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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 computationTue, 20 Oct 2009 14:19:14 -0600
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2009/Oct/20/t12560699980bztxz3eop7vf68.htm/, Retrieved Thu, 02 May 2024 15:40:27 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=49124, Retrieved Thu, 02 May 2024 15:40:27 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact76
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [onderzoek tijdree...] [2009-10-20 20:19:14] [99bf2a1e962091d45abf4c2600a412f9] [Current]
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Dataseries X:
562
561
555
544
537
543
594
611
613
611
594
595
591
589
584
573
567
569
621
629
628
612
595
597
593
590
580
574
573
573
620
626
620
588
566
557
561
549
532
526
511
499
555
565
542
527
510
514
517
508
493
490
469
478
528
534
518
506
502
516





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'Sir Ronald Aylmer Fisher' @ 193.190.124.24
R Framework error message
Warning: there are blank lines in the 'Data' field.
Please, use NA for missing data - blank lines are simply
 deleted and are NOT treated as missing values.

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 3 seconds \tabularnewline
R Server & 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 \tabularnewline
R Framework error message & 
Warning: there are blank lines in the 'Data' field.
Please, use NA for missing data - blank lines are simply
 deleted and are NOT treated as missing values.
\tabularnewline \hline \end{tabular} %Source: https://freestatistics.org/blog/index.php?pk=49124&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]3 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Sir Ronald Aylmer Fisher' @ 193.190.124.24[/C][/ROW]
[ROW][C]R Framework error message[/C][C]
Warning: there are blank lines in the 'Data' field.
Please, use NA for missing data - blank lines are simply
 deleted and are NOT treated as missing values.
[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=49124&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=49124&T=0

As an alternative you can also use a QR Code:  

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

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'Sir Ronald Aylmer Fisher' @ 193.190.124.24
R Framework error message
Warning: there are blank lines in the 'Data' field.
Please, use NA for missing data - blank lines are simply
 deleted and are NOT treated as missing values.







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean559.755.4183004924043103.307301022653
Geometric Mean558.181281997437
Harmonic Mean556.59267103469
Quadratic Mean561.295094699155
Winsorized Mean ( 1 / 20 )559.8833333333335.37403738150171104.182999407585
Winsorized Mean ( 2 / 20 )560.2166666666675.26286917014584106.447006101644
Winsorized Mean ( 3 / 20 )560.1166666666675.17802242133586108.171927637610
Winsorized Mean ( 4 / 20 )560.455.07978295946335110.329516924717
Winsorized Mean ( 5 / 20 )560.75.02942190969924111.483985648269
Winsorized Mean ( 6 / 20 )560.44.81670820852807116.345017331090
Winsorized Mean ( 7 / 20 )560.5166666666674.75100296676472117.978597485145
Winsorized Mean ( 8 / 20 )560.654.67713666088909119.870348174394
Winsorized Mean ( 9 / 20 )560.84.64975547622674120.608492826614
Winsorized Mean ( 10 / 20 )558.9666666666674.16265117244137134.281409493853
Winsorized Mean ( 11 / 20 )558.9666666666674.039911524082138.361115914211
Winsorized Mean ( 12 / 20 )559.1666666666674.00403515866046139.650788394609
Winsorized Mean ( 13 / 20 )559.1666666666673.93278029244264142.181008113059
Winsorized Mean ( 14 / 20 )561.0333333333333.61329674549408155.269099896919
Winsorized Mean ( 15 / 20 )561.0333333333333.53385296253659158.759670897746
Winsorized Mean ( 16 / 20 )560.7666666666673.40938938372668164.477155159589
Winsorized Mean ( 17 / 20 )561.6166666666673.1849834513993176.332679662723
Winsorized Mean ( 18 / 20 )561.9166666666673.04581695799659184.487995968173
Winsorized Mean ( 19 / 20 )562.552.85204109684259197.244703318890
Winsorized Mean ( 20 / 20 )562.8833333333332.40210496986546234.329198929579
Trimmed Mean ( 1 / 20 )560.1206896551725.24326996896567106.826597327710
Trimmed Mean ( 2 / 20 )560.3755.0815788079905110.275766877578
Trimmed Mean ( 3 / 20 )560.4629629629634.9551949857281113.106137009180
Trimmed Mean ( 4 / 20 )560.5961538461544.8373437059247115.889254087847
Trimmed Mean ( 5 / 20 )560.644.72654337173562118.615223834099
Trimmed Mean ( 6 / 20 )560.6254.60165181951928121.831251469731
Trimmed Mean ( 7 / 20 )560.6739130434784.50679083396246124.406464311219
Trimmed Mean ( 8 / 20 )560.7045454545454.40036270192746127.422347528067
Trimmed Mean ( 9 / 20 )560.7142857142864.27934098314699131.028185863782
Trimmed Mean ( 10 / 20 )560.74.12422486889728135.952819699164
Trimmed Mean ( 11 / 20 )560.9736842105264.04745794905486138.599014806694
Trimmed Mean ( 12 / 20 )561.2777777777783.96904912668231141.413663540855
Trimmed Mean ( 13 / 20 )561.5882352941183.86356388980254145.354975693910
Trimmed Mean ( 14 / 20 )561.93753.72895641264675150.695647204185
Trimmed Mean ( 15 / 20 )562.0666666666673.63157713540845154.772057899150
Trimmed Mean ( 16 / 20 )562.2142857142863.50485571820613160.410108408697
Trimmed Mean ( 17 / 20 )562.4230769230773.34809846235284167.982836600283
Trimmed Mean ( 18 / 20 )562.5416666666673.18509843696236176.616728744862
Trimmed Mean ( 19 / 20 )562.6363636363642.97358169803949189.211671570119
Trimmed Mean ( 20 / 20 )562.652.70698414437446207.851235911106
Median563.5
Midrange549
Midmean - Weighted Average at Xnp560.903225806452
Midmean - Weighted Average at X(n+1)p562.066666666667
Midmean - Empirical Distribution Function560.903225806452
Midmean - Empirical Distribution Function - Averaging562.066666666667
Midmean - Empirical Distribution Function - Interpolation562.066666666667
Midmean - Closest Observation560.903225806452
Midmean - True Basic - Statistics Graphics Toolkit562.066666666667
Midmean - MS Excel (old versions)562.909090909091
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 559.75 & 5.4183004924043 & 103.307301022653 \tabularnewline
Geometric Mean & 558.181281997437 &  &  \tabularnewline
Harmonic Mean & 556.59267103469 &  &  \tabularnewline
Quadratic Mean & 561.295094699155 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 559.883333333333 & 5.37403738150171 & 104.182999407585 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 560.216666666667 & 5.26286917014584 & 106.447006101644 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 560.116666666667 & 5.17802242133586 & 108.171927637610 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 560.45 & 5.07978295946335 & 110.329516924717 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 560.7 & 5.02942190969924 & 111.483985648269 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 560.4 & 4.81670820852807 & 116.345017331090 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 560.516666666667 & 4.75100296676472 & 117.978597485145 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 560.65 & 4.67713666088909 & 119.870348174394 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 560.8 & 4.64975547622674 & 120.608492826614 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 558.966666666667 & 4.16265117244137 & 134.281409493853 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 558.966666666667 & 4.039911524082 & 138.361115914211 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 559.166666666667 & 4.00403515866046 & 139.650788394609 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 559.166666666667 & 3.93278029244264 & 142.181008113059 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 561.033333333333 & 3.61329674549408 & 155.269099896919 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 561.033333333333 & 3.53385296253659 & 158.759670897746 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 560.766666666667 & 3.40938938372668 & 164.477155159589 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 561.616666666667 & 3.1849834513993 & 176.332679662723 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 561.916666666667 & 3.04581695799659 & 184.487995968173 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 562.55 & 2.85204109684259 & 197.244703318890 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 562.883333333333 & 2.40210496986546 & 234.329198929579 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 560.120689655172 & 5.24326996896567 & 106.826597327710 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 560.375 & 5.0815788079905 & 110.275766877578 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 560.462962962963 & 4.9551949857281 & 113.106137009180 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 560.596153846154 & 4.8373437059247 & 115.889254087847 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 560.64 & 4.72654337173562 & 118.615223834099 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 560.625 & 4.60165181951928 & 121.831251469731 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 560.673913043478 & 4.50679083396246 & 124.406464311219 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 560.704545454545 & 4.40036270192746 & 127.422347528067 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 560.714285714286 & 4.27934098314699 & 131.028185863782 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 560.7 & 4.12422486889728 & 135.952819699164 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 560.973684210526 & 4.04745794905486 & 138.599014806694 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 561.277777777778 & 3.96904912668231 & 141.413663540855 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 561.588235294118 & 3.86356388980254 & 145.354975693910 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 561.9375 & 3.72895641264675 & 150.695647204185 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 562.066666666667 & 3.63157713540845 & 154.772057899150 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 562.214285714286 & 3.50485571820613 & 160.410108408697 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 562.423076923077 & 3.34809846235284 & 167.982836600283 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 562.541666666667 & 3.18509843696236 & 176.616728744862 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 562.636363636364 & 2.97358169803949 & 189.211671570119 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 562.65 & 2.70698414437446 & 207.851235911106 \tabularnewline
Median & 563.5 &  &  \tabularnewline
Midrange & 549 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 560.903225806452 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 562.066666666667 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 560.903225806452 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 562.066666666667 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 562.066666666667 &  &  \tabularnewline
Midmean - Closest Observation & 560.903225806452 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 562.066666666667 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 562.909090909091 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=49124&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]559.75[/C][C]5.4183004924043[/C][C]103.307301022653[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]558.181281997437[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]556.59267103469[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]561.295094699155[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]559.883333333333[/C][C]5.37403738150171[/C][C]104.182999407585[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]560.216666666667[/C][C]5.26286917014584[/C][C]106.447006101644[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]560.116666666667[/C][C]5.17802242133586[/C][C]108.171927637610[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]560.45[/C][C]5.07978295946335[/C][C]110.329516924717[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]560.7[/C][C]5.02942190969924[/C][C]111.483985648269[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]560.4[/C][C]4.81670820852807[/C][C]116.345017331090[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]560.516666666667[/C][C]4.75100296676472[/C][C]117.978597485145[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]560.65[/C][C]4.67713666088909[/C][C]119.870348174394[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]560.8[/C][C]4.64975547622674[/C][C]120.608492826614[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]558.966666666667[/C][C]4.16265117244137[/C][C]134.281409493853[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]558.966666666667[/C][C]4.039911524082[/C][C]138.361115914211[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]559.166666666667[/C][C]4.00403515866046[/C][C]139.650788394609[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]559.166666666667[/C][C]3.93278029244264[/C][C]142.181008113059[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]561.033333333333[/C][C]3.61329674549408[/C][C]155.269099896919[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]561.033333333333[/C][C]3.53385296253659[/C][C]158.759670897746[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]560.766666666667[/C][C]3.40938938372668[/C][C]164.477155159589[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]561.616666666667[/C][C]3.1849834513993[/C][C]176.332679662723[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]561.916666666667[/C][C]3.04581695799659[/C][C]184.487995968173[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]562.55[/C][C]2.85204109684259[/C][C]197.244703318890[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]562.883333333333[/C][C]2.40210496986546[/C][C]234.329198929579[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]560.120689655172[/C][C]5.24326996896567[/C][C]106.826597327710[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]560.375[/C][C]5.0815788079905[/C][C]110.275766877578[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]560.462962962963[/C][C]4.9551949857281[/C][C]113.106137009180[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]560.596153846154[/C][C]4.8373437059247[/C][C]115.889254087847[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]560.64[/C][C]4.72654337173562[/C][C]118.615223834099[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]560.625[/C][C]4.60165181951928[/C][C]121.831251469731[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]560.673913043478[/C][C]4.50679083396246[/C][C]124.406464311219[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]560.704545454545[/C][C]4.40036270192746[/C][C]127.422347528067[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]560.714285714286[/C][C]4.27934098314699[/C][C]131.028185863782[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]560.7[/C][C]4.12422486889728[/C][C]135.952819699164[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]560.973684210526[/C][C]4.04745794905486[/C][C]138.599014806694[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]561.277777777778[/C][C]3.96904912668231[/C][C]141.413663540855[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]561.588235294118[/C][C]3.86356388980254[/C][C]145.354975693910[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]561.9375[/C][C]3.72895641264675[/C][C]150.695647204185[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]562.066666666667[/C][C]3.63157713540845[/C][C]154.772057899150[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]562.214285714286[/C][C]3.50485571820613[/C][C]160.410108408697[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]562.423076923077[/C][C]3.34809846235284[/C][C]167.982836600283[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]562.541666666667[/C][C]3.18509843696236[/C][C]176.616728744862[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]562.636363636364[/C][C]2.97358169803949[/C][C]189.211671570119[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]562.65[/C][C]2.70698414437446[/C][C]207.851235911106[/C][/ROW]
[ROW][C]Median[/C][C]563.5[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]549[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]560.903225806452[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]562.066666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]560.903225806452[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]562.066666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]562.066666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]560.903225806452[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]562.066666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]562.909090909091[/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=49124&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=49124&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 Mean559.755.4183004924043103.307301022653
Geometric Mean558.181281997437
Harmonic Mean556.59267103469
Quadratic Mean561.295094699155
Winsorized Mean ( 1 / 20 )559.8833333333335.37403738150171104.182999407585
Winsorized Mean ( 2 / 20 )560.2166666666675.26286917014584106.447006101644
Winsorized Mean ( 3 / 20 )560.1166666666675.17802242133586108.171927637610
Winsorized Mean ( 4 / 20 )560.455.07978295946335110.329516924717
Winsorized Mean ( 5 / 20 )560.75.02942190969924111.483985648269
Winsorized Mean ( 6 / 20 )560.44.81670820852807116.345017331090
Winsorized Mean ( 7 / 20 )560.5166666666674.75100296676472117.978597485145
Winsorized Mean ( 8 / 20 )560.654.67713666088909119.870348174394
Winsorized Mean ( 9 / 20 )560.84.64975547622674120.608492826614
Winsorized Mean ( 10 / 20 )558.9666666666674.16265117244137134.281409493853
Winsorized Mean ( 11 / 20 )558.9666666666674.039911524082138.361115914211
Winsorized Mean ( 12 / 20 )559.1666666666674.00403515866046139.650788394609
Winsorized Mean ( 13 / 20 )559.1666666666673.93278029244264142.181008113059
Winsorized Mean ( 14 / 20 )561.0333333333333.61329674549408155.269099896919
Winsorized Mean ( 15 / 20 )561.0333333333333.53385296253659158.759670897746
Winsorized Mean ( 16 / 20 )560.7666666666673.40938938372668164.477155159589
Winsorized Mean ( 17 / 20 )561.6166666666673.1849834513993176.332679662723
Winsorized Mean ( 18 / 20 )561.9166666666673.04581695799659184.487995968173
Winsorized Mean ( 19 / 20 )562.552.85204109684259197.244703318890
Winsorized Mean ( 20 / 20 )562.8833333333332.40210496986546234.329198929579
Trimmed Mean ( 1 / 20 )560.1206896551725.24326996896567106.826597327710
Trimmed Mean ( 2 / 20 )560.3755.0815788079905110.275766877578
Trimmed Mean ( 3 / 20 )560.4629629629634.9551949857281113.106137009180
Trimmed Mean ( 4 / 20 )560.5961538461544.8373437059247115.889254087847
Trimmed Mean ( 5 / 20 )560.644.72654337173562118.615223834099
Trimmed Mean ( 6 / 20 )560.6254.60165181951928121.831251469731
Trimmed Mean ( 7 / 20 )560.6739130434784.50679083396246124.406464311219
Trimmed Mean ( 8 / 20 )560.7045454545454.40036270192746127.422347528067
Trimmed Mean ( 9 / 20 )560.7142857142864.27934098314699131.028185863782
Trimmed Mean ( 10 / 20 )560.74.12422486889728135.952819699164
Trimmed Mean ( 11 / 20 )560.9736842105264.04745794905486138.599014806694
Trimmed Mean ( 12 / 20 )561.2777777777783.96904912668231141.413663540855
Trimmed Mean ( 13 / 20 )561.5882352941183.86356388980254145.354975693910
Trimmed Mean ( 14 / 20 )561.93753.72895641264675150.695647204185
Trimmed Mean ( 15 / 20 )562.0666666666673.63157713540845154.772057899150
Trimmed Mean ( 16 / 20 )562.2142857142863.50485571820613160.410108408697
Trimmed Mean ( 17 / 20 )562.4230769230773.34809846235284167.982836600283
Trimmed Mean ( 18 / 20 )562.5416666666673.18509843696236176.616728744862
Trimmed Mean ( 19 / 20 )562.6363636363642.97358169803949189.211671570119
Trimmed Mean ( 20 / 20 )562.652.70698414437446207.851235911106
Median563.5
Midrange549
Midmean - Weighted Average at Xnp560.903225806452
Midmean - Weighted Average at X(n+1)p562.066666666667
Midmean - Empirical Distribution Function560.903225806452
Midmean - Empirical Distribution Function - Averaging562.066666666667
Midmean - Empirical Distribution Function - Interpolation562.066666666667
Midmean - Closest Observation560.903225806452
Midmean - True Basic - Statistics Graphics Toolkit562.066666666667
Midmean - MS Excel (old versions)562.909090909091
Number of observations60



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')