Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationThu, 13 Oct 2016 14:49:10 +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/2016/Oct/13/t14763666452slu2vj3mfw1yds.htm/, Retrieved Tue, 30 Apr 2024 19:30:59 +0200
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=, Retrieved Tue, 30 Apr 2024 19:30:59 +0200
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact0
Dataseries X:
467
475
470
442
433
427
410
406
429
425
431
408
454
459
441
420
416
400
401
398
442
458
476
447
511
514
513
511
498
490
495
486
530
539
555
548
615
634
645
634
630
635
642
637
675
679
676
660
716
730
717
694
670
641
626
604
630
634
635
619
674
664
653
635
614
595
580
570
608
617
591
565




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Gwilym Jenkins' @ jenkins.wessa.net

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 2 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&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]'Gwilym Jenkins' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&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'Gwilym Jenkins' @ jenkins.wessa.net







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean550.95833333333311.687061943118347.1425869063484
Geometric Mean541.951553002409
Harmonic Mean532.874071149862
Quadratic Mean559.689906704299
Winsorized Mean ( 1 / 24 )550.80555555555611.644338776563647.3024330642245
Winsorized Mean ( 2 / 24 )550.80555555555611.633716697493147.3456222012217
Winsorized Mean ( 3 / 24 )550.09722222222211.423234287252648.1559957879954
Winsorized Mean ( 4 / 24 )549.37511.262020833887348.7812097050059
Winsorized Mean ( 5 / 24 )549.30555555555611.204103716825149.0271751707071
Winsorized Mean ( 6 / 24 )549.72222222222211.104659707667449.5037431757281
Winsorized Mean ( 7 / 24 )550.01388888888911.023954800465549.8926110315388
Winsorized Mean ( 8 / 24 )550.12510.862995460894450.6421089818542
Winsorized Mean ( 9 / 24 )549.62510.707840090209451.329212555438
Winsorized Mean ( 10 / 24 )549.34722222222210.580475561859751.9208441067147
Winsorized Mean ( 11 / 24 )548.58333333333310.377042005430752.865097110163
Winsorized Mean ( 12 / 24 )547.58333333333310.139167573934854.006734708777
Winsorized Mean ( 13 / 24 )548.4861111111119.8401343763399455.7396972575817
Winsorized Mean ( 14 / 24 )548.4861111111119.7843131023892156.057702300755
Winsorized Mean ( 15 / 24 )547.6527777777789.6746195171759356.6071644270348
Winsorized Mean ( 16 / 24 )548.3194444444449.4476116329397258.0378899713333
Winsorized Mean ( 17 / 24 )549.9722222222229.2013422725957759.7708688503195
Winsorized Mean ( 18 / 24 )550.9722222222229.0555789576970460.8434010454857
Winsorized Mean ( 19 / 24 )550.9722222222228.9830516000623561.3346384672218
Winsorized Mean ( 20 / 24 )553.1944444444448.6671099310824663.8268637231135
Winsorized Mean ( 21 / 24 )554.0694444444448.5452016935314964.8398322609356
Winsorized Mean ( 22 / 24 )554.3758.1746975340426567.8159647731754
Winsorized Mean ( 23 / 24 )554.6944444444448.1310817827700168.2190216829276
Winsorized Mean ( 24 / 24 )556.6944444444447.5090096871925174.1368659297313
Trimmed Mean ( 1 / 24 )550.58571428571411.53599987467747.7276109801562
Trimmed Mean ( 2 / 24 )550.35294117647111.40290470029448.2642761332804
Trimmed Mean ( 3 / 24 )550.10606060606111.246861852659648.9119603150431
Trimmed Mean ( 4 / 24 )550.10937511.148998041755649.3415975982518
Trimmed Mean ( 5 / 24 )550.32258064516111.080775826195149.664625408646
Trimmed Mean ( 6 / 24 )550.56666666666711.006915306180950.0200693247362
Trimmed Mean ( 7 / 24 )550.74137931034510.934622865929250.3667466233683
Trimmed Mean ( 8 / 24 )550.87510.856174929085750.7430106458679
Trimmed Mean ( 9 / 24 )55110.786052281974651.0844918599938
Trimmed Mean ( 10 / 24 )551.21153846153810.72089826139951.4146786045155
Trimmed Mean ( 11 / 24 )551.4810.652976588920251.7676909732043
Trimmed Mean ( 12 / 24 )551.87510.594292296105452.0917286945985
Trimmed Mean ( 13 / 24 )552.43478260869610.549934275222352.3638127211987
Trimmed Mean ( 14 / 24 )552.93181818181810.53391772061552.4906148734888
Trimmed Mean ( 15 / 24 )553.4761904761910.500497089900352.7095227718832
Trimmed Mean ( 16 / 24 )554.17510.452756200136353.0171171497117
Trimmed Mean ( 17 / 24 )554.86842105263210.411461777674853.2939977979301
Trimmed Mean ( 18 / 24 )555.44444444444410.381641644997753.50256379848
Trimmed Mean ( 19 / 24 )555.97058823529410.340330443431453.7671974098729
Trimmed Mean ( 20 / 24 )556.562510.261887039177554.2358825306861
Trimmed Mean ( 21 / 24 )556.96666666666710.195839058146154.6268593972825
Trimmed Mean ( 22 / 24 )557.32142857142910.088242091456955.2446524893954
Trimmed Mean ( 23 / 24 )557.6923076923089.9905754405407655.8218403946231
Trimmed Mean ( 24 / 24 )558.0833333333339.7960944352111556.9699829890731
Median560
Midrange564
Midmean - Weighted Average at Xnp556.923076923077
Midmean - Weighted Average at X(n+1)p559.631578947368
Midmean - Empirical Distribution Function556.923076923077
Midmean - Empirical Distribution Function - Averaging559.631578947368
Midmean - Empirical Distribution Function - Interpolation559.631578947368
Midmean - Closest Observation556.923076923077
Midmean - True Basic - Statistics Graphics Toolkit559.631578947368
Midmean - MS Excel (old versions)556.923076923077
Number of observations72

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 550.958333333333 & 11.6870619431183 & 47.1425869063484 \tabularnewline
Geometric Mean & 541.951553002409 &  &  \tabularnewline
Harmonic Mean & 532.874071149862 &  &  \tabularnewline
Quadratic Mean & 559.689906704299 &  &  \tabularnewline
Winsorized Mean ( 1 / 24 ) & 550.805555555556 & 11.6443387765636 & 47.3024330642245 \tabularnewline
Winsorized Mean ( 2 / 24 ) & 550.805555555556 & 11.6337166974931 & 47.3456222012217 \tabularnewline
Winsorized Mean ( 3 / 24 ) & 550.097222222222 & 11.4232342872526 & 48.1559957879954 \tabularnewline
Winsorized Mean ( 4 / 24 ) & 549.375 & 11.2620208338873 & 48.7812097050059 \tabularnewline
Winsorized Mean ( 5 / 24 ) & 549.305555555556 & 11.2041037168251 & 49.0271751707071 \tabularnewline
Winsorized Mean ( 6 / 24 ) & 549.722222222222 & 11.1046597076674 & 49.5037431757281 \tabularnewline
Winsorized Mean ( 7 / 24 ) & 550.013888888889 & 11.0239548004655 & 49.8926110315388 \tabularnewline
Winsorized Mean ( 8 / 24 ) & 550.125 & 10.8629954608944 & 50.6421089818542 \tabularnewline
Winsorized Mean ( 9 / 24 ) & 549.625 & 10.7078400902094 & 51.329212555438 \tabularnewline
Winsorized Mean ( 10 / 24 ) & 549.347222222222 & 10.5804755618597 & 51.9208441067147 \tabularnewline
Winsorized Mean ( 11 / 24 ) & 548.583333333333 & 10.3770420054307 & 52.865097110163 \tabularnewline
Winsorized Mean ( 12 / 24 ) & 547.583333333333 & 10.1391675739348 & 54.006734708777 \tabularnewline
Winsorized Mean ( 13 / 24 ) & 548.486111111111 & 9.84013437633994 & 55.7396972575817 \tabularnewline
Winsorized Mean ( 14 / 24 ) & 548.486111111111 & 9.78431310238921 & 56.057702300755 \tabularnewline
Winsorized Mean ( 15 / 24 ) & 547.652777777778 & 9.67461951717593 & 56.6071644270348 \tabularnewline
Winsorized Mean ( 16 / 24 ) & 548.319444444444 & 9.44761163293972 & 58.0378899713333 \tabularnewline
Winsorized Mean ( 17 / 24 ) & 549.972222222222 & 9.20134227259577 & 59.7708688503195 \tabularnewline
Winsorized Mean ( 18 / 24 ) & 550.972222222222 & 9.05557895769704 & 60.8434010454857 \tabularnewline
Winsorized Mean ( 19 / 24 ) & 550.972222222222 & 8.98305160006235 & 61.3346384672218 \tabularnewline
Winsorized Mean ( 20 / 24 ) & 553.194444444444 & 8.66710993108246 & 63.8268637231135 \tabularnewline
Winsorized Mean ( 21 / 24 ) & 554.069444444444 & 8.54520169353149 & 64.8398322609356 \tabularnewline
Winsorized Mean ( 22 / 24 ) & 554.375 & 8.17469753404265 & 67.8159647731754 \tabularnewline
Winsorized Mean ( 23 / 24 ) & 554.694444444444 & 8.13108178277001 & 68.2190216829276 \tabularnewline
Winsorized Mean ( 24 / 24 ) & 556.694444444444 & 7.50900968719251 & 74.1368659297313 \tabularnewline
Trimmed Mean ( 1 / 24 ) & 550.585714285714 & 11.535999874677 & 47.7276109801562 \tabularnewline
Trimmed Mean ( 2 / 24 ) & 550.352941176471 & 11.402904700294 & 48.2642761332804 \tabularnewline
Trimmed Mean ( 3 / 24 ) & 550.106060606061 & 11.2468618526596 & 48.9119603150431 \tabularnewline
Trimmed Mean ( 4 / 24 ) & 550.109375 & 11.1489980417556 & 49.3415975982518 \tabularnewline
Trimmed Mean ( 5 / 24 ) & 550.322580645161 & 11.0807758261951 & 49.664625408646 \tabularnewline
Trimmed Mean ( 6 / 24 ) & 550.566666666667 & 11.0069153061809 & 50.0200693247362 \tabularnewline
Trimmed Mean ( 7 / 24 ) & 550.741379310345 & 10.9346228659292 & 50.3667466233683 \tabularnewline
Trimmed Mean ( 8 / 24 ) & 550.875 & 10.8561749290857 & 50.7430106458679 \tabularnewline
Trimmed Mean ( 9 / 24 ) & 551 & 10.7860522819746 & 51.0844918599938 \tabularnewline
Trimmed Mean ( 10 / 24 ) & 551.211538461538 & 10.720898261399 & 51.4146786045155 \tabularnewline
Trimmed Mean ( 11 / 24 ) & 551.48 & 10.6529765889202 & 51.7676909732043 \tabularnewline
Trimmed Mean ( 12 / 24 ) & 551.875 & 10.5942922961054 & 52.0917286945985 \tabularnewline
Trimmed Mean ( 13 / 24 ) & 552.434782608696 & 10.5499342752223 & 52.3638127211987 \tabularnewline
Trimmed Mean ( 14 / 24 ) & 552.931818181818 & 10.533917720615 & 52.4906148734888 \tabularnewline
Trimmed Mean ( 15 / 24 ) & 553.47619047619 & 10.5004970899003 & 52.7095227718832 \tabularnewline
Trimmed Mean ( 16 / 24 ) & 554.175 & 10.4527562001363 & 53.0171171497117 \tabularnewline
Trimmed Mean ( 17 / 24 ) & 554.868421052632 & 10.4114617776748 & 53.2939977979301 \tabularnewline
Trimmed Mean ( 18 / 24 ) & 555.444444444444 & 10.3816416449977 & 53.50256379848 \tabularnewline
Trimmed Mean ( 19 / 24 ) & 555.970588235294 & 10.3403304434314 & 53.7671974098729 \tabularnewline
Trimmed Mean ( 20 / 24 ) & 556.5625 & 10.2618870391775 & 54.2358825306861 \tabularnewline
Trimmed Mean ( 21 / 24 ) & 556.966666666667 & 10.1958390581461 & 54.6268593972825 \tabularnewline
Trimmed Mean ( 22 / 24 ) & 557.321428571429 & 10.0882420914569 & 55.2446524893954 \tabularnewline
Trimmed Mean ( 23 / 24 ) & 557.692307692308 & 9.99057544054076 & 55.8218403946231 \tabularnewline
Trimmed Mean ( 24 / 24 ) & 558.083333333333 & 9.79609443521115 & 56.9699829890731 \tabularnewline
Median & 560 &  &  \tabularnewline
Midrange & 564 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 556.923076923077 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 559.631578947368 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 556.923076923077 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 559.631578947368 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 559.631578947368 &  &  \tabularnewline
Midmean - Closest Observation & 556.923076923077 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 559.631578947368 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 556.923076923077 &  &  \tabularnewline
Number of observations & 72 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&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]550.958333333333[/C][C]11.6870619431183[/C][C]47.1425869063484[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]541.951553002409[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]532.874071149862[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]559.689906704299[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 24 )[/C][C]550.805555555556[/C][C]11.6443387765636[/C][C]47.3024330642245[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 24 )[/C][C]550.805555555556[/C][C]11.6337166974931[/C][C]47.3456222012217[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 24 )[/C][C]550.097222222222[/C][C]11.4232342872526[/C][C]48.1559957879954[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 24 )[/C][C]549.375[/C][C]11.2620208338873[/C][C]48.7812097050059[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 24 )[/C][C]549.305555555556[/C][C]11.2041037168251[/C][C]49.0271751707071[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 24 )[/C][C]549.722222222222[/C][C]11.1046597076674[/C][C]49.5037431757281[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 24 )[/C][C]550.013888888889[/C][C]11.0239548004655[/C][C]49.8926110315388[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 24 )[/C][C]550.125[/C][C]10.8629954608944[/C][C]50.6421089818542[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 24 )[/C][C]549.625[/C][C]10.7078400902094[/C][C]51.329212555438[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 24 )[/C][C]549.347222222222[/C][C]10.5804755618597[/C][C]51.9208441067147[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 24 )[/C][C]548.583333333333[/C][C]10.3770420054307[/C][C]52.865097110163[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 24 )[/C][C]547.583333333333[/C][C]10.1391675739348[/C][C]54.006734708777[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 24 )[/C][C]548.486111111111[/C][C]9.84013437633994[/C][C]55.7396972575817[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 24 )[/C][C]548.486111111111[/C][C]9.78431310238921[/C][C]56.057702300755[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 24 )[/C][C]547.652777777778[/C][C]9.67461951717593[/C][C]56.6071644270348[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 24 )[/C][C]548.319444444444[/C][C]9.44761163293972[/C][C]58.0378899713333[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 24 )[/C][C]549.972222222222[/C][C]9.20134227259577[/C][C]59.7708688503195[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 24 )[/C][C]550.972222222222[/C][C]9.05557895769704[/C][C]60.8434010454857[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 24 )[/C][C]550.972222222222[/C][C]8.98305160006235[/C][C]61.3346384672218[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 24 )[/C][C]553.194444444444[/C][C]8.66710993108246[/C][C]63.8268637231135[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 24 )[/C][C]554.069444444444[/C][C]8.54520169353149[/C][C]64.8398322609356[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 24 )[/C][C]554.375[/C][C]8.17469753404265[/C][C]67.8159647731754[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 24 )[/C][C]554.694444444444[/C][C]8.13108178277001[/C][C]68.2190216829276[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 24 )[/C][C]556.694444444444[/C][C]7.50900968719251[/C][C]74.1368659297313[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 24 )[/C][C]550.585714285714[/C][C]11.535999874677[/C][C]47.7276109801562[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 24 )[/C][C]550.352941176471[/C][C]11.402904700294[/C][C]48.2642761332804[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 24 )[/C][C]550.106060606061[/C][C]11.2468618526596[/C][C]48.9119603150431[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 24 )[/C][C]550.109375[/C][C]11.1489980417556[/C][C]49.3415975982518[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 24 )[/C][C]550.322580645161[/C][C]11.0807758261951[/C][C]49.664625408646[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 24 )[/C][C]550.566666666667[/C][C]11.0069153061809[/C][C]50.0200693247362[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 24 )[/C][C]550.741379310345[/C][C]10.9346228659292[/C][C]50.3667466233683[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 24 )[/C][C]550.875[/C][C]10.8561749290857[/C][C]50.7430106458679[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 24 )[/C][C]551[/C][C]10.7860522819746[/C][C]51.0844918599938[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 24 )[/C][C]551.211538461538[/C][C]10.720898261399[/C][C]51.4146786045155[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 24 )[/C][C]551.48[/C][C]10.6529765889202[/C][C]51.7676909732043[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 24 )[/C][C]551.875[/C][C]10.5942922961054[/C][C]52.0917286945985[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 24 )[/C][C]552.434782608696[/C][C]10.5499342752223[/C][C]52.3638127211987[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 24 )[/C][C]552.931818181818[/C][C]10.533917720615[/C][C]52.4906148734888[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 24 )[/C][C]553.47619047619[/C][C]10.5004970899003[/C][C]52.7095227718832[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 24 )[/C][C]554.175[/C][C]10.4527562001363[/C][C]53.0171171497117[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 24 )[/C][C]554.868421052632[/C][C]10.4114617776748[/C][C]53.2939977979301[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 24 )[/C][C]555.444444444444[/C][C]10.3816416449977[/C][C]53.50256379848[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 24 )[/C][C]555.970588235294[/C][C]10.3403304434314[/C][C]53.7671974098729[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 24 )[/C][C]556.5625[/C][C]10.2618870391775[/C][C]54.2358825306861[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 24 )[/C][C]556.966666666667[/C][C]10.1958390581461[/C][C]54.6268593972825[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 24 )[/C][C]557.321428571429[/C][C]10.0882420914569[/C][C]55.2446524893954[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 24 )[/C][C]557.692307692308[/C][C]9.99057544054076[/C][C]55.8218403946231[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 24 )[/C][C]558.083333333333[/C][C]9.79609443521115[/C][C]56.9699829890731[/C][/ROW]
[ROW][C]Median[/C][C]560[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]564[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]556.923076923077[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]559.631578947368[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]556.923076923077[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]559.631578947368[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]559.631578947368[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]556.923076923077[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]559.631578947368[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]556.923076923077[/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=&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&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 Mean550.95833333333311.687061943118347.1425869063484
Geometric Mean541.951553002409
Harmonic Mean532.874071149862
Quadratic Mean559.689906704299
Winsorized Mean ( 1 / 24 )550.80555555555611.644338776563647.3024330642245
Winsorized Mean ( 2 / 24 )550.80555555555611.633716697493147.3456222012217
Winsorized Mean ( 3 / 24 )550.09722222222211.423234287252648.1559957879954
Winsorized Mean ( 4 / 24 )549.37511.262020833887348.7812097050059
Winsorized Mean ( 5 / 24 )549.30555555555611.204103716825149.0271751707071
Winsorized Mean ( 6 / 24 )549.72222222222211.104659707667449.5037431757281
Winsorized Mean ( 7 / 24 )550.01388888888911.023954800465549.8926110315388
Winsorized Mean ( 8 / 24 )550.12510.862995460894450.6421089818542
Winsorized Mean ( 9 / 24 )549.62510.707840090209451.329212555438
Winsorized Mean ( 10 / 24 )549.34722222222210.580475561859751.9208441067147
Winsorized Mean ( 11 / 24 )548.58333333333310.377042005430752.865097110163
Winsorized Mean ( 12 / 24 )547.58333333333310.139167573934854.006734708777
Winsorized Mean ( 13 / 24 )548.4861111111119.8401343763399455.7396972575817
Winsorized Mean ( 14 / 24 )548.4861111111119.7843131023892156.057702300755
Winsorized Mean ( 15 / 24 )547.6527777777789.6746195171759356.6071644270348
Winsorized Mean ( 16 / 24 )548.3194444444449.4476116329397258.0378899713333
Winsorized Mean ( 17 / 24 )549.9722222222229.2013422725957759.7708688503195
Winsorized Mean ( 18 / 24 )550.9722222222229.0555789576970460.8434010454857
Winsorized Mean ( 19 / 24 )550.9722222222228.9830516000623561.3346384672218
Winsorized Mean ( 20 / 24 )553.1944444444448.6671099310824663.8268637231135
Winsorized Mean ( 21 / 24 )554.0694444444448.5452016935314964.8398322609356
Winsorized Mean ( 22 / 24 )554.3758.1746975340426567.8159647731754
Winsorized Mean ( 23 / 24 )554.6944444444448.1310817827700168.2190216829276
Winsorized Mean ( 24 / 24 )556.6944444444447.5090096871925174.1368659297313
Trimmed Mean ( 1 / 24 )550.58571428571411.53599987467747.7276109801562
Trimmed Mean ( 2 / 24 )550.35294117647111.40290470029448.2642761332804
Trimmed Mean ( 3 / 24 )550.10606060606111.246861852659648.9119603150431
Trimmed Mean ( 4 / 24 )550.10937511.148998041755649.3415975982518
Trimmed Mean ( 5 / 24 )550.32258064516111.080775826195149.664625408646
Trimmed Mean ( 6 / 24 )550.56666666666711.006915306180950.0200693247362
Trimmed Mean ( 7 / 24 )550.74137931034510.934622865929250.3667466233683
Trimmed Mean ( 8 / 24 )550.87510.856174929085750.7430106458679
Trimmed Mean ( 9 / 24 )55110.786052281974651.0844918599938
Trimmed Mean ( 10 / 24 )551.21153846153810.72089826139951.4146786045155
Trimmed Mean ( 11 / 24 )551.4810.652976588920251.7676909732043
Trimmed Mean ( 12 / 24 )551.87510.594292296105452.0917286945985
Trimmed Mean ( 13 / 24 )552.43478260869610.549934275222352.3638127211987
Trimmed Mean ( 14 / 24 )552.93181818181810.53391772061552.4906148734888
Trimmed Mean ( 15 / 24 )553.4761904761910.500497089900352.7095227718832
Trimmed Mean ( 16 / 24 )554.17510.452756200136353.0171171497117
Trimmed Mean ( 17 / 24 )554.86842105263210.411461777674853.2939977979301
Trimmed Mean ( 18 / 24 )555.44444444444410.381641644997753.50256379848
Trimmed Mean ( 19 / 24 )555.97058823529410.340330443431453.7671974098729
Trimmed Mean ( 20 / 24 )556.562510.261887039177554.2358825306861
Trimmed Mean ( 21 / 24 )556.96666666666710.195839058146154.6268593972825
Trimmed Mean ( 22 / 24 )557.32142857142910.088242091456955.2446524893954
Trimmed Mean ( 23 / 24 )557.6923076923089.9905754405407655.8218403946231
Trimmed Mean ( 24 / 24 )558.0833333333339.7960944352111556.9699829890731
Median560
Midrange564
Midmean - Weighted Average at Xnp556.923076923077
Midmean - Weighted Average at X(n+1)p559.631578947368
Midmean - Empirical Distribution Function556.923076923077
Midmean - Empirical Distribution Function - Averaging559.631578947368
Midmean - Empirical Distribution Function - Interpolation559.631578947368
Midmean - Closest Observation556.923076923077
Midmean - True Basic - Statistics Graphics Toolkit559.631578947368
Midmean - MS Excel (old versions)556.923076923077
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')