Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationTue, 25 Dec 2007 06:05:50 -0700
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2007/Dec/25/t1198586790mmws3e15dfj6602.htm/, Retrieved Fri, 03 May 2024 17:00:18 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=4889, Retrieved Fri, 03 May 2024 17:00:18 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsKlaas Van Pelt
Estimated Impact245
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [RES CT 2] [2007-12-25 13:05:50] [6abd901c2e17b7d5559c695bbff3d863] [Current]
Feedback Forum

Post a new message
Dataseries X:
-0.506989902325989 
4.88007967776828 
1.21450068211499 
27.8822644132403 
4.36393480418803 
4.34429314520993 
4.85539101306677 
2.66600851392888 
8.28051837137848 
6.23163376152634 
-11.5390085155369 
2.5510634563959 
-3.04357152011076 
8.33849793902137 
11.7379487483667 
3.45419323762339 
-0.239377514124032 
9.83139985460656 
10.1425640912454 
-9.96997686691292 
-4.44916496608482 
-4.43964945807339 
11.9792892361410 
-1.1892576028676 
1.45333082023549 
6.27326711354841 
9.12179838003651 
17.0318887661480 
-6.03374596043278 
9.71377174099858 
-8.90439512965544 
7.16319380546682 
9.1117742507198 
8.76751672914546 
6.97897193233582 
-0.624146779536742 
1.34246749269283 
-3.12035782536661 
-1.81407113460095 
3.84116987188008 
-12.9504916860743 
3.61395105319151 
-11.7422028926221 
5.1768015413771 
4.84220949961766 
-14.4563471903241 
-1.80167294853758 
13.0423515103157 
-5.66647260942664 
6.18049057913837 
-4.90386336830106 
-15.5576336716000 
16.1110295774597 
5.6008016787895 
3.31811629022567 
-3.68261900199427 
-2.33060796595063 
11.2985182313596 
2.17465492335024 
23.5820079889651 
-9.27235736301466 
-13.5159367678475 
-9.00833983509705 
0.630633628292465 
-6.44449127383928 
4.95739032793351 
4.52795971406281 
15.0746061480379 




Summary of compuational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'Herman Ole Andreas Wold' @ 193.190.124.10:1001

\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 & 3 seconds \tabularnewline
R Server & 'Herman Ole Andreas Wold' @ 193.190.124.10:1001 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=4889&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]3 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Herman Ole Andreas Wold' @ 193.190.124.10:1001[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=4889&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=4889&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 time3 seconds
R Server'Herman Ole Andreas Wold' @ 193.190.124.10:1001







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean2.30113977633661.062808159216122.16515064960907
Geometric MeanNaN
Harmonic Mean-24.4687641149534
Quadratic Mean8.99865787498859
Winsorized Mean ( 1 / 22 )2.254096100704261.03775197436942.17209521771711
Winsorized Mean ( 2 / 22 )2.089104665400130.9794368276456452.13296519635869
Winsorized Mean ( 3 / 22 )2.073424631271520.9645309033103152.14967153893714
Winsorized Mean ( 4 / 22 )2.083534358567420.9354788520514872.22723833253769
Winsorized Mean ( 5 / 22 )1.949044633520590.9029475481708442.15853582798789
Winsorized Mean ( 6 / 22 )1.993688990089640.8562781847860342.32831926062419
Winsorized Mean ( 7 / 22 )2.040658888808280.8372363965048322.43737479322127
Winsorized Mean ( 8 / 22 )2.020022066562460.8221712505350172.45693590629441
Winsorized Mean ( 9 / 22 )1.880785523738150.794627857529752.36687589783842
Winsorized Mean ( 10 / 22 )2.19677664420540.718114244929343.05909075013761
Winsorized Mean ( 11 / 22 )2.244192661819870.7032919959691733.19098279901117
Winsorized Mean ( 12 / 22 )2.204539718886470.675696660828563.2626174534934
Winsorized Mean ( 13 / 22 )2.348416284379340.650589101739253.60967664244791
Winsorized Mean ( 14 / 22 )2.371154112746790.6242454654534133.79843225777304
Winsorized Mean ( 15 / 22 )2.278616624045470.6096425177238893.73762747479084
Winsorized Mean ( 16 / 22 )2.443099186030460.5788737095786864.22043555546613
Winsorized Mean ( 17 / 22 )2.304333338709460.5160116712635374.46566127674386
Winsorized Mean ( 18 / 22 )2.275894511918980.5060129688996734.49769996383279
Winsorized Mean ( 19 / 22 )2.277922687979010.4482529421375585.08177966912255
Winsorized Mean ( 20 / 22 )2.417600181898890.4236251479688185.70693263487947
Winsorized Mean ( 21 / 22 )2.405634815386880.4209359090739835.71496696653664
Winsorized Mean ( 22 / 22 )2.416222782990770.366881427060846.58584110497938
Trimmed Mean ( 1 / 22 )2.184134455291640.9861568015961762.21479429210085
Trimmed Mean ( 2 / 22 )2.109800207040740.923260807311192.28516166865689
Trimmed Mean ( 3 / 22 )2.121149375037210.8861826166792972.39358043716269
Trimmed Mean ( 4 / 22 )2.139178722682030.8482598047774422.52184379200107
Trimmed Mean ( 5 / 22 )2.155488277681140.8133703415077922.65006992225138
Trimmed Mean ( 6 / 22 )2.205624591262980.7814719214321172.82239774811228
Trimmed Mean ( 7 / 22 )2.250104902620350.7563092023879922.97511242163365
Trimmed Mean ( 8 / 22 )2.289232179925900.7302472783474513.13487259426209
Trimmed Mean ( 9 / 22 )2.334997899197690.7013984021721363.32906076199563
Trimmed Mean ( 10 / 22 )2.406494291631130.6716702419337973.58285084166097
Trimmed Mean ( 11 / 22 )2.437496030815810.6535893178994133.72940004382222
Trimmed Mean ( 12 / 22 )2.464654355385480.6335918699604393.88997156093461
Trimmed Mean ( 13 / 22 )2.499749187294080.6139292061697584.07172221515533
Trimmed Mean ( 14 / 22 )2.519538874598320.5940352010216684.24139658771908
Trimmed Mean ( 15 / 22 )2.538505347917690.5737722182511484.42423886547701
Trimmed Mean ( 16 / 22 )2.571232076109000.549532668132444.67894308239619
Trimmed Mean ( 17 / 22 )2.587248687368820.5246059788048444.93179413102208
Trimmed Mean ( 18 / 22 )2.622613105951240.507237101626385.17038895132518
Trimmed Mean ( 19 / 22 )2.666273965940490.4843415519548285.5049457457847
Trimmed Mean ( 20 / 22 )2.715912851093460.4686497571807575.79518672415728
Trimmed Mean ( 21 / 22 )2.754922969372750.452551105138566.0875400326981
Trimmed Mean ( 22 / 22 )2.802049148878780.426842226274126.56460157032189
Median3.38615476392453
Midrange6.16231537082015
Midmean - Weighted Average at Xnp2.40810961052988
Midmean - Weighted Average at X(n+1)p2.58724868736882
Midmean - Empirical Distribution Function2.40810961052988
Midmean - Empirical Distribution Function - Averaging2.58724868736882
Midmean - Empirical Distribution Function - Interpolation2.58724868736882
Midmean - Closest Observation2.40810961052988
Midmean - True Basic - Statistics Graphics Toolkit2.58724868736882
Midmean - MS Excel (old versions)2.57123207610900
Number of observations68

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 2.3011397763366 & 1.06280815921612 & 2.16515064960907 \tabularnewline
Geometric Mean & NaN &  &  \tabularnewline
Harmonic Mean & -24.4687641149534 &  &  \tabularnewline
Quadratic Mean & 8.99865787498859 &  &  \tabularnewline
Winsorized Mean ( 1 / 22 ) & 2.25409610070426 & 1.0377519743694 & 2.17209521771711 \tabularnewline
Winsorized Mean ( 2 / 22 ) & 2.08910466540013 & 0.979436827645645 & 2.13296519635869 \tabularnewline
Winsorized Mean ( 3 / 22 ) & 2.07342463127152 & 0.964530903310315 & 2.14967153893714 \tabularnewline
Winsorized Mean ( 4 / 22 ) & 2.08353435856742 & 0.935478852051487 & 2.22723833253769 \tabularnewline
Winsorized Mean ( 5 / 22 ) & 1.94904463352059 & 0.902947548170844 & 2.15853582798789 \tabularnewline
Winsorized Mean ( 6 / 22 ) & 1.99368899008964 & 0.856278184786034 & 2.32831926062419 \tabularnewline
Winsorized Mean ( 7 / 22 ) & 2.04065888880828 & 0.837236396504832 & 2.43737479322127 \tabularnewline
Winsorized Mean ( 8 / 22 ) & 2.02002206656246 & 0.822171250535017 & 2.45693590629441 \tabularnewline
Winsorized Mean ( 9 / 22 ) & 1.88078552373815 & 0.79462785752975 & 2.36687589783842 \tabularnewline
Winsorized Mean ( 10 / 22 ) & 2.1967766442054 & 0.71811424492934 & 3.05909075013761 \tabularnewline
Winsorized Mean ( 11 / 22 ) & 2.24419266181987 & 0.703291995969173 & 3.19098279901117 \tabularnewline
Winsorized Mean ( 12 / 22 ) & 2.20453971888647 & 0.67569666082856 & 3.2626174534934 \tabularnewline
Winsorized Mean ( 13 / 22 ) & 2.34841628437934 & 0.65058910173925 & 3.60967664244791 \tabularnewline
Winsorized Mean ( 14 / 22 ) & 2.37115411274679 & 0.624245465453413 & 3.79843225777304 \tabularnewline
Winsorized Mean ( 15 / 22 ) & 2.27861662404547 & 0.609642517723889 & 3.73762747479084 \tabularnewline
Winsorized Mean ( 16 / 22 ) & 2.44309918603046 & 0.578873709578686 & 4.22043555546613 \tabularnewline
Winsorized Mean ( 17 / 22 ) & 2.30433333870946 & 0.516011671263537 & 4.46566127674386 \tabularnewline
Winsorized Mean ( 18 / 22 ) & 2.27589451191898 & 0.506012968899673 & 4.49769996383279 \tabularnewline
Winsorized Mean ( 19 / 22 ) & 2.27792268797901 & 0.448252942137558 & 5.08177966912255 \tabularnewline
Winsorized Mean ( 20 / 22 ) & 2.41760018189889 & 0.423625147968818 & 5.70693263487947 \tabularnewline
Winsorized Mean ( 21 / 22 ) & 2.40563481538688 & 0.420935909073983 & 5.71496696653664 \tabularnewline
Winsorized Mean ( 22 / 22 ) & 2.41622278299077 & 0.36688142706084 & 6.58584110497938 \tabularnewline
Trimmed Mean ( 1 / 22 ) & 2.18413445529164 & 0.986156801596176 & 2.21479429210085 \tabularnewline
Trimmed Mean ( 2 / 22 ) & 2.10980020704074 & 0.92326080731119 & 2.28516166865689 \tabularnewline
Trimmed Mean ( 3 / 22 ) & 2.12114937503721 & 0.886182616679297 & 2.39358043716269 \tabularnewline
Trimmed Mean ( 4 / 22 ) & 2.13917872268203 & 0.848259804777442 & 2.52184379200107 \tabularnewline
Trimmed Mean ( 5 / 22 ) & 2.15548827768114 & 0.813370341507792 & 2.65006992225138 \tabularnewline
Trimmed Mean ( 6 / 22 ) & 2.20562459126298 & 0.781471921432117 & 2.82239774811228 \tabularnewline
Trimmed Mean ( 7 / 22 ) & 2.25010490262035 & 0.756309202387992 & 2.97511242163365 \tabularnewline
Trimmed Mean ( 8 / 22 ) & 2.28923217992590 & 0.730247278347451 & 3.13487259426209 \tabularnewline
Trimmed Mean ( 9 / 22 ) & 2.33499789919769 & 0.701398402172136 & 3.32906076199563 \tabularnewline
Trimmed Mean ( 10 / 22 ) & 2.40649429163113 & 0.671670241933797 & 3.58285084166097 \tabularnewline
Trimmed Mean ( 11 / 22 ) & 2.43749603081581 & 0.653589317899413 & 3.72940004382222 \tabularnewline
Trimmed Mean ( 12 / 22 ) & 2.46465435538548 & 0.633591869960439 & 3.88997156093461 \tabularnewline
Trimmed Mean ( 13 / 22 ) & 2.49974918729408 & 0.613929206169758 & 4.07172221515533 \tabularnewline
Trimmed Mean ( 14 / 22 ) & 2.51953887459832 & 0.594035201021668 & 4.24139658771908 \tabularnewline
Trimmed Mean ( 15 / 22 ) & 2.53850534791769 & 0.573772218251148 & 4.42423886547701 \tabularnewline
Trimmed Mean ( 16 / 22 ) & 2.57123207610900 & 0.54953266813244 & 4.67894308239619 \tabularnewline
Trimmed Mean ( 17 / 22 ) & 2.58724868736882 & 0.524605978804844 & 4.93179413102208 \tabularnewline
Trimmed Mean ( 18 / 22 ) & 2.62261310595124 & 0.50723710162638 & 5.17038895132518 \tabularnewline
Trimmed Mean ( 19 / 22 ) & 2.66627396594049 & 0.484341551954828 & 5.5049457457847 \tabularnewline
Trimmed Mean ( 20 / 22 ) & 2.71591285109346 & 0.468649757180757 & 5.79518672415728 \tabularnewline
Trimmed Mean ( 21 / 22 ) & 2.75492296937275 & 0.45255110513856 & 6.0875400326981 \tabularnewline
Trimmed Mean ( 22 / 22 ) & 2.80204914887878 & 0.42684222627412 & 6.56460157032189 \tabularnewline
Median & 3.38615476392453 &  &  \tabularnewline
Midrange & 6.16231537082015 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 2.40810961052988 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 2.58724868736882 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 2.40810961052988 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 2.58724868736882 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 2.58724868736882 &  &  \tabularnewline
Midmean - Closest Observation & 2.40810961052988 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 2.58724868736882 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 2.57123207610900 &  &  \tabularnewline
Number of observations & 68 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=4889&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]2.3011397763366[/C][C]1.06280815921612[/C][C]2.16515064960907[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]NaN[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]-24.4687641149534[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]8.99865787498859[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 22 )[/C][C]2.25409610070426[/C][C]1.0377519743694[/C][C]2.17209521771711[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 22 )[/C][C]2.08910466540013[/C][C]0.979436827645645[/C][C]2.13296519635869[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 22 )[/C][C]2.07342463127152[/C][C]0.964530903310315[/C][C]2.14967153893714[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 22 )[/C][C]2.08353435856742[/C][C]0.935478852051487[/C][C]2.22723833253769[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 22 )[/C][C]1.94904463352059[/C][C]0.902947548170844[/C][C]2.15853582798789[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 22 )[/C][C]1.99368899008964[/C][C]0.856278184786034[/C][C]2.32831926062419[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 22 )[/C][C]2.04065888880828[/C][C]0.837236396504832[/C][C]2.43737479322127[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 22 )[/C][C]2.02002206656246[/C][C]0.822171250535017[/C][C]2.45693590629441[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 22 )[/C][C]1.88078552373815[/C][C]0.79462785752975[/C][C]2.36687589783842[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 22 )[/C][C]2.1967766442054[/C][C]0.71811424492934[/C][C]3.05909075013761[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 22 )[/C][C]2.24419266181987[/C][C]0.703291995969173[/C][C]3.19098279901117[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 22 )[/C][C]2.20453971888647[/C][C]0.67569666082856[/C][C]3.2626174534934[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 22 )[/C][C]2.34841628437934[/C][C]0.65058910173925[/C][C]3.60967664244791[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 22 )[/C][C]2.37115411274679[/C][C]0.624245465453413[/C][C]3.79843225777304[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 22 )[/C][C]2.27861662404547[/C][C]0.609642517723889[/C][C]3.73762747479084[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 22 )[/C][C]2.44309918603046[/C][C]0.578873709578686[/C][C]4.22043555546613[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 22 )[/C][C]2.30433333870946[/C][C]0.516011671263537[/C][C]4.46566127674386[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 22 )[/C][C]2.27589451191898[/C][C]0.506012968899673[/C][C]4.49769996383279[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 22 )[/C][C]2.27792268797901[/C][C]0.448252942137558[/C][C]5.08177966912255[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 22 )[/C][C]2.41760018189889[/C][C]0.423625147968818[/C][C]5.70693263487947[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 22 )[/C][C]2.40563481538688[/C][C]0.420935909073983[/C][C]5.71496696653664[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 22 )[/C][C]2.41622278299077[/C][C]0.36688142706084[/C][C]6.58584110497938[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 22 )[/C][C]2.18413445529164[/C][C]0.986156801596176[/C][C]2.21479429210085[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 22 )[/C][C]2.10980020704074[/C][C]0.92326080731119[/C][C]2.28516166865689[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 22 )[/C][C]2.12114937503721[/C][C]0.886182616679297[/C][C]2.39358043716269[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 22 )[/C][C]2.13917872268203[/C][C]0.848259804777442[/C][C]2.52184379200107[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 22 )[/C][C]2.15548827768114[/C][C]0.813370341507792[/C][C]2.65006992225138[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 22 )[/C][C]2.20562459126298[/C][C]0.781471921432117[/C][C]2.82239774811228[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 22 )[/C][C]2.25010490262035[/C][C]0.756309202387992[/C][C]2.97511242163365[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 22 )[/C][C]2.28923217992590[/C][C]0.730247278347451[/C][C]3.13487259426209[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 22 )[/C][C]2.33499789919769[/C][C]0.701398402172136[/C][C]3.32906076199563[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 22 )[/C][C]2.40649429163113[/C][C]0.671670241933797[/C][C]3.58285084166097[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 22 )[/C][C]2.43749603081581[/C][C]0.653589317899413[/C][C]3.72940004382222[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 22 )[/C][C]2.46465435538548[/C][C]0.633591869960439[/C][C]3.88997156093461[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 22 )[/C][C]2.49974918729408[/C][C]0.613929206169758[/C][C]4.07172221515533[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 22 )[/C][C]2.51953887459832[/C][C]0.594035201021668[/C][C]4.24139658771908[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 22 )[/C][C]2.53850534791769[/C][C]0.573772218251148[/C][C]4.42423886547701[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 22 )[/C][C]2.57123207610900[/C][C]0.54953266813244[/C][C]4.67894308239619[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 22 )[/C][C]2.58724868736882[/C][C]0.524605978804844[/C][C]4.93179413102208[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 22 )[/C][C]2.62261310595124[/C][C]0.50723710162638[/C][C]5.17038895132518[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 22 )[/C][C]2.66627396594049[/C][C]0.484341551954828[/C][C]5.5049457457847[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 22 )[/C][C]2.71591285109346[/C][C]0.468649757180757[/C][C]5.79518672415728[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 22 )[/C][C]2.75492296937275[/C][C]0.45255110513856[/C][C]6.0875400326981[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 22 )[/C][C]2.80204914887878[/C][C]0.42684222627412[/C][C]6.56460157032189[/C][/ROW]
[ROW][C]Median[/C][C]3.38615476392453[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]6.16231537082015[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]2.40810961052988[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]2.58724868736882[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]2.40810961052988[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]2.58724868736882[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]2.58724868736882[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]2.40810961052988[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]2.58724868736882[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]2.57123207610900[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]68[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=4889&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=4889&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 Mean2.30113977633661.062808159216122.16515064960907
Geometric MeanNaN
Harmonic Mean-24.4687641149534
Quadratic Mean8.99865787498859
Winsorized Mean ( 1 / 22 )2.254096100704261.03775197436942.17209521771711
Winsorized Mean ( 2 / 22 )2.089104665400130.9794368276456452.13296519635869
Winsorized Mean ( 3 / 22 )2.073424631271520.9645309033103152.14967153893714
Winsorized Mean ( 4 / 22 )2.083534358567420.9354788520514872.22723833253769
Winsorized Mean ( 5 / 22 )1.949044633520590.9029475481708442.15853582798789
Winsorized Mean ( 6 / 22 )1.993688990089640.8562781847860342.32831926062419
Winsorized Mean ( 7 / 22 )2.040658888808280.8372363965048322.43737479322127
Winsorized Mean ( 8 / 22 )2.020022066562460.8221712505350172.45693590629441
Winsorized Mean ( 9 / 22 )1.880785523738150.794627857529752.36687589783842
Winsorized Mean ( 10 / 22 )2.19677664420540.718114244929343.05909075013761
Winsorized Mean ( 11 / 22 )2.244192661819870.7032919959691733.19098279901117
Winsorized Mean ( 12 / 22 )2.204539718886470.675696660828563.2626174534934
Winsorized Mean ( 13 / 22 )2.348416284379340.650589101739253.60967664244791
Winsorized Mean ( 14 / 22 )2.371154112746790.6242454654534133.79843225777304
Winsorized Mean ( 15 / 22 )2.278616624045470.6096425177238893.73762747479084
Winsorized Mean ( 16 / 22 )2.443099186030460.5788737095786864.22043555546613
Winsorized Mean ( 17 / 22 )2.304333338709460.5160116712635374.46566127674386
Winsorized Mean ( 18 / 22 )2.275894511918980.5060129688996734.49769996383279
Winsorized Mean ( 19 / 22 )2.277922687979010.4482529421375585.08177966912255
Winsorized Mean ( 20 / 22 )2.417600181898890.4236251479688185.70693263487947
Winsorized Mean ( 21 / 22 )2.405634815386880.4209359090739835.71496696653664
Winsorized Mean ( 22 / 22 )2.416222782990770.366881427060846.58584110497938
Trimmed Mean ( 1 / 22 )2.184134455291640.9861568015961762.21479429210085
Trimmed Mean ( 2 / 22 )2.109800207040740.923260807311192.28516166865689
Trimmed Mean ( 3 / 22 )2.121149375037210.8861826166792972.39358043716269
Trimmed Mean ( 4 / 22 )2.139178722682030.8482598047774422.52184379200107
Trimmed Mean ( 5 / 22 )2.155488277681140.8133703415077922.65006992225138
Trimmed Mean ( 6 / 22 )2.205624591262980.7814719214321172.82239774811228
Trimmed Mean ( 7 / 22 )2.250104902620350.7563092023879922.97511242163365
Trimmed Mean ( 8 / 22 )2.289232179925900.7302472783474513.13487259426209
Trimmed Mean ( 9 / 22 )2.334997899197690.7013984021721363.32906076199563
Trimmed Mean ( 10 / 22 )2.406494291631130.6716702419337973.58285084166097
Trimmed Mean ( 11 / 22 )2.437496030815810.6535893178994133.72940004382222
Trimmed Mean ( 12 / 22 )2.464654355385480.6335918699604393.88997156093461
Trimmed Mean ( 13 / 22 )2.499749187294080.6139292061697584.07172221515533
Trimmed Mean ( 14 / 22 )2.519538874598320.5940352010216684.24139658771908
Trimmed Mean ( 15 / 22 )2.538505347917690.5737722182511484.42423886547701
Trimmed Mean ( 16 / 22 )2.571232076109000.549532668132444.67894308239619
Trimmed Mean ( 17 / 22 )2.587248687368820.5246059788048444.93179413102208
Trimmed Mean ( 18 / 22 )2.622613105951240.507237101626385.17038895132518
Trimmed Mean ( 19 / 22 )2.666273965940490.4843415519548285.5049457457847
Trimmed Mean ( 20 / 22 )2.715912851093460.4686497571807575.79518672415728
Trimmed Mean ( 21 / 22 )2.754922969372750.452551105138566.0875400326981
Trimmed Mean ( 22 / 22 )2.802049148878780.426842226274126.56460157032189
Median3.38615476392453
Midrange6.16231537082015
Midmean - Weighted Average at Xnp2.40810961052988
Midmean - Weighted Average at X(n+1)p2.58724868736882
Midmean - Empirical Distribution Function2.40810961052988
Midmean - Empirical Distribution Function - Averaging2.58724868736882
Midmean - Empirical Distribution Function - Interpolation2.58724868736882
Midmean - Closest Observation2.40810961052988
Midmean - True Basic - Statistics Graphics Toolkit2.58724868736882
Midmean - MS Excel (old versions)2.57123207610900
Number of observations68



Parameters (Session):
par1 = 60 ; par2 = 1 ; par3 = 0 ; par4 = 0 ; par5 = 12 ;
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')