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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 computationThu, 25 Nov 2010 20:09:43 +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/Nov/25/t1290716617ueky2nj6mwzaahu.htm/, Retrieved Fri, 26 Apr 2024 21:13:50 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=101503, Retrieved Fri, 26 Apr 2024 21:13:50 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact119
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
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Dataseries X:
-200,5
-256
-52,3
-29,1
200,6
788,5
629,1
-331,8
754,1
896,5
839,3
-284,9
516,8
264,8
426
679,4
396,9
676,4
154,2
-75,3
371,8
575,9
282,4
-1607,2
-199,4
-215,5
-608,5
-323,5
-225,9
-131,2
-204
-981,4
-285,7
-187,8
-806,4
-854,1
153,5
4,3
-135,5
-144,2
-269,1
-320,8
309,1
-323,4
-65,9
-270,6
-246
-1478,7
-777,6
-673
-17,4
-1094,6
-238,1
-504,2
-517,1
-498,8




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Sir Ronald Aylmer Fisher' @ 193.190.124.24

\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 & 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=101503&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]'Sir Ronald Aylmer Fisher' @ 193.190.124.24[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=101503&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=101503&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'Sir Ronald Aylmer Fisher' @ 193.190.124.24







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean-116.35535714285772.9953338625968-1.59401089063966
Geometric MeanNaN
Harmonic Mean1545.50388940748
Quadratic Mean553.71120744482
Winsorized Mean ( 1 / 18 )-115.08214285714371.9214429446545-1.60010892642549
Winsorized Mean ( 2 / 18 )-103.17857142857167.2637675626049-1.53393981882652
Winsorized Mean ( 3 / 18 )-98.957142857142865.2636396580057-1.51626760897335
Winsorized Mean ( 4 / 18 )-95.261.8876749053865-1.53827074850592
Winsorized Mean ( 5 / 18 )-91.208928571428660.8968571404922-1.49776085095828
Winsorized Mean ( 6 / 18 )-93.191071428571459.0983972180749-1.57687984472224
Winsorized Mean ( 7 / 18 )-86.766071428571554.9827262293849-1.5780605542655
Winsorized Mean ( 8 / 18 )-85.994642857142951.4110291504592-1.67268860939297
Winsorized Mean ( 9 / 18 )-85.898214285714345.7452104150374-1.87775317910611
Winsorized Mean ( 10 / 18 )-88.791071428571444.3047720507919-2.00409724096491
Winsorized Mean ( 11 / 18 )-92.660714285714343.1496739448766-2.14742559594048
Winsorized Mean ( 12 / 18 )-70.310714285714334.9479116740948-2.01187169469219
Winsorized Mean ( 13 / 18 )-74.582142857142933.4736920452061-2.22808236260345
Winsorized Mean ( 14 / 18 )-78.957142857142832.6221498588002-2.42035375347414
Winsorized Mean ( 15 / 18 )-95.457142857142929.2952256489962-3.25845392013268
Winsorized Mean ( 16 / 18 )-98.685714285714325.5089276997941-3.86867356586341
Winsorized Mean ( 17 / 18 )-98.655357142857125.4382770846738-3.87822480329438
Winsorized Mean ( 18 / 18 )-142.01607142857116.5332659105042-8.58971676844219
Trimmed Mean ( 1 / 18 )-107.50370370370467.8060318792516-1.58545929800383
Trimmed Mean ( 2 / 18 )-99.342307692307762.5574152777304-1.58801809907373
Trimmed Mean ( 3 / 18 )-97.19459.244854450468-1.64054753617902
Trimmed Mean ( 4 / 18 )-96.508333333333356.0712882774227-1.72117203471126
Trimmed Mean ( 5 / 18 )-96.906521739130453.4638522879738-1.81256152693899
Trimmed Mean ( 6 / 18 )-98.356818181818250.4492362440514-1.94961956819348
Trimmed Mean ( 7 / 18 )-99.50476190476247.1286896789236-2.11134157522019
Trimmed Mean ( 8 / 18 )-102.052544.1401413314776-2.31201117444595
Trimmed Mean ( 9 / 18 )-105.01052631578941.312303746191-2.54187050329943
Trimmed Mean ( 10 / 18 )-108.31388888888939.3140237414400-2.75509547435914
Trimmed Mean ( 11 / 18 )-111.52941176470636.9892800218037-3.01518201216579
Trimmed Mean ( 12 / 18 )-114.5312534.0666727800711-3.36197346713004
Trimmed Mean ( 13 / 18 )-121.4132.5746750762281-3.72712850445593
Trimmed Mean ( 14 / 18 )-128.61428571428630.8136808731018-4.17393450149467
Trimmed Mean ( 15 / 18 )-136.25384615384628.3813423170219-4.80082459215212
Trimmed Mean ( 16 / 18 )-142.626.0671172447065-5.4704936745147
Trimmed Mean ( 17 / 18 )-149.58636363636423.9696491850488-6.240657194502
Trimmed Mean ( 18 / 18 )-157.97520.1220524157217-7.85083930486988
Median-193.6
Midrange-355.35
Midmean - Weighted Average at Xnp-135.334482758621
Midmean - Weighted Average at X(n+1)p-128.614285714286
Midmean - Empirical Distribution Function-135.334482758621
Midmean - Empirical Distribution Function - Averaging-128.614285714286
Midmean - Empirical Distribution Function - Interpolation-128.614285714286
Midmean - Closest Observation-135.334482758621
Midmean - True Basic - Statistics Graphics Toolkit-128.614285714286
Midmean - MS Excel (old versions)-121.41
Number of observations56

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & -116.355357142857 & 72.9953338625968 & -1.59401089063966 \tabularnewline
Geometric Mean & NaN &  &  \tabularnewline
Harmonic Mean & 1545.50388940748 &  &  \tabularnewline
Quadratic Mean & 553.71120744482 &  &  \tabularnewline
Winsorized Mean ( 1 / 18 ) & -115.082142857143 & 71.9214429446545 & -1.60010892642549 \tabularnewline
Winsorized Mean ( 2 / 18 ) & -103.178571428571 & 67.2637675626049 & -1.53393981882652 \tabularnewline
Winsorized Mean ( 3 / 18 ) & -98.9571428571428 & 65.2636396580057 & -1.51626760897335 \tabularnewline
Winsorized Mean ( 4 / 18 ) & -95.2 & 61.8876749053865 & -1.53827074850592 \tabularnewline
Winsorized Mean ( 5 / 18 ) & -91.2089285714286 & 60.8968571404922 & -1.49776085095828 \tabularnewline
Winsorized Mean ( 6 / 18 ) & -93.1910714285714 & 59.0983972180749 & -1.57687984472224 \tabularnewline
Winsorized Mean ( 7 / 18 ) & -86.7660714285715 & 54.9827262293849 & -1.5780605542655 \tabularnewline
Winsorized Mean ( 8 / 18 ) & -85.9946428571429 & 51.4110291504592 & -1.67268860939297 \tabularnewline
Winsorized Mean ( 9 / 18 ) & -85.8982142857143 & 45.7452104150374 & -1.87775317910611 \tabularnewline
Winsorized Mean ( 10 / 18 ) & -88.7910714285714 & 44.3047720507919 & -2.00409724096491 \tabularnewline
Winsorized Mean ( 11 / 18 ) & -92.6607142857143 & 43.1496739448766 & -2.14742559594048 \tabularnewline
Winsorized Mean ( 12 / 18 ) & -70.3107142857143 & 34.9479116740948 & -2.01187169469219 \tabularnewline
Winsorized Mean ( 13 / 18 ) & -74.5821428571429 & 33.4736920452061 & -2.22808236260345 \tabularnewline
Winsorized Mean ( 14 / 18 ) & -78.9571428571428 & 32.6221498588002 & -2.42035375347414 \tabularnewline
Winsorized Mean ( 15 / 18 ) & -95.4571428571429 & 29.2952256489962 & -3.25845392013268 \tabularnewline
Winsorized Mean ( 16 / 18 ) & -98.6857142857143 & 25.5089276997941 & -3.86867356586341 \tabularnewline
Winsorized Mean ( 17 / 18 ) & -98.6553571428571 & 25.4382770846738 & -3.87822480329438 \tabularnewline
Winsorized Mean ( 18 / 18 ) & -142.016071428571 & 16.5332659105042 & -8.58971676844219 \tabularnewline
Trimmed Mean ( 1 / 18 ) & -107.503703703704 & 67.8060318792516 & -1.58545929800383 \tabularnewline
Trimmed Mean ( 2 / 18 ) & -99.3423076923077 & 62.5574152777304 & -1.58801809907373 \tabularnewline
Trimmed Mean ( 3 / 18 ) & -97.194 & 59.244854450468 & -1.64054753617902 \tabularnewline
Trimmed Mean ( 4 / 18 ) & -96.5083333333333 & 56.0712882774227 & -1.72117203471126 \tabularnewline
Trimmed Mean ( 5 / 18 ) & -96.9065217391304 & 53.4638522879738 & -1.81256152693899 \tabularnewline
Trimmed Mean ( 6 / 18 ) & -98.3568181818182 & 50.4492362440514 & -1.94961956819348 \tabularnewline
Trimmed Mean ( 7 / 18 ) & -99.504761904762 & 47.1286896789236 & -2.11134157522019 \tabularnewline
Trimmed Mean ( 8 / 18 ) & -102.0525 & 44.1401413314776 & -2.31201117444595 \tabularnewline
Trimmed Mean ( 9 / 18 ) & -105.010526315789 & 41.312303746191 & -2.54187050329943 \tabularnewline
Trimmed Mean ( 10 / 18 ) & -108.313888888889 & 39.3140237414400 & -2.75509547435914 \tabularnewline
Trimmed Mean ( 11 / 18 ) & -111.529411764706 & 36.9892800218037 & -3.01518201216579 \tabularnewline
Trimmed Mean ( 12 / 18 ) & -114.53125 & 34.0666727800711 & -3.36197346713004 \tabularnewline
Trimmed Mean ( 13 / 18 ) & -121.41 & 32.5746750762281 & -3.72712850445593 \tabularnewline
Trimmed Mean ( 14 / 18 ) & -128.614285714286 & 30.8136808731018 & -4.17393450149467 \tabularnewline
Trimmed Mean ( 15 / 18 ) & -136.253846153846 & 28.3813423170219 & -4.80082459215212 \tabularnewline
Trimmed Mean ( 16 / 18 ) & -142.6 & 26.0671172447065 & -5.4704936745147 \tabularnewline
Trimmed Mean ( 17 / 18 ) & -149.586363636364 & 23.9696491850488 & -6.240657194502 \tabularnewline
Trimmed Mean ( 18 / 18 ) & -157.975 & 20.1220524157217 & -7.85083930486988 \tabularnewline
Median & -193.6 &  &  \tabularnewline
Midrange & -355.35 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & -135.334482758621 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & -128.614285714286 &  &  \tabularnewline
Midmean - Empirical Distribution Function & -135.334482758621 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & -128.614285714286 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & -128.614285714286 &  &  \tabularnewline
Midmean - Closest Observation & -135.334482758621 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & -128.614285714286 &  &  \tabularnewline
Midmean - MS Excel (old versions) & -121.41 &  &  \tabularnewline
Number of observations & 56 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=101503&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]-116.355357142857[/C][C]72.9953338625968[/C][C]-1.59401089063966[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]NaN[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]1545.50388940748[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]553.71120744482[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 18 )[/C][C]-115.082142857143[/C][C]71.9214429446545[/C][C]-1.60010892642549[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 18 )[/C][C]-103.178571428571[/C][C]67.2637675626049[/C][C]-1.53393981882652[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 18 )[/C][C]-98.9571428571428[/C][C]65.2636396580057[/C][C]-1.51626760897335[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 18 )[/C][C]-95.2[/C][C]61.8876749053865[/C][C]-1.53827074850592[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 18 )[/C][C]-91.2089285714286[/C][C]60.8968571404922[/C][C]-1.49776085095828[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 18 )[/C][C]-93.1910714285714[/C][C]59.0983972180749[/C][C]-1.57687984472224[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 18 )[/C][C]-86.7660714285715[/C][C]54.9827262293849[/C][C]-1.5780605542655[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 18 )[/C][C]-85.9946428571429[/C][C]51.4110291504592[/C][C]-1.67268860939297[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 18 )[/C][C]-85.8982142857143[/C][C]45.7452104150374[/C][C]-1.87775317910611[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 18 )[/C][C]-88.7910714285714[/C][C]44.3047720507919[/C][C]-2.00409724096491[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 18 )[/C][C]-92.6607142857143[/C][C]43.1496739448766[/C][C]-2.14742559594048[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 18 )[/C][C]-70.3107142857143[/C][C]34.9479116740948[/C][C]-2.01187169469219[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 18 )[/C][C]-74.5821428571429[/C][C]33.4736920452061[/C][C]-2.22808236260345[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 18 )[/C][C]-78.9571428571428[/C][C]32.6221498588002[/C][C]-2.42035375347414[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 18 )[/C][C]-95.4571428571429[/C][C]29.2952256489962[/C][C]-3.25845392013268[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 18 )[/C][C]-98.6857142857143[/C][C]25.5089276997941[/C][C]-3.86867356586341[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 18 )[/C][C]-98.6553571428571[/C][C]25.4382770846738[/C][C]-3.87822480329438[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 18 )[/C][C]-142.016071428571[/C][C]16.5332659105042[/C][C]-8.58971676844219[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 18 )[/C][C]-107.503703703704[/C][C]67.8060318792516[/C][C]-1.58545929800383[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 18 )[/C][C]-99.3423076923077[/C][C]62.5574152777304[/C][C]-1.58801809907373[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 18 )[/C][C]-97.194[/C][C]59.244854450468[/C][C]-1.64054753617902[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 18 )[/C][C]-96.5083333333333[/C][C]56.0712882774227[/C][C]-1.72117203471126[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 18 )[/C][C]-96.9065217391304[/C][C]53.4638522879738[/C][C]-1.81256152693899[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 18 )[/C][C]-98.3568181818182[/C][C]50.4492362440514[/C][C]-1.94961956819348[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 18 )[/C][C]-99.504761904762[/C][C]47.1286896789236[/C][C]-2.11134157522019[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 18 )[/C][C]-102.0525[/C][C]44.1401413314776[/C][C]-2.31201117444595[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 18 )[/C][C]-105.010526315789[/C][C]41.312303746191[/C][C]-2.54187050329943[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 18 )[/C][C]-108.313888888889[/C][C]39.3140237414400[/C][C]-2.75509547435914[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 18 )[/C][C]-111.529411764706[/C][C]36.9892800218037[/C][C]-3.01518201216579[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 18 )[/C][C]-114.53125[/C][C]34.0666727800711[/C][C]-3.36197346713004[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 18 )[/C][C]-121.41[/C][C]32.5746750762281[/C][C]-3.72712850445593[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 18 )[/C][C]-128.614285714286[/C][C]30.8136808731018[/C][C]-4.17393450149467[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 18 )[/C][C]-136.253846153846[/C][C]28.3813423170219[/C][C]-4.80082459215212[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 18 )[/C][C]-142.6[/C][C]26.0671172447065[/C][C]-5.4704936745147[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 18 )[/C][C]-149.586363636364[/C][C]23.9696491850488[/C][C]-6.240657194502[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 18 )[/C][C]-157.975[/C][C]20.1220524157217[/C][C]-7.85083930486988[/C][/ROW]
[ROW][C]Median[/C][C]-193.6[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]-355.35[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]-135.334482758621[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]-128.614285714286[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]-135.334482758621[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]-128.614285714286[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]-128.614285714286[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]-135.334482758621[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]-128.614285714286[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]-121.41[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]56[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=101503&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=101503&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-116.35535714285772.9953338625968-1.59401089063966
Geometric MeanNaN
Harmonic Mean1545.50388940748
Quadratic Mean553.71120744482
Winsorized Mean ( 1 / 18 )-115.08214285714371.9214429446545-1.60010892642549
Winsorized Mean ( 2 / 18 )-103.17857142857167.2637675626049-1.53393981882652
Winsorized Mean ( 3 / 18 )-98.957142857142865.2636396580057-1.51626760897335
Winsorized Mean ( 4 / 18 )-95.261.8876749053865-1.53827074850592
Winsorized Mean ( 5 / 18 )-91.208928571428660.8968571404922-1.49776085095828
Winsorized Mean ( 6 / 18 )-93.191071428571459.0983972180749-1.57687984472224
Winsorized Mean ( 7 / 18 )-86.766071428571554.9827262293849-1.5780605542655
Winsorized Mean ( 8 / 18 )-85.994642857142951.4110291504592-1.67268860939297
Winsorized Mean ( 9 / 18 )-85.898214285714345.7452104150374-1.87775317910611
Winsorized Mean ( 10 / 18 )-88.791071428571444.3047720507919-2.00409724096491
Winsorized Mean ( 11 / 18 )-92.660714285714343.1496739448766-2.14742559594048
Winsorized Mean ( 12 / 18 )-70.310714285714334.9479116740948-2.01187169469219
Winsorized Mean ( 13 / 18 )-74.582142857142933.4736920452061-2.22808236260345
Winsorized Mean ( 14 / 18 )-78.957142857142832.6221498588002-2.42035375347414
Winsorized Mean ( 15 / 18 )-95.457142857142929.2952256489962-3.25845392013268
Winsorized Mean ( 16 / 18 )-98.685714285714325.5089276997941-3.86867356586341
Winsorized Mean ( 17 / 18 )-98.655357142857125.4382770846738-3.87822480329438
Winsorized Mean ( 18 / 18 )-142.01607142857116.5332659105042-8.58971676844219
Trimmed Mean ( 1 / 18 )-107.50370370370467.8060318792516-1.58545929800383
Trimmed Mean ( 2 / 18 )-99.342307692307762.5574152777304-1.58801809907373
Trimmed Mean ( 3 / 18 )-97.19459.244854450468-1.64054753617902
Trimmed Mean ( 4 / 18 )-96.508333333333356.0712882774227-1.72117203471126
Trimmed Mean ( 5 / 18 )-96.906521739130453.4638522879738-1.81256152693899
Trimmed Mean ( 6 / 18 )-98.356818181818250.4492362440514-1.94961956819348
Trimmed Mean ( 7 / 18 )-99.50476190476247.1286896789236-2.11134157522019
Trimmed Mean ( 8 / 18 )-102.052544.1401413314776-2.31201117444595
Trimmed Mean ( 9 / 18 )-105.01052631578941.312303746191-2.54187050329943
Trimmed Mean ( 10 / 18 )-108.31388888888939.3140237414400-2.75509547435914
Trimmed Mean ( 11 / 18 )-111.52941176470636.9892800218037-3.01518201216579
Trimmed Mean ( 12 / 18 )-114.5312534.0666727800711-3.36197346713004
Trimmed Mean ( 13 / 18 )-121.4132.5746750762281-3.72712850445593
Trimmed Mean ( 14 / 18 )-128.61428571428630.8136808731018-4.17393450149467
Trimmed Mean ( 15 / 18 )-136.25384615384628.3813423170219-4.80082459215212
Trimmed Mean ( 16 / 18 )-142.626.0671172447065-5.4704936745147
Trimmed Mean ( 17 / 18 )-149.58636363636423.9696491850488-6.240657194502
Trimmed Mean ( 18 / 18 )-157.97520.1220524157217-7.85083930486988
Median-193.6
Midrange-355.35
Midmean - Weighted Average at Xnp-135.334482758621
Midmean - Weighted Average at X(n+1)p-128.614285714286
Midmean - Empirical Distribution Function-135.334482758621
Midmean - Empirical Distribution Function - Averaging-128.614285714286
Midmean - Empirical Distribution Function - Interpolation-128.614285714286
Midmean - Closest Observation-135.334482758621
Midmean - True Basic - Statistics Graphics Toolkit-128.614285714286
Midmean - MS Excel (old versions)-121.41
Number of observations56



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')