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Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationFri, 23 Oct 2009 08:26:42 -0600
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2009/Oct/23/t125630813681ja7yt91uhewwm.htm/, Retrieved Thu, 02 May 2024 13:10:12 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=49992, Retrieved Thu, 02 May 2024 13:10:12 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact114
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [workshop 3 review] [2009-10-23 14:26:42] [6198946fb53eb5eb18db46bb758f7fde] [Current]
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Dataseries X:
0,911111111
0,908163265
0,957081545
0,962025316
0,901477833
0,98245614
0,983539095
0,990697674
0,978723404
0,963963964
1,014354067
0,941441441
0,917948718
0,981042654
1,009090909
1,03125
0,994382022
1,020833333
1,045226131
1,010204082
1,027624309
1,029411765
1,027624309
1,016129032
0,982954545
1,030927835
1,031088083
1,048387097
0,958579882
1,073170732
1,042105263
1,037433155
1,005847953
0,981395349
1
0,966850829
0,947368421
1,010582011
1,053571429
1,060773481
0,961783439
1,079470199
1,016393443
1,042424242
1,053254438
1,038043478
1,012195122
1,01910828
0,98816568
1,048192771
1,071856287
1,072289157
0,965277778
1,096551724
1,022857143
1,076923077
1,064935065
1,040697674
1,047945205
1,028169014
1
1,063829787
1,070512821
1,116438356
0,983193277
1,118518519
1,091549296
1,094890511
1,069444444
1,045751634
1,027972028
1,020689655




Summary of computational 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 computational 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=49992&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]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=49992&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=49992&T=0

As an alternative you can also use a QR Code:  

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

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean1.017863357333330.00572269475166582177.864345645387
Geometric Mean1.01670726494258
Harmonic Mean1.01553678834841
Quadratic Mean1.01900491161847
Winsorized Mean ( 1 / 24 )1.017927319402780.00568967788206858178.907723864447
Winsorized Mean ( 2 / 24 )1.017456797569440.00554448857402949183.507781463422
Winsorized Mean ( 3 / 24 )1.017672480652780.00545546283805341186.541914199144
Winsorized Mean ( 4 / 24 )1.0187920088750.00511027636825623199.361430861838
Winsorized Mean ( 5 / 24 )1.018364778527780.00486553432591235209.301735495787
Winsorized Mean ( 6 / 24 )1.018961945361110.00466932754747399218.224559104308
Winsorized Mean ( 7 / 24 )1.018742805694440.00457981940214091222.441698294526
Winsorized Mean ( 8 / 24 )1.019000803694440.00449862926688875226.513620758793
Winsorized Mean ( 9 / 24 )1.018976929569440.00448420981872328227.236675080374
Winsorized Mean ( 10 / 24 )1.019059593736110.00440556727099958231.311776906518
Winsorized Mean ( 11 / 24 )1.019097091055560.00434362529023234.619015905397
Winsorized Mean ( 12 / 24 )1.018607703055560.0041777851765616243.815241810468
Winsorized Mean ( 13 / 24 )1.020551798347220.00379163120357605269.159035663779
Winsorized Mean ( 14 / 24 )1.020408481902780.00362776052491694281.277795183612
Winsorized Mean ( 15 / 24 )1.018981532527780.00339072309411691300.520421232795
Winsorized Mean ( 16 / 24 )1.019146821416670.00334398475090313304.770176102454
Winsorized Mean ( 17 / 24 )1.018115267083330.00316560790832741321.617615499725
Winsorized Mean ( 18 / 24 )1.018126368583330.00314974061655664323.241337153778
Winsorized Mean ( 19 / 24 )1.018152296194440.00312672320039431325.62917499894
Winsorized Mean ( 20 / 24 )1.018828133416670.00284747402423985357.800676931073
Winsorized Mean ( 21 / 24 )1.019413359958330.00271599866251441375.336473477710
Winsorized Mean ( 22 / 24 )1.019683000208330.00243612159312258418.568187682832
Winsorized Mean ( 23 / 24 )1.0213757360.00216621256615038471.503005734616
Winsorized Mean ( 24 / 24 )1.020906539666670.00210349713131256485.337738031347
Trimmed Mean ( 1 / 24 )1.01808807680.00545513422161425186.629335858712
Trimmed Mean ( 2 / 24 )1.018258290514710.00517421028980751196.794918157953
Trimmed Mean ( 3 / 24 )1.018695468484850.00493199198625319206.548484126542
Trimmed Mean ( 4 / 24 )1.019079088921880.00468203483185093217.657306175786
Trimmed Mean ( 5 / 24 )1.019162434741940.00451530451986237225.712890516850
Trimmed Mean ( 6 / 24 )1.019353872233330.00439291016371296232.045235218686
Trimmed Mean ( 7 / 24 )1.019434960551720.00429976567391566237.090817933657
Trimmed Mean ( 8 / 24 )1.019562091035710.00420765764172868242.31108560839
Trimmed Mean ( 9 / 24 )1.019655638925930.00411277561783246247.923965145298
Trimmed Mean ( 10 / 24 )1.019760055750.00399678328925128255.145196011123
Trimmed Mean ( 11 / 24 )1.019860922280.00386898847549801263.598852449082
Trimmed Mean ( 12 / 24 )1.019965081083330.0037209787154402274.112043923011
Trimmed Mean ( 13 / 24 )1.020142130391300.00357061239029872285.705088898198
Trimmed Mean ( 14 / 24 )1.020090563795450.00346888582876646294.068647441821
Trimmed Mean ( 15 / 24 )1.020051635047620.00337260715580243302.451957172854
Trimmed Mean ( 16 / 24 )1.020180047350.00329804801036695309.328440381464
Trimmed Mean ( 17 / 24 )1.020302403052630.00320591678958896318.256046559290
Trimmed Mean ( 18 / 24 )1.020559713166670.00311992251890428327.110595530138
Trimmed Mean ( 19 / 24 )1.0208459890.00300061074475185340.212735285803
Trimmed Mean ( 20 / 24 )1.02116497893750.00283495675385827360.204781800546
Trimmed Mean ( 21 / 24 )1.02144540040.00268603616310009380.279839278522
Trimmed Mean ( 22 / 24 )1.021694221678570.00251034583375196406.993414190884
Trimmed Mean ( 23 / 24 )1.021947382423080.00234908552674360435.040517166586
Trimmed Mean ( 24 / 24 )1.0220219450.00221108482675238462.226474821021
Median1.021845238
Midrange1.009998176
Midmean - Weighted Average at Xnp1.01954335727027
Midmean - Weighted Average at X(n+1)p1.02055971316667
Midmean - Empirical Distribution Function1.01954335727027
Midmean - Empirical Distribution Function - Averaging1.02055971316667
Midmean - Empirical Distribution Function - Interpolation1.02055971316667
Midmean - Closest Observation1.01954335727027
Midmean - True Basic - Statistics Graphics Toolkit1.02055971316667
Midmean - MS Excel (old versions)1.02030240305263
Number of observations72

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 1.01786335733333 & 0.00572269475166582 & 177.864345645387 \tabularnewline
Geometric Mean & 1.01670726494258 &  &  \tabularnewline
Harmonic Mean & 1.01553678834841 &  &  \tabularnewline
Quadratic Mean & 1.01900491161847 &  &  \tabularnewline
Winsorized Mean ( 1 / 24 ) & 1.01792731940278 & 0.00568967788206858 & 178.907723864447 \tabularnewline
Winsorized Mean ( 2 / 24 ) & 1.01745679756944 & 0.00554448857402949 & 183.507781463422 \tabularnewline
Winsorized Mean ( 3 / 24 ) & 1.01767248065278 & 0.00545546283805341 & 186.541914199144 \tabularnewline
Winsorized Mean ( 4 / 24 ) & 1.018792008875 & 0.00511027636825623 & 199.361430861838 \tabularnewline
Winsorized Mean ( 5 / 24 ) & 1.01836477852778 & 0.00486553432591235 & 209.301735495787 \tabularnewline
Winsorized Mean ( 6 / 24 ) & 1.01896194536111 & 0.00466932754747399 & 218.224559104308 \tabularnewline
Winsorized Mean ( 7 / 24 ) & 1.01874280569444 & 0.00457981940214091 & 222.441698294526 \tabularnewline
Winsorized Mean ( 8 / 24 ) & 1.01900080369444 & 0.00449862926688875 & 226.513620758793 \tabularnewline
Winsorized Mean ( 9 / 24 ) & 1.01897692956944 & 0.00448420981872328 & 227.236675080374 \tabularnewline
Winsorized Mean ( 10 / 24 ) & 1.01905959373611 & 0.00440556727099958 & 231.311776906518 \tabularnewline
Winsorized Mean ( 11 / 24 ) & 1.01909709105556 & 0.00434362529023 & 234.619015905397 \tabularnewline
Winsorized Mean ( 12 / 24 ) & 1.01860770305556 & 0.0041777851765616 & 243.815241810468 \tabularnewline
Winsorized Mean ( 13 / 24 ) & 1.02055179834722 & 0.00379163120357605 & 269.159035663779 \tabularnewline
Winsorized Mean ( 14 / 24 ) & 1.02040848190278 & 0.00362776052491694 & 281.277795183612 \tabularnewline
Winsorized Mean ( 15 / 24 ) & 1.01898153252778 & 0.00339072309411691 & 300.520421232795 \tabularnewline
Winsorized Mean ( 16 / 24 ) & 1.01914682141667 & 0.00334398475090313 & 304.770176102454 \tabularnewline
Winsorized Mean ( 17 / 24 ) & 1.01811526708333 & 0.00316560790832741 & 321.617615499725 \tabularnewline
Winsorized Mean ( 18 / 24 ) & 1.01812636858333 & 0.00314974061655664 & 323.241337153778 \tabularnewline
Winsorized Mean ( 19 / 24 ) & 1.01815229619444 & 0.00312672320039431 & 325.62917499894 \tabularnewline
Winsorized Mean ( 20 / 24 ) & 1.01882813341667 & 0.00284747402423985 & 357.800676931073 \tabularnewline
Winsorized Mean ( 21 / 24 ) & 1.01941335995833 & 0.00271599866251441 & 375.336473477710 \tabularnewline
Winsorized Mean ( 22 / 24 ) & 1.01968300020833 & 0.00243612159312258 & 418.568187682832 \tabularnewline
Winsorized Mean ( 23 / 24 ) & 1.021375736 & 0.00216621256615038 & 471.503005734616 \tabularnewline
Winsorized Mean ( 24 / 24 ) & 1.02090653966667 & 0.00210349713131256 & 485.337738031347 \tabularnewline
Trimmed Mean ( 1 / 24 ) & 1.0180880768 & 0.00545513422161425 & 186.629335858712 \tabularnewline
Trimmed Mean ( 2 / 24 ) & 1.01825829051471 & 0.00517421028980751 & 196.794918157953 \tabularnewline
Trimmed Mean ( 3 / 24 ) & 1.01869546848485 & 0.00493199198625319 & 206.548484126542 \tabularnewline
Trimmed Mean ( 4 / 24 ) & 1.01907908892188 & 0.00468203483185093 & 217.657306175786 \tabularnewline
Trimmed Mean ( 5 / 24 ) & 1.01916243474194 & 0.00451530451986237 & 225.712890516850 \tabularnewline
Trimmed Mean ( 6 / 24 ) & 1.01935387223333 & 0.00439291016371296 & 232.045235218686 \tabularnewline
Trimmed Mean ( 7 / 24 ) & 1.01943496055172 & 0.00429976567391566 & 237.090817933657 \tabularnewline
Trimmed Mean ( 8 / 24 ) & 1.01956209103571 & 0.00420765764172868 & 242.31108560839 \tabularnewline
Trimmed Mean ( 9 / 24 ) & 1.01965563892593 & 0.00411277561783246 & 247.923965145298 \tabularnewline
Trimmed Mean ( 10 / 24 ) & 1.01976005575 & 0.00399678328925128 & 255.145196011123 \tabularnewline
Trimmed Mean ( 11 / 24 ) & 1.01986092228 & 0.00386898847549801 & 263.598852449082 \tabularnewline
Trimmed Mean ( 12 / 24 ) & 1.01996508108333 & 0.0037209787154402 & 274.112043923011 \tabularnewline
Trimmed Mean ( 13 / 24 ) & 1.02014213039130 & 0.00357061239029872 & 285.705088898198 \tabularnewline
Trimmed Mean ( 14 / 24 ) & 1.02009056379545 & 0.00346888582876646 & 294.068647441821 \tabularnewline
Trimmed Mean ( 15 / 24 ) & 1.02005163504762 & 0.00337260715580243 & 302.451957172854 \tabularnewline
Trimmed Mean ( 16 / 24 ) & 1.02018004735 & 0.00329804801036695 & 309.328440381464 \tabularnewline
Trimmed Mean ( 17 / 24 ) & 1.02030240305263 & 0.00320591678958896 & 318.256046559290 \tabularnewline
Trimmed Mean ( 18 / 24 ) & 1.02055971316667 & 0.00311992251890428 & 327.110595530138 \tabularnewline
Trimmed Mean ( 19 / 24 ) & 1.020845989 & 0.00300061074475185 & 340.212735285803 \tabularnewline
Trimmed Mean ( 20 / 24 ) & 1.0211649789375 & 0.00283495675385827 & 360.204781800546 \tabularnewline
Trimmed Mean ( 21 / 24 ) & 1.0214454004 & 0.00268603616310009 & 380.279839278522 \tabularnewline
Trimmed Mean ( 22 / 24 ) & 1.02169422167857 & 0.00251034583375196 & 406.993414190884 \tabularnewline
Trimmed Mean ( 23 / 24 ) & 1.02194738242308 & 0.00234908552674360 & 435.040517166586 \tabularnewline
Trimmed Mean ( 24 / 24 ) & 1.022021945 & 0.00221108482675238 & 462.226474821021 \tabularnewline
Median & 1.021845238 &  &  \tabularnewline
Midrange & 1.009998176 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 1.01954335727027 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 1.02055971316667 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 1.01954335727027 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 1.02055971316667 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 1.02055971316667 &  &  \tabularnewline
Midmean - Closest Observation & 1.01954335727027 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 1.02055971316667 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 1.02030240305263 &  &  \tabularnewline
Number of observations & 72 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=49992&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]1.01786335733333[/C][C]0.00572269475166582[/C][C]177.864345645387[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]1.01670726494258[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]1.01553678834841[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]1.01900491161847[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 24 )[/C][C]1.01792731940278[/C][C]0.00568967788206858[/C][C]178.907723864447[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 24 )[/C][C]1.01745679756944[/C][C]0.00554448857402949[/C][C]183.507781463422[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 24 )[/C][C]1.01767248065278[/C][C]0.00545546283805341[/C][C]186.541914199144[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 24 )[/C][C]1.018792008875[/C][C]0.00511027636825623[/C][C]199.361430861838[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 24 )[/C][C]1.01836477852778[/C][C]0.00486553432591235[/C][C]209.301735495787[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 24 )[/C][C]1.01896194536111[/C][C]0.00466932754747399[/C][C]218.224559104308[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 24 )[/C][C]1.01874280569444[/C][C]0.00457981940214091[/C][C]222.441698294526[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 24 )[/C][C]1.01900080369444[/C][C]0.00449862926688875[/C][C]226.513620758793[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 24 )[/C][C]1.01897692956944[/C][C]0.00448420981872328[/C][C]227.236675080374[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 24 )[/C][C]1.01905959373611[/C][C]0.00440556727099958[/C][C]231.311776906518[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 24 )[/C][C]1.01909709105556[/C][C]0.00434362529023[/C][C]234.619015905397[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 24 )[/C][C]1.01860770305556[/C][C]0.0041777851765616[/C][C]243.815241810468[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 24 )[/C][C]1.02055179834722[/C][C]0.00379163120357605[/C][C]269.159035663779[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 24 )[/C][C]1.02040848190278[/C][C]0.00362776052491694[/C][C]281.277795183612[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 24 )[/C][C]1.01898153252778[/C][C]0.00339072309411691[/C][C]300.520421232795[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 24 )[/C][C]1.01914682141667[/C][C]0.00334398475090313[/C][C]304.770176102454[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 24 )[/C][C]1.01811526708333[/C][C]0.00316560790832741[/C][C]321.617615499725[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 24 )[/C][C]1.01812636858333[/C][C]0.00314974061655664[/C][C]323.241337153778[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 24 )[/C][C]1.01815229619444[/C][C]0.00312672320039431[/C][C]325.62917499894[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 24 )[/C][C]1.01882813341667[/C][C]0.00284747402423985[/C][C]357.800676931073[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 24 )[/C][C]1.01941335995833[/C][C]0.00271599866251441[/C][C]375.336473477710[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 24 )[/C][C]1.01968300020833[/C][C]0.00243612159312258[/C][C]418.568187682832[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 24 )[/C][C]1.021375736[/C][C]0.00216621256615038[/C][C]471.503005734616[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 24 )[/C][C]1.02090653966667[/C][C]0.00210349713131256[/C][C]485.337738031347[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 24 )[/C][C]1.0180880768[/C][C]0.00545513422161425[/C][C]186.629335858712[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 24 )[/C][C]1.01825829051471[/C][C]0.00517421028980751[/C][C]196.794918157953[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 24 )[/C][C]1.01869546848485[/C][C]0.00493199198625319[/C][C]206.548484126542[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 24 )[/C][C]1.01907908892188[/C][C]0.00468203483185093[/C][C]217.657306175786[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 24 )[/C][C]1.01916243474194[/C][C]0.00451530451986237[/C][C]225.712890516850[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 24 )[/C][C]1.01935387223333[/C][C]0.00439291016371296[/C][C]232.045235218686[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 24 )[/C][C]1.01943496055172[/C][C]0.00429976567391566[/C][C]237.090817933657[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 24 )[/C][C]1.01956209103571[/C][C]0.00420765764172868[/C][C]242.31108560839[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 24 )[/C][C]1.01965563892593[/C][C]0.00411277561783246[/C][C]247.923965145298[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 24 )[/C][C]1.01976005575[/C][C]0.00399678328925128[/C][C]255.145196011123[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 24 )[/C][C]1.01986092228[/C][C]0.00386898847549801[/C][C]263.598852449082[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 24 )[/C][C]1.01996508108333[/C][C]0.0037209787154402[/C][C]274.112043923011[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 24 )[/C][C]1.02014213039130[/C][C]0.00357061239029872[/C][C]285.705088898198[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 24 )[/C][C]1.02009056379545[/C][C]0.00346888582876646[/C][C]294.068647441821[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 24 )[/C][C]1.02005163504762[/C][C]0.00337260715580243[/C][C]302.451957172854[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 24 )[/C][C]1.02018004735[/C][C]0.00329804801036695[/C][C]309.328440381464[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 24 )[/C][C]1.02030240305263[/C][C]0.00320591678958896[/C][C]318.256046559290[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 24 )[/C][C]1.02055971316667[/C][C]0.00311992251890428[/C][C]327.110595530138[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 24 )[/C][C]1.020845989[/C][C]0.00300061074475185[/C][C]340.212735285803[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 24 )[/C][C]1.0211649789375[/C][C]0.00283495675385827[/C][C]360.204781800546[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 24 )[/C][C]1.0214454004[/C][C]0.00268603616310009[/C][C]380.279839278522[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 24 )[/C][C]1.02169422167857[/C][C]0.00251034583375196[/C][C]406.993414190884[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 24 )[/C][C]1.02194738242308[/C][C]0.00234908552674360[/C][C]435.040517166586[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 24 )[/C][C]1.022021945[/C][C]0.00221108482675238[/C][C]462.226474821021[/C][/ROW]
[ROW][C]Median[/C][C]1.021845238[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]1.009998176[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]1.01954335727027[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]1.02055971316667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]1.01954335727027[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]1.02055971316667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]1.02055971316667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]1.01954335727027[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]1.02055971316667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]1.02030240305263[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]72[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=49992&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=49992&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 Mean1.017863357333330.00572269475166582177.864345645387
Geometric Mean1.01670726494258
Harmonic Mean1.01553678834841
Quadratic Mean1.01900491161847
Winsorized Mean ( 1 / 24 )1.017927319402780.00568967788206858178.907723864447
Winsorized Mean ( 2 / 24 )1.017456797569440.00554448857402949183.507781463422
Winsorized Mean ( 3 / 24 )1.017672480652780.00545546283805341186.541914199144
Winsorized Mean ( 4 / 24 )1.0187920088750.00511027636825623199.361430861838
Winsorized Mean ( 5 / 24 )1.018364778527780.00486553432591235209.301735495787
Winsorized Mean ( 6 / 24 )1.018961945361110.00466932754747399218.224559104308
Winsorized Mean ( 7 / 24 )1.018742805694440.00457981940214091222.441698294526
Winsorized Mean ( 8 / 24 )1.019000803694440.00449862926688875226.513620758793
Winsorized Mean ( 9 / 24 )1.018976929569440.00448420981872328227.236675080374
Winsorized Mean ( 10 / 24 )1.019059593736110.00440556727099958231.311776906518
Winsorized Mean ( 11 / 24 )1.019097091055560.00434362529023234.619015905397
Winsorized Mean ( 12 / 24 )1.018607703055560.0041777851765616243.815241810468
Winsorized Mean ( 13 / 24 )1.020551798347220.00379163120357605269.159035663779
Winsorized Mean ( 14 / 24 )1.020408481902780.00362776052491694281.277795183612
Winsorized Mean ( 15 / 24 )1.018981532527780.00339072309411691300.520421232795
Winsorized Mean ( 16 / 24 )1.019146821416670.00334398475090313304.770176102454
Winsorized Mean ( 17 / 24 )1.018115267083330.00316560790832741321.617615499725
Winsorized Mean ( 18 / 24 )1.018126368583330.00314974061655664323.241337153778
Winsorized Mean ( 19 / 24 )1.018152296194440.00312672320039431325.62917499894
Winsorized Mean ( 20 / 24 )1.018828133416670.00284747402423985357.800676931073
Winsorized Mean ( 21 / 24 )1.019413359958330.00271599866251441375.336473477710
Winsorized Mean ( 22 / 24 )1.019683000208330.00243612159312258418.568187682832
Winsorized Mean ( 23 / 24 )1.0213757360.00216621256615038471.503005734616
Winsorized Mean ( 24 / 24 )1.020906539666670.00210349713131256485.337738031347
Trimmed Mean ( 1 / 24 )1.01808807680.00545513422161425186.629335858712
Trimmed Mean ( 2 / 24 )1.018258290514710.00517421028980751196.794918157953
Trimmed Mean ( 3 / 24 )1.018695468484850.00493199198625319206.548484126542
Trimmed Mean ( 4 / 24 )1.019079088921880.00468203483185093217.657306175786
Trimmed Mean ( 5 / 24 )1.019162434741940.00451530451986237225.712890516850
Trimmed Mean ( 6 / 24 )1.019353872233330.00439291016371296232.045235218686
Trimmed Mean ( 7 / 24 )1.019434960551720.00429976567391566237.090817933657
Trimmed Mean ( 8 / 24 )1.019562091035710.00420765764172868242.31108560839
Trimmed Mean ( 9 / 24 )1.019655638925930.00411277561783246247.923965145298
Trimmed Mean ( 10 / 24 )1.019760055750.00399678328925128255.145196011123
Trimmed Mean ( 11 / 24 )1.019860922280.00386898847549801263.598852449082
Trimmed Mean ( 12 / 24 )1.019965081083330.0037209787154402274.112043923011
Trimmed Mean ( 13 / 24 )1.020142130391300.00357061239029872285.705088898198
Trimmed Mean ( 14 / 24 )1.020090563795450.00346888582876646294.068647441821
Trimmed Mean ( 15 / 24 )1.020051635047620.00337260715580243302.451957172854
Trimmed Mean ( 16 / 24 )1.020180047350.00329804801036695309.328440381464
Trimmed Mean ( 17 / 24 )1.020302403052630.00320591678958896318.256046559290
Trimmed Mean ( 18 / 24 )1.020559713166670.00311992251890428327.110595530138
Trimmed Mean ( 19 / 24 )1.0208459890.00300061074475185340.212735285803
Trimmed Mean ( 20 / 24 )1.02116497893750.00283495675385827360.204781800546
Trimmed Mean ( 21 / 24 )1.02144540040.00268603616310009380.279839278522
Trimmed Mean ( 22 / 24 )1.021694221678570.00251034583375196406.993414190884
Trimmed Mean ( 23 / 24 )1.021947382423080.00234908552674360435.040517166586
Trimmed Mean ( 24 / 24 )1.0220219450.00221108482675238462.226474821021
Median1.021845238
Midrange1.009998176
Midmean - Weighted Average at Xnp1.01954335727027
Midmean - Weighted Average at X(n+1)p1.02055971316667
Midmean - Empirical Distribution Function1.01954335727027
Midmean - Empirical Distribution Function - Averaging1.02055971316667
Midmean - Empirical Distribution Function - Interpolation1.02055971316667
Midmean - Closest Observation1.01954335727027
Midmean - True Basic - Statistics Graphics Toolkit1.02055971316667
Midmean - MS Excel (old versions)1.02030240305263
Number of observations72



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')