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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 computationMon, 20 Oct 2008 15:26:01 -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/t1224538044ow12r1o96r2g8jc.htm/, Retrieved Sun, 19 May 2024 14:57:59 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=18179, Retrieved Sun, 19 May 2024 14:57:59 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact129
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
F     [Univariate Data Series] [uitvoer van belgi...] [2008-10-13 19:23:12] [1e1d8320a8a1170c475bf6e4ce119de6]
- RMP   [Central Tendency] [Central Tendency ...] [2008-10-18 10:47:17] [1e1d8320a8a1170c475bf6e4ce119de6]
F    D    [Central Tendency] [Central Tendency ...] [2008-10-20 21:11:22] [3754dd41128068acfc463ebbabce5a9c]
-    D      [Central Tendency] [] [2008-10-20 21:17:29] [3754dd41128068acfc463ebbabce5a9c]
-    D        [Central Tendency] [Central Tendency ...] [2008-10-20 21:22:30] [3754dd41128068acfc463ebbabce5a9c]
-    D            [Central Tendency] [Central Tendency ...] [2008-10-20 21:26:01] [02e7fb326979b65614900650d62c19a6] [Current]
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Dataseries X:
3118.6
3089.8
3312.3
3106.1
2843.1
3300.4
3147.9
2742.7
3397.3
3461.4
3314.8
3248
2938
3473.8
3839.1
3601.9
3173.2
3938.3
3034.2
2900.5
4236.3
3433.4
3777.8
3709.8
3192.8
3640.2
4275.3
3708.9
3312.1
3948
3084.8
3412.8
4036.3
3608.7
3911.8
3857.3
3567.3
4022.2
4948.6
3645
3982.5
4175.4
3660.9
4019.7
4447.6
4211.6
4252.3
3703.1
4052.1
4462
4862.6
4114.4
4630.4
4694.1
4189.4
4158
4533.8
4906.2
4858.8
4059




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'Herman Ole Andreas Wold' @ 193.190.124.10:1001

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 3 seconds \tabularnewline
R Server & 'Herman Ole Andreas Wold' @ 193.190.124.10:1001 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=18179&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]3 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Herman Ole Andreas Wold' @ 193.190.124.10:1001[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=18179&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=18179&T=0

As an alternative you can also use a QR Code:  

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

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'Herman Ole Andreas Wold' @ 193.190.124.10:1001







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean3771.4116666666772.862723805056251.7605089367378
Geometric Mean3730.20234320786
Harmonic Mean3689.44271488854
Quadratic Mean3812.71236446793
Winsorized Mean ( 1 / 20 )3772.3783333333372.289452430636752.1843534083069
Winsorized Mean ( 2 / 20 )3772.8383333333371.502214026471852.7653357969662
Winsorized Mean ( 3 / 20 )3774.5233333333371.072205719256953.1082902962533
Winsorized Mean ( 4 / 20 )3769.9566666666767.131068332068856.1581509178179
Winsorized Mean ( 5 / 20 )3768.86565.149417479217457.8495579212549
Winsorized Mean ( 6 / 20 )3759.70562.969615820055859.7066529791744
Winsorized Mean ( 7 / 20 )3753.2360.927735898315861.6013371359127
Winsorized Mean ( 8 / 20 )3752.9766666666760.252124437622262.2878728625088
Winsorized Mean ( 9 / 20 )3731.5266666666754.7458387793468.1609187084896
Winsorized Mean ( 10 / 20 )3731.9153.350958124183369.9501964203408
Winsorized Mean ( 11 / 20 )3732.5752.235105589365971.4571160120309
Winsorized Mean ( 12 / 20 )3738.6749.537027941612975.4722306797777
Winsorized Mean ( 13 / 20 )3745.2133333333346.894928680720579.8639306785654
Winsorized Mean ( 14 / 20 )3744.6766666666745.935771628066981.5198381119315
Winsorized Mean ( 15 / 20 )3740.3766666666745.24177444148282.6752865651779
Winsorized Mean ( 16 / 20 )3729.4166666666743.348965422504786.03242615637
Winsorized Mean ( 17 / 20 )3737.09537.3119402304016100.158152508913
Winsorized Mean ( 18 / 20 )3739.67536.2957702960576103.03335538814
Winsorized Mean ( 19 / 20 )3741.19534.5787616003459108.193435127607
Winsorized Mean ( 20 / 20 )3745.8283333333332.5035581791163115.243639256087
Trimmed Mean ( 1 / 20 )3768.8517241379370.32328924712453.5932230202396
Trimmed Mean ( 2 / 20 )3765.0732142857167.895067648401355.4542965298065
Trimmed Mean ( 3 / 20 )3760.7592592592665.409912683615957.4952496489308
Trimmed Mean ( 4 / 20 )3755.4653846153862.504477781352460.0831415271146
Trimmed Mean ( 5 / 20 )3751.11860.469779106794262.0329370374454
Trimmed Mean ( 6 / 20 )3746.6812558.575716189342663.9630463567713
Trimmed Mean ( 7 / 20 )3743.8556.846163858352265.8593253421432
Trimmed Mean ( 8 / 20 )3742.0227272727355.207495092738667.781063440513
Trimmed Mean ( 9 / 20 )3740.0666666666753.234025502093870.2570701988255
Trimmed Mean ( 10 / 20 )3741.4952.150499272384571.7440878266193
Trimmed Mean ( 11 / 20 )3743.0026315789551.011985104281273.3749651954795
Trimmed Mean ( 12 / 20 )3744.5833333333349.702047401218975.340625369117
Trimmed Mean ( 13 / 20 )3745.4529411764748.579139034077577.1000272061038
Trimmed Mean ( 14 / 20 )3745.487547.653438454875278.5984730891296
Trimmed Mean ( 15 / 20 )3745.6033333333346.486106065018280.574684575527
Trimmed Mean ( 16 / 20 )3746.3544.871879782755983.4899277261772
Trimmed Mean ( 17 / 20 )3748.7923076923142.973047339386387.2358964465713
Trimmed Mean ( 18 / 20 )3750.512542.145734613422988.9891357785352
Trimmed Mean ( 19 / 20 )3752.1545454545540.968604666014791.5860956467264
Trimmed Mean ( 20 / 20 )3753.88539.504499593817195.0242387221006
Median3709.35
Midrange3845.65
Midmean - Weighted Average at Xnp3731.61935483871
Midmean - Weighted Average at X(n+1)p3745.60333333333
Midmean - Empirical Distribution Function3731.61935483871
Midmean - Empirical Distribution Function - Averaging3745.60333333333
Midmean - Empirical Distribution Function - Interpolation3745.60333333333
Midmean - Closest Observation3731.61935483871
Midmean - True Basic - Statistics Graphics Toolkit3745.60333333333
Midmean - MS Excel (old versions)3745.4875
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 3771.41166666667 & 72.8627238050562 & 51.7605089367378 \tabularnewline
Geometric Mean & 3730.20234320786 &  &  \tabularnewline
Harmonic Mean & 3689.44271488854 &  &  \tabularnewline
Quadratic Mean & 3812.71236446793 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 3772.37833333333 & 72.2894524306367 & 52.1843534083069 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 3772.83833333333 & 71.5022140264718 & 52.7653357969662 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 3774.52333333333 & 71.0722057192569 & 53.1082902962533 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 3769.95666666667 & 67.1310683320688 & 56.1581509178179 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 3768.865 & 65.1494174792174 & 57.8495579212549 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 3759.705 & 62.9696158200558 & 59.7066529791744 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 3753.23 & 60.9277358983158 & 61.6013371359127 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 3752.97666666667 & 60.2521244376222 & 62.2878728625088 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 3731.52666666667 & 54.74583877934 & 68.1609187084896 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 3731.91 & 53.3509581241833 & 69.9501964203408 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 3732.57 & 52.2351055893659 & 71.4571160120309 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 3738.67 & 49.5370279416129 & 75.4722306797777 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 3745.21333333333 & 46.8949286807205 & 79.8639306785654 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 3744.67666666667 & 45.9357716280669 & 81.5198381119315 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 3740.37666666667 & 45.241774441482 & 82.6752865651779 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 3729.41666666667 & 43.3489654225047 & 86.03242615637 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 3737.095 & 37.3119402304016 & 100.158152508913 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 3739.675 & 36.2957702960576 & 103.03335538814 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 3741.195 & 34.5787616003459 & 108.193435127607 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 3745.82833333333 & 32.5035581791163 & 115.243639256087 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 3768.85172413793 & 70.323289247124 & 53.5932230202396 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 3765.07321428571 & 67.8950676484013 & 55.4542965298065 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 3760.75925925926 & 65.4099126836159 & 57.4952496489308 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 3755.46538461538 & 62.5044777813524 & 60.0831415271146 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 3751.118 & 60.4697791067942 & 62.0329370374454 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 3746.68125 & 58.5757161893426 & 63.9630463567713 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 3743.85 & 56.8461638583522 & 65.8593253421432 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 3742.02272727273 & 55.2074950927386 & 67.781063440513 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 3740.06666666667 & 53.2340255020938 & 70.2570701988255 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 3741.49 & 52.1504992723845 & 71.7440878266193 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 3743.00263157895 & 51.0119851042812 & 73.3749651954795 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 3744.58333333333 & 49.7020474012189 & 75.340625369117 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 3745.45294117647 & 48.5791390340775 & 77.1000272061038 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 3745.4875 & 47.6534384548752 & 78.5984730891296 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 3745.60333333333 & 46.4861060650182 & 80.574684575527 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 3746.35 & 44.8718797827559 & 83.4899277261772 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 3748.79230769231 & 42.9730473393863 & 87.2358964465713 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 3750.5125 & 42.1457346134229 & 88.9891357785352 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 3752.15454545455 & 40.9686046660147 & 91.5860956467264 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 3753.885 & 39.5044995938171 & 95.0242387221006 \tabularnewline
Median & 3709.35 &  &  \tabularnewline
Midrange & 3845.65 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 3731.61935483871 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 3745.60333333333 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 3731.61935483871 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 3745.60333333333 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 3745.60333333333 &  &  \tabularnewline
Midmean - Closest Observation & 3731.61935483871 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 3745.60333333333 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 3745.4875 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=18179&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]3771.41166666667[/C][C]72.8627238050562[/C][C]51.7605089367378[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]3730.20234320786[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]3689.44271488854[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]3812.71236446793[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]3772.37833333333[/C][C]72.2894524306367[/C][C]52.1843534083069[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]3772.83833333333[/C][C]71.5022140264718[/C][C]52.7653357969662[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]3774.52333333333[/C][C]71.0722057192569[/C][C]53.1082902962533[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]3769.95666666667[/C][C]67.1310683320688[/C][C]56.1581509178179[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]3768.865[/C][C]65.1494174792174[/C][C]57.8495579212549[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]3759.705[/C][C]62.9696158200558[/C][C]59.7066529791744[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]3753.23[/C][C]60.9277358983158[/C][C]61.6013371359127[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]3752.97666666667[/C][C]60.2521244376222[/C][C]62.2878728625088[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]3731.52666666667[/C][C]54.74583877934[/C][C]68.1609187084896[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]3731.91[/C][C]53.3509581241833[/C][C]69.9501964203408[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]3732.57[/C][C]52.2351055893659[/C][C]71.4571160120309[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]3738.67[/C][C]49.5370279416129[/C][C]75.4722306797777[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]3745.21333333333[/C][C]46.8949286807205[/C][C]79.8639306785654[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]3744.67666666667[/C][C]45.9357716280669[/C][C]81.5198381119315[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]3740.37666666667[/C][C]45.241774441482[/C][C]82.6752865651779[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]3729.41666666667[/C][C]43.3489654225047[/C][C]86.03242615637[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]3737.095[/C][C]37.3119402304016[/C][C]100.158152508913[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]3739.675[/C][C]36.2957702960576[/C][C]103.03335538814[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]3741.195[/C][C]34.5787616003459[/C][C]108.193435127607[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]3745.82833333333[/C][C]32.5035581791163[/C][C]115.243639256087[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]3768.85172413793[/C][C]70.323289247124[/C][C]53.5932230202396[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]3765.07321428571[/C][C]67.8950676484013[/C][C]55.4542965298065[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]3760.75925925926[/C][C]65.4099126836159[/C][C]57.4952496489308[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]3755.46538461538[/C][C]62.5044777813524[/C][C]60.0831415271146[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]3751.118[/C][C]60.4697791067942[/C][C]62.0329370374454[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]3746.68125[/C][C]58.5757161893426[/C][C]63.9630463567713[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]3743.85[/C][C]56.8461638583522[/C][C]65.8593253421432[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]3742.02272727273[/C][C]55.2074950927386[/C][C]67.781063440513[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]3740.06666666667[/C][C]53.2340255020938[/C][C]70.2570701988255[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]3741.49[/C][C]52.1504992723845[/C][C]71.7440878266193[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]3743.00263157895[/C][C]51.0119851042812[/C][C]73.3749651954795[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]3744.58333333333[/C][C]49.7020474012189[/C][C]75.340625369117[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]3745.45294117647[/C][C]48.5791390340775[/C][C]77.1000272061038[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]3745.4875[/C][C]47.6534384548752[/C][C]78.5984730891296[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]3745.60333333333[/C][C]46.4861060650182[/C][C]80.574684575527[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]3746.35[/C][C]44.8718797827559[/C][C]83.4899277261772[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]3748.79230769231[/C][C]42.9730473393863[/C][C]87.2358964465713[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]3750.5125[/C][C]42.1457346134229[/C][C]88.9891357785352[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]3752.15454545455[/C][C]40.9686046660147[/C][C]91.5860956467264[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]3753.885[/C][C]39.5044995938171[/C][C]95.0242387221006[/C][/ROW]
[ROW][C]Median[/C][C]3709.35[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]3845.65[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]3731.61935483871[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]3745.60333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]3731.61935483871[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]3745.60333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]3745.60333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]3731.61935483871[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]3745.60333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]3745.4875[/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=18179&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=18179&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 Mean3771.4116666666772.862723805056251.7605089367378
Geometric Mean3730.20234320786
Harmonic Mean3689.44271488854
Quadratic Mean3812.71236446793
Winsorized Mean ( 1 / 20 )3772.3783333333372.289452430636752.1843534083069
Winsorized Mean ( 2 / 20 )3772.8383333333371.502214026471852.7653357969662
Winsorized Mean ( 3 / 20 )3774.5233333333371.072205719256953.1082902962533
Winsorized Mean ( 4 / 20 )3769.9566666666767.131068332068856.1581509178179
Winsorized Mean ( 5 / 20 )3768.86565.149417479217457.8495579212549
Winsorized Mean ( 6 / 20 )3759.70562.969615820055859.7066529791744
Winsorized Mean ( 7 / 20 )3753.2360.927735898315861.6013371359127
Winsorized Mean ( 8 / 20 )3752.9766666666760.252124437622262.2878728625088
Winsorized Mean ( 9 / 20 )3731.5266666666754.7458387793468.1609187084896
Winsorized Mean ( 10 / 20 )3731.9153.350958124183369.9501964203408
Winsorized Mean ( 11 / 20 )3732.5752.235105589365971.4571160120309
Winsorized Mean ( 12 / 20 )3738.6749.537027941612975.4722306797777
Winsorized Mean ( 13 / 20 )3745.2133333333346.894928680720579.8639306785654
Winsorized Mean ( 14 / 20 )3744.6766666666745.935771628066981.5198381119315
Winsorized Mean ( 15 / 20 )3740.3766666666745.24177444148282.6752865651779
Winsorized Mean ( 16 / 20 )3729.4166666666743.348965422504786.03242615637
Winsorized Mean ( 17 / 20 )3737.09537.3119402304016100.158152508913
Winsorized Mean ( 18 / 20 )3739.67536.2957702960576103.03335538814
Winsorized Mean ( 19 / 20 )3741.19534.5787616003459108.193435127607
Winsorized Mean ( 20 / 20 )3745.8283333333332.5035581791163115.243639256087
Trimmed Mean ( 1 / 20 )3768.8517241379370.32328924712453.5932230202396
Trimmed Mean ( 2 / 20 )3765.0732142857167.895067648401355.4542965298065
Trimmed Mean ( 3 / 20 )3760.7592592592665.409912683615957.4952496489308
Trimmed Mean ( 4 / 20 )3755.4653846153862.504477781352460.0831415271146
Trimmed Mean ( 5 / 20 )3751.11860.469779106794262.0329370374454
Trimmed Mean ( 6 / 20 )3746.6812558.575716189342663.9630463567713
Trimmed Mean ( 7 / 20 )3743.8556.846163858352265.8593253421432
Trimmed Mean ( 8 / 20 )3742.0227272727355.207495092738667.781063440513
Trimmed Mean ( 9 / 20 )3740.0666666666753.234025502093870.2570701988255
Trimmed Mean ( 10 / 20 )3741.4952.150499272384571.7440878266193
Trimmed Mean ( 11 / 20 )3743.0026315789551.011985104281273.3749651954795
Trimmed Mean ( 12 / 20 )3744.5833333333349.702047401218975.340625369117
Trimmed Mean ( 13 / 20 )3745.4529411764748.579139034077577.1000272061038
Trimmed Mean ( 14 / 20 )3745.487547.653438454875278.5984730891296
Trimmed Mean ( 15 / 20 )3745.6033333333346.486106065018280.574684575527
Trimmed Mean ( 16 / 20 )3746.3544.871879782755983.4899277261772
Trimmed Mean ( 17 / 20 )3748.7923076923142.973047339386387.2358964465713
Trimmed Mean ( 18 / 20 )3750.512542.145734613422988.9891357785352
Trimmed Mean ( 19 / 20 )3752.1545454545540.968604666014791.5860956467264
Trimmed Mean ( 20 / 20 )3753.88539.504499593817195.0242387221006
Median3709.35
Midrange3845.65
Midmean - Weighted Average at Xnp3731.61935483871
Midmean - Weighted Average at X(n+1)p3745.60333333333
Midmean - Empirical Distribution Function3731.61935483871
Midmean - Empirical Distribution Function - Averaging3745.60333333333
Midmean - Empirical Distribution Function - Interpolation3745.60333333333
Midmean - Closest Observation3731.61935483871
Midmean - True Basic - Statistics Graphics Toolkit3745.60333333333
Midmean - MS Excel (old versions)3745.4875
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')