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Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationTue, 05 Mar 2013 05:13:17 -0500
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2013/Mar/05/t13624784227tx0lj7uqv04da0.htm/, Retrieved Sat, 04 May 2024 08:34:12 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=207353, Retrieved Sat, 04 May 2024 08:34:12 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact123
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [] [2013-03-05 10:13:17] [09b6c15525a7e41be57b956512900af9] [Current]
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Dataseries X:
15,58
15,66
15,73
15,74
15,77
15,78
15,8
15,81
15,82
15,88
15,85
15,89
15,92
16,02
16,1
16,13
16,21
16,25
16,27
16,21
16,21
16,24
16,32
16,32
16,36
16,48
16,54
16,58
16,56
16,55
16,58
16,53
16,6
16,46
16,48
16,48
16,49
16,54
16,67
16,72
16,79
16,86
16,84
16,86
16,96
17,01
17,02
17,04
17,04
17,39
17,54
17,57
17,58
17,56
17,63
17,67
17,71
17,75
17,82
17,86
17,89
17,96
18
18,08
18
18,02
18,01
18,02
17,95
17,96
18
18,01




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=207353&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=207353&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=207353&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 Mean16.81291666666670.0926803612123955181.407543590994
Geometric Mean16.7949060404201
Harmonic Mean16.7770363497217
Quadratic Mean16.8310436974195
Winsorized Mean ( 1 / 24 )16.81319444444440.0923215671874855182.115565805988
Winsorized Mean ( 2 / 24 )16.81513888888890.0919889752051518182.795153999576
Winsorized Mean ( 3 / 24 )16.81513888888890.0918434047491368183.084881650655
Winsorized Mean ( 4 / 24 )16.81680555555560.0915718302397741183.646056997244
Winsorized Mean ( 5 / 24 )16.81680555555560.0913333304180993184.125614149542
Winsorized Mean ( 6 / 24 )16.81847222222220.0910688272024893184.678695651002
Winsorized Mean ( 7 / 24 )16.81944444444440.0909162387920393184.999342998747
Winsorized Mean ( 8 / 24 )16.81611111111110.0899381537536133186.974164014741
Winsorized Mean ( 9 / 24 )16.81986111111110.0893590227093813188.227899110017
Winsorized Mean ( 10 / 24 )16.82263888888890.0884784866948307190.132534103024
Winsorized Mean ( 11 / 24 )16.8150.086625125472159194.112272950234
Winsorized Mean ( 12 / 24 )16.8150.0850085147166735197.803714793077
Winsorized Mean ( 13 / 24 )16.82583333333330.081157208962052207.323952468608
Winsorized Mean ( 14 / 24 )16.82777777777780.07670141645165219.393311835192
Winsorized Mean ( 15 / 24 )16.82569444444440.0744699124183072225.939495536564
Winsorized Mean ( 16 / 24 )16.83458333333330.0707098308856772238.079813266012
Winsorized Mean ( 17 / 24 )16.82513888888890.0691497640571042243.314480075371
Winsorized Mean ( 18 / 24 )16.81263888888890.0671184786935924250.4919541702
Winsorized Mean ( 19 / 24 )16.81791666666670.0657022190822485255.971821067617
Winsorized Mean ( 20 / 24 )16.81791666666670.0649114412669695259.090174835242
Winsorized Mean ( 21 / 24 )16.81791666666670.0632575954045783265.863989282297
Winsorized Mean ( 22 / 24 )16.78736111111110.0541100256604811310.244929774108
Winsorized Mean ( 23 / 24 )16.67555555555560.0374833760173234444.878698969077
Winsorized Mean ( 24 / 24 )16.68888888888890.0357277106695247467.11330158426
Trimmed Mean ( 1 / 24 )16.81242857142860.0918914283551323182.959704429163
Trimmed Mean ( 2 / 24 )16.81161764705880.0913251411172902184.085318033809
Trimmed Mean ( 3 / 24 )16.8096969696970.0907980596244235185.132777497983
Trimmed Mean ( 4 / 24 )16.807656250.0901700724940726186.399498027518
Trimmed Mean ( 5 / 24 )16.8050.0894485574000011187.873348530938
Trimmed Mean ( 6 / 24 )16.80216666666670.0885871818872625189.668147340429
Trimmed Mean ( 7 / 24 )16.79879310344830.0875508935341793191.874604876421
Trimmed Mean ( 8 / 24 )16.7950.0862637152656235194.693677965119
Trimmed Mean ( 9 / 24 )16.79148148148150.0848624518722168197.86703201512
Trimmed Mean ( 10 / 24 )16.78711538461540.083201103177901201.76553847755
Trimmed Mean ( 11 / 24 )16.7820.0812700210811503206.496808746275
Trimmed Mean ( 12 / 24 )16.77750.0792179751612756211.789053757605
Trimmed Mean ( 13 / 24 )16.77260869565220.0769254829733738218.037093136713
Trimmed Mean ( 14 / 24 )16.76590909090910.0747931030541106224.16383872694
Trimmed Mean ( 15 / 24 )16.75833333333330.0729723323275825229.653250743076
Trimmed Mean ( 16 / 24 )16.750250.0710114540237285235.88096075885
Trimmed Mean ( 17 / 24 )16.74026315789470.0691592333011098242.053914695814
Trimmed Mean ( 18 / 24 )16.73027777777780.0669547183053664249.874515213021
Trimmed Mean ( 19 / 24 )16.72058823529410.0643948121498381259.657380417347
Trimmed Mean ( 20 / 24 )16.70906250.0610383264297668273.74706151595
Trimmed Mean ( 21 / 24 )16.6960.0562825384815844296.646179266824
Trimmed Mean ( 22 / 24 )16.68107142857140.049546459640295336.675345719457
Trimmed Mean ( 23 / 24 )16.66769230769230.0432925919841959385.001025435874
Trimmed Mean ( 24 / 24 )16.66666666666670.0416753614116575399.916547862369
Median16.58
Midrange16.83
Midmean - Weighted Average at Xnp16.7028947368421
Midmean - Weighted Average at X(n+1)p16.7028947368421
Midmean - Empirical Distribution Function16.7028947368421
Midmean - Empirical Distribution Function - Averaging16.7028947368421
Midmean - Empirical Distribution Function - Interpolation16.7028947368421
Midmean - Closest Observation16.7028947368421
Midmean - True Basic - Statistics Graphics Toolkit16.7028947368421
Midmean - MS Excel (old versions)16.7266666666667
Number of observations72

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 16.8129166666667 & 0.0926803612123955 & 181.407543590994 \tabularnewline
Geometric Mean & 16.7949060404201 &  &  \tabularnewline
Harmonic Mean & 16.7770363497217 &  &  \tabularnewline
Quadratic Mean & 16.8310436974195 &  &  \tabularnewline
Winsorized Mean ( 1 / 24 ) & 16.8131944444444 & 0.0923215671874855 & 182.115565805988 \tabularnewline
Winsorized Mean ( 2 / 24 ) & 16.8151388888889 & 0.0919889752051518 & 182.795153999576 \tabularnewline
Winsorized Mean ( 3 / 24 ) & 16.8151388888889 & 0.0918434047491368 & 183.084881650655 \tabularnewline
Winsorized Mean ( 4 / 24 ) & 16.8168055555556 & 0.0915718302397741 & 183.646056997244 \tabularnewline
Winsorized Mean ( 5 / 24 ) & 16.8168055555556 & 0.0913333304180993 & 184.125614149542 \tabularnewline
Winsorized Mean ( 6 / 24 ) & 16.8184722222222 & 0.0910688272024893 & 184.678695651002 \tabularnewline
Winsorized Mean ( 7 / 24 ) & 16.8194444444444 & 0.0909162387920393 & 184.999342998747 \tabularnewline
Winsorized Mean ( 8 / 24 ) & 16.8161111111111 & 0.0899381537536133 & 186.974164014741 \tabularnewline
Winsorized Mean ( 9 / 24 ) & 16.8198611111111 & 0.0893590227093813 & 188.227899110017 \tabularnewline
Winsorized Mean ( 10 / 24 ) & 16.8226388888889 & 0.0884784866948307 & 190.132534103024 \tabularnewline
Winsorized Mean ( 11 / 24 ) & 16.815 & 0.086625125472159 & 194.112272950234 \tabularnewline
Winsorized Mean ( 12 / 24 ) & 16.815 & 0.0850085147166735 & 197.803714793077 \tabularnewline
Winsorized Mean ( 13 / 24 ) & 16.8258333333333 & 0.081157208962052 & 207.323952468608 \tabularnewline
Winsorized Mean ( 14 / 24 ) & 16.8277777777778 & 0.07670141645165 & 219.393311835192 \tabularnewline
Winsorized Mean ( 15 / 24 ) & 16.8256944444444 & 0.0744699124183072 & 225.939495536564 \tabularnewline
Winsorized Mean ( 16 / 24 ) & 16.8345833333333 & 0.0707098308856772 & 238.079813266012 \tabularnewline
Winsorized Mean ( 17 / 24 ) & 16.8251388888889 & 0.0691497640571042 & 243.314480075371 \tabularnewline
Winsorized Mean ( 18 / 24 ) & 16.8126388888889 & 0.0671184786935924 & 250.4919541702 \tabularnewline
Winsorized Mean ( 19 / 24 ) & 16.8179166666667 & 0.0657022190822485 & 255.971821067617 \tabularnewline
Winsorized Mean ( 20 / 24 ) & 16.8179166666667 & 0.0649114412669695 & 259.090174835242 \tabularnewline
Winsorized Mean ( 21 / 24 ) & 16.8179166666667 & 0.0632575954045783 & 265.863989282297 \tabularnewline
Winsorized Mean ( 22 / 24 ) & 16.7873611111111 & 0.0541100256604811 & 310.244929774108 \tabularnewline
Winsorized Mean ( 23 / 24 ) & 16.6755555555556 & 0.0374833760173234 & 444.878698969077 \tabularnewline
Winsorized Mean ( 24 / 24 ) & 16.6888888888889 & 0.0357277106695247 & 467.11330158426 \tabularnewline
Trimmed Mean ( 1 / 24 ) & 16.8124285714286 & 0.0918914283551323 & 182.959704429163 \tabularnewline
Trimmed Mean ( 2 / 24 ) & 16.8116176470588 & 0.0913251411172902 & 184.085318033809 \tabularnewline
Trimmed Mean ( 3 / 24 ) & 16.809696969697 & 0.0907980596244235 & 185.132777497983 \tabularnewline
Trimmed Mean ( 4 / 24 ) & 16.80765625 & 0.0901700724940726 & 186.399498027518 \tabularnewline
Trimmed Mean ( 5 / 24 ) & 16.805 & 0.0894485574000011 & 187.873348530938 \tabularnewline
Trimmed Mean ( 6 / 24 ) & 16.8021666666667 & 0.0885871818872625 & 189.668147340429 \tabularnewline
Trimmed Mean ( 7 / 24 ) & 16.7987931034483 & 0.0875508935341793 & 191.874604876421 \tabularnewline
Trimmed Mean ( 8 / 24 ) & 16.795 & 0.0862637152656235 & 194.693677965119 \tabularnewline
Trimmed Mean ( 9 / 24 ) & 16.7914814814815 & 0.0848624518722168 & 197.86703201512 \tabularnewline
Trimmed Mean ( 10 / 24 ) & 16.7871153846154 & 0.083201103177901 & 201.76553847755 \tabularnewline
Trimmed Mean ( 11 / 24 ) & 16.782 & 0.0812700210811503 & 206.496808746275 \tabularnewline
Trimmed Mean ( 12 / 24 ) & 16.7775 & 0.0792179751612756 & 211.789053757605 \tabularnewline
Trimmed Mean ( 13 / 24 ) & 16.7726086956522 & 0.0769254829733738 & 218.037093136713 \tabularnewline
Trimmed Mean ( 14 / 24 ) & 16.7659090909091 & 0.0747931030541106 & 224.16383872694 \tabularnewline
Trimmed Mean ( 15 / 24 ) & 16.7583333333333 & 0.0729723323275825 & 229.653250743076 \tabularnewline
Trimmed Mean ( 16 / 24 ) & 16.75025 & 0.0710114540237285 & 235.88096075885 \tabularnewline
Trimmed Mean ( 17 / 24 ) & 16.7402631578947 & 0.0691592333011098 & 242.053914695814 \tabularnewline
Trimmed Mean ( 18 / 24 ) & 16.7302777777778 & 0.0669547183053664 & 249.874515213021 \tabularnewline
Trimmed Mean ( 19 / 24 ) & 16.7205882352941 & 0.0643948121498381 & 259.657380417347 \tabularnewline
Trimmed Mean ( 20 / 24 ) & 16.7090625 & 0.0610383264297668 & 273.74706151595 \tabularnewline
Trimmed Mean ( 21 / 24 ) & 16.696 & 0.0562825384815844 & 296.646179266824 \tabularnewline
Trimmed Mean ( 22 / 24 ) & 16.6810714285714 & 0.049546459640295 & 336.675345719457 \tabularnewline
Trimmed Mean ( 23 / 24 ) & 16.6676923076923 & 0.0432925919841959 & 385.001025435874 \tabularnewline
Trimmed Mean ( 24 / 24 ) & 16.6666666666667 & 0.0416753614116575 & 399.916547862369 \tabularnewline
Median & 16.58 &  &  \tabularnewline
Midrange & 16.83 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 16.7028947368421 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 16.7028947368421 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 16.7028947368421 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 16.7028947368421 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 16.7028947368421 &  &  \tabularnewline
Midmean - Closest Observation & 16.7028947368421 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 16.7028947368421 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 16.7266666666667 &  &  \tabularnewline
Number of observations & 72 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=207353&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]16.8129166666667[/C][C]0.0926803612123955[/C][C]181.407543590994[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]16.7949060404201[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]16.7770363497217[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]16.8310436974195[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 24 )[/C][C]16.8131944444444[/C][C]0.0923215671874855[/C][C]182.115565805988[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 24 )[/C][C]16.8151388888889[/C][C]0.0919889752051518[/C][C]182.795153999576[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 24 )[/C][C]16.8151388888889[/C][C]0.0918434047491368[/C][C]183.084881650655[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 24 )[/C][C]16.8168055555556[/C][C]0.0915718302397741[/C][C]183.646056997244[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 24 )[/C][C]16.8168055555556[/C][C]0.0913333304180993[/C][C]184.125614149542[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 24 )[/C][C]16.8184722222222[/C][C]0.0910688272024893[/C][C]184.678695651002[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 24 )[/C][C]16.8194444444444[/C][C]0.0909162387920393[/C][C]184.999342998747[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 24 )[/C][C]16.8161111111111[/C][C]0.0899381537536133[/C][C]186.974164014741[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 24 )[/C][C]16.8198611111111[/C][C]0.0893590227093813[/C][C]188.227899110017[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 24 )[/C][C]16.8226388888889[/C][C]0.0884784866948307[/C][C]190.132534103024[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 24 )[/C][C]16.815[/C][C]0.086625125472159[/C][C]194.112272950234[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 24 )[/C][C]16.815[/C][C]0.0850085147166735[/C][C]197.803714793077[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 24 )[/C][C]16.8258333333333[/C][C]0.081157208962052[/C][C]207.323952468608[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 24 )[/C][C]16.8277777777778[/C][C]0.07670141645165[/C][C]219.393311835192[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 24 )[/C][C]16.8256944444444[/C][C]0.0744699124183072[/C][C]225.939495536564[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 24 )[/C][C]16.8345833333333[/C][C]0.0707098308856772[/C][C]238.079813266012[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 24 )[/C][C]16.8251388888889[/C][C]0.0691497640571042[/C][C]243.314480075371[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 24 )[/C][C]16.8126388888889[/C][C]0.0671184786935924[/C][C]250.4919541702[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 24 )[/C][C]16.8179166666667[/C][C]0.0657022190822485[/C][C]255.971821067617[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 24 )[/C][C]16.8179166666667[/C][C]0.0649114412669695[/C][C]259.090174835242[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 24 )[/C][C]16.8179166666667[/C][C]0.0632575954045783[/C][C]265.863989282297[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 24 )[/C][C]16.7873611111111[/C][C]0.0541100256604811[/C][C]310.244929774108[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 24 )[/C][C]16.6755555555556[/C][C]0.0374833760173234[/C][C]444.878698969077[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 24 )[/C][C]16.6888888888889[/C][C]0.0357277106695247[/C][C]467.11330158426[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 24 )[/C][C]16.8124285714286[/C][C]0.0918914283551323[/C][C]182.959704429163[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 24 )[/C][C]16.8116176470588[/C][C]0.0913251411172902[/C][C]184.085318033809[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 24 )[/C][C]16.809696969697[/C][C]0.0907980596244235[/C][C]185.132777497983[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 24 )[/C][C]16.80765625[/C][C]0.0901700724940726[/C][C]186.399498027518[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 24 )[/C][C]16.805[/C][C]0.0894485574000011[/C][C]187.873348530938[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 24 )[/C][C]16.8021666666667[/C][C]0.0885871818872625[/C][C]189.668147340429[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 24 )[/C][C]16.7987931034483[/C][C]0.0875508935341793[/C][C]191.874604876421[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 24 )[/C][C]16.795[/C][C]0.0862637152656235[/C][C]194.693677965119[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 24 )[/C][C]16.7914814814815[/C][C]0.0848624518722168[/C][C]197.86703201512[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 24 )[/C][C]16.7871153846154[/C][C]0.083201103177901[/C][C]201.76553847755[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 24 )[/C][C]16.782[/C][C]0.0812700210811503[/C][C]206.496808746275[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 24 )[/C][C]16.7775[/C][C]0.0792179751612756[/C][C]211.789053757605[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 24 )[/C][C]16.7726086956522[/C][C]0.0769254829733738[/C][C]218.037093136713[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 24 )[/C][C]16.7659090909091[/C][C]0.0747931030541106[/C][C]224.16383872694[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 24 )[/C][C]16.7583333333333[/C][C]0.0729723323275825[/C][C]229.653250743076[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 24 )[/C][C]16.75025[/C][C]0.0710114540237285[/C][C]235.88096075885[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 24 )[/C][C]16.7402631578947[/C][C]0.0691592333011098[/C][C]242.053914695814[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 24 )[/C][C]16.7302777777778[/C][C]0.0669547183053664[/C][C]249.874515213021[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 24 )[/C][C]16.7205882352941[/C][C]0.0643948121498381[/C][C]259.657380417347[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 24 )[/C][C]16.7090625[/C][C]0.0610383264297668[/C][C]273.74706151595[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 24 )[/C][C]16.696[/C][C]0.0562825384815844[/C][C]296.646179266824[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 24 )[/C][C]16.6810714285714[/C][C]0.049546459640295[/C][C]336.675345719457[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 24 )[/C][C]16.6676923076923[/C][C]0.0432925919841959[/C][C]385.001025435874[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 24 )[/C][C]16.6666666666667[/C][C]0.0416753614116575[/C][C]399.916547862369[/C][/ROW]
[ROW][C]Median[/C][C]16.58[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]16.83[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]16.7028947368421[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]16.7028947368421[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]16.7028947368421[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]16.7028947368421[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]16.7028947368421[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]16.7028947368421[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]16.7028947368421[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]16.7266666666667[/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=207353&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=207353&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 Mean16.81291666666670.0926803612123955181.407543590994
Geometric Mean16.7949060404201
Harmonic Mean16.7770363497217
Quadratic Mean16.8310436974195
Winsorized Mean ( 1 / 24 )16.81319444444440.0923215671874855182.115565805988
Winsorized Mean ( 2 / 24 )16.81513888888890.0919889752051518182.795153999576
Winsorized Mean ( 3 / 24 )16.81513888888890.0918434047491368183.084881650655
Winsorized Mean ( 4 / 24 )16.81680555555560.0915718302397741183.646056997244
Winsorized Mean ( 5 / 24 )16.81680555555560.0913333304180993184.125614149542
Winsorized Mean ( 6 / 24 )16.81847222222220.0910688272024893184.678695651002
Winsorized Mean ( 7 / 24 )16.81944444444440.0909162387920393184.999342998747
Winsorized Mean ( 8 / 24 )16.81611111111110.0899381537536133186.974164014741
Winsorized Mean ( 9 / 24 )16.81986111111110.0893590227093813188.227899110017
Winsorized Mean ( 10 / 24 )16.82263888888890.0884784866948307190.132534103024
Winsorized Mean ( 11 / 24 )16.8150.086625125472159194.112272950234
Winsorized Mean ( 12 / 24 )16.8150.0850085147166735197.803714793077
Winsorized Mean ( 13 / 24 )16.82583333333330.081157208962052207.323952468608
Winsorized Mean ( 14 / 24 )16.82777777777780.07670141645165219.393311835192
Winsorized Mean ( 15 / 24 )16.82569444444440.0744699124183072225.939495536564
Winsorized Mean ( 16 / 24 )16.83458333333330.0707098308856772238.079813266012
Winsorized Mean ( 17 / 24 )16.82513888888890.0691497640571042243.314480075371
Winsorized Mean ( 18 / 24 )16.81263888888890.0671184786935924250.4919541702
Winsorized Mean ( 19 / 24 )16.81791666666670.0657022190822485255.971821067617
Winsorized Mean ( 20 / 24 )16.81791666666670.0649114412669695259.090174835242
Winsorized Mean ( 21 / 24 )16.81791666666670.0632575954045783265.863989282297
Winsorized Mean ( 22 / 24 )16.78736111111110.0541100256604811310.244929774108
Winsorized Mean ( 23 / 24 )16.67555555555560.0374833760173234444.878698969077
Winsorized Mean ( 24 / 24 )16.68888888888890.0357277106695247467.11330158426
Trimmed Mean ( 1 / 24 )16.81242857142860.0918914283551323182.959704429163
Trimmed Mean ( 2 / 24 )16.81161764705880.0913251411172902184.085318033809
Trimmed Mean ( 3 / 24 )16.8096969696970.0907980596244235185.132777497983
Trimmed Mean ( 4 / 24 )16.807656250.0901700724940726186.399498027518
Trimmed Mean ( 5 / 24 )16.8050.0894485574000011187.873348530938
Trimmed Mean ( 6 / 24 )16.80216666666670.0885871818872625189.668147340429
Trimmed Mean ( 7 / 24 )16.79879310344830.0875508935341793191.874604876421
Trimmed Mean ( 8 / 24 )16.7950.0862637152656235194.693677965119
Trimmed Mean ( 9 / 24 )16.79148148148150.0848624518722168197.86703201512
Trimmed Mean ( 10 / 24 )16.78711538461540.083201103177901201.76553847755
Trimmed Mean ( 11 / 24 )16.7820.0812700210811503206.496808746275
Trimmed Mean ( 12 / 24 )16.77750.0792179751612756211.789053757605
Trimmed Mean ( 13 / 24 )16.77260869565220.0769254829733738218.037093136713
Trimmed Mean ( 14 / 24 )16.76590909090910.0747931030541106224.16383872694
Trimmed Mean ( 15 / 24 )16.75833333333330.0729723323275825229.653250743076
Trimmed Mean ( 16 / 24 )16.750250.0710114540237285235.88096075885
Trimmed Mean ( 17 / 24 )16.74026315789470.0691592333011098242.053914695814
Trimmed Mean ( 18 / 24 )16.73027777777780.0669547183053664249.874515213021
Trimmed Mean ( 19 / 24 )16.72058823529410.0643948121498381259.657380417347
Trimmed Mean ( 20 / 24 )16.70906250.0610383264297668273.74706151595
Trimmed Mean ( 21 / 24 )16.6960.0562825384815844296.646179266824
Trimmed Mean ( 22 / 24 )16.68107142857140.049546459640295336.675345719457
Trimmed Mean ( 23 / 24 )16.66769230769230.0432925919841959385.001025435874
Trimmed Mean ( 24 / 24 )16.66666666666670.0416753614116575399.916547862369
Median16.58
Midrange16.83
Midmean - Weighted Average at Xnp16.7028947368421
Midmean - Weighted Average at X(n+1)p16.7028947368421
Midmean - Empirical Distribution Function16.7028947368421
Midmean - Empirical Distribution Function - Averaging16.7028947368421
Midmean - Empirical Distribution Function - Interpolation16.7028947368421
Midmean - Closest Observation16.7028947368421
Midmean - True Basic - Statistics Graphics Toolkit16.7028947368421
Midmean - MS Excel (old versions)16.7266666666667
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')