Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationThu, 13 Dec 2007 01:55:08 -0700
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2007/Dec/13/t1197535194nvui0j5lmw3uuql.htm/, Retrieved Sun, 05 May 2024 09:07:20 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=3313, Retrieved Sun, 05 May 2024 09:07:20 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact231
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [gem. e(t)] [2007-12-13 08:55:08] [c40c597932a04e0e43159741c7e63e4c] [Current]
Feedback Forum

Post a new message
Dataseries X:
-897.8947977
157.8552023
161.2385356
-895.2447977
1155.671869
-352.3339884
-306.6939884
642.1660116
696.0660116
642.9460116
1090.986012
812.0260116
957.0905202
428.6405202
263.4238536
-718.4594798
184.5571869
290.3513295
-176.3086705
146.6513295
-1208.448671
-810.8686705
-740.8286705
-1522.588671
554.3480925
40.39809249
-281.3185742
637.0980925
578.9147592
-897.2910983
629.6489017
60.10890173
100.5089017
609.5889017
-75.17109827
-387.4310983
241.0334104
-230.9165896
-933.7332563
-42.3165896
-753.8999229
-325.2057803
-83.26578035
-1110.30578
-168.3057803
-398.0257803
-967.6857803
22.85421965
-735.6812717
-441.3312717
180.9520617
175.3687283
-1081.614605
1284.479538
-63.38046243
261.3795376
580.1795376
-43.64046243
692.6995376
1075.139538
-118.8959538
45.35404624
609.4373796
843.5540462
-83.62928709




Summary of compuational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135

\begin{tabular}{lllllllll}
\hline
Summary of compuational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 1 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=3313&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]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=3313&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=3313&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'Gwilym Jenkins' @ 72.249.127.135







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean1.44615358607018e-0880.38361790405211.79906506297880e-10
Geometric MeanNaN
Harmonic Mean1811.72087315632
Quadratic Mean643.068943232417
Winsorized Mean ( 1 / 21 )2.8512666452307678.6105015318020.0362708110197883
Winsorized Mean ( 2 / 21 )3.8807138452307777.46112328374880.0500988583784834
Winsorized Mean ( 3 / 21 )4.4735461990769177.0067647911620.0580928988668582
Winsorized Mean ( 4 / 21 )4.2199958544615473.99260727722390.0570326686644615
Winsorized Mean ( 5 / 21 )-1.9018464532307671.776139470754-0.0264969176003913
Winsorized Mean ( 6 / 21 )-1.5039611609230970.5823912900906-0.0213078805270549
Winsorized Mean ( 7 / 21 )-13.926947379384668.4309038466263-0.203518390033237
Winsorized Mean ( 8 / 21 )-14.089430259384668.3130488687771-0.206248008143350
Winsorized Mean ( 9 / 21 )-9.2955316316923164.9092749555723-0.143208064456963
Winsorized Mean ( 10 / 21 )-0.65110892399998963.228648884789-0.0102976883973339
Winsorized Mean ( 11 / 21 )0.7033013267692262.68217390901870.0112201170270521
Winsorized Mean ( 12 / 21 )0.27835511138462362.28898705773880.00446876927259391
Winsorized Mean ( 13 / 21 )-0.28928650861541461.0243721802994-0.00474050773944389
Winsorized Mean ( 14 / 21 )59.36723047650.85875677642781.16729614011162
Winsorized Mean ( 15 / 21 )62.608995722153848.20651831120841.29876618174262
Winsorized Mean ( 16 / 21 )64.905587377538547.76659695240681.35880702245145
Winsorized Mean ( 17 / 21 )67.659703291384645.34391403755581.49214519142185
Winsorized Mean ( 18 / 21 )40.36080243638.57384333978801.04632566893766
Winsorized Mean ( 19 / 21 )5.3489474021538331.70802617514750.168693799248416
Winsorized Mean ( 20 / 21 )4.8713899559999829.36065595304920.16591556959047
Winsorized Mean ( 21 / 21 )20.494636734461526.83487389854240.763731434399428
Trimmed Mean ( 1 / 21 )3.7795100625396876.58695581257240.0493492661046497
Trimmed Mean ( 2 / 21 )4.7686219006557474.13337475588870.0643248997682646
Trimmed Mean ( 3 / 21 )5.2577237955932271.90161123361940.0731238661468943
Trimmed Mean ( 4 / 21 )5.5558029989473669.38066211294840.0800771112547583
Trimmed Mean ( 5 / 21 )5.9504732916363667.4515129655410.0882185295780731
Trimmed Mean ( 6 / 21 )7.8765139837735865.78720240962140.119727145938366
Trimmed Mean ( 7 / 21 )9.8690985733333364.0482849865790.154088412756116
Trimmed Mean ( 8 / 21 )14.378553345714362.42602395715580.230329475341607
Trimmed Mean ( 9 / 21 )19.299880298723460.36081612145830.319741871281
Trimmed Mean ( 10 / 21 )23.889267398666758.59477977941470.407702998263667
Trimmed Mean ( 11 / 21 )27.598859168372156.72013431267740.486579580651725
Trimmed Mean ( 12 / 21 )31.475159079024454.36792763033490.578928799586296
Trimmed Mean ( 13 / 21 )35.808048518974451.30257647396260.69797758670362
Trimmed Mean ( 14 / 21 )40.686066765945947.47001552347610.85708981379677
Trimmed Mean ( 15 / 21 )38.207953212571445.33255508216890.842836966575487
Trimmed Mean ( 16 / 21 )35.003775913333343.09439937016510.812258122283217
Trimmed Mean ( 17 / 21 )31.085191749677439.97795075652450.777558408108356
Trimmed Mean ( 18 / 21 )26.262994487586236.21350385339270.725226550678712
Trimmed Mean ( 19 / 21 )24.377485194074133.31917095798170.73163540667972
Trimmed Mean ( 20 / 21 )26.981390365631.59159769884820.854068560343301
Trimmed Mean ( 21 / 21 )30.105629553913029.74326975741611.01218291732726
Median40.39809249
Midrange-119.0545665
Midmean - Weighted Average at Xnp18.006557685625
Midmean - Weighted Average at X(n+1)p35.0037759133333
Midmean - Empirical Distribution Function35.0037759133333
Midmean - Empirical Distribution Function - Averaging35.0037759133333
Midmean - Empirical Distribution Function - Interpolation35.0037759133333
Midmean - Closest Observation22.2676124952941
Midmean - True Basic - Statistics Graphics Toolkit35.0037759133333
Midmean - MS Excel (old versions)35.0037759133333
Number of observations65

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 1.44615358607018e-08 & 80.3836179040521 & 1.79906506297880e-10 \tabularnewline
Geometric Mean & NaN &  &  \tabularnewline
Harmonic Mean & 1811.72087315632 &  &  \tabularnewline
Quadratic Mean & 643.068943232417 &  &  \tabularnewline
Winsorized Mean ( 1 / 21 ) & 2.85126664523076 & 78.610501531802 & 0.0362708110197883 \tabularnewline
Winsorized Mean ( 2 / 21 ) & 3.88071384523077 & 77.4611232837488 & 0.0500988583784834 \tabularnewline
Winsorized Mean ( 3 / 21 ) & 4.47354619907691 & 77.006764791162 & 0.0580928988668582 \tabularnewline
Winsorized Mean ( 4 / 21 ) & 4.21999585446154 & 73.9926072772239 & 0.0570326686644615 \tabularnewline
Winsorized Mean ( 5 / 21 ) & -1.90184645323076 & 71.776139470754 & -0.0264969176003913 \tabularnewline
Winsorized Mean ( 6 / 21 ) & -1.50396116092309 & 70.5823912900906 & -0.0213078805270549 \tabularnewline
Winsorized Mean ( 7 / 21 ) & -13.9269473793846 & 68.4309038466263 & -0.203518390033237 \tabularnewline
Winsorized Mean ( 8 / 21 ) & -14.0894302593846 & 68.3130488687771 & -0.206248008143350 \tabularnewline
Winsorized Mean ( 9 / 21 ) & -9.29553163169231 & 64.9092749555723 & -0.143208064456963 \tabularnewline
Winsorized Mean ( 10 / 21 ) & -0.651108923999989 & 63.228648884789 & -0.0102976883973339 \tabularnewline
Winsorized Mean ( 11 / 21 ) & 0.70330132676922 & 62.6821739090187 & 0.0112201170270521 \tabularnewline
Winsorized Mean ( 12 / 21 ) & 0.278355111384623 & 62.2889870577388 & 0.00446876927259391 \tabularnewline
Winsorized Mean ( 13 / 21 ) & -0.289286508615414 & 61.0243721802994 & -0.00474050773944389 \tabularnewline
Winsorized Mean ( 14 / 21 ) & 59.367230476 & 50.8587567764278 & 1.16729614011162 \tabularnewline
Winsorized Mean ( 15 / 21 ) & 62.6089957221538 & 48.2065183112084 & 1.29876618174262 \tabularnewline
Winsorized Mean ( 16 / 21 ) & 64.9055873775385 & 47.7665969524068 & 1.35880702245145 \tabularnewline
Winsorized Mean ( 17 / 21 ) & 67.6597032913846 & 45.3439140375558 & 1.49214519142185 \tabularnewline
Winsorized Mean ( 18 / 21 ) & 40.360802436 & 38.5738433397880 & 1.04632566893766 \tabularnewline
Winsorized Mean ( 19 / 21 ) & 5.34894740215383 & 31.7080261751475 & 0.168693799248416 \tabularnewline
Winsorized Mean ( 20 / 21 ) & 4.87138995599998 & 29.3606559530492 & 0.16591556959047 \tabularnewline
Winsorized Mean ( 21 / 21 ) & 20.4946367344615 & 26.8348738985424 & 0.763731434399428 \tabularnewline
Trimmed Mean ( 1 / 21 ) & 3.77951006253968 & 76.5869558125724 & 0.0493492661046497 \tabularnewline
Trimmed Mean ( 2 / 21 ) & 4.76862190065574 & 74.1333747558887 & 0.0643248997682646 \tabularnewline
Trimmed Mean ( 3 / 21 ) & 5.25772379559322 & 71.9016112336194 & 0.0731238661468943 \tabularnewline
Trimmed Mean ( 4 / 21 ) & 5.55580299894736 & 69.3806621129484 & 0.0800771112547583 \tabularnewline
Trimmed Mean ( 5 / 21 ) & 5.95047329163636 & 67.451512965541 & 0.0882185295780731 \tabularnewline
Trimmed Mean ( 6 / 21 ) & 7.87651398377358 & 65.7872024096214 & 0.119727145938366 \tabularnewline
Trimmed Mean ( 7 / 21 ) & 9.86909857333333 & 64.048284986579 & 0.154088412756116 \tabularnewline
Trimmed Mean ( 8 / 21 ) & 14.3785533457143 & 62.4260239571558 & 0.230329475341607 \tabularnewline
Trimmed Mean ( 9 / 21 ) & 19.2998802987234 & 60.3608161214583 & 0.319741871281 \tabularnewline
Trimmed Mean ( 10 / 21 ) & 23.8892673986667 & 58.5947797794147 & 0.407702998263667 \tabularnewline
Trimmed Mean ( 11 / 21 ) & 27.5988591683721 & 56.7201343126774 & 0.486579580651725 \tabularnewline
Trimmed Mean ( 12 / 21 ) & 31.4751590790244 & 54.3679276303349 & 0.578928799586296 \tabularnewline
Trimmed Mean ( 13 / 21 ) & 35.8080485189744 & 51.3025764739626 & 0.69797758670362 \tabularnewline
Trimmed Mean ( 14 / 21 ) & 40.6860667659459 & 47.4700155234761 & 0.85708981379677 \tabularnewline
Trimmed Mean ( 15 / 21 ) & 38.2079532125714 & 45.3325550821689 & 0.842836966575487 \tabularnewline
Trimmed Mean ( 16 / 21 ) & 35.0037759133333 & 43.0943993701651 & 0.812258122283217 \tabularnewline
Trimmed Mean ( 17 / 21 ) & 31.0851917496774 & 39.9779507565245 & 0.777558408108356 \tabularnewline
Trimmed Mean ( 18 / 21 ) & 26.2629944875862 & 36.2135038533927 & 0.725226550678712 \tabularnewline
Trimmed Mean ( 19 / 21 ) & 24.3774851940741 & 33.3191709579817 & 0.73163540667972 \tabularnewline
Trimmed Mean ( 20 / 21 ) & 26.9813903656 & 31.5915976988482 & 0.854068560343301 \tabularnewline
Trimmed Mean ( 21 / 21 ) & 30.1056295539130 & 29.7432697574161 & 1.01218291732726 \tabularnewline
Median & 40.39809249 &  &  \tabularnewline
Midrange & -119.0545665 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 18.006557685625 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 35.0037759133333 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 35.0037759133333 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 35.0037759133333 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 35.0037759133333 &  &  \tabularnewline
Midmean - Closest Observation & 22.2676124952941 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 35.0037759133333 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 35.0037759133333 &  &  \tabularnewline
Number of observations & 65 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=3313&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]1.44615358607018e-08[/C][C]80.3836179040521[/C][C]1.79906506297880e-10[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]NaN[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]1811.72087315632[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]643.068943232417[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 21 )[/C][C]2.85126664523076[/C][C]78.610501531802[/C][C]0.0362708110197883[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 21 )[/C][C]3.88071384523077[/C][C]77.4611232837488[/C][C]0.0500988583784834[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 21 )[/C][C]4.47354619907691[/C][C]77.006764791162[/C][C]0.0580928988668582[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 21 )[/C][C]4.21999585446154[/C][C]73.9926072772239[/C][C]0.0570326686644615[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 21 )[/C][C]-1.90184645323076[/C][C]71.776139470754[/C][C]-0.0264969176003913[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 21 )[/C][C]-1.50396116092309[/C][C]70.5823912900906[/C][C]-0.0213078805270549[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 21 )[/C][C]-13.9269473793846[/C][C]68.4309038466263[/C][C]-0.203518390033237[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 21 )[/C][C]-14.0894302593846[/C][C]68.3130488687771[/C][C]-0.206248008143350[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 21 )[/C][C]-9.29553163169231[/C][C]64.9092749555723[/C][C]-0.143208064456963[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 21 )[/C][C]-0.651108923999989[/C][C]63.228648884789[/C][C]-0.0102976883973339[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 21 )[/C][C]0.70330132676922[/C][C]62.6821739090187[/C][C]0.0112201170270521[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 21 )[/C][C]0.278355111384623[/C][C]62.2889870577388[/C][C]0.00446876927259391[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 21 )[/C][C]-0.289286508615414[/C][C]61.0243721802994[/C][C]-0.00474050773944389[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 21 )[/C][C]59.367230476[/C][C]50.8587567764278[/C][C]1.16729614011162[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 21 )[/C][C]62.6089957221538[/C][C]48.2065183112084[/C][C]1.29876618174262[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 21 )[/C][C]64.9055873775385[/C][C]47.7665969524068[/C][C]1.35880702245145[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 21 )[/C][C]67.6597032913846[/C][C]45.3439140375558[/C][C]1.49214519142185[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 21 )[/C][C]40.360802436[/C][C]38.5738433397880[/C][C]1.04632566893766[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 21 )[/C][C]5.34894740215383[/C][C]31.7080261751475[/C][C]0.168693799248416[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 21 )[/C][C]4.87138995599998[/C][C]29.3606559530492[/C][C]0.16591556959047[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 21 )[/C][C]20.4946367344615[/C][C]26.8348738985424[/C][C]0.763731434399428[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 21 )[/C][C]3.77951006253968[/C][C]76.5869558125724[/C][C]0.0493492661046497[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 21 )[/C][C]4.76862190065574[/C][C]74.1333747558887[/C][C]0.0643248997682646[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 21 )[/C][C]5.25772379559322[/C][C]71.9016112336194[/C][C]0.0731238661468943[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 21 )[/C][C]5.55580299894736[/C][C]69.3806621129484[/C][C]0.0800771112547583[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 21 )[/C][C]5.95047329163636[/C][C]67.451512965541[/C][C]0.0882185295780731[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 21 )[/C][C]7.87651398377358[/C][C]65.7872024096214[/C][C]0.119727145938366[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 21 )[/C][C]9.86909857333333[/C][C]64.048284986579[/C][C]0.154088412756116[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 21 )[/C][C]14.3785533457143[/C][C]62.4260239571558[/C][C]0.230329475341607[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 21 )[/C][C]19.2998802987234[/C][C]60.3608161214583[/C][C]0.319741871281[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 21 )[/C][C]23.8892673986667[/C][C]58.5947797794147[/C][C]0.407702998263667[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 21 )[/C][C]27.5988591683721[/C][C]56.7201343126774[/C][C]0.486579580651725[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 21 )[/C][C]31.4751590790244[/C][C]54.3679276303349[/C][C]0.578928799586296[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 21 )[/C][C]35.8080485189744[/C][C]51.3025764739626[/C][C]0.69797758670362[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 21 )[/C][C]40.6860667659459[/C][C]47.4700155234761[/C][C]0.85708981379677[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 21 )[/C][C]38.2079532125714[/C][C]45.3325550821689[/C][C]0.842836966575487[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 21 )[/C][C]35.0037759133333[/C][C]43.0943993701651[/C][C]0.812258122283217[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 21 )[/C][C]31.0851917496774[/C][C]39.9779507565245[/C][C]0.777558408108356[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 21 )[/C][C]26.2629944875862[/C][C]36.2135038533927[/C][C]0.725226550678712[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 21 )[/C][C]24.3774851940741[/C][C]33.3191709579817[/C][C]0.73163540667972[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 21 )[/C][C]26.9813903656[/C][C]31.5915976988482[/C][C]0.854068560343301[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 21 )[/C][C]30.1056295539130[/C][C]29.7432697574161[/C][C]1.01218291732726[/C][/ROW]
[ROW][C]Median[/C][C]40.39809249[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]-119.0545665[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]18.006557685625[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]35.0037759133333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]35.0037759133333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]35.0037759133333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]35.0037759133333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]22.2676124952941[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]35.0037759133333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]35.0037759133333[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]65[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=3313&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=3313&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 Mean1.44615358607018e-0880.38361790405211.79906506297880e-10
Geometric MeanNaN
Harmonic Mean1811.72087315632
Quadratic Mean643.068943232417
Winsorized Mean ( 1 / 21 )2.8512666452307678.6105015318020.0362708110197883
Winsorized Mean ( 2 / 21 )3.8807138452307777.46112328374880.0500988583784834
Winsorized Mean ( 3 / 21 )4.4735461990769177.0067647911620.0580928988668582
Winsorized Mean ( 4 / 21 )4.2199958544615473.99260727722390.0570326686644615
Winsorized Mean ( 5 / 21 )-1.9018464532307671.776139470754-0.0264969176003913
Winsorized Mean ( 6 / 21 )-1.5039611609230970.5823912900906-0.0213078805270549
Winsorized Mean ( 7 / 21 )-13.926947379384668.4309038466263-0.203518390033237
Winsorized Mean ( 8 / 21 )-14.089430259384668.3130488687771-0.206248008143350
Winsorized Mean ( 9 / 21 )-9.2955316316923164.9092749555723-0.143208064456963
Winsorized Mean ( 10 / 21 )-0.65110892399998963.228648884789-0.0102976883973339
Winsorized Mean ( 11 / 21 )0.7033013267692262.68217390901870.0112201170270521
Winsorized Mean ( 12 / 21 )0.27835511138462362.28898705773880.00446876927259391
Winsorized Mean ( 13 / 21 )-0.28928650861541461.0243721802994-0.00474050773944389
Winsorized Mean ( 14 / 21 )59.36723047650.85875677642781.16729614011162
Winsorized Mean ( 15 / 21 )62.608995722153848.20651831120841.29876618174262
Winsorized Mean ( 16 / 21 )64.905587377538547.76659695240681.35880702245145
Winsorized Mean ( 17 / 21 )67.659703291384645.34391403755581.49214519142185
Winsorized Mean ( 18 / 21 )40.36080243638.57384333978801.04632566893766
Winsorized Mean ( 19 / 21 )5.3489474021538331.70802617514750.168693799248416
Winsorized Mean ( 20 / 21 )4.8713899559999829.36065595304920.16591556959047
Winsorized Mean ( 21 / 21 )20.494636734461526.83487389854240.763731434399428
Trimmed Mean ( 1 / 21 )3.7795100625396876.58695581257240.0493492661046497
Trimmed Mean ( 2 / 21 )4.7686219006557474.13337475588870.0643248997682646
Trimmed Mean ( 3 / 21 )5.2577237955932271.90161123361940.0731238661468943
Trimmed Mean ( 4 / 21 )5.5558029989473669.38066211294840.0800771112547583
Trimmed Mean ( 5 / 21 )5.9504732916363667.4515129655410.0882185295780731
Trimmed Mean ( 6 / 21 )7.8765139837735865.78720240962140.119727145938366
Trimmed Mean ( 7 / 21 )9.8690985733333364.0482849865790.154088412756116
Trimmed Mean ( 8 / 21 )14.378553345714362.42602395715580.230329475341607
Trimmed Mean ( 9 / 21 )19.299880298723460.36081612145830.319741871281
Trimmed Mean ( 10 / 21 )23.889267398666758.59477977941470.407702998263667
Trimmed Mean ( 11 / 21 )27.598859168372156.72013431267740.486579580651725
Trimmed Mean ( 12 / 21 )31.475159079024454.36792763033490.578928799586296
Trimmed Mean ( 13 / 21 )35.808048518974451.30257647396260.69797758670362
Trimmed Mean ( 14 / 21 )40.686066765945947.47001552347610.85708981379677
Trimmed Mean ( 15 / 21 )38.207953212571445.33255508216890.842836966575487
Trimmed Mean ( 16 / 21 )35.003775913333343.09439937016510.812258122283217
Trimmed Mean ( 17 / 21 )31.085191749677439.97795075652450.777558408108356
Trimmed Mean ( 18 / 21 )26.262994487586236.21350385339270.725226550678712
Trimmed Mean ( 19 / 21 )24.377485194074133.31917095798170.73163540667972
Trimmed Mean ( 20 / 21 )26.981390365631.59159769884820.854068560343301
Trimmed Mean ( 21 / 21 )30.105629553913029.74326975741611.01218291732726
Median40.39809249
Midrange-119.0545665
Midmean - Weighted Average at Xnp18.006557685625
Midmean - Weighted Average at X(n+1)p35.0037759133333
Midmean - Empirical Distribution Function35.0037759133333
Midmean - Empirical Distribution Function - Averaging35.0037759133333
Midmean - Empirical Distribution Function - Interpolation35.0037759133333
Midmean - Closest Observation22.2676124952941
Midmean - True Basic - Statistics Graphics Toolkit35.0037759133333
Midmean - MS Excel (old versions)35.0037759133333
Number of observations65



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')