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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 08:15:27 -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/t1362489340zv2mi7aot5btk1m.htm/, Retrieved Sat, 04 May 2024 15:44:14 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=207384, Retrieved Sat, 04 May 2024 15:44:14 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact114
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [] [2013-03-05 13:15:27] [a20b39b66cdf12df5e07217cd6d70728] [Current]
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Dataseries X:
130,65
130,39
130,37
128,53
126,7
126,7
126,7
126,82
127,26
126,87
126,57
126,39
126,39
126,13
125,98
123,02
122,49
121,83
121,83
121,73
122,23
121,91
122,03
122,14
122,14
122
121,37
119,04
118,55
118,55
118,55
118,54
118,45
118,49
118,47
118,08
118,08
117,94
117
115,46
113,8
113,71
113,71
113,71
113,47
113,37
113,21
113,15
113,15
113,04
112,46
111,46
110,92
110,84
110,84
110,84
110,86
110,71
110,75
110,82
110,82
110,72
110,49
108,95
108,1
108,16
108,16
108,16
108,14
107,72
107,56
107,2




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Sir Ronald Aylmer Fisher' @ fisher.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 & 'Sir Ronald Aylmer Fisher' @ fisher.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=207384&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]'Sir Ronald Aylmer Fisher' @ fisher.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=207384&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=207384&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'Sir Ronald Aylmer Fisher' @ fisher.wessa.net







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean117.5190277777780.80819460984077145.409318927444
Geometric Mean117.322989721973
Harmonic Mean117.128456130341
Quadratic Mean117.716173762477
Winsorized Mean ( 1 / 24 )117.5204166666670.806491159599731145.718170953037
Winsorized Mean ( 2 / 24 )117.5243055555560.805598874874037145.884396342946
Winsorized Mean ( 3 / 24 )117.4634722222220.786698375060268149.311954805072
Winsorized Mean ( 4 / 24 )117.3951388888890.772988504578374151.871778420459
Winsorized Mean ( 5 / 24 )117.3694444444440.767960275468929152.832702671732
Winsorized Mean ( 6 / 24 )117.3652777777780.767235678111812152.971611104709
Winsorized Mean ( 7 / 24 )117.3536111111110.765219707870109153.359368432564
Winsorized Mean ( 8 / 24 )117.4413888888890.750797653702896156.422157567587
Winsorized Mean ( 9 / 24 )117.6338888888890.722015023847702162.92443370777
Winsorized Mean ( 10 / 24 )117.6463888888890.714612661576814164.629589166946
Winsorized Mean ( 11 / 24 )117.6204166666670.709591796668381165.757858558834
Winsorized Mean ( 12 / 24 )117.6254166666670.708907884559821165.924824971729
Winsorized Mean ( 13 / 24 )117.5911111111110.699056696056808168.213982892105
Winsorized Mean ( 14 / 24 )117.5619444444440.694056469869787169.383831933013
Winsorized Mean ( 15 / 24 )116.9494444444440.595919578737539196.250381120558
Winsorized Mean ( 16 / 24 )116.8316666666670.579364972636417201.654694682388
Winsorized Mean ( 17 / 24 )116.7702777777780.571008530813871204.498306901549
Winsorized Mean ( 18 / 24 )116.7527777777780.567257191002651205.819828518017
Winsorized Mean ( 19 / 24 )116.7686111111110.564944542320841206.690395895171
Winsorized Mean ( 20 / 24 )116.8880555555560.539271615015023216.751730113404
Winsorized Mean ( 21 / 24 )117.1709722222220.497929836477852235.316230597951
Winsorized Mean ( 22 / 24 )117.3206944444440.471001261190863249.087856257147
Winsorized Mean ( 23 / 24 )117.3302777777780.463015392831928253.404702293274
Winsorized Mean ( 24 / 24 )117.3302777777780.463015392831928253.404702293274
Trimmed Mean ( 1 / 24 )117.4788571428570.795956513863011147.594567161336
Trimmed Mean ( 2 / 24 )117.4348529411760.783222040281747149.93813618796
Trimmed Mean ( 3 / 24 )117.3860606060610.768397414378574152.767381057619
Trimmed Mean ( 4 / 24 )117.357031250.758956464276469154.629463973114
Trimmed Mean ( 5 / 24 )117.3459677419350.75212761708973156.01869293936
Trimmed Mean ( 6 / 24 )117.3403333333330.744920841609129157.52054014204
Trimmed Mean ( 7 / 24 )117.3351724137930.735872559317112159.450397936675
Trimmed Mean ( 8 / 24 )117.3317857142860.724869540754178161.866072606955
Trimmed Mean ( 9 / 24 )117.3135185185190.714310795918791164.23315899576
Trimmed Mean ( 10 / 24 )117.2642307692310.706977151520319165.867072955696
Trimmed Mean ( 11 / 24 )117.20920.698630487716752167.769947147684
Trimmed Mean ( 12 / 24 )117.1531250.688449354602029170.169561808541
Trimmed Mean ( 13 / 24 )117.091521739130.674864449971184173.503763228497
Trimmed Mean ( 14 / 24 )117.0286363636360.658962008974398177.595422452015
Trimmed Mean ( 15 / 24 )116.9633333333330.638810475081573183.095515643192
Trimmed Mean ( 16 / 24 )116.9650.634748688408174184.269778159488
Trimmed Mean ( 17 / 24 )116.9807894736840.631376421120052185.278996111641
Trimmed Mean ( 18 / 24 )117.0055555555560.626907811308864186.639173168492
Trimmed Mean ( 19 / 24 )117.0352941176470.619812839799575188.823603840624
Trimmed Mean ( 20 / 24 )117.0668750.608698445770206192.323269121989
Trimmed Mean ( 21 / 24 )117.0883333333330.598336983307793195.689614046641
Trimmed Mean ( 22 / 24 )117.0782142857140.593078921194244197.40747833351
Trimmed Mean ( 23 / 24 )117.0476923076920.589967224041969198.396940605917
Trimmed Mean ( 24 / 24 )117.0108333333330.583816751037747200.423905489769
Median118.08
Midrange118.925
Midmean - Weighted Average at Xnp116.531282051282
Midmean - Weighted Average at X(n+1)p117.005555555556
Midmean - Empirical Distribution Function116.531282051282
Midmean - Empirical Distribution Function - Averaging117.005555555556
Midmean - Empirical Distribution Function - Interpolation117.005555555556
Midmean - Closest Observation116.531282051282
Midmean - True Basic - Statistics Graphics Toolkit117.005555555556
Midmean - MS Excel (old versions)116.67375
Number of observations72

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 117.519027777778 & 0.80819460984077 & 145.409318927444 \tabularnewline
Geometric Mean & 117.322989721973 &  &  \tabularnewline
Harmonic Mean & 117.128456130341 &  &  \tabularnewline
Quadratic Mean & 117.716173762477 &  &  \tabularnewline
Winsorized Mean ( 1 / 24 ) & 117.520416666667 & 0.806491159599731 & 145.718170953037 \tabularnewline
Winsorized Mean ( 2 / 24 ) & 117.524305555556 & 0.805598874874037 & 145.884396342946 \tabularnewline
Winsorized Mean ( 3 / 24 ) & 117.463472222222 & 0.786698375060268 & 149.311954805072 \tabularnewline
Winsorized Mean ( 4 / 24 ) & 117.395138888889 & 0.772988504578374 & 151.871778420459 \tabularnewline
Winsorized Mean ( 5 / 24 ) & 117.369444444444 & 0.767960275468929 & 152.832702671732 \tabularnewline
Winsorized Mean ( 6 / 24 ) & 117.365277777778 & 0.767235678111812 & 152.971611104709 \tabularnewline
Winsorized Mean ( 7 / 24 ) & 117.353611111111 & 0.765219707870109 & 153.359368432564 \tabularnewline
Winsorized Mean ( 8 / 24 ) & 117.441388888889 & 0.750797653702896 & 156.422157567587 \tabularnewline
Winsorized Mean ( 9 / 24 ) & 117.633888888889 & 0.722015023847702 & 162.92443370777 \tabularnewline
Winsorized Mean ( 10 / 24 ) & 117.646388888889 & 0.714612661576814 & 164.629589166946 \tabularnewline
Winsorized Mean ( 11 / 24 ) & 117.620416666667 & 0.709591796668381 & 165.757858558834 \tabularnewline
Winsorized Mean ( 12 / 24 ) & 117.625416666667 & 0.708907884559821 & 165.924824971729 \tabularnewline
Winsorized Mean ( 13 / 24 ) & 117.591111111111 & 0.699056696056808 & 168.213982892105 \tabularnewline
Winsorized Mean ( 14 / 24 ) & 117.561944444444 & 0.694056469869787 & 169.383831933013 \tabularnewline
Winsorized Mean ( 15 / 24 ) & 116.949444444444 & 0.595919578737539 & 196.250381120558 \tabularnewline
Winsorized Mean ( 16 / 24 ) & 116.831666666667 & 0.579364972636417 & 201.654694682388 \tabularnewline
Winsorized Mean ( 17 / 24 ) & 116.770277777778 & 0.571008530813871 & 204.498306901549 \tabularnewline
Winsorized Mean ( 18 / 24 ) & 116.752777777778 & 0.567257191002651 & 205.819828518017 \tabularnewline
Winsorized Mean ( 19 / 24 ) & 116.768611111111 & 0.564944542320841 & 206.690395895171 \tabularnewline
Winsorized Mean ( 20 / 24 ) & 116.888055555556 & 0.539271615015023 & 216.751730113404 \tabularnewline
Winsorized Mean ( 21 / 24 ) & 117.170972222222 & 0.497929836477852 & 235.316230597951 \tabularnewline
Winsorized Mean ( 22 / 24 ) & 117.320694444444 & 0.471001261190863 & 249.087856257147 \tabularnewline
Winsorized Mean ( 23 / 24 ) & 117.330277777778 & 0.463015392831928 & 253.404702293274 \tabularnewline
Winsorized Mean ( 24 / 24 ) & 117.330277777778 & 0.463015392831928 & 253.404702293274 \tabularnewline
Trimmed Mean ( 1 / 24 ) & 117.478857142857 & 0.795956513863011 & 147.594567161336 \tabularnewline
Trimmed Mean ( 2 / 24 ) & 117.434852941176 & 0.783222040281747 & 149.93813618796 \tabularnewline
Trimmed Mean ( 3 / 24 ) & 117.386060606061 & 0.768397414378574 & 152.767381057619 \tabularnewline
Trimmed Mean ( 4 / 24 ) & 117.35703125 & 0.758956464276469 & 154.629463973114 \tabularnewline
Trimmed Mean ( 5 / 24 ) & 117.345967741935 & 0.75212761708973 & 156.01869293936 \tabularnewline
Trimmed Mean ( 6 / 24 ) & 117.340333333333 & 0.744920841609129 & 157.52054014204 \tabularnewline
Trimmed Mean ( 7 / 24 ) & 117.335172413793 & 0.735872559317112 & 159.450397936675 \tabularnewline
Trimmed Mean ( 8 / 24 ) & 117.331785714286 & 0.724869540754178 & 161.866072606955 \tabularnewline
Trimmed Mean ( 9 / 24 ) & 117.313518518519 & 0.714310795918791 & 164.23315899576 \tabularnewline
Trimmed Mean ( 10 / 24 ) & 117.264230769231 & 0.706977151520319 & 165.867072955696 \tabularnewline
Trimmed Mean ( 11 / 24 ) & 117.2092 & 0.698630487716752 & 167.769947147684 \tabularnewline
Trimmed Mean ( 12 / 24 ) & 117.153125 & 0.688449354602029 & 170.169561808541 \tabularnewline
Trimmed Mean ( 13 / 24 ) & 117.09152173913 & 0.674864449971184 & 173.503763228497 \tabularnewline
Trimmed Mean ( 14 / 24 ) & 117.028636363636 & 0.658962008974398 & 177.595422452015 \tabularnewline
Trimmed Mean ( 15 / 24 ) & 116.963333333333 & 0.638810475081573 & 183.095515643192 \tabularnewline
Trimmed Mean ( 16 / 24 ) & 116.965 & 0.634748688408174 & 184.269778159488 \tabularnewline
Trimmed Mean ( 17 / 24 ) & 116.980789473684 & 0.631376421120052 & 185.278996111641 \tabularnewline
Trimmed Mean ( 18 / 24 ) & 117.005555555556 & 0.626907811308864 & 186.639173168492 \tabularnewline
Trimmed Mean ( 19 / 24 ) & 117.035294117647 & 0.619812839799575 & 188.823603840624 \tabularnewline
Trimmed Mean ( 20 / 24 ) & 117.066875 & 0.608698445770206 & 192.323269121989 \tabularnewline
Trimmed Mean ( 21 / 24 ) & 117.088333333333 & 0.598336983307793 & 195.689614046641 \tabularnewline
Trimmed Mean ( 22 / 24 ) & 117.078214285714 & 0.593078921194244 & 197.40747833351 \tabularnewline
Trimmed Mean ( 23 / 24 ) & 117.047692307692 & 0.589967224041969 & 198.396940605917 \tabularnewline
Trimmed Mean ( 24 / 24 ) & 117.010833333333 & 0.583816751037747 & 200.423905489769 \tabularnewline
Median & 118.08 &  &  \tabularnewline
Midrange & 118.925 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 116.531282051282 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 117.005555555556 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 116.531282051282 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 117.005555555556 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 117.005555555556 &  &  \tabularnewline
Midmean - Closest Observation & 116.531282051282 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 117.005555555556 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 116.67375 &  &  \tabularnewline
Number of observations & 72 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=207384&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]117.519027777778[/C][C]0.80819460984077[/C][C]145.409318927444[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]117.322989721973[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]117.128456130341[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]117.716173762477[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 24 )[/C][C]117.520416666667[/C][C]0.806491159599731[/C][C]145.718170953037[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 24 )[/C][C]117.524305555556[/C][C]0.805598874874037[/C][C]145.884396342946[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 24 )[/C][C]117.463472222222[/C][C]0.786698375060268[/C][C]149.311954805072[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 24 )[/C][C]117.395138888889[/C][C]0.772988504578374[/C][C]151.871778420459[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 24 )[/C][C]117.369444444444[/C][C]0.767960275468929[/C][C]152.832702671732[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 24 )[/C][C]117.365277777778[/C][C]0.767235678111812[/C][C]152.971611104709[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 24 )[/C][C]117.353611111111[/C][C]0.765219707870109[/C][C]153.359368432564[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 24 )[/C][C]117.441388888889[/C][C]0.750797653702896[/C][C]156.422157567587[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 24 )[/C][C]117.633888888889[/C][C]0.722015023847702[/C][C]162.92443370777[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 24 )[/C][C]117.646388888889[/C][C]0.714612661576814[/C][C]164.629589166946[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 24 )[/C][C]117.620416666667[/C][C]0.709591796668381[/C][C]165.757858558834[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 24 )[/C][C]117.625416666667[/C][C]0.708907884559821[/C][C]165.924824971729[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 24 )[/C][C]117.591111111111[/C][C]0.699056696056808[/C][C]168.213982892105[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 24 )[/C][C]117.561944444444[/C][C]0.694056469869787[/C][C]169.383831933013[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 24 )[/C][C]116.949444444444[/C][C]0.595919578737539[/C][C]196.250381120558[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 24 )[/C][C]116.831666666667[/C][C]0.579364972636417[/C][C]201.654694682388[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 24 )[/C][C]116.770277777778[/C][C]0.571008530813871[/C][C]204.498306901549[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 24 )[/C][C]116.752777777778[/C][C]0.567257191002651[/C][C]205.819828518017[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 24 )[/C][C]116.768611111111[/C][C]0.564944542320841[/C][C]206.690395895171[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 24 )[/C][C]116.888055555556[/C][C]0.539271615015023[/C][C]216.751730113404[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 24 )[/C][C]117.170972222222[/C][C]0.497929836477852[/C][C]235.316230597951[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 24 )[/C][C]117.320694444444[/C][C]0.471001261190863[/C][C]249.087856257147[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 24 )[/C][C]117.330277777778[/C][C]0.463015392831928[/C][C]253.404702293274[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 24 )[/C][C]117.330277777778[/C][C]0.463015392831928[/C][C]253.404702293274[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 24 )[/C][C]117.478857142857[/C][C]0.795956513863011[/C][C]147.594567161336[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 24 )[/C][C]117.434852941176[/C][C]0.783222040281747[/C][C]149.93813618796[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 24 )[/C][C]117.386060606061[/C][C]0.768397414378574[/C][C]152.767381057619[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 24 )[/C][C]117.35703125[/C][C]0.758956464276469[/C][C]154.629463973114[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 24 )[/C][C]117.345967741935[/C][C]0.75212761708973[/C][C]156.01869293936[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 24 )[/C][C]117.340333333333[/C][C]0.744920841609129[/C][C]157.52054014204[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 24 )[/C][C]117.335172413793[/C][C]0.735872559317112[/C][C]159.450397936675[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 24 )[/C][C]117.331785714286[/C][C]0.724869540754178[/C][C]161.866072606955[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 24 )[/C][C]117.313518518519[/C][C]0.714310795918791[/C][C]164.23315899576[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 24 )[/C][C]117.264230769231[/C][C]0.706977151520319[/C][C]165.867072955696[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 24 )[/C][C]117.2092[/C][C]0.698630487716752[/C][C]167.769947147684[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 24 )[/C][C]117.153125[/C][C]0.688449354602029[/C][C]170.169561808541[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 24 )[/C][C]117.09152173913[/C][C]0.674864449971184[/C][C]173.503763228497[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 24 )[/C][C]117.028636363636[/C][C]0.658962008974398[/C][C]177.595422452015[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 24 )[/C][C]116.963333333333[/C][C]0.638810475081573[/C][C]183.095515643192[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 24 )[/C][C]116.965[/C][C]0.634748688408174[/C][C]184.269778159488[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 24 )[/C][C]116.980789473684[/C][C]0.631376421120052[/C][C]185.278996111641[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 24 )[/C][C]117.005555555556[/C][C]0.626907811308864[/C][C]186.639173168492[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 24 )[/C][C]117.035294117647[/C][C]0.619812839799575[/C][C]188.823603840624[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 24 )[/C][C]117.066875[/C][C]0.608698445770206[/C][C]192.323269121989[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 24 )[/C][C]117.088333333333[/C][C]0.598336983307793[/C][C]195.689614046641[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 24 )[/C][C]117.078214285714[/C][C]0.593078921194244[/C][C]197.40747833351[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 24 )[/C][C]117.047692307692[/C][C]0.589967224041969[/C][C]198.396940605917[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 24 )[/C][C]117.010833333333[/C][C]0.583816751037747[/C][C]200.423905489769[/C][/ROW]
[ROW][C]Median[/C][C]118.08[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]118.925[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]116.531282051282[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]117.005555555556[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]116.531282051282[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]117.005555555556[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]117.005555555556[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]116.531282051282[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]117.005555555556[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]116.67375[/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=207384&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=207384&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 Mean117.5190277777780.80819460984077145.409318927444
Geometric Mean117.322989721973
Harmonic Mean117.128456130341
Quadratic Mean117.716173762477
Winsorized Mean ( 1 / 24 )117.5204166666670.806491159599731145.718170953037
Winsorized Mean ( 2 / 24 )117.5243055555560.805598874874037145.884396342946
Winsorized Mean ( 3 / 24 )117.4634722222220.786698375060268149.311954805072
Winsorized Mean ( 4 / 24 )117.3951388888890.772988504578374151.871778420459
Winsorized Mean ( 5 / 24 )117.3694444444440.767960275468929152.832702671732
Winsorized Mean ( 6 / 24 )117.3652777777780.767235678111812152.971611104709
Winsorized Mean ( 7 / 24 )117.3536111111110.765219707870109153.359368432564
Winsorized Mean ( 8 / 24 )117.4413888888890.750797653702896156.422157567587
Winsorized Mean ( 9 / 24 )117.6338888888890.722015023847702162.92443370777
Winsorized Mean ( 10 / 24 )117.6463888888890.714612661576814164.629589166946
Winsorized Mean ( 11 / 24 )117.6204166666670.709591796668381165.757858558834
Winsorized Mean ( 12 / 24 )117.6254166666670.708907884559821165.924824971729
Winsorized Mean ( 13 / 24 )117.5911111111110.699056696056808168.213982892105
Winsorized Mean ( 14 / 24 )117.5619444444440.694056469869787169.383831933013
Winsorized Mean ( 15 / 24 )116.9494444444440.595919578737539196.250381120558
Winsorized Mean ( 16 / 24 )116.8316666666670.579364972636417201.654694682388
Winsorized Mean ( 17 / 24 )116.7702777777780.571008530813871204.498306901549
Winsorized Mean ( 18 / 24 )116.7527777777780.567257191002651205.819828518017
Winsorized Mean ( 19 / 24 )116.7686111111110.564944542320841206.690395895171
Winsorized Mean ( 20 / 24 )116.8880555555560.539271615015023216.751730113404
Winsorized Mean ( 21 / 24 )117.1709722222220.497929836477852235.316230597951
Winsorized Mean ( 22 / 24 )117.3206944444440.471001261190863249.087856257147
Winsorized Mean ( 23 / 24 )117.3302777777780.463015392831928253.404702293274
Winsorized Mean ( 24 / 24 )117.3302777777780.463015392831928253.404702293274
Trimmed Mean ( 1 / 24 )117.4788571428570.795956513863011147.594567161336
Trimmed Mean ( 2 / 24 )117.4348529411760.783222040281747149.93813618796
Trimmed Mean ( 3 / 24 )117.3860606060610.768397414378574152.767381057619
Trimmed Mean ( 4 / 24 )117.357031250.758956464276469154.629463973114
Trimmed Mean ( 5 / 24 )117.3459677419350.75212761708973156.01869293936
Trimmed Mean ( 6 / 24 )117.3403333333330.744920841609129157.52054014204
Trimmed Mean ( 7 / 24 )117.3351724137930.735872559317112159.450397936675
Trimmed Mean ( 8 / 24 )117.3317857142860.724869540754178161.866072606955
Trimmed Mean ( 9 / 24 )117.3135185185190.714310795918791164.23315899576
Trimmed Mean ( 10 / 24 )117.2642307692310.706977151520319165.867072955696
Trimmed Mean ( 11 / 24 )117.20920.698630487716752167.769947147684
Trimmed Mean ( 12 / 24 )117.1531250.688449354602029170.169561808541
Trimmed Mean ( 13 / 24 )117.091521739130.674864449971184173.503763228497
Trimmed Mean ( 14 / 24 )117.0286363636360.658962008974398177.595422452015
Trimmed Mean ( 15 / 24 )116.9633333333330.638810475081573183.095515643192
Trimmed Mean ( 16 / 24 )116.9650.634748688408174184.269778159488
Trimmed Mean ( 17 / 24 )116.9807894736840.631376421120052185.278996111641
Trimmed Mean ( 18 / 24 )117.0055555555560.626907811308864186.639173168492
Trimmed Mean ( 19 / 24 )117.0352941176470.619812839799575188.823603840624
Trimmed Mean ( 20 / 24 )117.0668750.608698445770206192.323269121989
Trimmed Mean ( 21 / 24 )117.0883333333330.598336983307793195.689614046641
Trimmed Mean ( 22 / 24 )117.0782142857140.593078921194244197.40747833351
Trimmed Mean ( 23 / 24 )117.0476923076920.589967224041969198.396940605917
Trimmed Mean ( 24 / 24 )117.0108333333330.583816751037747200.423905489769
Median118.08
Midrange118.925
Midmean - Weighted Average at Xnp116.531282051282
Midmean - Weighted Average at X(n+1)p117.005555555556
Midmean - Empirical Distribution Function116.531282051282
Midmean - Empirical Distribution Function - Averaging117.005555555556
Midmean - Empirical Distribution Function - Interpolation117.005555555556
Midmean - Closest Observation116.531282051282
Midmean - True Basic - Statistics Graphics Toolkit117.005555555556
Midmean - MS Excel (old versions)116.67375
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')