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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, 18 Oct 2009 11:38:21 -0600
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/Oct/18/t1255887809b4zqccrj75lntmg.htm/, Retrieved Mon, 29 Apr 2024 15:29:10 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=47415, Retrieved Mon, 29 Apr 2024 15:29:10 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsWorkshop3, totaleinflatie
Estimated Impact142
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Univariate Data Series] [] [2009-10-12 17:11:03] [0750c128064677e728c9436fc3f45ae7]
- RMPD    [Central Tendency] [] [2009-10-18 17:38:21] [30f5b608e5a1bbbae86b1702c0071566] [Current]
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Dataseries X:
1.3
1.2
1.1
1.4
1.2
1.5
1.1
1.3
1.5
1.1
1.4
1.3
1.5
1.6
1.7
1.1
1.6
1.3
1.7
1.6
1.7
1.9
1.8
1.9
1.6
1.5
1.6
1.6
1.7
2
2
1.9
1.7
1.8
1.9
1.7
2
2.1
2.4
2.5
2.5
2.6
2.2
2.5
2.8
2.8
2.9
3
3.1
2.9
2.7
2.2
2.5
2.3
2.6
2.3
2.2
1.8
1.8
2




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=47415&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=47415&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=47415&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 Mean1.908333333333330.06967607321676327.3886464209383
Geometric Mean1.83497332609738
Harmonic Mean1.76431133310967
Quadratic Mean1.98196030905431
Winsorized Mean ( 1 / 20 )1.906666666666670.06921132245744827.5484790489144
Winsorized Mean ( 2 / 20 )1.903333333333330.068352966726131627.8456579794024
Winsorized Mean ( 3 / 20 )1.903333333333330.068352966726131627.8456579794024
Winsorized Mean ( 4 / 20 )1.903333333333330.065482419543746229.0663256885581
Winsorized Mean ( 5 / 20 )1.903333333333330.065482419543746229.0663256885581
Winsorized Mean ( 6 / 20 )1.903333333333330.06147741612195530.9598784951798
Winsorized Mean ( 7 / 20 )1.891666666666670.059007404814781732.0581234271261
Winsorized Mean ( 8 / 20 )1.891666666666670.059007404814781732.0581234271261
Winsorized Mean ( 9 / 20 )1.876666666666670.056065270006855633.4728909079933
Winsorized Mean ( 10 / 20 )1.893333333333330.053301544198418635.521172262576
Winsorized Mean ( 11 / 20 )1.893333333333330.053301544198418635.521172262576
Winsorized Mean ( 12 / 20 )1.913333333333330.05033597104623738.0112530574966
Winsorized Mean ( 13 / 20 )1.891666666666670.046169160021596840.9725164109937
Winsorized Mean ( 14 / 20 )1.868333333333330.041950446060446544.5366738327704
Winsorized Mean ( 15 / 20 )1.868333333333330.041950446060446544.5366738327704
Winsorized Mean ( 16 / 20 )1.868333333333330.03357188649880355.6517231583023
Winsorized Mean ( 17 / 20 )1.868333333333330.03357188649880355.6517231583023
Winsorized Mean ( 18 / 20 )1.868333333333330.03357188649880355.6517231583023
Winsorized Mean ( 19 / 20 )1.836666666666670.028420437727146964.6248549828738
Winsorized Mean ( 20 / 20 )1.803333333333330.023405859842204477.0462331010647
Trimmed Mean ( 1 / 20 )1.901724137931030.067604924133917428.1299648256974
Trimmed Mean ( 2 / 20 )1.896428571428570.065612216044335928.9035896935276
Trimmed Mean ( 3 / 20 )1.892592592592590.063710772688900229.7060059502672
Trimmed Mean ( 4 / 20 )1.888461538461540.061323625749516130.7950078844847
Trimmed Mean ( 5 / 20 )1.8840.05947800142120831.6755767675849
Trimmed Mean ( 6 / 20 )1.879166666666670.057114288599044532.9018659386419
Trimmed Mean ( 7 / 20 )1.873913043478260.055380526636343933.8370390694062
Trimmed Mean ( 8 / 20 )1.870454545454550.053875153762802434.7183147483838
Trimmed Mean ( 9 / 20 )1.866666666666670.051871666291343435.986248372711
Trimmed Mean ( 10 / 20 )1.8650.050070463169929637.2475084496531
Trimmed Mean ( 11 / 20 )1.860526315789470.048379055941899638.4572679141126
Trimmed Mean ( 12 / 20 )1.855555555555560.046023535118811240.3175364683608
Trimmed Mean ( 13 / 20 )1.847058823529410.043516402160553942.4451179744751
Trimmed Mean ( 14 / 20 )1.8406250.041362718672347244.4996136395294
Trimmed Mean ( 15 / 20 )1.836666666666670.039677821284890546.2895039896275
Trimmed Mean ( 16 / 20 )1.832142857142860.037109009811923949.3719144334094
Trimmed Mean ( 17 / 20 )1.826923076923080.03618656457335150.4862259919662
Trimmed Mean ( 18 / 20 )1.820833333333330.03456728718015352.6750428474114
Trimmed Mean ( 19 / 20 )1.813636363636360.031756278682080557.1111112165596
Trimmed Mean ( 20 / 20 )1.810.02982404540317360.6892852908355
Median1.8
Midrange2.1
Midmean - Weighted Average at Xnp1.82058823529412
Midmean - Weighted Average at X(n+1)p1.82058823529412
Midmean - Empirical Distribution Function1.82058823529412
Midmean - Empirical Distribution Function - Averaging1.82058823529412
Midmean - Empirical Distribution Function - Interpolation1.82058823529412
Midmean - Closest Observation1.82058823529412
Midmean - True Basic - Statistics Graphics Toolkit1.82058823529412
Midmean - MS Excel (old versions)1.82058823529412
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 1.90833333333333 & 0.069676073216763 & 27.3886464209383 \tabularnewline
Geometric Mean & 1.83497332609738 &  &  \tabularnewline
Harmonic Mean & 1.76431133310967 &  &  \tabularnewline
Quadratic Mean & 1.98196030905431 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 1.90666666666667 & 0.069211322457448 & 27.5484790489144 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 1.90333333333333 & 0.0683529667261316 & 27.8456579794024 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 1.90333333333333 & 0.0683529667261316 & 27.8456579794024 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 1.90333333333333 & 0.0654824195437462 & 29.0663256885581 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 1.90333333333333 & 0.0654824195437462 & 29.0663256885581 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 1.90333333333333 & 0.061477416121955 & 30.9598784951798 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 1.89166666666667 & 0.0590074048147817 & 32.0581234271261 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 1.89166666666667 & 0.0590074048147817 & 32.0581234271261 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 1.87666666666667 & 0.0560652700068556 & 33.4728909079933 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 1.89333333333333 & 0.0533015441984186 & 35.521172262576 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 1.89333333333333 & 0.0533015441984186 & 35.521172262576 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 1.91333333333333 & 0.050335971046237 & 38.0112530574966 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 1.89166666666667 & 0.0461691600215968 & 40.9725164109937 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 1.86833333333333 & 0.0419504460604465 & 44.5366738327704 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 1.86833333333333 & 0.0419504460604465 & 44.5366738327704 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 1.86833333333333 & 0.033571886498803 & 55.6517231583023 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 1.86833333333333 & 0.033571886498803 & 55.6517231583023 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 1.86833333333333 & 0.033571886498803 & 55.6517231583023 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 1.83666666666667 & 0.0284204377271469 & 64.6248549828738 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 1.80333333333333 & 0.0234058598422044 & 77.0462331010647 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 1.90172413793103 & 0.0676049241339174 & 28.1299648256974 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 1.89642857142857 & 0.0656122160443359 & 28.9035896935276 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 1.89259259259259 & 0.0637107726889002 & 29.7060059502672 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 1.88846153846154 & 0.0613236257495161 & 30.7950078844847 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 1.884 & 0.059478001421208 & 31.6755767675849 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 1.87916666666667 & 0.0571142885990445 & 32.9018659386419 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 1.87391304347826 & 0.0553805266363439 & 33.8370390694062 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 1.87045454545455 & 0.0538751537628024 & 34.7183147483838 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 1.86666666666667 & 0.0518716662913434 & 35.986248372711 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 1.865 & 0.0500704631699296 & 37.2475084496531 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 1.86052631578947 & 0.0483790559418996 & 38.4572679141126 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 1.85555555555556 & 0.0460235351188112 & 40.3175364683608 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 1.84705882352941 & 0.0435164021605539 & 42.4451179744751 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 1.840625 & 0.0413627186723472 & 44.4996136395294 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 1.83666666666667 & 0.0396778212848905 & 46.2895039896275 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 1.83214285714286 & 0.0371090098119239 & 49.3719144334094 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 1.82692307692308 & 0.036186564573351 & 50.4862259919662 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 1.82083333333333 & 0.034567287180153 & 52.6750428474114 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 1.81363636363636 & 0.0317562786820805 & 57.1111112165596 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 1.81 & 0.029824045403173 & 60.6892852908355 \tabularnewline
Median & 1.8 &  &  \tabularnewline
Midrange & 2.1 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 1.82058823529412 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 1.82058823529412 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 1.82058823529412 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 1.82058823529412 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 1.82058823529412 &  &  \tabularnewline
Midmean - Closest Observation & 1.82058823529412 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 1.82058823529412 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 1.82058823529412 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=47415&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]1.90833333333333[/C][C]0.069676073216763[/C][C]27.3886464209383[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]1.83497332609738[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]1.76431133310967[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]1.98196030905431[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]1.90666666666667[/C][C]0.069211322457448[/C][C]27.5484790489144[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]1.90333333333333[/C][C]0.0683529667261316[/C][C]27.8456579794024[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]1.90333333333333[/C][C]0.0683529667261316[/C][C]27.8456579794024[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]1.90333333333333[/C][C]0.0654824195437462[/C][C]29.0663256885581[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]1.90333333333333[/C][C]0.0654824195437462[/C][C]29.0663256885581[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]1.90333333333333[/C][C]0.061477416121955[/C][C]30.9598784951798[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]1.89166666666667[/C][C]0.0590074048147817[/C][C]32.0581234271261[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]1.89166666666667[/C][C]0.0590074048147817[/C][C]32.0581234271261[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]1.87666666666667[/C][C]0.0560652700068556[/C][C]33.4728909079933[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]1.89333333333333[/C][C]0.0533015441984186[/C][C]35.521172262576[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]1.89333333333333[/C][C]0.0533015441984186[/C][C]35.521172262576[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]1.91333333333333[/C][C]0.050335971046237[/C][C]38.0112530574966[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]1.89166666666667[/C][C]0.0461691600215968[/C][C]40.9725164109937[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]1.86833333333333[/C][C]0.0419504460604465[/C][C]44.5366738327704[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]1.86833333333333[/C][C]0.0419504460604465[/C][C]44.5366738327704[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]1.86833333333333[/C][C]0.033571886498803[/C][C]55.6517231583023[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]1.86833333333333[/C][C]0.033571886498803[/C][C]55.6517231583023[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]1.86833333333333[/C][C]0.033571886498803[/C][C]55.6517231583023[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]1.83666666666667[/C][C]0.0284204377271469[/C][C]64.6248549828738[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]1.80333333333333[/C][C]0.0234058598422044[/C][C]77.0462331010647[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]1.90172413793103[/C][C]0.0676049241339174[/C][C]28.1299648256974[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]1.89642857142857[/C][C]0.0656122160443359[/C][C]28.9035896935276[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]1.89259259259259[/C][C]0.0637107726889002[/C][C]29.7060059502672[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]1.88846153846154[/C][C]0.0613236257495161[/C][C]30.7950078844847[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]1.884[/C][C]0.059478001421208[/C][C]31.6755767675849[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]1.87916666666667[/C][C]0.0571142885990445[/C][C]32.9018659386419[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]1.87391304347826[/C][C]0.0553805266363439[/C][C]33.8370390694062[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]1.87045454545455[/C][C]0.0538751537628024[/C][C]34.7183147483838[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]1.86666666666667[/C][C]0.0518716662913434[/C][C]35.986248372711[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]1.865[/C][C]0.0500704631699296[/C][C]37.2475084496531[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]1.86052631578947[/C][C]0.0483790559418996[/C][C]38.4572679141126[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]1.85555555555556[/C][C]0.0460235351188112[/C][C]40.3175364683608[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]1.84705882352941[/C][C]0.0435164021605539[/C][C]42.4451179744751[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]1.840625[/C][C]0.0413627186723472[/C][C]44.4996136395294[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]1.83666666666667[/C][C]0.0396778212848905[/C][C]46.2895039896275[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]1.83214285714286[/C][C]0.0371090098119239[/C][C]49.3719144334094[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]1.82692307692308[/C][C]0.036186564573351[/C][C]50.4862259919662[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]1.82083333333333[/C][C]0.034567287180153[/C][C]52.6750428474114[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]1.81363636363636[/C][C]0.0317562786820805[/C][C]57.1111112165596[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]1.81[/C][C]0.029824045403173[/C][C]60.6892852908355[/C][/ROW]
[ROW][C]Median[/C][C]1.8[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]2.1[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]1.82058823529412[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]1.82058823529412[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]1.82058823529412[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]1.82058823529412[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]1.82058823529412[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]1.82058823529412[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]1.82058823529412[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]1.82058823529412[/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=47415&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=47415&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 Mean1.908333333333330.06967607321676327.3886464209383
Geometric Mean1.83497332609738
Harmonic Mean1.76431133310967
Quadratic Mean1.98196030905431
Winsorized Mean ( 1 / 20 )1.906666666666670.06921132245744827.5484790489144
Winsorized Mean ( 2 / 20 )1.903333333333330.068352966726131627.8456579794024
Winsorized Mean ( 3 / 20 )1.903333333333330.068352966726131627.8456579794024
Winsorized Mean ( 4 / 20 )1.903333333333330.065482419543746229.0663256885581
Winsorized Mean ( 5 / 20 )1.903333333333330.065482419543746229.0663256885581
Winsorized Mean ( 6 / 20 )1.903333333333330.06147741612195530.9598784951798
Winsorized Mean ( 7 / 20 )1.891666666666670.059007404814781732.0581234271261
Winsorized Mean ( 8 / 20 )1.891666666666670.059007404814781732.0581234271261
Winsorized Mean ( 9 / 20 )1.876666666666670.056065270006855633.4728909079933
Winsorized Mean ( 10 / 20 )1.893333333333330.053301544198418635.521172262576
Winsorized Mean ( 11 / 20 )1.893333333333330.053301544198418635.521172262576
Winsorized Mean ( 12 / 20 )1.913333333333330.05033597104623738.0112530574966
Winsorized Mean ( 13 / 20 )1.891666666666670.046169160021596840.9725164109937
Winsorized Mean ( 14 / 20 )1.868333333333330.041950446060446544.5366738327704
Winsorized Mean ( 15 / 20 )1.868333333333330.041950446060446544.5366738327704
Winsorized Mean ( 16 / 20 )1.868333333333330.03357188649880355.6517231583023
Winsorized Mean ( 17 / 20 )1.868333333333330.03357188649880355.6517231583023
Winsorized Mean ( 18 / 20 )1.868333333333330.03357188649880355.6517231583023
Winsorized Mean ( 19 / 20 )1.836666666666670.028420437727146964.6248549828738
Winsorized Mean ( 20 / 20 )1.803333333333330.023405859842204477.0462331010647
Trimmed Mean ( 1 / 20 )1.901724137931030.067604924133917428.1299648256974
Trimmed Mean ( 2 / 20 )1.896428571428570.065612216044335928.9035896935276
Trimmed Mean ( 3 / 20 )1.892592592592590.063710772688900229.7060059502672
Trimmed Mean ( 4 / 20 )1.888461538461540.061323625749516130.7950078844847
Trimmed Mean ( 5 / 20 )1.8840.05947800142120831.6755767675849
Trimmed Mean ( 6 / 20 )1.879166666666670.057114288599044532.9018659386419
Trimmed Mean ( 7 / 20 )1.873913043478260.055380526636343933.8370390694062
Trimmed Mean ( 8 / 20 )1.870454545454550.053875153762802434.7183147483838
Trimmed Mean ( 9 / 20 )1.866666666666670.051871666291343435.986248372711
Trimmed Mean ( 10 / 20 )1.8650.050070463169929637.2475084496531
Trimmed Mean ( 11 / 20 )1.860526315789470.048379055941899638.4572679141126
Trimmed Mean ( 12 / 20 )1.855555555555560.046023535118811240.3175364683608
Trimmed Mean ( 13 / 20 )1.847058823529410.043516402160553942.4451179744751
Trimmed Mean ( 14 / 20 )1.8406250.041362718672347244.4996136395294
Trimmed Mean ( 15 / 20 )1.836666666666670.039677821284890546.2895039896275
Trimmed Mean ( 16 / 20 )1.832142857142860.037109009811923949.3719144334094
Trimmed Mean ( 17 / 20 )1.826923076923080.03618656457335150.4862259919662
Trimmed Mean ( 18 / 20 )1.820833333333330.03456728718015352.6750428474114
Trimmed Mean ( 19 / 20 )1.813636363636360.031756278682080557.1111112165596
Trimmed Mean ( 20 / 20 )1.810.02982404540317360.6892852908355
Median1.8
Midrange2.1
Midmean - Weighted Average at Xnp1.82058823529412
Midmean - Weighted Average at X(n+1)p1.82058823529412
Midmean - Empirical Distribution Function1.82058823529412
Midmean - Empirical Distribution Function - Averaging1.82058823529412
Midmean - Empirical Distribution Function - Interpolation1.82058823529412
Midmean - Closest Observation1.82058823529412
Midmean - True Basic - Statistics Graphics Toolkit1.82058823529412
Midmean - MS Excel (old versions)1.82058823529412
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')