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Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationMon, 17 Oct 2011 10:08:02 -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/2011/Oct/17/t13188605180livhh88n822wlj.htm/, Retrieved Wed, 15 May 2024 20:36:54 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=130516, Retrieved Wed, 15 May 2024 20:36:54 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsKDG2011W52a
Estimated Impact84
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [centrummaten eige...] [2011-10-17 14:08:02] [2a4af61e9205cb322e653ff199304e24] [Current]
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Dataseries X:
36,68
36,77
36,78
36,78
37
37,12
37,3
37,34
37,4
37,4
37,34
37,29
37,39
37,42
37,42
43,49
44,3
44,36
44,52
44,66
44,77
44,77
44,82
44,97
45,28
45,5
45,52
45,52
45,17
45,25
45,32
45,41
45,44
45,44
45,46
45,53
45,61
45,8
45,83
45,83
45,96
46,01
46,18
46,32
46,51
46,51
46,56
46,54
46,62
46,76
46,82
46,82
46,7
46,72
46,47
46,74
46,89
46,89
46,96
47,6
47,67
47,58
47,58
47,58
47,57
47,53
47,68
47,56
47,81
47,81
47,81
47,81
48,12
48,13
48,01




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 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 & 1 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=130516&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]1 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=130516&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=130516&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 time1 seconds
R Server'Gwilym Jenkins' @ jenkins.wessa.net







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean44.46440.440894718490472100.850380227362
Geometric Mean44.2895834536608
Harmonic Mean44.1014092312809
Quadratic Mean44.6258623520786
Winsorized Mean ( 1 / 25 )44.46546666666670.440594982380075100.92140955956
Winsorized Mean ( 2 / 25 )44.46280.44020795904573101.004080199697
Winsorized Mean ( 3 / 25 )44.45480.439359581438486101.180904839841
Winsorized Mean ( 4 / 25 )44.46653333333330.436618888521573101.842898927027
Winsorized Mean ( 5 / 25 )44.47453333333330.434780147127645102.292005803743
Winsorized Mean ( 6 / 25 )44.48813333333330.431693447010946103.054919275171
Winsorized Mean ( 7 / 25 )44.47693333333330.430241875125041103.376579326238
Winsorized Mean ( 8 / 25 )44.48013333333330.429174128055492103.641227244672
Winsorized Mean ( 9 / 25 )44.47173333333330.428337762377634103.823984806938
Winsorized Mean ( 10 / 25 )44.47573333333330.426576827816549104.261953376568
Winsorized Mean ( 11 / 25 )44.47720.426247678284871104.345905598751
Winsorized Mean ( 12 / 25 )44.47720.426247678284871104.345905598751
Winsorized Mean ( 13 / 25 )44.47893333333330.42529962192366104.582583760954
Winsorized Mean ( 14 / 25 )44.47706666666670.42511648741006104.623245590014
Winsorized Mean ( 15 / 25 )45.68506666666670.168936298387626270.427771312012
Winsorized Mean ( 16 / 25 )45.73626666666670.122544902354578373.220475008669
Winsorized Mean ( 17 / 25 )45.7340.118281539229596386.653744091254
Winsorized Mean ( 18 / 25 )45.77240.112372745244894407.326526554532
Winsorized Mean ( 19 / 25 )45.79013333333330.10474309942367437.166110085391
Winsorized Mean ( 20 / 25 )45.81946666666670.100534229450925455.75986325168
Winsorized Mean ( 21 / 25 )45.80266666666670.0982987418161728465.953742849747
Winsorized Mean ( 22 / 25 )45.81146666666670.095456549869105479.91957314072
Winsorized Mean ( 23 / 25 )45.85133333333330.0883109439583952519.20329778079
Winsorized Mean ( 24 / 25 )45.90893333333330.0790820245479756580.522989841799
Winsorized Mean ( 25 / 25 )45.90893333333330.0721728588983528636.09692111533
Trimmed Mean ( 1 / 25 )44.52082191780820.437186145454306101.834933198864
Trimmed Mean ( 2 / 25 )44.57929577464790.432882869178622102.982351459727
Trimmed Mean ( 3 / 25 )44.64260869565220.427736396711049104.369441176664
Trimmed Mean ( 4 / 25 )44.71268656716420.421670697807956106.036978143376
Trimmed Mean ( 5 / 25 )44.78369230769230.415114764554911107.882677590882
Trimmed Mean ( 6 / 25 )44.85730158730160.407501422622404110.078883402738
Trimmed Mean ( 7 / 25 )44.93295081967210.398867477633595112.651327418948
Trimmed Mean ( 8 / 25 )45.01576271186440.388344144992205115.917191728919
Trimmed Mean ( 9 / 25 )45.10385964912280.375332413602762120.170435631118
Trimmed Mean ( 10 / 25 )45.19963636363640.358944577438471125.92371971794
Trimmed Mean ( 11 / 25 )45.30207547169810.338316110896176133.904576260634
Trimmed Mean ( 12 / 25 )45.41235294117650.311349823836096145.856363050595
Trimmed Mean ( 13 / 25 )45.53163265306120.274791254561038165.695348368328
Trimmed Mean ( 14 / 25 )45.66085106382980.22232245455836205.381193521519
Trimmed Mean ( 15 / 25 )45.80177777777780.131904575582061347.234184831468
Trimmed Mean ( 16 / 25 )45.81534883720930.120240322678871381.031486081167
Trimmed Mean ( 17 / 25 )45.82439024390240.117132429108424391.218645363232
Trimmed Mean ( 18 / 25 )45.83461538461540.113871773752186402.510770442226
Trimmed Mean ( 19 / 25 )45.84162162162160.110869152589993413.474988765806
Trimmed Mean ( 20 / 25 )45.84742857142860.108535973866038422.416890348416
Trimmed Mean ( 21 / 25 )45.85060606060610.106205150421836431.717349662347
Trimmed Mean ( 22 / 25 )45.85612903225810.103256312696557444.100005459395
Trimmed Mean ( 23 / 25 )45.86137931034480.0996295158477739460.319202799474
Trimmed Mean ( 24 / 25 )45.86259259259260.0964329514685916475.59046875725
Trimmed Mean ( 25 / 25 )45.85680.0943958332413742485.79262903207
Median45.8
Midrange42.405
Midmean - Weighted Average at Xnp45.8068421052632
Midmean - Weighted Average at X(n+1)p45.861
Midmean - Empirical Distribution Function45.861
Midmean - Empirical Distribution Function - Averaging45.861
Midmean - Empirical Distribution Function - Interpolation45.8416216216216
Midmean - Closest Observation45.8068421052632
Midmean - True Basic - Statistics Graphics Toolkit45.861
Midmean - MS Excel (old versions)45.861
Number of observations75

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 44.4644 & 0.440894718490472 & 100.850380227362 \tabularnewline
Geometric Mean & 44.2895834536608 &  &  \tabularnewline
Harmonic Mean & 44.1014092312809 &  &  \tabularnewline
Quadratic Mean & 44.6258623520786 &  &  \tabularnewline
Winsorized Mean ( 1 / 25 ) & 44.4654666666667 & 0.440594982380075 & 100.92140955956 \tabularnewline
Winsorized Mean ( 2 / 25 ) & 44.4628 & 0.44020795904573 & 101.004080199697 \tabularnewline
Winsorized Mean ( 3 / 25 ) & 44.4548 & 0.439359581438486 & 101.180904839841 \tabularnewline
Winsorized Mean ( 4 / 25 ) & 44.4665333333333 & 0.436618888521573 & 101.842898927027 \tabularnewline
Winsorized Mean ( 5 / 25 ) & 44.4745333333333 & 0.434780147127645 & 102.292005803743 \tabularnewline
Winsorized Mean ( 6 / 25 ) & 44.4881333333333 & 0.431693447010946 & 103.054919275171 \tabularnewline
Winsorized Mean ( 7 / 25 ) & 44.4769333333333 & 0.430241875125041 & 103.376579326238 \tabularnewline
Winsorized Mean ( 8 / 25 ) & 44.4801333333333 & 0.429174128055492 & 103.641227244672 \tabularnewline
Winsorized Mean ( 9 / 25 ) & 44.4717333333333 & 0.428337762377634 & 103.823984806938 \tabularnewline
Winsorized Mean ( 10 / 25 ) & 44.4757333333333 & 0.426576827816549 & 104.261953376568 \tabularnewline
Winsorized Mean ( 11 / 25 ) & 44.4772 & 0.426247678284871 & 104.345905598751 \tabularnewline
Winsorized Mean ( 12 / 25 ) & 44.4772 & 0.426247678284871 & 104.345905598751 \tabularnewline
Winsorized Mean ( 13 / 25 ) & 44.4789333333333 & 0.42529962192366 & 104.582583760954 \tabularnewline
Winsorized Mean ( 14 / 25 ) & 44.4770666666667 & 0.42511648741006 & 104.623245590014 \tabularnewline
Winsorized Mean ( 15 / 25 ) & 45.6850666666667 & 0.168936298387626 & 270.427771312012 \tabularnewline
Winsorized Mean ( 16 / 25 ) & 45.7362666666667 & 0.122544902354578 & 373.220475008669 \tabularnewline
Winsorized Mean ( 17 / 25 ) & 45.734 & 0.118281539229596 & 386.653744091254 \tabularnewline
Winsorized Mean ( 18 / 25 ) & 45.7724 & 0.112372745244894 & 407.326526554532 \tabularnewline
Winsorized Mean ( 19 / 25 ) & 45.7901333333333 & 0.10474309942367 & 437.166110085391 \tabularnewline
Winsorized Mean ( 20 / 25 ) & 45.8194666666667 & 0.100534229450925 & 455.75986325168 \tabularnewline
Winsorized Mean ( 21 / 25 ) & 45.8026666666667 & 0.0982987418161728 & 465.953742849747 \tabularnewline
Winsorized Mean ( 22 / 25 ) & 45.8114666666667 & 0.095456549869105 & 479.91957314072 \tabularnewline
Winsorized Mean ( 23 / 25 ) & 45.8513333333333 & 0.0883109439583952 & 519.20329778079 \tabularnewline
Winsorized Mean ( 24 / 25 ) & 45.9089333333333 & 0.0790820245479756 & 580.522989841799 \tabularnewline
Winsorized Mean ( 25 / 25 ) & 45.9089333333333 & 0.0721728588983528 & 636.09692111533 \tabularnewline
Trimmed Mean ( 1 / 25 ) & 44.5208219178082 & 0.437186145454306 & 101.834933198864 \tabularnewline
Trimmed Mean ( 2 / 25 ) & 44.5792957746479 & 0.432882869178622 & 102.982351459727 \tabularnewline
Trimmed Mean ( 3 / 25 ) & 44.6426086956522 & 0.427736396711049 & 104.369441176664 \tabularnewline
Trimmed Mean ( 4 / 25 ) & 44.7126865671642 & 0.421670697807956 & 106.036978143376 \tabularnewline
Trimmed Mean ( 5 / 25 ) & 44.7836923076923 & 0.415114764554911 & 107.882677590882 \tabularnewline
Trimmed Mean ( 6 / 25 ) & 44.8573015873016 & 0.407501422622404 & 110.078883402738 \tabularnewline
Trimmed Mean ( 7 / 25 ) & 44.9329508196721 & 0.398867477633595 & 112.651327418948 \tabularnewline
Trimmed Mean ( 8 / 25 ) & 45.0157627118644 & 0.388344144992205 & 115.917191728919 \tabularnewline
Trimmed Mean ( 9 / 25 ) & 45.1038596491228 & 0.375332413602762 & 120.170435631118 \tabularnewline
Trimmed Mean ( 10 / 25 ) & 45.1996363636364 & 0.358944577438471 & 125.92371971794 \tabularnewline
Trimmed Mean ( 11 / 25 ) & 45.3020754716981 & 0.338316110896176 & 133.904576260634 \tabularnewline
Trimmed Mean ( 12 / 25 ) & 45.4123529411765 & 0.311349823836096 & 145.856363050595 \tabularnewline
Trimmed Mean ( 13 / 25 ) & 45.5316326530612 & 0.274791254561038 & 165.695348368328 \tabularnewline
Trimmed Mean ( 14 / 25 ) & 45.6608510638298 & 0.22232245455836 & 205.381193521519 \tabularnewline
Trimmed Mean ( 15 / 25 ) & 45.8017777777778 & 0.131904575582061 & 347.234184831468 \tabularnewline
Trimmed Mean ( 16 / 25 ) & 45.8153488372093 & 0.120240322678871 & 381.031486081167 \tabularnewline
Trimmed Mean ( 17 / 25 ) & 45.8243902439024 & 0.117132429108424 & 391.218645363232 \tabularnewline
Trimmed Mean ( 18 / 25 ) & 45.8346153846154 & 0.113871773752186 & 402.510770442226 \tabularnewline
Trimmed Mean ( 19 / 25 ) & 45.8416216216216 & 0.110869152589993 & 413.474988765806 \tabularnewline
Trimmed Mean ( 20 / 25 ) & 45.8474285714286 & 0.108535973866038 & 422.416890348416 \tabularnewline
Trimmed Mean ( 21 / 25 ) & 45.8506060606061 & 0.106205150421836 & 431.717349662347 \tabularnewline
Trimmed Mean ( 22 / 25 ) & 45.8561290322581 & 0.103256312696557 & 444.100005459395 \tabularnewline
Trimmed Mean ( 23 / 25 ) & 45.8613793103448 & 0.0996295158477739 & 460.319202799474 \tabularnewline
Trimmed Mean ( 24 / 25 ) & 45.8625925925926 & 0.0964329514685916 & 475.59046875725 \tabularnewline
Trimmed Mean ( 25 / 25 ) & 45.8568 & 0.0943958332413742 & 485.79262903207 \tabularnewline
Median & 45.8 &  &  \tabularnewline
Midrange & 42.405 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 45.8068421052632 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 45.861 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 45.861 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 45.861 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 45.8416216216216 &  &  \tabularnewline
Midmean - Closest Observation & 45.8068421052632 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 45.861 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 45.861 &  &  \tabularnewline
Number of observations & 75 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=130516&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]44.4644[/C][C]0.440894718490472[/C][C]100.850380227362[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]44.2895834536608[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]44.1014092312809[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]44.6258623520786[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 25 )[/C][C]44.4654666666667[/C][C]0.440594982380075[/C][C]100.92140955956[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 25 )[/C][C]44.4628[/C][C]0.44020795904573[/C][C]101.004080199697[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 25 )[/C][C]44.4548[/C][C]0.439359581438486[/C][C]101.180904839841[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 25 )[/C][C]44.4665333333333[/C][C]0.436618888521573[/C][C]101.842898927027[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 25 )[/C][C]44.4745333333333[/C][C]0.434780147127645[/C][C]102.292005803743[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 25 )[/C][C]44.4881333333333[/C][C]0.431693447010946[/C][C]103.054919275171[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 25 )[/C][C]44.4769333333333[/C][C]0.430241875125041[/C][C]103.376579326238[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 25 )[/C][C]44.4801333333333[/C][C]0.429174128055492[/C][C]103.641227244672[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 25 )[/C][C]44.4717333333333[/C][C]0.428337762377634[/C][C]103.823984806938[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 25 )[/C][C]44.4757333333333[/C][C]0.426576827816549[/C][C]104.261953376568[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 25 )[/C][C]44.4772[/C][C]0.426247678284871[/C][C]104.345905598751[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 25 )[/C][C]44.4772[/C][C]0.426247678284871[/C][C]104.345905598751[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 25 )[/C][C]44.4789333333333[/C][C]0.42529962192366[/C][C]104.582583760954[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 25 )[/C][C]44.4770666666667[/C][C]0.42511648741006[/C][C]104.623245590014[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 25 )[/C][C]45.6850666666667[/C][C]0.168936298387626[/C][C]270.427771312012[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 25 )[/C][C]45.7362666666667[/C][C]0.122544902354578[/C][C]373.220475008669[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 25 )[/C][C]45.734[/C][C]0.118281539229596[/C][C]386.653744091254[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 25 )[/C][C]45.7724[/C][C]0.112372745244894[/C][C]407.326526554532[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 25 )[/C][C]45.7901333333333[/C][C]0.10474309942367[/C][C]437.166110085391[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 25 )[/C][C]45.8194666666667[/C][C]0.100534229450925[/C][C]455.75986325168[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 25 )[/C][C]45.8026666666667[/C][C]0.0982987418161728[/C][C]465.953742849747[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 25 )[/C][C]45.8114666666667[/C][C]0.095456549869105[/C][C]479.91957314072[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 25 )[/C][C]45.8513333333333[/C][C]0.0883109439583952[/C][C]519.20329778079[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 25 )[/C][C]45.9089333333333[/C][C]0.0790820245479756[/C][C]580.522989841799[/C][/ROW]
[ROW][C]Winsorized Mean ( 25 / 25 )[/C][C]45.9089333333333[/C][C]0.0721728588983528[/C][C]636.09692111533[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 25 )[/C][C]44.5208219178082[/C][C]0.437186145454306[/C][C]101.834933198864[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 25 )[/C][C]44.5792957746479[/C][C]0.432882869178622[/C][C]102.982351459727[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 25 )[/C][C]44.6426086956522[/C][C]0.427736396711049[/C][C]104.369441176664[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 25 )[/C][C]44.7126865671642[/C][C]0.421670697807956[/C][C]106.036978143376[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 25 )[/C][C]44.7836923076923[/C][C]0.415114764554911[/C][C]107.882677590882[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 25 )[/C][C]44.8573015873016[/C][C]0.407501422622404[/C][C]110.078883402738[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 25 )[/C][C]44.9329508196721[/C][C]0.398867477633595[/C][C]112.651327418948[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 25 )[/C][C]45.0157627118644[/C][C]0.388344144992205[/C][C]115.917191728919[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 25 )[/C][C]45.1038596491228[/C][C]0.375332413602762[/C][C]120.170435631118[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 25 )[/C][C]45.1996363636364[/C][C]0.358944577438471[/C][C]125.92371971794[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 25 )[/C][C]45.3020754716981[/C][C]0.338316110896176[/C][C]133.904576260634[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 25 )[/C][C]45.4123529411765[/C][C]0.311349823836096[/C][C]145.856363050595[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 25 )[/C][C]45.5316326530612[/C][C]0.274791254561038[/C][C]165.695348368328[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 25 )[/C][C]45.6608510638298[/C][C]0.22232245455836[/C][C]205.381193521519[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 25 )[/C][C]45.8017777777778[/C][C]0.131904575582061[/C][C]347.234184831468[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 25 )[/C][C]45.8153488372093[/C][C]0.120240322678871[/C][C]381.031486081167[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 25 )[/C][C]45.8243902439024[/C][C]0.117132429108424[/C][C]391.218645363232[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 25 )[/C][C]45.8346153846154[/C][C]0.113871773752186[/C][C]402.510770442226[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 25 )[/C][C]45.8416216216216[/C][C]0.110869152589993[/C][C]413.474988765806[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 25 )[/C][C]45.8474285714286[/C][C]0.108535973866038[/C][C]422.416890348416[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 25 )[/C][C]45.8506060606061[/C][C]0.106205150421836[/C][C]431.717349662347[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 25 )[/C][C]45.8561290322581[/C][C]0.103256312696557[/C][C]444.100005459395[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 25 )[/C][C]45.8613793103448[/C][C]0.0996295158477739[/C][C]460.319202799474[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 25 )[/C][C]45.8625925925926[/C][C]0.0964329514685916[/C][C]475.59046875725[/C][/ROW]
[ROW][C]Trimmed Mean ( 25 / 25 )[/C][C]45.8568[/C][C]0.0943958332413742[/C][C]485.79262903207[/C][/ROW]
[ROW][C]Median[/C][C]45.8[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]42.405[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]45.8068421052632[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]45.861[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]45.861[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]45.861[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]45.8416216216216[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]45.8068421052632[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]45.861[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]45.861[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]75[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=130516&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=130516&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 Mean44.46440.440894718490472100.850380227362
Geometric Mean44.2895834536608
Harmonic Mean44.1014092312809
Quadratic Mean44.6258623520786
Winsorized Mean ( 1 / 25 )44.46546666666670.440594982380075100.92140955956
Winsorized Mean ( 2 / 25 )44.46280.44020795904573101.004080199697
Winsorized Mean ( 3 / 25 )44.45480.439359581438486101.180904839841
Winsorized Mean ( 4 / 25 )44.46653333333330.436618888521573101.842898927027
Winsorized Mean ( 5 / 25 )44.47453333333330.434780147127645102.292005803743
Winsorized Mean ( 6 / 25 )44.48813333333330.431693447010946103.054919275171
Winsorized Mean ( 7 / 25 )44.47693333333330.430241875125041103.376579326238
Winsorized Mean ( 8 / 25 )44.48013333333330.429174128055492103.641227244672
Winsorized Mean ( 9 / 25 )44.47173333333330.428337762377634103.823984806938
Winsorized Mean ( 10 / 25 )44.47573333333330.426576827816549104.261953376568
Winsorized Mean ( 11 / 25 )44.47720.426247678284871104.345905598751
Winsorized Mean ( 12 / 25 )44.47720.426247678284871104.345905598751
Winsorized Mean ( 13 / 25 )44.47893333333330.42529962192366104.582583760954
Winsorized Mean ( 14 / 25 )44.47706666666670.42511648741006104.623245590014
Winsorized Mean ( 15 / 25 )45.68506666666670.168936298387626270.427771312012
Winsorized Mean ( 16 / 25 )45.73626666666670.122544902354578373.220475008669
Winsorized Mean ( 17 / 25 )45.7340.118281539229596386.653744091254
Winsorized Mean ( 18 / 25 )45.77240.112372745244894407.326526554532
Winsorized Mean ( 19 / 25 )45.79013333333330.10474309942367437.166110085391
Winsorized Mean ( 20 / 25 )45.81946666666670.100534229450925455.75986325168
Winsorized Mean ( 21 / 25 )45.80266666666670.0982987418161728465.953742849747
Winsorized Mean ( 22 / 25 )45.81146666666670.095456549869105479.91957314072
Winsorized Mean ( 23 / 25 )45.85133333333330.0883109439583952519.20329778079
Winsorized Mean ( 24 / 25 )45.90893333333330.0790820245479756580.522989841799
Winsorized Mean ( 25 / 25 )45.90893333333330.0721728588983528636.09692111533
Trimmed Mean ( 1 / 25 )44.52082191780820.437186145454306101.834933198864
Trimmed Mean ( 2 / 25 )44.57929577464790.432882869178622102.982351459727
Trimmed Mean ( 3 / 25 )44.64260869565220.427736396711049104.369441176664
Trimmed Mean ( 4 / 25 )44.71268656716420.421670697807956106.036978143376
Trimmed Mean ( 5 / 25 )44.78369230769230.415114764554911107.882677590882
Trimmed Mean ( 6 / 25 )44.85730158730160.407501422622404110.078883402738
Trimmed Mean ( 7 / 25 )44.93295081967210.398867477633595112.651327418948
Trimmed Mean ( 8 / 25 )45.01576271186440.388344144992205115.917191728919
Trimmed Mean ( 9 / 25 )45.10385964912280.375332413602762120.170435631118
Trimmed Mean ( 10 / 25 )45.19963636363640.358944577438471125.92371971794
Trimmed Mean ( 11 / 25 )45.30207547169810.338316110896176133.904576260634
Trimmed Mean ( 12 / 25 )45.41235294117650.311349823836096145.856363050595
Trimmed Mean ( 13 / 25 )45.53163265306120.274791254561038165.695348368328
Trimmed Mean ( 14 / 25 )45.66085106382980.22232245455836205.381193521519
Trimmed Mean ( 15 / 25 )45.80177777777780.131904575582061347.234184831468
Trimmed Mean ( 16 / 25 )45.81534883720930.120240322678871381.031486081167
Trimmed Mean ( 17 / 25 )45.82439024390240.117132429108424391.218645363232
Trimmed Mean ( 18 / 25 )45.83461538461540.113871773752186402.510770442226
Trimmed Mean ( 19 / 25 )45.84162162162160.110869152589993413.474988765806
Trimmed Mean ( 20 / 25 )45.84742857142860.108535973866038422.416890348416
Trimmed Mean ( 21 / 25 )45.85060606060610.106205150421836431.717349662347
Trimmed Mean ( 22 / 25 )45.85612903225810.103256312696557444.100005459395
Trimmed Mean ( 23 / 25 )45.86137931034480.0996295158477739460.319202799474
Trimmed Mean ( 24 / 25 )45.86259259259260.0964329514685916475.59046875725
Trimmed Mean ( 25 / 25 )45.85680.0943958332413742485.79262903207
Median45.8
Midrange42.405
Midmean - Weighted Average at Xnp45.8068421052632
Midmean - Weighted Average at X(n+1)p45.861
Midmean - Empirical Distribution Function45.861
Midmean - Empirical Distribution Function - Averaging45.861
Midmean - Empirical Distribution Function - Interpolation45.8416216216216
Midmean - Closest Observation45.8068421052632
Midmean - True Basic - Statistics Graphics Toolkit45.861
Midmean - MS Excel (old versions)45.861
Number of observations75



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')