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Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationMon, 22 Oct 2012 13:45:14 -0400
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2012/Oct/22/t1350928247bg43psxxquvji1s.htm/, Retrieved Fri, 03 May 2024 15:30:16 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=181949, Retrieved Fri, 03 May 2024 15:30:16 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact59
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [] [2012-10-22 17:45:14] [1f67b74fe1ed310301b27ef9f29963ed] [Current]
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Dataseries X:
1,44
1,45
1,45
1,47
1,49
1,5
1,5
1,5
1,5
1,5
1,5
1,51
1,52
1,51
1,51
1,51
1,52
1,52
1,52
1,52
1,52
1,53
1,53
1,53
1,53
1,54
1,54
1,55
1,56
1,55
1,56
1,56
1,56
1,56
1,57
1,56
1,57
1,58
1,58
1,58
1,6
1,61
1,61
1,61
1,6
1,59
1,56
1,57
1,55
1,59
1,62
1,63
1,62
1,56
1,56
1,54
1,54
1,52
1,56
1,59
1,61
1,56
1,51
1,48
1,49
1,48
1,47
1,47
1,46
1,45
1,45
1,45




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

\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' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=181949&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' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=181949&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=181949&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' @ jenkins.wessa.net







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean1.534861111111110.0057087400237415268.861623533027
Geometric Mean1.53410556741301
Harmonic Mean1.53334834758018
Quadratic Mean1.53561469776764
Winsorized Mean ( 1 / 24 )1.534861111111110.00564672359041555271.814457806347
Winsorized Mean ( 2 / 24 )1.534861111111110.00564672359041555271.814457806347
Winsorized Mean ( 3 / 24 )1.534444444444440.00556259335132545275.850551627833
Winsorized Mean ( 4 / 24 )1.534444444444440.00556259335132545275.850551627833
Winsorized Mean ( 5 / 24 )1.534444444444440.00556259335132545275.850551627833
Winsorized Mean ( 6 / 24 )1.535277777777780.00539145349812699284.761387316266
Winsorized Mean ( 7 / 24 )1.535277777777780.0050233111606309305.630634592215
Winsorized Mean ( 8 / 24 )1.535277777777780.0050233111606309305.630634592215
Winsorized Mean ( 9 / 24 )1.534027777777780.00480715641784159319.113347775472
Winsorized Mean ( 10 / 24 )1.535416666666670.00455765319659218336.887560425773
Winsorized Mean ( 11 / 24 )1.535416666666670.00455765319659218336.887560425773
Winsorized Mean ( 12 / 24 )1.535416666666670.00400965920991495382.929467639031
Winsorized Mean ( 13 / 24 )1.535416666666670.00400965920991495382.929467639031
Winsorized Mean ( 14 / 24 )1.537361111111110.00371623060851495413.68829684266
Winsorized Mean ( 15 / 24 )1.535277777777780.00339711411068198451.935886683997
Winsorized Mean ( 16 / 24 )1.535277777777780.00339711411068198451.935886683997
Winsorized Mean ( 17 / 24 )1.535277777777780.00339711411068198451.935886683997
Winsorized Mean ( 18 / 24 )1.532777777777780.00305928780453539501.024380741634
Winsorized Mean ( 19 / 24 )1.532777777777780.00305928780453539501.024380741634
Winsorized Mean ( 20 / 24 )1.535555555555560.00266026879877296577.218195493562
Winsorized Mean ( 21 / 24 )1.535555555555560.00266026879877296577.218195493562
Winsorized Mean ( 22 / 24 )1.535555555555560.00266026879877296577.218195493562
Winsorized Mean ( 23 / 24 )1.535555555555560.00266026879877296577.218195493562
Winsorized Mean ( 24 / 24 )1.535555555555560.00266026879877296577.218195493562
Trimmed Mean ( 1 / 24 )1.534857142857140.00554575493610189276.762525669047
Trimmed Mean ( 2 / 24 )1.534852941176470.00542525492520492282.908907016659
Trimmed Mean ( 3 / 24 )1.534848484848480.00528110686393218290.630075170582
Trimmed Mean ( 4 / 24 )1.5350.00514665864790888298.251760027582
Trimmed Mean ( 5 / 24 )1.535161290322580.00498406734632848308.013753356174
Trimmed Mean ( 6 / 24 )1.535333333333330.00478620113248521320.783287378506
Trimmed Mean ( 7 / 24 )1.535344827586210.00459632087569395334.037781327528
Trimmed Mean ( 8 / 24 )1.535357142857140.00446461037780488343.894990364654
Trimmed Mean ( 9 / 24 )1.535370370370370.00430098361138058356.981218507254
Trimmed Mean ( 10 / 24 )1.535576923076920.00415039169805026369.983614750939
Trimmed Mean ( 11 / 24 )1.53560.00402198042394692381.801957776079
Trimmed Mean ( 12 / 24 )1.5356250.00385814798200689398.021280459339
Trimmed Mean ( 13 / 24 )1.535652173913040.00377702402997378406.577284583414
Trimmed Mean ( 14 / 24 )1.535681818181820.00366973979976275418.471581631237
Trimmed Mean ( 15 / 24 )1.535476190476190.00359381293333584427.255457910252
Trimmed Mean ( 16 / 24 )1.53550.00356172674919027431.111117760251
Trimmed Mean ( 17 / 24 )1.535526315789470.00351176377898771437.252165130565
Trimmed Mean ( 18 / 24 )1.535555555555560.0034375250520171446.703815192418
Trimmed Mean ( 19 / 24 )1.535882352941180.00340696693822385450.806356736141
Trimmed Mean ( 20 / 24 )1.536250.00335259889560901458.226602058502
Trimmed Mean ( 21 / 24 )1.536333333333330.00337275539095308455.512824159831
Trimmed Mean ( 22 / 24 )1.536428571428570.00338117593716521454.406573328663
Trimmed Mean ( 23 / 24 )1.536538461538460.00337147800012479455.74625178678
Trimmed Mean ( 24 / 24 )1.536666666666670.00333333333333334460.999999999999
Median1.535
Midrange1.535
Midmean - Weighted Average at Xnp1.532
Midmean - Weighted Average at X(n+1)p1.532
Midmean - Empirical Distribution Function1.532
Midmean - Empirical Distribution Function - Averaging1.532
Midmean - Empirical Distribution Function - Interpolation1.532
Midmean - Closest Observation1.532
Midmean - True Basic - Statistics Graphics Toolkit1.532
Midmean - MS Excel (old versions)1.5346511627907
Number of observations72

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 1.53486111111111 & 0.0057087400237415 & 268.861623533027 \tabularnewline
Geometric Mean & 1.53410556741301 &  &  \tabularnewline
Harmonic Mean & 1.53334834758018 &  &  \tabularnewline
Quadratic Mean & 1.53561469776764 &  &  \tabularnewline
Winsorized Mean ( 1 / 24 ) & 1.53486111111111 & 0.00564672359041555 & 271.814457806347 \tabularnewline
Winsorized Mean ( 2 / 24 ) & 1.53486111111111 & 0.00564672359041555 & 271.814457806347 \tabularnewline
Winsorized Mean ( 3 / 24 ) & 1.53444444444444 & 0.00556259335132545 & 275.850551627833 \tabularnewline
Winsorized Mean ( 4 / 24 ) & 1.53444444444444 & 0.00556259335132545 & 275.850551627833 \tabularnewline
Winsorized Mean ( 5 / 24 ) & 1.53444444444444 & 0.00556259335132545 & 275.850551627833 \tabularnewline
Winsorized Mean ( 6 / 24 ) & 1.53527777777778 & 0.00539145349812699 & 284.761387316266 \tabularnewline
Winsorized Mean ( 7 / 24 ) & 1.53527777777778 & 0.0050233111606309 & 305.630634592215 \tabularnewline
Winsorized Mean ( 8 / 24 ) & 1.53527777777778 & 0.0050233111606309 & 305.630634592215 \tabularnewline
Winsorized Mean ( 9 / 24 ) & 1.53402777777778 & 0.00480715641784159 & 319.113347775472 \tabularnewline
Winsorized Mean ( 10 / 24 ) & 1.53541666666667 & 0.00455765319659218 & 336.887560425773 \tabularnewline
Winsorized Mean ( 11 / 24 ) & 1.53541666666667 & 0.00455765319659218 & 336.887560425773 \tabularnewline
Winsorized Mean ( 12 / 24 ) & 1.53541666666667 & 0.00400965920991495 & 382.929467639031 \tabularnewline
Winsorized Mean ( 13 / 24 ) & 1.53541666666667 & 0.00400965920991495 & 382.929467639031 \tabularnewline
Winsorized Mean ( 14 / 24 ) & 1.53736111111111 & 0.00371623060851495 & 413.68829684266 \tabularnewline
Winsorized Mean ( 15 / 24 ) & 1.53527777777778 & 0.00339711411068198 & 451.935886683997 \tabularnewline
Winsorized Mean ( 16 / 24 ) & 1.53527777777778 & 0.00339711411068198 & 451.935886683997 \tabularnewline
Winsorized Mean ( 17 / 24 ) & 1.53527777777778 & 0.00339711411068198 & 451.935886683997 \tabularnewline
Winsorized Mean ( 18 / 24 ) & 1.53277777777778 & 0.00305928780453539 & 501.024380741634 \tabularnewline
Winsorized Mean ( 19 / 24 ) & 1.53277777777778 & 0.00305928780453539 & 501.024380741634 \tabularnewline
Winsorized Mean ( 20 / 24 ) & 1.53555555555556 & 0.00266026879877296 & 577.218195493562 \tabularnewline
Winsorized Mean ( 21 / 24 ) & 1.53555555555556 & 0.00266026879877296 & 577.218195493562 \tabularnewline
Winsorized Mean ( 22 / 24 ) & 1.53555555555556 & 0.00266026879877296 & 577.218195493562 \tabularnewline
Winsorized Mean ( 23 / 24 ) & 1.53555555555556 & 0.00266026879877296 & 577.218195493562 \tabularnewline
Winsorized Mean ( 24 / 24 ) & 1.53555555555556 & 0.00266026879877296 & 577.218195493562 \tabularnewline
Trimmed Mean ( 1 / 24 ) & 1.53485714285714 & 0.00554575493610189 & 276.762525669047 \tabularnewline
Trimmed Mean ( 2 / 24 ) & 1.53485294117647 & 0.00542525492520492 & 282.908907016659 \tabularnewline
Trimmed Mean ( 3 / 24 ) & 1.53484848484848 & 0.00528110686393218 & 290.630075170582 \tabularnewline
Trimmed Mean ( 4 / 24 ) & 1.535 & 0.00514665864790888 & 298.251760027582 \tabularnewline
Trimmed Mean ( 5 / 24 ) & 1.53516129032258 & 0.00498406734632848 & 308.013753356174 \tabularnewline
Trimmed Mean ( 6 / 24 ) & 1.53533333333333 & 0.00478620113248521 & 320.783287378506 \tabularnewline
Trimmed Mean ( 7 / 24 ) & 1.53534482758621 & 0.00459632087569395 & 334.037781327528 \tabularnewline
Trimmed Mean ( 8 / 24 ) & 1.53535714285714 & 0.00446461037780488 & 343.894990364654 \tabularnewline
Trimmed Mean ( 9 / 24 ) & 1.53537037037037 & 0.00430098361138058 & 356.981218507254 \tabularnewline
Trimmed Mean ( 10 / 24 ) & 1.53557692307692 & 0.00415039169805026 & 369.983614750939 \tabularnewline
Trimmed Mean ( 11 / 24 ) & 1.5356 & 0.00402198042394692 & 381.801957776079 \tabularnewline
Trimmed Mean ( 12 / 24 ) & 1.535625 & 0.00385814798200689 & 398.021280459339 \tabularnewline
Trimmed Mean ( 13 / 24 ) & 1.53565217391304 & 0.00377702402997378 & 406.577284583414 \tabularnewline
Trimmed Mean ( 14 / 24 ) & 1.53568181818182 & 0.00366973979976275 & 418.471581631237 \tabularnewline
Trimmed Mean ( 15 / 24 ) & 1.53547619047619 & 0.00359381293333584 & 427.255457910252 \tabularnewline
Trimmed Mean ( 16 / 24 ) & 1.5355 & 0.00356172674919027 & 431.111117760251 \tabularnewline
Trimmed Mean ( 17 / 24 ) & 1.53552631578947 & 0.00351176377898771 & 437.252165130565 \tabularnewline
Trimmed Mean ( 18 / 24 ) & 1.53555555555556 & 0.0034375250520171 & 446.703815192418 \tabularnewline
Trimmed Mean ( 19 / 24 ) & 1.53588235294118 & 0.00340696693822385 & 450.806356736141 \tabularnewline
Trimmed Mean ( 20 / 24 ) & 1.53625 & 0.00335259889560901 & 458.226602058502 \tabularnewline
Trimmed Mean ( 21 / 24 ) & 1.53633333333333 & 0.00337275539095308 & 455.512824159831 \tabularnewline
Trimmed Mean ( 22 / 24 ) & 1.53642857142857 & 0.00338117593716521 & 454.406573328663 \tabularnewline
Trimmed Mean ( 23 / 24 ) & 1.53653846153846 & 0.00337147800012479 & 455.74625178678 \tabularnewline
Trimmed Mean ( 24 / 24 ) & 1.53666666666667 & 0.00333333333333334 & 460.999999999999 \tabularnewline
Median & 1.535 &  &  \tabularnewline
Midrange & 1.535 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 1.532 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 1.532 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 1.532 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 1.532 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 1.532 &  &  \tabularnewline
Midmean - Closest Observation & 1.532 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 1.532 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 1.5346511627907 &  &  \tabularnewline
Number of observations & 72 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=181949&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]1.53486111111111[/C][C]0.0057087400237415[/C][C]268.861623533027[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]1.53410556741301[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]1.53334834758018[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]1.53561469776764[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 24 )[/C][C]1.53486111111111[/C][C]0.00564672359041555[/C][C]271.814457806347[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 24 )[/C][C]1.53486111111111[/C][C]0.00564672359041555[/C][C]271.814457806347[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 24 )[/C][C]1.53444444444444[/C][C]0.00556259335132545[/C][C]275.850551627833[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 24 )[/C][C]1.53444444444444[/C][C]0.00556259335132545[/C][C]275.850551627833[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 24 )[/C][C]1.53444444444444[/C][C]0.00556259335132545[/C][C]275.850551627833[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 24 )[/C][C]1.53527777777778[/C][C]0.00539145349812699[/C][C]284.761387316266[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 24 )[/C][C]1.53527777777778[/C][C]0.0050233111606309[/C][C]305.630634592215[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 24 )[/C][C]1.53527777777778[/C][C]0.0050233111606309[/C][C]305.630634592215[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 24 )[/C][C]1.53402777777778[/C][C]0.00480715641784159[/C][C]319.113347775472[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 24 )[/C][C]1.53541666666667[/C][C]0.00455765319659218[/C][C]336.887560425773[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 24 )[/C][C]1.53541666666667[/C][C]0.00455765319659218[/C][C]336.887560425773[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 24 )[/C][C]1.53541666666667[/C][C]0.00400965920991495[/C][C]382.929467639031[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 24 )[/C][C]1.53541666666667[/C][C]0.00400965920991495[/C][C]382.929467639031[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 24 )[/C][C]1.53736111111111[/C][C]0.00371623060851495[/C][C]413.68829684266[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 24 )[/C][C]1.53527777777778[/C][C]0.00339711411068198[/C][C]451.935886683997[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 24 )[/C][C]1.53527777777778[/C][C]0.00339711411068198[/C][C]451.935886683997[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 24 )[/C][C]1.53527777777778[/C][C]0.00339711411068198[/C][C]451.935886683997[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 24 )[/C][C]1.53277777777778[/C][C]0.00305928780453539[/C][C]501.024380741634[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 24 )[/C][C]1.53277777777778[/C][C]0.00305928780453539[/C][C]501.024380741634[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 24 )[/C][C]1.53555555555556[/C][C]0.00266026879877296[/C][C]577.218195493562[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 24 )[/C][C]1.53555555555556[/C][C]0.00266026879877296[/C][C]577.218195493562[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 24 )[/C][C]1.53555555555556[/C][C]0.00266026879877296[/C][C]577.218195493562[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 24 )[/C][C]1.53555555555556[/C][C]0.00266026879877296[/C][C]577.218195493562[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 24 )[/C][C]1.53555555555556[/C][C]0.00266026879877296[/C][C]577.218195493562[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 24 )[/C][C]1.53485714285714[/C][C]0.00554575493610189[/C][C]276.762525669047[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 24 )[/C][C]1.53485294117647[/C][C]0.00542525492520492[/C][C]282.908907016659[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 24 )[/C][C]1.53484848484848[/C][C]0.00528110686393218[/C][C]290.630075170582[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 24 )[/C][C]1.535[/C][C]0.00514665864790888[/C][C]298.251760027582[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 24 )[/C][C]1.53516129032258[/C][C]0.00498406734632848[/C][C]308.013753356174[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 24 )[/C][C]1.53533333333333[/C][C]0.00478620113248521[/C][C]320.783287378506[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 24 )[/C][C]1.53534482758621[/C][C]0.00459632087569395[/C][C]334.037781327528[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 24 )[/C][C]1.53535714285714[/C][C]0.00446461037780488[/C][C]343.894990364654[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 24 )[/C][C]1.53537037037037[/C][C]0.00430098361138058[/C][C]356.981218507254[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 24 )[/C][C]1.53557692307692[/C][C]0.00415039169805026[/C][C]369.983614750939[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 24 )[/C][C]1.5356[/C][C]0.00402198042394692[/C][C]381.801957776079[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 24 )[/C][C]1.535625[/C][C]0.00385814798200689[/C][C]398.021280459339[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 24 )[/C][C]1.53565217391304[/C][C]0.00377702402997378[/C][C]406.577284583414[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 24 )[/C][C]1.53568181818182[/C][C]0.00366973979976275[/C][C]418.471581631237[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 24 )[/C][C]1.53547619047619[/C][C]0.00359381293333584[/C][C]427.255457910252[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 24 )[/C][C]1.5355[/C][C]0.00356172674919027[/C][C]431.111117760251[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 24 )[/C][C]1.53552631578947[/C][C]0.00351176377898771[/C][C]437.252165130565[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 24 )[/C][C]1.53555555555556[/C][C]0.0034375250520171[/C][C]446.703815192418[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 24 )[/C][C]1.53588235294118[/C][C]0.00340696693822385[/C][C]450.806356736141[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 24 )[/C][C]1.53625[/C][C]0.00335259889560901[/C][C]458.226602058502[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 24 )[/C][C]1.53633333333333[/C][C]0.00337275539095308[/C][C]455.512824159831[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 24 )[/C][C]1.53642857142857[/C][C]0.00338117593716521[/C][C]454.406573328663[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 24 )[/C][C]1.53653846153846[/C][C]0.00337147800012479[/C][C]455.74625178678[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 24 )[/C][C]1.53666666666667[/C][C]0.00333333333333334[/C][C]460.999999999999[/C][/ROW]
[ROW][C]Median[/C][C]1.535[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]1.535[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]1.532[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]1.532[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]1.532[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]1.532[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]1.532[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]1.532[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]1.532[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]1.5346511627907[/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=181949&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=181949&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 Mean1.534861111111110.0057087400237415268.861623533027
Geometric Mean1.53410556741301
Harmonic Mean1.53334834758018
Quadratic Mean1.53561469776764
Winsorized Mean ( 1 / 24 )1.534861111111110.00564672359041555271.814457806347
Winsorized Mean ( 2 / 24 )1.534861111111110.00564672359041555271.814457806347
Winsorized Mean ( 3 / 24 )1.534444444444440.00556259335132545275.850551627833
Winsorized Mean ( 4 / 24 )1.534444444444440.00556259335132545275.850551627833
Winsorized Mean ( 5 / 24 )1.534444444444440.00556259335132545275.850551627833
Winsorized Mean ( 6 / 24 )1.535277777777780.00539145349812699284.761387316266
Winsorized Mean ( 7 / 24 )1.535277777777780.0050233111606309305.630634592215
Winsorized Mean ( 8 / 24 )1.535277777777780.0050233111606309305.630634592215
Winsorized Mean ( 9 / 24 )1.534027777777780.00480715641784159319.113347775472
Winsorized Mean ( 10 / 24 )1.535416666666670.00455765319659218336.887560425773
Winsorized Mean ( 11 / 24 )1.535416666666670.00455765319659218336.887560425773
Winsorized Mean ( 12 / 24 )1.535416666666670.00400965920991495382.929467639031
Winsorized Mean ( 13 / 24 )1.535416666666670.00400965920991495382.929467639031
Winsorized Mean ( 14 / 24 )1.537361111111110.00371623060851495413.68829684266
Winsorized Mean ( 15 / 24 )1.535277777777780.00339711411068198451.935886683997
Winsorized Mean ( 16 / 24 )1.535277777777780.00339711411068198451.935886683997
Winsorized Mean ( 17 / 24 )1.535277777777780.00339711411068198451.935886683997
Winsorized Mean ( 18 / 24 )1.532777777777780.00305928780453539501.024380741634
Winsorized Mean ( 19 / 24 )1.532777777777780.00305928780453539501.024380741634
Winsorized Mean ( 20 / 24 )1.535555555555560.00266026879877296577.218195493562
Winsorized Mean ( 21 / 24 )1.535555555555560.00266026879877296577.218195493562
Winsorized Mean ( 22 / 24 )1.535555555555560.00266026879877296577.218195493562
Winsorized Mean ( 23 / 24 )1.535555555555560.00266026879877296577.218195493562
Winsorized Mean ( 24 / 24 )1.535555555555560.00266026879877296577.218195493562
Trimmed Mean ( 1 / 24 )1.534857142857140.00554575493610189276.762525669047
Trimmed Mean ( 2 / 24 )1.534852941176470.00542525492520492282.908907016659
Trimmed Mean ( 3 / 24 )1.534848484848480.00528110686393218290.630075170582
Trimmed Mean ( 4 / 24 )1.5350.00514665864790888298.251760027582
Trimmed Mean ( 5 / 24 )1.535161290322580.00498406734632848308.013753356174
Trimmed Mean ( 6 / 24 )1.535333333333330.00478620113248521320.783287378506
Trimmed Mean ( 7 / 24 )1.535344827586210.00459632087569395334.037781327528
Trimmed Mean ( 8 / 24 )1.535357142857140.00446461037780488343.894990364654
Trimmed Mean ( 9 / 24 )1.535370370370370.00430098361138058356.981218507254
Trimmed Mean ( 10 / 24 )1.535576923076920.00415039169805026369.983614750939
Trimmed Mean ( 11 / 24 )1.53560.00402198042394692381.801957776079
Trimmed Mean ( 12 / 24 )1.5356250.00385814798200689398.021280459339
Trimmed Mean ( 13 / 24 )1.535652173913040.00377702402997378406.577284583414
Trimmed Mean ( 14 / 24 )1.535681818181820.00366973979976275418.471581631237
Trimmed Mean ( 15 / 24 )1.535476190476190.00359381293333584427.255457910252
Trimmed Mean ( 16 / 24 )1.53550.00356172674919027431.111117760251
Trimmed Mean ( 17 / 24 )1.535526315789470.00351176377898771437.252165130565
Trimmed Mean ( 18 / 24 )1.535555555555560.0034375250520171446.703815192418
Trimmed Mean ( 19 / 24 )1.535882352941180.00340696693822385450.806356736141
Trimmed Mean ( 20 / 24 )1.536250.00335259889560901458.226602058502
Trimmed Mean ( 21 / 24 )1.536333333333330.00337275539095308455.512824159831
Trimmed Mean ( 22 / 24 )1.536428571428570.00338117593716521454.406573328663
Trimmed Mean ( 23 / 24 )1.536538461538460.00337147800012479455.74625178678
Trimmed Mean ( 24 / 24 )1.536666666666670.00333333333333334460.999999999999
Median1.535
Midrange1.535
Midmean - Weighted Average at Xnp1.532
Midmean - Weighted Average at X(n+1)p1.532
Midmean - Empirical Distribution Function1.532
Midmean - Empirical Distribution Function - Averaging1.532
Midmean - Empirical Distribution Function - Interpolation1.532
Midmean - Closest Observation1.532
Midmean - True Basic - Statistics Graphics Toolkit1.532
Midmean - MS Excel (old versions)1.5346511627907
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')