Free Statistics

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 computationTue, 20 Oct 2009 10:21:39 -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/20/t1256056133c7f60pxhu1hxds0.htm/, Retrieved Thu, 02 May 2024 16:26:15 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=48791, Retrieved Thu, 02 May 2024 16:26:15 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact138
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Bivariate Data Series] [Bivariate dataset] [2008-01-05 23:51:08] [74be16979710d4c4e7c6647856088456]
F RMPD  [Univariate Explorative Data Analysis] [Colombia Coffee] [2008-01-07 14:21:11] [74be16979710d4c4e7c6647856088456]
F RMPD    [Univariate Data Series] [] [2009-10-14 08:30:28] [74be16979710d4c4e7c6647856088456]
- RMPD        [Central Tendency] [] [2009-10-20 16:21:39] [8b8f95c5f2993a04d1b74eff1a82c018] [Current]
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Post a new message
Dataseries X:
-27
-24
-26
-28
-32
-37
-35
-34
-30
-32
-31
-32
-21
-27
-25
-33
-31
-37
-34
-29
-33
-27
-24
-16
-15
-8
-6
-10
-11
-21
-22
-16
-15
-22
-22
-19
-26
-20
-21
-29
-24
-29
-27
-29
-29
-29
-36
-35
-38
-37
-26
-23
-17
-26
-25
-17
-23
-23
-25
-21




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'RServer@AstonUniversity' @ vre.aston.ac.uk

\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 & 'RServer@AstonUniversity' @ vre.aston.ac.uk \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=48791&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]'RServer@AstonUniversity' @ vre.aston.ac.uk[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=48791&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=48791&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'RServer@AstonUniversity' @ vre.aston.ac.uk







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean-25.450.965045884568207-26.3718030478801
Geometric MeanNaN
Harmonic Mean-22.1286750072844
Quadratic Mean26.5075460954046
Winsorized Mean ( 1 / 20 )-25.46666666666670.9506069029796-26.7899029418401
Winsorized Mean ( 2 / 20 )-25.53333333333330.930787488312583-27.4319687941041
Winsorized Mean ( 3 / 20 )-25.58333333333330.916974781294006-27.8997131166802
Winsorized Mean ( 4 / 20 )-25.78333333333330.837703231658712-30.7786007728304
Winsorized Mean ( 5 / 20 )-25.70.821085130154269-31.3000431455523
Winsorized Mean ( 6 / 20 )-25.80.799646814692954-32.2642440711861
Winsorized Mean ( 7 / 20 )-25.68333333333330.777687309777572-33.0252699387355
Winsorized Mean ( 8 / 20 )-25.81666666666670.75032635711706-34.4072501542672
Winsorized Mean ( 9 / 20 )-25.66666666666670.723560978523707-35.4727071089914
Winsorized Mean ( 10 / 20 )-260.659566712764956-39.4198183395368
Winsorized Mean ( 11 / 20 )-260.595178366656243-43.6843834665396
Winsorized Mean ( 12 / 20 )-26.20.562379930688034-46.5877222324525
Winsorized Mean ( 13 / 20 )-26.20.562379930688034-46.5877222324525
Winsorized Mean ( 14 / 20 )-25.96666666666670.522902950165613-49.658673102614
Winsorized Mean ( 15 / 20 )-25.96666666666670.522902950165613-49.658673102614
Winsorized Mean ( 16 / 20 )-25.96666666666670.438259698225279-59.2494969804844
Winsorized Mean ( 17 / 20 )-25.68333333333330.395948169485629-64.865392272676
Winsorized Mean ( 18 / 20 )-25.68333333333330.395948169485629-64.865392272676
Winsorized Mean ( 19 / 20 )-260.347712459946807-74.7744271343554
Winsorized Mean ( 20 / 20 )-260.347712459946807-74.7744271343554
Trimmed Mean ( 1 / 20 )-25.56896551724140.913736029903897-27.9828798257311
Trimmed Mean ( 2 / 20 )-25.67857142857140.867937973895953-29.5857217922
Trimmed Mean ( 3 / 20 )-25.75925925925930.824559762337937-31.2400148974309
Trimmed Mean ( 4 / 20 )-25.82692307692310.77708564970212-33.2356196344937
Trimmed Mean ( 5 / 20 )-25.840.750705790355629-34.4209413753941
Trimmed Mean ( 6 / 20 )-25.8750.722991838530395-35.7887857387096
Trimmed Mean ( 7 / 20 )-25.89130434782610.694511443942932-37.2798815248228
Trimmed Mean ( 8 / 20 )-25.93181818181820.664246801410967-39.0394325222716
Trimmed Mean ( 9 / 20 )-25.95238095238100.632962524511509-41.0014494498072
Trimmed Mean ( 10 / 20 )-260.599144689515278-43.3951939406066
Trimmed Mean ( 11 / 20 )-260.573229229579565-45.3570729794601
Trimmed Mean ( 12 / 20 )-260.556348640264187-46.7332857821917
Trimmed Mean ( 13 / 20 )-25.97058823529410.541479609743194-47.962264447245
Trimmed Mean ( 14 / 20 )-25.93750.519649191530271-49.9134809074153
Trimmed Mean ( 15 / 20 )-25.93333333333330.500421278463154-51.8230028366846
Trimmed Mean ( 16 / 20 )-25.92857142857140.471204051072933-55.0262065224863
Trimmed Mean ( 17 / 20 )-25.92307692307690.457158706403189-56.7047648004634
Trimmed Mean ( 18 / 20 )-25.95833333333330.448343030981805-57.8983758852868
Trimmed Mean ( 19 / 20 )-260.431447779165899-60.2622177132648
Trimmed Mean ( 20 / 20 )-260.423021711524424-61.4625663214898
Median-26
Midrange-22
Midmean - Weighted Average at Xnp-25.6470588235294
Midmean - Weighted Average at X(n+1)p-25.6470588235294
Midmean - Empirical Distribution Function-25.6470588235294
Midmean - Empirical Distribution Function - Averaging-25.6470588235294
Midmean - Empirical Distribution Function - Interpolation-25.6470588235294
Midmean - Closest Observation-25.6470588235294
Midmean - True Basic - Statistics Graphics Toolkit-25.6470588235294
Midmean - MS Excel (old versions)-25.6470588235294
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & -25.45 & 0.965045884568207 & -26.3718030478801 \tabularnewline
Geometric Mean & NaN &  &  \tabularnewline
Harmonic Mean & -22.1286750072844 &  &  \tabularnewline
Quadratic Mean & 26.5075460954046 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & -25.4666666666667 & 0.9506069029796 & -26.7899029418401 \tabularnewline
Winsorized Mean ( 2 / 20 ) & -25.5333333333333 & 0.930787488312583 & -27.4319687941041 \tabularnewline
Winsorized Mean ( 3 / 20 ) & -25.5833333333333 & 0.916974781294006 & -27.8997131166802 \tabularnewline
Winsorized Mean ( 4 / 20 ) & -25.7833333333333 & 0.837703231658712 & -30.7786007728304 \tabularnewline
Winsorized Mean ( 5 / 20 ) & -25.7 & 0.821085130154269 & -31.3000431455523 \tabularnewline
Winsorized Mean ( 6 / 20 ) & -25.8 & 0.799646814692954 & -32.2642440711861 \tabularnewline
Winsorized Mean ( 7 / 20 ) & -25.6833333333333 & 0.777687309777572 & -33.0252699387355 \tabularnewline
Winsorized Mean ( 8 / 20 ) & -25.8166666666667 & 0.75032635711706 & -34.4072501542672 \tabularnewline
Winsorized Mean ( 9 / 20 ) & -25.6666666666667 & 0.723560978523707 & -35.4727071089914 \tabularnewline
Winsorized Mean ( 10 / 20 ) & -26 & 0.659566712764956 & -39.4198183395368 \tabularnewline
Winsorized Mean ( 11 / 20 ) & -26 & 0.595178366656243 & -43.6843834665396 \tabularnewline
Winsorized Mean ( 12 / 20 ) & -26.2 & 0.562379930688034 & -46.5877222324525 \tabularnewline
Winsorized Mean ( 13 / 20 ) & -26.2 & 0.562379930688034 & -46.5877222324525 \tabularnewline
Winsorized Mean ( 14 / 20 ) & -25.9666666666667 & 0.522902950165613 & -49.658673102614 \tabularnewline
Winsorized Mean ( 15 / 20 ) & -25.9666666666667 & 0.522902950165613 & -49.658673102614 \tabularnewline
Winsorized Mean ( 16 / 20 ) & -25.9666666666667 & 0.438259698225279 & -59.2494969804844 \tabularnewline
Winsorized Mean ( 17 / 20 ) & -25.6833333333333 & 0.395948169485629 & -64.865392272676 \tabularnewline
Winsorized Mean ( 18 / 20 ) & -25.6833333333333 & 0.395948169485629 & -64.865392272676 \tabularnewline
Winsorized Mean ( 19 / 20 ) & -26 & 0.347712459946807 & -74.7744271343554 \tabularnewline
Winsorized Mean ( 20 / 20 ) & -26 & 0.347712459946807 & -74.7744271343554 \tabularnewline
Trimmed Mean ( 1 / 20 ) & -25.5689655172414 & 0.913736029903897 & -27.9828798257311 \tabularnewline
Trimmed Mean ( 2 / 20 ) & -25.6785714285714 & 0.867937973895953 & -29.5857217922 \tabularnewline
Trimmed Mean ( 3 / 20 ) & -25.7592592592593 & 0.824559762337937 & -31.2400148974309 \tabularnewline
Trimmed Mean ( 4 / 20 ) & -25.8269230769231 & 0.77708564970212 & -33.2356196344937 \tabularnewline
Trimmed Mean ( 5 / 20 ) & -25.84 & 0.750705790355629 & -34.4209413753941 \tabularnewline
Trimmed Mean ( 6 / 20 ) & -25.875 & 0.722991838530395 & -35.7887857387096 \tabularnewline
Trimmed Mean ( 7 / 20 ) & -25.8913043478261 & 0.694511443942932 & -37.2798815248228 \tabularnewline
Trimmed Mean ( 8 / 20 ) & -25.9318181818182 & 0.664246801410967 & -39.0394325222716 \tabularnewline
Trimmed Mean ( 9 / 20 ) & -25.9523809523810 & 0.632962524511509 & -41.0014494498072 \tabularnewline
Trimmed Mean ( 10 / 20 ) & -26 & 0.599144689515278 & -43.3951939406066 \tabularnewline
Trimmed Mean ( 11 / 20 ) & -26 & 0.573229229579565 & -45.3570729794601 \tabularnewline
Trimmed Mean ( 12 / 20 ) & -26 & 0.556348640264187 & -46.7332857821917 \tabularnewline
Trimmed Mean ( 13 / 20 ) & -25.9705882352941 & 0.541479609743194 & -47.962264447245 \tabularnewline
Trimmed Mean ( 14 / 20 ) & -25.9375 & 0.519649191530271 & -49.9134809074153 \tabularnewline
Trimmed Mean ( 15 / 20 ) & -25.9333333333333 & 0.500421278463154 & -51.8230028366846 \tabularnewline
Trimmed Mean ( 16 / 20 ) & -25.9285714285714 & 0.471204051072933 & -55.0262065224863 \tabularnewline
Trimmed Mean ( 17 / 20 ) & -25.9230769230769 & 0.457158706403189 & -56.7047648004634 \tabularnewline
Trimmed Mean ( 18 / 20 ) & -25.9583333333333 & 0.448343030981805 & -57.8983758852868 \tabularnewline
Trimmed Mean ( 19 / 20 ) & -26 & 0.431447779165899 & -60.2622177132648 \tabularnewline
Trimmed Mean ( 20 / 20 ) & -26 & 0.423021711524424 & -61.4625663214898 \tabularnewline
Median & -26 &  &  \tabularnewline
Midrange & -22 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & -25.6470588235294 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & -25.6470588235294 &  &  \tabularnewline
Midmean - Empirical Distribution Function & -25.6470588235294 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & -25.6470588235294 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & -25.6470588235294 &  &  \tabularnewline
Midmean - Closest Observation & -25.6470588235294 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & -25.6470588235294 &  &  \tabularnewline
Midmean - MS Excel (old versions) & -25.6470588235294 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=48791&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]-25.45[/C][C]0.965045884568207[/C][C]-26.3718030478801[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]NaN[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]-22.1286750072844[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]26.5075460954046[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]-25.4666666666667[/C][C]0.9506069029796[/C][C]-26.7899029418401[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]-25.5333333333333[/C][C]0.930787488312583[/C][C]-27.4319687941041[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]-25.5833333333333[/C][C]0.916974781294006[/C][C]-27.8997131166802[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]-25.7833333333333[/C][C]0.837703231658712[/C][C]-30.7786007728304[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]-25.7[/C][C]0.821085130154269[/C][C]-31.3000431455523[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]-25.8[/C][C]0.799646814692954[/C][C]-32.2642440711861[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]-25.6833333333333[/C][C]0.777687309777572[/C][C]-33.0252699387355[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]-25.8166666666667[/C][C]0.75032635711706[/C][C]-34.4072501542672[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]-25.6666666666667[/C][C]0.723560978523707[/C][C]-35.4727071089914[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]-26[/C][C]0.659566712764956[/C][C]-39.4198183395368[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]-26[/C][C]0.595178366656243[/C][C]-43.6843834665396[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]-26.2[/C][C]0.562379930688034[/C][C]-46.5877222324525[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]-26.2[/C][C]0.562379930688034[/C][C]-46.5877222324525[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]-25.9666666666667[/C][C]0.522902950165613[/C][C]-49.658673102614[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]-25.9666666666667[/C][C]0.522902950165613[/C][C]-49.658673102614[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]-25.9666666666667[/C][C]0.438259698225279[/C][C]-59.2494969804844[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]-25.6833333333333[/C][C]0.395948169485629[/C][C]-64.865392272676[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]-25.6833333333333[/C][C]0.395948169485629[/C][C]-64.865392272676[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]-26[/C][C]0.347712459946807[/C][C]-74.7744271343554[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]-26[/C][C]0.347712459946807[/C][C]-74.7744271343554[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]-25.5689655172414[/C][C]0.913736029903897[/C][C]-27.9828798257311[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]-25.6785714285714[/C][C]0.867937973895953[/C][C]-29.5857217922[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]-25.7592592592593[/C][C]0.824559762337937[/C][C]-31.2400148974309[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]-25.8269230769231[/C][C]0.77708564970212[/C][C]-33.2356196344937[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]-25.84[/C][C]0.750705790355629[/C][C]-34.4209413753941[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]-25.875[/C][C]0.722991838530395[/C][C]-35.7887857387096[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]-25.8913043478261[/C][C]0.694511443942932[/C][C]-37.2798815248228[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]-25.9318181818182[/C][C]0.664246801410967[/C][C]-39.0394325222716[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]-25.9523809523810[/C][C]0.632962524511509[/C][C]-41.0014494498072[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]-26[/C][C]0.599144689515278[/C][C]-43.3951939406066[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]-26[/C][C]0.573229229579565[/C][C]-45.3570729794601[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]-26[/C][C]0.556348640264187[/C][C]-46.7332857821917[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]-25.9705882352941[/C][C]0.541479609743194[/C][C]-47.962264447245[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]-25.9375[/C][C]0.519649191530271[/C][C]-49.9134809074153[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]-25.9333333333333[/C][C]0.500421278463154[/C][C]-51.8230028366846[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]-25.9285714285714[/C][C]0.471204051072933[/C][C]-55.0262065224863[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]-25.9230769230769[/C][C]0.457158706403189[/C][C]-56.7047648004634[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]-25.9583333333333[/C][C]0.448343030981805[/C][C]-57.8983758852868[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]-26[/C][C]0.431447779165899[/C][C]-60.2622177132648[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]-26[/C][C]0.423021711524424[/C][C]-61.4625663214898[/C][/ROW]
[ROW][C]Median[/C][C]-26[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]-22[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]-25.6470588235294[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]-25.6470588235294[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]-25.6470588235294[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]-25.6470588235294[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]-25.6470588235294[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]-25.6470588235294[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]-25.6470588235294[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]-25.6470588235294[/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=48791&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=48791&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-25.450.965045884568207-26.3718030478801
Geometric MeanNaN
Harmonic Mean-22.1286750072844
Quadratic Mean26.5075460954046
Winsorized Mean ( 1 / 20 )-25.46666666666670.9506069029796-26.7899029418401
Winsorized Mean ( 2 / 20 )-25.53333333333330.930787488312583-27.4319687941041
Winsorized Mean ( 3 / 20 )-25.58333333333330.916974781294006-27.8997131166802
Winsorized Mean ( 4 / 20 )-25.78333333333330.837703231658712-30.7786007728304
Winsorized Mean ( 5 / 20 )-25.70.821085130154269-31.3000431455523
Winsorized Mean ( 6 / 20 )-25.80.799646814692954-32.2642440711861
Winsorized Mean ( 7 / 20 )-25.68333333333330.777687309777572-33.0252699387355
Winsorized Mean ( 8 / 20 )-25.81666666666670.75032635711706-34.4072501542672
Winsorized Mean ( 9 / 20 )-25.66666666666670.723560978523707-35.4727071089914
Winsorized Mean ( 10 / 20 )-260.659566712764956-39.4198183395368
Winsorized Mean ( 11 / 20 )-260.595178366656243-43.6843834665396
Winsorized Mean ( 12 / 20 )-26.20.562379930688034-46.5877222324525
Winsorized Mean ( 13 / 20 )-26.20.562379930688034-46.5877222324525
Winsorized Mean ( 14 / 20 )-25.96666666666670.522902950165613-49.658673102614
Winsorized Mean ( 15 / 20 )-25.96666666666670.522902950165613-49.658673102614
Winsorized Mean ( 16 / 20 )-25.96666666666670.438259698225279-59.2494969804844
Winsorized Mean ( 17 / 20 )-25.68333333333330.395948169485629-64.865392272676
Winsorized Mean ( 18 / 20 )-25.68333333333330.395948169485629-64.865392272676
Winsorized Mean ( 19 / 20 )-260.347712459946807-74.7744271343554
Winsorized Mean ( 20 / 20 )-260.347712459946807-74.7744271343554
Trimmed Mean ( 1 / 20 )-25.56896551724140.913736029903897-27.9828798257311
Trimmed Mean ( 2 / 20 )-25.67857142857140.867937973895953-29.5857217922
Trimmed Mean ( 3 / 20 )-25.75925925925930.824559762337937-31.2400148974309
Trimmed Mean ( 4 / 20 )-25.82692307692310.77708564970212-33.2356196344937
Trimmed Mean ( 5 / 20 )-25.840.750705790355629-34.4209413753941
Trimmed Mean ( 6 / 20 )-25.8750.722991838530395-35.7887857387096
Trimmed Mean ( 7 / 20 )-25.89130434782610.694511443942932-37.2798815248228
Trimmed Mean ( 8 / 20 )-25.93181818181820.664246801410967-39.0394325222716
Trimmed Mean ( 9 / 20 )-25.95238095238100.632962524511509-41.0014494498072
Trimmed Mean ( 10 / 20 )-260.599144689515278-43.3951939406066
Trimmed Mean ( 11 / 20 )-260.573229229579565-45.3570729794601
Trimmed Mean ( 12 / 20 )-260.556348640264187-46.7332857821917
Trimmed Mean ( 13 / 20 )-25.97058823529410.541479609743194-47.962264447245
Trimmed Mean ( 14 / 20 )-25.93750.519649191530271-49.9134809074153
Trimmed Mean ( 15 / 20 )-25.93333333333330.500421278463154-51.8230028366846
Trimmed Mean ( 16 / 20 )-25.92857142857140.471204051072933-55.0262065224863
Trimmed Mean ( 17 / 20 )-25.92307692307690.457158706403189-56.7047648004634
Trimmed Mean ( 18 / 20 )-25.95833333333330.448343030981805-57.8983758852868
Trimmed Mean ( 19 / 20 )-260.431447779165899-60.2622177132648
Trimmed Mean ( 20 / 20 )-260.423021711524424-61.4625663214898
Median-26
Midrange-22
Midmean - Weighted Average at Xnp-25.6470588235294
Midmean - Weighted Average at X(n+1)p-25.6470588235294
Midmean - Empirical Distribution Function-25.6470588235294
Midmean - Empirical Distribution Function - Averaging-25.6470588235294
Midmean - Empirical Distribution Function - Interpolation-25.6470588235294
Midmean - Closest Observation-25.6470588235294
Midmean - True Basic - Statistics Graphics Toolkit-25.6470588235294
Midmean - MS Excel (old versions)-25.6470588235294
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')