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Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationThu, 13 Dec 2007 02:51:57 -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/2007/Dec/13/t1197538600x08jrsvj7nyo4oi.htm/, Retrieved Sun, 05 May 2024 12:04:12 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=3362, Retrieved Sun, 05 May 2024 12:04:12 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact271
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [Paper CT echtsche...] [2007-12-13 09:51:57] [142ab5472309a9ae9a3b52678758dc4a] [Current]
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Dataseries X:
183
118
-110
-41
85
314
242
-34
164
-160
-118
114
-152
-214
223
124
-410
356
-432
363
-20
-10
173
44
-328
273
-188
1
238
-237
112
-174
-18
-148
-65
-40
30
-219
103
-507
74
-54
-302
-76
-280
67
-45
-452




Summary of compuational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135

\begin{tabular}{lllllllll}
\hline
Summary of compuational 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 & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=3362&T=0

[TABLE]
[ROW][C]Summary of compuational 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]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=3362&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=3362&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 compuational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean-29.854166666666730.9083951617451-0.965891839755459
Geometric MeanNaN
Harmonic Mean64.1198799290264
Quadratic Mean213.990021184790
Winsorized Mean ( 1 / 16 )-28.854166666666730.5117549371865-0.94567378133666
Winsorized Mean ( 2 / 16 )-29.770833333333329.8195108373858-0.998367595487467
Winsorized Mean ( 3 / 16 )-30.958333333333328.8276235225015-1.07391208675834
Winsorized Mean ( 4 / 16 )-26.708333333333326.4696393445981-1.00901765171893
Winsorized Mean ( 5 / 16 )-24.416666666666725.7405534785213-0.948568051850194
Winsorized Mean ( 6 / 16 )-23.541666666666724.7189155457213-0.952374574164586
Winsorized Mean ( 7 / 16 )-23.104166666666722.1830960734444-1.04152128224900
Winsorized Mean ( 8 / 16 )-21.770833333333321.2516423975926-1.02443062639712
Winsorized Mean ( 9 / 16 )-22.520833333333320.7409937214349-1.08581264889247
Winsorized Mean ( 10 / 16 )-25.437518.1609213924974-1.40067232549714
Winsorized Mean ( 11 / 16 )-23.604166666666717.3188122715117-1.36292063777919
Winsorized Mean ( 12 / 16 )-21.104166666666716.5079026740057-1.27842810097848
Winsorized Mean ( 13 / 16 )-19.479166666666716.0289241437185-1.21525103569102
Winsorized Mean ( 14 / 16 )-20.937515.3693707981905-1.36228738800844
Winsorized Mean ( 15 / 16 )-17.187512.7945666746414-1.34334365805958
Winsorized Mean ( 16 / 16 )-18.187511.7306372923836-1.55042727404151
Trimmed Mean ( 1 / 16 )-28.021739130434829.2669289402667-0.957454032420915
Trimmed Mean ( 2 / 16 )-27.113636363636427.6435177937584-0.980831620849583
Trimmed Mean ( 3 / 16 )-25.595238095238126.0149394121467-0.983866911613384
Trimmed Mean ( 4 / 16 )-23.4524.3939344604666-0.961304542241993
Trimmed Mean ( 5 / 16 )-22.421052631578923.3265711403312-0.96118081378936
Trimmed Mean ( 6 / 16 )-21.888888888888922.1655308616199-0.987519271500506
Trimmed Mean ( 7 / 16 )-21.520.9501253936747-1.02624684081802
Trimmed Mean ( 8 / 16 )-21.1562520.185386230843-1.04809735905244
Trimmed Mean ( 9 / 16 )-21.033333333333319.3975637369027-1.08432861046971
Trimmed Mean ( 10 / 16 )-20.7518.3972640736830-1.12788509839801
Trimmed Mean ( 11 / 16 )-19.884615384615417.8425012840410-1.11445223223276
Trimmed Mean ( 12 / 16 )-19.208333333333317.244824803051-1.11386074098793
Trimmed Mean ( 13 / 16 )-18.863636363636416.5528532289656-1.13960029142451
Trimmed Mean ( 14 / 16 )-18.7515.5373700612765-1.20676793601835
Trimmed Mean ( 15 / 16 )-18.333333333333314.0265854019863-1.30704179298956
Trimmed Mean ( 16 / 16 )-18.562512.8439248771550-1.44523579649835
Median-27
Midrange-72
Midmean - Weighted Average at Xnp-25.4
Midmean - Weighted Average at X(n+1)p-19.2083333333333
Midmean - Empirical Distribution Function-25.4
Midmean - Empirical Distribution Function - Averaging-19.2083333333333
Midmean - Empirical Distribution Function - Interpolation-19.2083333333333
Midmean - Closest Observation-25.4
Midmean - True Basic - Statistics Graphics Toolkit-19.2083333333333
Midmean - MS Excel (old versions)-19.8846153846154
Number of observations48

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & -29.8541666666667 & 30.9083951617451 & -0.965891839755459 \tabularnewline
Geometric Mean & NaN &  &  \tabularnewline
Harmonic Mean & 64.1198799290264 &  &  \tabularnewline
Quadratic Mean & 213.990021184790 &  &  \tabularnewline
Winsorized Mean ( 1 / 16 ) & -28.8541666666667 & 30.5117549371865 & -0.94567378133666 \tabularnewline
Winsorized Mean ( 2 / 16 ) & -29.7708333333333 & 29.8195108373858 & -0.998367595487467 \tabularnewline
Winsorized Mean ( 3 / 16 ) & -30.9583333333333 & 28.8276235225015 & -1.07391208675834 \tabularnewline
Winsorized Mean ( 4 / 16 ) & -26.7083333333333 & 26.4696393445981 & -1.00901765171893 \tabularnewline
Winsorized Mean ( 5 / 16 ) & -24.4166666666667 & 25.7405534785213 & -0.948568051850194 \tabularnewline
Winsorized Mean ( 6 / 16 ) & -23.5416666666667 & 24.7189155457213 & -0.952374574164586 \tabularnewline
Winsorized Mean ( 7 / 16 ) & -23.1041666666667 & 22.1830960734444 & -1.04152128224900 \tabularnewline
Winsorized Mean ( 8 / 16 ) & -21.7708333333333 & 21.2516423975926 & -1.02443062639712 \tabularnewline
Winsorized Mean ( 9 / 16 ) & -22.5208333333333 & 20.7409937214349 & -1.08581264889247 \tabularnewline
Winsorized Mean ( 10 / 16 ) & -25.4375 & 18.1609213924974 & -1.40067232549714 \tabularnewline
Winsorized Mean ( 11 / 16 ) & -23.6041666666667 & 17.3188122715117 & -1.36292063777919 \tabularnewline
Winsorized Mean ( 12 / 16 ) & -21.1041666666667 & 16.5079026740057 & -1.27842810097848 \tabularnewline
Winsorized Mean ( 13 / 16 ) & -19.4791666666667 & 16.0289241437185 & -1.21525103569102 \tabularnewline
Winsorized Mean ( 14 / 16 ) & -20.9375 & 15.3693707981905 & -1.36228738800844 \tabularnewline
Winsorized Mean ( 15 / 16 ) & -17.1875 & 12.7945666746414 & -1.34334365805958 \tabularnewline
Winsorized Mean ( 16 / 16 ) & -18.1875 & 11.7306372923836 & -1.55042727404151 \tabularnewline
Trimmed Mean ( 1 / 16 ) & -28.0217391304348 & 29.2669289402667 & -0.957454032420915 \tabularnewline
Trimmed Mean ( 2 / 16 ) & -27.1136363636364 & 27.6435177937584 & -0.980831620849583 \tabularnewline
Trimmed Mean ( 3 / 16 ) & -25.5952380952381 & 26.0149394121467 & -0.983866911613384 \tabularnewline
Trimmed Mean ( 4 / 16 ) & -23.45 & 24.3939344604666 & -0.961304542241993 \tabularnewline
Trimmed Mean ( 5 / 16 ) & -22.4210526315789 & 23.3265711403312 & -0.96118081378936 \tabularnewline
Trimmed Mean ( 6 / 16 ) & -21.8888888888889 & 22.1655308616199 & -0.987519271500506 \tabularnewline
Trimmed Mean ( 7 / 16 ) & -21.5 & 20.9501253936747 & -1.02624684081802 \tabularnewline
Trimmed Mean ( 8 / 16 ) & -21.15625 & 20.185386230843 & -1.04809735905244 \tabularnewline
Trimmed Mean ( 9 / 16 ) & -21.0333333333333 & 19.3975637369027 & -1.08432861046971 \tabularnewline
Trimmed Mean ( 10 / 16 ) & -20.75 & 18.3972640736830 & -1.12788509839801 \tabularnewline
Trimmed Mean ( 11 / 16 ) & -19.8846153846154 & 17.8425012840410 & -1.11445223223276 \tabularnewline
Trimmed Mean ( 12 / 16 ) & -19.2083333333333 & 17.244824803051 & -1.11386074098793 \tabularnewline
Trimmed Mean ( 13 / 16 ) & -18.8636363636364 & 16.5528532289656 & -1.13960029142451 \tabularnewline
Trimmed Mean ( 14 / 16 ) & -18.75 & 15.5373700612765 & -1.20676793601835 \tabularnewline
Trimmed Mean ( 15 / 16 ) & -18.3333333333333 & 14.0265854019863 & -1.30704179298956 \tabularnewline
Trimmed Mean ( 16 / 16 ) & -18.5625 & 12.8439248771550 & -1.44523579649835 \tabularnewline
Median & -27 &  &  \tabularnewline
Midrange & -72 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & -25.4 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & -19.2083333333333 &  &  \tabularnewline
Midmean - Empirical Distribution Function & -25.4 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & -19.2083333333333 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & -19.2083333333333 &  &  \tabularnewline
Midmean - Closest Observation & -25.4 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & -19.2083333333333 &  &  \tabularnewline
Midmean - MS Excel (old versions) & -19.8846153846154 &  &  \tabularnewline
Number of observations & 48 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=3362&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]-29.8541666666667[/C][C]30.9083951617451[/C][C]-0.965891839755459[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]NaN[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]64.1198799290264[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]213.990021184790[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 16 )[/C][C]-28.8541666666667[/C][C]30.5117549371865[/C][C]-0.94567378133666[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 16 )[/C][C]-29.7708333333333[/C][C]29.8195108373858[/C][C]-0.998367595487467[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 16 )[/C][C]-30.9583333333333[/C][C]28.8276235225015[/C][C]-1.07391208675834[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 16 )[/C][C]-26.7083333333333[/C][C]26.4696393445981[/C][C]-1.00901765171893[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 16 )[/C][C]-24.4166666666667[/C][C]25.7405534785213[/C][C]-0.948568051850194[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 16 )[/C][C]-23.5416666666667[/C][C]24.7189155457213[/C][C]-0.952374574164586[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 16 )[/C][C]-23.1041666666667[/C][C]22.1830960734444[/C][C]-1.04152128224900[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 16 )[/C][C]-21.7708333333333[/C][C]21.2516423975926[/C][C]-1.02443062639712[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 16 )[/C][C]-22.5208333333333[/C][C]20.7409937214349[/C][C]-1.08581264889247[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 16 )[/C][C]-25.4375[/C][C]18.1609213924974[/C][C]-1.40067232549714[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 16 )[/C][C]-23.6041666666667[/C][C]17.3188122715117[/C][C]-1.36292063777919[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 16 )[/C][C]-21.1041666666667[/C][C]16.5079026740057[/C][C]-1.27842810097848[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 16 )[/C][C]-19.4791666666667[/C][C]16.0289241437185[/C][C]-1.21525103569102[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 16 )[/C][C]-20.9375[/C][C]15.3693707981905[/C][C]-1.36228738800844[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 16 )[/C][C]-17.1875[/C][C]12.7945666746414[/C][C]-1.34334365805958[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 16 )[/C][C]-18.1875[/C][C]11.7306372923836[/C][C]-1.55042727404151[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 16 )[/C][C]-28.0217391304348[/C][C]29.2669289402667[/C][C]-0.957454032420915[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 16 )[/C][C]-27.1136363636364[/C][C]27.6435177937584[/C][C]-0.980831620849583[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 16 )[/C][C]-25.5952380952381[/C][C]26.0149394121467[/C][C]-0.983866911613384[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 16 )[/C][C]-23.45[/C][C]24.3939344604666[/C][C]-0.961304542241993[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 16 )[/C][C]-22.4210526315789[/C][C]23.3265711403312[/C][C]-0.96118081378936[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 16 )[/C][C]-21.8888888888889[/C][C]22.1655308616199[/C][C]-0.987519271500506[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 16 )[/C][C]-21.5[/C][C]20.9501253936747[/C][C]-1.02624684081802[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 16 )[/C][C]-21.15625[/C][C]20.185386230843[/C][C]-1.04809735905244[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 16 )[/C][C]-21.0333333333333[/C][C]19.3975637369027[/C][C]-1.08432861046971[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 16 )[/C][C]-20.75[/C][C]18.3972640736830[/C][C]-1.12788509839801[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 16 )[/C][C]-19.8846153846154[/C][C]17.8425012840410[/C][C]-1.11445223223276[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 16 )[/C][C]-19.2083333333333[/C][C]17.244824803051[/C][C]-1.11386074098793[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 16 )[/C][C]-18.8636363636364[/C][C]16.5528532289656[/C][C]-1.13960029142451[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 16 )[/C][C]-18.75[/C][C]15.5373700612765[/C][C]-1.20676793601835[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 16 )[/C][C]-18.3333333333333[/C][C]14.0265854019863[/C][C]-1.30704179298956[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 16 )[/C][C]-18.5625[/C][C]12.8439248771550[/C][C]-1.44523579649835[/C][/ROW]
[ROW][C]Median[/C][C]-27[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]-72[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]-25.4[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]-19.2083333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]-25.4[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]-19.2083333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]-19.2083333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]-25.4[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]-19.2083333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]-19.8846153846154[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]48[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=3362&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=3362&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-29.854166666666730.9083951617451-0.965891839755459
Geometric MeanNaN
Harmonic Mean64.1198799290264
Quadratic Mean213.990021184790
Winsorized Mean ( 1 / 16 )-28.854166666666730.5117549371865-0.94567378133666
Winsorized Mean ( 2 / 16 )-29.770833333333329.8195108373858-0.998367595487467
Winsorized Mean ( 3 / 16 )-30.958333333333328.8276235225015-1.07391208675834
Winsorized Mean ( 4 / 16 )-26.708333333333326.4696393445981-1.00901765171893
Winsorized Mean ( 5 / 16 )-24.416666666666725.7405534785213-0.948568051850194
Winsorized Mean ( 6 / 16 )-23.541666666666724.7189155457213-0.952374574164586
Winsorized Mean ( 7 / 16 )-23.104166666666722.1830960734444-1.04152128224900
Winsorized Mean ( 8 / 16 )-21.770833333333321.2516423975926-1.02443062639712
Winsorized Mean ( 9 / 16 )-22.520833333333320.7409937214349-1.08581264889247
Winsorized Mean ( 10 / 16 )-25.437518.1609213924974-1.40067232549714
Winsorized Mean ( 11 / 16 )-23.604166666666717.3188122715117-1.36292063777919
Winsorized Mean ( 12 / 16 )-21.104166666666716.5079026740057-1.27842810097848
Winsorized Mean ( 13 / 16 )-19.479166666666716.0289241437185-1.21525103569102
Winsorized Mean ( 14 / 16 )-20.937515.3693707981905-1.36228738800844
Winsorized Mean ( 15 / 16 )-17.187512.7945666746414-1.34334365805958
Winsorized Mean ( 16 / 16 )-18.187511.7306372923836-1.55042727404151
Trimmed Mean ( 1 / 16 )-28.021739130434829.2669289402667-0.957454032420915
Trimmed Mean ( 2 / 16 )-27.113636363636427.6435177937584-0.980831620849583
Trimmed Mean ( 3 / 16 )-25.595238095238126.0149394121467-0.983866911613384
Trimmed Mean ( 4 / 16 )-23.4524.3939344604666-0.961304542241993
Trimmed Mean ( 5 / 16 )-22.421052631578923.3265711403312-0.96118081378936
Trimmed Mean ( 6 / 16 )-21.888888888888922.1655308616199-0.987519271500506
Trimmed Mean ( 7 / 16 )-21.520.9501253936747-1.02624684081802
Trimmed Mean ( 8 / 16 )-21.1562520.185386230843-1.04809735905244
Trimmed Mean ( 9 / 16 )-21.033333333333319.3975637369027-1.08432861046971
Trimmed Mean ( 10 / 16 )-20.7518.3972640736830-1.12788509839801
Trimmed Mean ( 11 / 16 )-19.884615384615417.8425012840410-1.11445223223276
Trimmed Mean ( 12 / 16 )-19.208333333333317.244824803051-1.11386074098793
Trimmed Mean ( 13 / 16 )-18.863636363636416.5528532289656-1.13960029142451
Trimmed Mean ( 14 / 16 )-18.7515.5373700612765-1.20676793601835
Trimmed Mean ( 15 / 16 )-18.333333333333314.0265854019863-1.30704179298956
Trimmed Mean ( 16 / 16 )-18.562512.8439248771550-1.44523579649835
Median-27
Midrange-72
Midmean - Weighted Average at Xnp-25.4
Midmean - Weighted Average at X(n+1)p-19.2083333333333
Midmean - Empirical Distribution Function-25.4
Midmean - Empirical Distribution Function - Averaging-19.2083333333333
Midmean - Empirical Distribution Function - Interpolation-19.2083333333333
Midmean - Closest Observation-25.4
Midmean - True Basic - Statistics Graphics Toolkit-19.2083333333333
Midmean - MS Excel (old versions)-19.8846153846154
Number of observations48



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')