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of Irreproducible Research!

Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationMon, 22 Dec 2008 06:25:19 -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/22/t1229952373g6rosy1vre9eqq8.htm/, Retrieved Mon, 13 May 2024 13:15:45 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=36050, Retrieved Mon, 13 May 2024 13:15:45 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact198
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Standard Deviation-Mean Plot] [SMP inschrijvinge...] [2008-12-21 10:55:25] [8d78428855b119373cac369316c08983]
-    D  [Standard Deviation-Mean Plot] [Standard deviatio...] [2008-12-21 13:36:43] [8d78428855b119373cac369316c08983]
- RM      [Variance Reduction Matrix] [variance reductio...] [2008-12-21 14:07:07] [8d78428855b119373cac369316c08983]
- RMP       [(Partial) Autocorrelation Function] [(P)ACF inschrijvi...] [2008-12-21 14:18:33] [8d78428855b119373cac369316c08983]
- RM          [Spectral Analysis] [spectrum (d=0, D=0)] [2008-12-21 14:50:56] [8d78428855b119373cac369316c08983]
- RM            [ARIMA Backward Selection] [Arima backward se...] [2008-12-21 15:23:44] [8d78428855b119373cac369316c08983]
- RMPD              [Central Tendency] [central tendency ...] [2008-12-22 13:25:19] [d6e9f26c3644bfc30f06303d9993b878] [Current]
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Dataseries X:
17.7039819159960
2621.68507175314
-2923.95389396323
1546.87160143998
4935.16140662082
2837.62465278769
-1368.17006107065
-246.085597653679
-2334.82711735647
305.947423579271
454.200177183295
-1275.21732009605
1373.62159578109
465.035152858511
-213.957036389146
-2065.19491572396
-2591.35058299742
-1139.84076992921
617.768205456236
2482.68099681074
-2240.86866410842
340.555544327929
-732.753091751593
-3526.01191118544
532.99855197638
-2282.93064824325
1953.67092941654
1503.00822260186
1227.73227444214
-1956.31315679326
3206.63876932604
-1627.68717784601
-1352.85910380866
-268.622333403090
-1523.14676634828
-1007.52503844433
-556.635281559039
-2985.04291201024
1065.70232209988
-1073.07792141964
-1835.73820186902
-1834.71080245561
1401.60969219643
400.674233381302
399.710799742569
-126.750579518405
-78.7739715301584
1876.40103288510
759.51701677101
-185.38777544463




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'George Udny Yule' @ 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 & 1 seconds \tabularnewline
R Server & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=36050&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'George Udny Yule' @ 72.249.76.132[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=36050&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=36050&T=0

As an alternative you can also use a QR Code:  

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

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'George Udny Yule' @ 72.249.76.132







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean-140.538259551299253.453977538481-0.554492223464756
Geometric MeanNaN
Harmonic Mean1593.2761971516
Quadratic Mean1779.73537925487
Winsorized Mean ( 1 / 16 )-164.289332313690238.556703608226-0.688680426199624
Winsorized Mean ( 2 / 16 )-176.606336253344233.897814515347-0.755057658915219
Winsorized Mean ( 3 / 16 )-169.606512457468225.982085617150-0.750530786519112
Winsorized Mean ( 4 / 16 )-160.204961201584218.882661636155-0.731921660692751
Winsorized Mean ( 5 / 16 )-207.916321029682205.602934955391-1.01125171717414
Winsorized Mean ( 6 / 16 )-212.141270517276202.597094155293-1.04710914735365
Winsorized Mean ( 7 / 16 )-233.681066145768188.322141792093-1.24085815890811
Winsorized Mean ( 8 / 16 )-223.278125330955183.563726338306-1.21635210716662
Winsorized Mean ( 9 / 16 )-219.826368917569175.969666610672-1.24922876284087
Winsorized Mean ( 10 / 16 )-225.218508317955174.882597304921-1.28782687236323
Winsorized Mean ( 11 / 16 )-211.768961598412160.566710522159-1.31888459886701
Winsorized Mean ( 12 / 16 )-225.566451401100149.080784075973-1.51304846428865
Winsorized Mean ( 13 / 16 )-264.880687414422128.408025468037-2.06280476978719
Winsorized Mean ( 14 / 16 )-300.283286549202121.35333184913-2.47445440494804
Winsorized Mean ( 15 / 16 )-302.421647479375113.374630350220-2.6674543197643
Winsorized Mean ( 16 / 16 )-280.849439143705102.627913249544-2.73657945729451
Trimmed Mean ( 1 / 16 )-175.75130152084230.730486928818-0.761716857881293
Trimmed Mean ( 2 / 16 )-188.209963702524220.629153032875-0.853060264771447
Trimmed Mean ( 3 / 16 )-194.802933844104210.857467941235-0.923860728036414
Trimmed Mean ( 4 / 16 )-204.801513759436202.251733779678-1.01260696228461
Trimmed Mean ( 5 / 16 )-218.737936433764193.934275512580-1.12789725207484
Trimmed Mean ( 6 / 16 )-221.585729961154187.996521357575-1.17866930920329
Trimmed Mean ( 7 / 16 )-223.771947425015180.854674893659-1.23730253341027
Trimmed Mean ( 8 / 16 )-221.690199794605175.826128598585-1.26084900783278
Trimmed Mean ( 9 / 16 )-221.380058088286170.101167488616-1.30146113255279
Trimmed Mean ( 10 / 16 )-221.667778305086164.221190528339-1.34981227204557
Trimmed Mean ( 11 / 16 )-221.033719374216155.651108347110-1.4200587565448
Trimmed Mean ( 12 / 16 )-222.653432272084148.002854365172-1.50438606895192
Trimmed Mean ( 13 / 16 )-222.147699784408140.437976826499-1.58182070693637
Trimmed Mean ( 14 / 16 )-214.676897751188136.505068910388-1.57266612489034
Trimmed Mean ( 15 / 16 )-199.390042608686131.945378356062-1.51115594265546
Trimmed Mean ( 16 / 16 )-180.310115780780126.740062855950-1.42267655323571
Median-156.069177481517
Midrange704.57474771769
Midmean - Weighted Average at Xnp-274.187662446962
Midmean - Weighted Average at X(n+1)p-222.653432272084
Midmean - Empirical Distribution Function-222.653432272084
Midmean - Empirical Distribution Function - Averaging-222.653432272084
Midmean - Empirical Distribution Function - Interpolation-222.147699784407
Midmean - Closest Observation-222.653432272084
Midmean - True Basic - Statistics Graphics Toolkit-222.653432272084
Midmean - MS Excel (old versions)-222.653432272084
Number of observations50

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & -140.538259551299 & 253.453977538481 & -0.554492223464756 \tabularnewline
Geometric Mean & NaN &  &  \tabularnewline
Harmonic Mean & 1593.2761971516 &  &  \tabularnewline
Quadratic Mean & 1779.73537925487 &  &  \tabularnewline
Winsorized Mean ( 1 / 16 ) & -164.289332313690 & 238.556703608226 & -0.688680426199624 \tabularnewline
Winsorized Mean ( 2 / 16 ) & -176.606336253344 & 233.897814515347 & -0.755057658915219 \tabularnewline
Winsorized Mean ( 3 / 16 ) & -169.606512457468 & 225.982085617150 & -0.750530786519112 \tabularnewline
Winsorized Mean ( 4 / 16 ) & -160.204961201584 & 218.882661636155 & -0.731921660692751 \tabularnewline
Winsorized Mean ( 5 / 16 ) & -207.916321029682 & 205.602934955391 & -1.01125171717414 \tabularnewline
Winsorized Mean ( 6 / 16 ) & -212.141270517276 & 202.597094155293 & -1.04710914735365 \tabularnewline
Winsorized Mean ( 7 / 16 ) & -233.681066145768 & 188.322141792093 & -1.24085815890811 \tabularnewline
Winsorized Mean ( 8 / 16 ) & -223.278125330955 & 183.563726338306 & -1.21635210716662 \tabularnewline
Winsorized Mean ( 9 / 16 ) & -219.826368917569 & 175.969666610672 & -1.24922876284087 \tabularnewline
Winsorized Mean ( 10 / 16 ) & -225.218508317955 & 174.882597304921 & -1.28782687236323 \tabularnewline
Winsorized Mean ( 11 / 16 ) & -211.768961598412 & 160.566710522159 & -1.31888459886701 \tabularnewline
Winsorized Mean ( 12 / 16 ) & -225.566451401100 & 149.080784075973 & -1.51304846428865 \tabularnewline
Winsorized Mean ( 13 / 16 ) & -264.880687414422 & 128.408025468037 & -2.06280476978719 \tabularnewline
Winsorized Mean ( 14 / 16 ) & -300.283286549202 & 121.35333184913 & -2.47445440494804 \tabularnewline
Winsorized Mean ( 15 / 16 ) & -302.421647479375 & 113.374630350220 & -2.6674543197643 \tabularnewline
Winsorized Mean ( 16 / 16 ) & -280.849439143705 & 102.627913249544 & -2.73657945729451 \tabularnewline
Trimmed Mean ( 1 / 16 ) & -175.75130152084 & 230.730486928818 & -0.761716857881293 \tabularnewline
Trimmed Mean ( 2 / 16 ) & -188.209963702524 & 220.629153032875 & -0.853060264771447 \tabularnewline
Trimmed Mean ( 3 / 16 ) & -194.802933844104 & 210.857467941235 & -0.923860728036414 \tabularnewline
Trimmed Mean ( 4 / 16 ) & -204.801513759436 & 202.251733779678 & -1.01260696228461 \tabularnewline
Trimmed Mean ( 5 / 16 ) & -218.737936433764 & 193.934275512580 & -1.12789725207484 \tabularnewline
Trimmed Mean ( 6 / 16 ) & -221.585729961154 & 187.996521357575 & -1.17866930920329 \tabularnewline
Trimmed Mean ( 7 / 16 ) & -223.771947425015 & 180.854674893659 & -1.23730253341027 \tabularnewline
Trimmed Mean ( 8 / 16 ) & -221.690199794605 & 175.826128598585 & -1.26084900783278 \tabularnewline
Trimmed Mean ( 9 / 16 ) & -221.380058088286 & 170.101167488616 & -1.30146113255279 \tabularnewline
Trimmed Mean ( 10 / 16 ) & -221.667778305086 & 164.221190528339 & -1.34981227204557 \tabularnewline
Trimmed Mean ( 11 / 16 ) & -221.033719374216 & 155.651108347110 & -1.4200587565448 \tabularnewline
Trimmed Mean ( 12 / 16 ) & -222.653432272084 & 148.002854365172 & -1.50438606895192 \tabularnewline
Trimmed Mean ( 13 / 16 ) & -222.147699784408 & 140.437976826499 & -1.58182070693637 \tabularnewline
Trimmed Mean ( 14 / 16 ) & -214.676897751188 & 136.505068910388 & -1.57266612489034 \tabularnewline
Trimmed Mean ( 15 / 16 ) & -199.390042608686 & 131.945378356062 & -1.51115594265546 \tabularnewline
Trimmed Mean ( 16 / 16 ) & -180.310115780780 & 126.740062855950 & -1.42267655323571 \tabularnewline
Median & -156.069177481517 &  &  \tabularnewline
Midrange & 704.57474771769 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & -274.187662446962 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & -222.653432272084 &  &  \tabularnewline
Midmean - Empirical Distribution Function & -222.653432272084 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & -222.653432272084 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & -222.147699784407 &  &  \tabularnewline
Midmean - Closest Observation & -222.653432272084 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & -222.653432272084 &  &  \tabularnewline
Midmean - MS Excel (old versions) & -222.653432272084 &  &  \tabularnewline
Number of observations & 50 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=36050&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]-140.538259551299[/C][C]253.453977538481[/C][C]-0.554492223464756[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]NaN[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]1593.2761971516[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]1779.73537925487[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 16 )[/C][C]-164.289332313690[/C][C]238.556703608226[/C][C]-0.688680426199624[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 16 )[/C][C]-176.606336253344[/C][C]233.897814515347[/C][C]-0.755057658915219[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 16 )[/C][C]-169.606512457468[/C][C]225.982085617150[/C][C]-0.750530786519112[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 16 )[/C][C]-160.204961201584[/C][C]218.882661636155[/C][C]-0.731921660692751[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 16 )[/C][C]-207.916321029682[/C][C]205.602934955391[/C][C]-1.01125171717414[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 16 )[/C][C]-212.141270517276[/C][C]202.597094155293[/C][C]-1.04710914735365[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 16 )[/C][C]-233.681066145768[/C][C]188.322141792093[/C][C]-1.24085815890811[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 16 )[/C][C]-223.278125330955[/C][C]183.563726338306[/C][C]-1.21635210716662[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 16 )[/C][C]-219.826368917569[/C][C]175.969666610672[/C][C]-1.24922876284087[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 16 )[/C][C]-225.218508317955[/C][C]174.882597304921[/C][C]-1.28782687236323[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 16 )[/C][C]-211.768961598412[/C][C]160.566710522159[/C][C]-1.31888459886701[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 16 )[/C][C]-225.566451401100[/C][C]149.080784075973[/C][C]-1.51304846428865[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 16 )[/C][C]-264.880687414422[/C][C]128.408025468037[/C][C]-2.06280476978719[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 16 )[/C][C]-300.283286549202[/C][C]121.35333184913[/C][C]-2.47445440494804[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 16 )[/C][C]-302.421647479375[/C][C]113.374630350220[/C][C]-2.6674543197643[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 16 )[/C][C]-280.849439143705[/C][C]102.627913249544[/C][C]-2.73657945729451[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 16 )[/C][C]-175.75130152084[/C][C]230.730486928818[/C][C]-0.761716857881293[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 16 )[/C][C]-188.209963702524[/C][C]220.629153032875[/C][C]-0.853060264771447[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 16 )[/C][C]-194.802933844104[/C][C]210.857467941235[/C][C]-0.923860728036414[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 16 )[/C][C]-204.801513759436[/C][C]202.251733779678[/C][C]-1.01260696228461[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 16 )[/C][C]-218.737936433764[/C][C]193.934275512580[/C][C]-1.12789725207484[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 16 )[/C][C]-221.585729961154[/C][C]187.996521357575[/C][C]-1.17866930920329[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 16 )[/C][C]-223.771947425015[/C][C]180.854674893659[/C][C]-1.23730253341027[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 16 )[/C][C]-221.690199794605[/C][C]175.826128598585[/C][C]-1.26084900783278[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 16 )[/C][C]-221.380058088286[/C][C]170.101167488616[/C][C]-1.30146113255279[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 16 )[/C][C]-221.667778305086[/C][C]164.221190528339[/C][C]-1.34981227204557[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 16 )[/C][C]-221.033719374216[/C][C]155.651108347110[/C][C]-1.4200587565448[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 16 )[/C][C]-222.653432272084[/C][C]148.002854365172[/C][C]-1.50438606895192[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 16 )[/C][C]-222.147699784408[/C][C]140.437976826499[/C][C]-1.58182070693637[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 16 )[/C][C]-214.676897751188[/C][C]136.505068910388[/C][C]-1.57266612489034[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 16 )[/C][C]-199.390042608686[/C][C]131.945378356062[/C][C]-1.51115594265546[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 16 )[/C][C]-180.310115780780[/C][C]126.740062855950[/C][C]-1.42267655323571[/C][/ROW]
[ROW][C]Median[/C][C]-156.069177481517[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]704.57474771769[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]-274.187662446962[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]-222.653432272084[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]-222.653432272084[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]-222.653432272084[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]-222.147699784407[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]-222.653432272084[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]-222.653432272084[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]-222.653432272084[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]50[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=36050&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=36050&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 Mean-140.538259551299253.453977538481-0.554492223464756
Geometric MeanNaN
Harmonic Mean1593.2761971516
Quadratic Mean1779.73537925487
Winsorized Mean ( 1 / 16 )-164.289332313690238.556703608226-0.688680426199624
Winsorized Mean ( 2 / 16 )-176.606336253344233.897814515347-0.755057658915219
Winsorized Mean ( 3 / 16 )-169.606512457468225.982085617150-0.750530786519112
Winsorized Mean ( 4 / 16 )-160.204961201584218.882661636155-0.731921660692751
Winsorized Mean ( 5 / 16 )-207.916321029682205.602934955391-1.01125171717414
Winsorized Mean ( 6 / 16 )-212.141270517276202.597094155293-1.04710914735365
Winsorized Mean ( 7 / 16 )-233.681066145768188.322141792093-1.24085815890811
Winsorized Mean ( 8 / 16 )-223.278125330955183.563726338306-1.21635210716662
Winsorized Mean ( 9 / 16 )-219.826368917569175.969666610672-1.24922876284087
Winsorized Mean ( 10 / 16 )-225.218508317955174.882597304921-1.28782687236323
Winsorized Mean ( 11 / 16 )-211.768961598412160.566710522159-1.31888459886701
Winsorized Mean ( 12 / 16 )-225.566451401100149.080784075973-1.51304846428865
Winsorized Mean ( 13 / 16 )-264.880687414422128.408025468037-2.06280476978719
Winsorized Mean ( 14 / 16 )-300.283286549202121.35333184913-2.47445440494804
Winsorized Mean ( 15 / 16 )-302.421647479375113.374630350220-2.6674543197643
Winsorized Mean ( 16 / 16 )-280.849439143705102.627913249544-2.73657945729451
Trimmed Mean ( 1 / 16 )-175.75130152084230.730486928818-0.761716857881293
Trimmed Mean ( 2 / 16 )-188.209963702524220.629153032875-0.853060264771447
Trimmed Mean ( 3 / 16 )-194.802933844104210.857467941235-0.923860728036414
Trimmed Mean ( 4 / 16 )-204.801513759436202.251733779678-1.01260696228461
Trimmed Mean ( 5 / 16 )-218.737936433764193.934275512580-1.12789725207484
Trimmed Mean ( 6 / 16 )-221.585729961154187.996521357575-1.17866930920329
Trimmed Mean ( 7 / 16 )-223.771947425015180.854674893659-1.23730253341027
Trimmed Mean ( 8 / 16 )-221.690199794605175.826128598585-1.26084900783278
Trimmed Mean ( 9 / 16 )-221.380058088286170.101167488616-1.30146113255279
Trimmed Mean ( 10 / 16 )-221.667778305086164.221190528339-1.34981227204557
Trimmed Mean ( 11 / 16 )-221.033719374216155.651108347110-1.4200587565448
Trimmed Mean ( 12 / 16 )-222.653432272084148.002854365172-1.50438606895192
Trimmed Mean ( 13 / 16 )-222.147699784408140.437976826499-1.58182070693637
Trimmed Mean ( 14 / 16 )-214.676897751188136.505068910388-1.57266612489034
Trimmed Mean ( 15 / 16 )-199.390042608686131.945378356062-1.51115594265546
Trimmed Mean ( 16 / 16 )-180.310115780780126.740062855950-1.42267655323571
Median-156.069177481517
Midrange704.57474771769
Midmean - Weighted Average at Xnp-274.187662446962
Midmean - Weighted Average at X(n+1)p-222.653432272084
Midmean - Empirical Distribution Function-222.653432272084
Midmean - Empirical Distribution Function - Averaging-222.653432272084
Midmean - Empirical Distribution Function - Interpolation-222.147699784407
Midmean - Closest Observation-222.653432272084
Midmean - True Basic - Statistics Graphics Toolkit-222.653432272084
Midmean - MS Excel (old versions)-222.653432272084
Number of observations50



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')