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Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationTue, 05 Mar 2013 11:37:12 -0500
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2013/Mar/05/t13625014613gn6b6phk5saxl1.htm/, Retrieved Sat, 04 May 2024 13:38:26 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=207417, Retrieved Sat, 04 May 2024 13:38:26 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact65
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [Centrummaten eige...] [2013-03-05 16:37:12] [bc2cf5f41ec5ca561b7a550898b8dd0d] [Current]
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Dataseries X:
122,27
124,69
147,56
120,03
136,01
138,16
122,87
112,22
137,35
139,08
139,64
121,12
132,37
130,69
149,41
130,72
139,14
146,55
137,35
122,73
138,97
154,73
143,4
123,88
140,25
142,39
143,81
153,58
144,71
153,84
151,3
121,92
153,05
149,29
118,81
109,19
103,68
106,94
114,43
107,87
103,14
117,02
112,44
95,85
123,86
121,83
121,95
120,34
113,32
117,31
141,69
130,35
127,28
148,1
131,21
120,37
146,91
144,04
141,77
132,15
142,04
149,77
172,31
150,24
163,23
155,92
146,96
134,51
152,83
150,54
150,98
138,82




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Sir Ronald Aylmer Fisher' @ fisher.wessa.net

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 2 seconds \tabularnewline
R Server & 'Sir Ronald Aylmer Fisher' @ fisher.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=207417&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Sir Ronald Aylmer Fisher' @ fisher.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=207417&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=207417&T=0

As an alternative you can also use a QR Code:  

The GUIDs for individual cells are displayed in the table below:

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Sir Ronald Aylmer Fisher' @ fisher.wessa.net







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean133.9594444444441.8852150420181271.057911940402
Geometric Mean132.989090620711
Harmonic Mean131.990128555335
Quadratic Mean134.897995887428
Winsorized Mean ( 1 / 24 )133.9345833333331.8263682775365273.3338313968034
Winsorized Mean ( 2 / 24 )133.7465277777781.7820115890724575.0536801207865
Winsorized Mean ( 3 / 24 )133.8327777777781.7425599414479976.8023954840652
Winsorized Mean ( 4 / 24 )133.8351.7232429417545177.6646152188715
Winsorized Mean ( 5 / 24 )133.9086111111111.7011877617379178.7147745374749
Winsorized Mean ( 6 / 24 )134.1169444444441.6444587638291981.5568911756399
Winsorized Mean ( 7 / 24 )134.1169444444441.6370024257934281.9283724515194
Winsorized Mean ( 8 / 24 )134.0447222222221.592250623884.1856930175457
Winsorized Mean ( 9 / 24 )134.1434722222221.5610989889168785.9288700938142
Winsorized Mean ( 10 / 24 )134.4420833333331.4901459835626490.2207467028899
Winsorized Mean ( 11 / 24 )134.4405555555561.4759344257597591.0884340178943
Winsorized Mean ( 12 / 24 )134.6122222222221.4241724833092694.5196061571364
Winsorized Mean ( 13 / 24 )134.76751.3806649521494797.6105751002001
Winsorized Mean ( 14 / 24 )134.8044444444441.3681634264725698.5294898519556
Winsorized Mean ( 15 / 24 )134.5627777777781.33097672053397101.100774868393
Winsorized Mean ( 16 / 24 )134.6094444444441.28908852030429104.422188487622
Winsorized Mean ( 17 / 24 )134.6354166666671.24468168994802108.168552453189
Winsorized Mean ( 18 / 24 )134.6454166666671.23968248903141108.612824540151
Winsorized Mean ( 19 / 24 )134.5583333333331.22537029311248109.810343934119
Winsorized Mean ( 20 / 24 )134.1361111111111.14387397658899117.264763301201
Winsorized Mean ( 21 / 24 )134.0748611111111.09911601970285121.984266180889
Winsorized Mean ( 22 / 24 )134.0473611111111.0839553467655123.665021360064
Winsorized Mean ( 23 / 24 )134.2326388888891.02178807022209131.370332851618
Winsorized Mean ( 24 / 24 )133.9026388888890.978989750135678136.77634405297
Trimmed Mean ( 1 / 24 )133.9561.7766098802682275.3997833107717
Trimmed Mean ( 2 / 24 )133.9786764705881.7174482355544678.0103141957782
Trimmed Mean ( 3 / 24 )134.1053030303031.6751312403053580.0565948527458
Trimmed Mean ( 4 / 24 )134.20751.6422328912330481.7225746216988
Trimmed Mean ( 5 / 24 )134.315645161291.6092501911557983.4647377390229
Trimmed Mean ( 6 / 24 )134.4133333333331.5758781188830585.2942443471469
Trimmed Mean ( 7 / 24 )134.4746551724141.5508247364902986.7117037846241
Trimmed Mean ( 8 / 24 )134.5403571428571.5213238844234588.4363668515236
Trimmed Mean ( 9 / 24 )134.6229629629631.4950273417548890.0471578031081
Trimmed Mean ( 10 / 24 )134.6967307692311.4687909866211891.7058533148329
Trimmed Mean ( 11 / 24 )134.73341.4509308654538192.8599723170542
Trimmed Mean ( 12 / 24 )134.7733333333331.4300527668850794.2436086655008
Trimmed Mean ( 13 / 24 )134.7943478260871.413169003714895.3844497521194
Trimmed Mean ( 14 / 24 )134.7977272727271.3988599202544796.362563056497
Trimmed Mean ( 15 / 24 )134.7969047619051.3808106864908997.6215683154001
Trimmed Mean ( 16 / 24 )134.8251.3629933592779998.9183102633898
Trimmed Mean ( 17 / 24 )134.8505263157891.34620783162982100.170659498043
Trimmed Mean ( 18 / 24 )134.8758333333331.33090936658493101.341110611777
Trimmed Mean ( 19 / 24 )134.9029411764711.30785475171693103.148259391475
Trimmed Mean ( 20 / 24 )134.943751.27620797851897105.738055451276
Trimmed Mean ( 21 / 24 )135.0406666666671.25000771798384108.031866302775
Trimmed Mean ( 22 / 24 )135.1589285714291.22066621796626110.725541988551
Trimmed Mean ( 23 / 24 )135.2988461538461.17675686357732114.976041645969
Trimmed Mean ( 24 / 24 )135.4379166666671.12863887806923120.001108679121
Median137.35
Midrange134.08
Midmean - Weighted Average at Xnp134.523243243243
Midmean - Weighted Average at X(n+1)p134.875833333333
Midmean - Empirical Distribution Function134.523243243243
Midmean - Empirical Distribution Function - Averaging134.875833333333
Midmean - Empirical Distribution Function - Interpolation134.875833333333
Midmean - Closest Observation134.523243243243
Midmean - True Basic - Statistics Graphics Toolkit134.875833333333
Midmean - MS Excel (old versions)134.850526315789
Number of observations72

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 133.959444444444 & 1.88521504201812 & 71.057911940402 \tabularnewline
Geometric Mean & 132.989090620711 &  &  \tabularnewline
Harmonic Mean & 131.990128555335 &  &  \tabularnewline
Quadratic Mean & 134.897995887428 &  &  \tabularnewline
Winsorized Mean ( 1 / 24 ) & 133.934583333333 & 1.82636827753652 & 73.3338313968034 \tabularnewline
Winsorized Mean ( 2 / 24 ) & 133.746527777778 & 1.78201158907245 & 75.0536801207865 \tabularnewline
Winsorized Mean ( 3 / 24 ) & 133.832777777778 & 1.74255994144799 & 76.8023954840652 \tabularnewline
Winsorized Mean ( 4 / 24 ) & 133.835 & 1.72324294175451 & 77.6646152188715 \tabularnewline
Winsorized Mean ( 5 / 24 ) & 133.908611111111 & 1.70118776173791 & 78.7147745374749 \tabularnewline
Winsorized Mean ( 6 / 24 ) & 134.116944444444 & 1.64445876382919 & 81.5568911756399 \tabularnewline
Winsorized Mean ( 7 / 24 ) & 134.116944444444 & 1.63700242579342 & 81.9283724515194 \tabularnewline
Winsorized Mean ( 8 / 24 ) & 134.044722222222 & 1.5922506238 & 84.1856930175457 \tabularnewline
Winsorized Mean ( 9 / 24 ) & 134.143472222222 & 1.56109898891687 & 85.9288700938142 \tabularnewline
Winsorized Mean ( 10 / 24 ) & 134.442083333333 & 1.49014598356264 & 90.2207467028899 \tabularnewline
Winsorized Mean ( 11 / 24 ) & 134.440555555556 & 1.47593442575975 & 91.0884340178943 \tabularnewline
Winsorized Mean ( 12 / 24 ) & 134.612222222222 & 1.42417248330926 & 94.5196061571364 \tabularnewline
Winsorized Mean ( 13 / 24 ) & 134.7675 & 1.38066495214947 & 97.6105751002001 \tabularnewline
Winsorized Mean ( 14 / 24 ) & 134.804444444444 & 1.36816342647256 & 98.5294898519556 \tabularnewline
Winsorized Mean ( 15 / 24 ) & 134.562777777778 & 1.33097672053397 & 101.100774868393 \tabularnewline
Winsorized Mean ( 16 / 24 ) & 134.609444444444 & 1.28908852030429 & 104.422188487622 \tabularnewline
Winsorized Mean ( 17 / 24 ) & 134.635416666667 & 1.24468168994802 & 108.168552453189 \tabularnewline
Winsorized Mean ( 18 / 24 ) & 134.645416666667 & 1.23968248903141 & 108.612824540151 \tabularnewline
Winsorized Mean ( 19 / 24 ) & 134.558333333333 & 1.22537029311248 & 109.810343934119 \tabularnewline
Winsorized Mean ( 20 / 24 ) & 134.136111111111 & 1.14387397658899 & 117.264763301201 \tabularnewline
Winsorized Mean ( 21 / 24 ) & 134.074861111111 & 1.09911601970285 & 121.984266180889 \tabularnewline
Winsorized Mean ( 22 / 24 ) & 134.047361111111 & 1.0839553467655 & 123.665021360064 \tabularnewline
Winsorized Mean ( 23 / 24 ) & 134.232638888889 & 1.02178807022209 & 131.370332851618 \tabularnewline
Winsorized Mean ( 24 / 24 ) & 133.902638888889 & 0.978989750135678 & 136.77634405297 \tabularnewline
Trimmed Mean ( 1 / 24 ) & 133.956 & 1.77660988026822 & 75.3997833107717 \tabularnewline
Trimmed Mean ( 2 / 24 ) & 133.978676470588 & 1.71744823555446 & 78.0103141957782 \tabularnewline
Trimmed Mean ( 3 / 24 ) & 134.105303030303 & 1.67513124030535 & 80.0565948527458 \tabularnewline
Trimmed Mean ( 4 / 24 ) & 134.2075 & 1.64223289123304 & 81.7225746216988 \tabularnewline
Trimmed Mean ( 5 / 24 ) & 134.31564516129 & 1.60925019115579 & 83.4647377390229 \tabularnewline
Trimmed Mean ( 6 / 24 ) & 134.413333333333 & 1.57587811888305 & 85.2942443471469 \tabularnewline
Trimmed Mean ( 7 / 24 ) & 134.474655172414 & 1.55082473649029 & 86.7117037846241 \tabularnewline
Trimmed Mean ( 8 / 24 ) & 134.540357142857 & 1.52132388442345 & 88.4363668515236 \tabularnewline
Trimmed Mean ( 9 / 24 ) & 134.622962962963 & 1.49502734175488 & 90.0471578031081 \tabularnewline
Trimmed Mean ( 10 / 24 ) & 134.696730769231 & 1.46879098662118 & 91.7058533148329 \tabularnewline
Trimmed Mean ( 11 / 24 ) & 134.7334 & 1.45093086545381 & 92.8599723170542 \tabularnewline
Trimmed Mean ( 12 / 24 ) & 134.773333333333 & 1.43005276688507 & 94.2436086655008 \tabularnewline
Trimmed Mean ( 13 / 24 ) & 134.794347826087 & 1.4131690037148 & 95.3844497521194 \tabularnewline
Trimmed Mean ( 14 / 24 ) & 134.797727272727 & 1.39885992025447 & 96.362563056497 \tabularnewline
Trimmed Mean ( 15 / 24 ) & 134.796904761905 & 1.38081068649089 & 97.6215683154001 \tabularnewline
Trimmed Mean ( 16 / 24 ) & 134.825 & 1.36299335927799 & 98.9183102633898 \tabularnewline
Trimmed Mean ( 17 / 24 ) & 134.850526315789 & 1.34620783162982 & 100.170659498043 \tabularnewline
Trimmed Mean ( 18 / 24 ) & 134.875833333333 & 1.33090936658493 & 101.341110611777 \tabularnewline
Trimmed Mean ( 19 / 24 ) & 134.902941176471 & 1.30785475171693 & 103.148259391475 \tabularnewline
Trimmed Mean ( 20 / 24 ) & 134.94375 & 1.27620797851897 & 105.738055451276 \tabularnewline
Trimmed Mean ( 21 / 24 ) & 135.040666666667 & 1.25000771798384 & 108.031866302775 \tabularnewline
Trimmed Mean ( 22 / 24 ) & 135.158928571429 & 1.22066621796626 & 110.725541988551 \tabularnewline
Trimmed Mean ( 23 / 24 ) & 135.298846153846 & 1.17675686357732 & 114.976041645969 \tabularnewline
Trimmed Mean ( 24 / 24 ) & 135.437916666667 & 1.12863887806923 & 120.001108679121 \tabularnewline
Median & 137.35 &  &  \tabularnewline
Midrange & 134.08 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 134.523243243243 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 134.875833333333 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 134.523243243243 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 134.875833333333 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 134.875833333333 &  &  \tabularnewline
Midmean - Closest Observation & 134.523243243243 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 134.875833333333 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 134.850526315789 &  &  \tabularnewline
Number of observations & 72 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=207417&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]133.959444444444[/C][C]1.88521504201812[/C][C]71.057911940402[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]132.989090620711[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]131.990128555335[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]134.897995887428[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 24 )[/C][C]133.934583333333[/C][C]1.82636827753652[/C][C]73.3338313968034[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 24 )[/C][C]133.746527777778[/C][C]1.78201158907245[/C][C]75.0536801207865[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 24 )[/C][C]133.832777777778[/C][C]1.74255994144799[/C][C]76.8023954840652[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 24 )[/C][C]133.835[/C][C]1.72324294175451[/C][C]77.6646152188715[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 24 )[/C][C]133.908611111111[/C][C]1.70118776173791[/C][C]78.7147745374749[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 24 )[/C][C]134.116944444444[/C][C]1.64445876382919[/C][C]81.5568911756399[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 24 )[/C][C]134.116944444444[/C][C]1.63700242579342[/C][C]81.9283724515194[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 24 )[/C][C]134.044722222222[/C][C]1.5922506238[/C][C]84.1856930175457[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 24 )[/C][C]134.143472222222[/C][C]1.56109898891687[/C][C]85.9288700938142[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 24 )[/C][C]134.442083333333[/C][C]1.49014598356264[/C][C]90.2207467028899[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 24 )[/C][C]134.440555555556[/C][C]1.47593442575975[/C][C]91.0884340178943[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 24 )[/C][C]134.612222222222[/C][C]1.42417248330926[/C][C]94.5196061571364[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 24 )[/C][C]134.7675[/C][C]1.38066495214947[/C][C]97.6105751002001[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 24 )[/C][C]134.804444444444[/C][C]1.36816342647256[/C][C]98.5294898519556[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 24 )[/C][C]134.562777777778[/C][C]1.33097672053397[/C][C]101.100774868393[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 24 )[/C][C]134.609444444444[/C][C]1.28908852030429[/C][C]104.422188487622[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 24 )[/C][C]134.635416666667[/C][C]1.24468168994802[/C][C]108.168552453189[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 24 )[/C][C]134.645416666667[/C][C]1.23968248903141[/C][C]108.612824540151[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 24 )[/C][C]134.558333333333[/C][C]1.22537029311248[/C][C]109.810343934119[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 24 )[/C][C]134.136111111111[/C][C]1.14387397658899[/C][C]117.264763301201[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 24 )[/C][C]134.074861111111[/C][C]1.09911601970285[/C][C]121.984266180889[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 24 )[/C][C]134.047361111111[/C][C]1.0839553467655[/C][C]123.665021360064[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 24 )[/C][C]134.232638888889[/C][C]1.02178807022209[/C][C]131.370332851618[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 24 )[/C][C]133.902638888889[/C][C]0.978989750135678[/C][C]136.77634405297[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 24 )[/C][C]133.956[/C][C]1.77660988026822[/C][C]75.3997833107717[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 24 )[/C][C]133.978676470588[/C][C]1.71744823555446[/C][C]78.0103141957782[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 24 )[/C][C]134.105303030303[/C][C]1.67513124030535[/C][C]80.0565948527458[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 24 )[/C][C]134.2075[/C][C]1.64223289123304[/C][C]81.7225746216988[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 24 )[/C][C]134.31564516129[/C][C]1.60925019115579[/C][C]83.4647377390229[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 24 )[/C][C]134.413333333333[/C][C]1.57587811888305[/C][C]85.2942443471469[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 24 )[/C][C]134.474655172414[/C][C]1.55082473649029[/C][C]86.7117037846241[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 24 )[/C][C]134.540357142857[/C][C]1.52132388442345[/C][C]88.4363668515236[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 24 )[/C][C]134.622962962963[/C][C]1.49502734175488[/C][C]90.0471578031081[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 24 )[/C][C]134.696730769231[/C][C]1.46879098662118[/C][C]91.7058533148329[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 24 )[/C][C]134.7334[/C][C]1.45093086545381[/C][C]92.8599723170542[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 24 )[/C][C]134.773333333333[/C][C]1.43005276688507[/C][C]94.2436086655008[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 24 )[/C][C]134.794347826087[/C][C]1.4131690037148[/C][C]95.3844497521194[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 24 )[/C][C]134.797727272727[/C][C]1.39885992025447[/C][C]96.362563056497[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 24 )[/C][C]134.796904761905[/C][C]1.38081068649089[/C][C]97.6215683154001[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 24 )[/C][C]134.825[/C][C]1.36299335927799[/C][C]98.9183102633898[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 24 )[/C][C]134.850526315789[/C][C]1.34620783162982[/C][C]100.170659498043[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 24 )[/C][C]134.875833333333[/C][C]1.33090936658493[/C][C]101.341110611777[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 24 )[/C][C]134.902941176471[/C][C]1.30785475171693[/C][C]103.148259391475[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 24 )[/C][C]134.94375[/C][C]1.27620797851897[/C][C]105.738055451276[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 24 )[/C][C]135.040666666667[/C][C]1.25000771798384[/C][C]108.031866302775[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 24 )[/C][C]135.158928571429[/C][C]1.22066621796626[/C][C]110.725541988551[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 24 )[/C][C]135.298846153846[/C][C]1.17675686357732[/C][C]114.976041645969[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 24 )[/C][C]135.437916666667[/C][C]1.12863887806923[/C][C]120.001108679121[/C][/ROW]
[ROW][C]Median[/C][C]137.35[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]134.08[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]134.523243243243[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]134.875833333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]134.523243243243[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]134.875833333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]134.875833333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]134.523243243243[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]134.875833333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]134.850526315789[/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=207417&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=207417&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 Mean133.9594444444441.8852150420181271.057911940402
Geometric Mean132.989090620711
Harmonic Mean131.990128555335
Quadratic Mean134.897995887428
Winsorized Mean ( 1 / 24 )133.9345833333331.8263682775365273.3338313968034
Winsorized Mean ( 2 / 24 )133.7465277777781.7820115890724575.0536801207865
Winsorized Mean ( 3 / 24 )133.8327777777781.7425599414479976.8023954840652
Winsorized Mean ( 4 / 24 )133.8351.7232429417545177.6646152188715
Winsorized Mean ( 5 / 24 )133.9086111111111.7011877617379178.7147745374749
Winsorized Mean ( 6 / 24 )134.1169444444441.6444587638291981.5568911756399
Winsorized Mean ( 7 / 24 )134.1169444444441.6370024257934281.9283724515194
Winsorized Mean ( 8 / 24 )134.0447222222221.592250623884.1856930175457
Winsorized Mean ( 9 / 24 )134.1434722222221.5610989889168785.9288700938142
Winsorized Mean ( 10 / 24 )134.4420833333331.4901459835626490.2207467028899
Winsorized Mean ( 11 / 24 )134.4405555555561.4759344257597591.0884340178943
Winsorized Mean ( 12 / 24 )134.6122222222221.4241724833092694.5196061571364
Winsorized Mean ( 13 / 24 )134.76751.3806649521494797.6105751002001
Winsorized Mean ( 14 / 24 )134.8044444444441.3681634264725698.5294898519556
Winsorized Mean ( 15 / 24 )134.5627777777781.33097672053397101.100774868393
Winsorized Mean ( 16 / 24 )134.6094444444441.28908852030429104.422188487622
Winsorized Mean ( 17 / 24 )134.6354166666671.24468168994802108.168552453189
Winsorized Mean ( 18 / 24 )134.6454166666671.23968248903141108.612824540151
Winsorized Mean ( 19 / 24 )134.5583333333331.22537029311248109.810343934119
Winsorized Mean ( 20 / 24 )134.1361111111111.14387397658899117.264763301201
Winsorized Mean ( 21 / 24 )134.0748611111111.09911601970285121.984266180889
Winsorized Mean ( 22 / 24 )134.0473611111111.0839553467655123.665021360064
Winsorized Mean ( 23 / 24 )134.2326388888891.02178807022209131.370332851618
Winsorized Mean ( 24 / 24 )133.9026388888890.978989750135678136.77634405297
Trimmed Mean ( 1 / 24 )133.9561.7766098802682275.3997833107717
Trimmed Mean ( 2 / 24 )133.9786764705881.7174482355544678.0103141957782
Trimmed Mean ( 3 / 24 )134.1053030303031.6751312403053580.0565948527458
Trimmed Mean ( 4 / 24 )134.20751.6422328912330481.7225746216988
Trimmed Mean ( 5 / 24 )134.315645161291.6092501911557983.4647377390229
Trimmed Mean ( 6 / 24 )134.4133333333331.5758781188830585.2942443471469
Trimmed Mean ( 7 / 24 )134.4746551724141.5508247364902986.7117037846241
Trimmed Mean ( 8 / 24 )134.5403571428571.5213238844234588.4363668515236
Trimmed Mean ( 9 / 24 )134.6229629629631.4950273417548890.0471578031081
Trimmed Mean ( 10 / 24 )134.6967307692311.4687909866211891.7058533148329
Trimmed Mean ( 11 / 24 )134.73341.4509308654538192.8599723170542
Trimmed Mean ( 12 / 24 )134.7733333333331.4300527668850794.2436086655008
Trimmed Mean ( 13 / 24 )134.7943478260871.413169003714895.3844497521194
Trimmed Mean ( 14 / 24 )134.7977272727271.3988599202544796.362563056497
Trimmed Mean ( 15 / 24 )134.7969047619051.3808106864908997.6215683154001
Trimmed Mean ( 16 / 24 )134.8251.3629933592779998.9183102633898
Trimmed Mean ( 17 / 24 )134.8505263157891.34620783162982100.170659498043
Trimmed Mean ( 18 / 24 )134.8758333333331.33090936658493101.341110611777
Trimmed Mean ( 19 / 24 )134.9029411764711.30785475171693103.148259391475
Trimmed Mean ( 20 / 24 )134.943751.27620797851897105.738055451276
Trimmed Mean ( 21 / 24 )135.0406666666671.25000771798384108.031866302775
Trimmed Mean ( 22 / 24 )135.1589285714291.22066621796626110.725541988551
Trimmed Mean ( 23 / 24 )135.2988461538461.17675686357732114.976041645969
Trimmed Mean ( 24 / 24 )135.4379166666671.12863887806923120.001108679121
Median137.35
Midrange134.08
Midmean - Weighted Average at Xnp134.523243243243
Midmean - Weighted Average at X(n+1)p134.875833333333
Midmean - Empirical Distribution Function134.523243243243
Midmean - Empirical Distribution Function - Averaging134.875833333333
Midmean - Empirical Distribution Function - Interpolation134.875833333333
Midmean - Closest Observation134.523243243243
Midmean - True Basic - Statistics Graphics Toolkit134.875833333333
Midmean - MS Excel (old versions)134.850526315789
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')