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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 computationWed, 20 Oct 2010 09:39:51 +0000
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2010/Oct/20/t1287568688dvj4fboa0m3lj2z.htm/, Retrieved Fri, 03 May 2024 16:16:29 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=87142, Retrieved Fri, 03 May 2024 16:16:29 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsKDGP1W52
Estimated Impact108
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [Centrummaten Waar...] [2010-10-20 09:39:51] [e2eb61add35e149c3ec50f04fb8f2afe] [Current]
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Dataseries X:
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
1862,83
1905,41
1810,99
1670,07
1864,44
2052,02
2029,6
2070,83
2293,41
2443,27
2513,17
2466,92
2502,66




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'RServer@AstonUniversity' @ vre.aston.ac.uk

\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 & 'RServer@AstonUniversity' @ vre.aston.ac.uk \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=87142&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]'RServer@AstonUniversity' @ vre.aston.ac.uk[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=87142&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=87142&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'RServer@AstonUniversity' @ vre.aston.ac.uk







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean3353.3105111.47595703622730.0810200616646
Geometric Mean3229.98047350521
Harmonic Mean3093.98926596037
Quadratic Mean3460.90707188761
Winsorized Mean ( 1 / 20 )3354.39983333333110.64682297258330.3162778940749
Winsorized Mean ( 2 / 20 )3355.1235110.05089405115730.4870172016991
Winsorized Mean ( 3 / 20 )3353.7825109.7643761807130.5543803617899
Winsorized Mean ( 4 / 20 )3352.5005108.40572387227830.9254934172098
Winsorized Mean ( 5 / 20 )3356.693105.53018025926831.8078960137585
Winsorized Mean ( 6 / 20 )3357.34105.05335050333931.9584285880848
Winsorized Mean ( 7 / 20 )3350.8265102.94316599555232.5502569072411
Winsorized Mean ( 8 / 20 )3345.26916666667101.09567992728533.0901297570067
Winsorized Mean ( 9 / 20 )3363.4776666666796.983452817852934.680943696485
Winsorized Mean ( 10 / 20 )3364.68191.439004878680736.7969993162566
Winsorized Mean ( 11 / 20 )3391.647586.060684651205239.4099525671448
Winsorized Mean ( 12 / 20 )3384.131583.262047467406740.6443464091456
Winsorized Mean ( 13 / 20 )3387.1431666666781.099215940984741.7654243307539
Winsorized Mean ( 14 / 20 )3386.9121666666780.238119098732342.2107622251102
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 )3359.16551724138109.09974537146930.789856619774
Trimmed Mean ( 2 / 20 )3364.27160714286107.14561462193831.3990602323171
Trimmed Mean ( 3 / 20 )3369.35388888889105.07345948401832.0666503742685
Trimmed Mean ( 4 / 20 )3375.34288461538102.58108666490532.9041443637794
Trimmed Mean ( 5 / 20 )3382.195699.94452860693333.840727923203
Trimmed Mean ( 6 / 20 )3388.5712597.560923670994834.73287380332
Trimmed Mean ( 7 / 20 )3395.3606521739194.609525780166735.8881478812537
Trimmed Mean ( 8 / 20 )3404.0361363636491.371695783778537.2548206221205
Trimmed Mean ( 9 / 20 )3414.5302380952487.610447325330438.9740075794364
Trimmed Mean ( 10 / 20 )3423.03983.842345225566540.827090306107
Trimmed Mean ( 11 / 20 )3432.2534210526380.358380647542642.711829101021
Trimmed Mean ( 12 / 20 )3438.4058333333377.206690269953144.5350761871925
Trimmed Mean ( 13 / 20 )3446.3873529411873.580382029878746.8383998270314
Trimmed Mean ( 14 / 20 )3454.932187569.068831636096750.021581452297
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
Midrange3183.515
Midmean - Weighted Average at Xnp3433.9564516129
Midmean - Weighted Average at X(n+1)p3464.64933333333
Midmean - Empirical Distribution Function3433.9564516129
Midmean - Empirical Distribution Function - Averaging3464.64933333333
Midmean - Empirical Distribution Function - Interpolation3464.64933333333
Midmean - Closest Observation3433.9564516129
Midmean - True Basic - Statistics Graphics Toolkit3464.64933333333
Midmean - MS Excel (old versions)3454.9321875
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 3353.3105 & 111.475957036227 & 30.0810200616646 \tabularnewline
Geometric Mean & 3229.98047350521 &  &  \tabularnewline
Harmonic Mean & 3093.98926596037 &  &  \tabularnewline
Quadratic Mean & 3460.90707188761 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 3354.39983333333 & 110.646822972583 & 30.3162778940749 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 3355.1235 & 110.050894051157 & 30.4870172016991 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 3353.7825 & 109.76437618071 & 30.5543803617899 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 3352.5005 & 108.405723872278 & 30.9254934172098 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 3356.693 & 105.530180259268 & 31.8078960137585 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 3357.34 & 105.053350503339 & 31.9584285880848 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 3350.8265 & 102.943165995552 & 32.5502569072411 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 3345.26916666667 & 101.095679927285 & 33.0901297570067 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 3363.47766666667 & 96.9834528178529 & 34.680943696485 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 3364.681 & 91.4390048786807 & 36.7969993162566 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 3391.6475 & 86.0606846512052 & 39.4099525671448 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 3384.1315 & 83.2620474674067 & 40.6443464091456 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 3387.14316666667 & 81.0992159409847 & 41.7654243307539 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 3386.91216666667 & 80.2381190987323 & 42.2107622251102 \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 ) & 3359.16551724138 & 109.099745371469 & 30.789856619774 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 3364.27160714286 & 107.145614621938 & 31.3990602323171 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 3369.35388888889 & 105.073459484018 & 32.0666503742685 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 3375.34288461538 & 102.581086664905 & 32.9041443637794 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 3382.1956 & 99.944528606933 & 33.840727923203 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 3388.57125 & 97.5609236709948 & 34.73287380332 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 3395.36065217391 & 94.6095257801667 & 35.8881478812537 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 3404.03613636364 & 91.3716957837785 & 37.2548206221205 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 3414.53023809524 & 87.6104473253304 & 38.9740075794364 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 3423.039 & 83.8423452255665 & 40.827090306107 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 3432.25342105263 & 80.3583806475426 & 42.711829101021 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 3438.40583333333 & 77.2066902699531 & 44.5350761871925 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 3446.38735294118 & 73.5803820298787 & 46.8383998270314 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 3454.9321875 & 69.0688316360967 & 50.021581452297 \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 & 3183.515 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 3433.9564516129 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 3464.64933333333 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 3433.9564516129 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 3464.64933333333 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 3464.64933333333 &  &  \tabularnewline
Midmean - Closest Observation & 3433.9564516129 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 3464.64933333333 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 3454.9321875 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=87142&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]3353.3105[/C][C]111.475957036227[/C][C]30.0810200616646[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]3229.98047350521[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]3093.98926596037[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]3460.90707188761[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]3354.39983333333[/C][C]110.646822972583[/C][C]30.3162778940749[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]3355.1235[/C][C]110.050894051157[/C][C]30.4870172016991[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]3353.7825[/C][C]109.76437618071[/C][C]30.5543803617899[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]3352.5005[/C][C]108.405723872278[/C][C]30.9254934172098[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]3356.693[/C][C]105.530180259268[/C][C]31.8078960137585[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]3357.34[/C][C]105.053350503339[/C][C]31.9584285880848[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]3350.8265[/C][C]102.943165995552[/C][C]32.5502569072411[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]3345.26916666667[/C][C]101.095679927285[/C][C]33.0901297570067[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]3363.47766666667[/C][C]96.9834528178529[/C][C]34.680943696485[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]3364.681[/C][C]91.4390048786807[/C][C]36.7969993162566[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]3391.6475[/C][C]86.0606846512052[/C][C]39.4099525671448[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]3384.1315[/C][C]83.2620474674067[/C][C]40.6443464091456[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]3387.14316666667[/C][C]81.0992159409847[/C][C]41.7654243307539[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]3386.91216666667[/C][C]80.2381190987323[/C][C]42.2107622251102[/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]3359.16551724138[/C][C]109.099745371469[/C][C]30.789856619774[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]3364.27160714286[/C][C]107.145614621938[/C][C]31.3990602323171[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]3369.35388888889[/C][C]105.073459484018[/C][C]32.0666503742685[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]3375.34288461538[/C][C]102.581086664905[/C][C]32.9041443637794[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]3382.1956[/C][C]99.944528606933[/C][C]33.840727923203[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]3388.57125[/C][C]97.5609236709948[/C][C]34.73287380332[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]3395.36065217391[/C][C]94.6095257801667[/C][C]35.8881478812537[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]3404.03613636364[/C][C]91.3716957837785[/C][C]37.2548206221205[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]3414.53023809524[/C][C]87.6104473253304[/C][C]38.9740075794364[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]3423.039[/C][C]83.8423452255665[/C][C]40.827090306107[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]3432.25342105263[/C][C]80.3583806475426[/C][C]42.711829101021[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]3438.40583333333[/C][C]77.2066902699531[/C][C]44.5350761871925[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]3446.38735294118[/C][C]73.5803820298787[/C][C]46.8383998270314[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]3454.9321875[/C][C]69.0688316360967[/C][C]50.021581452297[/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]3183.515[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]3433.9564516129[/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]3433.9564516129[/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]3433.9564516129[/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]3454.9321875[/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=87142&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=87142&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 Mean3353.3105111.47595703622730.0810200616646
Geometric Mean3229.98047350521
Harmonic Mean3093.98926596037
Quadratic Mean3460.90707188761
Winsorized Mean ( 1 / 20 )3354.39983333333110.64682297258330.3162778940749
Winsorized Mean ( 2 / 20 )3355.1235110.05089405115730.4870172016991
Winsorized Mean ( 3 / 20 )3353.7825109.7643761807130.5543803617899
Winsorized Mean ( 4 / 20 )3352.5005108.40572387227830.9254934172098
Winsorized Mean ( 5 / 20 )3356.693105.53018025926831.8078960137585
Winsorized Mean ( 6 / 20 )3357.34105.05335050333931.9584285880848
Winsorized Mean ( 7 / 20 )3350.8265102.94316599555232.5502569072411
Winsorized Mean ( 8 / 20 )3345.26916666667101.09567992728533.0901297570067
Winsorized Mean ( 9 / 20 )3363.4776666666796.983452817852934.680943696485
Winsorized Mean ( 10 / 20 )3364.68191.439004878680736.7969993162566
Winsorized Mean ( 11 / 20 )3391.647586.060684651205239.4099525671448
Winsorized Mean ( 12 / 20 )3384.131583.262047467406740.6443464091456
Winsorized Mean ( 13 / 20 )3387.1431666666781.099215940984741.7654243307539
Winsorized Mean ( 14 / 20 )3386.9121666666780.238119098732342.2107622251102
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 )3359.16551724138109.09974537146930.789856619774
Trimmed Mean ( 2 / 20 )3364.27160714286107.14561462193831.3990602323171
Trimmed Mean ( 3 / 20 )3369.35388888889105.07345948401832.0666503742685
Trimmed Mean ( 4 / 20 )3375.34288461538102.58108666490532.9041443637794
Trimmed Mean ( 5 / 20 )3382.195699.94452860693333.840727923203
Trimmed Mean ( 6 / 20 )3388.5712597.560923670994834.73287380332
Trimmed Mean ( 7 / 20 )3395.3606521739194.609525780166735.8881478812537
Trimmed Mean ( 8 / 20 )3404.0361363636491.371695783778537.2548206221205
Trimmed Mean ( 9 / 20 )3414.5302380952487.610447325330438.9740075794364
Trimmed Mean ( 10 / 20 )3423.03983.842345225566540.827090306107
Trimmed Mean ( 11 / 20 )3432.2534210526380.358380647542642.711829101021
Trimmed Mean ( 12 / 20 )3438.4058333333377.206690269953144.5350761871925
Trimmed Mean ( 13 / 20 )3446.3873529411873.580382029878746.8383998270314
Trimmed Mean ( 14 / 20 )3454.932187569.068831636096750.021581452297
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
Midrange3183.515
Midmean - Weighted Average at Xnp3433.9564516129
Midmean - Weighted Average at X(n+1)p3464.64933333333
Midmean - Empirical Distribution Function3433.9564516129
Midmean - Empirical Distribution Function - Averaging3464.64933333333
Midmean - Empirical Distribution Function - Interpolation3464.64933333333
Midmean - Closest Observation3433.9564516129
Midmean - True Basic - Statistics Graphics Toolkit3464.64933333333
Midmean - MS Excel (old versions)3454.9321875
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')