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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, 21 Oct 2008 01:16:27 -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/21/t1224573444ijok07ugefcxxmz.htm/, Retrieved Sun, 19 May 2024 21:16:10 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=18348, Retrieved Sun, 19 May 2024 21:16:10 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact119
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [Q9 Tijdreeks4] [2008-10-21 07:16:27] [d7f41258beeebb8716e3f5d39f3cdc01] [Current]
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Dataseries X:
7,2
6,7
10,4
12,1
9
9,8
9,5
10,7
16,9
12,2
18,8
19,9
14,9
22,7
17,5
25
26,8
23,9
35,3
37,5
54,2
24,8
54,8
49
43,5
40,1
39,4
42,3
29,2
48,6
38,9
43,4
40,8
94,6
47,7
34,8
43,4
43,3
41,8
52,3
32,3
65,1
44,8
45,3
55,6
50
44,9
40,6
39,6
38,9
55,3
35,1
27,2
52,4
54,8
39,7
45,8
30,6
32,1
21,5




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=18348&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=18348&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=18348&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 Mean35.08833333333332.1892122408311416.0278353459288
Geometric Mean30.2341950948989
Harmonic Mean24.5663500163922
Quadratic Mean38.9096067829013
Winsorized Mean ( 1 / 20 )34.6052.0086598182710617.2279047378894
Winsorized Mean ( 2 / 20 )34.34833333333331.9244039236588617.8488169302976
Winsorized Mean ( 3 / 20 )34.35833333333331.9160713273388617.9316567411152
Winsorized Mean ( 4 / 20 )34.3451.9055693352710718.0234848264466
Winsorized Mean ( 5 / 20 )34.3951.8947450747541418.1528377924207
Winsorized Mean ( 6 / 20 )34.3651.877472494099918.303863363109
Winsorized Mean ( 7 / 20 )34.31833333333331.8063564658540118.9986494814623
Winsorized Mean ( 8 / 20 )34.31833333333331.8013201242997219.0517681284857
Winsorized Mean ( 9 / 20 )34.37833333333331.6621443023193220.683121968028
Winsorized Mean ( 10 / 20 )34.5451.5709949076938521.9892501438535
Winsorized Mean ( 11 / 20 )34.58166666666671.5387949127247322.4732135391800
Winsorized Mean ( 12 / 20 )34.66166666666671.4629319907009323.6932864186388
Winsorized Mean ( 13 / 20 )34.48833333333331.3591416609809125.3750836453963
Winsorized Mean ( 14 / 20 )34.7451.2758943357238527.2318788689411
Winsorized Mean ( 15 / 20 )34.9451.2097658759347928.8857544216957
Winsorized Mean ( 16 / 20 )35.23833333333331.1518692537687530.5923030917255
Winsorized Mean ( 17 / 20 )35.1251.0588652517997433.1723039738045
Winsorized Mean ( 18 / 20 )35.1551.0449486376694533.642801887762
Winsorized Mean ( 19 / 20 )35.7250.9526727937636337.4997588194628
Winsorized Mean ( 20 / 20 )35.8250.9270194782173438.6453584221246
Trimmed Mean ( 1 / 20 )34.5517241379311.9523780485966117.6972508796476
Trimmed Mean ( 2 / 20 )34.49464285714291.8829591584753218.319379207924
Trimmed Mean ( 3 / 20 )34.57592592592591.8527633151762218.6618148377130
Trimmed Mean ( 4 / 20 )34.65961538461541.8180659913308919.0640029294224
Trimmed Mean ( 5 / 20 )34.7541.7776095161302319.5509754446285
Trimmed Mean ( 6 / 20 )34.843751.7292844476250520.1492299591623
Trimmed Mean ( 7 / 20 )34.94782608695651.6722103141033320.8991810373422
Trimmed Mean ( 8 / 20 )35.07045454545451.6192962332995721.6578374137220
Trimmed Mean ( 9 / 20 )35.20476190476191.5506132029740822.7037676689706
Trimmed Mean ( 10 / 20 )35.34251.4996661487452223.5669118954051
Trimmed Mean ( 11 / 20 )35.46842105263161.4561348380616324.357923542195
Trimmed Mean ( 12 / 20 )35.60277777777781.4044232059625825.3504624721549
Trimmed Mean ( 13 / 20 )35.74117647058821.3536450931732426.403653846078
Trimmed Mean ( 14 / 20 )35.9218751.3101398470586327.4183516215063
Trimmed Mean ( 15 / 20 )36.091.2712320930824428.3897804314319
Trimmed Mean ( 16 / 20 )36.25357142857141.2324372779135429.4161594088968
Trimmed Mean ( 17 / 20 )36.41.1910434985275030.5614362909515
Trimmed Mean ( 18 / 20 )36.58751.1549093775226931.6799748206054
Trimmed Mean ( 19 / 20 )36.80454545454551.0955928493103933.5932691398194
Trimmed Mean ( 20 / 20 )36.9751.0392019964731035.5801856862166
Median38.9
Midrange50.65
Midmean - Weighted Average at Xnp35.6193548387097
Midmean - Weighted Average at X(n+1)p36.09
Midmean - Empirical Distribution Function35.6193548387097
Midmean - Empirical Distribution Function - Averaging36.09
Midmean - Empirical Distribution Function - Interpolation36.09
Midmean - Closest Observation35.6193548387097
Midmean - True Basic - Statistics Graphics Toolkit36.09
Midmean - MS Excel (old versions)35.921875
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 35.0883333333333 & 2.18921224083114 & 16.0278353459288 \tabularnewline
Geometric Mean & 30.2341950948989 &  &  \tabularnewline
Harmonic Mean & 24.5663500163922 &  &  \tabularnewline
Quadratic Mean & 38.9096067829013 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 34.605 & 2.00865981827106 & 17.2279047378894 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 34.3483333333333 & 1.92440392365886 & 17.8488169302976 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 34.3583333333333 & 1.91607132733886 & 17.9316567411152 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 34.345 & 1.90556933527107 & 18.0234848264466 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 34.395 & 1.89474507475414 & 18.1528377924207 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 34.365 & 1.8774724940999 & 18.303863363109 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 34.3183333333333 & 1.80635646585401 & 18.9986494814623 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 34.3183333333333 & 1.80132012429972 & 19.0517681284857 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 34.3783333333333 & 1.66214430231932 & 20.683121968028 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 34.545 & 1.57099490769385 & 21.9892501438535 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 34.5816666666667 & 1.53879491272473 & 22.4732135391800 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 34.6616666666667 & 1.46293199070093 & 23.6932864186388 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 34.4883333333333 & 1.35914166098091 & 25.3750836453963 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 34.745 & 1.27589433572385 & 27.2318788689411 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 34.945 & 1.20976587593479 & 28.8857544216957 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 35.2383333333333 & 1.15186925376875 & 30.5923030917255 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 35.125 & 1.05886525179974 & 33.1723039738045 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 35.155 & 1.04494863766945 & 33.642801887762 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 35.725 & 0.95267279376363 & 37.4997588194628 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 35.825 & 0.92701947821734 & 38.6453584221246 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 34.551724137931 & 1.95237804859661 & 17.6972508796476 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 34.4946428571429 & 1.88295915847532 & 18.319379207924 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 34.5759259259259 & 1.85276331517622 & 18.6618148377130 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 34.6596153846154 & 1.81806599133089 & 19.0640029294224 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 34.754 & 1.77760951613023 & 19.5509754446285 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 34.84375 & 1.72928444762505 & 20.1492299591623 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 34.9478260869565 & 1.67221031410333 & 20.8991810373422 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 35.0704545454545 & 1.61929623329957 & 21.6578374137220 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 35.2047619047619 & 1.55061320297408 & 22.7037676689706 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 35.3425 & 1.49966614874522 & 23.5669118954051 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 35.4684210526316 & 1.45613483806163 & 24.357923542195 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 35.6027777777778 & 1.40442320596258 & 25.3504624721549 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 35.7411764705882 & 1.35364509317324 & 26.403653846078 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 35.921875 & 1.31013984705863 & 27.4183516215063 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 36.09 & 1.27123209308244 & 28.3897804314319 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 36.2535714285714 & 1.23243727791354 & 29.4161594088968 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 36.4 & 1.19104349852750 & 30.5614362909515 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 36.5875 & 1.15490937752269 & 31.6799748206054 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 36.8045454545455 & 1.09559284931039 & 33.5932691398194 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 36.975 & 1.03920199647310 & 35.5801856862166 \tabularnewline
Median & 38.9 &  &  \tabularnewline
Midrange & 50.65 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 35.6193548387097 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 36.09 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 35.6193548387097 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 36.09 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 36.09 &  &  \tabularnewline
Midmean - Closest Observation & 35.6193548387097 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 36.09 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 35.921875 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=18348&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]35.0883333333333[/C][C]2.18921224083114[/C][C]16.0278353459288[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]30.2341950948989[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]24.5663500163922[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]38.9096067829013[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]34.605[/C][C]2.00865981827106[/C][C]17.2279047378894[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]34.3483333333333[/C][C]1.92440392365886[/C][C]17.8488169302976[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]34.3583333333333[/C][C]1.91607132733886[/C][C]17.9316567411152[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]34.345[/C][C]1.90556933527107[/C][C]18.0234848264466[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]34.395[/C][C]1.89474507475414[/C][C]18.1528377924207[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]34.365[/C][C]1.8774724940999[/C][C]18.303863363109[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]34.3183333333333[/C][C]1.80635646585401[/C][C]18.9986494814623[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]34.3183333333333[/C][C]1.80132012429972[/C][C]19.0517681284857[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]34.3783333333333[/C][C]1.66214430231932[/C][C]20.683121968028[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]34.545[/C][C]1.57099490769385[/C][C]21.9892501438535[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]34.5816666666667[/C][C]1.53879491272473[/C][C]22.4732135391800[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]34.6616666666667[/C][C]1.46293199070093[/C][C]23.6932864186388[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]34.4883333333333[/C][C]1.35914166098091[/C][C]25.3750836453963[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]34.745[/C][C]1.27589433572385[/C][C]27.2318788689411[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]34.945[/C][C]1.20976587593479[/C][C]28.8857544216957[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]35.2383333333333[/C][C]1.15186925376875[/C][C]30.5923030917255[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]35.125[/C][C]1.05886525179974[/C][C]33.1723039738045[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]35.155[/C][C]1.04494863766945[/C][C]33.642801887762[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]35.725[/C][C]0.95267279376363[/C][C]37.4997588194628[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]35.825[/C][C]0.92701947821734[/C][C]38.6453584221246[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]34.551724137931[/C][C]1.95237804859661[/C][C]17.6972508796476[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]34.4946428571429[/C][C]1.88295915847532[/C][C]18.319379207924[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]34.5759259259259[/C][C]1.85276331517622[/C][C]18.6618148377130[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]34.6596153846154[/C][C]1.81806599133089[/C][C]19.0640029294224[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]34.754[/C][C]1.77760951613023[/C][C]19.5509754446285[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]34.84375[/C][C]1.72928444762505[/C][C]20.1492299591623[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]34.9478260869565[/C][C]1.67221031410333[/C][C]20.8991810373422[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]35.0704545454545[/C][C]1.61929623329957[/C][C]21.6578374137220[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]35.2047619047619[/C][C]1.55061320297408[/C][C]22.7037676689706[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]35.3425[/C][C]1.49966614874522[/C][C]23.5669118954051[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]35.4684210526316[/C][C]1.45613483806163[/C][C]24.357923542195[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]35.6027777777778[/C][C]1.40442320596258[/C][C]25.3504624721549[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]35.7411764705882[/C][C]1.35364509317324[/C][C]26.403653846078[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]35.921875[/C][C]1.31013984705863[/C][C]27.4183516215063[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]36.09[/C][C]1.27123209308244[/C][C]28.3897804314319[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]36.2535714285714[/C][C]1.23243727791354[/C][C]29.4161594088968[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]36.4[/C][C]1.19104349852750[/C][C]30.5614362909515[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]36.5875[/C][C]1.15490937752269[/C][C]31.6799748206054[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]36.8045454545455[/C][C]1.09559284931039[/C][C]33.5932691398194[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]36.975[/C][C]1.03920199647310[/C][C]35.5801856862166[/C][/ROW]
[ROW][C]Median[/C][C]38.9[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]50.65[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]35.6193548387097[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]36.09[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]35.6193548387097[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]36.09[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]36.09[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]35.6193548387097[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]36.09[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]35.921875[/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=18348&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=18348&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 Mean35.08833333333332.1892122408311416.0278353459288
Geometric Mean30.2341950948989
Harmonic Mean24.5663500163922
Quadratic Mean38.9096067829013
Winsorized Mean ( 1 / 20 )34.6052.0086598182710617.2279047378894
Winsorized Mean ( 2 / 20 )34.34833333333331.9244039236588617.8488169302976
Winsorized Mean ( 3 / 20 )34.35833333333331.9160713273388617.9316567411152
Winsorized Mean ( 4 / 20 )34.3451.9055693352710718.0234848264466
Winsorized Mean ( 5 / 20 )34.3951.8947450747541418.1528377924207
Winsorized Mean ( 6 / 20 )34.3651.877472494099918.303863363109
Winsorized Mean ( 7 / 20 )34.31833333333331.8063564658540118.9986494814623
Winsorized Mean ( 8 / 20 )34.31833333333331.8013201242997219.0517681284857
Winsorized Mean ( 9 / 20 )34.37833333333331.6621443023193220.683121968028
Winsorized Mean ( 10 / 20 )34.5451.5709949076938521.9892501438535
Winsorized Mean ( 11 / 20 )34.58166666666671.5387949127247322.4732135391800
Winsorized Mean ( 12 / 20 )34.66166666666671.4629319907009323.6932864186388
Winsorized Mean ( 13 / 20 )34.48833333333331.3591416609809125.3750836453963
Winsorized Mean ( 14 / 20 )34.7451.2758943357238527.2318788689411
Winsorized Mean ( 15 / 20 )34.9451.2097658759347928.8857544216957
Winsorized Mean ( 16 / 20 )35.23833333333331.1518692537687530.5923030917255
Winsorized Mean ( 17 / 20 )35.1251.0588652517997433.1723039738045
Winsorized Mean ( 18 / 20 )35.1551.0449486376694533.642801887762
Winsorized Mean ( 19 / 20 )35.7250.9526727937636337.4997588194628
Winsorized Mean ( 20 / 20 )35.8250.9270194782173438.6453584221246
Trimmed Mean ( 1 / 20 )34.5517241379311.9523780485966117.6972508796476
Trimmed Mean ( 2 / 20 )34.49464285714291.8829591584753218.319379207924
Trimmed Mean ( 3 / 20 )34.57592592592591.8527633151762218.6618148377130
Trimmed Mean ( 4 / 20 )34.65961538461541.8180659913308919.0640029294224
Trimmed Mean ( 5 / 20 )34.7541.7776095161302319.5509754446285
Trimmed Mean ( 6 / 20 )34.843751.7292844476250520.1492299591623
Trimmed Mean ( 7 / 20 )34.94782608695651.6722103141033320.8991810373422
Trimmed Mean ( 8 / 20 )35.07045454545451.6192962332995721.6578374137220
Trimmed Mean ( 9 / 20 )35.20476190476191.5506132029740822.7037676689706
Trimmed Mean ( 10 / 20 )35.34251.4996661487452223.5669118954051
Trimmed Mean ( 11 / 20 )35.46842105263161.4561348380616324.357923542195
Trimmed Mean ( 12 / 20 )35.60277777777781.4044232059625825.3504624721549
Trimmed Mean ( 13 / 20 )35.74117647058821.3536450931732426.403653846078
Trimmed Mean ( 14 / 20 )35.9218751.3101398470586327.4183516215063
Trimmed Mean ( 15 / 20 )36.091.2712320930824428.3897804314319
Trimmed Mean ( 16 / 20 )36.25357142857141.2324372779135429.4161594088968
Trimmed Mean ( 17 / 20 )36.41.1910434985275030.5614362909515
Trimmed Mean ( 18 / 20 )36.58751.1549093775226931.6799748206054
Trimmed Mean ( 19 / 20 )36.80454545454551.0955928493103933.5932691398194
Trimmed Mean ( 20 / 20 )36.9751.0392019964731035.5801856862166
Median38.9
Midrange50.65
Midmean - Weighted Average at Xnp35.6193548387097
Midmean - Weighted Average at X(n+1)p36.09
Midmean - Empirical Distribution Function35.6193548387097
Midmean - Empirical Distribution Function - Averaging36.09
Midmean - Empirical Distribution Function - Interpolation36.09
Midmean - Closest Observation35.6193548387097
Midmean - True Basic - Statistics Graphics Toolkit36.09
Midmean - MS Excel (old versions)35.921875
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')