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Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationTue, 18 Oct 2011 09:50:21 -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/18/t1318945891s7xjerookxgocmt.htm/, Retrieved Thu, 16 May 2024 07:36:48 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=131886, Retrieved Thu, 16 May 2024 07:36:48 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsKDG2011W52a
Estimated Impact63
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [] [2011-10-18 13:50:21] [a37c4e2766dbfff97993810aa18b7ce1] [Current]
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Dataseries X:
18,94
18,97
19
19,08
19,18
19,24
19,23
19,25
19,3
19,33
19,35
19,35
19,31
19,47
19,7
19,76
19,9
19,97
20,1
20,26
20,44
20,43
20,57
20,6
20,69
20,93
20,98
21,11
21,14
21,16
21,32
21,32
21,48
21,58
21,74
21,75
21,81
21,89
22,21
22,37
22,47
22,51
22,55
22,61
22,58
22,85
22,93
22,98
23,01
23,11
23,18
23,18
23,21
23,22
23,12
23,15
23,16
23,21
23,21
23,22
23,25
23,39
23,41
23,45
23,46
23,44
23,54
23,62
23,86
24,07
24,13
24,12




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=131886&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=131886&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=131886&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 Mean21.63069444444440.195477558797181110.655640358633
Geometric Mean21.5670012407256
Harmonic Mean21.5024920320847
Quadratic Mean21.693315950874
Winsorized Mean ( 1 / 24 )21.63097222222220.195372238082161110.716714076468
Winsorized Mean ( 2 / 24 )21.63041666666670.194966133801286110.944481715542
Winsorized Mean ( 3 / 24 )21.6250.192854149565662112.131369994905
Winsorized Mean ( 4 / 24 )21.61722222222220.189755239578941113.92160906961
Winsorized Mean ( 5 / 24 )21.61513888888890.188318582771847114.779638688531
Winsorized Mean ( 6 / 24 )21.60930555555560.187225994509068115.418297615233
Winsorized Mean ( 7 / 24 )21.60930555555560.186917831359976115.608582650091
Winsorized Mean ( 8 / 24 )21.613750.18578276617846116.33883187657
Winsorized Mean ( 9 / 24 )21.611250.185047358644523116.78767077954
Winsorized Mean ( 10 / 24 )21.611250.184182724800736117.335922917749
Winsorized Mean ( 11 / 24 )21.59291666666670.180813502244431119.420930398641
Winsorized Mean ( 12 / 24 )21.58791666666670.180171837806294119.818485116837
Winsorized Mean ( 13 / 24 )21.60958333333330.176425719017908122.485448570794
Winsorized Mean ( 14 / 24 )21.65236111111110.168706240260863128.343569731807
Winsorized Mean ( 15 / 24 )21.66486111111110.166681453927996129.977634587169
Winsorized Mean ( 16 / 24 )21.69597222222220.16174380567607134.137886341524
Winsorized Mean ( 17 / 24 )21.70541666666670.158242986022116137.165110519547
Winsorized Mean ( 18 / 24 )21.73791666666670.153286369810876141.812456603199
Winsorized Mean ( 19 / 24 )21.77486111111110.14632723113026148.809356555972
Winsorized Mean ( 20 / 24 )21.81930555555560.139189938790841156.759215106367
Winsorized Mean ( 21 / 24 )21.81347222222220.137605722582351158.521548470979
Winsorized Mean ( 22 / 24 )21.85013888888890.131682487469237165.930484066785
Winsorized Mean ( 23 / 24 )21.82777777777780.12610718145174173.089093947684
Winsorized Mean ( 24 / 24 )21.84777777777780.120702369083121181.005376644534
Trimmed Mean ( 1 / 24 )21.63342857142860.194036440379658111.491576165281
Trimmed Mean ( 2 / 24 )21.63602941176470.192354312988963112.480084670658
Trimmed Mean ( 3 / 24 )21.63909090909090.190508670981161113.585858311041
Trimmed Mean ( 4 / 24 )21.6443750.189124034817458114.445395694371
Trimmed Mean ( 5 / 24 )21.65225806451610.188396953046569114.928918511564
Trimmed Mean ( 6 / 24 )21.66116666666670.187761432305449115.365367640722
Trimmed Mean ( 7 / 24 )21.67189655172410.187071463402717115.848222692683
Trimmed Mean ( 8 / 24 )21.68339285714290.186092121577884116.519671404078
Trimmed Mean ( 9 / 24 )21.6950.184939363398309117.308720011515
Trimmed Mean ( 10 / 24 )21.70788461538460.183449504508074118.331661203419
Trimmed Mean ( 11 / 24 )21.72180.181553543010297119.644043513753
Trimmed Mean ( 12 / 24 )21.7393750.179613060822168121.034488808828
Trimmed Mean ( 13 / 24 )21.75913043478260.177013830646889122.923335172539
Trimmed Mean ( 14 / 24 )21.77795454545450.174287004056004124.95455219631
Trimmed Mean ( 15 / 24 )21.79333333333330.172251493022922126.520432136012
Trimmed Mean ( 16 / 24 )21.808750.169731759527519128.48950638766
Trimmed Mean ( 17 / 24 )21.82210526315790.167247466962912130.477941815389
Trimmed Mean ( 18 / 24 )21.83583333333330.164382623246488132.835411079862
Trimmed Mean ( 19 / 24 )21.84735294117650.161385660270956135.373569773771
Trimmed Mean ( 20 / 24 )21.85593750.158679568688452137.736305188171
Trimmed Mean ( 21 / 24 )21.86033333333330.156356859244966139.810517037084
Trimmed Mean ( 22 / 24 )21.86607142857140.152857560079537143.048674970304
Trimmed Mean ( 23 / 24 )21.86807692307690.14903279889987146.733316991311
Trimmed Mean ( 24 / 24 )21.87333333333330.144490191566546151.382824648408
Median21.78
Midrange21.535
Midmean - Weighted Average at Xnp21.8221052631579
Midmean - Weighted Average at X(n+1)p21.8721621621622
Midmean - Empirical Distribution Function21.8221052631579
Midmean - Empirical Distribution Function - Averaging21.8721621621622
Midmean - Empirical Distribution Function - Interpolation21.8721621621622
Midmean - Closest Observation21.8221052631579
Midmean - True Basic - Statistics Graphics Toolkit21.8721621621622
Midmean - MS Excel (old versions)21.8221052631579
Number of observations72

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 21.6306944444444 & 0.195477558797181 & 110.655640358633 \tabularnewline
Geometric Mean & 21.5670012407256 &  &  \tabularnewline
Harmonic Mean & 21.5024920320847 &  &  \tabularnewline
Quadratic Mean & 21.693315950874 &  &  \tabularnewline
Winsorized Mean ( 1 / 24 ) & 21.6309722222222 & 0.195372238082161 & 110.716714076468 \tabularnewline
Winsorized Mean ( 2 / 24 ) & 21.6304166666667 & 0.194966133801286 & 110.944481715542 \tabularnewline
Winsorized Mean ( 3 / 24 ) & 21.625 & 0.192854149565662 & 112.131369994905 \tabularnewline
Winsorized Mean ( 4 / 24 ) & 21.6172222222222 & 0.189755239578941 & 113.92160906961 \tabularnewline
Winsorized Mean ( 5 / 24 ) & 21.6151388888889 & 0.188318582771847 & 114.779638688531 \tabularnewline
Winsorized Mean ( 6 / 24 ) & 21.6093055555556 & 0.187225994509068 & 115.418297615233 \tabularnewline
Winsorized Mean ( 7 / 24 ) & 21.6093055555556 & 0.186917831359976 & 115.608582650091 \tabularnewline
Winsorized Mean ( 8 / 24 ) & 21.61375 & 0.18578276617846 & 116.33883187657 \tabularnewline
Winsorized Mean ( 9 / 24 ) & 21.61125 & 0.185047358644523 & 116.78767077954 \tabularnewline
Winsorized Mean ( 10 / 24 ) & 21.61125 & 0.184182724800736 & 117.335922917749 \tabularnewline
Winsorized Mean ( 11 / 24 ) & 21.5929166666667 & 0.180813502244431 & 119.420930398641 \tabularnewline
Winsorized Mean ( 12 / 24 ) & 21.5879166666667 & 0.180171837806294 & 119.818485116837 \tabularnewline
Winsorized Mean ( 13 / 24 ) & 21.6095833333333 & 0.176425719017908 & 122.485448570794 \tabularnewline
Winsorized Mean ( 14 / 24 ) & 21.6523611111111 & 0.168706240260863 & 128.343569731807 \tabularnewline
Winsorized Mean ( 15 / 24 ) & 21.6648611111111 & 0.166681453927996 & 129.977634587169 \tabularnewline
Winsorized Mean ( 16 / 24 ) & 21.6959722222222 & 0.16174380567607 & 134.137886341524 \tabularnewline
Winsorized Mean ( 17 / 24 ) & 21.7054166666667 & 0.158242986022116 & 137.165110519547 \tabularnewline
Winsorized Mean ( 18 / 24 ) & 21.7379166666667 & 0.153286369810876 & 141.812456603199 \tabularnewline
Winsorized Mean ( 19 / 24 ) & 21.7748611111111 & 0.14632723113026 & 148.809356555972 \tabularnewline
Winsorized Mean ( 20 / 24 ) & 21.8193055555556 & 0.139189938790841 & 156.759215106367 \tabularnewline
Winsorized Mean ( 21 / 24 ) & 21.8134722222222 & 0.137605722582351 & 158.521548470979 \tabularnewline
Winsorized Mean ( 22 / 24 ) & 21.8501388888889 & 0.131682487469237 & 165.930484066785 \tabularnewline
Winsorized Mean ( 23 / 24 ) & 21.8277777777778 & 0.12610718145174 & 173.089093947684 \tabularnewline
Winsorized Mean ( 24 / 24 ) & 21.8477777777778 & 0.120702369083121 & 181.005376644534 \tabularnewline
Trimmed Mean ( 1 / 24 ) & 21.6334285714286 & 0.194036440379658 & 111.491576165281 \tabularnewline
Trimmed Mean ( 2 / 24 ) & 21.6360294117647 & 0.192354312988963 & 112.480084670658 \tabularnewline
Trimmed Mean ( 3 / 24 ) & 21.6390909090909 & 0.190508670981161 & 113.585858311041 \tabularnewline
Trimmed Mean ( 4 / 24 ) & 21.644375 & 0.189124034817458 & 114.445395694371 \tabularnewline
Trimmed Mean ( 5 / 24 ) & 21.6522580645161 & 0.188396953046569 & 114.928918511564 \tabularnewline
Trimmed Mean ( 6 / 24 ) & 21.6611666666667 & 0.187761432305449 & 115.365367640722 \tabularnewline
Trimmed Mean ( 7 / 24 ) & 21.6718965517241 & 0.187071463402717 & 115.848222692683 \tabularnewline
Trimmed Mean ( 8 / 24 ) & 21.6833928571429 & 0.186092121577884 & 116.519671404078 \tabularnewline
Trimmed Mean ( 9 / 24 ) & 21.695 & 0.184939363398309 & 117.308720011515 \tabularnewline
Trimmed Mean ( 10 / 24 ) & 21.7078846153846 & 0.183449504508074 & 118.331661203419 \tabularnewline
Trimmed Mean ( 11 / 24 ) & 21.7218 & 0.181553543010297 & 119.644043513753 \tabularnewline
Trimmed Mean ( 12 / 24 ) & 21.739375 & 0.179613060822168 & 121.034488808828 \tabularnewline
Trimmed Mean ( 13 / 24 ) & 21.7591304347826 & 0.177013830646889 & 122.923335172539 \tabularnewline
Trimmed Mean ( 14 / 24 ) & 21.7779545454545 & 0.174287004056004 & 124.95455219631 \tabularnewline
Trimmed Mean ( 15 / 24 ) & 21.7933333333333 & 0.172251493022922 & 126.520432136012 \tabularnewline
Trimmed Mean ( 16 / 24 ) & 21.80875 & 0.169731759527519 & 128.48950638766 \tabularnewline
Trimmed Mean ( 17 / 24 ) & 21.8221052631579 & 0.167247466962912 & 130.477941815389 \tabularnewline
Trimmed Mean ( 18 / 24 ) & 21.8358333333333 & 0.164382623246488 & 132.835411079862 \tabularnewline
Trimmed Mean ( 19 / 24 ) & 21.8473529411765 & 0.161385660270956 & 135.373569773771 \tabularnewline
Trimmed Mean ( 20 / 24 ) & 21.8559375 & 0.158679568688452 & 137.736305188171 \tabularnewline
Trimmed Mean ( 21 / 24 ) & 21.8603333333333 & 0.156356859244966 & 139.810517037084 \tabularnewline
Trimmed Mean ( 22 / 24 ) & 21.8660714285714 & 0.152857560079537 & 143.048674970304 \tabularnewline
Trimmed Mean ( 23 / 24 ) & 21.8680769230769 & 0.14903279889987 & 146.733316991311 \tabularnewline
Trimmed Mean ( 24 / 24 ) & 21.8733333333333 & 0.144490191566546 & 151.382824648408 \tabularnewline
Median & 21.78 &  &  \tabularnewline
Midrange & 21.535 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 21.8221052631579 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 21.8721621621622 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 21.8221052631579 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 21.8721621621622 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 21.8721621621622 &  &  \tabularnewline
Midmean - Closest Observation & 21.8221052631579 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 21.8721621621622 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 21.8221052631579 &  &  \tabularnewline
Number of observations & 72 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=131886&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]21.6306944444444[/C][C]0.195477558797181[/C][C]110.655640358633[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]21.5670012407256[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]21.5024920320847[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]21.693315950874[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 24 )[/C][C]21.6309722222222[/C][C]0.195372238082161[/C][C]110.716714076468[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 24 )[/C][C]21.6304166666667[/C][C]0.194966133801286[/C][C]110.944481715542[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 24 )[/C][C]21.625[/C][C]0.192854149565662[/C][C]112.131369994905[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 24 )[/C][C]21.6172222222222[/C][C]0.189755239578941[/C][C]113.92160906961[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 24 )[/C][C]21.6151388888889[/C][C]0.188318582771847[/C][C]114.779638688531[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 24 )[/C][C]21.6093055555556[/C][C]0.187225994509068[/C][C]115.418297615233[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 24 )[/C][C]21.6093055555556[/C][C]0.186917831359976[/C][C]115.608582650091[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 24 )[/C][C]21.61375[/C][C]0.18578276617846[/C][C]116.33883187657[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 24 )[/C][C]21.61125[/C][C]0.185047358644523[/C][C]116.78767077954[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 24 )[/C][C]21.61125[/C][C]0.184182724800736[/C][C]117.335922917749[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 24 )[/C][C]21.5929166666667[/C][C]0.180813502244431[/C][C]119.420930398641[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 24 )[/C][C]21.5879166666667[/C][C]0.180171837806294[/C][C]119.818485116837[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 24 )[/C][C]21.6095833333333[/C][C]0.176425719017908[/C][C]122.485448570794[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 24 )[/C][C]21.6523611111111[/C][C]0.168706240260863[/C][C]128.343569731807[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 24 )[/C][C]21.6648611111111[/C][C]0.166681453927996[/C][C]129.977634587169[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 24 )[/C][C]21.6959722222222[/C][C]0.16174380567607[/C][C]134.137886341524[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 24 )[/C][C]21.7054166666667[/C][C]0.158242986022116[/C][C]137.165110519547[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 24 )[/C][C]21.7379166666667[/C][C]0.153286369810876[/C][C]141.812456603199[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 24 )[/C][C]21.7748611111111[/C][C]0.14632723113026[/C][C]148.809356555972[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 24 )[/C][C]21.8193055555556[/C][C]0.139189938790841[/C][C]156.759215106367[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 24 )[/C][C]21.8134722222222[/C][C]0.137605722582351[/C][C]158.521548470979[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 24 )[/C][C]21.8501388888889[/C][C]0.131682487469237[/C][C]165.930484066785[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 24 )[/C][C]21.8277777777778[/C][C]0.12610718145174[/C][C]173.089093947684[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 24 )[/C][C]21.8477777777778[/C][C]0.120702369083121[/C][C]181.005376644534[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 24 )[/C][C]21.6334285714286[/C][C]0.194036440379658[/C][C]111.491576165281[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 24 )[/C][C]21.6360294117647[/C][C]0.192354312988963[/C][C]112.480084670658[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 24 )[/C][C]21.6390909090909[/C][C]0.190508670981161[/C][C]113.585858311041[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 24 )[/C][C]21.644375[/C][C]0.189124034817458[/C][C]114.445395694371[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 24 )[/C][C]21.6522580645161[/C][C]0.188396953046569[/C][C]114.928918511564[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 24 )[/C][C]21.6611666666667[/C][C]0.187761432305449[/C][C]115.365367640722[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 24 )[/C][C]21.6718965517241[/C][C]0.187071463402717[/C][C]115.848222692683[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 24 )[/C][C]21.6833928571429[/C][C]0.186092121577884[/C][C]116.519671404078[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 24 )[/C][C]21.695[/C][C]0.184939363398309[/C][C]117.308720011515[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 24 )[/C][C]21.7078846153846[/C][C]0.183449504508074[/C][C]118.331661203419[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 24 )[/C][C]21.7218[/C][C]0.181553543010297[/C][C]119.644043513753[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 24 )[/C][C]21.739375[/C][C]0.179613060822168[/C][C]121.034488808828[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 24 )[/C][C]21.7591304347826[/C][C]0.177013830646889[/C][C]122.923335172539[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 24 )[/C][C]21.7779545454545[/C][C]0.174287004056004[/C][C]124.95455219631[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 24 )[/C][C]21.7933333333333[/C][C]0.172251493022922[/C][C]126.520432136012[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 24 )[/C][C]21.80875[/C][C]0.169731759527519[/C][C]128.48950638766[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 24 )[/C][C]21.8221052631579[/C][C]0.167247466962912[/C][C]130.477941815389[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 24 )[/C][C]21.8358333333333[/C][C]0.164382623246488[/C][C]132.835411079862[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 24 )[/C][C]21.8473529411765[/C][C]0.161385660270956[/C][C]135.373569773771[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 24 )[/C][C]21.8559375[/C][C]0.158679568688452[/C][C]137.736305188171[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 24 )[/C][C]21.8603333333333[/C][C]0.156356859244966[/C][C]139.810517037084[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 24 )[/C][C]21.8660714285714[/C][C]0.152857560079537[/C][C]143.048674970304[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 24 )[/C][C]21.8680769230769[/C][C]0.14903279889987[/C][C]146.733316991311[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 24 )[/C][C]21.8733333333333[/C][C]0.144490191566546[/C][C]151.382824648408[/C][/ROW]
[ROW][C]Median[/C][C]21.78[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]21.535[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]21.8221052631579[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]21.8721621621622[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]21.8221052631579[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]21.8721621621622[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]21.8721621621622[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]21.8221052631579[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]21.8721621621622[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]21.8221052631579[/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=131886&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=131886&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 Mean21.63069444444440.195477558797181110.655640358633
Geometric Mean21.5670012407256
Harmonic Mean21.5024920320847
Quadratic Mean21.693315950874
Winsorized Mean ( 1 / 24 )21.63097222222220.195372238082161110.716714076468
Winsorized Mean ( 2 / 24 )21.63041666666670.194966133801286110.944481715542
Winsorized Mean ( 3 / 24 )21.6250.192854149565662112.131369994905
Winsorized Mean ( 4 / 24 )21.61722222222220.189755239578941113.92160906961
Winsorized Mean ( 5 / 24 )21.61513888888890.188318582771847114.779638688531
Winsorized Mean ( 6 / 24 )21.60930555555560.187225994509068115.418297615233
Winsorized Mean ( 7 / 24 )21.60930555555560.186917831359976115.608582650091
Winsorized Mean ( 8 / 24 )21.613750.18578276617846116.33883187657
Winsorized Mean ( 9 / 24 )21.611250.185047358644523116.78767077954
Winsorized Mean ( 10 / 24 )21.611250.184182724800736117.335922917749
Winsorized Mean ( 11 / 24 )21.59291666666670.180813502244431119.420930398641
Winsorized Mean ( 12 / 24 )21.58791666666670.180171837806294119.818485116837
Winsorized Mean ( 13 / 24 )21.60958333333330.176425719017908122.485448570794
Winsorized Mean ( 14 / 24 )21.65236111111110.168706240260863128.343569731807
Winsorized Mean ( 15 / 24 )21.66486111111110.166681453927996129.977634587169
Winsorized Mean ( 16 / 24 )21.69597222222220.16174380567607134.137886341524
Winsorized Mean ( 17 / 24 )21.70541666666670.158242986022116137.165110519547
Winsorized Mean ( 18 / 24 )21.73791666666670.153286369810876141.812456603199
Winsorized Mean ( 19 / 24 )21.77486111111110.14632723113026148.809356555972
Winsorized Mean ( 20 / 24 )21.81930555555560.139189938790841156.759215106367
Winsorized Mean ( 21 / 24 )21.81347222222220.137605722582351158.521548470979
Winsorized Mean ( 22 / 24 )21.85013888888890.131682487469237165.930484066785
Winsorized Mean ( 23 / 24 )21.82777777777780.12610718145174173.089093947684
Winsorized Mean ( 24 / 24 )21.84777777777780.120702369083121181.005376644534
Trimmed Mean ( 1 / 24 )21.63342857142860.194036440379658111.491576165281
Trimmed Mean ( 2 / 24 )21.63602941176470.192354312988963112.480084670658
Trimmed Mean ( 3 / 24 )21.63909090909090.190508670981161113.585858311041
Trimmed Mean ( 4 / 24 )21.6443750.189124034817458114.445395694371
Trimmed Mean ( 5 / 24 )21.65225806451610.188396953046569114.928918511564
Trimmed Mean ( 6 / 24 )21.66116666666670.187761432305449115.365367640722
Trimmed Mean ( 7 / 24 )21.67189655172410.187071463402717115.848222692683
Trimmed Mean ( 8 / 24 )21.68339285714290.186092121577884116.519671404078
Trimmed Mean ( 9 / 24 )21.6950.184939363398309117.308720011515
Trimmed Mean ( 10 / 24 )21.70788461538460.183449504508074118.331661203419
Trimmed Mean ( 11 / 24 )21.72180.181553543010297119.644043513753
Trimmed Mean ( 12 / 24 )21.7393750.179613060822168121.034488808828
Trimmed Mean ( 13 / 24 )21.75913043478260.177013830646889122.923335172539
Trimmed Mean ( 14 / 24 )21.77795454545450.174287004056004124.95455219631
Trimmed Mean ( 15 / 24 )21.79333333333330.172251493022922126.520432136012
Trimmed Mean ( 16 / 24 )21.808750.169731759527519128.48950638766
Trimmed Mean ( 17 / 24 )21.82210526315790.167247466962912130.477941815389
Trimmed Mean ( 18 / 24 )21.83583333333330.164382623246488132.835411079862
Trimmed Mean ( 19 / 24 )21.84735294117650.161385660270956135.373569773771
Trimmed Mean ( 20 / 24 )21.85593750.158679568688452137.736305188171
Trimmed Mean ( 21 / 24 )21.86033333333330.156356859244966139.810517037084
Trimmed Mean ( 22 / 24 )21.86607142857140.152857560079537143.048674970304
Trimmed Mean ( 23 / 24 )21.86807692307690.14903279889987146.733316991311
Trimmed Mean ( 24 / 24 )21.87333333333330.144490191566546151.382824648408
Median21.78
Midrange21.535
Midmean - Weighted Average at Xnp21.8221052631579
Midmean - Weighted Average at X(n+1)p21.8721621621622
Midmean - Empirical Distribution Function21.8221052631579
Midmean - Empirical Distribution Function - Averaging21.8721621621622
Midmean - Empirical Distribution Function - Interpolation21.8721621621622
Midmean - Closest Observation21.8221052631579
Midmean - True Basic - Statistics Graphics Toolkit21.8721621621622
Midmean - MS Excel (old versions)21.8221052631579
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')