Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationTue, 19 Oct 2010 10:36:28 +0000
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2010/Oct/19/t1287484729es3eojqgwhwyv68.htm/, Retrieved Sun, 28 Apr 2024 19:10:54 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=86173, Retrieved Sun, 28 Apr 2024 19:10:54 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsKDGP1W52
Estimated Impact92
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [Centrummaten Visp...] [2010-10-19 10:36:28] [bf26e49ed6e1a435b77b49c7144b8136] [Current]
Feedback Forum

Post a new message
Dataseries X:
96,1
96,5
96,9
97,8
98,9
100,2
101,2
101
101,6
102,4
103,7
103,7
104,6
104,5
104,5
105,6
106,1
107,6
107,7
108,3
108,1
108,1
108
108,2
108,9
109,8
109,9
109,8
110,9
111,1
112,2
112,7
114,6
114,2
114,7
114,7
116
116,3
116,4
116,6
118,1
117,2
108,3
109,5
110,5
110,6
111,2
111,1
111
112,4
112,5
112,4
111,8
111,6
112,9
112,8
113,7
113,8
114
113,8
113,9
114,4
114,4
114,5
113,8
114,3
115
115,4
115,3
114,9
114,3
114,5
115,5
115,8
115,8
116
114,9
114,1
114,1
113,5
115
114,7
115,4
116,1
116,6
117,2
118,2
118
117,7
118,5
117,5
118
117,7
116,3
115
115,7
113,6
114,8
114,9
117,3
117,3
117,7
120
119,6
119,2
117,3
117,5
119
112,5
118,9
118,4
119,4
120,6
118,6
122
122,6
120,6
117,4
116,4
122,2
121
122,4
124,9
126,1
124,5
123,2
126,4
123,9
116
126,6
125,9
126,6
116,7
126,4
129
128,7
128,4
129,2
133,3
128,9
132,7
127,7
131,8
133,9




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' @ 193.190.124.24

\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' @ 193.190.124.24 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=86173&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' @ 193.190.124.24[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=86173&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=86173&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' @ 193.190.124.24







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean115.0923611111110.627897386577005183.298041322547
Geometric Mean114.845486773045
Harmonic Mean114.596136321190
Quadratic Mean115.337028180218
Winsorized Mean ( 1 / 48 )115.0909722222220.62645550271875183.717712946474
Winsorized Mean ( 2 / 48 )115.0881944444440.62364265704229184.541889726187
Winsorized Mean ( 3 / 48 )115.0881944444440.616261361583436186.752247696877
Winsorized Mean ( 4 / 48 )115.0465277777780.597532735701965192.535941386750
Winsorized Mean ( 5 / 48 )115.0847222222220.58812163911684195.681836150495
Winsorized Mean ( 6 / 48 )115.1138888888890.581653100535015197.90814969095
Winsorized Mean ( 7 / 48 )115.1138888888890.578406274253214199.019087470158
Winsorized Mean ( 8 / 48 )115.1194444444440.571978461745744201.265348511702
Winsorized Mean ( 9 / 48 )115.1256944444440.556841627069764206.747643940098
Winsorized Mean ( 10 / 48 )115.1395833333330.531015705453819216.828960331658
Winsorized Mean ( 11 / 48 )115.1395833333330.531015705453819216.828960331658
Winsorized Mean ( 12 / 48 )115.1895833333330.518670187455093222.086378047912
Winsorized Mean ( 13 / 48 )115.1895833333330.518670187455093222.086378047912
Winsorized Mean ( 14 / 48 )115.1701388888890.512891387744696224.550736551298
Winsorized Mean ( 15 / 48 )115.2534722222220.495159076330643232.760496033525
Winsorized Mean ( 16 / 48 )115.1979166666670.471260758349494244.446231997179
Winsorized Mean ( 17 / 48 )115.3277777777780.441608326670344261.153992831908
Winsorized Mean ( 18 / 48 )115.2652777777780.429350442065941268.464327701973
Winsorized Mean ( 19 / 48 )115.21250.411722266047119279.830627345315
Winsorized Mean ( 20 / 48 )115.1430555555560.398911510414039288.64310141376
Winsorized Mean ( 21 / 48 )115.1138888888890.395124486288849291.335750841665
Winsorized Mean ( 22 / 48 )115.0986111111110.389310582084723295.64727086217
Winsorized Mean ( 23 / 48 )115.0826388888890.383279272894590300.25792425394
Winsorized Mean ( 24 / 48 )114.9159722222220.362973645224376316.595911946129
Winsorized Mean ( 25 / 48 )114.9506944444440.341796689864869336.313071053704
Winsorized Mean ( 26 / 48 )115.0590277777780.328678768853172350.065287694859
Winsorized Mean ( 27 / 48 )115.0027777777780.309040398326229372.128622667573
Winsorized Mean ( 28 / 48 )114.9250.300408456722245382.562465963662
Winsorized Mean ( 29 / 48 )114.9048611111110.293659244045468391.28637507941
Winsorized Mean ( 30 / 48 )114.9881944444440.274591765450535418.760534409246
Winsorized Mean ( 31 / 48 )114.9666666666670.267553885385882429.695373329582
Winsorized Mean ( 32 / 48 )115.0111111111110.257685123878523446.324216858282
Winsorized Mean ( 33 / 48 )114.9652777777780.247972194511050463.621649211379
Winsorized Mean ( 34 / 48 )114.9652777777780.242926983420813473.250341147273
Winsorized Mean ( 35 / 48 )114.9409722222220.240467875484239477.988887250579
Winsorized Mean ( 36 / 48 )114.9159722222220.232692808813567493.852701371156
Winsorized Mean ( 37 / 48 )114.9930555555560.218833642634262525.481613207637
Winsorized Mean ( 38 / 48 )115.0194444444440.210533320678571546.32418314462
Winsorized Mean ( 39 / 48 )115.1277777777780.199166494631901578.047919106858
Winsorized Mean ( 40 / 48 )115.10.185180879255818621.554452395676
Winsorized Mean ( 41 / 48 )115.10.185180879255818621.554452395676
Winsorized Mean ( 42 / 48 )115.1291666666670.182222410253944631.805750490421
Winsorized Mean ( 43 / 48 )115.0694444444440.176397951115946652.328690421179
Winsorized Mean ( 44 / 48 )115.1305555555560.170233618950992676.30915834962
Winsorized Mean ( 45 / 48 )115.1305555555560.164089272095881701.63365395565
Winsorized Mean ( 46 / 48 )115.1305555555560.157844226078961729.393519266024
Winsorized Mean ( 47 / 48 )115.3263888888890.139136482884172828.872388451097
Winsorized Mean ( 48 / 48 )115.3597222222220.136099366396226847.613954986207
Trimmed Mean ( 1 / 48 )115.0936619718310.608108903656373189.264885417411
Trimmed Mean ( 2 / 48 )115.0964285714290.587942753254172195.761284469258
Trimmed Mean ( 3 / 48 )115.1007246376810.567363647861256202.869403197697
Trimmed Mean ( 4 / 48 )115.1051470588240.547706964744637210.158267957191
Trimmed Mean ( 5 / 48 )115.1208955223880.532122741346606216.342746846451
Trimmed Mean ( 6 / 48 )115.1287878787880.517511450314264222.466165355133
Trimmed Mean ( 7 / 48 )115.1315384615380.502933593925766228.919960511789
Trimmed Mean ( 8 / 48 )115.1343750.487519479597692236.163640261124
Trimmed Mean ( 9 / 48 )115.1365079365080.47170693508011244.084831860601
Trimmed Mean ( 10 / 48 )115.1379032258060.456933060290665251.979804552914
Trimmed Mean ( 11 / 48 )115.1377049180330.444922471654972258.781500717994
Trimmed Mean ( 12 / 48 )115.13750.431597031847022266.770833680826
Trimmed Mean ( 13 / 48 )115.1322033898310.418673362254893274.992903225920
Trimmed Mean ( 14 / 48 )115.1267241379310.404250945854575284.790240612935
Trimmed Mean ( 15 / 48 )115.1228070175440.388946473092901295.986247418797
Trimmed Mean ( 16 / 48 )115.1116071428570.374322093253404307.520205773509
Trimmed Mean ( 17 / 48 )115.1045454545450.361272393157539318.608749615563
Trimmed Mean ( 18 / 48 )115.0870370370370.350577066167469328.278852621981
Trimmed Mean ( 19 / 48 )115.0735849056600.340184670229958338.267990817672
Trimmed Mean ( 20 / 48 )115.0634615384620.330763531829954347.872272683361
Trimmed Mean ( 21 / 48 )115.0578431372550.321773249692461357.574295710483
Trimmed Mean ( 22 / 48 )115.0540.312100799567879368.643720744384
Trimmed Mean ( 23 / 48 )115.0510204081630.301878001846893381.117602820609
Trimmed Mean ( 24 / 48 )115.0489583333330.29102433578107395.324184915868
Trimmed Mean ( 25 / 48 )115.0574468085110.281238596908374409.109731286263
Trimmed Mean ( 26 / 48 )115.0641304347830.272749364382388421.867639161445
Trimmed Mean ( 27 / 48 )115.0644444444440.264694538627648434.706530180089
Trimmed Mean ( 28 / 48 )115.0681818181820.257877688917326446.212242328074
Trimmed Mean ( 29 / 48 )115.0767441860470.251080697938267458.325730058072
Trimmed Mean ( 30 / 48 )115.0869047619050.244073645114632471.525324693917
Trimmed Mean ( 31 / 48 )115.0926829268290.238362251091848482.84777643957
Trimmed Mean ( 32 / 48 )115.10.232596788074953494.84776188272
Trimmed Mean ( 33 / 48 )115.1051282051280.227130072974955506.780659634712
Trimmed Mean ( 34 / 48 )115.1131578947370.221939948455031518.668039242431
Trimmed Mean ( 35 / 48 )115.1216216216220.216492095378186531.759006815089
Trimmed Mean ( 36 / 48 )115.1319444444440.210380332138208547.256215798773
Trimmed Mean ( 37 / 48 )115.1442857142860.204186369160822563.917592479424
Trimmed Mean ( 38 / 48 )115.1529411764710.198805371889608579.22449520334
Trimmed Mean ( 39 / 48 )115.1606060606060.193554396417119594.977991677489
Trimmed Mean ( 40 / 48 )115.16250.188910041999503609.615554478057
Trimmed Mean ( 41 / 48 )115.1661290322580.185271301182101621.608032638919
Trimmed Mean ( 42 / 48 )115.170.180822040054556636.924569401229
Trimmed Mean ( 43 / 48 )115.1724137931030.175835970686046654.999163958001
Trimmed Mean ( 44 / 48 )115.1785714285710.170612233801741675.089756824905
Trimmed Mean ( 45 / 48 )115.1814814814810.165215359827135697.159644248549
Trimmed Mean ( 46 / 48 )115.1846153846150.159571083641191721.838899356087
Trimmed Mean ( 47 / 48 )115.1880.153639918282313749.727032452218
Trimmed Mean ( 48 / 48 )115.1791666666670.149643735705621769.689196300518
Median114.95
Midrange115
Midmean - Weighted Average at Xnp115.022972972973
Midmean - Weighted Average at X(n+1)p115.131944444444
Midmean - Empirical Distribution Function115.022972972973
Midmean - Empirical Distribution Function - Averaging115.131944444444
Midmean - Empirical Distribution Function - Interpolation115.131944444444
Midmean - Closest Observation115.022972972973
Midmean - True Basic - Statistics Graphics Toolkit115.131944444444
Midmean - MS Excel (old versions)115.068
Number of observations144

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 115.092361111111 & 0.627897386577005 & 183.298041322547 \tabularnewline
Geometric Mean & 114.845486773045 &  &  \tabularnewline
Harmonic Mean & 114.596136321190 &  &  \tabularnewline
Quadratic Mean & 115.337028180218 &  &  \tabularnewline
Winsorized Mean ( 1 / 48 ) & 115.090972222222 & 0.62645550271875 & 183.717712946474 \tabularnewline
Winsorized Mean ( 2 / 48 ) & 115.088194444444 & 0.62364265704229 & 184.541889726187 \tabularnewline
Winsorized Mean ( 3 / 48 ) & 115.088194444444 & 0.616261361583436 & 186.752247696877 \tabularnewline
Winsorized Mean ( 4 / 48 ) & 115.046527777778 & 0.597532735701965 & 192.535941386750 \tabularnewline
Winsorized Mean ( 5 / 48 ) & 115.084722222222 & 0.58812163911684 & 195.681836150495 \tabularnewline
Winsorized Mean ( 6 / 48 ) & 115.113888888889 & 0.581653100535015 & 197.90814969095 \tabularnewline
Winsorized Mean ( 7 / 48 ) & 115.113888888889 & 0.578406274253214 & 199.019087470158 \tabularnewline
Winsorized Mean ( 8 / 48 ) & 115.119444444444 & 0.571978461745744 & 201.265348511702 \tabularnewline
Winsorized Mean ( 9 / 48 ) & 115.125694444444 & 0.556841627069764 & 206.747643940098 \tabularnewline
Winsorized Mean ( 10 / 48 ) & 115.139583333333 & 0.531015705453819 & 216.828960331658 \tabularnewline
Winsorized Mean ( 11 / 48 ) & 115.139583333333 & 0.531015705453819 & 216.828960331658 \tabularnewline
Winsorized Mean ( 12 / 48 ) & 115.189583333333 & 0.518670187455093 & 222.086378047912 \tabularnewline
Winsorized Mean ( 13 / 48 ) & 115.189583333333 & 0.518670187455093 & 222.086378047912 \tabularnewline
Winsorized Mean ( 14 / 48 ) & 115.170138888889 & 0.512891387744696 & 224.550736551298 \tabularnewline
Winsorized Mean ( 15 / 48 ) & 115.253472222222 & 0.495159076330643 & 232.760496033525 \tabularnewline
Winsorized Mean ( 16 / 48 ) & 115.197916666667 & 0.471260758349494 & 244.446231997179 \tabularnewline
Winsorized Mean ( 17 / 48 ) & 115.327777777778 & 0.441608326670344 & 261.153992831908 \tabularnewline
Winsorized Mean ( 18 / 48 ) & 115.265277777778 & 0.429350442065941 & 268.464327701973 \tabularnewline
Winsorized Mean ( 19 / 48 ) & 115.2125 & 0.411722266047119 & 279.830627345315 \tabularnewline
Winsorized Mean ( 20 / 48 ) & 115.143055555556 & 0.398911510414039 & 288.64310141376 \tabularnewline
Winsorized Mean ( 21 / 48 ) & 115.113888888889 & 0.395124486288849 & 291.335750841665 \tabularnewline
Winsorized Mean ( 22 / 48 ) & 115.098611111111 & 0.389310582084723 & 295.64727086217 \tabularnewline
Winsorized Mean ( 23 / 48 ) & 115.082638888889 & 0.383279272894590 & 300.25792425394 \tabularnewline
Winsorized Mean ( 24 / 48 ) & 114.915972222222 & 0.362973645224376 & 316.595911946129 \tabularnewline
Winsorized Mean ( 25 / 48 ) & 114.950694444444 & 0.341796689864869 & 336.313071053704 \tabularnewline
Winsorized Mean ( 26 / 48 ) & 115.059027777778 & 0.328678768853172 & 350.065287694859 \tabularnewline
Winsorized Mean ( 27 / 48 ) & 115.002777777778 & 0.309040398326229 & 372.128622667573 \tabularnewline
Winsorized Mean ( 28 / 48 ) & 114.925 & 0.300408456722245 & 382.562465963662 \tabularnewline
Winsorized Mean ( 29 / 48 ) & 114.904861111111 & 0.293659244045468 & 391.28637507941 \tabularnewline
Winsorized Mean ( 30 / 48 ) & 114.988194444444 & 0.274591765450535 & 418.760534409246 \tabularnewline
Winsorized Mean ( 31 / 48 ) & 114.966666666667 & 0.267553885385882 & 429.695373329582 \tabularnewline
Winsorized Mean ( 32 / 48 ) & 115.011111111111 & 0.257685123878523 & 446.324216858282 \tabularnewline
Winsorized Mean ( 33 / 48 ) & 114.965277777778 & 0.247972194511050 & 463.621649211379 \tabularnewline
Winsorized Mean ( 34 / 48 ) & 114.965277777778 & 0.242926983420813 & 473.250341147273 \tabularnewline
Winsorized Mean ( 35 / 48 ) & 114.940972222222 & 0.240467875484239 & 477.988887250579 \tabularnewline
Winsorized Mean ( 36 / 48 ) & 114.915972222222 & 0.232692808813567 & 493.852701371156 \tabularnewline
Winsorized Mean ( 37 / 48 ) & 114.993055555556 & 0.218833642634262 & 525.481613207637 \tabularnewline
Winsorized Mean ( 38 / 48 ) & 115.019444444444 & 0.210533320678571 & 546.32418314462 \tabularnewline
Winsorized Mean ( 39 / 48 ) & 115.127777777778 & 0.199166494631901 & 578.047919106858 \tabularnewline
Winsorized Mean ( 40 / 48 ) & 115.1 & 0.185180879255818 & 621.554452395676 \tabularnewline
Winsorized Mean ( 41 / 48 ) & 115.1 & 0.185180879255818 & 621.554452395676 \tabularnewline
Winsorized Mean ( 42 / 48 ) & 115.129166666667 & 0.182222410253944 & 631.805750490421 \tabularnewline
Winsorized Mean ( 43 / 48 ) & 115.069444444444 & 0.176397951115946 & 652.328690421179 \tabularnewline
Winsorized Mean ( 44 / 48 ) & 115.130555555556 & 0.170233618950992 & 676.30915834962 \tabularnewline
Winsorized Mean ( 45 / 48 ) & 115.130555555556 & 0.164089272095881 & 701.63365395565 \tabularnewline
Winsorized Mean ( 46 / 48 ) & 115.130555555556 & 0.157844226078961 & 729.393519266024 \tabularnewline
Winsorized Mean ( 47 / 48 ) & 115.326388888889 & 0.139136482884172 & 828.872388451097 \tabularnewline
Winsorized Mean ( 48 / 48 ) & 115.359722222222 & 0.136099366396226 & 847.613954986207 \tabularnewline
Trimmed Mean ( 1 / 48 ) & 115.093661971831 & 0.608108903656373 & 189.264885417411 \tabularnewline
Trimmed Mean ( 2 / 48 ) & 115.096428571429 & 0.587942753254172 & 195.761284469258 \tabularnewline
Trimmed Mean ( 3 / 48 ) & 115.100724637681 & 0.567363647861256 & 202.869403197697 \tabularnewline
Trimmed Mean ( 4 / 48 ) & 115.105147058824 & 0.547706964744637 & 210.158267957191 \tabularnewline
Trimmed Mean ( 5 / 48 ) & 115.120895522388 & 0.532122741346606 & 216.342746846451 \tabularnewline
Trimmed Mean ( 6 / 48 ) & 115.128787878788 & 0.517511450314264 & 222.466165355133 \tabularnewline
Trimmed Mean ( 7 / 48 ) & 115.131538461538 & 0.502933593925766 & 228.919960511789 \tabularnewline
Trimmed Mean ( 8 / 48 ) & 115.134375 & 0.487519479597692 & 236.163640261124 \tabularnewline
Trimmed Mean ( 9 / 48 ) & 115.136507936508 & 0.47170693508011 & 244.084831860601 \tabularnewline
Trimmed Mean ( 10 / 48 ) & 115.137903225806 & 0.456933060290665 & 251.979804552914 \tabularnewline
Trimmed Mean ( 11 / 48 ) & 115.137704918033 & 0.444922471654972 & 258.781500717994 \tabularnewline
Trimmed Mean ( 12 / 48 ) & 115.1375 & 0.431597031847022 & 266.770833680826 \tabularnewline
Trimmed Mean ( 13 / 48 ) & 115.132203389831 & 0.418673362254893 & 274.992903225920 \tabularnewline
Trimmed Mean ( 14 / 48 ) & 115.126724137931 & 0.404250945854575 & 284.790240612935 \tabularnewline
Trimmed Mean ( 15 / 48 ) & 115.122807017544 & 0.388946473092901 & 295.986247418797 \tabularnewline
Trimmed Mean ( 16 / 48 ) & 115.111607142857 & 0.374322093253404 & 307.520205773509 \tabularnewline
Trimmed Mean ( 17 / 48 ) & 115.104545454545 & 0.361272393157539 & 318.608749615563 \tabularnewline
Trimmed Mean ( 18 / 48 ) & 115.087037037037 & 0.350577066167469 & 328.278852621981 \tabularnewline
Trimmed Mean ( 19 / 48 ) & 115.073584905660 & 0.340184670229958 & 338.267990817672 \tabularnewline
Trimmed Mean ( 20 / 48 ) & 115.063461538462 & 0.330763531829954 & 347.872272683361 \tabularnewline
Trimmed Mean ( 21 / 48 ) & 115.057843137255 & 0.321773249692461 & 357.574295710483 \tabularnewline
Trimmed Mean ( 22 / 48 ) & 115.054 & 0.312100799567879 & 368.643720744384 \tabularnewline
Trimmed Mean ( 23 / 48 ) & 115.051020408163 & 0.301878001846893 & 381.117602820609 \tabularnewline
Trimmed Mean ( 24 / 48 ) & 115.048958333333 & 0.29102433578107 & 395.324184915868 \tabularnewline
Trimmed Mean ( 25 / 48 ) & 115.057446808511 & 0.281238596908374 & 409.109731286263 \tabularnewline
Trimmed Mean ( 26 / 48 ) & 115.064130434783 & 0.272749364382388 & 421.867639161445 \tabularnewline
Trimmed Mean ( 27 / 48 ) & 115.064444444444 & 0.264694538627648 & 434.706530180089 \tabularnewline
Trimmed Mean ( 28 / 48 ) & 115.068181818182 & 0.257877688917326 & 446.212242328074 \tabularnewline
Trimmed Mean ( 29 / 48 ) & 115.076744186047 & 0.251080697938267 & 458.325730058072 \tabularnewline
Trimmed Mean ( 30 / 48 ) & 115.086904761905 & 0.244073645114632 & 471.525324693917 \tabularnewline
Trimmed Mean ( 31 / 48 ) & 115.092682926829 & 0.238362251091848 & 482.84777643957 \tabularnewline
Trimmed Mean ( 32 / 48 ) & 115.1 & 0.232596788074953 & 494.84776188272 \tabularnewline
Trimmed Mean ( 33 / 48 ) & 115.105128205128 & 0.227130072974955 & 506.780659634712 \tabularnewline
Trimmed Mean ( 34 / 48 ) & 115.113157894737 & 0.221939948455031 & 518.668039242431 \tabularnewline
Trimmed Mean ( 35 / 48 ) & 115.121621621622 & 0.216492095378186 & 531.759006815089 \tabularnewline
Trimmed Mean ( 36 / 48 ) & 115.131944444444 & 0.210380332138208 & 547.256215798773 \tabularnewline
Trimmed Mean ( 37 / 48 ) & 115.144285714286 & 0.204186369160822 & 563.917592479424 \tabularnewline
Trimmed Mean ( 38 / 48 ) & 115.152941176471 & 0.198805371889608 & 579.22449520334 \tabularnewline
Trimmed Mean ( 39 / 48 ) & 115.160606060606 & 0.193554396417119 & 594.977991677489 \tabularnewline
Trimmed Mean ( 40 / 48 ) & 115.1625 & 0.188910041999503 & 609.615554478057 \tabularnewline
Trimmed Mean ( 41 / 48 ) & 115.166129032258 & 0.185271301182101 & 621.608032638919 \tabularnewline
Trimmed Mean ( 42 / 48 ) & 115.17 & 0.180822040054556 & 636.924569401229 \tabularnewline
Trimmed Mean ( 43 / 48 ) & 115.172413793103 & 0.175835970686046 & 654.999163958001 \tabularnewline
Trimmed Mean ( 44 / 48 ) & 115.178571428571 & 0.170612233801741 & 675.089756824905 \tabularnewline
Trimmed Mean ( 45 / 48 ) & 115.181481481481 & 0.165215359827135 & 697.159644248549 \tabularnewline
Trimmed Mean ( 46 / 48 ) & 115.184615384615 & 0.159571083641191 & 721.838899356087 \tabularnewline
Trimmed Mean ( 47 / 48 ) & 115.188 & 0.153639918282313 & 749.727032452218 \tabularnewline
Trimmed Mean ( 48 / 48 ) & 115.179166666667 & 0.149643735705621 & 769.689196300518 \tabularnewline
Median & 114.95 &  &  \tabularnewline
Midrange & 115 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 115.022972972973 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 115.131944444444 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 115.022972972973 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 115.131944444444 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 115.131944444444 &  &  \tabularnewline
Midmean - Closest Observation & 115.022972972973 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 115.131944444444 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 115.068 &  &  \tabularnewline
Number of observations & 144 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=86173&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]115.092361111111[/C][C]0.627897386577005[/C][C]183.298041322547[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]114.845486773045[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]114.596136321190[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]115.337028180218[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 48 )[/C][C]115.090972222222[/C][C]0.62645550271875[/C][C]183.717712946474[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 48 )[/C][C]115.088194444444[/C][C]0.62364265704229[/C][C]184.541889726187[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 48 )[/C][C]115.088194444444[/C][C]0.616261361583436[/C][C]186.752247696877[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 48 )[/C][C]115.046527777778[/C][C]0.597532735701965[/C][C]192.535941386750[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 48 )[/C][C]115.084722222222[/C][C]0.58812163911684[/C][C]195.681836150495[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 48 )[/C][C]115.113888888889[/C][C]0.581653100535015[/C][C]197.90814969095[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 48 )[/C][C]115.113888888889[/C][C]0.578406274253214[/C][C]199.019087470158[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 48 )[/C][C]115.119444444444[/C][C]0.571978461745744[/C][C]201.265348511702[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 48 )[/C][C]115.125694444444[/C][C]0.556841627069764[/C][C]206.747643940098[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 48 )[/C][C]115.139583333333[/C][C]0.531015705453819[/C][C]216.828960331658[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 48 )[/C][C]115.139583333333[/C][C]0.531015705453819[/C][C]216.828960331658[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 48 )[/C][C]115.189583333333[/C][C]0.518670187455093[/C][C]222.086378047912[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 48 )[/C][C]115.189583333333[/C][C]0.518670187455093[/C][C]222.086378047912[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 48 )[/C][C]115.170138888889[/C][C]0.512891387744696[/C][C]224.550736551298[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 48 )[/C][C]115.253472222222[/C][C]0.495159076330643[/C][C]232.760496033525[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 48 )[/C][C]115.197916666667[/C][C]0.471260758349494[/C][C]244.446231997179[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 48 )[/C][C]115.327777777778[/C][C]0.441608326670344[/C][C]261.153992831908[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 48 )[/C][C]115.265277777778[/C][C]0.429350442065941[/C][C]268.464327701973[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 48 )[/C][C]115.2125[/C][C]0.411722266047119[/C][C]279.830627345315[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 48 )[/C][C]115.143055555556[/C][C]0.398911510414039[/C][C]288.64310141376[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 48 )[/C][C]115.113888888889[/C][C]0.395124486288849[/C][C]291.335750841665[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 48 )[/C][C]115.098611111111[/C][C]0.389310582084723[/C][C]295.64727086217[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 48 )[/C][C]115.082638888889[/C][C]0.383279272894590[/C][C]300.25792425394[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 48 )[/C][C]114.915972222222[/C][C]0.362973645224376[/C][C]316.595911946129[/C][/ROW]
[ROW][C]Winsorized Mean ( 25 / 48 )[/C][C]114.950694444444[/C][C]0.341796689864869[/C][C]336.313071053704[/C][/ROW]
[ROW][C]Winsorized Mean ( 26 / 48 )[/C][C]115.059027777778[/C][C]0.328678768853172[/C][C]350.065287694859[/C][/ROW]
[ROW][C]Winsorized Mean ( 27 / 48 )[/C][C]115.002777777778[/C][C]0.309040398326229[/C][C]372.128622667573[/C][/ROW]
[ROW][C]Winsorized Mean ( 28 / 48 )[/C][C]114.925[/C][C]0.300408456722245[/C][C]382.562465963662[/C][/ROW]
[ROW][C]Winsorized Mean ( 29 / 48 )[/C][C]114.904861111111[/C][C]0.293659244045468[/C][C]391.28637507941[/C][/ROW]
[ROW][C]Winsorized Mean ( 30 / 48 )[/C][C]114.988194444444[/C][C]0.274591765450535[/C][C]418.760534409246[/C][/ROW]
[ROW][C]Winsorized Mean ( 31 / 48 )[/C][C]114.966666666667[/C][C]0.267553885385882[/C][C]429.695373329582[/C][/ROW]
[ROW][C]Winsorized Mean ( 32 / 48 )[/C][C]115.011111111111[/C][C]0.257685123878523[/C][C]446.324216858282[/C][/ROW]
[ROW][C]Winsorized Mean ( 33 / 48 )[/C][C]114.965277777778[/C][C]0.247972194511050[/C][C]463.621649211379[/C][/ROW]
[ROW][C]Winsorized Mean ( 34 / 48 )[/C][C]114.965277777778[/C][C]0.242926983420813[/C][C]473.250341147273[/C][/ROW]
[ROW][C]Winsorized Mean ( 35 / 48 )[/C][C]114.940972222222[/C][C]0.240467875484239[/C][C]477.988887250579[/C][/ROW]
[ROW][C]Winsorized Mean ( 36 / 48 )[/C][C]114.915972222222[/C][C]0.232692808813567[/C][C]493.852701371156[/C][/ROW]
[ROW][C]Winsorized Mean ( 37 / 48 )[/C][C]114.993055555556[/C][C]0.218833642634262[/C][C]525.481613207637[/C][/ROW]
[ROW][C]Winsorized Mean ( 38 / 48 )[/C][C]115.019444444444[/C][C]0.210533320678571[/C][C]546.32418314462[/C][/ROW]
[ROW][C]Winsorized Mean ( 39 / 48 )[/C][C]115.127777777778[/C][C]0.199166494631901[/C][C]578.047919106858[/C][/ROW]
[ROW][C]Winsorized Mean ( 40 / 48 )[/C][C]115.1[/C][C]0.185180879255818[/C][C]621.554452395676[/C][/ROW]
[ROW][C]Winsorized Mean ( 41 / 48 )[/C][C]115.1[/C][C]0.185180879255818[/C][C]621.554452395676[/C][/ROW]
[ROW][C]Winsorized Mean ( 42 / 48 )[/C][C]115.129166666667[/C][C]0.182222410253944[/C][C]631.805750490421[/C][/ROW]
[ROW][C]Winsorized Mean ( 43 / 48 )[/C][C]115.069444444444[/C][C]0.176397951115946[/C][C]652.328690421179[/C][/ROW]
[ROW][C]Winsorized Mean ( 44 / 48 )[/C][C]115.130555555556[/C][C]0.170233618950992[/C][C]676.30915834962[/C][/ROW]
[ROW][C]Winsorized Mean ( 45 / 48 )[/C][C]115.130555555556[/C][C]0.164089272095881[/C][C]701.63365395565[/C][/ROW]
[ROW][C]Winsorized Mean ( 46 / 48 )[/C][C]115.130555555556[/C][C]0.157844226078961[/C][C]729.393519266024[/C][/ROW]
[ROW][C]Winsorized Mean ( 47 / 48 )[/C][C]115.326388888889[/C][C]0.139136482884172[/C][C]828.872388451097[/C][/ROW]
[ROW][C]Winsorized Mean ( 48 / 48 )[/C][C]115.359722222222[/C][C]0.136099366396226[/C][C]847.613954986207[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 48 )[/C][C]115.093661971831[/C][C]0.608108903656373[/C][C]189.264885417411[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 48 )[/C][C]115.096428571429[/C][C]0.587942753254172[/C][C]195.761284469258[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 48 )[/C][C]115.100724637681[/C][C]0.567363647861256[/C][C]202.869403197697[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 48 )[/C][C]115.105147058824[/C][C]0.547706964744637[/C][C]210.158267957191[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 48 )[/C][C]115.120895522388[/C][C]0.532122741346606[/C][C]216.342746846451[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 48 )[/C][C]115.128787878788[/C][C]0.517511450314264[/C][C]222.466165355133[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 48 )[/C][C]115.131538461538[/C][C]0.502933593925766[/C][C]228.919960511789[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 48 )[/C][C]115.134375[/C][C]0.487519479597692[/C][C]236.163640261124[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 48 )[/C][C]115.136507936508[/C][C]0.47170693508011[/C][C]244.084831860601[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 48 )[/C][C]115.137903225806[/C][C]0.456933060290665[/C][C]251.979804552914[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 48 )[/C][C]115.137704918033[/C][C]0.444922471654972[/C][C]258.781500717994[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 48 )[/C][C]115.1375[/C][C]0.431597031847022[/C][C]266.770833680826[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 48 )[/C][C]115.132203389831[/C][C]0.418673362254893[/C][C]274.992903225920[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 48 )[/C][C]115.126724137931[/C][C]0.404250945854575[/C][C]284.790240612935[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 48 )[/C][C]115.122807017544[/C][C]0.388946473092901[/C][C]295.986247418797[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 48 )[/C][C]115.111607142857[/C][C]0.374322093253404[/C][C]307.520205773509[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 48 )[/C][C]115.104545454545[/C][C]0.361272393157539[/C][C]318.608749615563[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 48 )[/C][C]115.087037037037[/C][C]0.350577066167469[/C][C]328.278852621981[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 48 )[/C][C]115.073584905660[/C][C]0.340184670229958[/C][C]338.267990817672[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 48 )[/C][C]115.063461538462[/C][C]0.330763531829954[/C][C]347.872272683361[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 48 )[/C][C]115.057843137255[/C][C]0.321773249692461[/C][C]357.574295710483[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 48 )[/C][C]115.054[/C][C]0.312100799567879[/C][C]368.643720744384[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 48 )[/C][C]115.051020408163[/C][C]0.301878001846893[/C][C]381.117602820609[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 48 )[/C][C]115.048958333333[/C][C]0.29102433578107[/C][C]395.324184915868[/C][/ROW]
[ROW][C]Trimmed Mean ( 25 / 48 )[/C][C]115.057446808511[/C][C]0.281238596908374[/C][C]409.109731286263[/C][/ROW]
[ROW][C]Trimmed Mean ( 26 / 48 )[/C][C]115.064130434783[/C][C]0.272749364382388[/C][C]421.867639161445[/C][/ROW]
[ROW][C]Trimmed Mean ( 27 / 48 )[/C][C]115.064444444444[/C][C]0.264694538627648[/C][C]434.706530180089[/C][/ROW]
[ROW][C]Trimmed Mean ( 28 / 48 )[/C][C]115.068181818182[/C][C]0.257877688917326[/C][C]446.212242328074[/C][/ROW]
[ROW][C]Trimmed Mean ( 29 / 48 )[/C][C]115.076744186047[/C][C]0.251080697938267[/C][C]458.325730058072[/C][/ROW]
[ROW][C]Trimmed Mean ( 30 / 48 )[/C][C]115.086904761905[/C][C]0.244073645114632[/C][C]471.525324693917[/C][/ROW]
[ROW][C]Trimmed Mean ( 31 / 48 )[/C][C]115.092682926829[/C][C]0.238362251091848[/C][C]482.84777643957[/C][/ROW]
[ROW][C]Trimmed Mean ( 32 / 48 )[/C][C]115.1[/C][C]0.232596788074953[/C][C]494.84776188272[/C][/ROW]
[ROW][C]Trimmed Mean ( 33 / 48 )[/C][C]115.105128205128[/C][C]0.227130072974955[/C][C]506.780659634712[/C][/ROW]
[ROW][C]Trimmed Mean ( 34 / 48 )[/C][C]115.113157894737[/C][C]0.221939948455031[/C][C]518.668039242431[/C][/ROW]
[ROW][C]Trimmed Mean ( 35 / 48 )[/C][C]115.121621621622[/C][C]0.216492095378186[/C][C]531.759006815089[/C][/ROW]
[ROW][C]Trimmed Mean ( 36 / 48 )[/C][C]115.131944444444[/C][C]0.210380332138208[/C][C]547.256215798773[/C][/ROW]
[ROW][C]Trimmed Mean ( 37 / 48 )[/C][C]115.144285714286[/C][C]0.204186369160822[/C][C]563.917592479424[/C][/ROW]
[ROW][C]Trimmed Mean ( 38 / 48 )[/C][C]115.152941176471[/C][C]0.198805371889608[/C][C]579.22449520334[/C][/ROW]
[ROW][C]Trimmed Mean ( 39 / 48 )[/C][C]115.160606060606[/C][C]0.193554396417119[/C][C]594.977991677489[/C][/ROW]
[ROW][C]Trimmed Mean ( 40 / 48 )[/C][C]115.1625[/C][C]0.188910041999503[/C][C]609.615554478057[/C][/ROW]
[ROW][C]Trimmed Mean ( 41 / 48 )[/C][C]115.166129032258[/C][C]0.185271301182101[/C][C]621.608032638919[/C][/ROW]
[ROW][C]Trimmed Mean ( 42 / 48 )[/C][C]115.17[/C][C]0.180822040054556[/C][C]636.924569401229[/C][/ROW]
[ROW][C]Trimmed Mean ( 43 / 48 )[/C][C]115.172413793103[/C][C]0.175835970686046[/C][C]654.999163958001[/C][/ROW]
[ROW][C]Trimmed Mean ( 44 / 48 )[/C][C]115.178571428571[/C][C]0.170612233801741[/C][C]675.089756824905[/C][/ROW]
[ROW][C]Trimmed Mean ( 45 / 48 )[/C][C]115.181481481481[/C][C]0.165215359827135[/C][C]697.159644248549[/C][/ROW]
[ROW][C]Trimmed Mean ( 46 / 48 )[/C][C]115.184615384615[/C][C]0.159571083641191[/C][C]721.838899356087[/C][/ROW]
[ROW][C]Trimmed Mean ( 47 / 48 )[/C][C]115.188[/C][C]0.153639918282313[/C][C]749.727032452218[/C][/ROW]
[ROW][C]Trimmed Mean ( 48 / 48 )[/C][C]115.179166666667[/C][C]0.149643735705621[/C][C]769.689196300518[/C][/ROW]
[ROW][C]Median[/C][C]114.95[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]115[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]115.022972972973[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]115.131944444444[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]115.022972972973[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]115.131944444444[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]115.131944444444[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]115.022972972973[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]115.131944444444[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]115.068[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]144[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=86173&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=86173&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 Mean115.0923611111110.627897386577005183.298041322547
Geometric Mean114.845486773045
Harmonic Mean114.596136321190
Quadratic Mean115.337028180218
Winsorized Mean ( 1 / 48 )115.0909722222220.62645550271875183.717712946474
Winsorized Mean ( 2 / 48 )115.0881944444440.62364265704229184.541889726187
Winsorized Mean ( 3 / 48 )115.0881944444440.616261361583436186.752247696877
Winsorized Mean ( 4 / 48 )115.0465277777780.597532735701965192.535941386750
Winsorized Mean ( 5 / 48 )115.0847222222220.58812163911684195.681836150495
Winsorized Mean ( 6 / 48 )115.1138888888890.581653100535015197.90814969095
Winsorized Mean ( 7 / 48 )115.1138888888890.578406274253214199.019087470158
Winsorized Mean ( 8 / 48 )115.1194444444440.571978461745744201.265348511702
Winsorized Mean ( 9 / 48 )115.1256944444440.556841627069764206.747643940098
Winsorized Mean ( 10 / 48 )115.1395833333330.531015705453819216.828960331658
Winsorized Mean ( 11 / 48 )115.1395833333330.531015705453819216.828960331658
Winsorized Mean ( 12 / 48 )115.1895833333330.518670187455093222.086378047912
Winsorized Mean ( 13 / 48 )115.1895833333330.518670187455093222.086378047912
Winsorized Mean ( 14 / 48 )115.1701388888890.512891387744696224.550736551298
Winsorized Mean ( 15 / 48 )115.2534722222220.495159076330643232.760496033525
Winsorized Mean ( 16 / 48 )115.1979166666670.471260758349494244.446231997179
Winsorized Mean ( 17 / 48 )115.3277777777780.441608326670344261.153992831908
Winsorized Mean ( 18 / 48 )115.2652777777780.429350442065941268.464327701973
Winsorized Mean ( 19 / 48 )115.21250.411722266047119279.830627345315
Winsorized Mean ( 20 / 48 )115.1430555555560.398911510414039288.64310141376
Winsorized Mean ( 21 / 48 )115.1138888888890.395124486288849291.335750841665
Winsorized Mean ( 22 / 48 )115.0986111111110.389310582084723295.64727086217
Winsorized Mean ( 23 / 48 )115.0826388888890.383279272894590300.25792425394
Winsorized Mean ( 24 / 48 )114.9159722222220.362973645224376316.595911946129
Winsorized Mean ( 25 / 48 )114.9506944444440.341796689864869336.313071053704
Winsorized Mean ( 26 / 48 )115.0590277777780.328678768853172350.065287694859
Winsorized Mean ( 27 / 48 )115.0027777777780.309040398326229372.128622667573
Winsorized Mean ( 28 / 48 )114.9250.300408456722245382.562465963662
Winsorized Mean ( 29 / 48 )114.9048611111110.293659244045468391.28637507941
Winsorized Mean ( 30 / 48 )114.9881944444440.274591765450535418.760534409246
Winsorized Mean ( 31 / 48 )114.9666666666670.267553885385882429.695373329582
Winsorized Mean ( 32 / 48 )115.0111111111110.257685123878523446.324216858282
Winsorized Mean ( 33 / 48 )114.9652777777780.247972194511050463.621649211379
Winsorized Mean ( 34 / 48 )114.9652777777780.242926983420813473.250341147273
Winsorized Mean ( 35 / 48 )114.9409722222220.240467875484239477.988887250579
Winsorized Mean ( 36 / 48 )114.9159722222220.232692808813567493.852701371156
Winsorized Mean ( 37 / 48 )114.9930555555560.218833642634262525.481613207637
Winsorized Mean ( 38 / 48 )115.0194444444440.210533320678571546.32418314462
Winsorized Mean ( 39 / 48 )115.1277777777780.199166494631901578.047919106858
Winsorized Mean ( 40 / 48 )115.10.185180879255818621.554452395676
Winsorized Mean ( 41 / 48 )115.10.185180879255818621.554452395676
Winsorized Mean ( 42 / 48 )115.1291666666670.182222410253944631.805750490421
Winsorized Mean ( 43 / 48 )115.0694444444440.176397951115946652.328690421179
Winsorized Mean ( 44 / 48 )115.1305555555560.170233618950992676.30915834962
Winsorized Mean ( 45 / 48 )115.1305555555560.164089272095881701.63365395565
Winsorized Mean ( 46 / 48 )115.1305555555560.157844226078961729.393519266024
Winsorized Mean ( 47 / 48 )115.3263888888890.139136482884172828.872388451097
Winsorized Mean ( 48 / 48 )115.3597222222220.136099366396226847.613954986207
Trimmed Mean ( 1 / 48 )115.0936619718310.608108903656373189.264885417411
Trimmed Mean ( 2 / 48 )115.0964285714290.587942753254172195.761284469258
Trimmed Mean ( 3 / 48 )115.1007246376810.567363647861256202.869403197697
Trimmed Mean ( 4 / 48 )115.1051470588240.547706964744637210.158267957191
Trimmed Mean ( 5 / 48 )115.1208955223880.532122741346606216.342746846451
Trimmed Mean ( 6 / 48 )115.1287878787880.517511450314264222.466165355133
Trimmed Mean ( 7 / 48 )115.1315384615380.502933593925766228.919960511789
Trimmed Mean ( 8 / 48 )115.1343750.487519479597692236.163640261124
Trimmed Mean ( 9 / 48 )115.1365079365080.47170693508011244.084831860601
Trimmed Mean ( 10 / 48 )115.1379032258060.456933060290665251.979804552914
Trimmed Mean ( 11 / 48 )115.1377049180330.444922471654972258.781500717994
Trimmed Mean ( 12 / 48 )115.13750.431597031847022266.770833680826
Trimmed Mean ( 13 / 48 )115.1322033898310.418673362254893274.992903225920
Trimmed Mean ( 14 / 48 )115.1267241379310.404250945854575284.790240612935
Trimmed Mean ( 15 / 48 )115.1228070175440.388946473092901295.986247418797
Trimmed Mean ( 16 / 48 )115.1116071428570.374322093253404307.520205773509
Trimmed Mean ( 17 / 48 )115.1045454545450.361272393157539318.608749615563
Trimmed Mean ( 18 / 48 )115.0870370370370.350577066167469328.278852621981
Trimmed Mean ( 19 / 48 )115.0735849056600.340184670229958338.267990817672
Trimmed Mean ( 20 / 48 )115.0634615384620.330763531829954347.872272683361
Trimmed Mean ( 21 / 48 )115.0578431372550.321773249692461357.574295710483
Trimmed Mean ( 22 / 48 )115.0540.312100799567879368.643720744384
Trimmed Mean ( 23 / 48 )115.0510204081630.301878001846893381.117602820609
Trimmed Mean ( 24 / 48 )115.0489583333330.29102433578107395.324184915868
Trimmed Mean ( 25 / 48 )115.0574468085110.281238596908374409.109731286263
Trimmed Mean ( 26 / 48 )115.0641304347830.272749364382388421.867639161445
Trimmed Mean ( 27 / 48 )115.0644444444440.264694538627648434.706530180089
Trimmed Mean ( 28 / 48 )115.0681818181820.257877688917326446.212242328074
Trimmed Mean ( 29 / 48 )115.0767441860470.251080697938267458.325730058072
Trimmed Mean ( 30 / 48 )115.0869047619050.244073645114632471.525324693917
Trimmed Mean ( 31 / 48 )115.0926829268290.238362251091848482.84777643957
Trimmed Mean ( 32 / 48 )115.10.232596788074953494.84776188272
Trimmed Mean ( 33 / 48 )115.1051282051280.227130072974955506.780659634712
Trimmed Mean ( 34 / 48 )115.1131578947370.221939948455031518.668039242431
Trimmed Mean ( 35 / 48 )115.1216216216220.216492095378186531.759006815089
Trimmed Mean ( 36 / 48 )115.1319444444440.210380332138208547.256215798773
Trimmed Mean ( 37 / 48 )115.1442857142860.204186369160822563.917592479424
Trimmed Mean ( 38 / 48 )115.1529411764710.198805371889608579.22449520334
Trimmed Mean ( 39 / 48 )115.1606060606060.193554396417119594.977991677489
Trimmed Mean ( 40 / 48 )115.16250.188910041999503609.615554478057
Trimmed Mean ( 41 / 48 )115.1661290322580.185271301182101621.608032638919
Trimmed Mean ( 42 / 48 )115.170.180822040054556636.924569401229
Trimmed Mean ( 43 / 48 )115.1724137931030.175835970686046654.999163958001
Trimmed Mean ( 44 / 48 )115.1785714285710.170612233801741675.089756824905
Trimmed Mean ( 45 / 48 )115.1814814814810.165215359827135697.159644248549
Trimmed Mean ( 46 / 48 )115.1846153846150.159571083641191721.838899356087
Trimmed Mean ( 47 / 48 )115.1880.153639918282313749.727032452218
Trimmed Mean ( 48 / 48 )115.1791666666670.149643735705621769.689196300518
Median114.95
Midrange115
Midmean - Weighted Average at Xnp115.022972972973
Midmean - Weighted Average at X(n+1)p115.131944444444
Midmean - Empirical Distribution Function115.022972972973
Midmean - Empirical Distribution Function - Averaging115.131944444444
Midmean - Empirical Distribution Function - Interpolation115.131944444444
Midmean - Closest Observation115.022972972973
Midmean - True Basic - Statistics Graphics Toolkit115.131944444444
Midmean - MS Excel (old versions)115.068
Number of observations144



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')