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Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationFri, 05 Dec 2008 07:18:06 -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/2008/Dec/05/t1228486972irmb9wi3gubrob0.htm/, Retrieved Thu, 16 May 2024 20:17:14 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=29275, Retrieved Thu, 16 May 2024 20:17:14 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordspaper121
Estimated Impact161
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [paper ct Totale i...] [2008-12-05 14:18:06] [d8c5724db236abb5950452133b88474d] [Current]
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Dataseries X:
99.1
98.6
100.4
100.7
101.3
100.1
100.4
99.5
101.5
100.2
99.7
98.9
100.6
99.8
99.4
100.5
98.9
99.9
102
99.5
100
100.2
99.3
100.9
100.8
103.1
101.5
101.3
100
101.2
103.8
104.2
103.8
104.4
101.8
102
100.6
99.3
94.3
101.8
100.2
103.4
102.9
100.8
103.5
99.6
104.9
104.7
104.4
104.2
104.7
104.4
107.9
105.9
104.8
105.9
107
108.6
106.8
110
108.9
108.8
109.1
108.7
108.7
109
109.2
109.7
108.1
109.4
110.1
107.8




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

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 3 seconds \tabularnewline
R Server & 'Herman Ole Andreas Wold' @ 193.190.124.10:1001 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=29275&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]3 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Herman Ole Andreas Wold' @ 193.190.124.10:1001[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=29275&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=29275&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 time3 seconds
R Server'Herman Ole Andreas Wold' @ 193.190.124.10:1001







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean103.1583333333330.436350770945995236.411484067484
Geometric Mean103.093344461018
Harmonic Mean103.028902052925
Quadratic Mean103.223835802482
Winsorized Mean ( 1 / 24 )103.2166666666670.422846194896373244.099788321288
Winsorized Mean ( 2 / 24 )103.2166666666670.419753821585372245.898098739939
Winsorized Mean ( 3 / 24 )103.2041666666670.417086349672274247.440767955507
Winsorized Mean ( 4 / 24 )103.2041666666670.413203625244858249.765879003384
Winsorized Mean ( 5 / 24 )103.2111111111110.409886409107106251.804179933522
Winsorized Mean ( 6 / 24 )103.2027777777780.408209822377385252.817967918391
Winsorized Mean ( 7 / 24 )103.2027777777780.404976729089655254.836316174924
Winsorized Mean ( 8 / 24 )103.2027777777780.401327863569864257.153283252689
Winsorized Mean ( 9 / 24 )103.1902777777780.39888420138178258.697329752131
Winsorized Mean ( 10 / 24 )103.2041666666670.397091526426764259.900198816508
Winsorized Mean ( 11 / 24 )103.2041666666670.392184192597455263.152285621561
Winsorized Mean ( 12 / 24 )103.13750.374225530466031275.602522018102
Winsorized Mean ( 13 / 24 )103.1194444444440.365269633128880282.310477225081
Winsorized Mean ( 14 / 24 )103.1194444444440.359297691801215287.002802404576
Winsorized Mean ( 15 / 24 )102.9527777777780.32955589824989312.398528821695
Winsorized Mean ( 16 / 24 )102.9305555555560.319125853241195322.539068866228
Winsorized Mean ( 17 / 24 )102.7416666666670.281106618816438365.490030434882
Winsorized Mean ( 18 / 24 )102.7416666666670.281106618816438365.490030434882
Winsorized Mean ( 19 / 24 )102.4777777777780.241411328782239424.494485386045
Winsorized Mean ( 20 / 24 )102.5055555555560.230226540886739445.237786923897
Winsorized Mean ( 21 / 24 )102.4763888888890.226159791720505453.11497728797
Winsorized Mean ( 22 / 24 )102.5069444444440.222240744044239461.242806242763
Winsorized Mean ( 23 / 24 )102.4430555555560.20507857943651499.530744932192
Winsorized Mean ( 24 / 24 )102.4430555555560.20507857943651499.530744932192
Trimmed Mean ( 1 / 24 )103.1857142857140.418670308207148246.460549656797
Trimmed Mean ( 2 / 24 )103.1529411764710.413525021925778249.447882732922
Trimmed Mean ( 3 / 24 )103.1181818181820.409120434054995252.048475790188
Trimmed Mean ( 4 / 24 )103.08593750.404812733426637254.650926188521
Trimmed Mean ( 5 / 24 )103.0516129032260.400751158367987257.146138573602
Trimmed Mean ( 6 / 24 )103.0133333333330.396542020961143259.779110127216
Trimmed Mean ( 7 / 24 )102.9741379310340.391582332593286262.969315415943
Trimmed Mean ( 8 / 24 )102.9321428571430.386014493561229266.653570200249
Trimmed Mean ( 9 / 24 )102.8870370370370.379700186042747270.969150974959
Trimmed Mean ( 10 / 24 )102.8403846153850.372127101003868276.358223676688
Trimmed Mean ( 11 / 24 )102.7880.36268432329968283.408996189416
Trimmed Mean ( 12 / 24 )102.731250.351543660842751292.228992989729
Trimmed Mean ( 13 / 24 )102.6782608695650.341394031110755300.761734279573
Trimmed Mean ( 14 / 24 )102.6227272727270.330078849513297310.903674755426
Trimmed Mean ( 15 / 24 )102.5619047619050.316318698376394324.235985062964
Trimmed Mean ( 16 / 24 )102.5150.305873067355289335.155366526347
Trimmed Mean ( 17 / 24 )102.4657894736840.294165074852553348.327514831745
Trimmed Mean ( 18 / 24 )102.4333333333330.288262446557366355.347477816360
Trimmed Mean ( 19 / 24 )102.3970588235290.279498063415612366.36053063189
Trimmed Mean ( 20 / 24 )102.38750.2777991703232368.566615518971
Trimmed Mean ( 21 / 24 )102.3733333333330.277050695943189369.511193555441
Trimmed Mean ( 22 / 24 )102.3607142857140.275706849421335371.266490116417
Trimmed Mean ( 23 / 24 )102.3423076923080.273224228958453374.572592198147
Trimmed Mean ( 24 / 24 )102.3291666666670.273363322409294374.333929529339
Median101.9
Midrange102.2
Midmean - Weighted Average at Xnp102.465789473684
Midmean - Weighted Average at X(n+1)p102.465789473684
Midmean - Empirical Distribution Function102.465789473684
Midmean - Empirical Distribution Function - Averaging102.465789473684
Midmean - Empirical Distribution Function - Interpolation102.465789473684
Midmean - Closest Observation102.465789473684
Midmean - True Basic - Statistics Graphics Toolkit102.465789473684
Midmean - MS Excel (old versions)102.465789473684
Number of observations72

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 103.158333333333 & 0.436350770945995 & 236.411484067484 \tabularnewline
Geometric Mean & 103.093344461018 &  &  \tabularnewline
Harmonic Mean & 103.028902052925 &  &  \tabularnewline
Quadratic Mean & 103.223835802482 &  &  \tabularnewline
Winsorized Mean ( 1 / 24 ) & 103.216666666667 & 0.422846194896373 & 244.099788321288 \tabularnewline
Winsorized Mean ( 2 / 24 ) & 103.216666666667 & 0.419753821585372 & 245.898098739939 \tabularnewline
Winsorized Mean ( 3 / 24 ) & 103.204166666667 & 0.417086349672274 & 247.440767955507 \tabularnewline
Winsorized Mean ( 4 / 24 ) & 103.204166666667 & 0.413203625244858 & 249.765879003384 \tabularnewline
Winsorized Mean ( 5 / 24 ) & 103.211111111111 & 0.409886409107106 & 251.804179933522 \tabularnewline
Winsorized Mean ( 6 / 24 ) & 103.202777777778 & 0.408209822377385 & 252.817967918391 \tabularnewline
Winsorized Mean ( 7 / 24 ) & 103.202777777778 & 0.404976729089655 & 254.836316174924 \tabularnewline
Winsorized Mean ( 8 / 24 ) & 103.202777777778 & 0.401327863569864 & 257.153283252689 \tabularnewline
Winsorized Mean ( 9 / 24 ) & 103.190277777778 & 0.39888420138178 & 258.697329752131 \tabularnewline
Winsorized Mean ( 10 / 24 ) & 103.204166666667 & 0.397091526426764 & 259.900198816508 \tabularnewline
Winsorized Mean ( 11 / 24 ) & 103.204166666667 & 0.392184192597455 & 263.152285621561 \tabularnewline
Winsorized Mean ( 12 / 24 ) & 103.1375 & 0.374225530466031 & 275.602522018102 \tabularnewline
Winsorized Mean ( 13 / 24 ) & 103.119444444444 & 0.365269633128880 & 282.310477225081 \tabularnewline
Winsorized Mean ( 14 / 24 ) & 103.119444444444 & 0.359297691801215 & 287.002802404576 \tabularnewline
Winsorized Mean ( 15 / 24 ) & 102.952777777778 & 0.32955589824989 & 312.398528821695 \tabularnewline
Winsorized Mean ( 16 / 24 ) & 102.930555555556 & 0.319125853241195 & 322.539068866228 \tabularnewline
Winsorized Mean ( 17 / 24 ) & 102.741666666667 & 0.281106618816438 & 365.490030434882 \tabularnewline
Winsorized Mean ( 18 / 24 ) & 102.741666666667 & 0.281106618816438 & 365.490030434882 \tabularnewline
Winsorized Mean ( 19 / 24 ) & 102.477777777778 & 0.241411328782239 & 424.494485386045 \tabularnewline
Winsorized Mean ( 20 / 24 ) & 102.505555555556 & 0.230226540886739 & 445.237786923897 \tabularnewline
Winsorized Mean ( 21 / 24 ) & 102.476388888889 & 0.226159791720505 & 453.11497728797 \tabularnewline
Winsorized Mean ( 22 / 24 ) & 102.506944444444 & 0.222240744044239 & 461.242806242763 \tabularnewline
Winsorized Mean ( 23 / 24 ) & 102.443055555556 & 0.20507857943651 & 499.530744932192 \tabularnewline
Winsorized Mean ( 24 / 24 ) & 102.443055555556 & 0.20507857943651 & 499.530744932192 \tabularnewline
Trimmed Mean ( 1 / 24 ) & 103.185714285714 & 0.418670308207148 & 246.460549656797 \tabularnewline
Trimmed Mean ( 2 / 24 ) & 103.152941176471 & 0.413525021925778 & 249.447882732922 \tabularnewline
Trimmed Mean ( 3 / 24 ) & 103.118181818182 & 0.409120434054995 & 252.048475790188 \tabularnewline
Trimmed Mean ( 4 / 24 ) & 103.0859375 & 0.404812733426637 & 254.650926188521 \tabularnewline
Trimmed Mean ( 5 / 24 ) & 103.051612903226 & 0.400751158367987 & 257.146138573602 \tabularnewline
Trimmed Mean ( 6 / 24 ) & 103.013333333333 & 0.396542020961143 & 259.779110127216 \tabularnewline
Trimmed Mean ( 7 / 24 ) & 102.974137931034 & 0.391582332593286 & 262.969315415943 \tabularnewline
Trimmed Mean ( 8 / 24 ) & 102.932142857143 & 0.386014493561229 & 266.653570200249 \tabularnewline
Trimmed Mean ( 9 / 24 ) & 102.887037037037 & 0.379700186042747 & 270.969150974959 \tabularnewline
Trimmed Mean ( 10 / 24 ) & 102.840384615385 & 0.372127101003868 & 276.358223676688 \tabularnewline
Trimmed Mean ( 11 / 24 ) & 102.788 & 0.36268432329968 & 283.408996189416 \tabularnewline
Trimmed Mean ( 12 / 24 ) & 102.73125 & 0.351543660842751 & 292.228992989729 \tabularnewline
Trimmed Mean ( 13 / 24 ) & 102.678260869565 & 0.341394031110755 & 300.761734279573 \tabularnewline
Trimmed Mean ( 14 / 24 ) & 102.622727272727 & 0.330078849513297 & 310.903674755426 \tabularnewline
Trimmed Mean ( 15 / 24 ) & 102.561904761905 & 0.316318698376394 & 324.235985062964 \tabularnewline
Trimmed Mean ( 16 / 24 ) & 102.515 & 0.305873067355289 & 335.155366526347 \tabularnewline
Trimmed Mean ( 17 / 24 ) & 102.465789473684 & 0.294165074852553 & 348.327514831745 \tabularnewline
Trimmed Mean ( 18 / 24 ) & 102.433333333333 & 0.288262446557366 & 355.347477816360 \tabularnewline
Trimmed Mean ( 19 / 24 ) & 102.397058823529 & 0.279498063415612 & 366.36053063189 \tabularnewline
Trimmed Mean ( 20 / 24 ) & 102.3875 & 0.2777991703232 & 368.566615518971 \tabularnewline
Trimmed Mean ( 21 / 24 ) & 102.373333333333 & 0.277050695943189 & 369.511193555441 \tabularnewline
Trimmed Mean ( 22 / 24 ) & 102.360714285714 & 0.275706849421335 & 371.266490116417 \tabularnewline
Trimmed Mean ( 23 / 24 ) & 102.342307692308 & 0.273224228958453 & 374.572592198147 \tabularnewline
Trimmed Mean ( 24 / 24 ) & 102.329166666667 & 0.273363322409294 & 374.333929529339 \tabularnewline
Median & 101.9 &  &  \tabularnewline
Midrange & 102.2 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 102.465789473684 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 102.465789473684 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 102.465789473684 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 102.465789473684 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 102.465789473684 &  &  \tabularnewline
Midmean - Closest Observation & 102.465789473684 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 102.465789473684 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 102.465789473684 &  &  \tabularnewline
Number of observations & 72 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=29275&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]103.158333333333[/C][C]0.436350770945995[/C][C]236.411484067484[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]103.093344461018[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]103.028902052925[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]103.223835802482[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 24 )[/C][C]103.216666666667[/C][C]0.422846194896373[/C][C]244.099788321288[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 24 )[/C][C]103.216666666667[/C][C]0.419753821585372[/C][C]245.898098739939[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 24 )[/C][C]103.204166666667[/C][C]0.417086349672274[/C][C]247.440767955507[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 24 )[/C][C]103.204166666667[/C][C]0.413203625244858[/C][C]249.765879003384[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 24 )[/C][C]103.211111111111[/C][C]0.409886409107106[/C][C]251.804179933522[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 24 )[/C][C]103.202777777778[/C][C]0.408209822377385[/C][C]252.817967918391[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 24 )[/C][C]103.202777777778[/C][C]0.404976729089655[/C][C]254.836316174924[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 24 )[/C][C]103.202777777778[/C][C]0.401327863569864[/C][C]257.153283252689[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 24 )[/C][C]103.190277777778[/C][C]0.39888420138178[/C][C]258.697329752131[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 24 )[/C][C]103.204166666667[/C][C]0.397091526426764[/C][C]259.900198816508[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 24 )[/C][C]103.204166666667[/C][C]0.392184192597455[/C][C]263.152285621561[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 24 )[/C][C]103.1375[/C][C]0.374225530466031[/C][C]275.602522018102[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 24 )[/C][C]103.119444444444[/C][C]0.365269633128880[/C][C]282.310477225081[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 24 )[/C][C]103.119444444444[/C][C]0.359297691801215[/C][C]287.002802404576[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 24 )[/C][C]102.952777777778[/C][C]0.32955589824989[/C][C]312.398528821695[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 24 )[/C][C]102.930555555556[/C][C]0.319125853241195[/C][C]322.539068866228[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 24 )[/C][C]102.741666666667[/C][C]0.281106618816438[/C][C]365.490030434882[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 24 )[/C][C]102.741666666667[/C][C]0.281106618816438[/C][C]365.490030434882[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 24 )[/C][C]102.477777777778[/C][C]0.241411328782239[/C][C]424.494485386045[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 24 )[/C][C]102.505555555556[/C][C]0.230226540886739[/C][C]445.237786923897[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 24 )[/C][C]102.476388888889[/C][C]0.226159791720505[/C][C]453.11497728797[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 24 )[/C][C]102.506944444444[/C][C]0.222240744044239[/C][C]461.242806242763[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 24 )[/C][C]102.443055555556[/C][C]0.20507857943651[/C][C]499.530744932192[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 24 )[/C][C]102.443055555556[/C][C]0.20507857943651[/C][C]499.530744932192[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 24 )[/C][C]103.185714285714[/C][C]0.418670308207148[/C][C]246.460549656797[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 24 )[/C][C]103.152941176471[/C][C]0.413525021925778[/C][C]249.447882732922[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 24 )[/C][C]103.118181818182[/C][C]0.409120434054995[/C][C]252.048475790188[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 24 )[/C][C]103.0859375[/C][C]0.404812733426637[/C][C]254.650926188521[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 24 )[/C][C]103.051612903226[/C][C]0.400751158367987[/C][C]257.146138573602[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 24 )[/C][C]103.013333333333[/C][C]0.396542020961143[/C][C]259.779110127216[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 24 )[/C][C]102.974137931034[/C][C]0.391582332593286[/C][C]262.969315415943[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 24 )[/C][C]102.932142857143[/C][C]0.386014493561229[/C][C]266.653570200249[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 24 )[/C][C]102.887037037037[/C][C]0.379700186042747[/C][C]270.969150974959[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 24 )[/C][C]102.840384615385[/C][C]0.372127101003868[/C][C]276.358223676688[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 24 )[/C][C]102.788[/C][C]0.36268432329968[/C][C]283.408996189416[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 24 )[/C][C]102.73125[/C][C]0.351543660842751[/C][C]292.228992989729[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 24 )[/C][C]102.678260869565[/C][C]0.341394031110755[/C][C]300.761734279573[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 24 )[/C][C]102.622727272727[/C][C]0.330078849513297[/C][C]310.903674755426[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 24 )[/C][C]102.561904761905[/C][C]0.316318698376394[/C][C]324.235985062964[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 24 )[/C][C]102.515[/C][C]0.305873067355289[/C][C]335.155366526347[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 24 )[/C][C]102.465789473684[/C][C]0.294165074852553[/C][C]348.327514831745[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 24 )[/C][C]102.433333333333[/C][C]0.288262446557366[/C][C]355.347477816360[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 24 )[/C][C]102.397058823529[/C][C]0.279498063415612[/C][C]366.36053063189[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 24 )[/C][C]102.3875[/C][C]0.2777991703232[/C][C]368.566615518971[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 24 )[/C][C]102.373333333333[/C][C]0.277050695943189[/C][C]369.511193555441[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 24 )[/C][C]102.360714285714[/C][C]0.275706849421335[/C][C]371.266490116417[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 24 )[/C][C]102.342307692308[/C][C]0.273224228958453[/C][C]374.572592198147[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 24 )[/C][C]102.329166666667[/C][C]0.273363322409294[/C][C]374.333929529339[/C][/ROW]
[ROW][C]Median[/C][C]101.9[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]102.2[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]102.465789473684[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]102.465789473684[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]102.465789473684[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]102.465789473684[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]102.465789473684[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]102.465789473684[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]102.465789473684[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]102.465789473684[/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=29275&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=29275&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 Mean103.1583333333330.436350770945995236.411484067484
Geometric Mean103.093344461018
Harmonic Mean103.028902052925
Quadratic Mean103.223835802482
Winsorized Mean ( 1 / 24 )103.2166666666670.422846194896373244.099788321288
Winsorized Mean ( 2 / 24 )103.2166666666670.419753821585372245.898098739939
Winsorized Mean ( 3 / 24 )103.2041666666670.417086349672274247.440767955507
Winsorized Mean ( 4 / 24 )103.2041666666670.413203625244858249.765879003384
Winsorized Mean ( 5 / 24 )103.2111111111110.409886409107106251.804179933522
Winsorized Mean ( 6 / 24 )103.2027777777780.408209822377385252.817967918391
Winsorized Mean ( 7 / 24 )103.2027777777780.404976729089655254.836316174924
Winsorized Mean ( 8 / 24 )103.2027777777780.401327863569864257.153283252689
Winsorized Mean ( 9 / 24 )103.1902777777780.39888420138178258.697329752131
Winsorized Mean ( 10 / 24 )103.2041666666670.397091526426764259.900198816508
Winsorized Mean ( 11 / 24 )103.2041666666670.392184192597455263.152285621561
Winsorized Mean ( 12 / 24 )103.13750.374225530466031275.602522018102
Winsorized Mean ( 13 / 24 )103.1194444444440.365269633128880282.310477225081
Winsorized Mean ( 14 / 24 )103.1194444444440.359297691801215287.002802404576
Winsorized Mean ( 15 / 24 )102.9527777777780.32955589824989312.398528821695
Winsorized Mean ( 16 / 24 )102.9305555555560.319125853241195322.539068866228
Winsorized Mean ( 17 / 24 )102.7416666666670.281106618816438365.490030434882
Winsorized Mean ( 18 / 24 )102.7416666666670.281106618816438365.490030434882
Winsorized Mean ( 19 / 24 )102.4777777777780.241411328782239424.494485386045
Winsorized Mean ( 20 / 24 )102.5055555555560.230226540886739445.237786923897
Winsorized Mean ( 21 / 24 )102.4763888888890.226159791720505453.11497728797
Winsorized Mean ( 22 / 24 )102.5069444444440.222240744044239461.242806242763
Winsorized Mean ( 23 / 24 )102.4430555555560.20507857943651499.530744932192
Winsorized Mean ( 24 / 24 )102.4430555555560.20507857943651499.530744932192
Trimmed Mean ( 1 / 24 )103.1857142857140.418670308207148246.460549656797
Trimmed Mean ( 2 / 24 )103.1529411764710.413525021925778249.447882732922
Trimmed Mean ( 3 / 24 )103.1181818181820.409120434054995252.048475790188
Trimmed Mean ( 4 / 24 )103.08593750.404812733426637254.650926188521
Trimmed Mean ( 5 / 24 )103.0516129032260.400751158367987257.146138573602
Trimmed Mean ( 6 / 24 )103.0133333333330.396542020961143259.779110127216
Trimmed Mean ( 7 / 24 )102.9741379310340.391582332593286262.969315415943
Trimmed Mean ( 8 / 24 )102.9321428571430.386014493561229266.653570200249
Trimmed Mean ( 9 / 24 )102.8870370370370.379700186042747270.969150974959
Trimmed Mean ( 10 / 24 )102.8403846153850.372127101003868276.358223676688
Trimmed Mean ( 11 / 24 )102.7880.36268432329968283.408996189416
Trimmed Mean ( 12 / 24 )102.731250.351543660842751292.228992989729
Trimmed Mean ( 13 / 24 )102.6782608695650.341394031110755300.761734279573
Trimmed Mean ( 14 / 24 )102.6227272727270.330078849513297310.903674755426
Trimmed Mean ( 15 / 24 )102.5619047619050.316318698376394324.235985062964
Trimmed Mean ( 16 / 24 )102.5150.305873067355289335.155366526347
Trimmed Mean ( 17 / 24 )102.4657894736840.294165074852553348.327514831745
Trimmed Mean ( 18 / 24 )102.4333333333330.288262446557366355.347477816360
Trimmed Mean ( 19 / 24 )102.3970588235290.279498063415612366.36053063189
Trimmed Mean ( 20 / 24 )102.38750.2777991703232368.566615518971
Trimmed Mean ( 21 / 24 )102.3733333333330.277050695943189369.511193555441
Trimmed Mean ( 22 / 24 )102.3607142857140.275706849421335371.266490116417
Trimmed Mean ( 23 / 24 )102.3423076923080.273224228958453374.572592198147
Trimmed Mean ( 24 / 24 )102.3291666666670.273363322409294374.333929529339
Median101.9
Midrange102.2
Midmean - Weighted Average at Xnp102.465789473684
Midmean - Weighted Average at X(n+1)p102.465789473684
Midmean - Empirical Distribution Function102.465789473684
Midmean - Empirical Distribution Function - Averaging102.465789473684
Midmean - Empirical Distribution Function - Interpolation102.465789473684
Midmean - Closest Observation102.465789473684
Midmean - True Basic - Statistics Graphics Toolkit102.465789473684
Midmean - MS Excel (old versions)102.465789473684
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')