Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationSun, 04 Mar 2012 07:44:08 -0500
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2012/Mar/04/t13308651073ruvc1w2je9ong8.htm/, Retrieved Fri, 03 May 2024 15:39:22 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=163453, Retrieved Fri, 03 May 2024 15:39:22 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact165
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Harrell-Davis Quantiles] [] [2012-02-22 15:53:03] [aedd9af56bfe2946a9f9da3d899aa64c]
- RMPD    [Central Tendency] [OPG5 OEF2 stap 1 ] [2012-03-04 12:44:08] [2d897010b3abf24abba169db0d9c5a05] [Current]
Feedback Forum

Post a new message
Dataseries X:
67,22
67,31
67,14
67,22
67,17
67,27
67,27
67,27
67,48
67,38
67,22
67,2
67,2
67,19
67,32
67,61
67,85
67,74
67,74
67,61
67,85
67,89
67,97
67,94
67,94
68,07
67,85
67,84
67,89
67,86
67,86
67,89
67,7
68,05
68,18
68,19
68,19
68,27
68,22
68,14
68,36
68,34
68,34
68,24
68,14
68,23
68,09
68,03
68,03
67,89
67,63
67,61
67,41
67,29
67,29
67,49
67,68
68,05
67,7
67,86




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gwilym Jenkins' @ jenkins.wessa.net

\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 & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=163453&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]'Gwilym Jenkins' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=163453&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=163453&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'Gwilym Jenkins' @ jenkins.wessa.net







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean67.74833333333330.0480508009578721409.93140557076
Geometric Mean67.7473273747192
Harmonic Mean67.746320835657
Quadratic Mean67.7493386929595
Winsorized Mean ( 1 / 20 )67.74850.04787508758529261415.10968265701
Winsorized Mean ( 2 / 20 )67.74916666666670.04774064327923991419.10879311774
Winsorized Mean ( 3 / 20 )67.74616666666670.04694334346094121443.14745546478
Winsorized Mean ( 4 / 20 )67.74416666666670.04657373211951651454.55739928299
Winsorized Mean ( 5 / 20 )67.7450.04609833508029491469.57585088486
Winsorized Mean ( 6 / 20 )67.7440.04592132795969561475.21866221852
Winsorized Mean ( 7 / 20 )67.74050.04531959641489581494.72866836331
Winsorized Mean ( 8 / 20 )67.74716666666670.04405831502010211537.67039515143
Winsorized Mean ( 9 / 20 )67.74566666666670.04380450062439871546.54580467773
Winsorized Mean ( 10 / 20 )67.7390.04271353799070771585.89063764132
Winsorized Mean ( 11 / 20 )67.74266666666670.04203769270888011611.47442453131
Winsorized Mean ( 12 / 20 )67.73266666666670.04048775128068321672.91747563619
Winsorized Mean ( 13 / 20 )67.73266666666670.03904717317015421734.63688066511
Winsorized Mean ( 14 / 20 )67.73033333333330.03794432932679511784.99223823425
Winsorized Mean ( 15 / 20 )67.74533333333330.03525008848541751921.84860362432
Winsorized Mean ( 16 / 20 )67.7480.03307823289605172048.11424518649
Winsorized Mean ( 17 / 20 )67.76783333333330.02972861398791032279.54903517845
Winsorized Mean ( 18 / 20 )67.75283333333330.02663743984519912543.51896154707
Winsorized Mean ( 19 / 20 )67.78133333333330.01921990885571113526.62095549909
Winsorized Mean ( 20 / 20 )67.78133333333330.01921990885571113526.62095549909
Trimmed Mean ( 1 / 20 )67.7482758620690.04740459130859131429.15008845969
Trimmed Mean ( 2 / 20 )67.74803571428570.04679564557030251447.74230355484
Trimmed Mean ( 3 / 20 )67.74740740740740.04610184179914721469.51628749593
Trimmed Mean ( 4 / 20 )67.74788461538460.0455818231832661486.29168129142
Trimmed Mean ( 5 / 20 )67.7490.04502901558881741504.56320472671
Trimmed Mean ( 6 / 20 )67.750.04444496158091581524.35726323344
Trimmed Mean ( 7 / 20 )67.75130434782610.04370808821517291550.08619947616
Trimmed Mean ( 8 / 20 )67.75340909090910.04288479969161171579.8933323259
Trimmed Mean ( 9 / 20 )67.75452380952380.04212172281865571608.54113449309
Trimmed Mean ( 10 / 20 )67.7560.04113268087418361647.25465396364
Trimmed Mean ( 11 / 20 )67.75868421052630.04005183528404681691.77476462647
Trimmed Mean ( 12 / 20 )67.76111111111110.03873142724958791749.51237077978
Trimmed Mean ( 13 / 20 )67.76529411764710.03728111471111031817.68422545187
Trimmed Mean ( 14 / 20 )67.770.03561951712193761902.60861111622
Trimmed Mean ( 15 / 20 )67.77566666666670.03350650420074872022.7614990988
Trimmed Mean ( 16 / 20 )67.780.03137923014760062160.0274984816
Trimmed Mean ( 17 / 20 )67.78461538461540.02894148350474832342.12649719543
Trimmed Mean ( 18 / 20 )67.78708333333330.02662459883801112546.03210158253
Trimmed Mean ( 19 / 20 )67.79227272727270.02412926783622892809.54536985519
Trimmed Mean ( 20 / 20 )67.7940.02372429356720982857.57718382395
Median67.85
Midrange67.75
Midmean - Weighted Average at Xnp67.77
Midmean - Weighted Average at X(n+1)p67.7845161290323
Midmean - Empirical Distribution Function67.77
Midmean - Empirical Distribution Function - Averaging67.7845161290323
Midmean - Empirical Distribution Function - Interpolation67.7845161290323
Midmean - Closest Observation67.77
Midmean - True Basic - Statistics Graphics Toolkit67.7845161290323
Midmean - MS Excel (old versions)67.77
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 67.7483333333333 & 0.048050800957872 & 1409.93140557076 \tabularnewline
Geometric Mean & 67.7473273747192 &  &  \tabularnewline
Harmonic Mean & 67.746320835657 &  &  \tabularnewline
Quadratic Mean & 67.7493386929595 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 67.7485 & 0.0478750875852926 & 1415.10968265701 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 67.7491666666667 & 0.0477406432792399 & 1419.10879311774 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 67.7461666666667 & 0.0469433434609412 & 1443.14745546478 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 67.7441666666667 & 0.0465737321195165 & 1454.55739928299 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 67.745 & 0.0460983350802949 & 1469.57585088486 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 67.744 & 0.0459213279596956 & 1475.21866221852 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 67.7405 & 0.0453195964148958 & 1494.72866836331 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 67.7471666666667 & 0.0440583150201021 & 1537.67039515143 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 67.7456666666667 & 0.0438045006243987 & 1546.54580467773 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 67.739 & 0.0427135379907077 & 1585.89063764132 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 67.7426666666667 & 0.0420376927088801 & 1611.47442453131 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 67.7326666666667 & 0.0404877512806832 & 1672.91747563619 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 67.7326666666667 & 0.0390471731701542 & 1734.63688066511 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 67.7303333333333 & 0.0379443293267951 & 1784.99223823425 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 67.7453333333333 & 0.0352500884854175 & 1921.84860362432 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 67.748 & 0.0330782328960517 & 2048.11424518649 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 67.7678333333333 & 0.0297286139879103 & 2279.54903517845 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 67.7528333333333 & 0.0266374398451991 & 2543.51896154707 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 67.7813333333333 & 0.0192199088557111 & 3526.62095549909 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 67.7813333333333 & 0.0192199088557111 & 3526.62095549909 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 67.748275862069 & 0.0474045913085913 & 1429.15008845969 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 67.7480357142857 & 0.0467956455703025 & 1447.74230355484 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 67.7474074074074 & 0.0461018417991472 & 1469.51628749593 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 67.7478846153846 & 0.045581823183266 & 1486.29168129142 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 67.749 & 0.0450290155888174 & 1504.56320472671 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 67.75 & 0.0444449615809158 & 1524.35726323344 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 67.7513043478261 & 0.0437080882151729 & 1550.08619947616 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 67.7534090909091 & 0.0428847996916117 & 1579.8933323259 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 67.7545238095238 & 0.0421217228186557 & 1608.54113449309 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 67.756 & 0.0411326808741836 & 1647.25465396364 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 67.7586842105263 & 0.0400518352840468 & 1691.77476462647 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 67.7611111111111 & 0.0387314272495879 & 1749.51237077978 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 67.7652941176471 & 0.0372811147111103 & 1817.68422545187 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 67.77 & 0.0356195171219376 & 1902.60861111622 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 67.7756666666667 & 0.0335065042007487 & 2022.7614990988 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 67.78 & 0.0313792301476006 & 2160.0274984816 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 67.7846153846154 & 0.0289414835047483 & 2342.12649719543 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 67.7870833333333 & 0.0266245988380111 & 2546.03210158253 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 67.7922727272727 & 0.0241292678362289 & 2809.54536985519 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 67.794 & 0.0237242935672098 & 2857.57718382395 \tabularnewline
Median & 67.85 &  &  \tabularnewline
Midrange & 67.75 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 67.77 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 67.7845161290323 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 67.77 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 67.7845161290323 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 67.7845161290323 &  &  \tabularnewline
Midmean - Closest Observation & 67.77 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 67.7845161290323 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 67.77 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=163453&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]67.7483333333333[/C][C]0.048050800957872[/C][C]1409.93140557076[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]67.7473273747192[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]67.746320835657[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]67.7493386929595[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]67.7485[/C][C]0.0478750875852926[/C][C]1415.10968265701[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]67.7491666666667[/C][C]0.0477406432792399[/C][C]1419.10879311774[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]67.7461666666667[/C][C]0.0469433434609412[/C][C]1443.14745546478[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]67.7441666666667[/C][C]0.0465737321195165[/C][C]1454.55739928299[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]67.745[/C][C]0.0460983350802949[/C][C]1469.57585088486[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]67.744[/C][C]0.0459213279596956[/C][C]1475.21866221852[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]67.7405[/C][C]0.0453195964148958[/C][C]1494.72866836331[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]67.7471666666667[/C][C]0.0440583150201021[/C][C]1537.67039515143[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]67.7456666666667[/C][C]0.0438045006243987[/C][C]1546.54580467773[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]67.739[/C][C]0.0427135379907077[/C][C]1585.89063764132[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]67.7426666666667[/C][C]0.0420376927088801[/C][C]1611.47442453131[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]67.7326666666667[/C][C]0.0404877512806832[/C][C]1672.91747563619[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]67.7326666666667[/C][C]0.0390471731701542[/C][C]1734.63688066511[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]67.7303333333333[/C][C]0.0379443293267951[/C][C]1784.99223823425[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]67.7453333333333[/C][C]0.0352500884854175[/C][C]1921.84860362432[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]67.748[/C][C]0.0330782328960517[/C][C]2048.11424518649[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]67.7678333333333[/C][C]0.0297286139879103[/C][C]2279.54903517845[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]67.7528333333333[/C][C]0.0266374398451991[/C][C]2543.51896154707[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]67.7813333333333[/C][C]0.0192199088557111[/C][C]3526.62095549909[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]67.7813333333333[/C][C]0.0192199088557111[/C][C]3526.62095549909[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]67.748275862069[/C][C]0.0474045913085913[/C][C]1429.15008845969[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]67.7480357142857[/C][C]0.0467956455703025[/C][C]1447.74230355484[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]67.7474074074074[/C][C]0.0461018417991472[/C][C]1469.51628749593[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]67.7478846153846[/C][C]0.045581823183266[/C][C]1486.29168129142[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]67.749[/C][C]0.0450290155888174[/C][C]1504.56320472671[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]67.75[/C][C]0.0444449615809158[/C][C]1524.35726323344[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]67.7513043478261[/C][C]0.0437080882151729[/C][C]1550.08619947616[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]67.7534090909091[/C][C]0.0428847996916117[/C][C]1579.8933323259[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]67.7545238095238[/C][C]0.0421217228186557[/C][C]1608.54113449309[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]67.756[/C][C]0.0411326808741836[/C][C]1647.25465396364[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]67.7586842105263[/C][C]0.0400518352840468[/C][C]1691.77476462647[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]67.7611111111111[/C][C]0.0387314272495879[/C][C]1749.51237077978[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]67.7652941176471[/C][C]0.0372811147111103[/C][C]1817.68422545187[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]67.77[/C][C]0.0356195171219376[/C][C]1902.60861111622[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]67.7756666666667[/C][C]0.0335065042007487[/C][C]2022.7614990988[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]67.78[/C][C]0.0313792301476006[/C][C]2160.0274984816[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]67.7846153846154[/C][C]0.0289414835047483[/C][C]2342.12649719543[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]67.7870833333333[/C][C]0.0266245988380111[/C][C]2546.03210158253[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]67.7922727272727[/C][C]0.0241292678362289[/C][C]2809.54536985519[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]67.794[/C][C]0.0237242935672098[/C][C]2857.57718382395[/C][/ROW]
[ROW][C]Median[/C][C]67.85[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]67.75[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]67.77[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]67.7845161290323[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]67.77[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]67.7845161290323[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]67.7845161290323[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]67.77[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]67.7845161290323[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]67.77[/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=163453&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=163453&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 Mean67.74833333333330.0480508009578721409.93140557076
Geometric Mean67.7473273747192
Harmonic Mean67.746320835657
Quadratic Mean67.7493386929595
Winsorized Mean ( 1 / 20 )67.74850.04787508758529261415.10968265701
Winsorized Mean ( 2 / 20 )67.74916666666670.04774064327923991419.10879311774
Winsorized Mean ( 3 / 20 )67.74616666666670.04694334346094121443.14745546478
Winsorized Mean ( 4 / 20 )67.74416666666670.04657373211951651454.55739928299
Winsorized Mean ( 5 / 20 )67.7450.04609833508029491469.57585088486
Winsorized Mean ( 6 / 20 )67.7440.04592132795969561475.21866221852
Winsorized Mean ( 7 / 20 )67.74050.04531959641489581494.72866836331
Winsorized Mean ( 8 / 20 )67.74716666666670.04405831502010211537.67039515143
Winsorized Mean ( 9 / 20 )67.74566666666670.04380450062439871546.54580467773
Winsorized Mean ( 10 / 20 )67.7390.04271353799070771585.89063764132
Winsorized Mean ( 11 / 20 )67.74266666666670.04203769270888011611.47442453131
Winsorized Mean ( 12 / 20 )67.73266666666670.04048775128068321672.91747563619
Winsorized Mean ( 13 / 20 )67.73266666666670.03904717317015421734.63688066511
Winsorized Mean ( 14 / 20 )67.73033333333330.03794432932679511784.99223823425
Winsorized Mean ( 15 / 20 )67.74533333333330.03525008848541751921.84860362432
Winsorized Mean ( 16 / 20 )67.7480.03307823289605172048.11424518649
Winsorized Mean ( 17 / 20 )67.76783333333330.02972861398791032279.54903517845
Winsorized Mean ( 18 / 20 )67.75283333333330.02663743984519912543.51896154707
Winsorized Mean ( 19 / 20 )67.78133333333330.01921990885571113526.62095549909
Winsorized Mean ( 20 / 20 )67.78133333333330.01921990885571113526.62095549909
Trimmed Mean ( 1 / 20 )67.7482758620690.04740459130859131429.15008845969
Trimmed Mean ( 2 / 20 )67.74803571428570.04679564557030251447.74230355484
Trimmed Mean ( 3 / 20 )67.74740740740740.04610184179914721469.51628749593
Trimmed Mean ( 4 / 20 )67.74788461538460.0455818231832661486.29168129142
Trimmed Mean ( 5 / 20 )67.7490.04502901558881741504.56320472671
Trimmed Mean ( 6 / 20 )67.750.04444496158091581524.35726323344
Trimmed Mean ( 7 / 20 )67.75130434782610.04370808821517291550.08619947616
Trimmed Mean ( 8 / 20 )67.75340909090910.04288479969161171579.8933323259
Trimmed Mean ( 9 / 20 )67.75452380952380.04212172281865571608.54113449309
Trimmed Mean ( 10 / 20 )67.7560.04113268087418361647.25465396364
Trimmed Mean ( 11 / 20 )67.75868421052630.04005183528404681691.77476462647
Trimmed Mean ( 12 / 20 )67.76111111111110.03873142724958791749.51237077978
Trimmed Mean ( 13 / 20 )67.76529411764710.03728111471111031817.68422545187
Trimmed Mean ( 14 / 20 )67.770.03561951712193761902.60861111622
Trimmed Mean ( 15 / 20 )67.77566666666670.03350650420074872022.7614990988
Trimmed Mean ( 16 / 20 )67.780.03137923014760062160.0274984816
Trimmed Mean ( 17 / 20 )67.78461538461540.02894148350474832342.12649719543
Trimmed Mean ( 18 / 20 )67.78708333333330.02662459883801112546.03210158253
Trimmed Mean ( 19 / 20 )67.79227272727270.02412926783622892809.54536985519
Trimmed Mean ( 20 / 20 )67.7940.02372429356720982857.57718382395
Median67.85
Midrange67.75
Midmean - Weighted Average at Xnp67.77
Midmean - Weighted Average at X(n+1)p67.7845161290323
Midmean - Empirical Distribution Function67.77
Midmean - Empirical Distribution Function - Averaging67.7845161290323
Midmean - Empirical Distribution Function - Interpolation67.7845161290323
Midmean - Closest Observation67.77
Midmean - True Basic - Statistics Graphics Toolkit67.7845161290323
Midmean - MS Excel (old versions)67.77
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')