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of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationFri, 06 May 2011 11:35:25 +0000
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2011/May/06/t1304681499tlfum57ade5gja1.htm/, Retrieved Mon, 13 May 2024 13:09:36 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=121150, Retrieved Mon, 13 May 2024 13:09:36 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsKDGP1W52
Estimated Impact168
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [] [2011-05-06 11:35:25] [e142b37b6acbb6a3ec873415888faca6] [Current]
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Dataseries X:
116
111
104
100
93
91
119
139
134
124
113
109
109
106
101
98
93
91
122
139
140
132
117
114
113
110
107
103
98
98
137
148
147
139
130
128
127
123
118
114
108
111
151
159
158
148
138
137
136
133
126
120
114
116
153
162
161
149
139
135
130
127
122
117
112
113
149
157
157
147
137
132
125
123
117
114
111
112
144
150
149
134
123
116
117
111
105
102
95
93
124
130
124
115
106
105
105
101
95
93
84
87
116
120
117
109
105
107
109
109
108
107
99
103
131
137
135
124
118
121
121
118
113
107
100
102
130
136
133
120
112
109
110




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Gwilym Jenkins' @ www.wessa.org

\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 & 'Gwilym Jenkins' @ www.wessa.org \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=121150&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]'Gwilym Jenkins' @ www.wessa.org[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=121150&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=121150&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'Gwilym Jenkins' @ www.wessa.org







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean120.3383458646621.5406649791700878.1080556069271
Geometric Mean119.060117496799
Harmonic Mean117.806473981964
Quadratic Mean121.633215437825
Winsorized Mean ( 1 / 44 )120.3533834586471.5352690989789278.392370131524
Winsorized Mean ( 2 / 44 )120.3834586466171.520001146875179.199584088543
Winsorized Mean ( 3 / 44 )120.3609022556391.515708675655879.4089947420552
Winsorized Mean ( 4 / 44 )120.3909774436091.5015308731899780.1788225558364
Winsorized Mean ( 5 / 44 )120.3909774436091.5015308731899780.1788225558364
Winsorized Mean ( 6 / 44 )120.2105263157891.4695997657041981.7981392765042
Winsorized Mean ( 7 / 44 )120.1052631578951.4522185147142282.7046769759232
Winsorized Mean ( 8 / 44 )120.1654135338351.4260530499725684.2643361242042
Winsorized Mean ( 9 / 44 )120.0977443609021.4154561590741384.8473784164815
Winsorized Mean ( 10 / 44 )120.3233082706771.3865360484807786.7797908337942
Winsorized Mean ( 11 / 44 )120.3233082706771.3865360484807786.7797908337942
Winsorized Mean ( 12 / 44 )120.2330827067671.3725529071882487.5981407179939
Winsorized Mean ( 13 / 44 )120.3308270676691.3607508768300488.4297259083808
Winsorized Mean ( 14 / 44 )120.3308270676691.3323242566546290.3164724853186
Winsorized Mean ( 15 / 44 )120.3308270676691.3323242566546290.3164724853186
Winsorized Mean ( 16 / 44 )120.090225563911.2652558958395694.9137846018286
Winsorized Mean ( 17 / 44 )119.5789473684211.19547689973821100.026146381086
Winsorized Mean ( 18 / 44 )119.5789473684211.16242975696839102.869826457542
Winsorized Mean ( 19 / 44 )119.5789473684211.16242975696839102.869826457542
Winsorized Mean ( 20 / 44 )119.7293233082711.14549489641231104.521917717192
Winsorized Mean ( 21 / 44 )119.7293233082711.14549489641231104.521917717192
Winsorized Mean ( 22 / 44 )119.7293233082711.1065438353093108.201157051138
Winsorized Mean ( 23 / 44 )119.7293233082711.06675821723926112.236607483677
Winsorized Mean ( 24 / 44 )119.7293233082711.06675821723926112.236607483677
Winsorized Mean ( 25 / 44 )119.7293233082711.06675821723926112.236607483677
Winsorized Mean ( 26 / 44 )119.7293233082711.06675821723926112.236607483677
Winsorized Mean ( 27 / 44 )119.7293233082711.02108818308844117.256594769446
Winsorized Mean ( 28 / 44 )119.7293233082711.02108818308844117.256594769446
Winsorized Mean ( 29 / 44 )119.7293233082710.973043358012367123.04623665778
Winsorized Mean ( 30 / 44 )119.7293233082710.973043358012367123.04623665778
Winsorized Mean ( 31 / 44 )119.4962406015040.94564175559925126.365232810368
Winsorized Mean ( 32 / 44 )119.4962406015040.94564175559925126.365232810368
Winsorized Mean ( 33 / 44 )119.4962406015040.892465108018556133.89457977445
Winsorized Mean ( 34 / 44 )119.4962406015040.892465108018556133.89457977445
Winsorized Mean ( 35 / 44 )119.4962406015040.837138094418279142.74376163056
Winsorized Mean ( 36 / 44 )119.4962406015040.837138094418279142.74376163056
Winsorized Mean ( 37 / 44 )119.2180451127820.80598823591871147.915366254559
Winsorized Mean ( 38 / 44 )118.9323308270680.774699280820048153.52064184334
Winsorized Mean ( 39 / 44 )118.9323308270680.774699280820048153.52064184334
Winsorized Mean ( 40 / 44 )118.9323308270680.774699280820048153.52064184334
Winsorized Mean ( 41 / 44 )119.2406015037590.745240107580854160.002930989356
Winsorized Mean ( 42 / 44 )118.6090225563910.677472904209662175.075669918873
Winsorized Mean ( 43 / 44 )118.6090225563910.612938139772862193.508960953783
Winsorized Mean ( 44 / 44 )118.6090225563910.612938139772862193.508960953783
Trimmed Mean ( 1 / 44 )120.2977099236641.5058193890605779.8885382919086
Trimmed Mean ( 2 / 44 )120.2403100775191.4734724382833381.6033655964446
Trimmed Mean ( 3 / 44 )120.1653543307091.4467062081101283.0613386858168
Trimmed Mean ( 4 / 44 )120.0961.4189693670111984.6360765722247
Trimmed Mean ( 5 / 44 )120.0162601626021.3928466617862286.1661685060793
Trimmed Mean ( 6 / 44 )119.9338842975211.3639764998616987.9295825915493
Trimmed Mean ( 7 / 44 )119.8823529411761.339482734739689.4989907910104
Trimmed Mean ( 8 / 44 )119.8461538461541.3159574797492691.0714485007445
Trimmed Mean ( 9 / 44 )119.81.2947231988763592.5294303090964
Trimmed Mean ( 10 / 44 )119.7610619469031.2729731129088694.0798047754816
Trimmed Mean ( 11 / 44 )119.6936936936941.253319444622695.5013458119102
Trimmed Mean ( 12 / 44 )119.6238532110091.2313707965257697.1468980330874
Trimmed Mean ( 13 / 44 )119.5607476635511.208925949780798.8983218411684
Trimmed Mean ( 14 / 44 )119.4857142857141.18538986691202100.798663478521
Trimmed Mean ( 15 / 44 )119.4077669902911.16286838337856102.683819335915
Trimmed Mean ( 16 / 44 )119.3267326732671.13748975936124104.903566551909
Trimmed Mean ( 17 / 44 )119.2626262626261.11783445879052106.690776371008
Trimmed Mean ( 18 / 44 )119.2371134020621.10448293751048107.957406450138
Trimmed Mean ( 19 / 44 )119.2105263157891.09318306480595109.049005746307
Trimmed Mean ( 20 / 44 )119.1827956989251.08022583441294110.331369517464
Trimmed Mean ( 21 / 44 )119.1428571428571.06728135088487111.632098737674
Trimmed Mean ( 22 / 44 )119.1011235955061.05238735162007113.172325201513
Trimmed Mean ( 23 / 44 )119.0574712643681.03975460291328114.505356293477
Trimmed Mean ( 24 / 44 )119.0117647058821.0296030234491115.589952627762
Trimmed Mean ( 25 / 44 )118.9638554216871.0176875054225116.896252324821
Trimmed Mean ( 26 / 44 )118.9135802469141.00372724070014118.472006562228
Trimmed Mean ( 27 / 44 )118.8607594936710.987381302315383120.379795743494
Trimmed Mean ( 28 / 44 )118.8051948051950.973686429767291122.015867915083
Trimmed Mean ( 29 / 44 )118.7466666666670.957491718183708124.018479127862
Trimmed Mean ( 30 / 44 )118.6849315068490.944195741516884125.699498830802
Trimmed Mean ( 31 / 44 )118.6197183098590.928287013563447127.783451213553
Trimmed Mean ( 32 / 44 )118.5652173913040.912982582307338129.865804330746
Trimmed Mean ( 33 / 44 )118.5074626865670.894572087372654132.47391055384
Trimmed Mean ( 34 / 44 )118.4461538461540.879529695466333134.669874657675
Trimmed Mean ( 35 / 44 )118.3809523809520.8611869098614137.462554325175
Trimmed Mean ( 36 / 44 )118.3114754098360.846574900454819139.75311026381
Trimmed Mean ( 37 / 44 )118.2372881355930.828460361780105142.719306306385
Trimmed Mean ( 38 / 44 )118.1754385964910.811154537431032145.687946184409
Trimmed Mean ( 39 / 44 )118.1272727272730.79478711778416148.627563386542
Trimmed Mean ( 40 / 44 )118.0754716981130.774151090196653152.522515557162
Trimmed Mean ( 41 / 44 )118.0196078431370.748064271160577157.766668444193
Trimmed Mean ( 42 / 44 )117.9387755102040.719864029149739163.834794814663
Trimmed Mean ( 43 / 44 )117.8936170212770.698375306670328168.811262218538
Trimmed Mean ( 44 / 44 )117.8444444444440.68309719168537172.514901069485
Median117
Midrange123
Midmean - Weighted Average at Xnp118.507462686567
Midmean - Weighted Average at X(n+1)p118.507462686567
Midmean - Empirical Distribution Function118.507462686567
Midmean - Empirical Distribution Function - Averaging118.507462686567
Midmean - Empirical Distribution Function - Interpolation118.507462686567
Midmean - Closest Observation117.859154929577
Midmean - True Basic - Statistics Graphics Toolkit118.507462686567
Midmean - MS Excel (old versions)118.507462686567
Number of observations133

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 120.338345864662 & 1.54066497917008 & 78.1080556069271 \tabularnewline
Geometric Mean & 119.060117496799 &  &  \tabularnewline
Harmonic Mean & 117.806473981964 &  &  \tabularnewline
Quadratic Mean & 121.633215437825 &  &  \tabularnewline
Winsorized Mean ( 1 / 44 ) & 120.353383458647 & 1.53526909897892 & 78.392370131524 \tabularnewline
Winsorized Mean ( 2 / 44 ) & 120.383458646617 & 1.5200011468751 & 79.199584088543 \tabularnewline
Winsorized Mean ( 3 / 44 ) & 120.360902255639 & 1.5157086756558 & 79.4089947420552 \tabularnewline
Winsorized Mean ( 4 / 44 ) & 120.390977443609 & 1.50153087318997 & 80.1788225558364 \tabularnewline
Winsorized Mean ( 5 / 44 ) & 120.390977443609 & 1.50153087318997 & 80.1788225558364 \tabularnewline
Winsorized Mean ( 6 / 44 ) & 120.210526315789 & 1.46959976570419 & 81.7981392765042 \tabularnewline
Winsorized Mean ( 7 / 44 ) & 120.105263157895 & 1.45221851471422 & 82.7046769759232 \tabularnewline
Winsorized Mean ( 8 / 44 ) & 120.165413533835 & 1.42605304997256 & 84.2643361242042 \tabularnewline
Winsorized Mean ( 9 / 44 ) & 120.097744360902 & 1.41545615907413 & 84.8473784164815 \tabularnewline
Winsorized Mean ( 10 / 44 ) & 120.323308270677 & 1.38653604848077 & 86.7797908337942 \tabularnewline
Winsorized Mean ( 11 / 44 ) & 120.323308270677 & 1.38653604848077 & 86.7797908337942 \tabularnewline
Winsorized Mean ( 12 / 44 ) & 120.233082706767 & 1.37255290718824 & 87.5981407179939 \tabularnewline
Winsorized Mean ( 13 / 44 ) & 120.330827067669 & 1.36075087683004 & 88.4297259083808 \tabularnewline
Winsorized Mean ( 14 / 44 ) & 120.330827067669 & 1.33232425665462 & 90.3164724853186 \tabularnewline
Winsorized Mean ( 15 / 44 ) & 120.330827067669 & 1.33232425665462 & 90.3164724853186 \tabularnewline
Winsorized Mean ( 16 / 44 ) & 120.09022556391 & 1.26525589583956 & 94.9137846018286 \tabularnewline
Winsorized Mean ( 17 / 44 ) & 119.578947368421 & 1.19547689973821 & 100.026146381086 \tabularnewline
Winsorized Mean ( 18 / 44 ) & 119.578947368421 & 1.16242975696839 & 102.869826457542 \tabularnewline
Winsorized Mean ( 19 / 44 ) & 119.578947368421 & 1.16242975696839 & 102.869826457542 \tabularnewline
Winsorized Mean ( 20 / 44 ) & 119.729323308271 & 1.14549489641231 & 104.521917717192 \tabularnewline
Winsorized Mean ( 21 / 44 ) & 119.729323308271 & 1.14549489641231 & 104.521917717192 \tabularnewline
Winsorized Mean ( 22 / 44 ) & 119.729323308271 & 1.1065438353093 & 108.201157051138 \tabularnewline
Winsorized Mean ( 23 / 44 ) & 119.729323308271 & 1.06675821723926 & 112.236607483677 \tabularnewline
Winsorized Mean ( 24 / 44 ) & 119.729323308271 & 1.06675821723926 & 112.236607483677 \tabularnewline
Winsorized Mean ( 25 / 44 ) & 119.729323308271 & 1.06675821723926 & 112.236607483677 \tabularnewline
Winsorized Mean ( 26 / 44 ) & 119.729323308271 & 1.06675821723926 & 112.236607483677 \tabularnewline
Winsorized Mean ( 27 / 44 ) & 119.729323308271 & 1.02108818308844 & 117.256594769446 \tabularnewline
Winsorized Mean ( 28 / 44 ) & 119.729323308271 & 1.02108818308844 & 117.256594769446 \tabularnewline
Winsorized Mean ( 29 / 44 ) & 119.729323308271 & 0.973043358012367 & 123.04623665778 \tabularnewline
Winsorized Mean ( 30 / 44 ) & 119.729323308271 & 0.973043358012367 & 123.04623665778 \tabularnewline
Winsorized Mean ( 31 / 44 ) & 119.496240601504 & 0.94564175559925 & 126.365232810368 \tabularnewline
Winsorized Mean ( 32 / 44 ) & 119.496240601504 & 0.94564175559925 & 126.365232810368 \tabularnewline
Winsorized Mean ( 33 / 44 ) & 119.496240601504 & 0.892465108018556 & 133.89457977445 \tabularnewline
Winsorized Mean ( 34 / 44 ) & 119.496240601504 & 0.892465108018556 & 133.89457977445 \tabularnewline
Winsorized Mean ( 35 / 44 ) & 119.496240601504 & 0.837138094418279 & 142.74376163056 \tabularnewline
Winsorized Mean ( 36 / 44 ) & 119.496240601504 & 0.837138094418279 & 142.74376163056 \tabularnewline
Winsorized Mean ( 37 / 44 ) & 119.218045112782 & 0.80598823591871 & 147.915366254559 \tabularnewline
Winsorized Mean ( 38 / 44 ) & 118.932330827068 & 0.774699280820048 & 153.52064184334 \tabularnewline
Winsorized Mean ( 39 / 44 ) & 118.932330827068 & 0.774699280820048 & 153.52064184334 \tabularnewline
Winsorized Mean ( 40 / 44 ) & 118.932330827068 & 0.774699280820048 & 153.52064184334 \tabularnewline
Winsorized Mean ( 41 / 44 ) & 119.240601503759 & 0.745240107580854 & 160.002930989356 \tabularnewline
Winsorized Mean ( 42 / 44 ) & 118.609022556391 & 0.677472904209662 & 175.075669918873 \tabularnewline
Winsorized Mean ( 43 / 44 ) & 118.609022556391 & 0.612938139772862 & 193.508960953783 \tabularnewline
Winsorized Mean ( 44 / 44 ) & 118.609022556391 & 0.612938139772862 & 193.508960953783 \tabularnewline
Trimmed Mean ( 1 / 44 ) & 120.297709923664 & 1.50581938906057 & 79.8885382919086 \tabularnewline
Trimmed Mean ( 2 / 44 ) & 120.240310077519 & 1.47347243828333 & 81.6033655964446 \tabularnewline
Trimmed Mean ( 3 / 44 ) & 120.165354330709 & 1.44670620811012 & 83.0613386858168 \tabularnewline
Trimmed Mean ( 4 / 44 ) & 120.096 & 1.41896936701119 & 84.6360765722247 \tabularnewline
Trimmed Mean ( 5 / 44 ) & 120.016260162602 & 1.39284666178622 & 86.1661685060793 \tabularnewline
Trimmed Mean ( 6 / 44 ) & 119.933884297521 & 1.36397649986169 & 87.9295825915493 \tabularnewline
Trimmed Mean ( 7 / 44 ) & 119.882352941176 & 1.3394827347396 & 89.4989907910104 \tabularnewline
Trimmed Mean ( 8 / 44 ) & 119.846153846154 & 1.31595747974926 & 91.0714485007445 \tabularnewline
Trimmed Mean ( 9 / 44 ) & 119.8 & 1.29472319887635 & 92.5294303090964 \tabularnewline
Trimmed Mean ( 10 / 44 ) & 119.761061946903 & 1.27297311290886 & 94.0798047754816 \tabularnewline
Trimmed Mean ( 11 / 44 ) & 119.693693693694 & 1.2533194446226 & 95.5013458119102 \tabularnewline
Trimmed Mean ( 12 / 44 ) & 119.623853211009 & 1.23137079652576 & 97.1468980330874 \tabularnewline
Trimmed Mean ( 13 / 44 ) & 119.560747663551 & 1.2089259497807 & 98.8983218411684 \tabularnewline
Trimmed Mean ( 14 / 44 ) & 119.485714285714 & 1.18538986691202 & 100.798663478521 \tabularnewline
Trimmed Mean ( 15 / 44 ) & 119.407766990291 & 1.16286838337856 & 102.683819335915 \tabularnewline
Trimmed Mean ( 16 / 44 ) & 119.326732673267 & 1.13748975936124 & 104.903566551909 \tabularnewline
Trimmed Mean ( 17 / 44 ) & 119.262626262626 & 1.11783445879052 & 106.690776371008 \tabularnewline
Trimmed Mean ( 18 / 44 ) & 119.237113402062 & 1.10448293751048 & 107.957406450138 \tabularnewline
Trimmed Mean ( 19 / 44 ) & 119.210526315789 & 1.09318306480595 & 109.049005746307 \tabularnewline
Trimmed Mean ( 20 / 44 ) & 119.182795698925 & 1.08022583441294 & 110.331369517464 \tabularnewline
Trimmed Mean ( 21 / 44 ) & 119.142857142857 & 1.06728135088487 & 111.632098737674 \tabularnewline
Trimmed Mean ( 22 / 44 ) & 119.101123595506 & 1.05238735162007 & 113.172325201513 \tabularnewline
Trimmed Mean ( 23 / 44 ) & 119.057471264368 & 1.03975460291328 & 114.505356293477 \tabularnewline
Trimmed Mean ( 24 / 44 ) & 119.011764705882 & 1.0296030234491 & 115.589952627762 \tabularnewline
Trimmed Mean ( 25 / 44 ) & 118.963855421687 & 1.0176875054225 & 116.896252324821 \tabularnewline
Trimmed Mean ( 26 / 44 ) & 118.913580246914 & 1.00372724070014 & 118.472006562228 \tabularnewline
Trimmed Mean ( 27 / 44 ) & 118.860759493671 & 0.987381302315383 & 120.379795743494 \tabularnewline
Trimmed Mean ( 28 / 44 ) & 118.805194805195 & 0.973686429767291 & 122.015867915083 \tabularnewline
Trimmed Mean ( 29 / 44 ) & 118.746666666667 & 0.957491718183708 & 124.018479127862 \tabularnewline
Trimmed Mean ( 30 / 44 ) & 118.684931506849 & 0.944195741516884 & 125.699498830802 \tabularnewline
Trimmed Mean ( 31 / 44 ) & 118.619718309859 & 0.928287013563447 & 127.783451213553 \tabularnewline
Trimmed Mean ( 32 / 44 ) & 118.565217391304 & 0.912982582307338 & 129.865804330746 \tabularnewline
Trimmed Mean ( 33 / 44 ) & 118.507462686567 & 0.894572087372654 & 132.47391055384 \tabularnewline
Trimmed Mean ( 34 / 44 ) & 118.446153846154 & 0.879529695466333 & 134.669874657675 \tabularnewline
Trimmed Mean ( 35 / 44 ) & 118.380952380952 & 0.8611869098614 & 137.462554325175 \tabularnewline
Trimmed Mean ( 36 / 44 ) & 118.311475409836 & 0.846574900454819 & 139.75311026381 \tabularnewline
Trimmed Mean ( 37 / 44 ) & 118.237288135593 & 0.828460361780105 & 142.719306306385 \tabularnewline
Trimmed Mean ( 38 / 44 ) & 118.175438596491 & 0.811154537431032 & 145.687946184409 \tabularnewline
Trimmed Mean ( 39 / 44 ) & 118.127272727273 & 0.79478711778416 & 148.627563386542 \tabularnewline
Trimmed Mean ( 40 / 44 ) & 118.075471698113 & 0.774151090196653 & 152.522515557162 \tabularnewline
Trimmed Mean ( 41 / 44 ) & 118.019607843137 & 0.748064271160577 & 157.766668444193 \tabularnewline
Trimmed Mean ( 42 / 44 ) & 117.938775510204 & 0.719864029149739 & 163.834794814663 \tabularnewline
Trimmed Mean ( 43 / 44 ) & 117.893617021277 & 0.698375306670328 & 168.811262218538 \tabularnewline
Trimmed Mean ( 44 / 44 ) & 117.844444444444 & 0.68309719168537 & 172.514901069485 \tabularnewline
Median & 117 &  &  \tabularnewline
Midrange & 123 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 118.507462686567 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 118.507462686567 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 118.507462686567 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 118.507462686567 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 118.507462686567 &  &  \tabularnewline
Midmean - Closest Observation & 117.859154929577 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 118.507462686567 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 118.507462686567 &  &  \tabularnewline
Number of observations & 133 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=121150&T=1

[TABLE]
[ROW][C]Central Tendency - Ungrouped Data[/C][/ROW]
[ROW][C]Measure[/C][C]Value[/C][C]S.E.[/C][C]Value/S.E.[/C][/ROW]
[ROW][C]Arithmetic Mean[/C][C]120.338345864662[/C][C]1.54066497917008[/C][C]78.1080556069271[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]119.060117496799[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]117.806473981964[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]121.633215437825[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 44 )[/C][C]120.353383458647[/C][C]1.53526909897892[/C][C]78.392370131524[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 44 )[/C][C]120.383458646617[/C][C]1.5200011468751[/C][C]79.199584088543[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 44 )[/C][C]120.360902255639[/C][C]1.5157086756558[/C][C]79.4089947420552[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 44 )[/C][C]120.390977443609[/C][C]1.50153087318997[/C][C]80.1788225558364[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 44 )[/C][C]120.390977443609[/C][C]1.50153087318997[/C][C]80.1788225558364[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 44 )[/C][C]120.210526315789[/C][C]1.46959976570419[/C][C]81.7981392765042[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 44 )[/C][C]120.105263157895[/C][C]1.45221851471422[/C][C]82.7046769759232[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 44 )[/C][C]120.165413533835[/C][C]1.42605304997256[/C][C]84.2643361242042[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 44 )[/C][C]120.097744360902[/C][C]1.41545615907413[/C][C]84.8473784164815[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 44 )[/C][C]120.323308270677[/C][C]1.38653604848077[/C][C]86.7797908337942[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 44 )[/C][C]120.323308270677[/C][C]1.38653604848077[/C][C]86.7797908337942[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 44 )[/C][C]120.233082706767[/C][C]1.37255290718824[/C][C]87.5981407179939[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 44 )[/C][C]120.330827067669[/C][C]1.36075087683004[/C][C]88.4297259083808[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 44 )[/C][C]120.330827067669[/C][C]1.33232425665462[/C][C]90.3164724853186[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 44 )[/C][C]120.330827067669[/C][C]1.33232425665462[/C][C]90.3164724853186[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 44 )[/C][C]120.09022556391[/C][C]1.26525589583956[/C][C]94.9137846018286[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 44 )[/C][C]119.578947368421[/C][C]1.19547689973821[/C][C]100.026146381086[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 44 )[/C][C]119.578947368421[/C][C]1.16242975696839[/C][C]102.869826457542[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 44 )[/C][C]119.578947368421[/C][C]1.16242975696839[/C][C]102.869826457542[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 44 )[/C][C]119.729323308271[/C][C]1.14549489641231[/C][C]104.521917717192[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 44 )[/C][C]119.729323308271[/C][C]1.14549489641231[/C][C]104.521917717192[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 44 )[/C][C]119.729323308271[/C][C]1.1065438353093[/C][C]108.201157051138[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 44 )[/C][C]119.729323308271[/C][C]1.06675821723926[/C][C]112.236607483677[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 44 )[/C][C]119.729323308271[/C][C]1.06675821723926[/C][C]112.236607483677[/C][/ROW]
[ROW][C]Winsorized Mean ( 25 / 44 )[/C][C]119.729323308271[/C][C]1.06675821723926[/C][C]112.236607483677[/C][/ROW]
[ROW][C]Winsorized Mean ( 26 / 44 )[/C][C]119.729323308271[/C][C]1.06675821723926[/C][C]112.236607483677[/C][/ROW]
[ROW][C]Winsorized Mean ( 27 / 44 )[/C][C]119.729323308271[/C][C]1.02108818308844[/C][C]117.256594769446[/C][/ROW]
[ROW][C]Winsorized Mean ( 28 / 44 )[/C][C]119.729323308271[/C][C]1.02108818308844[/C][C]117.256594769446[/C][/ROW]
[ROW][C]Winsorized Mean ( 29 / 44 )[/C][C]119.729323308271[/C][C]0.973043358012367[/C][C]123.04623665778[/C][/ROW]
[ROW][C]Winsorized Mean ( 30 / 44 )[/C][C]119.729323308271[/C][C]0.973043358012367[/C][C]123.04623665778[/C][/ROW]
[ROW][C]Winsorized Mean ( 31 / 44 )[/C][C]119.496240601504[/C][C]0.94564175559925[/C][C]126.365232810368[/C][/ROW]
[ROW][C]Winsorized Mean ( 32 / 44 )[/C][C]119.496240601504[/C][C]0.94564175559925[/C][C]126.365232810368[/C][/ROW]
[ROW][C]Winsorized Mean ( 33 / 44 )[/C][C]119.496240601504[/C][C]0.892465108018556[/C][C]133.89457977445[/C][/ROW]
[ROW][C]Winsorized Mean ( 34 / 44 )[/C][C]119.496240601504[/C][C]0.892465108018556[/C][C]133.89457977445[/C][/ROW]
[ROW][C]Winsorized Mean ( 35 / 44 )[/C][C]119.496240601504[/C][C]0.837138094418279[/C][C]142.74376163056[/C][/ROW]
[ROW][C]Winsorized Mean ( 36 / 44 )[/C][C]119.496240601504[/C][C]0.837138094418279[/C][C]142.74376163056[/C][/ROW]
[ROW][C]Winsorized Mean ( 37 / 44 )[/C][C]119.218045112782[/C][C]0.80598823591871[/C][C]147.915366254559[/C][/ROW]
[ROW][C]Winsorized Mean ( 38 / 44 )[/C][C]118.932330827068[/C][C]0.774699280820048[/C][C]153.52064184334[/C][/ROW]
[ROW][C]Winsorized Mean ( 39 / 44 )[/C][C]118.932330827068[/C][C]0.774699280820048[/C][C]153.52064184334[/C][/ROW]
[ROW][C]Winsorized Mean ( 40 / 44 )[/C][C]118.932330827068[/C][C]0.774699280820048[/C][C]153.52064184334[/C][/ROW]
[ROW][C]Winsorized Mean ( 41 / 44 )[/C][C]119.240601503759[/C][C]0.745240107580854[/C][C]160.002930989356[/C][/ROW]
[ROW][C]Winsorized Mean ( 42 / 44 )[/C][C]118.609022556391[/C][C]0.677472904209662[/C][C]175.075669918873[/C][/ROW]
[ROW][C]Winsorized Mean ( 43 / 44 )[/C][C]118.609022556391[/C][C]0.612938139772862[/C][C]193.508960953783[/C][/ROW]
[ROW][C]Winsorized Mean ( 44 / 44 )[/C][C]118.609022556391[/C][C]0.612938139772862[/C][C]193.508960953783[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 44 )[/C][C]120.297709923664[/C][C]1.50581938906057[/C][C]79.8885382919086[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 44 )[/C][C]120.240310077519[/C][C]1.47347243828333[/C][C]81.6033655964446[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 44 )[/C][C]120.165354330709[/C][C]1.44670620811012[/C][C]83.0613386858168[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 44 )[/C][C]120.096[/C][C]1.41896936701119[/C][C]84.6360765722247[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 44 )[/C][C]120.016260162602[/C][C]1.39284666178622[/C][C]86.1661685060793[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 44 )[/C][C]119.933884297521[/C][C]1.36397649986169[/C][C]87.9295825915493[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 44 )[/C][C]119.882352941176[/C][C]1.3394827347396[/C][C]89.4989907910104[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 44 )[/C][C]119.846153846154[/C][C]1.31595747974926[/C][C]91.0714485007445[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 44 )[/C][C]119.8[/C][C]1.29472319887635[/C][C]92.5294303090964[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 44 )[/C][C]119.761061946903[/C][C]1.27297311290886[/C][C]94.0798047754816[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 44 )[/C][C]119.693693693694[/C][C]1.2533194446226[/C][C]95.5013458119102[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 44 )[/C][C]119.623853211009[/C][C]1.23137079652576[/C][C]97.1468980330874[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 44 )[/C][C]119.560747663551[/C][C]1.2089259497807[/C][C]98.8983218411684[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 44 )[/C][C]119.485714285714[/C][C]1.18538986691202[/C][C]100.798663478521[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 44 )[/C][C]119.407766990291[/C][C]1.16286838337856[/C][C]102.683819335915[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 44 )[/C][C]119.326732673267[/C][C]1.13748975936124[/C][C]104.903566551909[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 44 )[/C][C]119.262626262626[/C][C]1.11783445879052[/C][C]106.690776371008[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 44 )[/C][C]119.237113402062[/C][C]1.10448293751048[/C][C]107.957406450138[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 44 )[/C][C]119.210526315789[/C][C]1.09318306480595[/C][C]109.049005746307[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 44 )[/C][C]119.182795698925[/C][C]1.08022583441294[/C][C]110.331369517464[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 44 )[/C][C]119.142857142857[/C][C]1.06728135088487[/C][C]111.632098737674[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 44 )[/C][C]119.101123595506[/C][C]1.05238735162007[/C][C]113.172325201513[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 44 )[/C][C]119.057471264368[/C][C]1.03975460291328[/C][C]114.505356293477[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 44 )[/C][C]119.011764705882[/C][C]1.0296030234491[/C][C]115.589952627762[/C][/ROW]
[ROW][C]Trimmed Mean ( 25 / 44 )[/C][C]118.963855421687[/C][C]1.0176875054225[/C][C]116.896252324821[/C][/ROW]
[ROW][C]Trimmed Mean ( 26 / 44 )[/C][C]118.913580246914[/C][C]1.00372724070014[/C][C]118.472006562228[/C][/ROW]
[ROW][C]Trimmed Mean ( 27 / 44 )[/C][C]118.860759493671[/C][C]0.987381302315383[/C][C]120.379795743494[/C][/ROW]
[ROW][C]Trimmed Mean ( 28 / 44 )[/C][C]118.805194805195[/C][C]0.973686429767291[/C][C]122.015867915083[/C][/ROW]
[ROW][C]Trimmed Mean ( 29 / 44 )[/C][C]118.746666666667[/C][C]0.957491718183708[/C][C]124.018479127862[/C][/ROW]
[ROW][C]Trimmed Mean ( 30 / 44 )[/C][C]118.684931506849[/C][C]0.944195741516884[/C][C]125.699498830802[/C][/ROW]
[ROW][C]Trimmed Mean ( 31 / 44 )[/C][C]118.619718309859[/C][C]0.928287013563447[/C][C]127.783451213553[/C][/ROW]
[ROW][C]Trimmed Mean ( 32 / 44 )[/C][C]118.565217391304[/C][C]0.912982582307338[/C][C]129.865804330746[/C][/ROW]
[ROW][C]Trimmed Mean ( 33 / 44 )[/C][C]118.507462686567[/C][C]0.894572087372654[/C][C]132.47391055384[/C][/ROW]
[ROW][C]Trimmed Mean ( 34 / 44 )[/C][C]118.446153846154[/C][C]0.879529695466333[/C][C]134.669874657675[/C][/ROW]
[ROW][C]Trimmed Mean ( 35 / 44 )[/C][C]118.380952380952[/C][C]0.8611869098614[/C][C]137.462554325175[/C][/ROW]
[ROW][C]Trimmed Mean ( 36 / 44 )[/C][C]118.311475409836[/C][C]0.846574900454819[/C][C]139.75311026381[/C][/ROW]
[ROW][C]Trimmed Mean ( 37 / 44 )[/C][C]118.237288135593[/C][C]0.828460361780105[/C][C]142.719306306385[/C][/ROW]
[ROW][C]Trimmed Mean ( 38 / 44 )[/C][C]118.175438596491[/C][C]0.811154537431032[/C][C]145.687946184409[/C][/ROW]
[ROW][C]Trimmed Mean ( 39 / 44 )[/C][C]118.127272727273[/C][C]0.79478711778416[/C][C]148.627563386542[/C][/ROW]
[ROW][C]Trimmed Mean ( 40 / 44 )[/C][C]118.075471698113[/C][C]0.774151090196653[/C][C]152.522515557162[/C][/ROW]
[ROW][C]Trimmed Mean ( 41 / 44 )[/C][C]118.019607843137[/C][C]0.748064271160577[/C][C]157.766668444193[/C][/ROW]
[ROW][C]Trimmed Mean ( 42 / 44 )[/C][C]117.938775510204[/C][C]0.719864029149739[/C][C]163.834794814663[/C][/ROW]
[ROW][C]Trimmed Mean ( 43 / 44 )[/C][C]117.893617021277[/C][C]0.698375306670328[/C][C]168.811262218538[/C][/ROW]
[ROW][C]Trimmed Mean ( 44 / 44 )[/C][C]117.844444444444[/C][C]0.68309719168537[/C][C]172.514901069485[/C][/ROW]
[ROW][C]Median[/C][C]117[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]123[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]118.507462686567[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]118.507462686567[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]118.507462686567[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]118.507462686567[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]118.507462686567[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]117.859154929577[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]118.507462686567[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]118.507462686567[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]133[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=121150&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=121150&T=1

As an alternative you can also use a QR Code:  

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

Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean120.3383458646621.5406649791700878.1080556069271
Geometric Mean119.060117496799
Harmonic Mean117.806473981964
Quadratic Mean121.633215437825
Winsorized Mean ( 1 / 44 )120.3533834586471.5352690989789278.392370131524
Winsorized Mean ( 2 / 44 )120.3834586466171.520001146875179.199584088543
Winsorized Mean ( 3 / 44 )120.3609022556391.515708675655879.4089947420552
Winsorized Mean ( 4 / 44 )120.3909774436091.5015308731899780.1788225558364
Winsorized Mean ( 5 / 44 )120.3909774436091.5015308731899780.1788225558364
Winsorized Mean ( 6 / 44 )120.2105263157891.4695997657041981.7981392765042
Winsorized Mean ( 7 / 44 )120.1052631578951.4522185147142282.7046769759232
Winsorized Mean ( 8 / 44 )120.1654135338351.4260530499725684.2643361242042
Winsorized Mean ( 9 / 44 )120.0977443609021.4154561590741384.8473784164815
Winsorized Mean ( 10 / 44 )120.3233082706771.3865360484807786.7797908337942
Winsorized Mean ( 11 / 44 )120.3233082706771.3865360484807786.7797908337942
Winsorized Mean ( 12 / 44 )120.2330827067671.3725529071882487.5981407179939
Winsorized Mean ( 13 / 44 )120.3308270676691.3607508768300488.4297259083808
Winsorized Mean ( 14 / 44 )120.3308270676691.3323242566546290.3164724853186
Winsorized Mean ( 15 / 44 )120.3308270676691.3323242566546290.3164724853186
Winsorized Mean ( 16 / 44 )120.090225563911.2652558958395694.9137846018286
Winsorized Mean ( 17 / 44 )119.5789473684211.19547689973821100.026146381086
Winsorized Mean ( 18 / 44 )119.5789473684211.16242975696839102.869826457542
Winsorized Mean ( 19 / 44 )119.5789473684211.16242975696839102.869826457542
Winsorized Mean ( 20 / 44 )119.7293233082711.14549489641231104.521917717192
Winsorized Mean ( 21 / 44 )119.7293233082711.14549489641231104.521917717192
Winsorized Mean ( 22 / 44 )119.7293233082711.1065438353093108.201157051138
Winsorized Mean ( 23 / 44 )119.7293233082711.06675821723926112.236607483677
Winsorized Mean ( 24 / 44 )119.7293233082711.06675821723926112.236607483677
Winsorized Mean ( 25 / 44 )119.7293233082711.06675821723926112.236607483677
Winsorized Mean ( 26 / 44 )119.7293233082711.06675821723926112.236607483677
Winsorized Mean ( 27 / 44 )119.7293233082711.02108818308844117.256594769446
Winsorized Mean ( 28 / 44 )119.7293233082711.02108818308844117.256594769446
Winsorized Mean ( 29 / 44 )119.7293233082710.973043358012367123.04623665778
Winsorized Mean ( 30 / 44 )119.7293233082710.973043358012367123.04623665778
Winsorized Mean ( 31 / 44 )119.4962406015040.94564175559925126.365232810368
Winsorized Mean ( 32 / 44 )119.4962406015040.94564175559925126.365232810368
Winsorized Mean ( 33 / 44 )119.4962406015040.892465108018556133.89457977445
Winsorized Mean ( 34 / 44 )119.4962406015040.892465108018556133.89457977445
Winsorized Mean ( 35 / 44 )119.4962406015040.837138094418279142.74376163056
Winsorized Mean ( 36 / 44 )119.4962406015040.837138094418279142.74376163056
Winsorized Mean ( 37 / 44 )119.2180451127820.80598823591871147.915366254559
Winsorized Mean ( 38 / 44 )118.9323308270680.774699280820048153.52064184334
Winsorized Mean ( 39 / 44 )118.9323308270680.774699280820048153.52064184334
Winsorized Mean ( 40 / 44 )118.9323308270680.774699280820048153.52064184334
Winsorized Mean ( 41 / 44 )119.2406015037590.745240107580854160.002930989356
Winsorized Mean ( 42 / 44 )118.6090225563910.677472904209662175.075669918873
Winsorized Mean ( 43 / 44 )118.6090225563910.612938139772862193.508960953783
Winsorized Mean ( 44 / 44 )118.6090225563910.612938139772862193.508960953783
Trimmed Mean ( 1 / 44 )120.2977099236641.5058193890605779.8885382919086
Trimmed Mean ( 2 / 44 )120.2403100775191.4734724382833381.6033655964446
Trimmed Mean ( 3 / 44 )120.1653543307091.4467062081101283.0613386858168
Trimmed Mean ( 4 / 44 )120.0961.4189693670111984.6360765722247
Trimmed Mean ( 5 / 44 )120.0162601626021.3928466617862286.1661685060793
Trimmed Mean ( 6 / 44 )119.9338842975211.3639764998616987.9295825915493
Trimmed Mean ( 7 / 44 )119.8823529411761.339482734739689.4989907910104
Trimmed Mean ( 8 / 44 )119.8461538461541.3159574797492691.0714485007445
Trimmed Mean ( 9 / 44 )119.81.2947231988763592.5294303090964
Trimmed Mean ( 10 / 44 )119.7610619469031.2729731129088694.0798047754816
Trimmed Mean ( 11 / 44 )119.6936936936941.253319444622695.5013458119102
Trimmed Mean ( 12 / 44 )119.6238532110091.2313707965257697.1468980330874
Trimmed Mean ( 13 / 44 )119.5607476635511.208925949780798.8983218411684
Trimmed Mean ( 14 / 44 )119.4857142857141.18538986691202100.798663478521
Trimmed Mean ( 15 / 44 )119.4077669902911.16286838337856102.683819335915
Trimmed Mean ( 16 / 44 )119.3267326732671.13748975936124104.903566551909
Trimmed Mean ( 17 / 44 )119.2626262626261.11783445879052106.690776371008
Trimmed Mean ( 18 / 44 )119.2371134020621.10448293751048107.957406450138
Trimmed Mean ( 19 / 44 )119.2105263157891.09318306480595109.049005746307
Trimmed Mean ( 20 / 44 )119.1827956989251.08022583441294110.331369517464
Trimmed Mean ( 21 / 44 )119.1428571428571.06728135088487111.632098737674
Trimmed Mean ( 22 / 44 )119.1011235955061.05238735162007113.172325201513
Trimmed Mean ( 23 / 44 )119.0574712643681.03975460291328114.505356293477
Trimmed Mean ( 24 / 44 )119.0117647058821.0296030234491115.589952627762
Trimmed Mean ( 25 / 44 )118.9638554216871.0176875054225116.896252324821
Trimmed Mean ( 26 / 44 )118.9135802469141.00372724070014118.472006562228
Trimmed Mean ( 27 / 44 )118.8607594936710.987381302315383120.379795743494
Trimmed Mean ( 28 / 44 )118.8051948051950.973686429767291122.015867915083
Trimmed Mean ( 29 / 44 )118.7466666666670.957491718183708124.018479127862
Trimmed Mean ( 30 / 44 )118.6849315068490.944195741516884125.699498830802
Trimmed Mean ( 31 / 44 )118.6197183098590.928287013563447127.783451213553
Trimmed Mean ( 32 / 44 )118.5652173913040.912982582307338129.865804330746
Trimmed Mean ( 33 / 44 )118.5074626865670.894572087372654132.47391055384
Trimmed Mean ( 34 / 44 )118.4461538461540.879529695466333134.669874657675
Trimmed Mean ( 35 / 44 )118.3809523809520.8611869098614137.462554325175
Trimmed Mean ( 36 / 44 )118.3114754098360.846574900454819139.75311026381
Trimmed Mean ( 37 / 44 )118.2372881355930.828460361780105142.719306306385
Trimmed Mean ( 38 / 44 )118.1754385964910.811154537431032145.687946184409
Trimmed Mean ( 39 / 44 )118.1272727272730.79478711778416148.627563386542
Trimmed Mean ( 40 / 44 )118.0754716981130.774151090196653152.522515557162
Trimmed Mean ( 41 / 44 )118.0196078431370.748064271160577157.766668444193
Trimmed Mean ( 42 / 44 )117.9387755102040.719864029149739163.834794814663
Trimmed Mean ( 43 / 44 )117.8936170212770.698375306670328168.811262218538
Trimmed Mean ( 44 / 44 )117.8444444444440.68309719168537172.514901069485
Median117
Midrange123
Midmean - Weighted Average at Xnp118.507462686567
Midmean - Weighted Average at X(n+1)p118.507462686567
Midmean - Empirical Distribution Function118.507462686567
Midmean - Empirical Distribution Function - Averaging118.507462686567
Midmean - Empirical Distribution Function - Interpolation118.507462686567
Midmean - Closest Observation117.859154929577
Midmean - True Basic - Statistics Graphics Toolkit118.507462686567
Midmean - MS Excel (old versions)118.507462686567
Number of observations133



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')