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of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationMon, 21 Apr 2008 10:14:09 -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/2008/Apr/21/t1208794478pxkolxsix6w2rla.htm/, Retrieved Thu, 16 May 2024 20:32:04 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=10524, Retrieved Thu, 16 May 2024 20:32:04 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact179
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [] [2008-04-21 16:14:09] [92ac00bd259cd41fd6a466a7e7f24e71] [Current]
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Dataseries X:
102,8
103,1
103,1
103,3
103,5
103,3
103,5
103,8
103,9
103,9
104,2
104,6
104,9
105,2
105,2
105,6
105,6
106,2
106,3
106,4
106,9
107,2
107,3
107,3
107,4
107,55
107,87
108,37
108,38
107,92
108,03
108,14
108,3
108,64
108,66
109,04
109,03
109,03
109,54
109,75
109,83
109,65
109,82
109,95
110,12
110,15
110,2
109,99
110,14
110,14
110,81
110,97
110,99
109,73
109,81
110,02
110,18
110,21
110,25
110,36
110,51
110,64
110,95
111,18
111,19
111,69
111,7
111,83
111,77
111,73
112,01
111,86
112,04




Summary of compuational 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 compuational 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=10524&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]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=10524&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=10524&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 time1 seconds
R Server'George Udny Yule' @ 72.249.76.132







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean108.290.322262324959465336.030592510685
Geometric Mean108.255122977392
Harmonic Mean108.219898205174
Quadratic Mean108.324519460916
Winsorized Mean ( 1 / 24 )108.2936986301370.321248486475438337.102595620842
Winsorized Mean ( 2 / 24 )108.2895890410960.320600501909801337.771115129329
Winsorized Mean ( 3 / 24 )108.2965753424660.318591017843586339.923504672171
Winsorized Mean ( 4 / 24 )108.2932876712330.318088256732827340.450442224882
Winsorized Mean ( 5 / 24 )108.3042465753420.314727535385757344.120658024394
Winsorized Mean ( 6 / 24 )108.3017808219180.31435604628847344.519477517968
Winsorized Mean ( 7 / 24 )108.3295890410960.308223011138013351.464962467028
Winsorized Mean ( 8 / 24 )108.2857534246580.298122161800288363.226110969899
Winsorized Mean ( 9 / 24 )108.2845205479450.297955555375790363.42507664062
Winsorized Mean ( 10 / 24 )108.2995890410960.286209245226506378.393049306941
Winsorized Mean ( 11 / 24 )108.3568493150680.274074468315377395.355503126918
Winsorized Mean ( 12 / 24 )108.4028767123290.264402666678264409.991616477294
Winsorized Mean ( 13 / 24 )108.4313698630140.251408536998985431.29549679314
Winsorized Mean ( 14 / 24 )108.3987671232880.247213076865112438.483143763604
Winsorized Mean ( 15 / 24 )108.4542465753420.229369289236946472.836825436145
Winsorized Mean ( 16 / 24 )108.4213698630140.225358273445909481.106676072566
Winsorized Mean ( 17 / 24 )108.5354794520550.198693319085748546.246244974222
Winsorized Mean ( 18 / 24 )108.5502739726030.193510583662625560.952646196625
Winsorized Mean ( 19 / 24 )108.5736986301370.189019389980993574.405084267041
Winsorized Mean ( 20 / 24 )108.7052054794520.167099109025231650.543298007881
Winsorized Mean ( 21 / 24 )108.7828767123290.153363665782329709.3132272068
Winsorized Mean ( 22 / 24 )108.810.148704194947989731.721119488645
Winsorized Mean ( 23 / 24 )108.810.148704194947989731.721119488645
Winsorized Mean ( 24 / 24 )108.8363013698630.143279100238110759.6104469458
Trimmed Mean ( 1 / 24 )108.3145070422540.317689773683565340.944267063945
Trimmed Mean ( 2 / 24 )108.3365217391300.313358782551522345.726776371165
Trimmed Mean ( 3 / 24 )108.3620895522390.308497587551029351.257494142688
Trimmed Mean ( 4 / 24 )108.3866153846150.303487285638754357.137252575483
Trimmed Mean ( 5 / 24 )108.4136507936510.297535473502205364.372185667627
Trimmed Mean ( 6 / 24 )108.4398360655740.291315040984849372.242489433333
Trimmed Mean ( 7 / 24 )108.4683050847460.283753248530428382.262778123277
Trimmed Mean ( 8 / 24 )108.4936842105260.276092229647746392.961744519027
Trimmed Mean ( 9 / 24 )108.5281818181820.268979126386396403.481799038481
Trimmed Mean ( 10 / 24 )108.5654716981130.260033012032540417.506496000313
Trimmed Mean ( 11 / 24 )108.6035294117650.251539077933821431.756092547726
Trimmed Mean ( 12 / 24 )108.6369387755100.243678792857676445.820243532481
Trimmed Mean ( 13 / 24 )108.6672340425530.235889620882949460.669840562739
Trimmed Mean ( 14 / 24 )108.6966666666670.228797912683846475.077177897441
Trimmed Mean ( 15 / 24 )108.7327906976740.220226734461516493.731112907525
Trimmed Mean ( 16 / 24 )108.7658536585370.213240095875505510.062862296014
Trimmed Mean ( 17 / 24 )108.8061538461540.204447385701532532.196356890557
Trimmed Mean ( 18 / 24 )108.8375675675680.199534896661703545.456305580941
Trimmed Mean ( 19 / 24 )108.8708571428570.193748676950136561.917938520307
Trimmed Mean ( 20 / 24 )108.9054545454550.186575037157595583.708604348098
Trimmed Mean ( 21 / 24 )108.9290322580650.182856871484735595.706529230202
Trimmed Mean ( 22 / 24 )108.9465517241380.181016747899784601.85896050046
Trimmed Mean ( 23 / 24 )108.9633333333330.178884641877706609.12626254313
Trimmed Mean ( 24 / 24 )108.98280.174657302547971623.980780706649
Median109.03
Midrange107.42
Midmean - Weighted Average at Xnp108.799444444444
Midmean - Weighted Average at X(n+1)p108.837567567568
Midmean - Empirical Distribution Function108.837567567568
Midmean - Empirical Distribution Function - Averaging108.837567567568
Midmean - Empirical Distribution Function - Interpolation108.837567567568
Midmean - Closest Observation108.768157894737
Midmean - True Basic - Statistics Graphics Toolkit108.837567567568
Midmean - MS Excel (old versions)108.837567567568
Number of observations73

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 108.29 & 0.322262324959465 & 336.030592510685 \tabularnewline
Geometric Mean & 108.255122977392 &  &  \tabularnewline
Harmonic Mean & 108.219898205174 &  &  \tabularnewline
Quadratic Mean & 108.324519460916 &  &  \tabularnewline
Winsorized Mean ( 1 / 24 ) & 108.293698630137 & 0.321248486475438 & 337.102595620842 \tabularnewline
Winsorized Mean ( 2 / 24 ) & 108.289589041096 & 0.320600501909801 & 337.771115129329 \tabularnewline
Winsorized Mean ( 3 / 24 ) & 108.296575342466 & 0.318591017843586 & 339.923504672171 \tabularnewline
Winsorized Mean ( 4 / 24 ) & 108.293287671233 & 0.318088256732827 & 340.450442224882 \tabularnewline
Winsorized Mean ( 5 / 24 ) & 108.304246575342 & 0.314727535385757 & 344.120658024394 \tabularnewline
Winsorized Mean ( 6 / 24 ) & 108.301780821918 & 0.31435604628847 & 344.519477517968 \tabularnewline
Winsorized Mean ( 7 / 24 ) & 108.329589041096 & 0.308223011138013 & 351.464962467028 \tabularnewline
Winsorized Mean ( 8 / 24 ) & 108.285753424658 & 0.298122161800288 & 363.226110969899 \tabularnewline
Winsorized Mean ( 9 / 24 ) & 108.284520547945 & 0.297955555375790 & 363.42507664062 \tabularnewline
Winsorized Mean ( 10 / 24 ) & 108.299589041096 & 0.286209245226506 & 378.393049306941 \tabularnewline
Winsorized Mean ( 11 / 24 ) & 108.356849315068 & 0.274074468315377 & 395.355503126918 \tabularnewline
Winsorized Mean ( 12 / 24 ) & 108.402876712329 & 0.264402666678264 & 409.991616477294 \tabularnewline
Winsorized Mean ( 13 / 24 ) & 108.431369863014 & 0.251408536998985 & 431.29549679314 \tabularnewline
Winsorized Mean ( 14 / 24 ) & 108.398767123288 & 0.247213076865112 & 438.483143763604 \tabularnewline
Winsorized Mean ( 15 / 24 ) & 108.454246575342 & 0.229369289236946 & 472.836825436145 \tabularnewline
Winsorized Mean ( 16 / 24 ) & 108.421369863014 & 0.225358273445909 & 481.106676072566 \tabularnewline
Winsorized Mean ( 17 / 24 ) & 108.535479452055 & 0.198693319085748 & 546.246244974222 \tabularnewline
Winsorized Mean ( 18 / 24 ) & 108.550273972603 & 0.193510583662625 & 560.952646196625 \tabularnewline
Winsorized Mean ( 19 / 24 ) & 108.573698630137 & 0.189019389980993 & 574.405084267041 \tabularnewline
Winsorized Mean ( 20 / 24 ) & 108.705205479452 & 0.167099109025231 & 650.543298007881 \tabularnewline
Winsorized Mean ( 21 / 24 ) & 108.782876712329 & 0.153363665782329 & 709.3132272068 \tabularnewline
Winsorized Mean ( 22 / 24 ) & 108.81 & 0.148704194947989 & 731.721119488645 \tabularnewline
Winsorized Mean ( 23 / 24 ) & 108.81 & 0.148704194947989 & 731.721119488645 \tabularnewline
Winsorized Mean ( 24 / 24 ) & 108.836301369863 & 0.143279100238110 & 759.6104469458 \tabularnewline
Trimmed Mean ( 1 / 24 ) & 108.314507042254 & 0.317689773683565 & 340.944267063945 \tabularnewline
Trimmed Mean ( 2 / 24 ) & 108.336521739130 & 0.313358782551522 & 345.726776371165 \tabularnewline
Trimmed Mean ( 3 / 24 ) & 108.362089552239 & 0.308497587551029 & 351.257494142688 \tabularnewline
Trimmed Mean ( 4 / 24 ) & 108.386615384615 & 0.303487285638754 & 357.137252575483 \tabularnewline
Trimmed Mean ( 5 / 24 ) & 108.413650793651 & 0.297535473502205 & 364.372185667627 \tabularnewline
Trimmed Mean ( 6 / 24 ) & 108.439836065574 & 0.291315040984849 & 372.242489433333 \tabularnewline
Trimmed Mean ( 7 / 24 ) & 108.468305084746 & 0.283753248530428 & 382.262778123277 \tabularnewline
Trimmed Mean ( 8 / 24 ) & 108.493684210526 & 0.276092229647746 & 392.961744519027 \tabularnewline
Trimmed Mean ( 9 / 24 ) & 108.528181818182 & 0.268979126386396 & 403.481799038481 \tabularnewline
Trimmed Mean ( 10 / 24 ) & 108.565471698113 & 0.260033012032540 & 417.506496000313 \tabularnewline
Trimmed Mean ( 11 / 24 ) & 108.603529411765 & 0.251539077933821 & 431.756092547726 \tabularnewline
Trimmed Mean ( 12 / 24 ) & 108.636938775510 & 0.243678792857676 & 445.820243532481 \tabularnewline
Trimmed Mean ( 13 / 24 ) & 108.667234042553 & 0.235889620882949 & 460.669840562739 \tabularnewline
Trimmed Mean ( 14 / 24 ) & 108.696666666667 & 0.228797912683846 & 475.077177897441 \tabularnewline
Trimmed Mean ( 15 / 24 ) & 108.732790697674 & 0.220226734461516 & 493.731112907525 \tabularnewline
Trimmed Mean ( 16 / 24 ) & 108.765853658537 & 0.213240095875505 & 510.062862296014 \tabularnewline
Trimmed Mean ( 17 / 24 ) & 108.806153846154 & 0.204447385701532 & 532.196356890557 \tabularnewline
Trimmed Mean ( 18 / 24 ) & 108.837567567568 & 0.199534896661703 & 545.456305580941 \tabularnewline
Trimmed Mean ( 19 / 24 ) & 108.870857142857 & 0.193748676950136 & 561.917938520307 \tabularnewline
Trimmed Mean ( 20 / 24 ) & 108.905454545455 & 0.186575037157595 & 583.708604348098 \tabularnewline
Trimmed Mean ( 21 / 24 ) & 108.929032258065 & 0.182856871484735 & 595.706529230202 \tabularnewline
Trimmed Mean ( 22 / 24 ) & 108.946551724138 & 0.181016747899784 & 601.85896050046 \tabularnewline
Trimmed Mean ( 23 / 24 ) & 108.963333333333 & 0.178884641877706 & 609.12626254313 \tabularnewline
Trimmed Mean ( 24 / 24 ) & 108.9828 & 0.174657302547971 & 623.980780706649 \tabularnewline
Median & 109.03 &  &  \tabularnewline
Midrange & 107.42 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 108.799444444444 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 108.837567567568 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 108.837567567568 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 108.837567567568 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 108.837567567568 &  &  \tabularnewline
Midmean - Closest Observation & 108.768157894737 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 108.837567567568 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 108.837567567568 &  &  \tabularnewline
Number of observations & 73 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=10524&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]108.29[/C][C]0.322262324959465[/C][C]336.030592510685[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]108.255122977392[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]108.219898205174[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]108.324519460916[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 24 )[/C][C]108.293698630137[/C][C]0.321248486475438[/C][C]337.102595620842[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 24 )[/C][C]108.289589041096[/C][C]0.320600501909801[/C][C]337.771115129329[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 24 )[/C][C]108.296575342466[/C][C]0.318591017843586[/C][C]339.923504672171[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 24 )[/C][C]108.293287671233[/C][C]0.318088256732827[/C][C]340.450442224882[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 24 )[/C][C]108.304246575342[/C][C]0.314727535385757[/C][C]344.120658024394[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 24 )[/C][C]108.301780821918[/C][C]0.31435604628847[/C][C]344.519477517968[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 24 )[/C][C]108.329589041096[/C][C]0.308223011138013[/C][C]351.464962467028[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 24 )[/C][C]108.285753424658[/C][C]0.298122161800288[/C][C]363.226110969899[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 24 )[/C][C]108.284520547945[/C][C]0.297955555375790[/C][C]363.42507664062[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 24 )[/C][C]108.299589041096[/C][C]0.286209245226506[/C][C]378.393049306941[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 24 )[/C][C]108.356849315068[/C][C]0.274074468315377[/C][C]395.355503126918[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 24 )[/C][C]108.402876712329[/C][C]0.264402666678264[/C][C]409.991616477294[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 24 )[/C][C]108.431369863014[/C][C]0.251408536998985[/C][C]431.29549679314[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 24 )[/C][C]108.398767123288[/C][C]0.247213076865112[/C][C]438.483143763604[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 24 )[/C][C]108.454246575342[/C][C]0.229369289236946[/C][C]472.836825436145[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 24 )[/C][C]108.421369863014[/C][C]0.225358273445909[/C][C]481.106676072566[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 24 )[/C][C]108.535479452055[/C][C]0.198693319085748[/C][C]546.246244974222[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 24 )[/C][C]108.550273972603[/C][C]0.193510583662625[/C][C]560.952646196625[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 24 )[/C][C]108.573698630137[/C][C]0.189019389980993[/C][C]574.405084267041[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 24 )[/C][C]108.705205479452[/C][C]0.167099109025231[/C][C]650.543298007881[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 24 )[/C][C]108.782876712329[/C][C]0.153363665782329[/C][C]709.3132272068[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 24 )[/C][C]108.81[/C][C]0.148704194947989[/C][C]731.721119488645[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 24 )[/C][C]108.81[/C][C]0.148704194947989[/C][C]731.721119488645[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 24 )[/C][C]108.836301369863[/C][C]0.143279100238110[/C][C]759.6104469458[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 24 )[/C][C]108.314507042254[/C][C]0.317689773683565[/C][C]340.944267063945[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 24 )[/C][C]108.336521739130[/C][C]0.313358782551522[/C][C]345.726776371165[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 24 )[/C][C]108.362089552239[/C][C]0.308497587551029[/C][C]351.257494142688[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 24 )[/C][C]108.386615384615[/C][C]0.303487285638754[/C][C]357.137252575483[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 24 )[/C][C]108.413650793651[/C][C]0.297535473502205[/C][C]364.372185667627[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 24 )[/C][C]108.439836065574[/C][C]0.291315040984849[/C][C]372.242489433333[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 24 )[/C][C]108.468305084746[/C][C]0.283753248530428[/C][C]382.262778123277[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 24 )[/C][C]108.493684210526[/C][C]0.276092229647746[/C][C]392.961744519027[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 24 )[/C][C]108.528181818182[/C][C]0.268979126386396[/C][C]403.481799038481[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 24 )[/C][C]108.565471698113[/C][C]0.260033012032540[/C][C]417.506496000313[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 24 )[/C][C]108.603529411765[/C][C]0.251539077933821[/C][C]431.756092547726[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 24 )[/C][C]108.636938775510[/C][C]0.243678792857676[/C][C]445.820243532481[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 24 )[/C][C]108.667234042553[/C][C]0.235889620882949[/C][C]460.669840562739[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 24 )[/C][C]108.696666666667[/C][C]0.228797912683846[/C][C]475.077177897441[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 24 )[/C][C]108.732790697674[/C][C]0.220226734461516[/C][C]493.731112907525[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 24 )[/C][C]108.765853658537[/C][C]0.213240095875505[/C][C]510.062862296014[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 24 )[/C][C]108.806153846154[/C][C]0.204447385701532[/C][C]532.196356890557[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 24 )[/C][C]108.837567567568[/C][C]0.199534896661703[/C][C]545.456305580941[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 24 )[/C][C]108.870857142857[/C][C]0.193748676950136[/C][C]561.917938520307[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 24 )[/C][C]108.905454545455[/C][C]0.186575037157595[/C][C]583.708604348098[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 24 )[/C][C]108.929032258065[/C][C]0.182856871484735[/C][C]595.706529230202[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 24 )[/C][C]108.946551724138[/C][C]0.181016747899784[/C][C]601.85896050046[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 24 )[/C][C]108.963333333333[/C][C]0.178884641877706[/C][C]609.12626254313[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 24 )[/C][C]108.9828[/C][C]0.174657302547971[/C][C]623.980780706649[/C][/ROW]
[ROW][C]Median[/C][C]109.03[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]107.42[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]108.799444444444[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]108.837567567568[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]108.837567567568[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]108.837567567568[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]108.837567567568[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]108.768157894737[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]108.837567567568[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]108.837567567568[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]73[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=10524&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=10524&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 Mean108.290.322262324959465336.030592510685
Geometric Mean108.255122977392
Harmonic Mean108.219898205174
Quadratic Mean108.324519460916
Winsorized Mean ( 1 / 24 )108.2936986301370.321248486475438337.102595620842
Winsorized Mean ( 2 / 24 )108.2895890410960.320600501909801337.771115129329
Winsorized Mean ( 3 / 24 )108.2965753424660.318591017843586339.923504672171
Winsorized Mean ( 4 / 24 )108.2932876712330.318088256732827340.450442224882
Winsorized Mean ( 5 / 24 )108.3042465753420.314727535385757344.120658024394
Winsorized Mean ( 6 / 24 )108.3017808219180.31435604628847344.519477517968
Winsorized Mean ( 7 / 24 )108.3295890410960.308223011138013351.464962467028
Winsorized Mean ( 8 / 24 )108.2857534246580.298122161800288363.226110969899
Winsorized Mean ( 9 / 24 )108.2845205479450.297955555375790363.42507664062
Winsorized Mean ( 10 / 24 )108.2995890410960.286209245226506378.393049306941
Winsorized Mean ( 11 / 24 )108.3568493150680.274074468315377395.355503126918
Winsorized Mean ( 12 / 24 )108.4028767123290.264402666678264409.991616477294
Winsorized Mean ( 13 / 24 )108.4313698630140.251408536998985431.29549679314
Winsorized Mean ( 14 / 24 )108.3987671232880.247213076865112438.483143763604
Winsorized Mean ( 15 / 24 )108.4542465753420.229369289236946472.836825436145
Winsorized Mean ( 16 / 24 )108.4213698630140.225358273445909481.106676072566
Winsorized Mean ( 17 / 24 )108.5354794520550.198693319085748546.246244974222
Winsorized Mean ( 18 / 24 )108.5502739726030.193510583662625560.952646196625
Winsorized Mean ( 19 / 24 )108.5736986301370.189019389980993574.405084267041
Winsorized Mean ( 20 / 24 )108.7052054794520.167099109025231650.543298007881
Winsorized Mean ( 21 / 24 )108.7828767123290.153363665782329709.3132272068
Winsorized Mean ( 22 / 24 )108.810.148704194947989731.721119488645
Winsorized Mean ( 23 / 24 )108.810.148704194947989731.721119488645
Winsorized Mean ( 24 / 24 )108.8363013698630.143279100238110759.6104469458
Trimmed Mean ( 1 / 24 )108.3145070422540.317689773683565340.944267063945
Trimmed Mean ( 2 / 24 )108.3365217391300.313358782551522345.726776371165
Trimmed Mean ( 3 / 24 )108.3620895522390.308497587551029351.257494142688
Trimmed Mean ( 4 / 24 )108.3866153846150.303487285638754357.137252575483
Trimmed Mean ( 5 / 24 )108.4136507936510.297535473502205364.372185667627
Trimmed Mean ( 6 / 24 )108.4398360655740.291315040984849372.242489433333
Trimmed Mean ( 7 / 24 )108.4683050847460.283753248530428382.262778123277
Trimmed Mean ( 8 / 24 )108.4936842105260.276092229647746392.961744519027
Trimmed Mean ( 9 / 24 )108.5281818181820.268979126386396403.481799038481
Trimmed Mean ( 10 / 24 )108.5654716981130.260033012032540417.506496000313
Trimmed Mean ( 11 / 24 )108.6035294117650.251539077933821431.756092547726
Trimmed Mean ( 12 / 24 )108.6369387755100.243678792857676445.820243532481
Trimmed Mean ( 13 / 24 )108.6672340425530.235889620882949460.669840562739
Trimmed Mean ( 14 / 24 )108.6966666666670.228797912683846475.077177897441
Trimmed Mean ( 15 / 24 )108.7327906976740.220226734461516493.731112907525
Trimmed Mean ( 16 / 24 )108.7658536585370.213240095875505510.062862296014
Trimmed Mean ( 17 / 24 )108.8061538461540.204447385701532532.196356890557
Trimmed Mean ( 18 / 24 )108.8375675675680.199534896661703545.456305580941
Trimmed Mean ( 19 / 24 )108.8708571428570.193748676950136561.917938520307
Trimmed Mean ( 20 / 24 )108.9054545454550.186575037157595583.708604348098
Trimmed Mean ( 21 / 24 )108.9290322580650.182856871484735595.706529230202
Trimmed Mean ( 22 / 24 )108.9465517241380.181016747899784601.85896050046
Trimmed Mean ( 23 / 24 )108.9633333333330.178884641877706609.12626254313
Trimmed Mean ( 24 / 24 )108.98280.174657302547971623.980780706649
Median109.03
Midrange107.42
Midmean - Weighted Average at Xnp108.799444444444
Midmean - Weighted Average at X(n+1)p108.837567567568
Midmean - Empirical Distribution Function108.837567567568
Midmean - Empirical Distribution Function - Averaging108.837567567568
Midmean - Empirical Distribution Function - Interpolation108.837567567568
Midmean - Closest Observation108.768157894737
Midmean - True Basic - Statistics Graphics Toolkit108.837567567568
Midmean - MS Excel (old versions)108.837567567568
Number of observations73



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')