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Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationThu, 08 Oct 2015 14:07:45 +0100
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2015/Oct/08/t1444309715v85lv0pv7kd86yb.htm/, Retrieved Thu, 16 May 2024 02:37:27 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=281448, Retrieved Thu, 16 May 2024 02:37:27 +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] [centrummaten alch...] [2015-10-08 13:07:45] [4bedbbf2e5251222bc39a0f973d05821] [Current]
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Dataseries X:
89,56
89,84
89,97
90,65
91,17
91,35
91,41
91,55
91,63
91,54
91,74
91,87
92,13
92,14
92,05
92
92,51
92,67
92,68
92,77
92,85
92,71
92,73
92,28
92,49
92,46
92,55
92,24
92,41
92,83
92,85
93,04
93,04
92,83
92,96
92,83
93,01
93,21
93,58
94,07
94,57
95,03
95,21
95,89
96,43
96,35
96,71
96,32
97,23
97,88
98,2
98,56
99,31
99,69
99,77
101,06
101,77
101,91
102,52
102,09
102,22
102,74
103,56
104,4
104,76
104,86
104,84
104,96
104,83
104,58
104,8
104,17




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'George Udny Yule' @ yule.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 & 'George Udny Yule' @ yule.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=281448&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]'George Udny Yule' @ yule.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=281448&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=281448&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'George Udny Yule' @ yule.wessa.net







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean95.90861111111110.570991172981399167.968640583933
Geometric Mean95.7906863440438
Harmonic Mean95.6755824990315
Quadratic Mean96.0292136828973
Winsorized Mean ( 1 / 24 )95.91111111111110.570086427690912168.239597458216
Winsorized Mean ( 2 / 24 )95.91416666666670.569427400599928168.439675655957
Winsorized Mean ( 3 / 24 )95.94208333333330.565384005996888169.693663626313
Winsorized Mean ( 4 / 24 )95.96930555555560.561370734872594170.955305636544
Winsorized Mean ( 5 / 24 )95.97902777777780.559274665784907171.613401517262
Winsorized Mean ( 6 / 24 )95.96902777777780.555397831435127172.793306610142
Winsorized Mean ( 7 / 24 )95.96416666666670.550150845369165174.432462431776
Winsorized Mean ( 8 / 24 )95.93972222222220.544545005843388176.183274463478
Winsorized Mean ( 9 / 24 )95.87347222222220.527465229246677181.762639329133
Winsorized Mean ( 10 / 24 )95.77486111111110.502927384763344190.434770530896
Winsorized Mean ( 11 / 24 )95.76111111111110.494188113823973193.774614225587
Winsorized Mean ( 12 / 24 )95.73277777777780.482252118420173198.511886461779
Winsorized Mean ( 13 / 24 )95.71833333333330.476838506075558200.73532676945
Winsorized Mean ( 14 / 24 )95.69888888888890.468600643625677204.222700482106
Winsorized Mean ( 15 / 24 )95.67180555555560.462948776745353206.657432444584
Winsorized Mean ( 16 / 24 )95.536250.431691927293046221.306547470245
Winsorized Mean ( 17 / 24 )95.24111111111110.377360155338467252.387830998443
Winsorized Mean ( 18 / 24 )95.25361111111110.370429703613351257.143555665113
Winsorized Mean ( 19 / 24 )95.16652777777780.352234103741954270.179766146371
Winsorized Mean ( 20 / 24 )94.96652777777780.317424356676287299.178452378895
Winsorized Mean ( 21 / 24 )94.86736111111110.300196987560171316.017032289826
Winsorized Mean ( 22 / 24 )94.78180555555560.283675871814923334.120082011746
Winsorized Mean ( 23 / 24 )94.61250.247997516110283381.505837171072
Winsorized Mean ( 24 / 24 )94.44250.222267862586236424.90398252405
Trimmed Mean ( 1 / 24 )95.870.56545355473928169.545313132223
Trimmed Mean ( 2 / 24 )95.82647058823530.559659245250907171.222884999022
Trimmed Mean ( 3 / 24 )95.77863636363640.552875588730131173.237231514643
Trimmed Mean ( 4 / 24 )95.717343750.54619441174912175.244092013825
Trimmed Mean ( 5 / 24 )95.64419354838710.539148296565452177.398675202484
Trimmed Mean ( 6 / 24 )95.56383333333330.530810492728061180.033806118244
Trimmed Mean ( 7 / 24 )95.480.5213170300844183.151507604772
Trimmed Mean ( 8 / 24 )95.39107142857140.510583933505539186.827405190055
Trimmed Mean ( 9 / 24 )95.29962962962960.498309017795323191.24604658223
Trimmed Mean ( 10 / 24 )95.21134615384620.486841718515722195.569406919615
Trimmed Mean ( 11 / 24 )95.13020.477879370826179199.067391914271
Trimmed Mean ( 12 / 24 )95.04416666666670.467901402875904203.128620864328
Trimmed Mean ( 13 / 24 )94.9543478260870.457244070827232207.666657446861
Trimmed Mean ( 14 / 24 )94.85818181818180.444022821053142213.633573142018
Trimmed Mean ( 15 / 24 )94.75523809523810.427973269500693221.404570911139
Trimmed Mean ( 16 / 24 )94.645250.407362685296279232.336572337654
Trimmed Mean ( 17 / 24 )94.53973684210530.387863441609835243.744902715544
Trimmed Mean ( 18 / 24 )94.45722222222220.376711672640165250.741426620055
Trimmed Mean ( 19 / 24 )94.36352941176470.361884028841137260.756269664471
Trimmed Mean ( 20 / 24 )94.26843750.345706414862695272.683506718962
Trimmed Mean ( 21 / 24 )94.18466666666670.333504461819688282.409015318027
Trimmed Mean ( 22 / 24 )94.10107142857140.320471849247702293.632878049884
Trimmed Mean ( 23 / 24 )94.01538461538460.305754668255062307.486342406247
Trimmed Mean ( 24 / 24 )93.93750.296343813495577316.988226924474
Median93.04
Midrange97.26
Midmean - Weighted Average at Xnp94.3983783783784
Midmean - Weighted Average at X(n+1)p94.4572222222222
Midmean - Empirical Distribution Function94.3983783783784
Midmean - Empirical Distribution Function - Averaging94.4572222222222
Midmean - Empirical Distribution Function - Interpolation94.4572222222222
Midmean - Closest Observation94.3983783783784
Midmean - True Basic - Statistics Graphics Toolkit94.4572222222222
Midmean - MS Excel (old versions)94.5397368421053
Number of observations72

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 95.9086111111111 & 0.570991172981399 & 167.968640583933 \tabularnewline
Geometric Mean & 95.7906863440438 &  &  \tabularnewline
Harmonic Mean & 95.6755824990315 &  &  \tabularnewline
Quadratic Mean & 96.0292136828973 &  &  \tabularnewline
Winsorized Mean ( 1 / 24 ) & 95.9111111111111 & 0.570086427690912 & 168.239597458216 \tabularnewline
Winsorized Mean ( 2 / 24 ) & 95.9141666666667 & 0.569427400599928 & 168.439675655957 \tabularnewline
Winsorized Mean ( 3 / 24 ) & 95.9420833333333 & 0.565384005996888 & 169.693663626313 \tabularnewline
Winsorized Mean ( 4 / 24 ) & 95.9693055555556 & 0.561370734872594 & 170.955305636544 \tabularnewline
Winsorized Mean ( 5 / 24 ) & 95.9790277777778 & 0.559274665784907 & 171.613401517262 \tabularnewline
Winsorized Mean ( 6 / 24 ) & 95.9690277777778 & 0.555397831435127 & 172.793306610142 \tabularnewline
Winsorized Mean ( 7 / 24 ) & 95.9641666666667 & 0.550150845369165 & 174.432462431776 \tabularnewline
Winsorized Mean ( 8 / 24 ) & 95.9397222222222 & 0.544545005843388 & 176.183274463478 \tabularnewline
Winsorized Mean ( 9 / 24 ) & 95.8734722222222 & 0.527465229246677 & 181.762639329133 \tabularnewline
Winsorized Mean ( 10 / 24 ) & 95.7748611111111 & 0.502927384763344 & 190.434770530896 \tabularnewline
Winsorized Mean ( 11 / 24 ) & 95.7611111111111 & 0.494188113823973 & 193.774614225587 \tabularnewline
Winsorized Mean ( 12 / 24 ) & 95.7327777777778 & 0.482252118420173 & 198.511886461779 \tabularnewline
Winsorized Mean ( 13 / 24 ) & 95.7183333333333 & 0.476838506075558 & 200.73532676945 \tabularnewline
Winsorized Mean ( 14 / 24 ) & 95.6988888888889 & 0.468600643625677 & 204.222700482106 \tabularnewline
Winsorized Mean ( 15 / 24 ) & 95.6718055555556 & 0.462948776745353 & 206.657432444584 \tabularnewline
Winsorized Mean ( 16 / 24 ) & 95.53625 & 0.431691927293046 & 221.306547470245 \tabularnewline
Winsorized Mean ( 17 / 24 ) & 95.2411111111111 & 0.377360155338467 & 252.387830998443 \tabularnewline
Winsorized Mean ( 18 / 24 ) & 95.2536111111111 & 0.370429703613351 & 257.143555665113 \tabularnewline
Winsorized Mean ( 19 / 24 ) & 95.1665277777778 & 0.352234103741954 & 270.179766146371 \tabularnewline
Winsorized Mean ( 20 / 24 ) & 94.9665277777778 & 0.317424356676287 & 299.178452378895 \tabularnewline
Winsorized Mean ( 21 / 24 ) & 94.8673611111111 & 0.300196987560171 & 316.017032289826 \tabularnewline
Winsorized Mean ( 22 / 24 ) & 94.7818055555556 & 0.283675871814923 & 334.120082011746 \tabularnewline
Winsorized Mean ( 23 / 24 ) & 94.6125 & 0.247997516110283 & 381.505837171072 \tabularnewline
Winsorized Mean ( 24 / 24 ) & 94.4425 & 0.222267862586236 & 424.90398252405 \tabularnewline
Trimmed Mean ( 1 / 24 ) & 95.87 & 0.56545355473928 & 169.545313132223 \tabularnewline
Trimmed Mean ( 2 / 24 ) & 95.8264705882353 & 0.559659245250907 & 171.222884999022 \tabularnewline
Trimmed Mean ( 3 / 24 ) & 95.7786363636364 & 0.552875588730131 & 173.237231514643 \tabularnewline
Trimmed Mean ( 4 / 24 ) & 95.71734375 & 0.54619441174912 & 175.244092013825 \tabularnewline
Trimmed Mean ( 5 / 24 ) & 95.6441935483871 & 0.539148296565452 & 177.398675202484 \tabularnewline
Trimmed Mean ( 6 / 24 ) & 95.5638333333333 & 0.530810492728061 & 180.033806118244 \tabularnewline
Trimmed Mean ( 7 / 24 ) & 95.48 & 0.5213170300844 & 183.151507604772 \tabularnewline
Trimmed Mean ( 8 / 24 ) & 95.3910714285714 & 0.510583933505539 & 186.827405190055 \tabularnewline
Trimmed Mean ( 9 / 24 ) & 95.2996296296296 & 0.498309017795323 & 191.24604658223 \tabularnewline
Trimmed Mean ( 10 / 24 ) & 95.2113461538462 & 0.486841718515722 & 195.569406919615 \tabularnewline
Trimmed Mean ( 11 / 24 ) & 95.1302 & 0.477879370826179 & 199.067391914271 \tabularnewline
Trimmed Mean ( 12 / 24 ) & 95.0441666666667 & 0.467901402875904 & 203.128620864328 \tabularnewline
Trimmed Mean ( 13 / 24 ) & 94.954347826087 & 0.457244070827232 & 207.666657446861 \tabularnewline
Trimmed Mean ( 14 / 24 ) & 94.8581818181818 & 0.444022821053142 & 213.633573142018 \tabularnewline
Trimmed Mean ( 15 / 24 ) & 94.7552380952381 & 0.427973269500693 & 221.404570911139 \tabularnewline
Trimmed Mean ( 16 / 24 ) & 94.64525 & 0.407362685296279 & 232.336572337654 \tabularnewline
Trimmed Mean ( 17 / 24 ) & 94.5397368421053 & 0.387863441609835 & 243.744902715544 \tabularnewline
Trimmed Mean ( 18 / 24 ) & 94.4572222222222 & 0.376711672640165 & 250.741426620055 \tabularnewline
Trimmed Mean ( 19 / 24 ) & 94.3635294117647 & 0.361884028841137 & 260.756269664471 \tabularnewline
Trimmed Mean ( 20 / 24 ) & 94.2684375 & 0.345706414862695 & 272.683506718962 \tabularnewline
Trimmed Mean ( 21 / 24 ) & 94.1846666666667 & 0.333504461819688 & 282.409015318027 \tabularnewline
Trimmed Mean ( 22 / 24 ) & 94.1010714285714 & 0.320471849247702 & 293.632878049884 \tabularnewline
Trimmed Mean ( 23 / 24 ) & 94.0153846153846 & 0.305754668255062 & 307.486342406247 \tabularnewline
Trimmed Mean ( 24 / 24 ) & 93.9375 & 0.296343813495577 & 316.988226924474 \tabularnewline
Median & 93.04 &  &  \tabularnewline
Midrange & 97.26 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 94.3983783783784 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 94.4572222222222 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 94.3983783783784 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 94.4572222222222 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 94.4572222222222 &  &  \tabularnewline
Midmean - Closest Observation & 94.3983783783784 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 94.4572222222222 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 94.5397368421053 &  &  \tabularnewline
Number of observations & 72 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=281448&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]95.9086111111111[/C][C]0.570991172981399[/C][C]167.968640583933[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]95.7906863440438[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]95.6755824990315[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]96.0292136828973[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 24 )[/C][C]95.9111111111111[/C][C]0.570086427690912[/C][C]168.239597458216[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 24 )[/C][C]95.9141666666667[/C][C]0.569427400599928[/C][C]168.439675655957[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 24 )[/C][C]95.9420833333333[/C][C]0.565384005996888[/C][C]169.693663626313[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 24 )[/C][C]95.9693055555556[/C][C]0.561370734872594[/C][C]170.955305636544[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 24 )[/C][C]95.9790277777778[/C][C]0.559274665784907[/C][C]171.613401517262[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 24 )[/C][C]95.9690277777778[/C][C]0.555397831435127[/C][C]172.793306610142[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 24 )[/C][C]95.9641666666667[/C][C]0.550150845369165[/C][C]174.432462431776[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 24 )[/C][C]95.9397222222222[/C][C]0.544545005843388[/C][C]176.183274463478[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 24 )[/C][C]95.8734722222222[/C][C]0.527465229246677[/C][C]181.762639329133[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 24 )[/C][C]95.7748611111111[/C][C]0.502927384763344[/C][C]190.434770530896[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 24 )[/C][C]95.7611111111111[/C][C]0.494188113823973[/C][C]193.774614225587[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 24 )[/C][C]95.7327777777778[/C][C]0.482252118420173[/C][C]198.511886461779[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 24 )[/C][C]95.7183333333333[/C][C]0.476838506075558[/C][C]200.73532676945[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 24 )[/C][C]95.6988888888889[/C][C]0.468600643625677[/C][C]204.222700482106[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 24 )[/C][C]95.6718055555556[/C][C]0.462948776745353[/C][C]206.657432444584[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 24 )[/C][C]95.53625[/C][C]0.431691927293046[/C][C]221.306547470245[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 24 )[/C][C]95.2411111111111[/C][C]0.377360155338467[/C][C]252.387830998443[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 24 )[/C][C]95.2536111111111[/C][C]0.370429703613351[/C][C]257.143555665113[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 24 )[/C][C]95.1665277777778[/C][C]0.352234103741954[/C][C]270.179766146371[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 24 )[/C][C]94.9665277777778[/C][C]0.317424356676287[/C][C]299.178452378895[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 24 )[/C][C]94.8673611111111[/C][C]0.300196987560171[/C][C]316.017032289826[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 24 )[/C][C]94.7818055555556[/C][C]0.283675871814923[/C][C]334.120082011746[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 24 )[/C][C]94.6125[/C][C]0.247997516110283[/C][C]381.505837171072[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 24 )[/C][C]94.4425[/C][C]0.222267862586236[/C][C]424.90398252405[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 24 )[/C][C]95.87[/C][C]0.56545355473928[/C][C]169.545313132223[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 24 )[/C][C]95.8264705882353[/C][C]0.559659245250907[/C][C]171.222884999022[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 24 )[/C][C]95.7786363636364[/C][C]0.552875588730131[/C][C]173.237231514643[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 24 )[/C][C]95.71734375[/C][C]0.54619441174912[/C][C]175.244092013825[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 24 )[/C][C]95.6441935483871[/C][C]0.539148296565452[/C][C]177.398675202484[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 24 )[/C][C]95.5638333333333[/C][C]0.530810492728061[/C][C]180.033806118244[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 24 )[/C][C]95.48[/C][C]0.5213170300844[/C][C]183.151507604772[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 24 )[/C][C]95.3910714285714[/C][C]0.510583933505539[/C][C]186.827405190055[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 24 )[/C][C]95.2996296296296[/C][C]0.498309017795323[/C][C]191.24604658223[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 24 )[/C][C]95.2113461538462[/C][C]0.486841718515722[/C][C]195.569406919615[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 24 )[/C][C]95.1302[/C][C]0.477879370826179[/C][C]199.067391914271[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 24 )[/C][C]95.0441666666667[/C][C]0.467901402875904[/C][C]203.128620864328[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 24 )[/C][C]94.954347826087[/C][C]0.457244070827232[/C][C]207.666657446861[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 24 )[/C][C]94.8581818181818[/C][C]0.444022821053142[/C][C]213.633573142018[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 24 )[/C][C]94.7552380952381[/C][C]0.427973269500693[/C][C]221.404570911139[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 24 )[/C][C]94.64525[/C][C]0.407362685296279[/C][C]232.336572337654[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 24 )[/C][C]94.5397368421053[/C][C]0.387863441609835[/C][C]243.744902715544[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 24 )[/C][C]94.4572222222222[/C][C]0.376711672640165[/C][C]250.741426620055[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 24 )[/C][C]94.3635294117647[/C][C]0.361884028841137[/C][C]260.756269664471[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 24 )[/C][C]94.2684375[/C][C]0.345706414862695[/C][C]272.683506718962[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 24 )[/C][C]94.1846666666667[/C][C]0.333504461819688[/C][C]282.409015318027[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 24 )[/C][C]94.1010714285714[/C][C]0.320471849247702[/C][C]293.632878049884[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 24 )[/C][C]94.0153846153846[/C][C]0.305754668255062[/C][C]307.486342406247[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 24 )[/C][C]93.9375[/C][C]0.296343813495577[/C][C]316.988226924474[/C][/ROW]
[ROW][C]Median[/C][C]93.04[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]97.26[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]94.3983783783784[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]94.4572222222222[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]94.3983783783784[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]94.4572222222222[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]94.4572222222222[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]94.3983783783784[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]94.4572222222222[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]94.5397368421053[/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=281448&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=281448&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 Mean95.90861111111110.570991172981399167.968640583933
Geometric Mean95.7906863440438
Harmonic Mean95.6755824990315
Quadratic Mean96.0292136828973
Winsorized Mean ( 1 / 24 )95.91111111111110.570086427690912168.239597458216
Winsorized Mean ( 2 / 24 )95.91416666666670.569427400599928168.439675655957
Winsorized Mean ( 3 / 24 )95.94208333333330.565384005996888169.693663626313
Winsorized Mean ( 4 / 24 )95.96930555555560.561370734872594170.955305636544
Winsorized Mean ( 5 / 24 )95.97902777777780.559274665784907171.613401517262
Winsorized Mean ( 6 / 24 )95.96902777777780.555397831435127172.793306610142
Winsorized Mean ( 7 / 24 )95.96416666666670.550150845369165174.432462431776
Winsorized Mean ( 8 / 24 )95.93972222222220.544545005843388176.183274463478
Winsorized Mean ( 9 / 24 )95.87347222222220.527465229246677181.762639329133
Winsorized Mean ( 10 / 24 )95.77486111111110.502927384763344190.434770530896
Winsorized Mean ( 11 / 24 )95.76111111111110.494188113823973193.774614225587
Winsorized Mean ( 12 / 24 )95.73277777777780.482252118420173198.511886461779
Winsorized Mean ( 13 / 24 )95.71833333333330.476838506075558200.73532676945
Winsorized Mean ( 14 / 24 )95.69888888888890.468600643625677204.222700482106
Winsorized Mean ( 15 / 24 )95.67180555555560.462948776745353206.657432444584
Winsorized Mean ( 16 / 24 )95.536250.431691927293046221.306547470245
Winsorized Mean ( 17 / 24 )95.24111111111110.377360155338467252.387830998443
Winsorized Mean ( 18 / 24 )95.25361111111110.370429703613351257.143555665113
Winsorized Mean ( 19 / 24 )95.16652777777780.352234103741954270.179766146371
Winsorized Mean ( 20 / 24 )94.96652777777780.317424356676287299.178452378895
Winsorized Mean ( 21 / 24 )94.86736111111110.300196987560171316.017032289826
Winsorized Mean ( 22 / 24 )94.78180555555560.283675871814923334.120082011746
Winsorized Mean ( 23 / 24 )94.61250.247997516110283381.505837171072
Winsorized Mean ( 24 / 24 )94.44250.222267862586236424.90398252405
Trimmed Mean ( 1 / 24 )95.870.56545355473928169.545313132223
Trimmed Mean ( 2 / 24 )95.82647058823530.559659245250907171.222884999022
Trimmed Mean ( 3 / 24 )95.77863636363640.552875588730131173.237231514643
Trimmed Mean ( 4 / 24 )95.717343750.54619441174912175.244092013825
Trimmed Mean ( 5 / 24 )95.64419354838710.539148296565452177.398675202484
Trimmed Mean ( 6 / 24 )95.56383333333330.530810492728061180.033806118244
Trimmed Mean ( 7 / 24 )95.480.5213170300844183.151507604772
Trimmed Mean ( 8 / 24 )95.39107142857140.510583933505539186.827405190055
Trimmed Mean ( 9 / 24 )95.29962962962960.498309017795323191.24604658223
Trimmed Mean ( 10 / 24 )95.21134615384620.486841718515722195.569406919615
Trimmed Mean ( 11 / 24 )95.13020.477879370826179199.067391914271
Trimmed Mean ( 12 / 24 )95.04416666666670.467901402875904203.128620864328
Trimmed Mean ( 13 / 24 )94.9543478260870.457244070827232207.666657446861
Trimmed Mean ( 14 / 24 )94.85818181818180.444022821053142213.633573142018
Trimmed Mean ( 15 / 24 )94.75523809523810.427973269500693221.404570911139
Trimmed Mean ( 16 / 24 )94.645250.407362685296279232.336572337654
Trimmed Mean ( 17 / 24 )94.53973684210530.387863441609835243.744902715544
Trimmed Mean ( 18 / 24 )94.45722222222220.376711672640165250.741426620055
Trimmed Mean ( 19 / 24 )94.36352941176470.361884028841137260.756269664471
Trimmed Mean ( 20 / 24 )94.26843750.345706414862695272.683506718962
Trimmed Mean ( 21 / 24 )94.18466666666670.333504461819688282.409015318027
Trimmed Mean ( 22 / 24 )94.10107142857140.320471849247702293.632878049884
Trimmed Mean ( 23 / 24 )94.01538461538460.305754668255062307.486342406247
Trimmed Mean ( 24 / 24 )93.93750.296343813495577316.988226924474
Median93.04
Midrange97.26
Midmean - Weighted Average at Xnp94.3983783783784
Midmean - Weighted Average at X(n+1)p94.4572222222222
Midmean - Empirical Distribution Function94.3983783783784
Midmean - Empirical Distribution Function - Averaging94.4572222222222
Midmean - Empirical Distribution Function - Interpolation94.4572222222222
Midmean - Closest Observation94.3983783783784
Midmean - True Basic - Statistics Graphics Toolkit94.4572222222222
Midmean - MS Excel (old versions)94.5397368421053
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')