Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationWed, 12 Dec 2007 04:01:06 -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/2007/Dec/12/t1197456393122qipq9lgh8fre.htm/, Retrieved Fri, 03 May 2024 00:27:48 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=3205, Retrieved Fri, 03 May 2024 00:27:48 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact226
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [Centr. Ten. Ruwe ...] [2007-12-12 11:01:06] [6bdd947de0ee04552c8f0fc807f31807] [Current]
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Dataseries X:
68,4
70,6
83,9
90,1
90,6
87,1
90,8
94,1
99,8
96,8
87
96,3
107,1
115,2
106,1
89,5
91,3
97,6
100,7
104,6
94,7
101,8
102,5
105,3
110,3
109,8
117,3
118,8
131,3
125,9
133,1
147
145,8
164,4
149,8
137,7
151,7
156,8
180
180,4
170,4
191,6
199,5
218,2
217,5
205
194
199,3
219,3
211,1
215,2
240,2
242,2
240,7
255,4
253
218,2
203,7
205,6
215,6
188,5
202,9
214
230,3
230
241
259,6




Summary of compuational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Herman Ole Andreas Wold' @ 193.190.124.10:1001

\begin{tabular}{lllllllll}
\hline
Summary of compuational 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 & 'Herman Ole Andreas Wold' @ 193.190.124.10:1001 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=3205&T=0

[TABLE]
[ROW][C]Summary of compuational 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]'Herman Ole Andreas Wold' @ 193.190.124.10:1001[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=3205&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=3205&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 compuational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Herman Ole Andreas Wold' @ 193.190.124.10:1001







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean155.4328358208967.0524754638080922.0394720433337
Geometric Mean144.687330897084
Harmonic Mean134.470338043232
Quadratic Mean165.656377850018
Winsorized Mean ( 1 / 22 )155.4029850746277.0326385725699222.0973939540644
Winsorized Mean ( 2 / 22 )155.7283582089556.9499407980357322.4071488857817
Winsorized Mean ( 3 / 22 )155.3835820895526.8306647546611122.7479444051945
Winsorized Mean ( 4 / 22 )155.3179104477616.8160384744829322.7871234925128
Winsorized Mean ( 5 / 22 )155.4746268656726.785001665079522.9144567002623
Winsorized Mean ( 6 / 22 )155.4835820895526.7686050600982822.9712888710476
Winsorized Mean ( 7 / 22 )154.5014925373136.5723780544438523.5077001440671
Winsorized Mean ( 8 / 22 )154.4895522388066.562611204917123.540866191045
Winsorized Mean ( 9 / 22 )153.1194029850756.3130396518904324.2544655868308
Winsorized Mean ( 10 / 22 )153.3731343283586.2258995604937824.6346946072792
Winsorized Mean ( 11 / 22 )153.4716417910456.2117339853170324.7067311887169
Winsorized Mean ( 12 / 22 )153.6328358208966.1511984866790324.9760816780016
Winsorized Mean ( 13 / 22 )153.3611940298516.0799207438566125.2242094084553
Winsorized Mean ( 14 / 22 )153.4447761194036.0434849227642125.3901148228925
Winsorized Mean ( 15 / 22 )153.6686567164185.9336323448591325.897906675926
Winsorized Mean ( 16 / 22 )153.1910447761195.7983570137186626.4197331095129
Winsorized Mean ( 17 / 22 )152.0746268656725.5524917266817427.3885373182814
Winsorized Mean ( 18 / 22 )152.1014925373135.5032404797625627.6385328056527
Winsorized Mean ( 19 / 22 )152.3283582089555.3688936919271828.3723923306584
Winsorized Mean ( 20 / 22 )152.2985074626875.306236780213928.7017925831322
Winsorized Mean ( 21 / 22 )151.4835820895525.1198470678584129.5875208930638
Winsorized Mean ( 22 / 22 )151.7462686567165.0665402018713629.9506690188046
Trimmed Mean ( 1 / 22 )155.1692307692316.9598573990271522.2948865002493
Trimmed Mean ( 2 / 22 )154.9206349206356.8691736131539622.5530236452276
Trimmed Mean ( 3 / 22 )154.4770491803286.8078877402093722.6908925462947
Trimmed Mean ( 4 / 22 )154.1338983050856.7815507667267322.7284147250410
Trimmed Mean ( 5 / 22 )153.7859649122816.7475436162622522.7913999016829
Trimmed Mean ( 6 / 22 )153.3745454545456.7077929542974622.8651281426752
Trimmed Mean ( 7 / 22 )152.9301886792456.655552798563622.9778341946668
Trimmed Mean ( 8 / 22 )152.6352941176476.633404959823823.0100973846924
Trimmed Mean ( 9 / 22 )152.3183673469396.5980127867095923.0854913851871
Trimmed Mean ( 10 / 22 )152.1914893617026.6001463484091423.0588052639750
Trimmed Mean ( 11 / 22 )152.0155555555566.6076080694568323.0061398856624
Trimmed Mean ( 12 / 22 )151.8093023255816.6046594294397122.9851824984199
Trimmed Mean ( 13 / 22 )151.5609756097566.597366324165222.9729513509975
Trimmed Mean ( 14 / 22 )151.3230769230776.5858510481834622.9769965667255
Trimmed Mean ( 15 / 22 )151.0486486486496.5593966955302923.0278264389127
Trimmed Mean ( 16 / 22 )150.7142857142866.5283481932302623.0861285662693
Trimmed Mean ( 17 / 22 )150.46.4963480416914123.1514689537541
Trimmed Mean ( 18 / 22 )150.1870967741946.4886563414078423.1461012684188
Trimmed Mean ( 19 / 22 )149.9413793103456.4589658104777623.2144562628137
Trimmed Mean ( 20 / 22 )149.6296296296306.4192059906408723.3096787745693
Trimmed Mean ( 21 / 22 )149.2726.3404403632555423.5428442581164
Trimmed Mean ( 22 / 22 )148.9652173913046.2446613046749723.8548113537853
Median147
Midrange164
Midmean - Weighted Average at Xnp148.938235294118
Midmean - Weighted Average at X(n+1)p150.714285714286
Midmean - Empirical Distribution Function150.714285714286
Midmean - Empirical Distribution Function - Averaging150.714285714286
Midmean - Empirical Distribution Function - Interpolation150.4
Midmean - Closest Observation148.938235294118
Midmean - True Basic - Statistics Graphics Toolkit150.714285714286
Midmean - MS Excel (old versions)150.714285714286
Number of observations67

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 155.432835820896 & 7.05247546380809 & 22.0394720433337 \tabularnewline
Geometric Mean & 144.687330897084 &  &  \tabularnewline
Harmonic Mean & 134.470338043232 &  &  \tabularnewline
Quadratic Mean & 165.656377850018 &  &  \tabularnewline
Winsorized Mean ( 1 / 22 ) & 155.402985074627 & 7.03263857256992 & 22.0973939540644 \tabularnewline
Winsorized Mean ( 2 / 22 ) & 155.728358208955 & 6.94994079803573 & 22.4071488857817 \tabularnewline
Winsorized Mean ( 3 / 22 ) & 155.383582089552 & 6.83066475466111 & 22.7479444051945 \tabularnewline
Winsorized Mean ( 4 / 22 ) & 155.317910447761 & 6.81603847448293 & 22.7871234925128 \tabularnewline
Winsorized Mean ( 5 / 22 ) & 155.474626865672 & 6.7850016650795 & 22.9144567002623 \tabularnewline
Winsorized Mean ( 6 / 22 ) & 155.483582089552 & 6.76860506009828 & 22.9712888710476 \tabularnewline
Winsorized Mean ( 7 / 22 ) & 154.501492537313 & 6.57237805444385 & 23.5077001440671 \tabularnewline
Winsorized Mean ( 8 / 22 ) & 154.489552238806 & 6.5626112049171 & 23.540866191045 \tabularnewline
Winsorized Mean ( 9 / 22 ) & 153.119402985075 & 6.31303965189043 & 24.2544655868308 \tabularnewline
Winsorized Mean ( 10 / 22 ) & 153.373134328358 & 6.22589956049378 & 24.6346946072792 \tabularnewline
Winsorized Mean ( 11 / 22 ) & 153.471641791045 & 6.21173398531703 & 24.7067311887169 \tabularnewline
Winsorized Mean ( 12 / 22 ) & 153.632835820896 & 6.15119848667903 & 24.9760816780016 \tabularnewline
Winsorized Mean ( 13 / 22 ) & 153.361194029851 & 6.07992074385661 & 25.2242094084553 \tabularnewline
Winsorized Mean ( 14 / 22 ) & 153.444776119403 & 6.04348492276421 & 25.3901148228925 \tabularnewline
Winsorized Mean ( 15 / 22 ) & 153.668656716418 & 5.93363234485913 & 25.897906675926 \tabularnewline
Winsorized Mean ( 16 / 22 ) & 153.191044776119 & 5.79835701371866 & 26.4197331095129 \tabularnewline
Winsorized Mean ( 17 / 22 ) & 152.074626865672 & 5.55249172668174 & 27.3885373182814 \tabularnewline
Winsorized Mean ( 18 / 22 ) & 152.101492537313 & 5.50324047976256 & 27.6385328056527 \tabularnewline
Winsorized Mean ( 19 / 22 ) & 152.328358208955 & 5.36889369192718 & 28.3723923306584 \tabularnewline
Winsorized Mean ( 20 / 22 ) & 152.298507462687 & 5.3062367802139 & 28.7017925831322 \tabularnewline
Winsorized Mean ( 21 / 22 ) & 151.483582089552 & 5.11984706785841 & 29.5875208930638 \tabularnewline
Winsorized Mean ( 22 / 22 ) & 151.746268656716 & 5.06654020187136 & 29.9506690188046 \tabularnewline
Trimmed Mean ( 1 / 22 ) & 155.169230769231 & 6.95985739902715 & 22.2948865002493 \tabularnewline
Trimmed Mean ( 2 / 22 ) & 154.920634920635 & 6.86917361315396 & 22.5530236452276 \tabularnewline
Trimmed Mean ( 3 / 22 ) & 154.477049180328 & 6.80788774020937 & 22.6908925462947 \tabularnewline
Trimmed Mean ( 4 / 22 ) & 154.133898305085 & 6.78155076672673 & 22.7284147250410 \tabularnewline
Trimmed Mean ( 5 / 22 ) & 153.785964912281 & 6.74754361626225 & 22.7913999016829 \tabularnewline
Trimmed Mean ( 6 / 22 ) & 153.374545454545 & 6.70779295429746 & 22.8651281426752 \tabularnewline
Trimmed Mean ( 7 / 22 ) & 152.930188679245 & 6.6555527985636 & 22.9778341946668 \tabularnewline
Trimmed Mean ( 8 / 22 ) & 152.635294117647 & 6.6334049598238 & 23.0100973846924 \tabularnewline
Trimmed Mean ( 9 / 22 ) & 152.318367346939 & 6.59801278670959 & 23.0854913851871 \tabularnewline
Trimmed Mean ( 10 / 22 ) & 152.191489361702 & 6.60014634840914 & 23.0588052639750 \tabularnewline
Trimmed Mean ( 11 / 22 ) & 152.015555555556 & 6.60760806945683 & 23.0061398856624 \tabularnewline
Trimmed Mean ( 12 / 22 ) & 151.809302325581 & 6.60465942943971 & 22.9851824984199 \tabularnewline
Trimmed Mean ( 13 / 22 ) & 151.560975609756 & 6.5973663241652 & 22.9729513509975 \tabularnewline
Trimmed Mean ( 14 / 22 ) & 151.323076923077 & 6.58585104818346 & 22.9769965667255 \tabularnewline
Trimmed Mean ( 15 / 22 ) & 151.048648648649 & 6.55939669553029 & 23.0278264389127 \tabularnewline
Trimmed Mean ( 16 / 22 ) & 150.714285714286 & 6.52834819323026 & 23.0861285662693 \tabularnewline
Trimmed Mean ( 17 / 22 ) & 150.4 & 6.49634804169141 & 23.1514689537541 \tabularnewline
Trimmed Mean ( 18 / 22 ) & 150.187096774194 & 6.48865634140784 & 23.1461012684188 \tabularnewline
Trimmed Mean ( 19 / 22 ) & 149.941379310345 & 6.45896581047776 & 23.2144562628137 \tabularnewline
Trimmed Mean ( 20 / 22 ) & 149.629629629630 & 6.41920599064087 & 23.3096787745693 \tabularnewline
Trimmed Mean ( 21 / 22 ) & 149.272 & 6.34044036325554 & 23.5428442581164 \tabularnewline
Trimmed Mean ( 22 / 22 ) & 148.965217391304 & 6.24466130467497 & 23.8548113537853 \tabularnewline
Median & 147 &  &  \tabularnewline
Midrange & 164 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 148.938235294118 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 150.714285714286 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 150.714285714286 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 150.714285714286 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 150.4 &  &  \tabularnewline
Midmean - Closest Observation & 148.938235294118 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 150.714285714286 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 150.714285714286 &  &  \tabularnewline
Number of observations & 67 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=3205&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]155.432835820896[/C][C]7.05247546380809[/C][C]22.0394720433337[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]144.687330897084[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]134.470338043232[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]165.656377850018[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 22 )[/C][C]155.402985074627[/C][C]7.03263857256992[/C][C]22.0973939540644[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 22 )[/C][C]155.728358208955[/C][C]6.94994079803573[/C][C]22.4071488857817[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 22 )[/C][C]155.383582089552[/C][C]6.83066475466111[/C][C]22.7479444051945[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 22 )[/C][C]155.317910447761[/C][C]6.81603847448293[/C][C]22.7871234925128[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 22 )[/C][C]155.474626865672[/C][C]6.7850016650795[/C][C]22.9144567002623[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 22 )[/C][C]155.483582089552[/C][C]6.76860506009828[/C][C]22.9712888710476[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 22 )[/C][C]154.501492537313[/C][C]6.57237805444385[/C][C]23.5077001440671[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 22 )[/C][C]154.489552238806[/C][C]6.5626112049171[/C][C]23.540866191045[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 22 )[/C][C]153.119402985075[/C][C]6.31303965189043[/C][C]24.2544655868308[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 22 )[/C][C]153.373134328358[/C][C]6.22589956049378[/C][C]24.6346946072792[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 22 )[/C][C]153.471641791045[/C][C]6.21173398531703[/C][C]24.7067311887169[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 22 )[/C][C]153.632835820896[/C][C]6.15119848667903[/C][C]24.9760816780016[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 22 )[/C][C]153.361194029851[/C][C]6.07992074385661[/C][C]25.2242094084553[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 22 )[/C][C]153.444776119403[/C][C]6.04348492276421[/C][C]25.3901148228925[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 22 )[/C][C]153.668656716418[/C][C]5.93363234485913[/C][C]25.897906675926[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 22 )[/C][C]153.191044776119[/C][C]5.79835701371866[/C][C]26.4197331095129[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 22 )[/C][C]152.074626865672[/C][C]5.55249172668174[/C][C]27.3885373182814[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 22 )[/C][C]152.101492537313[/C][C]5.50324047976256[/C][C]27.6385328056527[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 22 )[/C][C]152.328358208955[/C][C]5.36889369192718[/C][C]28.3723923306584[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 22 )[/C][C]152.298507462687[/C][C]5.3062367802139[/C][C]28.7017925831322[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 22 )[/C][C]151.483582089552[/C][C]5.11984706785841[/C][C]29.5875208930638[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 22 )[/C][C]151.746268656716[/C][C]5.06654020187136[/C][C]29.9506690188046[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 22 )[/C][C]155.169230769231[/C][C]6.95985739902715[/C][C]22.2948865002493[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 22 )[/C][C]154.920634920635[/C][C]6.86917361315396[/C][C]22.5530236452276[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 22 )[/C][C]154.477049180328[/C][C]6.80788774020937[/C][C]22.6908925462947[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 22 )[/C][C]154.133898305085[/C][C]6.78155076672673[/C][C]22.7284147250410[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 22 )[/C][C]153.785964912281[/C][C]6.74754361626225[/C][C]22.7913999016829[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 22 )[/C][C]153.374545454545[/C][C]6.70779295429746[/C][C]22.8651281426752[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 22 )[/C][C]152.930188679245[/C][C]6.6555527985636[/C][C]22.9778341946668[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 22 )[/C][C]152.635294117647[/C][C]6.6334049598238[/C][C]23.0100973846924[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 22 )[/C][C]152.318367346939[/C][C]6.59801278670959[/C][C]23.0854913851871[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 22 )[/C][C]152.191489361702[/C][C]6.60014634840914[/C][C]23.0588052639750[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 22 )[/C][C]152.015555555556[/C][C]6.60760806945683[/C][C]23.0061398856624[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 22 )[/C][C]151.809302325581[/C][C]6.60465942943971[/C][C]22.9851824984199[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 22 )[/C][C]151.560975609756[/C][C]6.5973663241652[/C][C]22.9729513509975[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 22 )[/C][C]151.323076923077[/C][C]6.58585104818346[/C][C]22.9769965667255[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 22 )[/C][C]151.048648648649[/C][C]6.55939669553029[/C][C]23.0278264389127[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 22 )[/C][C]150.714285714286[/C][C]6.52834819323026[/C][C]23.0861285662693[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 22 )[/C][C]150.4[/C][C]6.49634804169141[/C][C]23.1514689537541[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 22 )[/C][C]150.187096774194[/C][C]6.48865634140784[/C][C]23.1461012684188[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 22 )[/C][C]149.941379310345[/C][C]6.45896581047776[/C][C]23.2144562628137[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 22 )[/C][C]149.629629629630[/C][C]6.41920599064087[/C][C]23.3096787745693[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 22 )[/C][C]149.272[/C][C]6.34044036325554[/C][C]23.5428442581164[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 22 )[/C][C]148.965217391304[/C][C]6.24466130467497[/C][C]23.8548113537853[/C][/ROW]
[ROW][C]Median[/C][C]147[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]164[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]148.938235294118[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]150.714285714286[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]150.714285714286[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]150.714285714286[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]150.4[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]148.938235294118[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]150.714285714286[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]150.714285714286[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]67[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=3205&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=3205&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 Mean155.4328358208967.0524754638080922.0394720433337
Geometric Mean144.687330897084
Harmonic Mean134.470338043232
Quadratic Mean165.656377850018
Winsorized Mean ( 1 / 22 )155.4029850746277.0326385725699222.0973939540644
Winsorized Mean ( 2 / 22 )155.7283582089556.9499407980357322.4071488857817
Winsorized Mean ( 3 / 22 )155.3835820895526.8306647546611122.7479444051945
Winsorized Mean ( 4 / 22 )155.3179104477616.8160384744829322.7871234925128
Winsorized Mean ( 5 / 22 )155.4746268656726.785001665079522.9144567002623
Winsorized Mean ( 6 / 22 )155.4835820895526.7686050600982822.9712888710476
Winsorized Mean ( 7 / 22 )154.5014925373136.5723780544438523.5077001440671
Winsorized Mean ( 8 / 22 )154.4895522388066.562611204917123.540866191045
Winsorized Mean ( 9 / 22 )153.1194029850756.3130396518904324.2544655868308
Winsorized Mean ( 10 / 22 )153.3731343283586.2258995604937824.6346946072792
Winsorized Mean ( 11 / 22 )153.4716417910456.2117339853170324.7067311887169
Winsorized Mean ( 12 / 22 )153.6328358208966.1511984866790324.9760816780016
Winsorized Mean ( 13 / 22 )153.3611940298516.0799207438566125.2242094084553
Winsorized Mean ( 14 / 22 )153.4447761194036.0434849227642125.3901148228925
Winsorized Mean ( 15 / 22 )153.6686567164185.9336323448591325.897906675926
Winsorized Mean ( 16 / 22 )153.1910447761195.7983570137186626.4197331095129
Winsorized Mean ( 17 / 22 )152.0746268656725.5524917266817427.3885373182814
Winsorized Mean ( 18 / 22 )152.1014925373135.5032404797625627.6385328056527
Winsorized Mean ( 19 / 22 )152.3283582089555.3688936919271828.3723923306584
Winsorized Mean ( 20 / 22 )152.2985074626875.306236780213928.7017925831322
Winsorized Mean ( 21 / 22 )151.4835820895525.1198470678584129.5875208930638
Winsorized Mean ( 22 / 22 )151.7462686567165.0665402018713629.9506690188046
Trimmed Mean ( 1 / 22 )155.1692307692316.9598573990271522.2948865002493
Trimmed Mean ( 2 / 22 )154.9206349206356.8691736131539622.5530236452276
Trimmed Mean ( 3 / 22 )154.4770491803286.8078877402093722.6908925462947
Trimmed Mean ( 4 / 22 )154.1338983050856.7815507667267322.7284147250410
Trimmed Mean ( 5 / 22 )153.7859649122816.7475436162622522.7913999016829
Trimmed Mean ( 6 / 22 )153.3745454545456.7077929542974622.8651281426752
Trimmed Mean ( 7 / 22 )152.9301886792456.655552798563622.9778341946668
Trimmed Mean ( 8 / 22 )152.6352941176476.633404959823823.0100973846924
Trimmed Mean ( 9 / 22 )152.3183673469396.5980127867095923.0854913851871
Trimmed Mean ( 10 / 22 )152.1914893617026.6001463484091423.0588052639750
Trimmed Mean ( 11 / 22 )152.0155555555566.6076080694568323.0061398856624
Trimmed Mean ( 12 / 22 )151.8093023255816.6046594294397122.9851824984199
Trimmed Mean ( 13 / 22 )151.5609756097566.597366324165222.9729513509975
Trimmed Mean ( 14 / 22 )151.3230769230776.5858510481834622.9769965667255
Trimmed Mean ( 15 / 22 )151.0486486486496.5593966955302923.0278264389127
Trimmed Mean ( 16 / 22 )150.7142857142866.5283481932302623.0861285662693
Trimmed Mean ( 17 / 22 )150.46.4963480416914123.1514689537541
Trimmed Mean ( 18 / 22 )150.1870967741946.4886563414078423.1461012684188
Trimmed Mean ( 19 / 22 )149.9413793103456.4589658104777623.2144562628137
Trimmed Mean ( 20 / 22 )149.6296296296306.4192059906408723.3096787745693
Trimmed Mean ( 21 / 22 )149.2726.3404403632555423.5428442581164
Trimmed Mean ( 22 / 22 )148.9652173913046.2446613046749723.8548113537853
Median147
Midrange164
Midmean - Weighted Average at Xnp148.938235294118
Midmean - Weighted Average at X(n+1)p150.714285714286
Midmean - Empirical Distribution Function150.714285714286
Midmean - Empirical Distribution Function - Averaging150.714285714286
Midmean - Empirical Distribution Function - Interpolation150.4
Midmean - Closest Observation148.938235294118
Midmean - True Basic - Statistics Graphics Toolkit150.714285714286
Midmean - MS Excel (old versions)150.714285714286
Number of observations67



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')