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of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationSat, 15 Aug 2015 15:01:47 +0100
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2015/Aug/15/t1439647336ix1urpamlt57gey.htm/, Retrieved Wed, 15 May 2024 01:58:12 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=280091, Retrieved Wed, 15 May 2024 01:58:12 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact120
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [] [2015-08-15 14:01:47] [f898ec974b62c60a8bec4044c4c271e3] [Current]
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Dataseries X:
5452304
5431998
5411406
5368792
5790356
5768048
5452304
5242380
5262686
5262686
5285280
5325892
5389098
5389098
5348486
5242380
5790356
5873868
5747742
5452304
5578716
5389098
5474612
5515510
5558124
5452304
5474612
5325892
5790356
5937074
5810948
5578716
5831254
5558124
5810948
5790356
5853562
5621330
5873868
5853562
6232512
6146998
5810948
5641636
5873868
5558124
5790356
5831254
5916768
5727436
5831254
5894460
6126692
5937074
5684536
5411406
5664230
4969250
5305586
5494918
5684536
5411406
5411406
5411406
5558124
5348486
5073354
4843124
5010148
4358068
4757610
4989842
5032456
4800224
4820530
4757610
4969250
4820530
4527380
4315454
4673812
3895606
4400968
4631198
4631198
4358068
4105530
4085224
4315454
4105530
3706274
3431142
3726580
3031886
3663374
3999424
4105530
3873298
3579862
3789786
3873298
3810092
3178318
2885168
3094806
2463318
3115398
3347630
3536962
3221218
2925780
3094806
3178318
3011294
2379806
2104674
2357212
1662518
2420418
2885168




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' @ yule.wessa.net

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 1 seconds \tabularnewline
R Server & 'George Udny Yule' @ yule.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=280091&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' @ yule.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=280091&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=280091&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' @ yule.wessa.net







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean4798105.2166666799021.398064854548.4552360442753
Geometric Mean4648047.18547039
Harmonic Mean4462447.94779354
Quadratic Mean4918194.4762174
Winsorized Mean ( 1 / 40 )4801077.2333333398020.456685395848.9803597706422
Winsorized Mean ( 2 / 40 )4804947.7666666797048.841779179549.5106142286543
Winsorized Mean ( 3 / 40 )4800772.1666666796423.284019310849.7885154555119
Winsorized Mean ( 4 / 40 )4802125.996139.559554733149.949530892807
Winsorized Mean ( 5 / 40 )4803067.3166666795686.499026642350.195872620748
Winsorized Mean ( 6 / 40 )4823044.4166666791527.179503540552.6952151571556
Winsorized Mean ( 7 / 40 )4821843.2166666791410.012203235652.7496179077853
Winsorized Mean ( 8 / 40 )4824550.6833333390931.440951223453.0570134253264
Winsorized Mean ( 9 / 40 )4830964.2333333389822.715245804953.7833244086769
Winsorized Mean ( 10 / 40 )4830988.0666666789367.589247433654.0574956463358
Winsorized Mean ( 11 / 40 )4836755.7333333388402.143996019554.7131043965531
Winsorized Mean ( 12 / 40 )4834524.9333333388188.394303344754.8204213436957
Winsorized Mean ( 13 / 40 )4836755.7333333387819.763096966155.0759369276917
Winsorized Mean ( 14 / 40 )4844096.486622.00056039155.9222411011254
Winsorized Mean ( 15 / 40 )4841558.1586380.774208196256.049024732411
Winsorized Mean ( 16 / 40 )4847278.1585460.696281831556.7193851781255
Winsorized Mean ( 17 / 40 )4865186.5166666782646.513779157458.8674136899119
Winsorized Mean ( 18 / 40 )4874624.5166666780438.973125659960.6002827640731
Winsorized Mean ( 19 / 40 )4891379.3577951.861538156762.7487176506454
Winsorized Mean ( 20 / 40 )4898529.3576914.777554755863.687752935549
Winsorized Mean ( 21 / 40 )4913143.9574836.145604568465.6520176220845
Winsorized Mean ( 22 / 40 )4921008.9573739.836955141566.7347413989215
Winsorized Mean ( 23 / 40 )4920625.2333333372781.169528476867.6084935871779
Winsorized Mean ( 24 / 40 )4929205.2333333370656.653063919369.7627897669331
Winsorized Mean ( 25 / 40 )4929205.2333333369674.936617935170.7457440594859
Winsorized Mean ( 26 / 40 )4933604.8666666766953.589803632873.686935698838
Winsorized Mean ( 27 / 40 )4933604.8666666766953.589803632873.686935698838
Winsorized Mean ( 28 / 40 )493407265818.005234002674.9653834457289
Winsorized Mean ( 29 / 40 )4953701.1333333362022.593030922279.8693007056896
Winsorized Mean ( 30 / 40 )4970074.6333333358806.173123388384.5162058565692
Winsorized Mean ( 31 / 40 )4964311.7333333357133.338851677386.8899285970505
Winsorized Mean ( 32 / 40 )4964311.7333333357133.338851677386.8899285970505
Winsorized Mean ( 33 / 40 )4958648.9333333356625.560245710487.5690926821156
Winsorized Mean ( 34 / 40 )5018127.449283.2571042225101.822154111849
Winsorized Mean ( 35 / 40 )5018127.449283.2571042225101.822154111849
Winsorized Mean ( 36 / 40 )5030911.647760.5202308549105.336197672944
Winsorized Mean ( 37 / 40 )5017772.2833333346560.6917275393107.768422185306
Winsorized Mean ( 38 / 40 )5024836.4833333344365.8938571572113.258993485211
Winsorized Mean ( 39 / 40 )5059320.9333333338989.7035969872129.760435873749
Winsorized Mean ( 40 / 40 )5093926.9333333335084.7588348274145.189167675759
Trimmed Mean ( 1 / 40 )481252296327.174658608149.9601697761405
Trimmed Mean ( 2 / 40 )4824361.413793194438.808716612451.0845221297721
Trimmed Mean ( 3 / 40 )4834579.1228070292901.492056372752.0398436644418
Trimmed Mean ( 4 / 40 )4846653.0357142991429.190836388653.0099084480285
Trimmed Mean ( 5 / 40 )4858796.889866.420831875554.0668778729929
Trimmed Mean ( 6 / 40 )4871181.1296296388229.350377475555.2104385761545
Trimmed Mean ( 7 / 40 )4880263.5283018987367.738967798755.8588740644944
Trimmed Mean ( 8 / 40 )4889893.2586407.937988287556.5907874188922
Trimmed Mean ( 9 / 40 )4899502.4509803985405.595375731357.3674643848057
Trimmed Mean ( 10 / 40 )4908640.8884459.607043215658.11820646393
Trimmed Mean ( 11 / 40 )4918149.387755183448.807077455958.9361257518055
Trimmed Mean ( 12 / 40 )4927398.6666666782444.275413136359.7664136409107
Trimmed Mean ( 13 / 40 )4937278.8510638381315.99445365760.7171920387403
Trimmed Mean ( 14 / 40 )4947364.782608780071.6706877361.7867060861366
Trimmed Mean ( 15 / 40 )4957199.8666666778815.63614872362.896147375028
Trimmed Mean ( 16 / 40 )4967712.7577390.772003948264.1899883069594
Trimmed Mean ( 17 / 40 )4978215.7674418675874.785354644165.6109370744619
Trimmed Mean ( 18 / 40 )4987714.0238095274526.344247899366.9255157239263
Trimmed Mean ( 19 / 40 )4996908.2926829373261.885760505368.2061107329114
Trimmed Mean ( 20 / 40 )5005239.52572131.952467403869.3900463495959
Trimmed Mean ( 21 / 40 )501344870945.417157269970.6662699422335
Trimmed Mean ( 22 / 40 )5020989.6578947469835.777714426571.8970966203977
Trimmed Mean ( 23 / 40 )5028359.2432432468671.590892183373.2232816789979
Trimmed Mean ( 24 / 40 )5036166.0555555667408.615937634474.7110140966987
Trimmed Mean ( 25 / 40 )5043806.1142857166196.015497195876.1950107782451
Trimmed Mean ( 26 / 40 )5051895.5882352964867.642290765477.8800555998392
Trimmed Mean ( 27 / 40 )5060167.6666666763644.08725491479.5072705874333
Trimmed Mean ( 28 / 40 )5068956.7562148.825578786481.5615854811939
Trimmed Mean ( 29 / 40 )5078280.5806451660486.773032948983.9568772809036
Trimmed Mean ( 30 / 40 )5086872.2666666759068.291742310786.1184929616466
Trimmed Mean ( 31 / 40 )5094927.2758620757835.990113431688.0926783801846
Trimmed Mean ( 32 / 40 )510395656525.630016581290.2945442360006
Trimmed Mean ( 33 / 40 )5113653.5185185254860.608887887793.2117528802624
Trimmed Mean ( 34 / 40 )512449352801.407131985197.052205203368
Trimmed Mean ( 35 / 40 )5132001.1651699.078992470399.2667811499592
Trimmed Mean ( 36 / 40 )514013550251.3257782482102.288545036258
Trimmed Mean ( 37 / 40 )5148049.7391304348691.161276762105.728629265356
Trimmed Mean ( 38 / 40 )5157652.546802.9744847707110.199246026089
Trimmed Mean ( 39 / 40 )5167638.6666666744785.9343440471115.385304389737
Trimmed Mean ( 40 / 40 )5175970.843463.8978414653119.086668638864
Median5295433
Midrange3947515
Midmean - Weighted Average at Xnp5069045.24590164
Midmean - Weighted Average at X(n+1)p5086872.26666667
Midmean - Empirical Distribution Function5069045.24590164
Midmean - Empirical Distribution Function - Averaging5086872.26666667
Midmean - Empirical Distribution Function - Interpolation5086872.26666667
Midmean - Closest Observation5069045.24590164
Midmean - True Basic - Statistics Graphics Toolkit5086872.26666667
Midmean - MS Excel (old versions)5078280.58064516
Number of observations120

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 4798105.21666667 & 99021.3980648545 & 48.4552360442753 \tabularnewline
Geometric Mean & 4648047.18547039 &  &  \tabularnewline
Harmonic Mean & 4462447.94779354 &  &  \tabularnewline
Quadratic Mean & 4918194.4762174 &  &  \tabularnewline
Winsorized Mean ( 1 / 40 ) & 4801077.23333333 & 98020.4566853958 & 48.9803597706422 \tabularnewline
Winsorized Mean ( 2 / 40 ) & 4804947.76666667 & 97048.8417791795 & 49.5106142286543 \tabularnewline
Winsorized Mean ( 3 / 40 ) & 4800772.16666667 & 96423.2840193108 & 49.7885154555119 \tabularnewline
Winsorized Mean ( 4 / 40 ) & 4802125.9 & 96139.5595547331 & 49.949530892807 \tabularnewline
Winsorized Mean ( 5 / 40 ) & 4803067.31666667 & 95686.4990266423 & 50.195872620748 \tabularnewline
Winsorized Mean ( 6 / 40 ) & 4823044.41666667 & 91527.1795035405 & 52.6952151571556 \tabularnewline
Winsorized Mean ( 7 / 40 ) & 4821843.21666667 & 91410.0122032356 & 52.7496179077853 \tabularnewline
Winsorized Mean ( 8 / 40 ) & 4824550.68333333 & 90931.4409512234 & 53.0570134253264 \tabularnewline
Winsorized Mean ( 9 / 40 ) & 4830964.23333333 & 89822.7152458049 & 53.7833244086769 \tabularnewline
Winsorized Mean ( 10 / 40 ) & 4830988.06666667 & 89367.5892474336 & 54.0574956463358 \tabularnewline
Winsorized Mean ( 11 / 40 ) & 4836755.73333333 & 88402.1439960195 & 54.7131043965531 \tabularnewline
Winsorized Mean ( 12 / 40 ) & 4834524.93333333 & 88188.3943033447 & 54.8204213436957 \tabularnewline
Winsorized Mean ( 13 / 40 ) & 4836755.73333333 & 87819.7630969661 & 55.0759369276917 \tabularnewline
Winsorized Mean ( 14 / 40 ) & 4844096.4 & 86622.000560391 & 55.9222411011254 \tabularnewline
Winsorized Mean ( 15 / 40 ) & 4841558.15 & 86380.7742081962 & 56.049024732411 \tabularnewline
Winsorized Mean ( 16 / 40 ) & 4847278.15 & 85460.6962818315 & 56.7193851781255 \tabularnewline
Winsorized Mean ( 17 / 40 ) & 4865186.51666667 & 82646.5137791574 & 58.8674136899119 \tabularnewline
Winsorized Mean ( 18 / 40 ) & 4874624.51666667 & 80438.9731256599 & 60.6002827640731 \tabularnewline
Winsorized Mean ( 19 / 40 ) & 4891379.35 & 77951.8615381567 & 62.7487176506454 \tabularnewline
Winsorized Mean ( 20 / 40 ) & 4898529.35 & 76914.7775547558 & 63.687752935549 \tabularnewline
Winsorized Mean ( 21 / 40 ) & 4913143.95 & 74836.1456045684 & 65.6520176220845 \tabularnewline
Winsorized Mean ( 22 / 40 ) & 4921008.95 & 73739.8369551415 & 66.7347413989215 \tabularnewline
Winsorized Mean ( 23 / 40 ) & 4920625.23333333 & 72781.1695284768 & 67.6084935871779 \tabularnewline
Winsorized Mean ( 24 / 40 ) & 4929205.23333333 & 70656.6530639193 & 69.7627897669331 \tabularnewline
Winsorized Mean ( 25 / 40 ) & 4929205.23333333 & 69674.9366179351 & 70.7457440594859 \tabularnewline
Winsorized Mean ( 26 / 40 ) & 4933604.86666667 & 66953.5898036328 & 73.686935698838 \tabularnewline
Winsorized Mean ( 27 / 40 ) & 4933604.86666667 & 66953.5898036328 & 73.686935698838 \tabularnewline
Winsorized Mean ( 28 / 40 ) & 4934072 & 65818.0052340026 & 74.9653834457289 \tabularnewline
Winsorized Mean ( 29 / 40 ) & 4953701.13333333 & 62022.5930309222 & 79.8693007056896 \tabularnewline
Winsorized Mean ( 30 / 40 ) & 4970074.63333333 & 58806.1731233883 & 84.5162058565692 \tabularnewline
Winsorized Mean ( 31 / 40 ) & 4964311.73333333 & 57133.3388516773 & 86.8899285970505 \tabularnewline
Winsorized Mean ( 32 / 40 ) & 4964311.73333333 & 57133.3388516773 & 86.8899285970505 \tabularnewline
Winsorized Mean ( 33 / 40 ) & 4958648.93333333 & 56625.5602457104 & 87.5690926821156 \tabularnewline
Winsorized Mean ( 34 / 40 ) & 5018127.4 & 49283.2571042225 & 101.822154111849 \tabularnewline
Winsorized Mean ( 35 / 40 ) & 5018127.4 & 49283.2571042225 & 101.822154111849 \tabularnewline
Winsorized Mean ( 36 / 40 ) & 5030911.6 & 47760.5202308549 & 105.336197672944 \tabularnewline
Winsorized Mean ( 37 / 40 ) & 5017772.28333333 & 46560.6917275393 & 107.768422185306 \tabularnewline
Winsorized Mean ( 38 / 40 ) & 5024836.48333333 & 44365.8938571572 & 113.258993485211 \tabularnewline
Winsorized Mean ( 39 / 40 ) & 5059320.93333333 & 38989.7035969872 & 129.760435873749 \tabularnewline
Winsorized Mean ( 40 / 40 ) & 5093926.93333333 & 35084.7588348274 & 145.189167675759 \tabularnewline
Trimmed Mean ( 1 / 40 ) & 4812522 & 96327.1746586081 & 49.9601697761405 \tabularnewline
Trimmed Mean ( 2 / 40 ) & 4824361.4137931 & 94438.8087166124 & 51.0845221297721 \tabularnewline
Trimmed Mean ( 3 / 40 ) & 4834579.12280702 & 92901.4920563727 & 52.0398436644418 \tabularnewline
Trimmed Mean ( 4 / 40 ) & 4846653.03571429 & 91429.1908363886 & 53.0099084480285 \tabularnewline
Trimmed Mean ( 5 / 40 ) & 4858796.8 & 89866.4208318755 & 54.0668778729929 \tabularnewline
Trimmed Mean ( 6 / 40 ) & 4871181.12962963 & 88229.3503774755 & 55.2104385761545 \tabularnewline
Trimmed Mean ( 7 / 40 ) & 4880263.52830189 & 87367.7389677987 & 55.8588740644944 \tabularnewline
Trimmed Mean ( 8 / 40 ) & 4889893.25 & 86407.9379882875 & 56.5907874188922 \tabularnewline
Trimmed Mean ( 9 / 40 ) & 4899502.45098039 & 85405.5953757313 & 57.3674643848057 \tabularnewline
Trimmed Mean ( 10 / 40 ) & 4908640.88 & 84459.6070432156 & 58.11820646393 \tabularnewline
Trimmed Mean ( 11 / 40 ) & 4918149.3877551 & 83448.8070774559 & 58.9361257518055 \tabularnewline
Trimmed Mean ( 12 / 40 ) & 4927398.66666667 & 82444.2754131363 & 59.7664136409107 \tabularnewline
Trimmed Mean ( 13 / 40 ) & 4937278.85106383 & 81315.994453657 & 60.7171920387403 \tabularnewline
Trimmed Mean ( 14 / 40 ) & 4947364.7826087 & 80071.67068773 & 61.7867060861366 \tabularnewline
Trimmed Mean ( 15 / 40 ) & 4957199.86666667 & 78815.636148723 & 62.896147375028 \tabularnewline
Trimmed Mean ( 16 / 40 ) & 4967712.75 & 77390.7720039482 & 64.1899883069594 \tabularnewline
Trimmed Mean ( 17 / 40 ) & 4978215.76744186 & 75874.7853546441 & 65.6109370744619 \tabularnewline
Trimmed Mean ( 18 / 40 ) & 4987714.02380952 & 74526.3442478993 & 66.9255157239263 \tabularnewline
Trimmed Mean ( 19 / 40 ) & 4996908.29268293 & 73261.8857605053 & 68.2061107329114 \tabularnewline
Trimmed Mean ( 20 / 40 ) & 5005239.525 & 72131.9524674038 & 69.3900463495959 \tabularnewline
Trimmed Mean ( 21 / 40 ) & 5013448 & 70945.4171572699 & 70.6662699422335 \tabularnewline
Trimmed Mean ( 22 / 40 ) & 5020989.65789474 & 69835.7777144265 & 71.8970966203977 \tabularnewline
Trimmed Mean ( 23 / 40 ) & 5028359.24324324 & 68671.5908921833 & 73.2232816789979 \tabularnewline
Trimmed Mean ( 24 / 40 ) & 5036166.05555556 & 67408.6159376344 & 74.7110140966987 \tabularnewline
Trimmed Mean ( 25 / 40 ) & 5043806.11428571 & 66196.0154971958 & 76.1950107782451 \tabularnewline
Trimmed Mean ( 26 / 40 ) & 5051895.58823529 & 64867.6422907654 & 77.8800555998392 \tabularnewline
Trimmed Mean ( 27 / 40 ) & 5060167.66666667 & 63644.087254914 & 79.5072705874333 \tabularnewline
Trimmed Mean ( 28 / 40 ) & 5068956.75 & 62148.8255787864 & 81.5615854811939 \tabularnewline
Trimmed Mean ( 29 / 40 ) & 5078280.58064516 & 60486.7730329489 & 83.9568772809036 \tabularnewline
Trimmed Mean ( 30 / 40 ) & 5086872.26666667 & 59068.2917423107 & 86.1184929616466 \tabularnewline
Trimmed Mean ( 31 / 40 ) & 5094927.27586207 & 57835.9901134316 & 88.0926783801846 \tabularnewline
Trimmed Mean ( 32 / 40 ) & 5103956 & 56525.6300165812 & 90.2945442360006 \tabularnewline
Trimmed Mean ( 33 / 40 ) & 5113653.51851852 & 54860.6088878877 & 93.2117528802624 \tabularnewline
Trimmed Mean ( 34 / 40 ) & 5124493 & 52801.4071319851 & 97.052205203368 \tabularnewline
Trimmed Mean ( 35 / 40 ) & 5132001.16 & 51699.0789924703 & 99.2667811499592 \tabularnewline
Trimmed Mean ( 36 / 40 ) & 5140135 & 50251.3257782482 & 102.288545036258 \tabularnewline
Trimmed Mean ( 37 / 40 ) & 5148049.73913043 & 48691.161276762 & 105.728629265356 \tabularnewline
Trimmed Mean ( 38 / 40 ) & 5157652.5 & 46802.9744847707 & 110.199246026089 \tabularnewline
Trimmed Mean ( 39 / 40 ) & 5167638.66666667 & 44785.9343440471 & 115.385304389737 \tabularnewline
Trimmed Mean ( 40 / 40 ) & 5175970.8 & 43463.8978414653 & 119.086668638864 \tabularnewline
Median & 5295433 &  &  \tabularnewline
Midrange & 3947515 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 5069045.24590164 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 5086872.26666667 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 5069045.24590164 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 5086872.26666667 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 5086872.26666667 &  &  \tabularnewline
Midmean - Closest Observation & 5069045.24590164 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 5086872.26666667 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 5078280.58064516 &  &  \tabularnewline
Number of observations & 120 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=280091&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]4798105.21666667[/C][C]99021.3980648545[/C][C]48.4552360442753[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]4648047.18547039[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]4462447.94779354[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]4918194.4762174[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 40 )[/C][C]4801077.23333333[/C][C]98020.4566853958[/C][C]48.9803597706422[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 40 )[/C][C]4804947.76666667[/C][C]97048.8417791795[/C][C]49.5106142286543[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 40 )[/C][C]4800772.16666667[/C][C]96423.2840193108[/C][C]49.7885154555119[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 40 )[/C][C]4802125.9[/C][C]96139.5595547331[/C][C]49.949530892807[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 40 )[/C][C]4803067.31666667[/C][C]95686.4990266423[/C][C]50.195872620748[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 40 )[/C][C]4823044.41666667[/C][C]91527.1795035405[/C][C]52.6952151571556[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 40 )[/C][C]4821843.21666667[/C][C]91410.0122032356[/C][C]52.7496179077853[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 40 )[/C][C]4824550.68333333[/C][C]90931.4409512234[/C][C]53.0570134253264[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 40 )[/C][C]4830964.23333333[/C][C]89822.7152458049[/C][C]53.7833244086769[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 40 )[/C][C]4830988.06666667[/C][C]89367.5892474336[/C][C]54.0574956463358[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 40 )[/C][C]4836755.73333333[/C][C]88402.1439960195[/C][C]54.7131043965531[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 40 )[/C][C]4834524.93333333[/C][C]88188.3943033447[/C][C]54.8204213436957[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 40 )[/C][C]4836755.73333333[/C][C]87819.7630969661[/C][C]55.0759369276917[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 40 )[/C][C]4844096.4[/C][C]86622.000560391[/C][C]55.9222411011254[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 40 )[/C][C]4841558.15[/C][C]86380.7742081962[/C][C]56.049024732411[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 40 )[/C][C]4847278.15[/C][C]85460.6962818315[/C][C]56.7193851781255[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 40 )[/C][C]4865186.51666667[/C][C]82646.5137791574[/C][C]58.8674136899119[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 40 )[/C][C]4874624.51666667[/C][C]80438.9731256599[/C][C]60.6002827640731[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 40 )[/C][C]4891379.35[/C][C]77951.8615381567[/C][C]62.7487176506454[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 40 )[/C][C]4898529.35[/C][C]76914.7775547558[/C][C]63.687752935549[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 40 )[/C][C]4913143.95[/C][C]74836.1456045684[/C][C]65.6520176220845[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 40 )[/C][C]4921008.95[/C][C]73739.8369551415[/C][C]66.7347413989215[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 40 )[/C][C]4920625.23333333[/C][C]72781.1695284768[/C][C]67.6084935871779[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 40 )[/C][C]4929205.23333333[/C][C]70656.6530639193[/C][C]69.7627897669331[/C][/ROW]
[ROW][C]Winsorized Mean ( 25 / 40 )[/C][C]4929205.23333333[/C][C]69674.9366179351[/C][C]70.7457440594859[/C][/ROW]
[ROW][C]Winsorized Mean ( 26 / 40 )[/C][C]4933604.86666667[/C][C]66953.5898036328[/C][C]73.686935698838[/C][/ROW]
[ROW][C]Winsorized Mean ( 27 / 40 )[/C][C]4933604.86666667[/C][C]66953.5898036328[/C][C]73.686935698838[/C][/ROW]
[ROW][C]Winsorized Mean ( 28 / 40 )[/C][C]4934072[/C][C]65818.0052340026[/C][C]74.9653834457289[/C][/ROW]
[ROW][C]Winsorized Mean ( 29 / 40 )[/C][C]4953701.13333333[/C][C]62022.5930309222[/C][C]79.8693007056896[/C][/ROW]
[ROW][C]Winsorized Mean ( 30 / 40 )[/C][C]4970074.63333333[/C][C]58806.1731233883[/C][C]84.5162058565692[/C][/ROW]
[ROW][C]Winsorized Mean ( 31 / 40 )[/C][C]4964311.73333333[/C][C]57133.3388516773[/C][C]86.8899285970505[/C][/ROW]
[ROW][C]Winsorized Mean ( 32 / 40 )[/C][C]4964311.73333333[/C][C]57133.3388516773[/C][C]86.8899285970505[/C][/ROW]
[ROW][C]Winsorized Mean ( 33 / 40 )[/C][C]4958648.93333333[/C][C]56625.5602457104[/C][C]87.5690926821156[/C][/ROW]
[ROW][C]Winsorized Mean ( 34 / 40 )[/C][C]5018127.4[/C][C]49283.2571042225[/C][C]101.822154111849[/C][/ROW]
[ROW][C]Winsorized Mean ( 35 / 40 )[/C][C]5018127.4[/C][C]49283.2571042225[/C][C]101.822154111849[/C][/ROW]
[ROW][C]Winsorized Mean ( 36 / 40 )[/C][C]5030911.6[/C][C]47760.5202308549[/C][C]105.336197672944[/C][/ROW]
[ROW][C]Winsorized Mean ( 37 / 40 )[/C][C]5017772.28333333[/C][C]46560.6917275393[/C][C]107.768422185306[/C][/ROW]
[ROW][C]Winsorized Mean ( 38 / 40 )[/C][C]5024836.48333333[/C][C]44365.8938571572[/C][C]113.258993485211[/C][/ROW]
[ROW][C]Winsorized Mean ( 39 / 40 )[/C][C]5059320.93333333[/C][C]38989.7035969872[/C][C]129.760435873749[/C][/ROW]
[ROW][C]Winsorized Mean ( 40 / 40 )[/C][C]5093926.93333333[/C][C]35084.7588348274[/C][C]145.189167675759[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 40 )[/C][C]4812522[/C][C]96327.1746586081[/C][C]49.9601697761405[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 40 )[/C][C]4824361.4137931[/C][C]94438.8087166124[/C][C]51.0845221297721[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 40 )[/C][C]4834579.12280702[/C][C]92901.4920563727[/C][C]52.0398436644418[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 40 )[/C][C]4846653.03571429[/C][C]91429.1908363886[/C][C]53.0099084480285[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 40 )[/C][C]4858796.8[/C][C]89866.4208318755[/C][C]54.0668778729929[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 40 )[/C][C]4871181.12962963[/C][C]88229.3503774755[/C][C]55.2104385761545[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 40 )[/C][C]4880263.52830189[/C][C]87367.7389677987[/C][C]55.8588740644944[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 40 )[/C][C]4889893.25[/C][C]86407.9379882875[/C][C]56.5907874188922[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 40 )[/C][C]4899502.45098039[/C][C]85405.5953757313[/C][C]57.3674643848057[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 40 )[/C][C]4908640.88[/C][C]84459.6070432156[/C][C]58.11820646393[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 40 )[/C][C]4918149.3877551[/C][C]83448.8070774559[/C][C]58.9361257518055[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 40 )[/C][C]4927398.66666667[/C][C]82444.2754131363[/C][C]59.7664136409107[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 40 )[/C][C]4937278.85106383[/C][C]81315.994453657[/C][C]60.7171920387403[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 40 )[/C][C]4947364.7826087[/C][C]80071.67068773[/C][C]61.7867060861366[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 40 )[/C][C]4957199.86666667[/C][C]78815.636148723[/C][C]62.896147375028[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 40 )[/C][C]4967712.75[/C][C]77390.7720039482[/C][C]64.1899883069594[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 40 )[/C][C]4978215.76744186[/C][C]75874.7853546441[/C][C]65.6109370744619[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 40 )[/C][C]4987714.02380952[/C][C]74526.3442478993[/C][C]66.9255157239263[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 40 )[/C][C]4996908.29268293[/C][C]73261.8857605053[/C][C]68.2061107329114[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 40 )[/C][C]5005239.525[/C][C]72131.9524674038[/C][C]69.3900463495959[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 40 )[/C][C]5013448[/C][C]70945.4171572699[/C][C]70.6662699422335[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 40 )[/C][C]5020989.65789474[/C][C]69835.7777144265[/C][C]71.8970966203977[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 40 )[/C][C]5028359.24324324[/C][C]68671.5908921833[/C][C]73.2232816789979[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 40 )[/C][C]5036166.05555556[/C][C]67408.6159376344[/C][C]74.7110140966987[/C][/ROW]
[ROW][C]Trimmed Mean ( 25 / 40 )[/C][C]5043806.11428571[/C][C]66196.0154971958[/C][C]76.1950107782451[/C][/ROW]
[ROW][C]Trimmed Mean ( 26 / 40 )[/C][C]5051895.58823529[/C][C]64867.6422907654[/C][C]77.8800555998392[/C][/ROW]
[ROW][C]Trimmed Mean ( 27 / 40 )[/C][C]5060167.66666667[/C][C]63644.087254914[/C][C]79.5072705874333[/C][/ROW]
[ROW][C]Trimmed Mean ( 28 / 40 )[/C][C]5068956.75[/C][C]62148.8255787864[/C][C]81.5615854811939[/C][/ROW]
[ROW][C]Trimmed Mean ( 29 / 40 )[/C][C]5078280.58064516[/C][C]60486.7730329489[/C][C]83.9568772809036[/C][/ROW]
[ROW][C]Trimmed Mean ( 30 / 40 )[/C][C]5086872.26666667[/C][C]59068.2917423107[/C][C]86.1184929616466[/C][/ROW]
[ROW][C]Trimmed Mean ( 31 / 40 )[/C][C]5094927.27586207[/C][C]57835.9901134316[/C][C]88.0926783801846[/C][/ROW]
[ROW][C]Trimmed Mean ( 32 / 40 )[/C][C]5103956[/C][C]56525.6300165812[/C][C]90.2945442360006[/C][/ROW]
[ROW][C]Trimmed Mean ( 33 / 40 )[/C][C]5113653.51851852[/C][C]54860.6088878877[/C][C]93.2117528802624[/C][/ROW]
[ROW][C]Trimmed Mean ( 34 / 40 )[/C][C]5124493[/C][C]52801.4071319851[/C][C]97.052205203368[/C][/ROW]
[ROW][C]Trimmed Mean ( 35 / 40 )[/C][C]5132001.16[/C][C]51699.0789924703[/C][C]99.2667811499592[/C][/ROW]
[ROW][C]Trimmed Mean ( 36 / 40 )[/C][C]5140135[/C][C]50251.3257782482[/C][C]102.288545036258[/C][/ROW]
[ROW][C]Trimmed Mean ( 37 / 40 )[/C][C]5148049.73913043[/C][C]48691.161276762[/C][C]105.728629265356[/C][/ROW]
[ROW][C]Trimmed Mean ( 38 / 40 )[/C][C]5157652.5[/C][C]46802.9744847707[/C][C]110.199246026089[/C][/ROW]
[ROW][C]Trimmed Mean ( 39 / 40 )[/C][C]5167638.66666667[/C][C]44785.9343440471[/C][C]115.385304389737[/C][/ROW]
[ROW][C]Trimmed Mean ( 40 / 40 )[/C][C]5175970.8[/C][C]43463.8978414653[/C][C]119.086668638864[/C][/ROW]
[ROW][C]Median[/C][C]5295433[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]3947515[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]5069045.24590164[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]5086872.26666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]5069045.24590164[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]5086872.26666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]5086872.26666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]5069045.24590164[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]5086872.26666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]5078280.58064516[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]120[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=280091&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=280091&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 Mean4798105.2166666799021.398064854548.4552360442753
Geometric Mean4648047.18547039
Harmonic Mean4462447.94779354
Quadratic Mean4918194.4762174
Winsorized Mean ( 1 / 40 )4801077.2333333398020.456685395848.9803597706422
Winsorized Mean ( 2 / 40 )4804947.7666666797048.841779179549.5106142286543
Winsorized Mean ( 3 / 40 )4800772.1666666796423.284019310849.7885154555119
Winsorized Mean ( 4 / 40 )4802125.996139.559554733149.949530892807
Winsorized Mean ( 5 / 40 )4803067.3166666795686.499026642350.195872620748
Winsorized Mean ( 6 / 40 )4823044.4166666791527.179503540552.6952151571556
Winsorized Mean ( 7 / 40 )4821843.2166666791410.012203235652.7496179077853
Winsorized Mean ( 8 / 40 )4824550.6833333390931.440951223453.0570134253264
Winsorized Mean ( 9 / 40 )4830964.2333333389822.715245804953.7833244086769
Winsorized Mean ( 10 / 40 )4830988.0666666789367.589247433654.0574956463358
Winsorized Mean ( 11 / 40 )4836755.7333333388402.143996019554.7131043965531
Winsorized Mean ( 12 / 40 )4834524.9333333388188.394303344754.8204213436957
Winsorized Mean ( 13 / 40 )4836755.7333333387819.763096966155.0759369276917
Winsorized Mean ( 14 / 40 )4844096.486622.00056039155.9222411011254
Winsorized Mean ( 15 / 40 )4841558.1586380.774208196256.049024732411
Winsorized Mean ( 16 / 40 )4847278.1585460.696281831556.7193851781255
Winsorized Mean ( 17 / 40 )4865186.5166666782646.513779157458.8674136899119
Winsorized Mean ( 18 / 40 )4874624.5166666780438.973125659960.6002827640731
Winsorized Mean ( 19 / 40 )4891379.3577951.861538156762.7487176506454
Winsorized Mean ( 20 / 40 )4898529.3576914.777554755863.687752935549
Winsorized Mean ( 21 / 40 )4913143.9574836.145604568465.6520176220845
Winsorized Mean ( 22 / 40 )4921008.9573739.836955141566.7347413989215
Winsorized Mean ( 23 / 40 )4920625.2333333372781.169528476867.6084935871779
Winsorized Mean ( 24 / 40 )4929205.2333333370656.653063919369.7627897669331
Winsorized Mean ( 25 / 40 )4929205.2333333369674.936617935170.7457440594859
Winsorized Mean ( 26 / 40 )4933604.8666666766953.589803632873.686935698838
Winsorized Mean ( 27 / 40 )4933604.8666666766953.589803632873.686935698838
Winsorized Mean ( 28 / 40 )493407265818.005234002674.9653834457289
Winsorized Mean ( 29 / 40 )4953701.1333333362022.593030922279.8693007056896
Winsorized Mean ( 30 / 40 )4970074.6333333358806.173123388384.5162058565692
Winsorized Mean ( 31 / 40 )4964311.7333333357133.338851677386.8899285970505
Winsorized Mean ( 32 / 40 )4964311.7333333357133.338851677386.8899285970505
Winsorized Mean ( 33 / 40 )4958648.9333333356625.560245710487.5690926821156
Winsorized Mean ( 34 / 40 )5018127.449283.2571042225101.822154111849
Winsorized Mean ( 35 / 40 )5018127.449283.2571042225101.822154111849
Winsorized Mean ( 36 / 40 )5030911.647760.5202308549105.336197672944
Winsorized Mean ( 37 / 40 )5017772.2833333346560.6917275393107.768422185306
Winsorized Mean ( 38 / 40 )5024836.4833333344365.8938571572113.258993485211
Winsorized Mean ( 39 / 40 )5059320.9333333338989.7035969872129.760435873749
Winsorized Mean ( 40 / 40 )5093926.9333333335084.7588348274145.189167675759
Trimmed Mean ( 1 / 40 )481252296327.174658608149.9601697761405
Trimmed Mean ( 2 / 40 )4824361.413793194438.808716612451.0845221297721
Trimmed Mean ( 3 / 40 )4834579.1228070292901.492056372752.0398436644418
Trimmed Mean ( 4 / 40 )4846653.0357142991429.190836388653.0099084480285
Trimmed Mean ( 5 / 40 )4858796.889866.420831875554.0668778729929
Trimmed Mean ( 6 / 40 )4871181.1296296388229.350377475555.2104385761545
Trimmed Mean ( 7 / 40 )4880263.5283018987367.738967798755.8588740644944
Trimmed Mean ( 8 / 40 )4889893.2586407.937988287556.5907874188922
Trimmed Mean ( 9 / 40 )4899502.4509803985405.595375731357.3674643848057
Trimmed Mean ( 10 / 40 )4908640.8884459.607043215658.11820646393
Trimmed Mean ( 11 / 40 )4918149.387755183448.807077455958.9361257518055
Trimmed Mean ( 12 / 40 )4927398.6666666782444.275413136359.7664136409107
Trimmed Mean ( 13 / 40 )4937278.8510638381315.99445365760.7171920387403
Trimmed Mean ( 14 / 40 )4947364.782608780071.6706877361.7867060861366
Trimmed Mean ( 15 / 40 )4957199.8666666778815.63614872362.896147375028
Trimmed Mean ( 16 / 40 )4967712.7577390.772003948264.1899883069594
Trimmed Mean ( 17 / 40 )4978215.7674418675874.785354644165.6109370744619
Trimmed Mean ( 18 / 40 )4987714.0238095274526.344247899366.9255157239263
Trimmed Mean ( 19 / 40 )4996908.2926829373261.885760505368.2061107329114
Trimmed Mean ( 20 / 40 )5005239.52572131.952467403869.3900463495959
Trimmed Mean ( 21 / 40 )501344870945.417157269970.6662699422335
Trimmed Mean ( 22 / 40 )5020989.6578947469835.777714426571.8970966203977
Trimmed Mean ( 23 / 40 )5028359.2432432468671.590892183373.2232816789979
Trimmed Mean ( 24 / 40 )5036166.0555555667408.615937634474.7110140966987
Trimmed Mean ( 25 / 40 )5043806.1142857166196.015497195876.1950107782451
Trimmed Mean ( 26 / 40 )5051895.5882352964867.642290765477.8800555998392
Trimmed Mean ( 27 / 40 )5060167.6666666763644.08725491479.5072705874333
Trimmed Mean ( 28 / 40 )5068956.7562148.825578786481.5615854811939
Trimmed Mean ( 29 / 40 )5078280.5806451660486.773032948983.9568772809036
Trimmed Mean ( 30 / 40 )5086872.2666666759068.291742310786.1184929616466
Trimmed Mean ( 31 / 40 )5094927.2758620757835.990113431688.0926783801846
Trimmed Mean ( 32 / 40 )510395656525.630016581290.2945442360006
Trimmed Mean ( 33 / 40 )5113653.5185185254860.608887887793.2117528802624
Trimmed Mean ( 34 / 40 )512449352801.407131985197.052205203368
Trimmed Mean ( 35 / 40 )5132001.1651699.078992470399.2667811499592
Trimmed Mean ( 36 / 40 )514013550251.3257782482102.288545036258
Trimmed Mean ( 37 / 40 )5148049.7391304348691.161276762105.728629265356
Trimmed Mean ( 38 / 40 )5157652.546802.9744847707110.199246026089
Trimmed Mean ( 39 / 40 )5167638.6666666744785.9343440471115.385304389737
Trimmed Mean ( 40 / 40 )5175970.843463.8978414653119.086668638864
Median5295433
Midrange3947515
Midmean - Weighted Average at Xnp5069045.24590164
Midmean - Weighted Average at X(n+1)p5086872.26666667
Midmean - Empirical Distribution Function5069045.24590164
Midmean - Empirical Distribution Function - Averaging5086872.26666667
Midmean - Empirical Distribution Function - Interpolation5086872.26666667
Midmean - Closest Observation5069045.24590164
Midmean - True Basic - Statistics Graphics Toolkit5086872.26666667
Midmean - MS Excel (old versions)5078280.58064516
Number of observations120



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')