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of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationSun, 06 Jun 2010 20:54:02 +0000
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2010/Jun/06/t1275857699b7k572cti2hbuj4.htm/, Retrieved Sun, 28 Apr 2024 16:32:45 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=77801, Retrieved Sun, 28 Apr 2024 16:32:45 +0000
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Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact101
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [] [2010-06-06 20:54:02] [aec95ccba2c38285ca49e8d90cbfedc9] [Current]
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Dataseries X:
133
126
120
114
116
153
162
161
149
139
135
130
127
122
117
112
113
149
157
157
147
137
132
125
123
117
114
111
112
144
150
149
134
123
116
117
111
105
102
95
93
124
130
124
115
106
105
105
101
95
93
84
87
116
120
117
109
105
107
109
109
108
107
99
103
131
137
135
124
118
121
121
118
113
107




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time41 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 & 41 seconds \tabularnewline
R Server & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=77801&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]41 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=77801&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=77801&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 time41 seconds
R Server'George Udny Yule' @ 72.249.76.132







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean120.6933333333332.0603483772011658.5790901523591
Geometric Mean119.419256046999
Harmonic Mean118.169790496441
Quadratic Mean121.987758948730
Winsorized Mean ( 1 / 25 )120.722.0475043037497858.9595830294054
Winsorized Mean ( 2 / 25 )120.7733333333331.9872180140677760.7750797740176
Winsorized Mean ( 3 / 25 )120.7733333333331.9872180140677760.7750797740176
Winsorized Mean ( 4 / 25 )120.6666666666671.9168605464024662.9501540386608
Winsorized Mean ( 5 / 25 )120.4666666666671.8727378746496164.3264966749316
Winsorized Mean ( 6 / 25 )120.7066666666671.8001775020922467.0526470452923
Winsorized Mean ( 7 / 25 )120.8933333333331.7707913773514168.2707939961593
Winsorized Mean ( 8 / 25 )1211.7548902072892368.9501824657783
Winsorized Mean ( 9 / 25 )120.881.6865082003684171.6747181979868
Winsorized Mean ( 10 / 25 )120.7466666666671.5672427539631077.0440101645602
Winsorized Mean ( 11 / 25 )120.0133333333331.4274646248700084.0744710883906
Winsorized Mean ( 12 / 25 )119.6933333333331.3713902111037287.2788301711748
Winsorized Mean ( 13 / 25 )119.6933333333331.3713902111037287.2788301711748
Winsorized Mean ( 14 / 25 )119.5066666666671.2822240437998793.2026405560985
Winsorized Mean ( 15 / 25 )119.7066666666671.2542932877328495.4375406752268
Winsorized Mean ( 16 / 25 )119.4933333333331.2195662104788597.9801935365326
Winsorized Mean ( 17 / 25 )119.2666666666671.18357122339166100.768474519762
Winsorized Mean ( 18 / 25 )119.2666666666671.11295942364431107.161738454162
Winsorized Mean ( 19 / 25 )119.2666666666671.03980825213171114.700634873938
Winsorized Mean ( 20 / 25 )1190.999639574686436119.042906076750
Winsorized Mean ( 21 / 25 )1190.999639574686436119.042906076750
Winsorized Mean ( 22 / 25 )118.7066666666670.793390110770148149.619544099734
Winsorized Mean ( 23 / 25 )118.40.750735375217928157.712029975449
Winsorized Mean ( 24 / 25 )118.40.66522366353169177.985249910401
Winsorized Mean ( 25 / 25 )118.0666666666670.62134214895343190.018763197595
Trimmed Mean ( 1 / 25 )120.6301369863011.9752566495396661.0706142993695
Trimmed Mean ( 2 / 25 )120.5352112676061.8895914184655463.7890340153466
Trimmed Mean ( 3 / 25 )120.4057971014491.8267127035154965.9139211490288
Trimmed Mean ( 4 / 25 )120.2686567164181.7514718356093368.6671942255794
Trimmed Mean ( 5 / 25 )120.1538461538461.6880847660928671.177614162082
Trimmed Mean ( 6 / 25 )120.0793650793651.6262852394749073.8365953060833
Trimmed Mean ( 7 / 25 )119.9508196721311.572375292301676.286380394944
Trimmed Mean ( 8 / 25 )119.7796610169491.5140232468296179.1134886916495
Trimmed Mean ( 9 / 25 )119.5789473684211.4457498354590982.7106767959268
Trimmed Mean ( 10 / 25 )119.3818181818181.3784026545881686.6088133133252
Trimmed Mean ( 11 / 25 )119.1886792452831.3235767073619590.0504508596562
Trimmed Mean ( 12 / 25 )119.0784313725491.2885143100713992.4152960054837
Trimmed Mean ( 13 / 25 )1191.256615148982894.6988424390139
Trimmed Mean ( 14 / 25 )118.9148936170211.2153922583129797.8407528957617
Trimmed Mean ( 15 / 25 )118.8444444444441.18234297249215100.516049242415
Trimmed Mean ( 16 / 25 )118.7441860465121.14463117866281103.740128925399
Trimmed Mean ( 17 / 25 )118.6585365853661.10299467973949107.578521243087
Trimmed Mean ( 18 / 25 )118.5897435897441.05625694942524112.273574772004
Trimmed Mean ( 19 / 25 )118.5135135135141.01091759645347117.233604330646
Trimmed Mean ( 20 / 25 )118.4285714285710.967788533646862122.370298170721
Trimmed Mean ( 21 / 25 )118.3636363636360.91888661818523128.812014476172
Trimmed Mean ( 22 / 25 )118.2903225806450.84775928363127139.532913250992
Trimmed Mean ( 23 / 25 )118.2413793103450.814969509559594145.086874936268
Trimmed Mean ( 24 / 25 )118.2222222222220.779607128272915151.643331538185
Trimmed Mean ( 25 / 25 )118.20.754983443527075156.559724605088
Median117
Midrange123
Midmean - Weighted Average at Xnp118.236842105263
Midmean - Weighted Average at X(n+1)p118.589743589744
Midmean - Empirical Distribution Function118.589743589744
Midmean - Empirical Distribution Function - Averaging118.589743589744
Midmean - Empirical Distribution Function - Interpolation118.513513513514
Midmean - Closest Observation118.236842105263
Midmean - True Basic - Statistics Graphics Toolkit118.589743589744
Midmean - MS Excel (old versions)118.589743589744
Number of observations75

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 120.693333333333 & 2.06034837720116 & 58.5790901523591 \tabularnewline
Geometric Mean & 119.419256046999 &  &  \tabularnewline
Harmonic Mean & 118.169790496441 &  &  \tabularnewline
Quadratic Mean & 121.987758948730 &  &  \tabularnewline
Winsorized Mean ( 1 / 25 ) & 120.72 & 2.04750430374978 & 58.9595830294054 \tabularnewline
Winsorized Mean ( 2 / 25 ) & 120.773333333333 & 1.98721801406777 & 60.7750797740176 \tabularnewline
Winsorized Mean ( 3 / 25 ) & 120.773333333333 & 1.98721801406777 & 60.7750797740176 \tabularnewline
Winsorized Mean ( 4 / 25 ) & 120.666666666667 & 1.91686054640246 & 62.9501540386608 \tabularnewline
Winsorized Mean ( 5 / 25 ) & 120.466666666667 & 1.87273787464961 & 64.3264966749316 \tabularnewline
Winsorized Mean ( 6 / 25 ) & 120.706666666667 & 1.80017750209224 & 67.0526470452923 \tabularnewline
Winsorized Mean ( 7 / 25 ) & 120.893333333333 & 1.77079137735141 & 68.2707939961593 \tabularnewline
Winsorized Mean ( 8 / 25 ) & 121 & 1.75489020728923 & 68.9501824657783 \tabularnewline
Winsorized Mean ( 9 / 25 ) & 120.88 & 1.68650820036841 & 71.6747181979868 \tabularnewline
Winsorized Mean ( 10 / 25 ) & 120.746666666667 & 1.56724275396310 & 77.0440101645602 \tabularnewline
Winsorized Mean ( 11 / 25 ) & 120.013333333333 & 1.42746462487000 & 84.0744710883906 \tabularnewline
Winsorized Mean ( 12 / 25 ) & 119.693333333333 & 1.37139021110372 & 87.2788301711748 \tabularnewline
Winsorized Mean ( 13 / 25 ) & 119.693333333333 & 1.37139021110372 & 87.2788301711748 \tabularnewline
Winsorized Mean ( 14 / 25 ) & 119.506666666667 & 1.28222404379987 & 93.2026405560985 \tabularnewline
Winsorized Mean ( 15 / 25 ) & 119.706666666667 & 1.25429328773284 & 95.4375406752268 \tabularnewline
Winsorized Mean ( 16 / 25 ) & 119.493333333333 & 1.21956621047885 & 97.9801935365326 \tabularnewline
Winsorized Mean ( 17 / 25 ) & 119.266666666667 & 1.18357122339166 & 100.768474519762 \tabularnewline
Winsorized Mean ( 18 / 25 ) & 119.266666666667 & 1.11295942364431 & 107.161738454162 \tabularnewline
Winsorized Mean ( 19 / 25 ) & 119.266666666667 & 1.03980825213171 & 114.700634873938 \tabularnewline
Winsorized Mean ( 20 / 25 ) & 119 & 0.999639574686436 & 119.042906076750 \tabularnewline
Winsorized Mean ( 21 / 25 ) & 119 & 0.999639574686436 & 119.042906076750 \tabularnewline
Winsorized Mean ( 22 / 25 ) & 118.706666666667 & 0.793390110770148 & 149.619544099734 \tabularnewline
Winsorized Mean ( 23 / 25 ) & 118.4 & 0.750735375217928 & 157.712029975449 \tabularnewline
Winsorized Mean ( 24 / 25 ) & 118.4 & 0.66522366353169 & 177.985249910401 \tabularnewline
Winsorized Mean ( 25 / 25 ) & 118.066666666667 & 0.62134214895343 & 190.018763197595 \tabularnewline
Trimmed Mean ( 1 / 25 ) & 120.630136986301 & 1.97525664953966 & 61.0706142993695 \tabularnewline
Trimmed Mean ( 2 / 25 ) & 120.535211267606 & 1.88959141846554 & 63.7890340153466 \tabularnewline
Trimmed Mean ( 3 / 25 ) & 120.405797101449 & 1.82671270351549 & 65.9139211490288 \tabularnewline
Trimmed Mean ( 4 / 25 ) & 120.268656716418 & 1.75147183560933 & 68.6671942255794 \tabularnewline
Trimmed Mean ( 5 / 25 ) & 120.153846153846 & 1.68808476609286 & 71.177614162082 \tabularnewline
Trimmed Mean ( 6 / 25 ) & 120.079365079365 & 1.62628523947490 & 73.8365953060833 \tabularnewline
Trimmed Mean ( 7 / 25 ) & 119.950819672131 & 1.5723752923016 & 76.286380394944 \tabularnewline
Trimmed Mean ( 8 / 25 ) & 119.779661016949 & 1.51402324682961 & 79.1134886916495 \tabularnewline
Trimmed Mean ( 9 / 25 ) & 119.578947368421 & 1.44574983545909 & 82.7106767959268 \tabularnewline
Trimmed Mean ( 10 / 25 ) & 119.381818181818 & 1.37840265458816 & 86.6088133133252 \tabularnewline
Trimmed Mean ( 11 / 25 ) & 119.188679245283 & 1.32357670736195 & 90.0504508596562 \tabularnewline
Trimmed Mean ( 12 / 25 ) & 119.078431372549 & 1.28851431007139 & 92.4152960054837 \tabularnewline
Trimmed Mean ( 13 / 25 ) & 119 & 1.2566151489828 & 94.6988424390139 \tabularnewline
Trimmed Mean ( 14 / 25 ) & 118.914893617021 & 1.21539225831297 & 97.8407528957617 \tabularnewline
Trimmed Mean ( 15 / 25 ) & 118.844444444444 & 1.18234297249215 & 100.516049242415 \tabularnewline
Trimmed Mean ( 16 / 25 ) & 118.744186046512 & 1.14463117866281 & 103.740128925399 \tabularnewline
Trimmed Mean ( 17 / 25 ) & 118.658536585366 & 1.10299467973949 & 107.578521243087 \tabularnewline
Trimmed Mean ( 18 / 25 ) & 118.589743589744 & 1.05625694942524 & 112.273574772004 \tabularnewline
Trimmed Mean ( 19 / 25 ) & 118.513513513514 & 1.01091759645347 & 117.233604330646 \tabularnewline
Trimmed Mean ( 20 / 25 ) & 118.428571428571 & 0.967788533646862 & 122.370298170721 \tabularnewline
Trimmed Mean ( 21 / 25 ) & 118.363636363636 & 0.91888661818523 & 128.812014476172 \tabularnewline
Trimmed Mean ( 22 / 25 ) & 118.290322580645 & 0.84775928363127 & 139.532913250992 \tabularnewline
Trimmed Mean ( 23 / 25 ) & 118.241379310345 & 0.814969509559594 & 145.086874936268 \tabularnewline
Trimmed Mean ( 24 / 25 ) & 118.222222222222 & 0.779607128272915 & 151.643331538185 \tabularnewline
Trimmed Mean ( 25 / 25 ) & 118.2 & 0.754983443527075 & 156.559724605088 \tabularnewline
Median & 117 &  &  \tabularnewline
Midrange & 123 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 118.236842105263 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 118.589743589744 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 118.589743589744 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 118.589743589744 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 118.513513513514 &  &  \tabularnewline
Midmean - Closest Observation & 118.236842105263 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 118.589743589744 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 118.589743589744 &  &  \tabularnewline
Number of observations & 75 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=77801&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]120.693333333333[/C][C]2.06034837720116[/C][C]58.5790901523591[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]119.419256046999[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]118.169790496441[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]121.987758948730[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 25 )[/C][C]120.72[/C][C]2.04750430374978[/C][C]58.9595830294054[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 25 )[/C][C]120.773333333333[/C][C]1.98721801406777[/C][C]60.7750797740176[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 25 )[/C][C]120.773333333333[/C][C]1.98721801406777[/C][C]60.7750797740176[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 25 )[/C][C]120.666666666667[/C][C]1.91686054640246[/C][C]62.9501540386608[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 25 )[/C][C]120.466666666667[/C][C]1.87273787464961[/C][C]64.3264966749316[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 25 )[/C][C]120.706666666667[/C][C]1.80017750209224[/C][C]67.0526470452923[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 25 )[/C][C]120.893333333333[/C][C]1.77079137735141[/C][C]68.2707939961593[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 25 )[/C][C]121[/C][C]1.75489020728923[/C][C]68.9501824657783[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 25 )[/C][C]120.88[/C][C]1.68650820036841[/C][C]71.6747181979868[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 25 )[/C][C]120.746666666667[/C][C]1.56724275396310[/C][C]77.0440101645602[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 25 )[/C][C]120.013333333333[/C][C]1.42746462487000[/C][C]84.0744710883906[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 25 )[/C][C]119.693333333333[/C][C]1.37139021110372[/C][C]87.2788301711748[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 25 )[/C][C]119.693333333333[/C][C]1.37139021110372[/C][C]87.2788301711748[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 25 )[/C][C]119.506666666667[/C][C]1.28222404379987[/C][C]93.2026405560985[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 25 )[/C][C]119.706666666667[/C][C]1.25429328773284[/C][C]95.4375406752268[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 25 )[/C][C]119.493333333333[/C][C]1.21956621047885[/C][C]97.9801935365326[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 25 )[/C][C]119.266666666667[/C][C]1.18357122339166[/C][C]100.768474519762[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 25 )[/C][C]119.266666666667[/C][C]1.11295942364431[/C][C]107.161738454162[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 25 )[/C][C]119.266666666667[/C][C]1.03980825213171[/C][C]114.700634873938[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 25 )[/C][C]119[/C][C]0.999639574686436[/C][C]119.042906076750[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 25 )[/C][C]119[/C][C]0.999639574686436[/C][C]119.042906076750[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 25 )[/C][C]118.706666666667[/C][C]0.793390110770148[/C][C]149.619544099734[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 25 )[/C][C]118.4[/C][C]0.750735375217928[/C][C]157.712029975449[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 25 )[/C][C]118.4[/C][C]0.66522366353169[/C][C]177.985249910401[/C][/ROW]
[ROW][C]Winsorized Mean ( 25 / 25 )[/C][C]118.066666666667[/C][C]0.62134214895343[/C][C]190.018763197595[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 25 )[/C][C]120.630136986301[/C][C]1.97525664953966[/C][C]61.0706142993695[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 25 )[/C][C]120.535211267606[/C][C]1.88959141846554[/C][C]63.7890340153466[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 25 )[/C][C]120.405797101449[/C][C]1.82671270351549[/C][C]65.9139211490288[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 25 )[/C][C]120.268656716418[/C][C]1.75147183560933[/C][C]68.6671942255794[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 25 )[/C][C]120.153846153846[/C][C]1.68808476609286[/C][C]71.177614162082[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 25 )[/C][C]120.079365079365[/C][C]1.62628523947490[/C][C]73.8365953060833[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 25 )[/C][C]119.950819672131[/C][C]1.5723752923016[/C][C]76.286380394944[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 25 )[/C][C]119.779661016949[/C][C]1.51402324682961[/C][C]79.1134886916495[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 25 )[/C][C]119.578947368421[/C][C]1.44574983545909[/C][C]82.7106767959268[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 25 )[/C][C]119.381818181818[/C][C]1.37840265458816[/C][C]86.6088133133252[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 25 )[/C][C]119.188679245283[/C][C]1.32357670736195[/C][C]90.0504508596562[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 25 )[/C][C]119.078431372549[/C][C]1.28851431007139[/C][C]92.4152960054837[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 25 )[/C][C]119[/C][C]1.2566151489828[/C][C]94.6988424390139[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 25 )[/C][C]118.914893617021[/C][C]1.21539225831297[/C][C]97.8407528957617[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 25 )[/C][C]118.844444444444[/C][C]1.18234297249215[/C][C]100.516049242415[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 25 )[/C][C]118.744186046512[/C][C]1.14463117866281[/C][C]103.740128925399[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 25 )[/C][C]118.658536585366[/C][C]1.10299467973949[/C][C]107.578521243087[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 25 )[/C][C]118.589743589744[/C][C]1.05625694942524[/C][C]112.273574772004[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 25 )[/C][C]118.513513513514[/C][C]1.01091759645347[/C][C]117.233604330646[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 25 )[/C][C]118.428571428571[/C][C]0.967788533646862[/C][C]122.370298170721[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 25 )[/C][C]118.363636363636[/C][C]0.91888661818523[/C][C]128.812014476172[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 25 )[/C][C]118.290322580645[/C][C]0.84775928363127[/C][C]139.532913250992[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 25 )[/C][C]118.241379310345[/C][C]0.814969509559594[/C][C]145.086874936268[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 25 )[/C][C]118.222222222222[/C][C]0.779607128272915[/C][C]151.643331538185[/C][/ROW]
[ROW][C]Trimmed Mean ( 25 / 25 )[/C][C]118.2[/C][C]0.754983443527075[/C][C]156.559724605088[/C][/ROW]
[ROW][C]Median[/C][C]117[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]123[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]118.236842105263[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]118.589743589744[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]118.589743589744[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]118.589743589744[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]118.513513513514[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]118.236842105263[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]118.589743589744[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]118.589743589744[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]75[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=77801&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=77801&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 Mean120.6933333333332.0603483772011658.5790901523591
Geometric Mean119.419256046999
Harmonic Mean118.169790496441
Quadratic Mean121.987758948730
Winsorized Mean ( 1 / 25 )120.722.0475043037497858.9595830294054
Winsorized Mean ( 2 / 25 )120.7733333333331.9872180140677760.7750797740176
Winsorized Mean ( 3 / 25 )120.7733333333331.9872180140677760.7750797740176
Winsorized Mean ( 4 / 25 )120.6666666666671.9168605464024662.9501540386608
Winsorized Mean ( 5 / 25 )120.4666666666671.8727378746496164.3264966749316
Winsorized Mean ( 6 / 25 )120.7066666666671.8001775020922467.0526470452923
Winsorized Mean ( 7 / 25 )120.8933333333331.7707913773514168.2707939961593
Winsorized Mean ( 8 / 25 )1211.7548902072892368.9501824657783
Winsorized Mean ( 9 / 25 )120.881.6865082003684171.6747181979868
Winsorized Mean ( 10 / 25 )120.7466666666671.5672427539631077.0440101645602
Winsorized Mean ( 11 / 25 )120.0133333333331.4274646248700084.0744710883906
Winsorized Mean ( 12 / 25 )119.6933333333331.3713902111037287.2788301711748
Winsorized Mean ( 13 / 25 )119.6933333333331.3713902111037287.2788301711748
Winsorized Mean ( 14 / 25 )119.5066666666671.2822240437998793.2026405560985
Winsorized Mean ( 15 / 25 )119.7066666666671.2542932877328495.4375406752268
Winsorized Mean ( 16 / 25 )119.4933333333331.2195662104788597.9801935365326
Winsorized Mean ( 17 / 25 )119.2666666666671.18357122339166100.768474519762
Winsorized Mean ( 18 / 25 )119.2666666666671.11295942364431107.161738454162
Winsorized Mean ( 19 / 25 )119.2666666666671.03980825213171114.700634873938
Winsorized Mean ( 20 / 25 )1190.999639574686436119.042906076750
Winsorized Mean ( 21 / 25 )1190.999639574686436119.042906076750
Winsorized Mean ( 22 / 25 )118.7066666666670.793390110770148149.619544099734
Winsorized Mean ( 23 / 25 )118.40.750735375217928157.712029975449
Winsorized Mean ( 24 / 25 )118.40.66522366353169177.985249910401
Winsorized Mean ( 25 / 25 )118.0666666666670.62134214895343190.018763197595
Trimmed Mean ( 1 / 25 )120.6301369863011.9752566495396661.0706142993695
Trimmed Mean ( 2 / 25 )120.5352112676061.8895914184655463.7890340153466
Trimmed Mean ( 3 / 25 )120.4057971014491.8267127035154965.9139211490288
Trimmed Mean ( 4 / 25 )120.2686567164181.7514718356093368.6671942255794
Trimmed Mean ( 5 / 25 )120.1538461538461.6880847660928671.177614162082
Trimmed Mean ( 6 / 25 )120.0793650793651.6262852394749073.8365953060833
Trimmed Mean ( 7 / 25 )119.9508196721311.572375292301676.286380394944
Trimmed Mean ( 8 / 25 )119.7796610169491.5140232468296179.1134886916495
Trimmed Mean ( 9 / 25 )119.5789473684211.4457498354590982.7106767959268
Trimmed Mean ( 10 / 25 )119.3818181818181.3784026545881686.6088133133252
Trimmed Mean ( 11 / 25 )119.1886792452831.3235767073619590.0504508596562
Trimmed Mean ( 12 / 25 )119.0784313725491.2885143100713992.4152960054837
Trimmed Mean ( 13 / 25 )1191.256615148982894.6988424390139
Trimmed Mean ( 14 / 25 )118.9148936170211.2153922583129797.8407528957617
Trimmed Mean ( 15 / 25 )118.8444444444441.18234297249215100.516049242415
Trimmed Mean ( 16 / 25 )118.7441860465121.14463117866281103.740128925399
Trimmed Mean ( 17 / 25 )118.6585365853661.10299467973949107.578521243087
Trimmed Mean ( 18 / 25 )118.5897435897441.05625694942524112.273574772004
Trimmed Mean ( 19 / 25 )118.5135135135141.01091759645347117.233604330646
Trimmed Mean ( 20 / 25 )118.4285714285710.967788533646862122.370298170721
Trimmed Mean ( 21 / 25 )118.3636363636360.91888661818523128.812014476172
Trimmed Mean ( 22 / 25 )118.2903225806450.84775928363127139.532913250992
Trimmed Mean ( 23 / 25 )118.2413793103450.814969509559594145.086874936268
Trimmed Mean ( 24 / 25 )118.2222222222220.779607128272915151.643331538185
Trimmed Mean ( 25 / 25 )118.20.754983443527075156.559724605088
Median117
Midrange123
Midmean - Weighted Average at Xnp118.236842105263
Midmean - Weighted Average at X(n+1)p118.589743589744
Midmean - Empirical Distribution Function118.589743589744
Midmean - Empirical Distribution Function - Averaging118.589743589744
Midmean - Empirical Distribution Function - Interpolation118.513513513514
Midmean - Closest Observation118.236842105263
Midmean - True Basic - Statistics Graphics Toolkit118.589743589744
Midmean - MS Excel (old versions)118.589743589744
Number of observations75



Parameters (Session):
Parameters (R input):
R code (references can be found in the software module):
geomean <- function(x) {
return(exp(mean(log(x))))
}
harmean <- function(x) {
return(1/mean(1/x))
}
quamean <- function(x) {
return(sqrt(mean(x*x)))
}
winmean <- function(x) {
x <-sort(x[!is.na(x)])
n<-length(x)
denom <- 3
nodenom <- n/denom
if (nodenom>40) denom <- n/40
sqrtn = sqrt(n)
roundnodenom = floor(nodenom)
win <- array(NA,dim=c(roundnodenom,2))
for (j in 1:roundnodenom) {
win[j,1] <- (j*x[j+1]+sum(x[(j+1):(n-j)])+j*x[n-j])/n
win[j,2] <- sd(c(rep(x[j+1],j),x[(j+1):(n-j)],rep(x[n-j],j)))/sqrtn
}
return(win)
}
trimean <- function(x) {
x <-sort(x[!is.na(x)])
n<-length(x)
denom <- 3
nodenom <- n/denom
if (nodenom>40) denom <- n/40
sqrtn = sqrt(n)
roundnodenom = floor(nodenom)
tri <- array(NA,dim=c(roundnodenom,2))
for (j in 1:roundnodenom) {
tri[j,1] <- mean(x,trim=j/n)
tri[j,2] <- sd(x[(j+1):(n-j)]) / sqrt(n-j*2)
}
return(tri)
}
midrange <- function(x) {
return((max(x)+min(x))/2)
}
q1 <- function(data,n,p,i,f) {
np <- n*p;
i <<- floor(np)
f <<- np - i
qvalue <- (1-f)*data[i] + f*data[i+1]
}
q2 <- function(data,n,p,i,f) {
np <- (n+1)*p
i <<- floor(np)
f <<- np - i
qvalue <- (1-f)*data[i] + f*data[i+1]
}
q3 <- function(data,n,p,i,f) {
np <- n*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- data[i]
} else {
qvalue <- data[i+1]
}
}
q4 <- function(data,n,p,i,f) {
np <- n*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- (data[i]+data[i+1])/2
} else {
qvalue <- data[i+1]
}
}
q5 <- function(data,n,p,i,f) {
np <- (n-1)*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- data[i+1]
} else {
qvalue <- data[i+1] + f*(data[i+2]-data[i+1])
}
}
q6 <- function(data,n,p,i,f) {
np <- n*p+0.5
i <<- floor(np)
f <<- np - i
qvalue <- data[i]
}
q7 <- function(data,n,p,i,f) {
np <- (n+1)*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- data[i]
} else {
qvalue <- f*data[i] + (1-f)*data[i+1]
}
}
q8 <- function(data,n,p,i,f) {
np <- (n+1)*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- data[i]
} else {
if (f == 0.5) {
qvalue <- (data[i]+data[i+1])/2
} else {
if (f < 0.5) {
qvalue <- data[i]
} else {
qvalue <- data[i+1]
}
}
}
}
midmean <- function(x,def) {
x <-sort(x[!is.na(x)])
n<-length(x)
if (def==1) {
qvalue1 <- q1(x,n,0.25,i,f)
qvalue3 <- q1(x,n,0.75,i,f)
}
if (def==2) {
qvalue1 <- q2(x,n,0.25,i,f)
qvalue3 <- q2(x,n,0.75,i,f)
}
if (def==3) {
qvalue1 <- q3(x,n,0.25,i,f)
qvalue3 <- q3(x,n,0.75,i,f)
}
if (def==4) {
qvalue1 <- q4(x,n,0.25,i,f)
qvalue3 <- q4(x,n,0.75,i,f)
}
if (def==5) {
qvalue1 <- q5(x,n,0.25,i,f)
qvalue3 <- q5(x,n,0.75,i,f)
}
if (def==6) {
qvalue1 <- q6(x,n,0.25,i,f)
qvalue3 <- q6(x,n,0.75,i,f)
}
if (def==7) {
qvalue1 <- q7(x,n,0.25,i,f)
qvalue3 <- q7(x,n,0.75,i,f)
}
if (def==8) {
qvalue1 <- q8(x,n,0.25,i,f)
qvalue3 <- q8(x,n,0.75,i,f)
}
midm <- 0
myn <- 0
roundno4 <- round(n/4)
round3no4 <- round(3*n/4)
for (i in 1:n) {
if ((x[i]>=qvalue1) & (x[i]<=qvalue3)){
midm = midm + x[i]
myn = myn + 1
}
}
midm = midm / myn
return(midm)
}
(arm <- mean(x))
sqrtn <- sqrt(length(x))
(armse <- sd(x) / sqrtn)
(armose <- arm / armse)
(geo <- geomean(x))
(har <- harmean(x))
(qua <- quamean(x))
(win <- winmean(x))
(tri <- trimean(x))
(midr <- midrange(x))
midm <- array(NA,dim=8)
for (j in 1:8) midm[j] <- midmean(x,j)
midm
bitmap(file='test1.png')
lb <- win[,1] - 2*win[,2]
ub <- win[,1] + 2*win[,2]
if ((ylimmin == '') | (ylimmax == '')) plot(win[,1],type='b',main=main, xlab='j', pch=19, ylab='Winsorized Mean(j/n)', ylim=c(min(lb),max(ub))) else plot(win[,1],type='l',main=main, xlab='j', pch=19, ylab='Winsorized Mean(j/n)', ylim=c(ylimmin,ylimmax))
lines(ub,lty=3)
lines(lb,lty=3)
grid()
dev.off()
bitmap(file='test2.png')
lb <- tri[,1] - 2*tri[,2]
ub <- tri[,1] + 2*tri[,2]
if ((ylimmin == '') | (ylimmax == '')) plot(tri[,1],type='b',main=main, xlab='j', pch=19, ylab='Trimmed Mean(j/n)', ylim=c(min(lb),max(ub))) else plot(tri[,1],type='l',main=main, xlab='j', pch=19, ylab='Trimmed Mean(j/n)', ylim=c(ylimmin,ylimmax))
lines(ub,lty=3)
lines(lb,lty=3)
grid()
dev.off()
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Central Tendency - Ungrouped Data',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Measure',header=TRUE)
a<-table.element(a,'Value',header=TRUE)
a<-table.element(a,'S.E.',header=TRUE)
a<-table.element(a,'Value/S.E.',header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('arithmetic_mean.htm', 'Arithmetic Mean', 'click to view the definition of the Arithmetic Mean'),header=TRUE)
a<-table.element(a,arm)
a<-table.element(a,hyperlink('arithmetic_mean_standard_error.htm', armse, 'click to view the definition of the Standard Error of the Arithmetic Mean'))
a<-table.element(a,armose)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('geometric_mean.htm', 'Geometric Mean', 'click to view the definition of the Geometric Mean'),header=TRUE)
a<-table.element(a,geo)
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('harmonic_mean.htm', 'Harmonic Mean', 'click to view the definition of the Harmonic Mean'),header=TRUE)
a<-table.element(a,har)
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('quadratic_mean.htm', 'Quadratic Mean', 'click to view the definition of the Quadratic Mean'),header=TRUE)
a<-table.element(a,qua)
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
for (j in 1:length(win[,1])) {
a<-table.row.start(a)
mylabel <- paste('Winsorized Mean (',j)
mylabel <- paste(mylabel,'/')
mylabel <- paste(mylabel,length(win[,1]))
mylabel <- paste(mylabel,')')
a<-table.element(a,hyperlink('winsorized_mean.htm', mylabel, 'click to view the definition of the Winsorized Mean'),header=TRUE)
a<-table.element(a,win[j,1])
a<-table.element(a,win[j,2])
a<-table.element(a,win[j,1]/win[j,2])
a<-table.row.end(a)
}
for (j in 1:length(tri[,1])) {
a<-table.row.start(a)
mylabel <- paste('Trimmed Mean (',j)
mylabel <- paste(mylabel,'/')
mylabel <- paste(mylabel,length(tri[,1]))
mylabel <- paste(mylabel,')')
a<-table.element(a,hyperlink('arithmetic_mean.htm', mylabel, 'click to view the definition of the Trimmed Mean'),header=TRUE)
a<-table.element(a,tri[j,1])
a<-table.element(a,tri[j,2])
a<-table.element(a,tri[j,1]/tri[j,2])
a<-table.row.end(a)
}
a<-table.row.start(a)
a<-table.element(a,hyperlink('median_1.htm', 'Median', 'click to view the definition of the Median'),header=TRUE)
a<-table.element(a,median(x))
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('midrange.htm', 'Midrange', 'click to view the definition of the Midrange'),header=TRUE)
a<-table.element(a,midr)
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_1.htm','Weighted Average at Xnp',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[1])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_2.htm','Weighted Average at X(n+1)p',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[2])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_3.htm','Empirical Distribution Function',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[3])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_4.htm','Empirical Distribution Function - Averaging',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[4])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_5.htm','Empirical Distribution Function - Interpolation',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[5])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_6.htm','Closest Observation',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[6])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_7.htm','True Basic - Statistics Graphics Toolkit',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[7])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_8.htm','MS Excel (old versions)',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[8])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Number of observations',header=TRUE)
a<-table.element(a,length(x))
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable.tab')