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Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationSun, 19 Oct 2008 06:22:19 -0600
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2008/Oct/19/t12244189730lrde8k7bacax9z.htm/, Retrieved Fri, 17 May 2024 15:56:35 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=16796, Retrieved Fri, 17 May 2024 15:56:35 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact179
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Univariate Data Series] [Werkloosheid BELGIE] [2008-10-19 10:57:42] [46c5a5fbda57fdfa1d4ef48658f82a0c]
- RMP   [Histogram] [Histogram - Werkl...] [2008-10-19 11:37:28] [46c5a5fbda57fdfa1d4ef48658f82a0c]
- RM        [Central Tendency] [] [2008-10-19 12:22:19] [b23db733701c4d62df5e228d507c1c6a] [Current]
F   PD        [Central Tendency] [Prijsindexcijfers...] [2008-10-20 18:57:54] [29647dffafb5b58c12a48dbf6cba2b57]
F   PD        [Central Tendency] [Voorspelling tijd...] [2008-10-20 20:07:38] [70cb582895831af4be81fec73c607e93]
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Dataseries X:
565464
547344
554788
562325
560854
555332
543599
536662
542722
593530
610763
612613
611324
594167
595454
590865
589379
584428
573100
567456
569028
620735
628884
628232
612117
595404
597141
593408
590072
579799
574205
572775
572942
619567
625809
619916
587625
565742
557274
560576
548854
531673
525919
511038
498662
555362
564591
541657
527070
509846
514258
516922
507561
492622
490243
469357
477580
528379
533590
517945




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135

\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' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=16796&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' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=16796&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=16796&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' @ 72.249.127.135







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean562109.155202.16081945056108.053012874632
Geometric Mean560662.895311134
Harmonic Mean559190.87218529
Quadratic Mean563527.623695606
Winsorized Mean ( 1 / 20 )562235.3333333335160.03165620445108.959667458105
Winsorized Mean ( 2 / 20 )562576.6666666675032.48299806372111.789084410841
Winsorized Mean ( 3 / 20 )562441.9166666674951.43714024899113.591650410891
Winsorized Mean ( 4 / 20 )562789.9833333334847.24072866551116.105226630301
Winsorized Mean ( 5 / 20 )563502.4833333334683.02984800865120.328612377508
Winsorized Mean ( 6 / 20 )563035.5833333334501.44138066404125.078954876954
Winsorized Mean ( 7 / 20 )563116.7833333334462.97729879318126.175139516305
Winsorized Mean ( 8 / 20 )563440.3833333334359.77990996434129.235969468455
Winsorized Mean ( 9 / 20 )563755.8333333334268.72749534011132.066484437985
Winsorized Mean ( 10 / 20 )5616563845.26435919436146.064339804631
Winsorized Mean ( 11 / 20 )562808.6166666673525.87478740184159.622405956563
Winsorized Mean ( 12 / 20 )563028.8166666673483.75375414033161.615560800624
Winsorized Mean ( 13 / 20 )563044.4166666673392.43226464749165.97071739181
Winsorized Mean ( 14 / 20 )563664.3833333333238.3033525971174.061637209274
Winsorized Mean ( 15 / 20 )564113.1333333333154.08110862921178.851815760217
Winsorized Mean ( 16 / 20 )564254.22915.26041396698193.551902703671
Winsorized Mean ( 17 / 20 )565444.7666666672659.16395567197212.640053826158
Winsorized Mean ( 18 / 20 )565556.3666666672578.36344351874219.347031190778
Winsorized Mean ( 19 / 20 )565278.652450.26269130441230.701243587508
Winsorized Mean ( 20 / 20 )565461.3166666672101.32180172435269.097915513296
Trimmed Mean ( 1 / 20 )562557.0344827595002.34949353946112.458562763218
Trimmed Mean ( 2 / 20 )562901.7142857144807.55432287010117.086917064655
Trimmed Mean ( 3 / 20 )563082.2962962964652.43283357001121.029645443418
Trimmed Mean ( 4 / 20 )563328.5961538464498.06073474992125.238103568018
Trimmed Mean ( 5 / 20 )563490.184345.84085433136129.661945498623
Trimmed Mean ( 6 / 20 )563487.1041666674210.69811834444133.822726856566
Trimmed Mean ( 7 / 20 )563585.2608695654094.75137860579137.636014683133
Trimmed Mean ( 8 / 20 )563676.5227272733954.73570939600142.532033528319
Trimmed Mean ( 9 / 20 )563718.690476193800.95722500936148.309664409549
Trimmed Mean ( 10 / 20 )563712.53622.85393079077155.599014138822
Trimmed Mean ( 11 / 20 )564037.2105263163503.60258305199160.987782477025
Trimmed Mean ( 12 / 20 )564223.3611111113429.29891977863164.530236153206
Trimmed Mean ( 13 / 20 )564399.0294117653332.98497212251169.337405998667
Trimmed Mean ( 14 / 20 )564594.406253219.03126107795175.392644699242
Trimmed Mean ( 15 / 20 )564727.2666666673099.43410293999182.203346775784
Trimmed Mean ( 16 / 20 )5648152946.91087250297191.663414482662
Trimmed Mean ( 17 / 20 )564895.8846153852799.43798223689201.789033441636
Trimmed Mean ( 18 / 20 )564815.1666666672664.82575066382211.952007190703
Trimmed Mean ( 19 / 20 )564702.8636363642474.17315874634228.239022656966
Trimmed Mean ( 20 / 20 )564611.952210.73068472728255.396079631315
Median565027.5
Midrange549120.5
Midmean - Weighted Average at Xnp563661
Midmean - Weighted Average at X(n+1)p564727.266666667
Midmean - Empirical Distribution Function563661
Midmean - Empirical Distribution Function - Averaging564727.266666667
Midmean - Empirical Distribution Function - Interpolation564727.266666667
Midmean - Closest Observation563661
Midmean - True Basic - Statistics Graphics Toolkit564727.266666667
Midmean - MS Excel (old versions)564594.40625
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 562109.15 & 5202.16081945056 & 108.053012874632 \tabularnewline
Geometric Mean & 560662.895311134 &  &  \tabularnewline
Harmonic Mean & 559190.87218529 &  &  \tabularnewline
Quadratic Mean & 563527.623695606 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 562235.333333333 & 5160.03165620445 & 108.959667458105 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 562576.666666667 & 5032.48299806372 & 111.789084410841 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 562441.916666667 & 4951.43714024899 & 113.591650410891 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 562789.983333333 & 4847.24072866551 & 116.105226630301 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 563502.483333333 & 4683.02984800865 & 120.328612377508 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 563035.583333333 & 4501.44138066404 & 125.078954876954 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 563116.783333333 & 4462.97729879318 & 126.175139516305 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 563440.383333333 & 4359.77990996434 & 129.235969468455 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 563755.833333333 & 4268.72749534011 & 132.066484437985 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 561656 & 3845.26435919436 & 146.064339804631 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 562808.616666667 & 3525.87478740184 & 159.622405956563 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 563028.816666667 & 3483.75375414033 & 161.615560800624 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 563044.416666667 & 3392.43226464749 & 165.97071739181 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 563664.383333333 & 3238.3033525971 & 174.061637209274 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 564113.133333333 & 3154.08110862921 & 178.851815760217 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 564254.2 & 2915.26041396698 & 193.551902703671 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 565444.766666667 & 2659.16395567197 & 212.640053826158 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 565556.366666667 & 2578.36344351874 & 219.347031190778 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 565278.65 & 2450.26269130441 & 230.701243587508 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 565461.316666667 & 2101.32180172435 & 269.097915513296 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 562557.034482759 & 5002.34949353946 & 112.458562763218 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 562901.714285714 & 4807.55432287010 & 117.086917064655 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 563082.296296296 & 4652.43283357001 & 121.029645443418 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 563328.596153846 & 4498.06073474992 & 125.238103568018 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 563490.18 & 4345.84085433136 & 129.661945498623 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 563487.104166667 & 4210.69811834444 & 133.822726856566 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 563585.260869565 & 4094.75137860579 & 137.636014683133 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 563676.522727273 & 3954.73570939600 & 142.532033528319 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 563718.69047619 & 3800.95722500936 & 148.309664409549 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 563712.5 & 3622.85393079077 & 155.599014138822 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 564037.210526316 & 3503.60258305199 & 160.987782477025 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 564223.361111111 & 3429.29891977863 & 164.530236153206 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 564399.029411765 & 3332.98497212251 & 169.337405998667 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 564594.40625 & 3219.03126107795 & 175.392644699242 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 564727.266666667 & 3099.43410293999 & 182.203346775784 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 564815 & 2946.91087250297 & 191.663414482662 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 564895.884615385 & 2799.43798223689 & 201.789033441636 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 564815.166666667 & 2664.82575066382 & 211.952007190703 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 564702.863636364 & 2474.17315874634 & 228.239022656966 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 564611.95 & 2210.73068472728 & 255.396079631315 \tabularnewline
Median & 565027.5 &  &  \tabularnewline
Midrange & 549120.5 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 563661 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 564727.266666667 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 563661 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 564727.266666667 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 564727.266666667 &  &  \tabularnewline
Midmean - Closest Observation & 563661 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 564727.266666667 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 564594.40625 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=16796&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]562109.15[/C][C]5202.16081945056[/C][C]108.053012874632[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]560662.895311134[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]559190.87218529[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]563527.623695606[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]562235.333333333[/C][C]5160.03165620445[/C][C]108.959667458105[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]562576.666666667[/C][C]5032.48299806372[/C][C]111.789084410841[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]562441.916666667[/C][C]4951.43714024899[/C][C]113.591650410891[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]562789.983333333[/C][C]4847.24072866551[/C][C]116.105226630301[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]563502.483333333[/C][C]4683.02984800865[/C][C]120.328612377508[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]563035.583333333[/C][C]4501.44138066404[/C][C]125.078954876954[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]563116.783333333[/C][C]4462.97729879318[/C][C]126.175139516305[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]563440.383333333[/C][C]4359.77990996434[/C][C]129.235969468455[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]563755.833333333[/C][C]4268.72749534011[/C][C]132.066484437985[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]561656[/C][C]3845.26435919436[/C][C]146.064339804631[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]562808.616666667[/C][C]3525.87478740184[/C][C]159.622405956563[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]563028.816666667[/C][C]3483.75375414033[/C][C]161.615560800624[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]563044.416666667[/C][C]3392.43226464749[/C][C]165.97071739181[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]563664.383333333[/C][C]3238.3033525971[/C][C]174.061637209274[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]564113.133333333[/C][C]3154.08110862921[/C][C]178.851815760217[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]564254.2[/C][C]2915.26041396698[/C][C]193.551902703671[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]565444.766666667[/C][C]2659.16395567197[/C][C]212.640053826158[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]565556.366666667[/C][C]2578.36344351874[/C][C]219.347031190778[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]565278.65[/C][C]2450.26269130441[/C][C]230.701243587508[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]565461.316666667[/C][C]2101.32180172435[/C][C]269.097915513296[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]562557.034482759[/C][C]5002.34949353946[/C][C]112.458562763218[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]562901.714285714[/C][C]4807.55432287010[/C][C]117.086917064655[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]563082.296296296[/C][C]4652.43283357001[/C][C]121.029645443418[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]563328.596153846[/C][C]4498.06073474992[/C][C]125.238103568018[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]563490.18[/C][C]4345.84085433136[/C][C]129.661945498623[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]563487.104166667[/C][C]4210.69811834444[/C][C]133.822726856566[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]563585.260869565[/C][C]4094.75137860579[/C][C]137.636014683133[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]563676.522727273[/C][C]3954.73570939600[/C][C]142.532033528319[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]563718.69047619[/C][C]3800.95722500936[/C][C]148.309664409549[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]563712.5[/C][C]3622.85393079077[/C][C]155.599014138822[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]564037.210526316[/C][C]3503.60258305199[/C][C]160.987782477025[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]564223.361111111[/C][C]3429.29891977863[/C][C]164.530236153206[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]564399.029411765[/C][C]3332.98497212251[/C][C]169.337405998667[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]564594.40625[/C][C]3219.03126107795[/C][C]175.392644699242[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]564727.266666667[/C][C]3099.43410293999[/C][C]182.203346775784[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]564815[/C][C]2946.91087250297[/C][C]191.663414482662[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]564895.884615385[/C][C]2799.43798223689[/C][C]201.789033441636[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]564815.166666667[/C][C]2664.82575066382[/C][C]211.952007190703[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]564702.863636364[/C][C]2474.17315874634[/C][C]228.239022656966[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]564611.95[/C][C]2210.73068472728[/C][C]255.396079631315[/C][/ROW]
[ROW][C]Median[/C][C]565027.5[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]549120.5[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]563661[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]564727.266666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]563661[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]564727.266666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]564727.266666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]563661[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]564727.266666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]564594.40625[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]60[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=16796&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=16796&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 Mean562109.155202.16081945056108.053012874632
Geometric Mean560662.895311134
Harmonic Mean559190.87218529
Quadratic Mean563527.623695606
Winsorized Mean ( 1 / 20 )562235.3333333335160.03165620445108.959667458105
Winsorized Mean ( 2 / 20 )562576.6666666675032.48299806372111.789084410841
Winsorized Mean ( 3 / 20 )562441.9166666674951.43714024899113.591650410891
Winsorized Mean ( 4 / 20 )562789.9833333334847.24072866551116.105226630301
Winsorized Mean ( 5 / 20 )563502.4833333334683.02984800865120.328612377508
Winsorized Mean ( 6 / 20 )563035.5833333334501.44138066404125.078954876954
Winsorized Mean ( 7 / 20 )563116.7833333334462.97729879318126.175139516305
Winsorized Mean ( 8 / 20 )563440.3833333334359.77990996434129.235969468455
Winsorized Mean ( 9 / 20 )563755.8333333334268.72749534011132.066484437985
Winsorized Mean ( 10 / 20 )5616563845.26435919436146.064339804631
Winsorized Mean ( 11 / 20 )562808.6166666673525.87478740184159.622405956563
Winsorized Mean ( 12 / 20 )563028.8166666673483.75375414033161.615560800624
Winsorized Mean ( 13 / 20 )563044.4166666673392.43226464749165.97071739181
Winsorized Mean ( 14 / 20 )563664.3833333333238.3033525971174.061637209274
Winsorized Mean ( 15 / 20 )564113.1333333333154.08110862921178.851815760217
Winsorized Mean ( 16 / 20 )564254.22915.26041396698193.551902703671
Winsorized Mean ( 17 / 20 )565444.7666666672659.16395567197212.640053826158
Winsorized Mean ( 18 / 20 )565556.3666666672578.36344351874219.347031190778
Winsorized Mean ( 19 / 20 )565278.652450.26269130441230.701243587508
Winsorized Mean ( 20 / 20 )565461.3166666672101.32180172435269.097915513296
Trimmed Mean ( 1 / 20 )562557.0344827595002.34949353946112.458562763218
Trimmed Mean ( 2 / 20 )562901.7142857144807.55432287010117.086917064655
Trimmed Mean ( 3 / 20 )563082.2962962964652.43283357001121.029645443418
Trimmed Mean ( 4 / 20 )563328.5961538464498.06073474992125.238103568018
Trimmed Mean ( 5 / 20 )563490.184345.84085433136129.661945498623
Trimmed Mean ( 6 / 20 )563487.1041666674210.69811834444133.822726856566
Trimmed Mean ( 7 / 20 )563585.2608695654094.75137860579137.636014683133
Trimmed Mean ( 8 / 20 )563676.5227272733954.73570939600142.532033528319
Trimmed Mean ( 9 / 20 )563718.690476193800.95722500936148.309664409549
Trimmed Mean ( 10 / 20 )563712.53622.85393079077155.599014138822
Trimmed Mean ( 11 / 20 )564037.2105263163503.60258305199160.987782477025
Trimmed Mean ( 12 / 20 )564223.3611111113429.29891977863164.530236153206
Trimmed Mean ( 13 / 20 )564399.0294117653332.98497212251169.337405998667
Trimmed Mean ( 14 / 20 )564594.406253219.03126107795175.392644699242
Trimmed Mean ( 15 / 20 )564727.2666666673099.43410293999182.203346775784
Trimmed Mean ( 16 / 20 )5648152946.91087250297191.663414482662
Trimmed Mean ( 17 / 20 )564895.8846153852799.43798223689201.789033441636
Trimmed Mean ( 18 / 20 )564815.1666666672664.82575066382211.952007190703
Trimmed Mean ( 19 / 20 )564702.8636363642474.17315874634228.239022656966
Trimmed Mean ( 20 / 20 )564611.952210.73068472728255.396079631315
Median565027.5
Midrange549120.5
Midmean - Weighted Average at Xnp563661
Midmean - Weighted Average at X(n+1)p564727.266666667
Midmean - Empirical Distribution Function563661
Midmean - Empirical Distribution Function - Averaging564727.266666667
Midmean - Empirical Distribution Function - Interpolation564727.266666667
Midmean - Closest Observation563661
Midmean - True Basic - Statistics Graphics Toolkit564727.266666667
Midmean - MS Excel (old versions)564594.40625
Number of observations60



Parameters (Session):
par2 = grey ; par3 = FALSE ; par4 = Unknown ;
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')