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of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationMon, 20 Oct 2008 13:45:28 -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/20/t1224531998eopshlrg2eezn16.htm/, Retrieved Fri, 17 May 2024 05:20:22 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=17999, Retrieved Fri, 17 May 2024 05:20:22 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact150
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Pearson Correlation] [investigating Ass...] [2007-10-22 22:15:01] [8cd6641b921d30ebe00b648d1481bba0]
F RM D    [Central Tendency] [Centrale tendens ...] [2008-10-20 19:45:28] [84a986a411c52e49a8807521f8b9f7a0] [Current]
Feedback Forum
2008-10-27 10:31:04 [Bonifer Spillemaeckers] [reply
De student maakt hier een goede voorspelling. Op basis van de grafiek kunnen we stellen dat de dalende tendens zich waarschijnlijk zal voortzetten in de toekomst.

Post a new message
Dataseries X:
118,63
121,83
119,97
124,98
129,99
126,60
121,71
119,28
122,63
116,74
114,23
113,23
112,75
113,54
115,30
121,05
119,51
116,78
117,17
117,50
119,65
120,97
117,18
116,87
119,46
122,52
124,10
118,39
113,10
113,94
114,58
118,79
120,44
118,37
118,44
117,93
117,76
118,29
121,11
124,86
131,17
130,16
131,76
134,70
135,32
140,23
136,31
131,62
128,90
133,89
138,21
146,12
144,69
149,18
156,60
158,87
164,85
162,89
153,31
150,91




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'George Udny Yule' @ 72.249.76.132

\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 & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=17999&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]'George Udny Yule' @ 72.249.76.132[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=17999&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=17999&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'George Udny Yule' @ 72.249.76.132







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean126.9976666666671.7483769449462572.6374635823003
Geometric Mean126.341393480115
Harmonic Mean125.735912395437
Quadratic Mean127.705754895123
Winsorized Mean ( 1 / 20 )126.9708333333331.7358561653108973.1459413923232
Winsorized Mean ( 2 / 20 )126.8411666666671.6902235350388675.0440187568154
Winsorized Mean ( 3 / 20 )126.7431666666671.6525011088599776.6977801026134
Winsorized Mean ( 4 / 20 )126.55051.5838625893610279.8999236739687
Winsorized Mean ( 5 / 20 )126.3746666666671.5246639245625682.886900274055
Winsorized Mean ( 6 / 20 )126.2366666666671.4735207974404885.6700949765627
Winsorized Mean ( 7 / 20 )125.9636666666671.3706552923037091.9003248839871
Winsorized Mean ( 8 / 20 )125.9651.2993548703476196.9442627835008
Winsorized Mean ( 9 / 20 )125.3021.14233423428735109.689437853686
Winsorized Mean ( 10 / 20 )124.9803333333331.0677196506359117.053510496785
Winsorized Mean ( 11 / 20 )124.6870.989307019347924126.034686463848
Winsorized Mean ( 12 / 20 )124.4910.95019910788885131.015698674559
Winsorized Mean ( 13 / 20 )124.4260.915477899957576135.913712396297
Winsorized Mean ( 14 / 20 )124.2976666666670.87213311994656142.521438326162
Winsorized Mean ( 15 / 20 )123.8076666666670.770275846351612160.731596678096
Winsorized Mean ( 16 / 20 )123.8663333333330.751498238611731164.825846514499
Winsorized Mean ( 17 / 20 )123.76150.726477991820034170.358223364678
Winsorized Mean ( 18 / 20 )123.46450.673998165306225183.182249381799
Winsorized Mean ( 19 / 20 )123.42650.662929588893503186.183422897161
Winsorized Mean ( 20 / 20 )123.12650.594409398046394207.14090390339
Trimmed Mean ( 1 / 20 )126.5906896551721.6659781977076175.9858021127538
Trimmed Mean ( 2 / 20 )126.1833928571431.5777284607609779.9778897290616
Trimmed Mean ( 3 / 20 )125.8179629629631.4981241095560583.9836714197516
Trimmed Mean ( 4 / 20 )125.4621153846151.4161502297933688.5937895183075
Trimmed Mean ( 5 / 20 )125.13561.3408712415928093.3240986295996
Trimmed Mean ( 6 / 20 )124.8258333333331.2662218272171198.5813312092986
Trimmed Mean ( 7 / 20 )124.5191304347831.18661112987152104.936762600790
Trimmed Mean ( 8 / 20 )124.2377272727271.11675235423095111.249129497724
Trimmed Mean ( 9 / 20 )123.9292857142861.04516859766469118.573487560946
Trimmed Mean ( 10 / 20 )123.70051.00069033543644123.615164071760
Trimmed Mean ( 11 / 20 )123.4984210526320.962830370510704128.2660215497
Trimmed Mean ( 12 / 20 )123.3183333333330.933532504258923132.098596214632
Trimmed Mean ( 13 / 20 )123.1458823529410.903221716073238136.340701470641
Trimmed Mean ( 14 / 20 )122.961250.868857326858376141.520645794177
Trimmed Mean ( 15 / 20 )122.7703333333330.831346848418564147.676428396733
Trimmed Mean ( 16 / 20 )122.6221428571430.810343084494498151.321267748754
Trimmed Mean ( 17 / 20 )122.4426923076920.78040000743057156.897348977262
Trimmed Mean ( 18 / 20 )122.248750.739920508974748165.218761363151
Trimmed Mean ( 19 / 20 )122.0645454545450.696288778995057175.307356856618
Trimmed Mean ( 20 / 20 )121.84950.622200879307098195.836270973605
Median121.08
Midrange138.8
Midmean - Weighted Average at Xnp122.608709677419
Midmean - Weighted Average at X(n+1)p122.770333333333
Midmean - Empirical Distribution Function122.608709677419
Midmean - Empirical Distribution Function - Averaging122.770333333333
Midmean - Empirical Distribution Function - Interpolation122.770333333333
Midmean - Closest Observation122.608709677419
Midmean - True Basic - Statistics Graphics Toolkit122.770333333333
Midmean - MS Excel (old versions)122.96125
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 126.997666666667 & 1.74837694494625 & 72.6374635823003 \tabularnewline
Geometric Mean & 126.341393480115 &  &  \tabularnewline
Harmonic Mean & 125.735912395437 &  &  \tabularnewline
Quadratic Mean & 127.705754895123 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 126.970833333333 & 1.73585616531089 & 73.1459413923232 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 126.841166666667 & 1.69022353503886 & 75.0440187568154 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 126.743166666667 & 1.65250110885997 & 76.6977801026134 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 126.5505 & 1.58386258936102 & 79.8999236739687 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 126.374666666667 & 1.52466392456256 & 82.886900274055 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 126.236666666667 & 1.47352079744048 & 85.6700949765627 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 125.963666666667 & 1.37065529230370 & 91.9003248839871 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 125.965 & 1.29935487034761 & 96.9442627835008 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 125.302 & 1.14233423428735 & 109.689437853686 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 124.980333333333 & 1.0677196506359 & 117.053510496785 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 124.687 & 0.989307019347924 & 126.034686463848 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 124.491 & 0.95019910788885 & 131.015698674559 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 124.426 & 0.915477899957576 & 135.913712396297 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 124.297666666667 & 0.87213311994656 & 142.521438326162 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 123.807666666667 & 0.770275846351612 & 160.731596678096 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 123.866333333333 & 0.751498238611731 & 164.825846514499 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 123.7615 & 0.726477991820034 & 170.358223364678 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 123.4645 & 0.673998165306225 & 183.182249381799 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 123.4265 & 0.662929588893503 & 186.183422897161 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 123.1265 & 0.594409398046394 & 207.14090390339 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 126.590689655172 & 1.66597819770761 & 75.9858021127538 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 126.183392857143 & 1.57772846076097 & 79.9778897290616 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 125.817962962963 & 1.49812410955605 & 83.9836714197516 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 125.462115384615 & 1.41615022979336 & 88.5937895183075 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 125.1356 & 1.34087124159280 & 93.3240986295996 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 124.825833333333 & 1.26622182721711 & 98.5813312092986 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 124.519130434783 & 1.18661112987152 & 104.936762600790 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 124.237727272727 & 1.11675235423095 & 111.249129497724 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 123.929285714286 & 1.04516859766469 & 118.573487560946 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 123.7005 & 1.00069033543644 & 123.615164071760 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 123.498421052632 & 0.962830370510704 & 128.2660215497 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 123.318333333333 & 0.933532504258923 & 132.098596214632 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 123.145882352941 & 0.903221716073238 & 136.340701470641 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 122.96125 & 0.868857326858376 & 141.520645794177 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 122.770333333333 & 0.831346848418564 & 147.676428396733 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 122.622142857143 & 0.810343084494498 & 151.321267748754 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 122.442692307692 & 0.78040000743057 & 156.897348977262 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 122.24875 & 0.739920508974748 & 165.218761363151 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 122.064545454545 & 0.696288778995057 & 175.307356856618 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 121.8495 & 0.622200879307098 & 195.836270973605 \tabularnewline
Median & 121.08 &  &  \tabularnewline
Midrange & 138.8 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 122.608709677419 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 122.770333333333 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 122.608709677419 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 122.770333333333 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 122.770333333333 &  &  \tabularnewline
Midmean - Closest Observation & 122.608709677419 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 122.770333333333 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 122.96125 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=17999&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]126.997666666667[/C][C]1.74837694494625[/C][C]72.6374635823003[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]126.341393480115[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]125.735912395437[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]127.705754895123[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]126.970833333333[/C][C]1.73585616531089[/C][C]73.1459413923232[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]126.841166666667[/C][C]1.69022353503886[/C][C]75.0440187568154[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]126.743166666667[/C][C]1.65250110885997[/C][C]76.6977801026134[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]126.5505[/C][C]1.58386258936102[/C][C]79.8999236739687[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]126.374666666667[/C][C]1.52466392456256[/C][C]82.886900274055[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]126.236666666667[/C][C]1.47352079744048[/C][C]85.6700949765627[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]125.963666666667[/C][C]1.37065529230370[/C][C]91.9003248839871[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]125.965[/C][C]1.29935487034761[/C][C]96.9442627835008[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]125.302[/C][C]1.14233423428735[/C][C]109.689437853686[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]124.980333333333[/C][C]1.0677196506359[/C][C]117.053510496785[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]124.687[/C][C]0.989307019347924[/C][C]126.034686463848[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]124.491[/C][C]0.95019910788885[/C][C]131.015698674559[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]124.426[/C][C]0.915477899957576[/C][C]135.913712396297[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]124.297666666667[/C][C]0.87213311994656[/C][C]142.521438326162[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]123.807666666667[/C][C]0.770275846351612[/C][C]160.731596678096[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]123.866333333333[/C][C]0.751498238611731[/C][C]164.825846514499[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]123.7615[/C][C]0.726477991820034[/C][C]170.358223364678[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]123.4645[/C][C]0.673998165306225[/C][C]183.182249381799[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]123.4265[/C][C]0.662929588893503[/C][C]186.183422897161[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]123.1265[/C][C]0.594409398046394[/C][C]207.14090390339[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]126.590689655172[/C][C]1.66597819770761[/C][C]75.9858021127538[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]126.183392857143[/C][C]1.57772846076097[/C][C]79.9778897290616[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]125.817962962963[/C][C]1.49812410955605[/C][C]83.9836714197516[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]125.462115384615[/C][C]1.41615022979336[/C][C]88.5937895183075[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]125.1356[/C][C]1.34087124159280[/C][C]93.3240986295996[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]124.825833333333[/C][C]1.26622182721711[/C][C]98.5813312092986[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]124.519130434783[/C][C]1.18661112987152[/C][C]104.936762600790[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]124.237727272727[/C][C]1.11675235423095[/C][C]111.249129497724[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]123.929285714286[/C][C]1.04516859766469[/C][C]118.573487560946[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]123.7005[/C][C]1.00069033543644[/C][C]123.615164071760[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]123.498421052632[/C][C]0.962830370510704[/C][C]128.2660215497[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]123.318333333333[/C][C]0.933532504258923[/C][C]132.098596214632[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]123.145882352941[/C][C]0.903221716073238[/C][C]136.340701470641[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]122.96125[/C][C]0.868857326858376[/C][C]141.520645794177[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]122.770333333333[/C][C]0.831346848418564[/C][C]147.676428396733[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]122.622142857143[/C][C]0.810343084494498[/C][C]151.321267748754[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]122.442692307692[/C][C]0.78040000743057[/C][C]156.897348977262[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]122.24875[/C][C]0.739920508974748[/C][C]165.218761363151[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]122.064545454545[/C][C]0.696288778995057[/C][C]175.307356856618[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]121.8495[/C][C]0.622200879307098[/C][C]195.836270973605[/C][/ROW]
[ROW][C]Median[/C][C]121.08[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]138.8[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]122.608709677419[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]122.770333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]122.608709677419[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]122.770333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]122.770333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]122.608709677419[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]122.770333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]122.96125[/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=17999&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=17999&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 Mean126.9976666666671.7483769449462572.6374635823003
Geometric Mean126.341393480115
Harmonic Mean125.735912395437
Quadratic Mean127.705754895123
Winsorized Mean ( 1 / 20 )126.9708333333331.7358561653108973.1459413923232
Winsorized Mean ( 2 / 20 )126.8411666666671.6902235350388675.0440187568154
Winsorized Mean ( 3 / 20 )126.7431666666671.6525011088599776.6977801026134
Winsorized Mean ( 4 / 20 )126.55051.5838625893610279.8999236739687
Winsorized Mean ( 5 / 20 )126.3746666666671.5246639245625682.886900274055
Winsorized Mean ( 6 / 20 )126.2366666666671.4735207974404885.6700949765627
Winsorized Mean ( 7 / 20 )125.9636666666671.3706552923037091.9003248839871
Winsorized Mean ( 8 / 20 )125.9651.2993548703476196.9442627835008
Winsorized Mean ( 9 / 20 )125.3021.14233423428735109.689437853686
Winsorized Mean ( 10 / 20 )124.9803333333331.0677196506359117.053510496785
Winsorized Mean ( 11 / 20 )124.6870.989307019347924126.034686463848
Winsorized Mean ( 12 / 20 )124.4910.95019910788885131.015698674559
Winsorized Mean ( 13 / 20 )124.4260.915477899957576135.913712396297
Winsorized Mean ( 14 / 20 )124.2976666666670.87213311994656142.521438326162
Winsorized Mean ( 15 / 20 )123.8076666666670.770275846351612160.731596678096
Winsorized Mean ( 16 / 20 )123.8663333333330.751498238611731164.825846514499
Winsorized Mean ( 17 / 20 )123.76150.726477991820034170.358223364678
Winsorized Mean ( 18 / 20 )123.46450.673998165306225183.182249381799
Winsorized Mean ( 19 / 20 )123.42650.662929588893503186.183422897161
Winsorized Mean ( 20 / 20 )123.12650.594409398046394207.14090390339
Trimmed Mean ( 1 / 20 )126.5906896551721.6659781977076175.9858021127538
Trimmed Mean ( 2 / 20 )126.1833928571431.5777284607609779.9778897290616
Trimmed Mean ( 3 / 20 )125.8179629629631.4981241095560583.9836714197516
Trimmed Mean ( 4 / 20 )125.4621153846151.4161502297933688.5937895183075
Trimmed Mean ( 5 / 20 )125.13561.3408712415928093.3240986295996
Trimmed Mean ( 6 / 20 )124.8258333333331.2662218272171198.5813312092986
Trimmed Mean ( 7 / 20 )124.5191304347831.18661112987152104.936762600790
Trimmed Mean ( 8 / 20 )124.2377272727271.11675235423095111.249129497724
Trimmed Mean ( 9 / 20 )123.9292857142861.04516859766469118.573487560946
Trimmed Mean ( 10 / 20 )123.70051.00069033543644123.615164071760
Trimmed Mean ( 11 / 20 )123.4984210526320.962830370510704128.2660215497
Trimmed Mean ( 12 / 20 )123.3183333333330.933532504258923132.098596214632
Trimmed Mean ( 13 / 20 )123.1458823529410.903221716073238136.340701470641
Trimmed Mean ( 14 / 20 )122.961250.868857326858376141.520645794177
Trimmed Mean ( 15 / 20 )122.7703333333330.831346848418564147.676428396733
Trimmed Mean ( 16 / 20 )122.6221428571430.810343084494498151.321267748754
Trimmed Mean ( 17 / 20 )122.4426923076920.78040000743057156.897348977262
Trimmed Mean ( 18 / 20 )122.248750.739920508974748165.218761363151
Trimmed Mean ( 19 / 20 )122.0645454545450.696288778995057175.307356856618
Trimmed Mean ( 20 / 20 )121.84950.622200879307098195.836270973605
Median121.08
Midrange138.8
Midmean - Weighted Average at Xnp122.608709677419
Midmean - Weighted Average at X(n+1)p122.770333333333
Midmean - Empirical Distribution Function122.608709677419
Midmean - Empirical Distribution Function - Averaging122.770333333333
Midmean - Empirical Distribution Function - Interpolation122.770333333333
Midmean - Closest Observation122.608709677419
Midmean - True Basic - Statistics Graphics Toolkit122.770333333333
Midmean - MS Excel (old versions)122.96125
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')