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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 computationThu, 18 Dec 2008 06:42:28 -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/18/t12296078165rth8rsdn8ch1kk.htm/, Retrieved Sat, 11 May 2024 15:44:57 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=34756, Retrieved Sat, 11 May 2024 15:44:57 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact169
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Central Tendency] [Central Tendency ...] [2008-12-16 22:34:06] [7458e879e85b911182071700fff19fbd]
-    D    [Central Tendency] [Central Tendency ...] [2008-12-18 13:42:28] [ee28d11f695cd3bc1f8bbd77ba77987a] [Current]
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Dataseries X:
2196,72
2350,44
2440,25
2408,64
2472,81
2407,6
2454,62
2448,05
2497,84
2645,64
2756,76
2849,27
2921,44
2981,85
3080,58
3106,22
3119,31
3061,26
3097,31
3161,69
3257,16
3277,01
3295,32
3363,99
3494,17
3667,03
3813,06
3917,96
3895,51
3801,06
3570,12
3701,61
3862,27
3970,1
4138,52
4199,75
4290,89
4443,91
4502,64
4356,98
4591,27
4696,96
4621,4
4562,84
4202,52
4296,49
4435,23
4105,18
4116,68
3844,49
3720,98
3674,4
3857,62
3801,06
3504,37
3032,6
3047,03
2962,34
2197,82
2014,45




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'George Udny Yule' @ 72.249.76.132

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 2 seconds \tabularnewline
R Server & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=34756&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]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'George Udny Yule' @ 72.249.76.132[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=34756&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=34756&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 time2 seconds
R Server'George Udny Yule' @ 72.249.76.132







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean3442.7181666666794.93263284656336.2648550180952
Geometric Mean3361.52738174271
Harmonic Mean3277.25533559420
Quadratic Mean3519.09483490689
Winsorized Mean ( 1 / 20 )3444.4966666666793.928306741201836.6715507408986
Winsorized Mean ( 2 / 20 )3443.52993.70915481107936.7469860009118
Winsorized Mean ( 3 / 20 )3449.738591.780356469159237.5868936743475
Winsorized Mean ( 4 / 20 )3449.5358333333390.210785224112438.2386188609664
Winsorized Mean ( 5 / 20 )3444.7283333333389.245123888120838.5985046942363
Winsorized Mean ( 6 / 20 )3447.0213333333388.464711140666238.9649306360396
Winsorized Mean ( 7 / 20 )3438.8021666666786.603796393897739.7072912488277
Winsorized Mean ( 8 / 20 )3431.6128333333385.013274924869840.3656115632060
Winsorized Mean ( 9 / 20 )3433.5013333333384.339355204756340.7105475847852
Winsorized Mean ( 10 / 20 )3422.9446666666781.062626928132842.2259282283231
Winsorized Mean ( 11 / 20 )3449.533575.920437090128945.4361649143944
Winsorized Mean ( 12 / 20 )3459.511569.998170130975849.422884820086
Winsorized Mean ( 13 / 20 )3474.8233333333365.897999097160952.7303314355571
Winsorized Mean ( 14 / 20 )3488.9796666666762.807636924977655.5502457580784
Winsorized Mean ( 15 / 20 )3465.4346666666755.836366025976462.0641154378575
Winsorized Mean ( 16 / 20 )3456.7333333333352.951277665622465.2813961385779
Winsorized Mean ( 17 / 20 )3464.7516666666749.865965299627569.481291414859
Winsorized Mean ( 18 / 20 )3459.1086666666747.788328337373472.3839646000221
Winsorized Mean ( 19 / 20 )3462.1423333333346.922294492236873.7845915422175
Winsorized Mean ( 20 / 20 )3464.2056666666745.370960304442276.3529280275668
Trimmed Mean ( 1 / 20 )3445.7186206896692.504329010209337.2492688456706
Trimmed Mean ( 2 / 20 )3447.0278571428690.717361090880137.9974441021233
Trimmed Mean ( 3 / 20 )3448.9716666666788.621076362983538.9181875036138
Trimmed Mean ( 4 / 20 )3448.6767307692386.906349846510839.6826783872535
Trimmed Mean ( 5 / 20 )3448.41985.320796635703240.4170980109787
Trimmed Mean ( 6 / 20 )3449.3416666666783.588961736242641.2655163435425
Trimmed Mean ( 7 / 20 )3449.8460869565281.568787439767942.2937032072956
Trimmed Mean ( 8 / 20 )3451.997579.460342440314443.4430231985587
Trimmed Mean ( 9 / 20 )3455.6376190476277.104616517088944.8175190428674
Trimmed Mean ( 10 / 20 )3459.32774.13327725065946.6636189346296
Trimmed Mean ( 11 / 20 )3465.0715789473771.03838477209348.7774544714677
Trimmed Mean ( 12 / 20 )3467.4258333333368.33560764319250.7411282773422
Trimmed Mean ( 13 / 20 )3468.5897058823566.276256217688352.3353294804336
Trimmed Mean ( 14 / 20 )3467.69062564.483278688594553.7765866674727
Trimmed Mean ( 15 / 20 )3464.6493333333362.695840779266755.2612308929922
Trimmed Mean ( 16 / 20 )3464.5371428571462.06300303292555.8229053308809
Trimmed Mean ( 17 / 20 )3465.6626923076961.686066915926956.1822606883189
Trimmed Mean ( 18 / 20 )3465.7966666666761.694793125451656.176485746848
Trimmed Mean ( 19 / 20 )3466.8161.869668270874556.0340809461237
Trimmed Mean ( 20 / 20 )3467.54761.798809425169556.1102557193882
Median3499.27
Midrange3355.705
Midmean - Weighted Average at Xnp3447.1264516129
Midmean - Weighted Average at X(n+1)p3464.64933333333
Midmean - Empirical Distribution Function3447.1264516129
Midmean - Empirical Distribution Function - Averaging3464.64933333333
Midmean - Empirical Distribution Function - Interpolation3464.64933333333
Midmean - Closest Observation3447.1264516129
Midmean - True Basic - Statistics Graphics Toolkit3464.64933333333
Midmean - MS Excel (old versions)3467.690625
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 3442.71816666667 & 94.932632846563 & 36.2648550180952 \tabularnewline
Geometric Mean & 3361.52738174271 &  &  \tabularnewline
Harmonic Mean & 3277.25533559420 &  &  \tabularnewline
Quadratic Mean & 3519.09483490689 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 3444.49666666667 & 93.9283067412018 & 36.6715507408986 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 3443.529 & 93.709154811079 & 36.7469860009118 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 3449.7385 & 91.7803564691592 & 37.5868936743475 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 3449.53583333333 & 90.2107852241124 & 38.2386188609664 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 3444.72833333333 & 89.2451238881208 & 38.5985046942363 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 3447.02133333333 & 88.4647111406662 & 38.9649306360396 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 3438.80216666667 & 86.6037963938977 & 39.7072912488277 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 3431.61283333333 & 85.0132749248698 & 40.3656115632060 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 3433.50133333333 & 84.3393552047563 & 40.7105475847852 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 3422.94466666667 & 81.0626269281328 & 42.2259282283231 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 3449.5335 & 75.9204370901289 & 45.4361649143944 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 3459.5115 & 69.9981701309758 & 49.422884820086 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 3474.82333333333 & 65.8979990971609 & 52.7303314355571 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 3488.97966666667 & 62.8076369249776 & 55.5502457580784 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 3465.43466666667 & 55.8363660259764 & 62.0641154378575 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 3456.73333333333 & 52.9512776656224 & 65.2813961385779 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 3464.75166666667 & 49.8659652996275 & 69.481291414859 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 3459.10866666667 & 47.7883283373734 & 72.3839646000221 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 3462.14233333333 & 46.9222944922368 & 73.7845915422175 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 3464.20566666667 & 45.3709603044422 & 76.3529280275668 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 3445.71862068966 & 92.5043290102093 & 37.2492688456706 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 3447.02785714286 & 90.7173610908801 & 37.9974441021233 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 3448.97166666667 & 88.6210763629835 & 38.9181875036138 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 3448.67673076923 & 86.9063498465108 & 39.6826783872535 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 3448.419 & 85.3207966357032 & 40.4170980109787 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 3449.34166666667 & 83.5889617362426 & 41.2655163435425 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 3449.84608695652 & 81.5687874397679 & 42.2937032072956 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 3451.9975 & 79.4603424403144 & 43.4430231985587 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 3455.63761904762 & 77.1046165170889 & 44.8175190428674 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 3459.327 & 74.133277250659 & 46.6636189346296 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 3465.07157894737 & 71.038384772093 & 48.7774544714677 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 3467.42583333333 & 68.335607643192 & 50.7411282773422 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 3468.58970588235 & 66.2762562176883 & 52.3353294804336 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 3467.690625 & 64.4832786885945 & 53.7765866674727 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 3464.64933333333 & 62.6958407792667 & 55.2612308929922 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 3464.53714285714 & 62.063003032925 & 55.8229053308809 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 3465.66269230769 & 61.6860669159269 & 56.1822606883189 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 3465.79666666667 & 61.6947931254516 & 56.176485746848 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 3466.81 & 61.8696682708745 & 56.0340809461237 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 3467.547 & 61.7988094251695 & 56.1102557193882 \tabularnewline
Median & 3499.27 &  &  \tabularnewline
Midrange & 3355.705 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 3447.1264516129 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 3464.64933333333 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 3447.1264516129 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 3464.64933333333 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 3464.64933333333 &  &  \tabularnewline
Midmean - Closest Observation & 3447.1264516129 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 3464.64933333333 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 3467.690625 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=34756&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]3442.71816666667[/C][C]94.932632846563[/C][C]36.2648550180952[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]3361.52738174271[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]3277.25533559420[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]3519.09483490689[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]3444.49666666667[/C][C]93.9283067412018[/C][C]36.6715507408986[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]3443.529[/C][C]93.709154811079[/C][C]36.7469860009118[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]3449.7385[/C][C]91.7803564691592[/C][C]37.5868936743475[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]3449.53583333333[/C][C]90.2107852241124[/C][C]38.2386188609664[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]3444.72833333333[/C][C]89.2451238881208[/C][C]38.5985046942363[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]3447.02133333333[/C][C]88.4647111406662[/C][C]38.9649306360396[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]3438.80216666667[/C][C]86.6037963938977[/C][C]39.7072912488277[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]3431.61283333333[/C][C]85.0132749248698[/C][C]40.3656115632060[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]3433.50133333333[/C][C]84.3393552047563[/C][C]40.7105475847852[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]3422.94466666667[/C][C]81.0626269281328[/C][C]42.2259282283231[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]3449.5335[/C][C]75.9204370901289[/C][C]45.4361649143944[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]3459.5115[/C][C]69.9981701309758[/C][C]49.422884820086[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]3474.82333333333[/C][C]65.8979990971609[/C][C]52.7303314355571[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]3488.97966666667[/C][C]62.8076369249776[/C][C]55.5502457580784[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]3465.43466666667[/C][C]55.8363660259764[/C][C]62.0641154378575[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]3456.73333333333[/C][C]52.9512776656224[/C][C]65.2813961385779[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]3464.75166666667[/C][C]49.8659652996275[/C][C]69.481291414859[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]3459.10866666667[/C][C]47.7883283373734[/C][C]72.3839646000221[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]3462.14233333333[/C][C]46.9222944922368[/C][C]73.7845915422175[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]3464.20566666667[/C][C]45.3709603044422[/C][C]76.3529280275668[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]3445.71862068966[/C][C]92.5043290102093[/C][C]37.2492688456706[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]3447.02785714286[/C][C]90.7173610908801[/C][C]37.9974441021233[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]3448.97166666667[/C][C]88.6210763629835[/C][C]38.9181875036138[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]3448.67673076923[/C][C]86.9063498465108[/C][C]39.6826783872535[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]3448.419[/C][C]85.3207966357032[/C][C]40.4170980109787[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]3449.34166666667[/C][C]83.5889617362426[/C][C]41.2655163435425[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]3449.84608695652[/C][C]81.5687874397679[/C][C]42.2937032072956[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]3451.9975[/C][C]79.4603424403144[/C][C]43.4430231985587[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]3455.63761904762[/C][C]77.1046165170889[/C][C]44.8175190428674[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]3459.327[/C][C]74.133277250659[/C][C]46.6636189346296[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]3465.07157894737[/C][C]71.038384772093[/C][C]48.7774544714677[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]3467.42583333333[/C][C]68.335607643192[/C][C]50.7411282773422[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]3468.58970588235[/C][C]66.2762562176883[/C][C]52.3353294804336[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]3467.690625[/C][C]64.4832786885945[/C][C]53.7765866674727[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]3464.64933333333[/C][C]62.6958407792667[/C][C]55.2612308929922[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]3464.53714285714[/C][C]62.063003032925[/C][C]55.8229053308809[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]3465.66269230769[/C][C]61.6860669159269[/C][C]56.1822606883189[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]3465.79666666667[/C][C]61.6947931254516[/C][C]56.176485746848[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]3466.81[/C][C]61.8696682708745[/C][C]56.0340809461237[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]3467.547[/C][C]61.7988094251695[/C][C]56.1102557193882[/C][/ROW]
[ROW][C]Median[/C][C]3499.27[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]3355.705[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]3447.1264516129[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]3464.64933333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]3447.1264516129[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]3464.64933333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]3464.64933333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]3447.1264516129[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]3464.64933333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]3467.690625[/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=34756&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=34756&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 Mean3442.7181666666794.93263284656336.2648550180952
Geometric Mean3361.52738174271
Harmonic Mean3277.25533559420
Quadratic Mean3519.09483490689
Winsorized Mean ( 1 / 20 )3444.4966666666793.928306741201836.6715507408986
Winsorized Mean ( 2 / 20 )3443.52993.70915481107936.7469860009118
Winsorized Mean ( 3 / 20 )3449.738591.780356469159237.5868936743475
Winsorized Mean ( 4 / 20 )3449.5358333333390.210785224112438.2386188609664
Winsorized Mean ( 5 / 20 )3444.7283333333389.245123888120838.5985046942363
Winsorized Mean ( 6 / 20 )3447.0213333333388.464711140666238.9649306360396
Winsorized Mean ( 7 / 20 )3438.8021666666786.603796393897739.7072912488277
Winsorized Mean ( 8 / 20 )3431.6128333333385.013274924869840.3656115632060
Winsorized Mean ( 9 / 20 )3433.5013333333384.339355204756340.7105475847852
Winsorized Mean ( 10 / 20 )3422.9446666666781.062626928132842.2259282283231
Winsorized Mean ( 11 / 20 )3449.533575.920437090128945.4361649143944
Winsorized Mean ( 12 / 20 )3459.511569.998170130975849.422884820086
Winsorized Mean ( 13 / 20 )3474.8233333333365.897999097160952.7303314355571
Winsorized Mean ( 14 / 20 )3488.9796666666762.807636924977655.5502457580784
Winsorized Mean ( 15 / 20 )3465.4346666666755.836366025976462.0641154378575
Winsorized Mean ( 16 / 20 )3456.7333333333352.951277665622465.2813961385779
Winsorized Mean ( 17 / 20 )3464.7516666666749.865965299627569.481291414859
Winsorized Mean ( 18 / 20 )3459.1086666666747.788328337373472.3839646000221
Winsorized Mean ( 19 / 20 )3462.1423333333346.922294492236873.7845915422175
Winsorized Mean ( 20 / 20 )3464.2056666666745.370960304442276.3529280275668
Trimmed Mean ( 1 / 20 )3445.7186206896692.504329010209337.2492688456706
Trimmed Mean ( 2 / 20 )3447.0278571428690.717361090880137.9974441021233
Trimmed Mean ( 3 / 20 )3448.9716666666788.621076362983538.9181875036138
Trimmed Mean ( 4 / 20 )3448.6767307692386.906349846510839.6826783872535
Trimmed Mean ( 5 / 20 )3448.41985.320796635703240.4170980109787
Trimmed Mean ( 6 / 20 )3449.3416666666783.588961736242641.2655163435425
Trimmed Mean ( 7 / 20 )3449.8460869565281.568787439767942.2937032072956
Trimmed Mean ( 8 / 20 )3451.997579.460342440314443.4430231985587
Trimmed Mean ( 9 / 20 )3455.6376190476277.104616517088944.8175190428674
Trimmed Mean ( 10 / 20 )3459.32774.13327725065946.6636189346296
Trimmed Mean ( 11 / 20 )3465.0715789473771.03838477209348.7774544714677
Trimmed Mean ( 12 / 20 )3467.4258333333368.33560764319250.7411282773422
Trimmed Mean ( 13 / 20 )3468.5897058823566.276256217688352.3353294804336
Trimmed Mean ( 14 / 20 )3467.69062564.483278688594553.7765866674727
Trimmed Mean ( 15 / 20 )3464.6493333333362.695840779266755.2612308929922
Trimmed Mean ( 16 / 20 )3464.5371428571462.06300303292555.8229053308809
Trimmed Mean ( 17 / 20 )3465.6626923076961.686066915926956.1822606883189
Trimmed Mean ( 18 / 20 )3465.7966666666761.694793125451656.176485746848
Trimmed Mean ( 19 / 20 )3466.8161.869668270874556.0340809461237
Trimmed Mean ( 20 / 20 )3467.54761.798809425169556.1102557193882
Median3499.27
Midrange3355.705
Midmean - Weighted Average at Xnp3447.1264516129
Midmean - Weighted Average at X(n+1)p3464.64933333333
Midmean - Empirical Distribution Function3447.1264516129
Midmean - Empirical Distribution Function - Averaging3464.64933333333
Midmean - Empirical Distribution Function - Interpolation3464.64933333333
Midmean - Closest Observation3447.1264516129
Midmean - True Basic - Statistics Graphics Toolkit3464.64933333333
Midmean - MS Excel (old versions)3467.690625
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')