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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 computationFri, 23 Dec 2011 11:00:30 -0500
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2011/Dec/23/t13246560933wzn3b1oa0tts7i.htm/, Retrieved Mon, 29 Apr 2024 18:24:51 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=160535, Retrieved Mon, 29 Apr 2024 18:24:51 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact89
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Histogram] [paper-frequency p...] [2011-12-21 18:33:32] [c2267e575f67090c7e8d960bdccd246a]
- RMP   [Stem-and-leaf Plot] [paper-stem and le...] [2011-12-22 10:02:22] [c2267e575f67090c7e8d960bdccd246a]
- RMP     [Central Tendency] [paper-central ten...] [2011-12-22 10:23:41] [c2267e575f67090c7e8d960bdccd246a]
- R  D        [Central Tendency] [paper-central ten...] [2011-12-23 16:00:30] [fe2dc4bc83c881ccd49ef12feaba2b65] [Current]
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Dataseries X:
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
528
533
536
537
524
536
587
597
581
564
558
575
580
575
563
552
537
545
601
604
586
564
549
551
556
548
540
531
521
519
572
581
563
548
539




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gertrude Mary Cox' @ cox.wessa.net

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 1 seconds \tabularnewline
R Server & 'Gertrude Mary Cox' @ cox.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=160535&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gertrude Mary Cox' @ cox.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=160535&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=160535&T=0

As an alternative you can also use a QR Code:  

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

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gertrude Mary Cox' @ cox.wessa.net







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean548.5428571428574.04885719706051135.480909907394
Geometric Mean547.510003390344
Harmonic Mean546.47491895706
Quadratic Mean549.572925097298
Winsorized Mean ( 1 / 23 )548.5857142857143.99106107080142137.45360057233
Winsorized Mean ( 2 / 23 )548.9285714285713.90960601916374140.405086532475
Winsorized Mean ( 3 / 23 )548.3714285714293.71657199901187147.547640330182
Winsorized Mean ( 4 / 23 )548.5428571428573.60874746508882152.003669541713
Winsorized Mean ( 5 / 23 )548.4714285714293.50809306427988156.344606178233
Winsorized Mean ( 6 / 23 )548.2142857142863.32876868767456164.689810903401
Winsorized Mean ( 7 / 23 )548.2142857142863.25658389377612168.340292648998
Winsorized Mean ( 8 / 23 )548.3285714285713.19612352084288171.560506924328
Winsorized Mean ( 9 / 23 )548.3285714285713.15150372787666173.989504304985
Winsorized Mean ( 10 / 23 )548.0428571428572.9593124736118185.192629041291
Winsorized Mean ( 11 / 23 )548.3571428571432.90776327308332188.583832780747
Winsorized Mean ( 12 / 23 )548.3571428571432.85255584168513192.233622509281
Winsorized Mean ( 13 / 23 )548.5428571428572.82320213145757194.298116677765
Winsorized Mean ( 14 / 23 )547.7428571428572.63584824068921207.80515687035
Winsorized Mean ( 15 / 23 )548.1714285714292.56912480192296213.368937219838
Winsorized Mean ( 16 / 23 )548.6285714285712.4316044876792225.624098906068
Winsorized Mean ( 17 / 23 )548.8714285714292.3246737947498236.106859298296
Winsorized Mean ( 18 / 23 )549.1285714285712.28831955562208239.970230591021
Winsorized Mean ( 19 / 23 )549.1285714285712.20960836384226248.518506905766
Winsorized Mean ( 20 / 23 )547.4142857142861.96274756264684278.90203311529
Winsorized Mean ( 21 / 23 )548.0142857142861.7951502249338305.274889033031
Winsorized Mean ( 22 / 23 )548.0142857142861.70936924392228320.594445970505
Winsorized Mean ( 23 / 23 )548.3428571428571.6651196606179329.311382305927
Trimmed Mean ( 1 / 23 )548.5735294117653.83060524107314143.208055878418
Trimmed Mean ( 2 / 23 )548.5606060606063.63774109497492150.797044577574
Trimmed Mean ( 3 / 23 )548.3593753.45875407563249158.542458645234
Trimmed Mean ( 4 / 23 )548.3548387096773.33539396000322164.404818526789
Trimmed Mean ( 5 / 23 )548.33.22711849570336169.90389436583
Trimmed Mean ( 6 / 23 )548.2586206896553.1281908423327175.263802089778
Trimmed Mean ( 7 / 23 )548.2678571428573.05910298704428179.225040629507
Trimmed Mean ( 8 / 23 )548.2777777777782.99211830553945183.240674930107
Trimmed Mean ( 9 / 23 )548.2692307692312.92298265308019187.571838714634
Trimmed Mean ( 10 / 23 )548.262.84609435212968192.635918619404
Trimmed Mean ( 11 / 23 )548.2916666666672.79309532618957196.302525562084
Trimmed Mean ( 12 / 23 )548.2826086956522.73528792671046200.44785901389
Trimmed Mean ( 13 / 23 )548.2727272727272.67146926427812205.232654032005
Trimmed Mean ( 14 / 23 )548.2380952380952.59316745491997211.416387398327
Trimmed Mean ( 15 / 23 )548.32.53291157082931216.470249618891
Trimmed Mean ( 16 / 23 )548.3157894736842.46601516931726222.348911837996
Trimmed Mean ( 17 / 23 )548.2777777777782.40687214236656227.796802383812
Trimmed Mean ( 18 / 23 )548.2058823529412.34911118768985233.367362611753
Trimmed Mean ( 19 / 23 )548.093752.27333747077912241.096518684557
Trimmed Mean ( 20 / 23 )547.9666666666672.18431363444901250.864462879613
Trimmed Mean ( 21 / 23 )548.0357142857142.12908936917878257.403809449811
Trimmed Mean ( 22 / 23 )548.0384615384622.09356579822066261.772742946147
Trimmed Mean ( 23 / 23 )548.0416666666672.05757628511852266.353024493135
Median548.5
Midrange547.5
Midmean - Weighted Average at Xnp548.277777777778
Midmean - Weighted Average at X(n+1)p548.277777777778
Midmean - Empirical Distribution Function548.277777777778
Midmean - Empirical Distribution Function - Averaging548.277777777778
Midmean - Empirical Distribution Function - Interpolation548.914285714286
Midmean - Closest Observation548.277777777778
Midmean - True Basic - Statistics Graphics Toolkit548.277777777778
Midmean - MS Excel (old versions)548.277777777778
Number of observations70

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 548.542857142857 & 4.04885719706051 & 135.480909907394 \tabularnewline
Geometric Mean & 547.510003390344 &  &  \tabularnewline
Harmonic Mean & 546.47491895706 &  &  \tabularnewline
Quadratic Mean & 549.572925097298 &  &  \tabularnewline
Winsorized Mean ( 1 / 23 ) & 548.585714285714 & 3.99106107080142 & 137.45360057233 \tabularnewline
Winsorized Mean ( 2 / 23 ) & 548.928571428571 & 3.90960601916374 & 140.405086532475 \tabularnewline
Winsorized Mean ( 3 / 23 ) & 548.371428571429 & 3.71657199901187 & 147.547640330182 \tabularnewline
Winsorized Mean ( 4 / 23 ) & 548.542857142857 & 3.60874746508882 & 152.003669541713 \tabularnewline
Winsorized Mean ( 5 / 23 ) & 548.471428571429 & 3.50809306427988 & 156.344606178233 \tabularnewline
Winsorized Mean ( 6 / 23 ) & 548.214285714286 & 3.32876868767456 & 164.689810903401 \tabularnewline
Winsorized Mean ( 7 / 23 ) & 548.214285714286 & 3.25658389377612 & 168.340292648998 \tabularnewline
Winsorized Mean ( 8 / 23 ) & 548.328571428571 & 3.19612352084288 & 171.560506924328 \tabularnewline
Winsorized Mean ( 9 / 23 ) & 548.328571428571 & 3.15150372787666 & 173.989504304985 \tabularnewline
Winsorized Mean ( 10 / 23 ) & 548.042857142857 & 2.9593124736118 & 185.192629041291 \tabularnewline
Winsorized Mean ( 11 / 23 ) & 548.357142857143 & 2.90776327308332 & 188.583832780747 \tabularnewline
Winsorized Mean ( 12 / 23 ) & 548.357142857143 & 2.85255584168513 & 192.233622509281 \tabularnewline
Winsorized Mean ( 13 / 23 ) & 548.542857142857 & 2.82320213145757 & 194.298116677765 \tabularnewline
Winsorized Mean ( 14 / 23 ) & 547.742857142857 & 2.63584824068921 & 207.80515687035 \tabularnewline
Winsorized Mean ( 15 / 23 ) & 548.171428571429 & 2.56912480192296 & 213.368937219838 \tabularnewline
Winsorized Mean ( 16 / 23 ) & 548.628571428571 & 2.4316044876792 & 225.624098906068 \tabularnewline
Winsorized Mean ( 17 / 23 ) & 548.871428571429 & 2.3246737947498 & 236.106859298296 \tabularnewline
Winsorized Mean ( 18 / 23 ) & 549.128571428571 & 2.28831955562208 & 239.970230591021 \tabularnewline
Winsorized Mean ( 19 / 23 ) & 549.128571428571 & 2.20960836384226 & 248.518506905766 \tabularnewline
Winsorized Mean ( 20 / 23 ) & 547.414285714286 & 1.96274756264684 & 278.90203311529 \tabularnewline
Winsorized Mean ( 21 / 23 ) & 548.014285714286 & 1.7951502249338 & 305.274889033031 \tabularnewline
Winsorized Mean ( 22 / 23 ) & 548.014285714286 & 1.70936924392228 & 320.594445970505 \tabularnewline
Winsorized Mean ( 23 / 23 ) & 548.342857142857 & 1.6651196606179 & 329.311382305927 \tabularnewline
Trimmed Mean ( 1 / 23 ) & 548.573529411765 & 3.83060524107314 & 143.208055878418 \tabularnewline
Trimmed Mean ( 2 / 23 ) & 548.560606060606 & 3.63774109497492 & 150.797044577574 \tabularnewline
Trimmed Mean ( 3 / 23 ) & 548.359375 & 3.45875407563249 & 158.542458645234 \tabularnewline
Trimmed Mean ( 4 / 23 ) & 548.354838709677 & 3.33539396000322 & 164.404818526789 \tabularnewline
Trimmed Mean ( 5 / 23 ) & 548.3 & 3.22711849570336 & 169.90389436583 \tabularnewline
Trimmed Mean ( 6 / 23 ) & 548.258620689655 & 3.1281908423327 & 175.263802089778 \tabularnewline
Trimmed Mean ( 7 / 23 ) & 548.267857142857 & 3.05910298704428 & 179.225040629507 \tabularnewline
Trimmed Mean ( 8 / 23 ) & 548.277777777778 & 2.99211830553945 & 183.240674930107 \tabularnewline
Trimmed Mean ( 9 / 23 ) & 548.269230769231 & 2.92298265308019 & 187.571838714634 \tabularnewline
Trimmed Mean ( 10 / 23 ) & 548.26 & 2.84609435212968 & 192.635918619404 \tabularnewline
Trimmed Mean ( 11 / 23 ) & 548.291666666667 & 2.79309532618957 & 196.302525562084 \tabularnewline
Trimmed Mean ( 12 / 23 ) & 548.282608695652 & 2.73528792671046 & 200.44785901389 \tabularnewline
Trimmed Mean ( 13 / 23 ) & 548.272727272727 & 2.67146926427812 & 205.232654032005 \tabularnewline
Trimmed Mean ( 14 / 23 ) & 548.238095238095 & 2.59316745491997 & 211.416387398327 \tabularnewline
Trimmed Mean ( 15 / 23 ) & 548.3 & 2.53291157082931 & 216.470249618891 \tabularnewline
Trimmed Mean ( 16 / 23 ) & 548.315789473684 & 2.46601516931726 & 222.348911837996 \tabularnewline
Trimmed Mean ( 17 / 23 ) & 548.277777777778 & 2.40687214236656 & 227.796802383812 \tabularnewline
Trimmed Mean ( 18 / 23 ) & 548.205882352941 & 2.34911118768985 & 233.367362611753 \tabularnewline
Trimmed Mean ( 19 / 23 ) & 548.09375 & 2.27333747077912 & 241.096518684557 \tabularnewline
Trimmed Mean ( 20 / 23 ) & 547.966666666667 & 2.18431363444901 & 250.864462879613 \tabularnewline
Trimmed Mean ( 21 / 23 ) & 548.035714285714 & 2.12908936917878 & 257.403809449811 \tabularnewline
Trimmed Mean ( 22 / 23 ) & 548.038461538462 & 2.09356579822066 & 261.772742946147 \tabularnewline
Trimmed Mean ( 23 / 23 ) & 548.041666666667 & 2.05757628511852 & 266.353024493135 \tabularnewline
Median & 548.5 &  &  \tabularnewline
Midrange & 547.5 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 548.277777777778 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 548.277777777778 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 548.277777777778 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 548.277777777778 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 548.914285714286 &  &  \tabularnewline
Midmean - Closest Observation & 548.277777777778 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 548.277777777778 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 548.277777777778 &  &  \tabularnewline
Number of observations & 70 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=160535&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]548.542857142857[/C][C]4.04885719706051[/C][C]135.480909907394[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]547.510003390344[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]546.47491895706[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]549.572925097298[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 23 )[/C][C]548.585714285714[/C][C]3.99106107080142[/C][C]137.45360057233[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 23 )[/C][C]548.928571428571[/C][C]3.90960601916374[/C][C]140.405086532475[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 23 )[/C][C]548.371428571429[/C][C]3.71657199901187[/C][C]147.547640330182[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 23 )[/C][C]548.542857142857[/C][C]3.60874746508882[/C][C]152.003669541713[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 23 )[/C][C]548.471428571429[/C][C]3.50809306427988[/C][C]156.344606178233[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 23 )[/C][C]548.214285714286[/C][C]3.32876868767456[/C][C]164.689810903401[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 23 )[/C][C]548.214285714286[/C][C]3.25658389377612[/C][C]168.340292648998[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 23 )[/C][C]548.328571428571[/C][C]3.19612352084288[/C][C]171.560506924328[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 23 )[/C][C]548.328571428571[/C][C]3.15150372787666[/C][C]173.989504304985[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 23 )[/C][C]548.042857142857[/C][C]2.9593124736118[/C][C]185.192629041291[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 23 )[/C][C]548.357142857143[/C][C]2.90776327308332[/C][C]188.583832780747[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 23 )[/C][C]548.357142857143[/C][C]2.85255584168513[/C][C]192.233622509281[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 23 )[/C][C]548.542857142857[/C][C]2.82320213145757[/C][C]194.298116677765[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 23 )[/C][C]547.742857142857[/C][C]2.63584824068921[/C][C]207.80515687035[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 23 )[/C][C]548.171428571429[/C][C]2.56912480192296[/C][C]213.368937219838[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 23 )[/C][C]548.628571428571[/C][C]2.4316044876792[/C][C]225.624098906068[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 23 )[/C][C]548.871428571429[/C][C]2.3246737947498[/C][C]236.106859298296[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 23 )[/C][C]549.128571428571[/C][C]2.28831955562208[/C][C]239.970230591021[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 23 )[/C][C]549.128571428571[/C][C]2.20960836384226[/C][C]248.518506905766[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 23 )[/C][C]547.414285714286[/C][C]1.96274756264684[/C][C]278.90203311529[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 23 )[/C][C]548.014285714286[/C][C]1.7951502249338[/C][C]305.274889033031[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 23 )[/C][C]548.014285714286[/C][C]1.70936924392228[/C][C]320.594445970505[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 23 )[/C][C]548.342857142857[/C][C]1.6651196606179[/C][C]329.311382305927[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 23 )[/C][C]548.573529411765[/C][C]3.83060524107314[/C][C]143.208055878418[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 23 )[/C][C]548.560606060606[/C][C]3.63774109497492[/C][C]150.797044577574[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 23 )[/C][C]548.359375[/C][C]3.45875407563249[/C][C]158.542458645234[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 23 )[/C][C]548.354838709677[/C][C]3.33539396000322[/C][C]164.404818526789[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 23 )[/C][C]548.3[/C][C]3.22711849570336[/C][C]169.90389436583[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 23 )[/C][C]548.258620689655[/C][C]3.1281908423327[/C][C]175.263802089778[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 23 )[/C][C]548.267857142857[/C][C]3.05910298704428[/C][C]179.225040629507[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 23 )[/C][C]548.277777777778[/C][C]2.99211830553945[/C][C]183.240674930107[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 23 )[/C][C]548.269230769231[/C][C]2.92298265308019[/C][C]187.571838714634[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 23 )[/C][C]548.26[/C][C]2.84609435212968[/C][C]192.635918619404[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 23 )[/C][C]548.291666666667[/C][C]2.79309532618957[/C][C]196.302525562084[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 23 )[/C][C]548.282608695652[/C][C]2.73528792671046[/C][C]200.44785901389[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 23 )[/C][C]548.272727272727[/C][C]2.67146926427812[/C][C]205.232654032005[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 23 )[/C][C]548.238095238095[/C][C]2.59316745491997[/C][C]211.416387398327[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 23 )[/C][C]548.3[/C][C]2.53291157082931[/C][C]216.470249618891[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 23 )[/C][C]548.315789473684[/C][C]2.46601516931726[/C][C]222.348911837996[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 23 )[/C][C]548.277777777778[/C][C]2.40687214236656[/C][C]227.796802383812[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 23 )[/C][C]548.205882352941[/C][C]2.34911118768985[/C][C]233.367362611753[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 23 )[/C][C]548.09375[/C][C]2.27333747077912[/C][C]241.096518684557[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 23 )[/C][C]547.966666666667[/C][C]2.18431363444901[/C][C]250.864462879613[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 23 )[/C][C]548.035714285714[/C][C]2.12908936917878[/C][C]257.403809449811[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 23 )[/C][C]548.038461538462[/C][C]2.09356579822066[/C][C]261.772742946147[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 23 )[/C][C]548.041666666667[/C][C]2.05757628511852[/C][C]266.353024493135[/C][/ROW]
[ROW][C]Median[/C][C]548.5[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]547.5[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]548.277777777778[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]548.277777777778[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]548.277777777778[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]548.277777777778[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]548.914285714286[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]548.277777777778[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]548.277777777778[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]548.277777777778[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]70[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=160535&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=160535&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 Mean548.5428571428574.04885719706051135.480909907394
Geometric Mean547.510003390344
Harmonic Mean546.47491895706
Quadratic Mean549.572925097298
Winsorized Mean ( 1 / 23 )548.5857142857143.99106107080142137.45360057233
Winsorized Mean ( 2 / 23 )548.9285714285713.90960601916374140.405086532475
Winsorized Mean ( 3 / 23 )548.3714285714293.71657199901187147.547640330182
Winsorized Mean ( 4 / 23 )548.5428571428573.60874746508882152.003669541713
Winsorized Mean ( 5 / 23 )548.4714285714293.50809306427988156.344606178233
Winsorized Mean ( 6 / 23 )548.2142857142863.32876868767456164.689810903401
Winsorized Mean ( 7 / 23 )548.2142857142863.25658389377612168.340292648998
Winsorized Mean ( 8 / 23 )548.3285714285713.19612352084288171.560506924328
Winsorized Mean ( 9 / 23 )548.3285714285713.15150372787666173.989504304985
Winsorized Mean ( 10 / 23 )548.0428571428572.9593124736118185.192629041291
Winsorized Mean ( 11 / 23 )548.3571428571432.90776327308332188.583832780747
Winsorized Mean ( 12 / 23 )548.3571428571432.85255584168513192.233622509281
Winsorized Mean ( 13 / 23 )548.5428571428572.82320213145757194.298116677765
Winsorized Mean ( 14 / 23 )547.7428571428572.63584824068921207.80515687035
Winsorized Mean ( 15 / 23 )548.1714285714292.56912480192296213.368937219838
Winsorized Mean ( 16 / 23 )548.6285714285712.4316044876792225.624098906068
Winsorized Mean ( 17 / 23 )548.8714285714292.3246737947498236.106859298296
Winsorized Mean ( 18 / 23 )549.1285714285712.28831955562208239.970230591021
Winsorized Mean ( 19 / 23 )549.1285714285712.20960836384226248.518506905766
Winsorized Mean ( 20 / 23 )547.4142857142861.96274756264684278.90203311529
Winsorized Mean ( 21 / 23 )548.0142857142861.7951502249338305.274889033031
Winsorized Mean ( 22 / 23 )548.0142857142861.70936924392228320.594445970505
Winsorized Mean ( 23 / 23 )548.3428571428571.6651196606179329.311382305927
Trimmed Mean ( 1 / 23 )548.5735294117653.83060524107314143.208055878418
Trimmed Mean ( 2 / 23 )548.5606060606063.63774109497492150.797044577574
Trimmed Mean ( 3 / 23 )548.3593753.45875407563249158.542458645234
Trimmed Mean ( 4 / 23 )548.3548387096773.33539396000322164.404818526789
Trimmed Mean ( 5 / 23 )548.33.22711849570336169.90389436583
Trimmed Mean ( 6 / 23 )548.2586206896553.1281908423327175.263802089778
Trimmed Mean ( 7 / 23 )548.2678571428573.05910298704428179.225040629507
Trimmed Mean ( 8 / 23 )548.2777777777782.99211830553945183.240674930107
Trimmed Mean ( 9 / 23 )548.2692307692312.92298265308019187.571838714634
Trimmed Mean ( 10 / 23 )548.262.84609435212968192.635918619404
Trimmed Mean ( 11 / 23 )548.2916666666672.79309532618957196.302525562084
Trimmed Mean ( 12 / 23 )548.2826086956522.73528792671046200.44785901389
Trimmed Mean ( 13 / 23 )548.2727272727272.67146926427812205.232654032005
Trimmed Mean ( 14 / 23 )548.2380952380952.59316745491997211.416387398327
Trimmed Mean ( 15 / 23 )548.32.53291157082931216.470249618891
Trimmed Mean ( 16 / 23 )548.3157894736842.46601516931726222.348911837996
Trimmed Mean ( 17 / 23 )548.2777777777782.40687214236656227.796802383812
Trimmed Mean ( 18 / 23 )548.2058823529412.34911118768985233.367362611753
Trimmed Mean ( 19 / 23 )548.093752.27333747077912241.096518684557
Trimmed Mean ( 20 / 23 )547.9666666666672.18431363444901250.864462879613
Trimmed Mean ( 21 / 23 )548.0357142857142.12908936917878257.403809449811
Trimmed Mean ( 22 / 23 )548.0384615384622.09356579822066261.772742946147
Trimmed Mean ( 23 / 23 )548.0416666666672.05757628511852266.353024493135
Median548.5
Midrange547.5
Midmean - Weighted Average at Xnp548.277777777778
Midmean - Weighted Average at X(n+1)p548.277777777778
Midmean - Empirical Distribution Function548.277777777778
Midmean - Empirical Distribution Function - Averaging548.277777777778
Midmean - Empirical Distribution Function - Interpolation548.914285714286
Midmean - Closest Observation548.277777777778
Midmean - True Basic - Statistics Graphics Toolkit548.277777777778
Midmean - MS Excel (old versions)548.277777777778
Number of observations70



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')