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Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationSun, 06 Dec 2009 07:15:08 -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/2009/Dec/06/t1260109035u7l9sxeopr4u3rn.htm/, Retrieved Sun, 05 May 2024 21:16:10 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=64406, Retrieved Sun, 05 May 2024 21:16:10 +0000
QR Codes:

Original text written by user:Central Tendency of US dollar
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact114
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [Paper: Central Te...] [2009-12-06 14:15:08] [7a39e26d7a09dd77604df90cb29f8d39] [Current]
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Dataseries X:
0.7461
0.7775
0.7790
0.7744
0.7905
0.7719
0.7811
0.7557
0.7637
0.7595
0.7471
0.7615
0.7487
0.7389
0.7337
0.7510
0.7382
0.7159
0.7542
0.7636
0.7433
0.7658
0.7627
0.7480
0.7692
0.7850
0.7913
0.7720
0.7880
0.8070
0.8268
0.8244
0.8487
0.8572
0.8214
0.8827
0.9216
0.8865
0.8816
0.8884
0.9466
0.9180
0.9337
0.9559
0.9626
0.9434
0.8639
0.7996
0.6680
0.6572
0.6928
0.6438
0.6454
0.6873
0.7265
0.7912
0.8114
0.8281
0.8393




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

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 1 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=64406&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=64406&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=64406&T=0

As an alternative you can also use a QR Code:  

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

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







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean0.7938728813559320.010096608104232578.627681015285
Geometric Mean0.790208720689093
Harmonic Mean0.786599641320612
Quadratic Mean0.797588088222596
Winsorized Mean ( 1 / 19 )0.7937864406779660.010057543803630078.9244825751069
Winsorized Mean ( 2 / 19 )0.7938711864406780.0098730427340239780.4079560706123
Winsorized Mean ( 3 / 19 )0.7942576271186440.0097026110723461881.8601942504313
Winsorized Mean ( 4 / 19 )0.7949084745762710.009252024369171185.917248253799
Winsorized Mean ( 5 / 19 )0.7943491525423730.0089003123727454189.2495812815327
Winsorized Mean ( 6 / 19 )0.796332203389830.0083829373060134294.994412378414
Winsorized Mean ( 7 / 19 )0.7940779661016950.00734753347760586108.074086157201
Winsorized Mean ( 8 / 19 )0.7947966101694920.00714101306527935111.300259907647
Winsorized Mean ( 9 / 19 )0.7949033898305080.00691418339395695114.96706762584
Winsorized Mean ( 10 / 19 )0.7948355932203390.00685670428877835115.920938069498
Winsorized Mean ( 11 / 19 )0.792355932203390.00604336088772834131.111801350859
Winsorized Mean ( 12 / 19 )0.7915627118644070.00568955788753496139.125522142698
Winsorized Mean ( 13 / 19 )0.7899101694915260.00529318822482007149.231452943160
Winsorized Mean ( 14 / 19 )0.7878932203389830.00484515089818915162.614795059005
Winsorized Mean ( 15 / 19 )0.785223728813560.0043141939758103182.009370282447
Winsorized Mean ( 16 / 19 )0.7854949152542370.00416375529017672188.650595559111
Winsorized Mean ( 17 / 19 )0.7857254237288140.00391583172840611200.653520943974
Winsorized Mean ( 18 / 19 )0.785267796610170.00369746342409479212.380139176743
Winsorized Mean ( 19 / 19 )0.7832711864406780.00299631085350708261.411857692898
Trimmed Mean ( 1 / 19 )0.7935456140350880.009659733838630382.1498425620812
Trimmed Mean ( 2 / 19 )0.7932872727272730.0091662027631174686.5448095823567
Trimmed Mean ( 3 / 19 )0.7929622641509430.0086771454754678391.3851526856176
Trimmed Mean ( 4 / 19 )0.792462745098040.008146869944248897.2720505569713
Trimmed Mean ( 5 / 19 )0.7917265306122450.0076657860198389103.280541429577
Trimmed Mean ( 6 / 19 )0.7910680851063830.00718268365966956110.135448335027
Trimmed Mean ( 7 / 19 )0.7899177777777780.00673143259167403117.347647327674
Trimmed Mean ( 8 / 19 )0.7891023255813950.00648573568017467121.667358106111
Trimmed Mean ( 9 / 19 )0.7880780487804880.00621613901831856126.779347511063
Trimmed Mean ( 10 / 19 )0.7869307692307690.00591652247891765133.00562484717
Trimmed Mean ( 11 / 19 )0.785670270270270.00551749587527772142.396168122323
Trimmed Mean ( 12 / 19 )0.7846457142857140.00523384965707778149.917511142994
Trimmed Mean ( 13 / 19 )0.7836151515151510.00494409488838767158.495168317997
Trimmed Mean ( 14 / 19 )0.7826935483870970.0046625041393135167.869780916128
Trimmed Mean ( 15 / 19 )0.7819379310344830.00441012162570656177.305298447229
Trimmed Mean ( 16 / 19 )0.781459259259260.00422832080677343184.815508323641
Trimmed Mean ( 17 / 19 )0.7808640.00399133177439979195.639962833565
Trimmed Mean ( 18 / 19 )0.7801304347826090.00370335514357869210.655042397241
Trimmed Mean ( 19 / 19 )0.7793285714285710.00331884333592825234.819330877093
Median0.7775
Midrange0.8032
Midmean - Weighted Average at Xnp0.780806666666667
Midmean - Weighted Average at X(n+1)p0.782693548387097
Midmean - Empirical Distribution Function0.782693548387097
Midmean - Empirical Distribution Function - Averaging0.782693548387097
Midmean - Empirical Distribution Function - Interpolation0.781937931034483
Midmean - Closest Observation0.780806666666667
Midmean - True Basic - Statistics Graphics Toolkit0.782693548387097
Midmean - MS Excel (old versions)0.782693548387097
Number of observations59

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 0.793872881355932 & 0.0100966081042325 & 78.627681015285 \tabularnewline
Geometric Mean & 0.790208720689093 &  &  \tabularnewline
Harmonic Mean & 0.786599641320612 &  &  \tabularnewline
Quadratic Mean & 0.797588088222596 &  &  \tabularnewline
Winsorized Mean ( 1 / 19 ) & 0.793786440677966 & 0.0100575438036300 & 78.9244825751069 \tabularnewline
Winsorized Mean ( 2 / 19 ) & 0.793871186440678 & 0.00987304273402397 & 80.4079560706123 \tabularnewline
Winsorized Mean ( 3 / 19 ) & 0.794257627118644 & 0.00970261107234618 & 81.8601942504313 \tabularnewline
Winsorized Mean ( 4 / 19 ) & 0.794908474576271 & 0.0092520243691711 & 85.917248253799 \tabularnewline
Winsorized Mean ( 5 / 19 ) & 0.794349152542373 & 0.00890031237274541 & 89.2495812815327 \tabularnewline
Winsorized Mean ( 6 / 19 ) & 0.79633220338983 & 0.00838293730601342 & 94.994412378414 \tabularnewline
Winsorized Mean ( 7 / 19 ) & 0.794077966101695 & 0.00734753347760586 & 108.074086157201 \tabularnewline
Winsorized Mean ( 8 / 19 ) & 0.794796610169492 & 0.00714101306527935 & 111.300259907647 \tabularnewline
Winsorized Mean ( 9 / 19 ) & 0.794903389830508 & 0.00691418339395695 & 114.96706762584 \tabularnewline
Winsorized Mean ( 10 / 19 ) & 0.794835593220339 & 0.00685670428877835 & 115.920938069498 \tabularnewline
Winsorized Mean ( 11 / 19 ) & 0.79235593220339 & 0.00604336088772834 & 131.111801350859 \tabularnewline
Winsorized Mean ( 12 / 19 ) & 0.791562711864407 & 0.00568955788753496 & 139.125522142698 \tabularnewline
Winsorized Mean ( 13 / 19 ) & 0.789910169491526 & 0.00529318822482007 & 149.231452943160 \tabularnewline
Winsorized Mean ( 14 / 19 ) & 0.787893220338983 & 0.00484515089818915 & 162.614795059005 \tabularnewline
Winsorized Mean ( 15 / 19 ) & 0.78522372881356 & 0.0043141939758103 & 182.009370282447 \tabularnewline
Winsorized Mean ( 16 / 19 ) & 0.785494915254237 & 0.00416375529017672 & 188.650595559111 \tabularnewline
Winsorized Mean ( 17 / 19 ) & 0.785725423728814 & 0.00391583172840611 & 200.653520943974 \tabularnewline
Winsorized Mean ( 18 / 19 ) & 0.78526779661017 & 0.00369746342409479 & 212.380139176743 \tabularnewline
Winsorized Mean ( 19 / 19 ) & 0.783271186440678 & 0.00299631085350708 & 261.411857692898 \tabularnewline
Trimmed Mean ( 1 / 19 ) & 0.793545614035088 & 0.0096597338386303 & 82.1498425620812 \tabularnewline
Trimmed Mean ( 2 / 19 ) & 0.793287272727273 & 0.00916620276311746 & 86.5448095823567 \tabularnewline
Trimmed Mean ( 3 / 19 ) & 0.792962264150943 & 0.00867714547546783 & 91.3851526856176 \tabularnewline
Trimmed Mean ( 4 / 19 ) & 0.79246274509804 & 0.0081468699442488 & 97.2720505569713 \tabularnewline
Trimmed Mean ( 5 / 19 ) & 0.791726530612245 & 0.0076657860198389 & 103.280541429577 \tabularnewline
Trimmed Mean ( 6 / 19 ) & 0.791068085106383 & 0.00718268365966956 & 110.135448335027 \tabularnewline
Trimmed Mean ( 7 / 19 ) & 0.789917777777778 & 0.00673143259167403 & 117.347647327674 \tabularnewline
Trimmed Mean ( 8 / 19 ) & 0.789102325581395 & 0.00648573568017467 & 121.667358106111 \tabularnewline
Trimmed Mean ( 9 / 19 ) & 0.788078048780488 & 0.00621613901831856 & 126.779347511063 \tabularnewline
Trimmed Mean ( 10 / 19 ) & 0.786930769230769 & 0.00591652247891765 & 133.00562484717 \tabularnewline
Trimmed Mean ( 11 / 19 ) & 0.78567027027027 & 0.00551749587527772 & 142.396168122323 \tabularnewline
Trimmed Mean ( 12 / 19 ) & 0.784645714285714 & 0.00523384965707778 & 149.917511142994 \tabularnewline
Trimmed Mean ( 13 / 19 ) & 0.783615151515151 & 0.00494409488838767 & 158.495168317997 \tabularnewline
Trimmed Mean ( 14 / 19 ) & 0.782693548387097 & 0.0046625041393135 & 167.869780916128 \tabularnewline
Trimmed Mean ( 15 / 19 ) & 0.781937931034483 & 0.00441012162570656 & 177.305298447229 \tabularnewline
Trimmed Mean ( 16 / 19 ) & 0.78145925925926 & 0.00422832080677343 & 184.815508323641 \tabularnewline
Trimmed Mean ( 17 / 19 ) & 0.780864 & 0.00399133177439979 & 195.639962833565 \tabularnewline
Trimmed Mean ( 18 / 19 ) & 0.780130434782609 & 0.00370335514357869 & 210.655042397241 \tabularnewline
Trimmed Mean ( 19 / 19 ) & 0.779328571428571 & 0.00331884333592825 & 234.819330877093 \tabularnewline
Median & 0.7775 &  &  \tabularnewline
Midrange & 0.8032 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 0.780806666666667 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 0.782693548387097 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 0.782693548387097 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 0.782693548387097 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 0.781937931034483 &  &  \tabularnewline
Midmean - Closest Observation & 0.780806666666667 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 0.782693548387097 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 0.782693548387097 &  &  \tabularnewline
Number of observations & 59 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=64406&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]0.793872881355932[/C][C]0.0100966081042325[/C][C]78.627681015285[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]0.790208720689093[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]0.786599641320612[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]0.797588088222596[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 19 )[/C][C]0.793786440677966[/C][C]0.0100575438036300[/C][C]78.9244825751069[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 19 )[/C][C]0.793871186440678[/C][C]0.00987304273402397[/C][C]80.4079560706123[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 19 )[/C][C]0.794257627118644[/C][C]0.00970261107234618[/C][C]81.8601942504313[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 19 )[/C][C]0.794908474576271[/C][C]0.0092520243691711[/C][C]85.917248253799[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 19 )[/C][C]0.794349152542373[/C][C]0.00890031237274541[/C][C]89.2495812815327[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 19 )[/C][C]0.79633220338983[/C][C]0.00838293730601342[/C][C]94.994412378414[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 19 )[/C][C]0.794077966101695[/C][C]0.00734753347760586[/C][C]108.074086157201[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 19 )[/C][C]0.794796610169492[/C][C]0.00714101306527935[/C][C]111.300259907647[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 19 )[/C][C]0.794903389830508[/C][C]0.00691418339395695[/C][C]114.96706762584[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 19 )[/C][C]0.794835593220339[/C][C]0.00685670428877835[/C][C]115.920938069498[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 19 )[/C][C]0.79235593220339[/C][C]0.00604336088772834[/C][C]131.111801350859[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 19 )[/C][C]0.791562711864407[/C][C]0.00568955788753496[/C][C]139.125522142698[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 19 )[/C][C]0.789910169491526[/C][C]0.00529318822482007[/C][C]149.231452943160[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 19 )[/C][C]0.787893220338983[/C][C]0.00484515089818915[/C][C]162.614795059005[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 19 )[/C][C]0.78522372881356[/C][C]0.0043141939758103[/C][C]182.009370282447[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 19 )[/C][C]0.785494915254237[/C][C]0.00416375529017672[/C][C]188.650595559111[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 19 )[/C][C]0.785725423728814[/C][C]0.00391583172840611[/C][C]200.653520943974[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 19 )[/C][C]0.78526779661017[/C][C]0.00369746342409479[/C][C]212.380139176743[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 19 )[/C][C]0.783271186440678[/C][C]0.00299631085350708[/C][C]261.411857692898[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 19 )[/C][C]0.793545614035088[/C][C]0.0096597338386303[/C][C]82.1498425620812[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 19 )[/C][C]0.793287272727273[/C][C]0.00916620276311746[/C][C]86.5448095823567[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 19 )[/C][C]0.792962264150943[/C][C]0.00867714547546783[/C][C]91.3851526856176[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 19 )[/C][C]0.79246274509804[/C][C]0.0081468699442488[/C][C]97.2720505569713[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 19 )[/C][C]0.791726530612245[/C][C]0.0076657860198389[/C][C]103.280541429577[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 19 )[/C][C]0.791068085106383[/C][C]0.00718268365966956[/C][C]110.135448335027[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 19 )[/C][C]0.789917777777778[/C][C]0.00673143259167403[/C][C]117.347647327674[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 19 )[/C][C]0.789102325581395[/C][C]0.00648573568017467[/C][C]121.667358106111[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 19 )[/C][C]0.788078048780488[/C][C]0.00621613901831856[/C][C]126.779347511063[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 19 )[/C][C]0.786930769230769[/C][C]0.00591652247891765[/C][C]133.00562484717[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 19 )[/C][C]0.78567027027027[/C][C]0.00551749587527772[/C][C]142.396168122323[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 19 )[/C][C]0.784645714285714[/C][C]0.00523384965707778[/C][C]149.917511142994[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 19 )[/C][C]0.783615151515151[/C][C]0.00494409488838767[/C][C]158.495168317997[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 19 )[/C][C]0.782693548387097[/C][C]0.0046625041393135[/C][C]167.869780916128[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 19 )[/C][C]0.781937931034483[/C][C]0.00441012162570656[/C][C]177.305298447229[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 19 )[/C][C]0.78145925925926[/C][C]0.00422832080677343[/C][C]184.815508323641[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 19 )[/C][C]0.780864[/C][C]0.00399133177439979[/C][C]195.639962833565[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 19 )[/C][C]0.780130434782609[/C][C]0.00370335514357869[/C][C]210.655042397241[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 19 )[/C][C]0.779328571428571[/C][C]0.00331884333592825[/C][C]234.819330877093[/C][/ROW]
[ROW][C]Median[/C][C]0.7775[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]0.8032[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]0.780806666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]0.782693548387097[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]0.782693548387097[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]0.782693548387097[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]0.781937931034483[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]0.780806666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]0.782693548387097[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]0.782693548387097[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]59[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=64406&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=64406&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 Mean0.7938728813559320.010096608104232578.627681015285
Geometric Mean0.790208720689093
Harmonic Mean0.786599641320612
Quadratic Mean0.797588088222596
Winsorized Mean ( 1 / 19 )0.7937864406779660.010057543803630078.9244825751069
Winsorized Mean ( 2 / 19 )0.7938711864406780.0098730427340239780.4079560706123
Winsorized Mean ( 3 / 19 )0.7942576271186440.0097026110723461881.8601942504313
Winsorized Mean ( 4 / 19 )0.7949084745762710.009252024369171185.917248253799
Winsorized Mean ( 5 / 19 )0.7943491525423730.0089003123727454189.2495812815327
Winsorized Mean ( 6 / 19 )0.796332203389830.0083829373060134294.994412378414
Winsorized Mean ( 7 / 19 )0.7940779661016950.00734753347760586108.074086157201
Winsorized Mean ( 8 / 19 )0.7947966101694920.00714101306527935111.300259907647
Winsorized Mean ( 9 / 19 )0.7949033898305080.00691418339395695114.96706762584
Winsorized Mean ( 10 / 19 )0.7948355932203390.00685670428877835115.920938069498
Winsorized Mean ( 11 / 19 )0.792355932203390.00604336088772834131.111801350859
Winsorized Mean ( 12 / 19 )0.7915627118644070.00568955788753496139.125522142698
Winsorized Mean ( 13 / 19 )0.7899101694915260.00529318822482007149.231452943160
Winsorized Mean ( 14 / 19 )0.7878932203389830.00484515089818915162.614795059005
Winsorized Mean ( 15 / 19 )0.785223728813560.0043141939758103182.009370282447
Winsorized Mean ( 16 / 19 )0.7854949152542370.00416375529017672188.650595559111
Winsorized Mean ( 17 / 19 )0.7857254237288140.00391583172840611200.653520943974
Winsorized Mean ( 18 / 19 )0.785267796610170.00369746342409479212.380139176743
Winsorized Mean ( 19 / 19 )0.7832711864406780.00299631085350708261.411857692898
Trimmed Mean ( 1 / 19 )0.7935456140350880.009659733838630382.1498425620812
Trimmed Mean ( 2 / 19 )0.7932872727272730.0091662027631174686.5448095823567
Trimmed Mean ( 3 / 19 )0.7929622641509430.0086771454754678391.3851526856176
Trimmed Mean ( 4 / 19 )0.792462745098040.008146869944248897.2720505569713
Trimmed Mean ( 5 / 19 )0.7917265306122450.0076657860198389103.280541429577
Trimmed Mean ( 6 / 19 )0.7910680851063830.00718268365966956110.135448335027
Trimmed Mean ( 7 / 19 )0.7899177777777780.00673143259167403117.347647327674
Trimmed Mean ( 8 / 19 )0.7891023255813950.00648573568017467121.667358106111
Trimmed Mean ( 9 / 19 )0.7880780487804880.00621613901831856126.779347511063
Trimmed Mean ( 10 / 19 )0.7869307692307690.00591652247891765133.00562484717
Trimmed Mean ( 11 / 19 )0.785670270270270.00551749587527772142.396168122323
Trimmed Mean ( 12 / 19 )0.7846457142857140.00523384965707778149.917511142994
Trimmed Mean ( 13 / 19 )0.7836151515151510.00494409488838767158.495168317997
Trimmed Mean ( 14 / 19 )0.7826935483870970.0046625041393135167.869780916128
Trimmed Mean ( 15 / 19 )0.7819379310344830.00441012162570656177.305298447229
Trimmed Mean ( 16 / 19 )0.781459259259260.00422832080677343184.815508323641
Trimmed Mean ( 17 / 19 )0.7808640.00399133177439979195.639962833565
Trimmed Mean ( 18 / 19 )0.7801304347826090.00370335514357869210.655042397241
Trimmed Mean ( 19 / 19 )0.7793285714285710.00331884333592825234.819330877093
Median0.7775
Midrange0.8032
Midmean - Weighted Average at Xnp0.780806666666667
Midmean - Weighted Average at X(n+1)p0.782693548387097
Midmean - Empirical Distribution Function0.782693548387097
Midmean - Empirical Distribution Function - Averaging0.782693548387097
Midmean - Empirical Distribution Function - Interpolation0.781937931034483
Midmean - Closest Observation0.780806666666667
Midmean - True Basic - Statistics Graphics Toolkit0.782693548387097
Midmean - MS Excel (old versions)0.782693548387097
Number of observations59



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')