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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, 17 Dec 2007 03:50:56 -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/17/t1197887663saalcnrfz2lydow.htm/, Retrieved Sat, 04 May 2024 00:36:55 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=4333, Retrieved Sat, 04 May 2024 00:36:55 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact189
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [paper - central t...] [2007-12-17 10:50:56] [5b9249e3962a4d9b95a2c513d8084bf7] [Current]
-    D    [Central Tendency] [paper - central t...] [2008-12-27 12:37:53] [1aad2bd7746abaf3ab17fe0d80878872]
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Dataseries X:
0.084299365852926 
-15.5692124815993 
-6.9953619930182 
-2.07575919037298 
6.06472185178652 
3.10063183929146 
-7.27872604143293 
11.9305592423578 
-15.1800926797913 
-4.96965957564265 
-3.06184332688462 
5.17876413221274 
-2.29638814463019 
-1.85853257792512 
-8.74637895628288 
-8.02346934029272 
4.80319999595127 
3.90173526693944 
-11.3069080265042 
4.26225040152088 
-6.88628010104842 
4.12797896412461 
4.24824928932737 
-5.91811547446539 
-2.62127541719435 
-5.11947651478644 
-6.19169292552164 
1.57682830128841 
6.93381888926023 
1.30435330636300 
0.701451547474772 
18.1487693268603 
-13.6251962127511 
-8.9684198944174 
-3.48024416476534 
0.133268755660886 
0.156896176204026 
-1.28412130463800 
-8.4586972345603 
-2.91518278408049 
0.150465578819962 
3.86877987666889 
7.70993797103159 
-4.11650976301151 
-2.74475852656699 
3.19286810860467 
-6.2212027713738 
1.25489355791219 
4.23585013027417 
0.153440583363572 
-2.05719003274709 
2.14422869581576 
-1.68156215590428 
5.0318450949173 
2.24823311061623 
-6.58372573676435 
-2.85420176875137 
5.0379752614482 
4.43711208741108 
-0.675511401722624 
-2.50684702275299 
2.35909448398834 
-6.31849429304567 
-3.81949862816358 
2.17307118170725 
4.13663986179168 
-6.96229654560136 
5.28008601863276 
4.2774558989149 




Summary of compuational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 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 & 2 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=4333&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]2 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=4333&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=4333&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 time2 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean-0.9423634616611070.733091035651206-1.28546580960986
Geometric MeanNaN
Harmonic Mean1.79653775616133
Quadratic Mean6.11823312888783
Winsorized Mean ( 1 / 23 )-1.026843030975520.701827899444391-1.46309804980456
Winsorized Mean ( 2 / 23 )-1.104110416607000.66008683252889-1.67267450613579
Winsorized Mean ( 3 / 23 )-1.037059585977630.627377636143494-1.65300693909407
Winsorized Mean ( 4 / 23 )-0.951877493536290.588253795036159-1.61814084595541
Winsorized Mean ( 5 / 23 )-0.9926452395521760.575499130813947-1.72484229150485
Winsorized Mean ( 6 / 23 )-0.9764400364823880.569195909712769-1.71547268668028
Winsorized Mean ( 7 / 23 )-0.9465694109096160.558552240694174-1.69468375909335
Winsorized Mean ( 8 / 23 )-0.8609331057120630.542881914042571-1.58585704080861
Winsorized Mean ( 9 / 23 )-0.8537958514361460.53181653071723-1.60543308100010
Winsorized Mean ( 10 / 23 )-0.9020599762366310.522866430013191-1.72522067674889
Winsorized Mean ( 11 / 23 )-0.9153938484594670.517013583708869-1.77054119524822
Winsorized Mean ( 12 / 23 )-0.8654201324785890.507795864468153-1.70426778363979
Winsorized Mean ( 13 / 23 )-0.8180868816115270.499216282053339-1.63874238686013
Winsorized Mean ( 14 / 23 )-0.8008623442686090.495653950845738-1.61576911250701
Winsorized Mean ( 15 / 23 )-0.8160146100578110.491412272060955-1.6605499220349
Winsorized Mean ( 16 / 23 )-0.7545846846342330.481002448239875-1.56877514323570
Winsorized Mean ( 17 / 23 )-0.6135597648893890.442357330727722-1.38702293885358
Winsorized Mean ( 18 / 23 )-0.5830741434441960.435241762239838-1.33965578221075
Winsorized Mean ( 19 / 23 )-0.5342694645054790.373521569678827-1.43035772998296
Winsorized Mean ( 20 / 23 )-0.4749144310171540.357599816130893-1.32806117227790
Winsorized Mean ( 21 / 23 )-0.5973483546403780.311035017015696-1.92051801874846
Winsorized Mean ( 22 / 23 )-0.4992922934927060.288261792617538-1.73207933302198
Winsorized Mean ( 23 / 23 )-0.4754594221943220.278407035605421-1.70778522590276
Trimmed Mean ( 1 / 23 )-1.008994562684740.662846248495786-1.52221509131940
Trimmed Mean ( 2 / 23 )-0.9900477271145210.615230819945521-1.60922973137495
Trimmed Mean ( 3 / 23 )-0.9275848257257840.585499544055828-1.58426225117152
Trimmed Mean ( 4 / 23 )-0.8863074571062360.565245437159129-1.56800462036586
Trimmed Mean ( 5 / 23 )-0.8671365566245680.555436382507464-1.5611806931155
Trimmed Mean ( 6 / 23 )-0.8367502439157790.547206487917104-1.52913070731453
Trimmed Mean ( 7 / 23 )-0.8075423781973060.538569285692856-1.49942152226231
Trimmed Mean ( 8 / 23 )-0.781685598528440.53035362392971-1.47389508293817
Trimmed Mean ( 9 / 23 )-0.7682834465782690.523628356943778-1.46723040566873
Trimmed Mean ( 10 / 23 )-0.754903954661730.517281809632188-1.45936690717677
Trimmed Mean ( 11 / 23 )-0.754903954661730.510680821752886-1.47823047685746
Trimmed Mean ( 12 / 23 )-0.707917447068910.502942225308569-1.40755222259293
Trimmed Mean ( 13 / 23 )-0.6868560414618020.494485638772429-1.38903132387613
Trimmed Mean ( 14 / 23 )-0.6698674336375410.484839383542983-1.38162751701906
Trimmed Mean ( 15 / 23 )-0.6533131317446040.472324096346082-1.38318823197601
Trimmed Mean ( 16 / 23 )-0.6330853803867460.456013389538782-1.38830436761310
Trimmed Mean ( 17 / 23 )-0.618114930399110.436159612335962-1.41717598997450
Trimmed Mean ( 18 / 23 )-0.6186751913976310.419334547417986-1.47537376828851
Trimmed Mean ( 19 / 23 )-0.6230774715209060.397058628542531-1.56923292111297
Trimmed Mean ( 20 / 23 )-0.634198619404870.384186443092272-1.65075741429156
Trimmed Mean ( 21 / 23 )-0.6545515990321890.369307293811772-1.77237658177907
Trimmed Mean ( 22 / 23 )-0.6545515990321890.362114796686531-1.80758037236134
Trimmed Mean ( 23 / 23 )-0.6842666642097270.35685319735429-1.91750184468818
Median-0.675511401722624
Midrange1.2897784226305
Midmean - Weighted Average at Xnp-0.751051700909066
Midmean - Weighted Average at X(n+1)p-0.618114930399109
Midmean - Empirical Distribution Function-0.618114930399109
Midmean - Empirical Distribution Function - Averaging-0.618114930399109
Midmean - Empirical Distribution Function - Interpolation-0.618114930399109
Midmean - Closest Observation-0.765337167734284
Midmean - True Basic - Statistics Graphics Toolkit-0.618114930399109
Midmean - MS Excel (old versions)-0.618114930399109
Number of observations69

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & -0.942363461661107 & 0.733091035651206 & -1.28546580960986 \tabularnewline
Geometric Mean & NaN &  &  \tabularnewline
Harmonic Mean & 1.79653775616133 &  &  \tabularnewline
Quadratic Mean & 6.11823312888783 &  &  \tabularnewline
Winsorized Mean ( 1 / 23 ) & -1.02684303097552 & 0.701827899444391 & -1.46309804980456 \tabularnewline
Winsorized Mean ( 2 / 23 ) & -1.10411041660700 & 0.66008683252889 & -1.67267450613579 \tabularnewline
Winsorized Mean ( 3 / 23 ) & -1.03705958597763 & 0.627377636143494 & -1.65300693909407 \tabularnewline
Winsorized Mean ( 4 / 23 ) & -0.95187749353629 & 0.588253795036159 & -1.61814084595541 \tabularnewline
Winsorized Mean ( 5 / 23 ) & -0.992645239552176 & 0.575499130813947 & -1.72484229150485 \tabularnewline
Winsorized Mean ( 6 / 23 ) & -0.976440036482388 & 0.569195909712769 & -1.71547268668028 \tabularnewline
Winsorized Mean ( 7 / 23 ) & -0.946569410909616 & 0.558552240694174 & -1.69468375909335 \tabularnewline
Winsorized Mean ( 8 / 23 ) & -0.860933105712063 & 0.542881914042571 & -1.58585704080861 \tabularnewline
Winsorized Mean ( 9 / 23 ) & -0.853795851436146 & 0.53181653071723 & -1.60543308100010 \tabularnewline
Winsorized Mean ( 10 / 23 ) & -0.902059976236631 & 0.522866430013191 & -1.72522067674889 \tabularnewline
Winsorized Mean ( 11 / 23 ) & -0.915393848459467 & 0.517013583708869 & -1.77054119524822 \tabularnewline
Winsorized Mean ( 12 / 23 ) & -0.865420132478589 & 0.507795864468153 & -1.70426778363979 \tabularnewline
Winsorized Mean ( 13 / 23 ) & -0.818086881611527 & 0.499216282053339 & -1.63874238686013 \tabularnewline
Winsorized Mean ( 14 / 23 ) & -0.800862344268609 & 0.495653950845738 & -1.61576911250701 \tabularnewline
Winsorized Mean ( 15 / 23 ) & -0.816014610057811 & 0.491412272060955 & -1.6605499220349 \tabularnewline
Winsorized Mean ( 16 / 23 ) & -0.754584684634233 & 0.481002448239875 & -1.56877514323570 \tabularnewline
Winsorized Mean ( 17 / 23 ) & -0.613559764889389 & 0.442357330727722 & -1.38702293885358 \tabularnewline
Winsorized Mean ( 18 / 23 ) & -0.583074143444196 & 0.435241762239838 & -1.33965578221075 \tabularnewline
Winsorized Mean ( 19 / 23 ) & -0.534269464505479 & 0.373521569678827 & -1.43035772998296 \tabularnewline
Winsorized Mean ( 20 / 23 ) & -0.474914431017154 & 0.357599816130893 & -1.32806117227790 \tabularnewline
Winsorized Mean ( 21 / 23 ) & -0.597348354640378 & 0.311035017015696 & -1.92051801874846 \tabularnewline
Winsorized Mean ( 22 / 23 ) & -0.499292293492706 & 0.288261792617538 & -1.73207933302198 \tabularnewline
Winsorized Mean ( 23 / 23 ) & -0.475459422194322 & 0.278407035605421 & -1.70778522590276 \tabularnewline
Trimmed Mean ( 1 / 23 ) & -1.00899456268474 & 0.662846248495786 & -1.52221509131940 \tabularnewline
Trimmed Mean ( 2 / 23 ) & -0.990047727114521 & 0.615230819945521 & -1.60922973137495 \tabularnewline
Trimmed Mean ( 3 / 23 ) & -0.927584825725784 & 0.585499544055828 & -1.58426225117152 \tabularnewline
Trimmed Mean ( 4 / 23 ) & -0.886307457106236 & 0.565245437159129 & -1.56800462036586 \tabularnewline
Trimmed Mean ( 5 / 23 ) & -0.867136556624568 & 0.555436382507464 & -1.5611806931155 \tabularnewline
Trimmed Mean ( 6 / 23 ) & -0.836750243915779 & 0.547206487917104 & -1.52913070731453 \tabularnewline
Trimmed Mean ( 7 / 23 ) & -0.807542378197306 & 0.538569285692856 & -1.49942152226231 \tabularnewline
Trimmed Mean ( 8 / 23 ) & -0.78168559852844 & 0.53035362392971 & -1.47389508293817 \tabularnewline
Trimmed Mean ( 9 / 23 ) & -0.768283446578269 & 0.523628356943778 & -1.46723040566873 \tabularnewline
Trimmed Mean ( 10 / 23 ) & -0.75490395466173 & 0.517281809632188 & -1.45936690717677 \tabularnewline
Trimmed Mean ( 11 / 23 ) & -0.75490395466173 & 0.510680821752886 & -1.47823047685746 \tabularnewline
Trimmed Mean ( 12 / 23 ) & -0.70791744706891 & 0.502942225308569 & -1.40755222259293 \tabularnewline
Trimmed Mean ( 13 / 23 ) & -0.686856041461802 & 0.494485638772429 & -1.38903132387613 \tabularnewline
Trimmed Mean ( 14 / 23 ) & -0.669867433637541 & 0.484839383542983 & -1.38162751701906 \tabularnewline
Trimmed Mean ( 15 / 23 ) & -0.653313131744604 & 0.472324096346082 & -1.38318823197601 \tabularnewline
Trimmed Mean ( 16 / 23 ) & -0.633085380386746 & 0.456013389538782 & -1.38830436761310 \tabularnewline
Trimmed Mean ( 17 / 23 ) & -0.61811493039911 & 0.436159612335962 & -1.41717598997450 \tabularnewline
Trimmed Mean ( 18 / 23 ) & -0.618675191397631 & 0.419334547417986 & -1.47537376828851 \tabularnewline
Trimmed Mean ( 19 / 23 ) & -0.623077471520906 & 0.397058628542531 & -1.56923292111297 \tabularnewline
Trimmed Mean ( 20 / 23 ) & -0.63419861940487 & 0.384186443092272 & -1.65075741429156 \tabularnewline
Trimmed Mean ( 21 / 23 ) & -0.654551599032189 & 0.369307293811772 & -1.77237658177907 \tabularnewline
Trimmed Mean ( 22 / 23 ) & -0.654551599032189 & 0.362114796686531 & -1.80758037236134 \tabularnewline
Trimmed Mean ( 23 / 23 ) & -0.684266664209727 & 0.35685319735429 & -1.91750184468818 \tabularnewline
Median & -0.675511401722624 &  &  \tabularnewline
Midrange & 1.2897784226305 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & -0.751051700909066 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & -0.618114930399109 &  &  \tabularnewline
Midmean - Empirical Distribution Function & -0.618114930399109 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & -0.618114930399109 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & -0.618114930399109 &  &  \tabularnewline
Midmean - Closest Observation & -0.765337167734284 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & -0.618114930399109 &  &  \tabularnewline
Midmean - MS Excel (old versions) & -0.618114930399109 &  &  \tabularnewline
Number of observations & 69 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=4333&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]-0.942363461661107[/C][C]0.733091035651206[/C][C]-1.28546580960986[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]NaN[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]1.79653775616133[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]6.11823312888783[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 23 )[/C][C]-1.02684303097552[/C][C]0.701827899444391[/C][C]-1.46309804980456[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 23 )[/C][C]-1.10411041660700[/C][C]0.66008683252889[/C][C]-1.67267450613579[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 23 )[/C][C]-1.03705958597763[/C][C]0.627377636143494[/C][C]-1.65300693909407[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 23 )[/C][C]-0.95187749353629[/C][C]0.588253795036159[/C][C]-1.61814084595541[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 23 )[/C][C]-0.992645239552176[/C][C]0.575499130813947[/C][C]-1.72484229150485[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 23 )[/C][C]-0.976440036482388[/C][C]0.569195909712769[/C][C]-1.71547268668028[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 23 )[/C][C]-0.946569410909616[/C][C]0.558552240694174[/C][C]-1.69468375909335[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 23 )[/C][C]-0.860933105712063[/C][C]0.542881914042571[/C][C]-1.58585704080861[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 23 )[/C][C]-0.853795851436146[/C][C]0.53181653071723[/C][C]-1.60543308100010[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 23 )[/C][C]-0.902059976236631[/C][C]0.522866430013191[/C][C]-1.72522067674889[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 23 )[/C][C]-0.915393848459467[/C][C]0.517013583708869[/C][C]-1.77054119524822[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 23 )[/C][C]-0.865420132478589[/C][C]0.507795864468153[/C][C]-1.70426778363979[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 23 )[/C][C]-0.818086881611527[/C][C]0.499216282053339[/C][C]-1.63874238686013[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 23 )[/C][C]-0.800862344268609[/C][C]0.495653950845738[/C][C]-1.61576911250701[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 23 )[/C][C]-0.816014610057811[/C][C]0.491412272060955[/C][C]-1.6605499220349[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 23 )[/C][C]-0.754584684634233[/C][C]0.481002448239875[/C][C]-1.56877514323570[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 23 )[/C][C]-0.613559764889389[/C][C]0.442357330727722[/C][C]-1.38702293885358[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 23 )[/C][C]-0.583074143444196[/C][C]0.435241762239838[/C][C]-1.33965578221075[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 23 )[/C][C]-0.534269464505479[/C][C]0.373521569678827[/C][C]-1.43035772998296[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 23 )[/C][C]-0.474914431017154[/C][C]0.357599816130893[/C][C]-1.32806117227790[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 23 )[/C][C]-0.597348354640378[/C][C]0.311035017015696[/C][C]-1.92051801874846[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 23 )[/C][C]-0.499292293492706[/C][C]0.288261792617538[/C][C]-1.73207933302198[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 23 )[/C][C]-0.475459422194322[/C][C]0.278407035605421[/C][C]-1.70778522590276[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 23 )[/C][C]-1.00899456268474[/C][C]0.662846248495786[/C][C]-1.52221509131940[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 23 )[/C][C]-0.990047727114521[/C][C]0.615230819945521[/C][C]-1.60922973137495[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 23 )[/C][C]-0.927584825725784[/C][C]0.585499544055828[/C][C]-1.58426225117152[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 23 )[/C][C]-0.886307457106236[/C][C]0.565245437159129[/C][C]-1.56800462036586[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 23 )[/C][C]-0.867136556624568[/C][C]0.555436382507464[/C][C]-1.5611806931155[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 23 )[/C][C]-0.836750243915779[/C][C]0.547206487917104[/C][C]-1.52913070731453[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 23 )[/C][C]-0.807542378197306[/C][C]0.538569285692856[/C][C]-1.49942152226231[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 23 )[/C][C]-0.78168559852844[/C][C]0.53035362392971[/C][C]-1.47389508293817[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 23 )[/C][C]-0.768283446578269[/C][C]0.523628356943778[/C][C]-1.46723040566873[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 23 )[/C][C]-0.75490395466173[/C][C]0.517281809632188[/C][C]-1.45936690717677[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 23 )[/C][C]-0.75490395466173[/C][C]0.510680821752886[/C][C]-1.47823047685746[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 23 )[/C][C]-0.70791744706891[/C][C]0.502942225308569[/C][C]-1.40755222259293[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 23 )[/C][C]-0.686856041461802[/C][C]0.494485638772429[/C][C]-1.38903132387613[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 23 )[/C][C]-0.669867433637541[/C][C]0.484839383542983[/C][C]-1.38162751701906[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 23 )[/C][C]-0.653313131744604[/C][C]0.472324096346082[/C][C]-1.38318823197601[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 23 )[/C][C]-0.633085380386746[/C][C]0.456013389538782[/C][C]-1.38830436761310[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 23 )[/C][C]-0.61811493039911[/C][C]0.436159612335962[/C][C]-1.41717598997450[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 23 )[/C][C]-0.618675191397631[/C][C]0.419334547417986[/C][C]-1.47537376828851[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 23 )[/C][C]-0.623077471520906[/C][C]0.397058628542531[/C][C]-1.56923292111297[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 23 )[/C][C]-0.63419861940487[/C][C]0.384186443092272[/C][C]-1.65075741429156[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 23 )[/C][C]-0.654551599032189[/C][C]0.369307293811772[/C][C]-1.77237658177907[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 23 )[/C][C]-0.654551599032189[/C][C]0.362114796686531[/C][C]-1.80758037236134[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 23 )[/C][C]-0.684266664209727[/C][C]0.35685319735429[/C][C]-1.91750184468818[/C][/ROW]
[ROW][C]Median[/C][C]-0.675511401722624[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]1.2897784226305[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]-0.751051700909066[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]-0.618114930399109[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]-0.618114930399109[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]-0.618114930399109[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]-0.618114930399109[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]-0.765337167734284[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]-0.618114930399109[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]-0.618114930399109[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]69[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=4333&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=4333&T=1

As an alternative you can also use a QR Code:  

The GUIDs for individual cells are displayed in the table below:

Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean-0.9423634616611070.733091035651206-1.28546580960986
Geometric MeanNaN
Harmonic Mean1.79653775616133
Quadratic Mean6.11823312888783
Winsorized Mean ( 1 / 23 )-1.026843030975520.701827899444391-1.46309804980456
Winsorized Mean ( 2 / 23 )-1.104110416607000.66008683252889-1.67267450613579
Winsorized Mean ( 3 / 23 )-1.037059585977630.627377636143494-1.65300693909407
Winsorized Mean ( 4 / 23 )-0.951877493536290.588253795036159-1.61814084595541
Winsorized Mean ( 5 / 23 )-0.9926452395521760.575499130813947-1.72484229150485
Winsorized Mean ( 6 / 23 )-0.9764400364823880.569195909712769-1.71547268668028
Winsorized Mean ( 7 / 23 )-0.9465694109096160.558552240694174-1.69468375909335
Winsorized Mean ( 8 / 23 )-0.8609331057120630.542881914042571-1.58585704080861
Winsorized Mean ( 9 / 23 )-0.8537958514361460.53181653071723-1.60543308100010
Winsorized Mean ( 10 / 23 )-0.9020599762366310.522866430013191-1.72522067674889
Winsorized Mean ( 11 / 23 )-0.9153938484594670.517013583708869-1.77054119524822
Winsorized Mean ( 12 / 23 )-0.8654201324785890.507795864468153-1.70426778363979
Winsorized Mean ( 13 / 23 )-0.8180868816115270.499216282053339-1.63874238686013
Winsorized Mean ( 14 / 23 )-0.8008623442686090.495653950845738-1.61576911250701
Winsorized Mean ( 15 / 23 )-0.8160146100578110.491412272060955-1.6605499220349
Winsorized Mean ( 16 / 23 )-0.7545846846342330.481002448239875-1.56877514323570
Winsorized Mean ( 17 / 23 )-0.6135597648893890.442357330727722-1.38702293885358
Winsorized Mean ( 18 / 23 )-0.5830741434441960.435241762239838-1.33965578221075
Winsorized Mean ( 19 / 23 )-0.5342694645054790.373521569678827-1.43035772998296
Winsorized Mean ( 20 / 23 )-0.4749144310171540.357599816130893-1.32806117227790
Winsorized Mean ( 21 / 23 )-0.5973483546403780.311035017015696-1.92051801874846
Winsorized Mean ( 22 / 23 )-0.4992922934927060.288261792617538-1.73207933302198
Winsorized Mean ( 23 / 23 )-0.4754594221943220.278407035605421-1.70778522590276
Trimmed Mean ( 1 / 23 )-1.008994562684740.662846248495786-1.52221509131940
Trimmed Mean ( 2 / 23 )-0.9900477271145210.615230819945521-1.60922973137495
Trimmed Mean ( 3 / 23 )-0.9275848257257840.585499544055828-1.58426225117152
Trimmed Mean ( 4 / 23 )-0.8863074571062360.565245437159129-1.56800462036586
Trimmed Mean ( 5 / 23 )-0.8671365566245680.555436382507464-1.5611806931155
Trimmed Mean ( 6 / 23 )-0.8367502439157790.547206487917104-1.52913070731453
Trimmed Mean ( 7 / 23 )-0.8075423781973060.538569285692856-1.49942152226231
Trimmed Mean ( 8 / 23 )-0.781685598528440.53035362392971-1.47389508293817
Trimmed Mean ( 9 / 23 )-0.7682834465782690.523628356943778-1.46723040566873
Trimmed Mean ( 10 / 23 )-0.754903954661730.517281809632188-1.45936690717677
Trimmed Mean ( 11 / 23 )-0.754903954661730.510680821752886-1.47823047685746
Trimmed Mean ( 12 / 23 )-0.707917447068910.502942225308569-1.40755222259293
Trimmed Mean ( 13 / 23 )-0.6868560414618020.494485638772429-1.38903132387613
Trimmed Mean ( 14 / 23 )-0.6698674336375410.484839383542983-1.38162751701906
Trimmed Mean ( 15 / 23 )-0.6533131317446040.472324096346082-1.38318823197601
Trimmed Mean ( 16 / 23 )-0.6330853803867460.456013389538782-1.38830436761310
Trimmed Mean ( 17 / 23 )-0.618114930399110.436159612335962-1.41717598997450
Trimmed Mean ( 18 / 23 )-0.6186751913976310.419334547417986-1.47537376828851
Trimmed Mean ( 19 / 23 )-0.6230774715209060.397058628542531-1.56923292111297
Trimmed Mean ( 20 / 23 )-0.634198619404870.384186443092272-1.65075741429156
Trimmed Mean ( 21 / 23 )-0.6545515990321890.369307293811772-1.77237658177907
Trimmed Mean ( 22 / 23 )-0.6545515990321890.362114796686531-1.80758037236134
Trimmed Mean ( 23 / 23 )-0.6842666642097270.35685319735429-1.91750184468818
Median-0.675511401722624
Midrange1.2897784226305
Midmean - Weighted Average at Xnp-0.751051700909066
Midmean - Weighted Average at X(n+1)p-0.618114930399109
Midmean - Empirical Distribution Function-0.618114930399109
Midmean - Empirical Distribution Function - Averaging-0.618114930399109
Midmean - Empirical Distribution Function - Interpolation-0.618114930399109
Midmean - Closest Observation-0.765337167734284
Midmean - True Basic - Statistics Graphics Toolkit-0.618114930399109
Midmean - MS Excel (old versions)-0.618114930399109
Number of observations69



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')