / 26 ) & 458.65875 & 8.32319138633969 & 55.1061159968959 \tabularnewline
Winsorized Mean ( 2 / 26 ) & 458.63125 & 8.30199411643585 & 55.2435045806677 \tabularnewline
Winsorized Mean ( 3 / 26 ) & 458.57875 & 8.27137807341595 & 55.4416381320863 \tabularnewline
Winsorized Mean ( 4 / 26 ) & 458.57875 & 8.23491787746399 & 55.6871066383024 \tabularnewline
Winsorized Mean ( 5 / 26 ) & 458.5975 & 8.18684650015429 & 56.0163794437036 \tabularnewline
Winsorized Mean ( 6 / 26 ) & 458.5975 & 8.14626107739859 & 56.295458203808 \tabularnewline
Winsorized Mean ( 7 / 26 ) & 458.5975 & 8.08478430526494 & 56.7235293712603 \tabularnewline
Winsorized Mean ( 8 / 26 ) & 458.9975 & 7.98785252089506 & 57.4619397140006 \tabularnewline
Winsorized Mean ( 9 / 26 ) & 459.245 & 7.86199456526801 & 58.4132940041462 \tabularnewline
Winsorized Mean ( 10 / 26 ) & 459.0825 & 7.76305368089978 & 59.1368447096439 \tabularnewline
Winsorized Mean ( 11 / 26 ) & 459 & 7.63687879447612 & 60.1030882318052 \tabularnewline
Winsorized Mean ( 12 / 26 ) & 458.64 & 7.54121661943653 & 60.817772933072 \tabularnewline
Winsorized Mean ( 13 / 26 ) & 458.33125 & 7.44180982856491 & 61.5886807857848 \tabularnewline
Winsorized Mean ( 14 / 26 ) & 458.31375 & 7.24670172547091 & 63.2444617375524 \tabularnewline
Winsorized Mean ( 15 / 26 ) & 458.46375 & 7.04987975562911 & 65.0314283210194 \tabularnewline
Winsorized Mean ( 16 / 26 ) & 457.80375 & 6.77715644688375 & 67.5510080943322 \tabularnewline
Winsorized Mean ( 17 / 26 ) & 457.485 & 6.59280872608437 & 69.3915171829521 \tabularnewline
Winsorized Mean ( 18 / 26 ) & 457.44 & 6.3197687127203 & 72.382395748008 \tabularnewline
Winsorized Mean ( 19 / 26 ) & 457.3925 & 6.03573922748091 & 75.7806927637757 \tabularnewline
Winsorized Mean ( 20 / 26 ) & 457.1175 & 5.73696038663751 & 79.6793892920569 \tabularnewline
Winsorized Mean ( 21 / 26 ) & 456.93375 & 5.42084845049735 & 84.2919248107882 \tabularnewline
Winsorized Mean ( 22 / 26 ) & 456.65875 & 5.09071899803263 & 89.7041754173587 \tabularnewline
Winsorized Mean ( 23 / 26 ) & 455.91125 & 4.73520781151115 & 96.2811492436918 \tabularnewline
Winsorized Mean ( 24 / 26 ) & 455.97125 & 4.43401166821789 & 102.834923342289 \tabularnewline
Winsorized Mean ( 25 / 26 ) & 455.7525 & 4.1527884390636 & 109.746139657133 \tabularnewline
Winsorized Mean ( 26 / 26 ) & 456.2725 & 3.79380740212657 & 120.26770250494 \tabularnewline
Trimmed Mean ( 1 / 26 ) & 458.570512820513 & 8.2574555075069 & 55.534118519152 \tabularnewline
Trimmed Mean ( 2 / 26 ) & 458.477631578947 & 8.17808959776471 & 56.0617031762848 \tabularnewline
Trimmed Mean ( 3 / 26 ) & 458.394594594595 & 8.09554383799635 & 56.6230760734225 \tabularnewline
Trimmed Mean ( 4 / 26 ) & 458.326388888889 & 8.00915018405801 & 57.2253458052485 \tabularnewline
Trimmed Mean ( 5 / 26 ) & 458.254285714286 & 7.91712369234519 & 57.8814104113792 \tabularnewline
Trimmed Mean ( 6 / 26 ) & 458.173529411765 & 7.81953150440656 & 58.5934757285099 \tabularnewline
Trimmed Mean ( 7 / 26 ) & 458.087878787879 & 7.71132292386576 & 59.4045773093153 \tabularnewline
Trimmed Mean ( 8 / 26 ) & 457.996875 & 7.59412398443835 & 60.3093755038123 \tabularnewline
Trimmed Mean ( 9 / 26 ) & 457.835483870968 & 7.47242740485699 & 61.2699808329192 \tabularnewline
Trimmed Mean ( 10 / 26 ) & 457.626666666667 & 7.34952431938834 & 62.2661612887557 \tabularnewline
Trimmed Mean ( 11 / 26 ) & 457.425862068966 & 7.2177608124308 & 63.3750374882419 \tabularnewline
Trimmed Mean ( 12 / 26 ) & 457.221428571429 & 7.07927958505763 & 64.5858696605929 \tabularnewline
Trimmed Mean ( 13 / 26 ) & 457.046296296296 & 6.92513813406215 & 65.9981486937073 \tabularnewline
Trimmed Mean ( 14 / 26 ) & 456.894230769231 & 6.75128299826307 & 67.67517091 \tabularnewline
Trimmed Mean ( 15 / 26 ) & 456.732 & 6.57119095222565 & 69.5052089218783 \tabularnewline
Trimmed Mean ( 16 / 26 ) & 456.539583333333 & 6.38200299516921 & 71.5354699267466 \tabularnewline
Trimmed Mean ( 17 / 26 ) & 456.402173913043 & 6.1964057597469 & 73.655953404137 \tabularnewline
Trimmed Mean ( 18 / 26 ) & 456.286363636364 & 5.99457435351336 & 76.1165575282153 \tabularnewline
Trimmed Mean ( 19 / 26 ) & 456.164285714286 & 5.79039095628097 & 78.7795313232648 \tabularnewline
Trimmed Mean ( 20 / 26 ) & 456.035 & 5.58444560295001 & 81.661642430378 \tabularnewline
Trimmed Mean ( 21 / 26 ) & 455.921052631579 & 5.37876357091902 & 84.7631703123326 \tabularnewline
Trimmed Mean ( 22 / 26 ) & 455.813888888889 & 5.17672929894619 & 88.0505551993374 \tabularnewline
Trimmed Mean ( 23 / 26 ) & 455.723529411765 & 4.98243806841478 & 91.4659697028123 \tabularnewline
Trimmed Mean ( 24 / 26 ) & 455.703125 & 4.80496107108656 & 94.8401284127263 \tabularnewline
Trimmed Mean ( 25 / 26 ) & 455.673333333333 & 4.63367467526245 & 98.3395178271819 \tabularnewline
Trimmed Mean ( 26 / 26 ) & 455.664285714286 & 4.46431830675933 & 102.068054830314 \tabularnewline
Median & 455.95 &  &  \tabularnewline
Midrange & 462.4 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 454.458536585366 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 456.035 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 454.458536585366 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 456.035 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 456.035 &  &  \tabularnewline
Midmean - Closest Observation & 454.458536585366 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 456.035 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 456.164285714286 &  &  \tabularnewline
Number of observations & 80 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=293679&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]458.66625[/C][C]8.33741698452779[/C][C]55.0129915357685[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]452.639355957976[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]446.628373208702[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]464.614052870767[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 26 )[/C][C]458.65875[/C][C]8.32319138633969[/C][C]55.1061159968959[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 26 )[/C][C]458.63125[/C][C]8.30199411643585[/C][C]55.2435045806677[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 26 )[/C][C]458.57875[/C][C]8.27137807341595[/C][C]55.4416381320863[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 26 )[/C][C]458.57875[/C][C]8.23491787746399[/C][C]55.6871066383024[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 26 )[/C][C]458.5975[/C][C]8.18684650015429[/C][C]56.0163794437036[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 26 )[/C][C]458.5975[/C][C]8.14626107739859[/C][C]56.295458203808[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 26 )[/C][C]458.5975[/C][C]8.08478430526494[/C][C]56.7235293712603[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 26 )[/C][C]458.9975[/C][C]7.98785252089506[/C][C]57.4619397140006[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 26 )[/C][C]459.245[/C][C]7.86199456526801[/C][C]58.4132940041462[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 26 )[/C][C]459.0825[/C][C]7.76305368089978[/C][C]59.1368447096439[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 26 )[/C][C]459[/C][C]7.63687879447612[/C][C]60.1030882318052[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 26 )[/C][C]458.64[/C][C]7.54121661943653[/C][C]60.817772933072[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 26 )[/C][C]458.33125[/C][C]7.44180982856491[/C][C]61.5886807857848[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 26 )[/C][C]458.31375[/C][C]7.24670172547091[/C][C]63.2444617375524[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 26 )[/C][C]458.46375[/C][C]7.04987975562911[/C][C]65.0314283210194[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 26 )[/C][C]457.80375[/C][C]6.77715644688375[/C][C]67.5510080943322[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 26 )[/C][C]457.485[/C][C]6.59280872608437[/C][C]69.3915171829521[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 26 )[/C][C]457.44[/C][C]6.3197687127203[/C][C]72.382395748008[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 26 )[/C][C]457.3925[/C][C]6.03573922748091[/C][C]75.7806927637757[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 26 )[/C][C]457.1175[/C][C]5.73696038663751[/C][C]79.6793892920569[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 26 )[/C][C]456.93375[/C][C]5.42084845049735[/C][C]84.2919248107882[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 26 )[/C][C]456.65875[/C][C]5.09071899803263[/C][C]89.7041754173587[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 26 )[/C][C]455.91125[/C][C]4.73520781151115[/C][C]96.2811492436918[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 26 )[/C][C]455.97125[/C][C]4.43401166821789[/C][C]102.834923342289[/C][/ROW]
[ROW][C]Winsorized Mean ( 25 / 26 )[/C][C]455.7525[/C][C]4.1527884390636[/C][C]109.746139657133[/C][/ROW]
[ROW][C]Winsorized Mean ( 26 / 26 )[/C][C]456.2725[/C][C]3.79380740212657[/C][C]120.26770250494[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 26 )[/C][C]458.570512820513[/C][C]8.2574555075069[/C][C]55.534118519152[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 26 )[/C][C]458.477631578947[/C][C]8.17808959776471[/C][C]56.0617031762848[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 26 )[/C][C]458.394594594595[/C][C]8.09554383799635[/C][C]56.6230760734225[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 26 )[/C][C]458.326388888889[/C][C]8.00915018405801[/C][C]57.2253458052485[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 26 )[/C][C]458.254285714286[/C][C]7.91712369234519[/C][C]57.8814104113792[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 26 )[/C][C]458.173529411765[/C][C]7.81953150440656[/C][C]58.5934757285099[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 26 )[/C][C]458.087878787879[/C][C]7.71132292386576[/C][C]59.4045773093153[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 26 )[/C][C]457.996875[/C][C]7.59412398443835[/C][C]60.3093755038123[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 26 )[/C][C]457.835483870968[/C][C]7.47242740485699[/C][C]61.2699808329192[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 26 )[/C][C]457.626666666667[/C][C]7.34952431938834[/C][C]62.2661612887557[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 26 )[/C][C]457.425862068966[/C][C]7.2177608124308[/C][C]63.3750374882419[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 26 )[/C][C]457.221428571429[/C][C]7.07927958505763[/C][C]64.5858696605929[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 26 )[/C][C]457.046296296296[/C][C]6.92513813406215[/C][C]65.9981486937073[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 26 )[/C][C]456.894230769231[/C][C]6.75128299826307[/C][C]67.67517091[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 26 )[/C][C]456.732[/C][C]6.57119095222565[/C][C]69.5052089218783[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 26 )[/C][C]456.539583333333[/C][C]6.38200299516921[/C][C]71.5354699267466[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 26 )[/C][C]456.402173913043[/C][C]6.1964057597469[/C][C]73.655953404137[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 26 )[/C][C]456.286363636364[/C][C]5.99457435351336[/C][C]76.1165575282153[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 26 )[/C][C]456.164285714286[/C][C]5.79039095628097[/C][C]78.7795313232648[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 26 )[/C][C]456.035[/C][C]5.58444560295001[/C][C]81.661642430378[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 26 )[/C][C]455.921052631579[/C][C]5.37876357091902[/C][C]84.7631703123326[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 26 )[/C][C]455.813888888889[/C][C]5.17672929894619[/C][C]88.0505551993374[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 26 )[/C][C]455.723529411765[/C][C]4.98243806841478[/C][C]91.4659697028123[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 26 )[/C][C]455.703125[/C][C]4.80496107108656[/C][C]94.8401284127263[/C][/ROW]
[ROW][C]Trimmed Mean ( 25 / 26 )[/C][C]455.673333333333[/C][C]4.63367467526245[/C][C]98.3395178271819[/C][/ROW]
[ROW][C]Trimmed Mean ( 26 / 26 )[/C][C]455.664285714286[/C][C]4.46431830675933[/C][C]102.068054830314[/C][/ROW]
[ROW][C]Median[/C][C]455.95[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]462.4[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]454.458536585366[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]456.035[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]454.458536585366[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]456.035[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]456.035[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]454.458536585366[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]456.035[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]456.164285714286[/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=293679&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=293679&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 Mean458.666258.3374169845277955.0129915357685
Geometric Mean452.639355957976
Harmonic Mean446.628373208702
Quadratic Mean464.614052870767
Winsorized Mean ( 1 / 26 )458.658758.3231913863396955.1061159968959
Winsorized Mean ( 2 / 26 )458.631258.3019941164358555.2435045806677
Winsorized Mean ( 3 / 26 )458.578758.2713780734159555.4416381320863
Winsorized Mean ( 4 / 26 )458.578758.2349178774639955.6871066383024
Winsorized Mean ( 5 / 26 )458.59758.1868465001542956.0163794437036
Winsorized Mean ( 6 / 26 )458.59758.1462610773985956.295458203808
Winsorized Mean ( 7 / 26 )458.59758.0847843052649456.7235293712603
Winsorized Mean ( 8 / 26 )458.99757.9878525208950657.4619397140006
Winsorized Mean ( 9 / 26 )459.2457.8619945652680158.4132940041462
Winsorized Mean ( 10 / 26 )459.08257.7630536808997859.1368447096439
Winsorized Mean ( 11 / 26 )4597.6368787944761260.1030882318052
Winsorized Mean ( 12 / 26 )458.647.5412166194365360.817772933072
Winsorized Mean ( 13 / 26 )458.331257.4418098285649161.5886807857848
Winsorized Mean ( 14 / 26 )458.313757.2467017254709163.2444617375524
Winsorized Mean ( 15 / 26 )458.463757.0498797556291165.0314283210194
Winsorized Mean ( 16 / 26 )457.803756.7771564468837567.5510080943322
Winsorized Mean ( 17 / 26 )457.4856.5928087260843769.3915171829521
Winsorized Mean ( 18 / 26 )457.446.319768712720372.382395748008
Winsorized Mean ( 19 / 26 )457.39256.0357392274809175.7806927637757
Winsorized Mean ( 20 / 26 )457.11755.7369603866375179.6793892920569
Winsorized Mean ( 21 / 26 )456.933755.4208484504973584.2919248107882
Winsorized Mean ( 22 / 26 )456.658755.0907189980326389.7041754173587
Winsorized Mean ( 23 / 26 )455.911254.7352078115111596.2811492436918
Winsorized Mean ( 24 / 26 )455.971254.43401166821789102.834923342289
Winsorized Mean ( 25 / 26 )455.75254.1527884390636109.746139657133
Winsorized Mean ( 26 / 26 )456.27253.79380740212657120.26770250494
Trimmed Mean ( 1 / 26 )458.5705128205138.257455507506955.534118519152
Trimmed Mean ( 2 / 26 )458.4776315789478.1780895977647156.0617031762848
Trimmed Mean ( 3 / 26 )458.3945945945958.0955438379963556.6230760734225
Trimmed Mean ( 4 / 26 )458.3263888888898.0091501840580157.2253458052485
Trimmed Mean ( 5 / 26 )458.2542857142867.9171236923451957.8814104113792
Trimmed Mean ( 6 / 26 )458.1735294117657.8195315044065658.5934757285099
Trimmed Mean ( 7 / 26 )458.0878787878797.7113229238657659.4045773093153
Trimmed Mean ( 8 / 26 )457.9968757.5941239844383560.3093755038123
Trimmed Mean ( 9 / 26 )457.8354838709687.4724274048569961.2699808329192
Trimmed Mean ( 10 / 26 )457.6266666666677.3495243193883462.2661612887557
Trimmed Mean ( 11 / 26 )457.4258620689667.217760812430863.3750374882419
Trimmed Mean ( 12 / 26 )457.2214285714297.0792795850576364.5858696605929
Trimmed Mean ( 13 / 26 )457.0462962962966.9251381340621565.9981486937073
Trimmed Mean ( 14 / 26 )456.8942307692316.7512829982630767.67517091
Trimmed Mean ( 15 / 26 )456.7326.5711909522256569.5052089218783
Trimmed Mean ( 16 / 26 )456.5395833333336.3820029951692171.5354699267466
Trimmed Mean ( 17 / 26 )456.4021739130436.196405759746973.655953404137
Trimmed Mean ( 18 / 26 )456.2863636363645.9945743535133676.1165575282153
Trimmed Mean ( 19 / 26 )456.1642857142865.7903909562809778.7795313232648
Trimmed Mean ( 20 / 26 )456.0355.5844456029500181.661642430378
Trimmed Mean ( 21 / 26 )455.9210526315795.3787635709190284.7631703123326
Trimmed Mean ( 22 / 26 )455.8138888888895.1767292989461988.0505551993374
Trimmed Mean ( 23 / 26 )455.7235294117654.9824380684147891.4659697028123
Trimmed Mean ( 24 / 26 )455.7031254.8049610710865694.8401284127263
Trimmed Mean ( 25 / 26 )455.6733333333334.6336746752624598.3395178271819
Trimmed Mean ( 26 / 26 )455.6642857142864.46431830675933102.068054830314
Median455.95
Midrange462.4
Midmean - Weighted Average at Xnp454.458536585366
Midmean - Weighted Average at X(n+1)p456.035
Midmean - Empirical Distribution Function454.458536585366
Midmean - Empirical Distribution Function - Averaging456.035
Midmean - Empirical Distribution Function - Interpolation456.035
Midmean - Closest Observation454.458536585366
Midmean - True Basic - Statistics Graphics Toolkit456.035
Midmean - MS Excel (old versions)456.164285714286
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')