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Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationFri, 05 Dec 2008 03:30:52 -0700
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/Dec/05/t1228473097mz7ghu9n52ex42f.htm/, Retrieved Thu, 16 May 2024 18:42:46 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=29141, Retrieved Thu, 16 May 2024 18:42:46 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact184
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Central Tendency] [paper central ten...] [2008-11-14 13:59:17] [077ffec662d24c06be4c491541a44245]
-       [Central Tendency] [paper central ten...] [2008-11-14 14:02:25] [077ffec662d24c06be4c491541a44245]
-    D      [Central Tendency] [paper centrale te...] [2008-12-05 10:30:52] [3817f5e632a8bfeb1be7b5e8c86bd450] [Current]
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Dataseries X:
3423.40
3242.80
3277.20
3833.00
2606.30
3643.80
3686.40
3281.60
3669.30
3191.50
3512.70
3970.70
3601.20
3610.00
4172.10
3956.20
3142.70
3884.30
3892.20
3613.00
3730.50
3481.30
3649.50
4215.20
4066.60
4196.80
4536.60
4441.60
3548.30
4735.90
4130.60
4356.20
4159.60
3988.00
4167.80
4902.20
3909.40
4697.60
4308.90
4420.40
3544.20
4433.00
4479.70
4533.20
4237.50
4207.40
4394.00
5148.40
4202.20
4682.50
4884.30
5288.90
4505.20
4611.50
5081.10
4523.10
4412.80
4647.40
4778.60
4495.30




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135

\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 & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=29141&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]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=29141&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=29141&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'Gwilym Jenkins' @ 72.249.127.135







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean4099.0616666666771.922330521448956.9928927072828
Geometric Mean4060.38968502989
Harmonic Mean4020.06795620152
Quadratic Mean4136.12173698583
Winsorized Mean ( 1 / 20 )4105.6668.64479563107259.8102152137748
Winsorized Mean ( 2 / 20 )4105.0433333333367.702375942696860.6336672262113
Winsorized Mean ( 3 / 20 )4098.6633333333365.091343943022562.9678707651372
Winsorized Mean ( 4 / 20 )4099.7633333333364.339118455675863.7211611184527
Winsorized Mean ( 5 / 20 )4091.3216666666762.527155596257365.4327168356202
Winsorized Mean ( 6 / 20 )4101.2316666666758.791623912984469.7587750380355
Winsorized Mean ( 7 / 20 )4103.5183333333356.697015908663772.3762665030539
Winsorized Mean ( 8 / 20 )4105.6916666666755.573050732792573.8791844703243
Winsorized Mean ( 9 / 20 )4105.1516666666753.815324277305676.2822062636505
Winsorized Mean ( 10 / 20 )4099.8516666666752.690852908060977.8095521403005
Winsorized Mean ( 11 / 20 )4095.8183333333348.812799822450283.9086950191611
Winsorized Mean ( 12 / 20 )4096.8983333333348.407659809182184.6332656749546
Winsorized Mean ( 13 / 20 )4095.3647.964316020344185.3834754625282
Winsorized Mean ( 14 / 20 )4098.3746.123422625486888.8565888372589
Winsorized Mean ( 15 / 20 )4097.3245.517183618055490.0169930191969
Winsorized Mean ( 16 / 20 )4098.4444.027156308980193.088910199818
Winsorized Mean ( 17 / 20 )4092.4941.667368357933498.2181059491078
Winsorized Mean ( 18 / 20 )4103.1439.1389668992872104.835163650544
Winsorized Mean ( 19 / 20 )4131.6083333333333.477450737213123.414663970835
Winsorized Mean ( 20 / 20 )4146.17530.5687117674967135.634600225730
Trimmed Mean ( 1 / 20 )4104.2844827586266.604978558621761.6212867503031
Trimmed Mean ( 2 / 20 )4102.8107142857164.090059994671564.0163344304378
Trimmed Mean ( 3 / 20 )4101.5703703703761.610093639130566.5730260758009
Trimmed Mean ( 4 / 20 )4102.6884615384659.80432728065868.6018662543398
Trimmed Mean ( 5 / 20 )4103.56657.826779871316770.9630729764266
Trimmed Mean ( 6 / 20 )4106.6270833333355.944880004833173.404877854391
Trimmed Mean ( 7 / 20 )4107.854.719524816424275.070096346433
Trimmed Mean ( 8 / 20 )4108.6340909090953.708415935651476.4988879178952
Trimmed Mean ( 9 / 20 )4109.1595238095252.648664691887878.0486940714884
Trimmed Mean ( 10 / 20 )4109.827551.666340154572179.5455510822806
Trimmed Mean ( 11 / 20 )4111.4026315789550.581244519190481.2831449811222
Trimmed Mean ( 12 / 20 )4113.7638888888950.046785595648382.1983637895536
Trimmed Mean ( 13 / 20 )4116.2441176470649.290725842004783.5095050302398
Trimmed Mean ( 14 / 20 )4119.2562548.223555334115585.4200031801856
Trimmed Mean ( 15 / 20 )4122.2447.11966780711587.484487727597
Trimmed Mean ( 16 / 20 )4125.845.550965119088690.5754683619435
Trimmed Mean ( 17 / 20 )4129.7461538461543.581485564671594.7591873094353
Trimmed Mean ( 18 / 20 )4135.22541.267195910715100.206105812154
Trimmed Mean ( 19 / 20 )4140.0863636363638.5633106791826107.358167406288
Trimmed Mean ( 20 / 20 )4141.42536.783146795209112.590285520091
Median4169.95
Midrange3947.6
Midmean - Weighted Average at Xnp4106.8064516129
Midmean - Weighted Average at X(n+1)p4122.24
Midmean - Empirical Distribution Function4106.8064516129
Midmean - Empirical Distribution Function - Averaging4122.24
Midmean - Empirical Distribution Function - Interpolation4122.24
Midmean - Closest Observation4106.8064516129
Midmean - True Basic - Statistics Graphics Toolkit4122.24
Midmean - MS Excel (old versions)4119.25625
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 4099.06166666667 & 71.9223305214489 & 56.9928927072828 \tabularnewline
Geometric Mean & 4060.38968502989 &  &  \tabularnewline
Harmonic Mean & 4020.06795620152 &  &  \tabularnewline
Quadratic Mean & 4136.12173698583 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 4105.66 & 68.644795631072 & 59.8102152137748 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 4105.04333333333 & 67.7023759426968 & 60.6336672262113 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 4098.66333333333 & 65.0913439430225 & 62.9678707651372 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 4099.76333333333 & 64.3391184556758 & 63.7211611184527 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 4091.32166666667 & 62.5271555962573 & 65.4327168356202 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 4101.23166666667 & 58.7916239129844 & 69.7587750380355 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 4103.51833333333 & 56.6970159086637 & 72.3762665030539 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 4105.69166666667 & 55.5730507327925 & 73.8791844703243 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 4105.15166666667 & 53.8153242773056 & 76.2822062636505 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 4099.85166666667 & 52.6908529080609 & 77.8095521403005 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 4095.81833333333 & 48.8127998224502 & 83.9086950191611 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 4096.89833333333 & 48.4076598091821 & 84.6332656749546 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 4095.36 & 47.9643160203441 & 85.3834754625282 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 4098.37 & 46.1234226254868 & 88.8565888372589 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 4097.32 & 45.5171836180554 & 90.0169930191969 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 4098.44 & 44.0271563089801 & 93.088910199818 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 4092.49 & 41.6673683579334 & 98.2181059491078 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 4103.14 & 39.1389668992872 & 104.835163650544 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 4131.60833333333 & 33.477450737213 & 123.414663970835 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 4146.175 & 30.5687117674967 & 135.634600225730 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 4104.28448275862 & 66.6049785586217 & 61.6212867503031 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 4102.81071428571 & 64.0900599946715 & 64.0163344304378 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 4101.57037037037 & 61.6100936391305 & 66.5730260758009 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 4102.68846153846 & 59.804327280658 & 68.6018662543398 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 4103.566 & 57.8267798713167 & 70.9630729764266 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 4106.62708333333 & 55.9448800048331 & 73.404877854391 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 4107.8 & 54.7195248164242 & 75.070096346433 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 4108.63409090909 & 53.7084159356514 & 76.4988879178952 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 4109.15952380952 & 52.6486646918878 & 78.0486940714884 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 4109.8275 & 51.6663401545721 & 79.5455510822806 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 4111.40263157895 & 50.5812445191904 & 81.2831449811222 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 4113.76388888889 & 50.0467855956483 & 82.1983637895536 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 4116.24411764706 & 49.2907258420047 & 83.5095050302398 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 4119.25625 & 48.2235553341155 & 85.4200031801856 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 4122.24 & 47.119667807115 & 87.484487727597 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 4125.8 & 45.5509651190886 & 90.5754683619435 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 4129.74615384615 & 43.5814855646715 & 94.7591873094353 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 4135.225 & 41.267195910715 & 100.206105812154 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 4140.08636363636 & 38.5633106791826 & 107.358167406288 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 4141.425 & 36.783146795209 & 112.590285520091 \tabularnewline
Median & 4169.95 &  &  \tabularnewline
Midrange & 3947.6 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 4106.8064516129 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 4122.24 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 4106.8064516129 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 4122.24 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 4122.24 &  &  \tabularnewline
Midmean - Closest Observation & 4106.8064516129 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 4122.24 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 4119.25625 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=29141&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]4099.06166666667[/C][C]71.9223305214489[/C][C]56.9928927072828[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]4060.38968502989[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]4020.06795620152[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]4136.12173698583[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]4105.66[/C][C]68.644795631072[/C][C]59.8102152137748[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]4105.04333333333[/C][C]67.7023759426968[/C][C]60.6336672262113[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]4098.66333333333[/C][C]65.0913439430225[/C][C]62.9678707651372[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]4099.76333333333[/C][C]64.3391184556758[/C][C]63.7211611184527[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]4091.32166666667[/C][C]62.5271555962573[/C][C]65.4327168356202[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]4101.23166666667[/C][C]58.7916239129844[/C][C]69.7587750380355[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]4103.51833333333[/C][C]56.6970159086637[/C][C]72.3762665030539[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]4105.69166666667[/C][C]55.5730507327925[/C][C]73.8791844703243[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]4105.15166666667[/C][C]53.8153242773056[/C][C]76.2822062636505[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]4099.85166666667[/C][C]52.6908529080609[/C][C]77.8095521403005[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]4095.81833333333[/C][C]48.8127998224502[/C][C]83.9086950191611[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]4096.89833333333[/C][C]48.4076598091821[/C][C]84.6332656749546[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]4095.36[/C][C]47.9643160203441[/C][C]85.3834754625282[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]4098.37[/C][C]46.1234226254868[/C][C]88.8565888372589[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]4097.32[/C][C]45.5171836180554[/C][C]90.0169930191969[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]4098.44[/C][C]44.0271563089801[/C][C]93.088910199818[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]4092.49[/C][C]41.6673683579334[/C][C]98.2181059491078[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]4103.14[/C][C]39.1389668992872[/C][C]104.835163650544[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]4131.60833333333[/C][C]33.477450737213[/C][C]123.414663970835[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]4146.175[/C][C]30.5687117674967[/C][C]135.634600225730[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]4104.28448275862[/C][C]66.6049785586217[/C][C]61.6212867503031[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]4102.81071428571[/C][C]64.0900599946715[/C][C]64.0163344304378[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]4101.57037037037[/C][C]61.6100936391305[/C][C]66.5730260758009[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]4102.68846153846[/C][C]59.804327280658[/C][C]68.6018662543398[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]4103.566[/C][C]57.8267798713167[/C][C]70.9630729764266[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]4106.62708333333[/C][C]55.9448800048331[/C][C]73.404877854391[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]4107.8[/C][C]54.7195248164242[/C][C]75.070096346433[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]4108.63409090909[/C][C]53.7084159356514[/C][C]76.4988879178952[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]4109.15952380952[/C][C]52.6486646918878[/C][C]78.0486940714884[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]4109.8275[/C][C]51.6663401545721[/C][C]79.5455510822806[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]4111.40263157895[/C][C]50.5812445191904[/C][C]81.2831449811222[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]4113.76388888889[/C][C]50.0467855956483[/C][C]82.1983637895536[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]4116.24411764706[/C][C]49.2907258420047[/C][C]83.5095050302398[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]4119.25625[/C][C]48.2235553341155[/C][C]85.4200031801856[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]4122.24[/C][C]47.119667807115[/C][C]87.484487727597[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]4125.8[/C][C]45.5509651190886[/C][C]90.5754683619435[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]4129.74615384615[/C][C]43.5814855646715[/C][C]94.7591873094353[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]4135.225[/C][C]41.267195910715[/C][C]100.206105812154[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]4140.08636363636[/C][C]38.5633106791826[/C][C]107.358167406288[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]4141.425[/C][C]36.783146795209[/C][C]112.590285520091[/C][/ROW]
[ROW][C]Median[/C][C]4169.95[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]3947.6[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]4106.8064516129[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]4122.24[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]4106.8064516129[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]4122.24[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]4122.24[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]4106.8064516129[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]4122.24[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]4119.25625[/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=29141&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=29141&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 Mean4099.0616666666771.922330521448956.9928927072828
Geometric Mean4060.38968502989
Harmonic Mean4020.06795620152
Quadratic Mean4136.12173698583
Winsorized Mean ( 1 / 20 )4105.6668.64479563107259.8102152137748
Winsorized Mean ( 2 / 20 )4105.0433333333367.702375942696860.6336672262113
Winsorized Mean ( 3 / 20 )4098.6633333333365.091343943022562.9678707651372
Winsorized Mean ( 4 / 20 )4099.7633333333364.339118455675863.7211611184527
Winsorized Mean ( 5 / 20 )4091.3216666666762.527155596257365.4327168356202
Winsorized Mean ( 6 / 20 )4101.2316666666758.791623912984469.7587750380355
Winsorized Mean ( 7 / 20 )4103.5183333333356.697015908663772.3762665030539
Winsorized Mean ( 8 / 20 )4105.6916666666755.573050732792573.8791844703243
Winsorized Mean ( 9 / 20 )4105.1516666666753.815324277305676.2822062636505
Winsorized Mean ( 10 / 20 )4099.8516666666752.690852908060977.8095521403005
Winsorized Mean ( 11 / 20 )4095.8183333333348.812799822450283.9086950191611
Winsorized Mean ( 12 / 20 )4096.8983333333348.407659809182184.6332656749546
Winsorized Mean ( 13 / 20 )4095.3647.964316020344185.3834754625282
Winsorized Mean ( 14 / 20 )4098.3746.123422625486888.8565888372589
Winsorized Mean ( 15 / 20 )4097.3245.517183618055490.0169930191969
Winsorized Mean ( 16 / 20 )4098.4444.027156308980193.088910199818
Winsorized Mean ( 17 / 20 )4092.4941.667368357933498.2181059491078
Winsorized Mean ( 18 / 20 )4103.1439.1389668992872104.835163650544
Winsorized Mean ( 19 / 20 )4131.6083333333333.477450737213123.414663970835
Winsorized Mean ( 20 / 20 )4146.17530.5687117674967135.634600225730
Trimmed Mean ( 1 / 20 )4104.2844827586266.604978558621761.6212867503031
Trimmed Mean ( 2 / 20 )4102.8107142857164.090059994671564.0163344304378
Trimmed Mean ( 3 / 20 )4101.5703703703761.610093639130566.5730260758009
Trimmed Mean ( 4 / 20 )4102.6884615384659.80432728065868.6018662543398
Trimmed Mean ( 5 / 20 )4103.56657.826779871316770.9630729764266
Trimmed Mean ( 6 / 20 )4106.6270833333355.944880004833173.404877854391
Trimmed Mean ( 7 / 20 )4107.854.719524816424275.070096346433
Trimmed Mean ( 8 / 20 )4108.6340909090953.708415935651476.4988879178952
Trimmed Mean ( 9 / 20 )4109.1595238095252.648664691887878.0486940714884
Trimmed Mean ( 10 / 20 )4109.827551.666340154572179.5455510822806
Trimmed Mean ( 11 / 20 )4111.4026315789550.581244519190481.2831449811222
Trimmed Mean ( 12 / 20 )4113.7638888888950.046785595648382.1983637895536
Trimmed Mean ( 13 / 20 )4116.2441176470649.290725842004783.5095050302398
Trimmed Mean ( 14 / 20 )4119.2562548.223555334115585.4200031801856
Trimmed Mean ( 15 / 20 )4122.2447.11966780711587.484487727597
Trimmed Mean ( 16 / 20 )4125.845.550965119088690.5754683619435
Trimmed Mean ( 17 / 20 )4129.7461538461543.581485564671594.7591873094353
Trimmed Mean ( 18 / 20 )4135.22541.267195910715100.206105812154
Trimmed Mean ( 19 / 20 )4140.0863636363638.5633106791826107.358167406288
Trimmed Mean ( 20 / 20 )4141.42536.783146795209112.590285520091
Median4169.95
Midrange3947.6
Midmean - Weighted Average at Xnp4106.8064516129
Midmean - Weighted Average at X(n+1)p4122.24
Midmean - Empirical Distribution Function4106.8064516129
Midmean - Empirical Distribution Function - Averaging4122.24
Midmean - Empirical Distribution Function - Interpolation4122.24
Midmean - Closest Observation4106.8064516129
Midmean - True Basic - Statistics Graphics Toolkit4122.24
Midmean - MS Excel (old versions)4119.25625
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')