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Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationMon, 08 Dec 2008 12:59:42 -0700
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2008/Dec/08/t1228766494clmv4dc31fn900b.htm/, Retrieved Thu, 16 May 2024 08:01:02 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=30890, Retrieved Thu, 16 May 2024 08:01:02 +0000
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Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords361paper ecosit
Estimated Impact139
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [paper ct economis...] [2008-12-08 19:59:42] [d8c5724db236abb5950452133b88474d] [Current]
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Dataseries X:
108
99
108
104
111
110
106
101
102
99
100
98
92
87
79
87
87
88
83
85
92
84
92
98
103
104
109
107
106
113
107
114
108
104
105
109
109
112
118
111
99
92
92
98
87
97
102
105
111
110
109
111
113
114
120
114
120
122
123
115
123
124
124
132
126
126
122
120
114
116
100
97




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'George Udny Yule' @ 72.249.76.132

\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 & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=30890&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]'George Udny Yule' @ 72.249.76.132[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=30890&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=30890&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'George Udny Yule' @ 72.249.76.132







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean105.7916666666671.4180726935948174.602428454133
Geometric Mean105.100569693040
Harmonic Mean104.393264985529
Quadratic Mean106.464326315333
Winsorized Mean ( 1 / 24 )105.7638888888891.3847895293201476.3754250371993
Winsorized Mean ( 2 / 24 )105.7916666666671.3784811531228476.745094720377
Winsorized Mean ( 3 / 24 )105.751.3528139686604478.1703933059722
Winsorized Mean ( 4 / 24 )105.8611111111111.329705386368279.6124556585032
Winsorized Mean ( 5 / 24 )105.7916666666671.3166410379629780.3496652590607
Winsorized Mean ( 6 / 24 )105.7916666666671.3166410379629780.3496652590607
Winsorized Mean ( 7 / 24 )105.6944444444441.2990966659385481.3599535859676
Winsorized Mean ( 8 / 24 )105.8055555555561.2769227254106482.859795232738
Winsorized Mean ( 9 / 24 )106.0555555555561.1401906755278393.0156313604824
Winsorized Mean ( 10 / 24 )106.0555555555561.1401906755278393.0156313604824
Winsorized Mean ( 11 / 24 )106.0555555555561.1401906755278393.0156313604824
Winsorized Mean ( 12 / 24 )105.7222222222221.0848620889510097.4522230050916
Winsorized Mean ( 13 / 24 )105.3611111111111.02974265506648102.317904956855
Winsorized Mean ( 14 / 24 )106.1388888888890.835983007151176126.962974104682
Winsorized Mean ( 15 / 24 )105.9305555555560.805722488234812131.472755325012
Winsorized Mean ( 16 / 24 )106.1527777777780.771828845099501137.534089910948
Winsorized Mean ( 17 / 24 )106.1527777777780.771828845099501137.534089910948
Winsorized Mean ( 18 / 24 )106.1527777777780.771828845099501137.534089910948
Winsorized Mean ( 19 / 24 )106.1527777777780.695857326403761152.549630146718
Winsorized Mean ( 20 / 24 )106.1527777777780.695857326403761152.549630146718
Winsorized Mean ( 21 / 24 )105.8611111111110.656407433029194161.273480135017
Winsorized Mean ( 22 / 24 )105.8611111111110.572349834593713184.958751995198
Winsorized Mean ( 23 / 24 )105.8611111111110.572349834593713184.958751995198
Winsorized Mean ( 24 / 24 )106.1944444444440.525052679706238202.254837560031
Trimmed Mean ( 1 / 24 )105.81.3555498987312578.0495060336953
Trimmed Mean ( 2 / 24 )105.8382352941181.3207352712667580.1358437202978
Trimmed Mean ( 3 / 24 )105.8636363636361.2831862956306682.5005977106437
Trimmed Mean ( 4 / 24 )105.906251.249944195182984.7287826193737
Trimmed Mean ( 5 / 24 )105.9193548387101.2184242207679586.9314258805123
Trimmed Mean ( 6 / 24 )105.951.184271928232789.4642501221067
Trimmed Mean ( 7 / 24 )105.9827586206901.1424523826614192.7677689058662
Trimmed Mean ( 8 / 24 )106.0357142857141.0957308791645696.7716766059943
Trimmed Mean ( 9 / 24 )106.0740740740741.04371663338185101.631104345222
Trimmed Mean ( 10 / 24 )106.0769230769231.01379852354375104.633140228030
Trimmed Mean ( 11 / 24 )106.080.975972565690036108.691579793535
Trimmed Mean ( 12 / 24 )106.0833333333330.927721859556928114.348209261769
Trimmed Mean ( 13 / 24 )106.1304347826090.87950836928628120.670181761583
Trimmed Mean ( 14 / 24 )106.2272727272730.83010457857914127.968542119233
Trimmed Mean ( 15 / 24 )106.2380952380950.814224243932292130.477686005785
Trimmed Mean ( 16 / 24 )106.2750.799027854846446133.005375664186
Trimmed Mean ( 17 / 24 )106.2894736842110.785635525455365135.291073583522
Trimmed Mean ( 18 / 24 )106.3055555555560.766169035645306138.749480349359
Trimmed Mean ( 19 / 24 )106.3235294117650.738211680527952144.028511355611
Trimmed Mean ( 20 / 24 )106.343750.719275754413491147.848372960541
Trimmed Mean ( 21 / 24 )106.3666666666670.690632449336569154.013421710555
Trimmed Mean ( 22 / 24 )106.4285714285710.659542432835452161.367284544563
Trimmed Mean ( 23 / 24 )106.50.640312423743285166.325056411365
Trimmed Mean ( 24 / 24 )106.5833333333330.607670375305687175.396625645469
Median107
Midrange105.5
Midmean - Weighted Average at Xnp106.463414634146
Midmean - Weighted Average at X(n+1)p106.463414634146
Midmean - Empirical Distribution Function106.463414634146
Midmean - Empirical Distribution Function - Averaging106.463414634146
Midmean - Empirical Distribution Function - Interpolation106.463414634146
Midmean - Closest Observation106.463414634146
Midmean - True Basic - Statistics Graphics Toolkit106.463414634146
Midmean - MS Excel (old versions)106.463414634146
Number of observations72

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 105.791666666667 & 1.41807269359481 & 74.602428454133 \tabularnewline
Geometric Mean & 105.100569693040 &  &  \tabularnewline
Harmonic Mean & 104.393264985529 &  &  \tabularnewline
Quadratic Mean & 106.464326315333 &  &  \tabularnewline
Winsorized Mean ( 1 / 24 ) & 105.763888888889 & 1.38478952932014 & 76.3754250371993 \tabularnewline
Winsorized Mean ( 2 / 24 ) & 105.791666666667 & 1.37848115312284 & 76.745094720377 \tabularnewline
Winsorized Mean ( 3 / 24 ) & 105.75 & 1.35281396866044 & 78.1703933059722 \tabularnewline
Winsorized Mean ( 4 / 24 ) & 105.861111111111 & 1.3297053863682 & 79.6124556585032 \tabularnewline
Winsorized Mean ( 5 / 24 ) & 105.791666666667 & 1.31664103796297 & 80.3496652590607 \tabularnewline
Winsorized Mean ( 6 / 24 ) & 105.791666666667 & 1.31664103796297 & 80.3496652590607 \tabularnewline
Winsorized Mean ( 7 / 24 ) & 105.694444444444 & 1.29909666593854 & 81.3599535859676 \tabularnewline
Winsorized Mean ( 8 / 24 ) & 105.805555555556 & 1.27692272541064 & 82.859795232738 \tabularnewline
Winsorized Mean ( 9 / 24 ) & 106.055555555556 & 1.14019067552783 & 93.0156313604824 \tabularnewline
Winsorized Mean ( 10 / 24 ) & 106.055555555556 & 1.14019067552783 & 93.0156313604824 \tabularnewline
Winsorized Mean ( 11 / 24 ) & 106.055555555556 & 1.14019067552783 & 93.0156313604824 \tabularnewline
Winsorized Mean ( 12 / 24 ) & 105.722222222222 & 1.08486208895100 & 97.4522230050916 \tabularnewline
Winsorized Mean ( 13 / 24 ) & 105.361111111111 & 1.02974265506648 & 102.317904956855 \tabularnewline
Winsorized Mean ( 14 / 24 ) & 106.138888888889 & 0.835983007151176 & 126.962974104682 \tabularnewline
Winsorized Mean ( 15 / 24 ) & 105.930555555556 & 0.805722488234812 & 131.472755325012 \tabularnewline
Winsorized Mean ( 16 / 24 ) & 106.152777777778 & 0.771828845099501 & 137.534089910948 \tabularnewline
Winsorized Mean ( 17 / 24 ) & 106.152777777778 & 0.771828845099501 & 137.534089910948 \tabularnewline
Winsorized Mean ( 18 / 24 ) & 106.152777777778 & 0.771828845099501 & 137.534089910948 \tabularnewline
Winsorized Mean ( 19 / 24 ) & 106.152777777778 & 0.695857326403761 & 152.549630146718 \tabularnewline
Winsorized Mean ( 20 / 24 ) & 106.152777777778 & 0.695857326403761 & 152.549630146718 \tabularnewline
Winsorized Mean ( 21 / 24 ) & 105.861111111111 & 0.656407433029194 & 161.273480135017 \tabularnewline
Winsorized Mean ( 22 / 24 ) & 105.861111111111 & 0.572349834593713 & 184.958751995198 \tabularnewline
Winsorized Mean ( 23 / 24 ) & 105.861111111111 & 0.572349834593713 & 184.958751995198 \tabularnewline
Winsorized Mean ( 24 / 24 ) & 106.194444444444 & 0.525052679706238 & 202.254837560031 \tabularnewline
Trimmed Mean ( 1 / 24 ) & 105.8 & 1.35554989873125 & 78.0495060336953 \tabularnewline
Trimmed Mean ( 2 / 24 ) & 105.838235294118 & 1.32073527126675 & 80.1358437202978 \tabularnewline
Trimmed Mean ( 3 / 24 ) & 105.863636363636 & 1.28318629563066 & 82.5005977106437 \tabularnewline
Trimmed Mean ( 4 / 24 ) & 105.90625 & 1.2499441951829 & 84.7287826193737 \tabularnewline
Trimmed Mean ( 5 / 24 ) & 105.919354838710 & 1.21842422076795 & 86.9314258805123 \tabularnewline
Trimmed Mean ( 6 / 24 ) & 105.95 & 1.1842719282327 & 89.4642501221067 \tabularnewline
Trimmed Mean ( 7 / 24 ) & 105.982758620690 & 1.14245238266141 & 92.7677689058662 \tabularnewline
Trimmed Mean ( 8 / 24 ) & 106.035714285714 & 1.09573087916456 & 96.7716766059943 \tabularnewline
Trimmed Mean ( 9 / 24 ) & 106.074074074074 & 1.04371663338185 & 101.631104345222 \tabularnewline
Trimmed Mean ( 10 / 24 ) & 106.076923076923 & 1.01379852354375 & 104.633140228030 \tabularnewline
Trimmed Mean ( 11 / 24 ) & 106.08 & 0.975972565690036 & 108.691579793535 \tabularnewline
Trimmed Mean ( 12 / 24 ) & 106.083333333333 & 0.927721859556928 & 114.348209261769 \tabularnewline
Trimmed Mean ( 13 / 24 ) & 106.130434782609 & 0.87950836928628 & 120.670181761583 \tabularnewline
Trimmed Mean ( 14 / 24 ) & 106.227272727273 & 0.83010457857914 & 127.968542119233 \tabularnewline
Trimmed Mean ( 15 / 24 ) & 106.238095238095 & 0.814224243932292 & 130.477686005785 \tabularnewline
Trimmed Mean ( 16 / 24 ) & 106.275 & 0.799027854846446 & 133.005375664186 \tabularnewline
Trimmed Mean ( 17 / 24 ) & 106.289473684211 & 0.785635525455365 & 135.291073583522 \tabularnewline
Trimmed Mean ( 18 / 24 ) & 106.305555555556 & 0.766169035645306 & 138.749480349359 \tabularnewline
Trimmed Mean ( 19 / 24 ) & 106.323529411765 & 0.738211680527952 & 144.028511355611 \tabularnewline
Trimmed Mean ( 20 / 24 ) & 106.34375 & 0.719275754413491 & 147.848372960541 \tabularnewline
Trimmed Mean ( 21 / 24 ) & 106.366666666667 & 0.690632449336569 & 154.013421710555 \tabularnewline
Trimmed Mean ( 22 / 24 ) & 106.428571428571 & 0.659542432835452 & 161.367284544563 \tabularnewline
Trimmed Mean ( 23 / 24 ) & 106.5 & 0.640312423743285 & 166.325056411365 \tabularnewline
Trimmed Mean ( 24 / 24 ) & 106.583333333333 & 0.607670375305687 & 175.396625645469 \tabularnewline
Median & 107 &  &  \tabularnewline
Midrange & 105.5 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 106.463414634146 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 106.463414634146 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 106.463414634146 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 106.463414634146 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 106.463414634146 &  &  \tabularnewline
Midmean - Closest Observation & 106.463414634146 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 106.463414634146 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 106.463414634146 &  &  \tabularnewline
Number of observations & 72 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=30890&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]105.791666666667[/C][C]1.41807269359481[/C][C]74.602428454133[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]105.100569693040[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]104.393264985529[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]106.464326315333[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 24 )[/C][C]105.763888888889[/C][C]1.38478952932014[/C][C]76.3754250371993[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 24 )[/C][C]105.791666666667[/C][C]1.37848115312284[/C][C]76.745094720377[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 24 )[/C][C]105.75[/C][C]1.35281396866044[/C][C]78.1703933059722[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 24 )[/C][C]105.861111111111[/C][C]1.3297053863682[/C][C]79.6124556585032[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 24 )[/C][C]105.791666666667[/C][C]1.31664103796297[/C][C]80.3496652590607[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 24 )[/C][C]105.791666666667[/C][C]1.31664103796297[/C][C]80.3496652590607[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 24 )[/C][C]105.694444444444[/C][C]1.29909666593854[/C][C]81.3599535859676[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 24 )[/C][C]105.805555555556[/C][C]1.27692272541064[/C][C]82.859795232738[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 24 )[/C][C]106.055555555556[/C][C]1.14019067552783[/C][C]93.0156313604824[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 24 )[/C][C]106.055555555556[/C][C]1.14019067552783[/C][C]93.0156313604824[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 24 )[/C][C]106.055555555556[/C][C]1.14019067552783[/C][C]93.0156313604824[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 24 )[/C][C]105.722222222222[/C][C]1.08486208895100[/C][C]97.4522230050916[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 24 )[/C][C]105.361111111111[/C][C]1.02974265506648[/C][C]102.317904956855[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 24 )[/C][C]106.138888888889[/C][C]0.835983007151176[/C][C]126.962974104682[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 24 )[/C][C]105.930555555556[/C][C]0.805722488234812[/C][C]131.472755325012[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 24 )[/C][C]106.152777777778[/C][C]0.771828845099501[/C][C]137.534089910948[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 24 )[/C][C]106.152777777778[/C][C]0.771828845099501[/C][C]137.534089910948[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 24 )[/C][C]106.152777777778[/C][C]0.771828845099501[/C][C]137.534089910948[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 24 )[/C][C]106.152777777778[/C][C]0.695857326403761[/C][C]152.549630146718[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 24 )[/C][C]106.152777777778[/C][C]0.695857326403761[/C][C]152.549630146718[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 24 )[/C][C]105.861111111111[/C][C]0.656407433029194[/C][C]161.273480135017[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 24 )[/C][C]105.861111111111[/C][C]0.572349834593713[/C][C]184.958751995198[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 24 )[/C][C]105.861111111111[/C][C]0.572349834593713[/C][C]184.958751995198[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 24 )[/C][C]106.194444444444[/C][C]0.525052679706238[/C][C]202.254837560031[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 24 )[/C][C]105.8[/C][C]1.35554989873125[/C][C]78.0495060336953[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 24 )[/C][C]105.838235294118[/C][C]1.32073527126675[/C][C]80.1358437202978[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 24 )[/C][C]105.863636363636[/C][C]1.28318629563066[/C][C]82.5005977106437[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 24 )[/C][C]105.90625[/C][C]1.2499441951829[/C][C]84.7287826193737[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 24 )[/C][C]105.919354838710[/C][C]1.21842422076795[/C][C]86.9314258805123[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 24 )[/C][C]105.95[/C][C]1.1842719282327[/C][C]89.4642501221067[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 24 )[/C][C]105.982758620690[/C][C]1.14245238266141[/C][C]92.7677689058662[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 24 )[/C][C]106.035714285714[/C][C]1.09573087916456[/C][C]96.7716766059943[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 24 )[/C][C]106.074074074074[/C][C]1.04371663338185[/C][C]101.631104345222[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 24 )[/C][C]106.076923076923[/C][C]1.01379852354375[/C][C]104.633140228030[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 24 )[/C][C]106.08[/C][C]0.975972565690036[/C][C]108.691579793535[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 24 )[/C][C]106.083333333333[/C][C]0.927721859556928[/C][C]114.348209261769[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 24 )[/C][C]106.130434782609[/C][C]0.87950836928628[/C][C]120.670181761583[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 24 )[/C][C]106.227272727273[/C][C]0.83010457857914[/C][C]127.968542119233[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 24 )[/C][C]106.238095238095[/C][C]0.814224243932292[/C][C]130.477686005785[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 24 )[/C][C]106.275[/C][C]0.799027854846446[/C][C]133.005375664186[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 24 )[/C][C]106.289473684211[/C][C]0.785635525455365[/C][C]135.291073583522[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 24 )[/C][C]106.305555555556[/C][C]0.766169035645306[/C][C]138.749480349359[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 24 )[/C][C]106.323529411765[/C][C]0.738211680527952[/C][C]144.028511355611[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 24 )[/C][C]106.34375[/C][C]0.719275754413491[/C][C]147.848372960541[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 24 )[/C][C]106.366666666667[/C][C]0.690632449336569[/C][C]154.013421710555[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 24 )[/C][C]106.428571428571[/C][C]0.659542432835452[/C][C]161.367284544563[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 24 )[/C][C]106.5[/C][C]0.640312423743285[/C][C]166.325056411365[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 24 )[/C][C]106.583333333333[/C][C]0.607670375305687[/C][C]175.396625645469[/C][/ROW]
[ROW][C]Median[/C][C]107[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]105.5[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]106.463414634146[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]106.463414634146[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]106.463414634146[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]106.463414634146[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]106.463414634146[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]106.463414634146[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]106.463414634146[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]106.463414634146[/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=30890&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=30890&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 Mean105.7916666666671.4180726935948174.602428454133
Geometric Mean105.100569693040
Harmonic Mean104.393264985529
Quadratic Mean106.464326315333
Winsorized Mean ( 1 / 24 )105.7638888888891.3847895293201476.3754250371993
Winsorized Mean ( 2 / 24 )105.7916666666671.3784811531228476.745094720377
Winsorized Mean ( 3 / 24 )105.751.3528139686604478.1703933059722
Winsorized Mean ( 4 / 24 )105.8611111111111.329705386368279.6124556585032
Winsorized Mean ( 5 / 24 )105.7916666666671.3166410379629780.3496652590607
Winsorized Mean ( 6 / 24 )105.7916666666671.3166410379629780.3496652590607
Winsorized Mean ( 7 / 24 )105.6944444444441.2990966659385481.3599535859676
Winsorized Mean ( 8 / 24 )105.8055555555561.2769227254106482.859795232738
Winsorized Mean ( 9 / 24 )106.0555555555561.1401906755278393.0156313604824
Winsorized Mean ( 10 / 24 )106.0555555555561.1401906755278393.0156313604824
Winsorized Mean ( 11 / 24 )106.0555555555561.1401906755278393.0156313604824
Winsorized Mean ( 12 / 24 )105.7222222222221.0848620889510097.4522230050916
Winsorized Mean ( 13 / 24 )105.3611111111111.02974265506648102.317904956855
Winsorized Mean ( 14 / 24 )106.1388888888890.835983007151176126.962974104682
Winsorized Mean ( 15 / 24 )105.9305555555560.805722488234812131.472755325012
Winsorized Mean ( 16 / 24 )106.1527777777780.771828845099501137.534089910948
Winsorized Mean ( 17 / 24 )106.1527777777780.771828845099501137.534089910948
Winsorized Mean ( 18 / 24 )106.1527777777780.771828845099501137.534089910948
Winsorized Mean ( 19 / 24 )106.1527777777780.695857326403761152.549630146718
Winsorized Mean ( 20 / 24 )106.1527777777780.695857326403761152.549630146718
Winsorized Mean ( 21 / 24 )105.8611111111110.656407433029194161.273480135017
Winsorized Mean ( 22 / 24 )105.8611111111110.572349834593713184.958751995198
Winsorized Mean ( 23 / 24 )105.8611111111110.572349834593713184.958751995198
Winsorized Mean ( 24 / 24 )106.1944444444440.525052679706238202.254837560031
Trimmed Mean ( 1 / 24 )105.81.3555498987312578.0495060336953
Trimmed Mean ( 2 / 24 )105.8382352941181.3207352712667580.1358437202978
Trimmed Mean ( 3 / 24 )105.8636363636361.2831862956306682.5005977106437
Trimmed Mean ( 4 / 24 )105.906251.249944195182984.7287826193737
Trimmed Mean ( 5 / 24 )105.9193548387101.2184242207679586.9314258805123
Trimmed Mean ( 6 / 24 )105.951.184271928232789.4642501221067
Trimmed Mean ( 7 / 24 )105.9827586206901.1424523826614192.7677689058662
Trimmed Mean ( 8 / 24 )106.0357142857141.0957308791645696.7716766059943
Trimmed Mean ( 9 / 24 )106.0740740740741.04371663338185101.631104345222
Trimmed Mean ( 10 / 24 )106.0769230769231.01379852354375104.633140228030
Trimmed Mean ( 11 / 24 )106.080.975972565690036108.691579793535
Trimmed Mean ( 12 / 24 )106.0833333333330.927721859556928114.348209261769
Trimmed Mean ( 13 / 24 )106.1304347826090.87950836928628120.670181761583
Trimmed Mean ( 14 / 24 )106.2272727272730.83010457857914127.968542119233
Trimmed Mean ( 15 / 24 )106.2380952380950.814224243932292130.477686005785
Trimmed Mean ( 16 / 24 )106.2750.799027854846446133.005375664186
Trimmed Mean ( 17 / 24 )106.2894736842110.785635525455365135.291073583522
Trimmed Mean ( 18 / 24 )106.3055555555560.766169035645306138.749480349359
Trimmed Mean ( 19 / 24 )106.3235294117650.738211680527952144.028511355611
Trimmed Mean ( 20 / 24 )106.343750.719275754413491147.848372960541
Trimmed Mean ( 21 / 24 )106.3666666666670.690632449336569154.013421710555
Trimmed Mean ( 22 / 24 )106.4285714285710.659542432835452161.367284544563
Trimmed Mean ( 23 / 24 )106.50.640312423743285166.325056411365
Trimmed Mean ( 24 / 24 )106.5833333333330.607670375305687175.396625645469
Median107
Midrange105.5
Midmean - Weighted Average at Xnp106.463414634146
Midmean - Weighted Average at X(n+1)p106.463414634146
Midmean - Empirical Distribution Function106.463414634146
Midmean - Empirical Distribution Function - Averaging106.463414634146
Midmean - Empirical Distribution Function - Interpolation106.463414634146
Midmean - Closest Observation106.463414634146
Midmean - True Basic - Statistics Graphics Toolkit106.463414634146
Midmean - MS Excel (old versions)106.463414634146
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')