Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationTue, 09 Mar 2010 05:31:02 -0700
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2010/Mar/09/t1268138031wog9d7q4r2ys0se.htm/, Retrieved Wed, 19 Jan 2022 10:23:37 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=74186, Retrieved Wed, 19 Jan 2022 10:23:37 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsKDGP1W52
Estimated Impact139
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Central Tendency] [] [2010-03-09 12:18:29] [268ea95fef628aaa77b5f343b7444613]
-    D    [Central Tendency] [] [2010-03-09 12:31:02] [fdb60bd07384c15b1c0e403f5c001d61] [Current]
- RM        [Mean versus Median] [] [2010-03-09 12:36:30] [268ea95fef628aaa77b5f343b7444613]
Feedback Forum

Post a new message
Dataseries X:
40801
49081
52431
59650
75428
78705
68870
70641
80074
76464
69976
92917
92559
73981
71107
96942
86270
69610
57768
80077
71454
70382
69881
84530
79322
80181
82137
88439
91575
82909
73282
94089
108112
95653
85273
105093
102275
99308
79687
93263
114918
103374
65124
104045
101183
95492
85035
90692
107486
98179
82551
106804
110898
89950
65184
95357
98280
92146
77874
100039
104777
102341
71316
88838
85457
70784
70522
88629
88452
98886
79601
108135
113835
101617
68698
79182
86003
84165
68550
90385
100368
99081
81288
103491
111695
82504
62237
78249
92341
84412
75102
90461
106451
98379
72615
98367
116949
95832
68060
83923
87653
78054
57566
78784
88916
84662
63442
77773
88102
87972
61790
95276
104418
95420
82141
104064
96287
78426
59111
76837
76615
65860
57703
68656
77955
65856
60947
69885
80550
73694
67538
76326
84727




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135

\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' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=74186&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' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=74186&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=74186&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' @ 72.249.127.135







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean84133.77443609021321.9302307346363.6446406020497
Geometric Mean82688.6538048968
Harmonic Mean81150.6940789484
Quadratic Mean85493.6368361628
Winsorized Mean ( 1 / 44 )84180.75939849621305.0501613692764.5038496529308
Winsorized Mean ( 2 / 44 )84214.84962406021292.3560058044865.1638165070753
Winsorized Mean ( 3 / 44 )84282.40601503761264.1183650859466.6728752171144
Winsorized Mean ( 4 / 44 )84262.55639097751259.5704276740066.897852267445
Winsorized Mean ( 5 / 44 )84161.12781954891243.2668226401367.6935363245913
Winsorized Mean ( 6 / 44 )84220.67669172931233.5708152363568.273888820556
Winsorized Mean ( 7 / 44 )84216.09774436091224.4384509433868.779363862247
Winsorized Mean ( 8 / 44 )84253.0902255641206.9448635132569.8069089753733
Winsorized Mean ( 9 / 44 )84286.24812030071195.3367946640970.5125521916075
Winsorized Mean ( 10 / 44 )84217.75187969931176.5258562334071.5817263458356
Winsorized Mean ( 11 / 44 )84291.27819548871159.1749722280372.7166132939138
Winsorized Mean ( 12 / 44 )84410.64661654141134.7273709783474.3884820049452
Winsorized Mean ( 13 / 44 )84381.90977443611129.3770269780174.7154473296002
Winsorized Mean ( 14 / 44 )84450.64661654141120.1093254788975.3950035907748
Winsorized Mean ( 15 / 44 )84388.61654135341111.8458612382575.8995643940884
Winsorized Mean ( 16 / 44 )84576.40601503761085.2502387285977.9326306475838
Winsorized Mean ( 17 / 44 )84511.09022556391060.2840512626379.7060845392562
Winsorized Mean ( 18 / 44 )84568.47368421051051.420509494380.4325889789665
Winsorized Mean ( 19 / 44 )84489.61654135341037.7981952514681.4123756698973
Winsorized Mean ( 20 / 44 )84430.66917293231028.9625889883982.0541680295096
Winsorized Mean ( 21 / 44 )84329.14285714291010.1381437745083.4827824064116
Winsorized Mean ( 22 / 44 )84397.1278195489989.58061622805785.285752808338
Winsorized Mean ( 23 / 44 )84317.5789473684969.30824094379586.9873744860254
Winsorized Mean ( 24 / 44 )84277.3383458647964.44548109140587.3842430683516
Winsorized Mean ( 25 / 44 )84257.7894736842958.2622886314887.927690021085
Winsorized Mean ( 26 / 44 )84238.045112782937.9480565741689.8109916880259
Winsorized Mean ( 27 / 44 )84264.030075188934.49619551534690.1705437427907
Winsorized Mean ( 28 / 44 )84270.7669172932929.61682260747990.6510778074373
Winsorized Mean ( 29 / 44 )84279.92481203923.64699601852891.2468997087925
Winsorized Mean ( 30 / 44 )84073.7593984962884.27190399752395.0768185876137
Winsorized Mean ( 31 / 44 )83969.8045112782862.17892775797197.392550209543
Winsorized Mean ( 32 / 44 )83893.5338345865846.71378796342599.0813366065209
Winsorized Mean ( 33 / 44 )84137.1879699248810.395128018912103.822425704367
Winsorized Mean ( 34 / 44 )84266.5413533835787.766697382282106.968905430247
Winsorized Mean ( 35 / 44 )84356.015037594774.336529518084108.939733335445
Winsorized Mean ( 36 / 44 )84416.6466165414764.420086100049110.432271667823
Winsorized Mean ( 37 / 44 )84705.969924812730.288527450953115.989731100494
Winsorized Mean ( 38 / 44 )84459.969924812684.305909934227123.424288317092
Winsorized Mean ( 39 / 44 )84481.0827067669632.618221880623133.541968575652
Winsorized Mean ( 40 / 44 )84418.5263157895617.671324006357136.672244662795
Winsorized Mean ( 41 / 44 )84354.7142857143601.67995442095140.198644920614
Winsorized Mean ( 42 / 44 )84355.977443609587.768356851024143.519086150788
Winsorized Mean ( 43 / 44 )84595.5488721805552.424668329837153.134995089812
Winsorized Mean ( 44 / 44 )84440.060150376529.875440269587159.358320339239
Trimmed Mean ( 1 / 44 )84214.06106870231275.9045482237366.0034178778828
Trimmed Mean ( 2 / 44 )84248.39534883721243.8431982445067.7323278912817
Trimmed Mean ( 3 / 44 )84265.96062992131215.9297665369369.301667702336
Trimmed Mean ( 4 / 44 )84260.1281196.5939773818870.416640558696
Trimmed Mean ( 5 / 44 )84259.47154471541176.727391951171.6049206647659
Trimmed Mean ( 6 / 44 )84281.0909090911159.0678241907972.7145462500713
Trimmed Mean ( 7 / 44 )84292.34453781511141.7564996494773.8269014134746
Trimmed Mean ( 8 / 44 )84304.72649572651124.4428642792774.9746644973043
Trimmed Mean ( 9 / 44 )84312.19130434781108.4670442032976.0619738270591
Trimmed Mean ( 10 / 44 )84315.58407079651092.6887926949077.1634015416672
Trimmed Mean ( 11 / 44 )84327.30630630631078.100407391778.2184161402215
Trimmed Mean ( 12 / 44 )84331.30275229361064.4097727726279.2282304329314
Trimmed Mean ( 13 / 44 )84323.08411214951052.5304386586080.1146275822822
Trimmed Mean ( 14 / 44 )84317.35238095241039.9037698489081.0818797139312
Trimmed Mean ( 15 / 44 )84305.05825242721026.9020457195582.0964946012496
Trimmed Mean ( 16 / 44 )84297.72277227721013.3047208274883.1908911896105
Trimmed Mean ( 17 / 44 )84274.32323232321001.2204648625684.1715947584952
Trimmed Mean ( 18 / 44 )84255.2268041237990.52382371170485.061282512521
Trimmed Mean ( 19 / 44 )84230.8631578947979.3460078278186.007256357453
Trimmed Mean ( 20 / 44 )84211.3870967742968.17278801855586.979708724431
Trimmed Mean ( 21 / 44 )84195.3626373626956.39455364962688.034130177834
Trimmed Mean ( 22 / 44 )84185.8426966292945.04828363483389.0809963410914
Trimmed Mean ( 23 / 44 )84171.1609195402934.29490856783190.0905700626852
Trimmed Mean ( 24 / 44 )84161.2924.13552348684791.0701924783199
Trimmed Mean ( 25 / 44 )84153.4457831325912.84412931422992.1881875346588
Trimmed Mean ( 26 / 44 )84146.5925925926900.3841540872593.4563232933557
Trimmed Mean ( 27 / 44 )84140.670886076888.20515361668494.7311221326103
Trimmed Mean ( 28 / 44 )84132.7792207792874.31176890699296.2274353529022
Trimmed Mean ( 29 / 44 )84124.04858.57774778256897.9806898295064
Trimmed Mean ( 30 / 44 )84114.2465753425840.800883603183100.040625807715
Trimmed Mean ( 31 / 44 )84116.7746478873824.910050872857101.970844650130
Trimmed Mean ( 32 / 44 )84125.9130434783808.889849401698104.001692079215
Trimmed Mean ( 33 / 44 )84140.328358209791.800601697493106.264542080198
Trimmed Mean ( 34 / 44 )84140.5230769231776.300104324901108.386592515139
Trimmed Mean ( 35 / 44 )84132.6984126984760.693133824597110.600049706901
Trimmed Mean ( 36 / 44 )84118.7868852459743.614214905253113.121542325497
Trimmed Mean ( 37 / 44 )84100.1355932203724.205485149759116.127449070383
Trimmed Mean ( 38 / 44 )84061.9298245614705.509782032567119.150622663771
Trimmed Mean ( 39 / 44 )84036.6689.917002571839121.806825584429
Trimmed Mean ( 40 / 44 )84008678.578961589406123.799888819470
Trimmed Mean ( 41 / 44 )83981.2352941177666.490643970774126.005122583237
Trimmed Mean ( 42 / 44 )83956.5102040816653.63501845374128.445551162011
Trimmed Mean ( 43 / 44 )83929.5957446808639.38148351451131.266853840280
Trimmed Mean ( 44 / 44 )83883.8222222222626.976516958219133.791011231466
Median84165
Midrange78875
Midmean - Weighted Average at Xnp83965.893939394
Midmean - Weighted Average at X(n+1)p84140.328358209
Midmean - Empirical Distribution Function84140.328358209
Midmean - Empirical Distribution Function - Averaging84140.328358209
Midmean - Empirical Distribution Function - Interpolation84140.328358209
Midmean - Closest Observation83953.7647058823
Midmean - True Basic - Statistics Graphics Toolkit84140.328358209
Midmean - MS Excel (old versions)84140.328358209
Number of observations133

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 84133.7744360902 & 1321.93023073463 & 63.6446406020497 \tabularnewline
Geometric Mean & 82688.6538048968 &  &  \tabularnewline
Harmonic Mean & 81150.6940789484 &  &  \tabularnewline
Quadratic Mean & 85493.6368361628 &  &  \tabularnewline
Winsorized Mean ( 1 / 44 ) & 84180.7593984962 & 1305.05016136927 & 64.5038496529308 \tabularnewline
Winsorized Mean ( 2 / 44 ) & 84214.8496240602 & 1292.35600580448 & 65.1638165070753 \tabularnewline
Winsorized Mean ( 3 / 44 ) & 84282.4060150376 & 1264.11836508594 & 66.6728752171144 \tabularnewline
Winsorized Mean ( 4 / 44 ) & 84262.5563909775 & 1259.57042767400 & 66.897852267445 \tabularnewline
Winsorized Mean ( 5 / 44 ) & 84161.1278195489 & 1243.26682264013 & 67.6935363245913 \tabularnewline
Winsorized Mean ( 6 / 44 ) & 84220.6766917293 & 1233.57081523635 & 68.273888820556 \tabularnewline
Winsorized Mean ( 7 / 44 ) & 84216.0977443609 & 1224.43845094338 & 68.779363862247 \tabularnewline
Winsorized Mean ( 8 / 44 ) & 84253.090225564 & 1206.94486351325 & 69.8069089753733 \tabularnewline
Winsorized Mean ( 9 / 44 ) & 84286.2481203007 & 1195.33679466409 & 70.5125521916075 \tabularnewline
Winsorized Mean ( 10 / 44 ) & 84217.7518796993 & 1176.52585623340 & 71.5817263458356 \tabularnewline
Winsorized Mean ( 11 / 44 ) & 84291.2781954887 & 1159.17497222803 & 72.7166132939138 \tabularnewline
Winsorized Mean ( 12 / 44 ) & 84410.6466165414 & 1134.72737097834 & 74.3884820049452 \tabularnewline
Winsorized Mean ( 13 / 44 ) & 84381.9097744361 & 1129.37702697801 & 74.7154473296002 \tabularnewline
Winsorized Mean ( 14 / 44 ) & 84450.6466165414 & 1120.10932547889 & 75.3950035907748 \tabularnewline
Winsorized Mean ( 15 / 44 ) & 84388.6165413534 & 1111.84586123825 & 75.8995643940884 \tabularnewline
Winsorized Mean ( 16 / 44 ) & 84576.4060150376 & 1085.25023872859 & 77.9326306475838 \tabularnewline
Winsorized Mean ( 17 / 44 ) & 84511.0902255639 & 1060.28405126263 & 79.7060845392562 \tabularnewline
Winsorized Mean ( 18 / 44 ) & 84568.4736842105 & 1051.4205094943 & 80.4325889789665 \tabularnewline
Winsorized Mean ( 19 / 44 ) & 84489.6165413534 & 1037.79819525146 & 81.4123756698973 \tabularnewline
Winsorized Mean ( 20 / 44 ) & 84430.6691729323 & 1028.96258898839 & 82.0541680295096 \tabularnewline
Winsorized Mean ( 21 / 44 ) & 84329.1428571429 & 1010.13814377450 & 83.4827824064116 \tabularnewline
Winsorized Mean ( 22 / 44 ) & 84397.1278195489 & 989.580616228057 & 85.285752808338 \tabularnewline
Winsorized Mean ( 23 / 44 ) & 84317.5789473684 & 969.308240943795 & 86.9873744860254 \tabularnewline
Winsorized Mean ( 24 / 44 ) & 84277.3383458647 & 964.445481091405 & 87.3842430683516 \tabularnewline
Winsorized Mean ( 25 / 44 ) & 84257.7894736842 & 958.26228863148 & 87.927690021085 \tabularnewline
Winsorized Mean ( 26 / 44 ) & 84238.045112782 & 937.94805657416 & 89.8109916880259 \tabularnewline
Winsorized Mean ( 27 / 44 ) & 84264.030075188 & 934.496195515346 & 90.1705437427907 \tabularnewline
Winsorized Mean ( 28 / 44 ) & 84270.7669172932 & 929.616822607479 & 90.6510778074373 \tabularnewline
Winsorized Mean ( 29 / 44 ) & 84279.92481203 & 923.646996018528 & 91.2468997087925 \tabularnewline
Winsorized Mean ( 30 / 44 ) & 84073.7593984962 & 884.271903997523 & 95.0768185876137 \tabularnewline
Winsorized Mean ( 31 / 44 ) & 83969.8045112782 & 862.178927757971 & 97.392550209543 \tabularnewline
Winsorized Mean ( 32 / 44 ) & 83893.5338345865 & 846.713787963425 & 99.0813366065209 \tabularnewline
Winsorized Mean ( 33 / 44 ) & 84137.1879699248 & 810.395128018912 & 103.822425704367 \tabularnewline
Winsorized Mean ( 34 / 44 ) & 84266.5413533835 & 787.766697382282 & 106.968905430247 \tabularnewline
Winsorized Mean ( 35 / 44 ) & 84356.015037594 & 774.336529518084 & 108.939733335445 \tabularnewline
Winsorized Mean ( 36 / 44 ) & 84416.6466165414 & 764.420086100049 & 110.432271667823 \tabularnewline
Winsorized Mean ( 37 / 44 ) & 84705.969924812 & 730.288527450953 & 115.989731100494 \tabularnewline
Winsorized Mean ( 38 / 44 ) & 84459.969924812 & 684.305909934227 & 123.424288317092 \tabularnewline
Winsorized Mean ( 39 / 44 ) & 84481.0827067669 & 632.618221880623 & 133.541968575652 \tabularnewline
Winsorized Mean ( 40 / 44 ) & 84418.5263157895 & 617.671324006357 & 136.672244662795 \tabularnewline
Winsorized Mean ( 41 / 44 ) & 84354.7142857143 & 601.67995442095 & 140.198644920614 \tabularnewline
Winsorized Mean ( 42 / 44 ) & 84355.977443609 & 587.768356851024 & 143.519086150788 \tabularnewline
Winsorized Mean ( 43 / 44 ) & 84595.5488721805 & 552.424668329837 & 153.134995089812 \tabularnewline
Winsorized Mean ( 44 / 44 ) & 84440.060150376 & 529.875440269587 & 159.358320339239 \tabularnewline
Trimmed Mean ( 1 / 44 ) & 84214.0610687023 & 1275.90454822373 & 66.0034178778828 \tabularnewline
Trimmed Mean ( 2 / 44 ) & 84248.3953488372 & 1243.84319824450 & 67.7323278912817 \tabularnewline
Trimmed Mean ( 3 / 44 ) & 84265.9606299213 & 1215.92976653693 & 69.301667702336 \tabularnewline
Trimmed Mean ( 4 / 44 ) & 84260.128 & 1196.59397738188 & 70.416640558696 \tabularnewline
Trimmed Mean ( 5 / 44 ) & 84259.4715447154 & 1176.7273919511 & 71.6049206647659 \tabularnewline
Trimmed Mean ( 6 / 44 ) & 84281.090909091 & 1159.06782419079 & 72.7145462500713 \tabularnewline
Trimmed Mean ( 7 / 44 ) & 84292.3445378151 & 1141.75649964947 & 73.8269014134746 \tabularnewline
Trimmed Mean ( 8 / 44 ) & 84304.7264957265 & 1124.44286427927 & 74.9746644973043 \tabularnewline
Trimmed Mean ( 9 / 44 ) & 84312.1913043478 & 1108.46704420329 & 76.0619738270591 \tabularnewline
Trimmed Mean ( 10 / 44 ) & 84315.5840707965 & 1092.68879269490 & 77.1634015416672 \tabularnewline
Trimmed Mean ( 11 / 44 ) & 84327.3063063063 & 1078.1004073917 & 78.2184161402215 \tabularnewline
Trimmed Mean ( 12 / 44 ) & 84331.3027522936 & 1064.40977277262 & 79.2282304329314 \tabularnewline
Trimmed Mean ( 13 / 44 ) & 84323.0841121495 & 1052.53043865860 & 80.1146275822822 \tabularnewline
Trimmed Mean ( 14 / 44 ) & 84317.3523809524 & 1039.90376984890 & 81.0818797139312 \tabularnewline
Trimmed Mean ( 15 / 44 ) & 84305.0582524272 & 1026.90204571955 & 82.0964946012496 \tabularnewline
Trimmed Mean ( 16 / 44 ) & 84297.7227722772 & 1013.30472082748 & 83.1908911896105 \tabularnewline
Trimmed Mean ( 17 / 44 ) & 84274.3232323232 & 1001.22046486256 & 84.1715947584952 \tabularnewline
Trimmed Mean ( 18 / 44 ) & 84255.2268041237 & 990.523823711704 & 85.061282512521 \tabularnewline
Trimmed Mean ( 19 / 44 ) & 84230.8631578947 & 979.34600782781 & 86.007256357453 \tabularnewline
Trimmed Mean ( 20 / 44 ) & 84211.3870967742 & 968.172788018555 & 86.979708724431 \tabularnewline
Trimmed Mean ( 21 / 44 ) & 84195.3626373626 & 956.394553649626 & 88.034130177834 \tabularnewline
Trimmed Mean ( 22 / 44 ) & 84185.8426966292 & 945.048283634833 & 89.0809963410914 \tabularnewline
Trimmed Mean ( 23 / 44 ) & 84171.1609195402 & 934.294908567831 & 90.0905700626852 \tabularnewline
Trimmed Mean ( 24 / 44 ) & 84161.2 & 924.135523486847 & 91.0701924783199 \tabularnewline
Trimmed Mean ( 25 / 44 ) & 84153.4457831325 & 912.844129314229 & 92.1881875346588 \tabularnewline
Trimmed Mean ( 26 / 44 ) & 84146.5925925926 & 900.38415408725 & 93.4563232933557 \tabularnewline
Trimmed Mean ( 27 / 44 ) & 84140.670886076 & 888.205153616684 & 94.7311221326103 \tabularnewline
Trimmed Mean ( 28 / 44 ) & 84132.7792207792 & 874.311768906992 & 96.2274353529022 \tabularnewline
Trimmed Mean ( 29 / 44 ) & 84124.04 & 858.577747782568 & 97.9806898295064 \tabularnewline
Trimmed Mean ( 30 / 44 ) & 84114.2465753425 & 840.800883603183 & 100.040625807715 \tabularnewline
Trimmed Mean ( 31 / 44 ) & 84116.7746478873 & 824.910050872857 & 101.970844650130 \tabularnewline
Trimmed Mean ( 32 / 44 ) & 84125.9130434783 & 808.889849401698 & 104.001692079215 \tabularnewline
Trimmed Mean ( 33 / 44 ) & 84140.328358209 & 791.800601697493 & 106.264542080198 \tabularnewline
Trimmed Mean ( 34 / 44 ) & 84140.5230769231 & 776.300104324901 & 108.386592515139 \tabularnewline
Trimmed Mean ( 35 / 44 ) & 84132.6984126984 & 760.693133824597 & 110.600049706901 \tabularnewline
Trimmed Mean ( 36 / 44 ) & 84118.7868852459 & 743.614214905253 & 113.121542325497 \tabularnewline
Trimmed Mean ( 37 / 44 ) & 84100.1355932203 & 724.205485149759 & 116.127449070383 \tabularnewline
Trimmed Mean ( 38 / 44 ) & 84061.9298245614 & 705.509782032567 & 119.150622663771 \tabularnewline
Trimmed Mean ( 39 / 44 ) & 84036.6 & 689.917002571839 & 121.806825584429 \tabularnewline
Trimmed Mean ( 40 / 44 ) & 84008 & 678.578961589406 & 123.799888819470 \tabularnewline
Trimmed Mean ( 41 / 44 ) & 83981.2352941177 & 666.490643970774 & 126.005122583237 \tabularnewline
Trimmed Mean ( 42 / 44 ) & 83956.5102040816 & 653.63501845374 & 128.445551162011 \tabularnewline
Trimmed Mean ( 43 / 44 ) & 83929.5957446808 & 639.38148351451 & 131.266853840280 \tabularnewline
Trimmed Mean ( 44 / 44 ) & 83883.8222222222 & 626.976516958219 & 133.791011231466 \tabularnewline
Median & 84165 &  &  \tabularnewline
Midrange & 78875 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 83965.893939394 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 84140.328358209 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 84140.328358209 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 84140.328358209 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 84140.328358209 &  &  \tabularnewline
Midmean - Closest Observation & 83953.7647058823 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 84140.328358209 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 84140.328358209 &  &  \tabularnewline
Number of observations & 133 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=74186&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]84133.7744360902[/C][C]1321.93023073463[/C][C]63.6446406020497[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]82688.6538048968[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]81150.6940789484[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]85493.6368361628[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 44 )[/C][C]84180.7593984962[/C][C]1305.05016136927[/C][C]64.5038496529308[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 44 )[/C][C]84214.8496240602[/C][C]1292.35600580448[/C][C]65.1638165070753[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 44 )[/C][C]84282.4060150376[/C][C]1264.11836508594[/C][C]66.6728752171144[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 44 )[/C][C]84262.5563909775[/C][C]1259.57042767400[/C][C]66.897852267445[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 44 )[/C][C]84161.1278195489[/C][C]1243.26682264013[/C][C]67.6935363245913[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 44 )[/C][C]84220.6766917293[/C][C]1233.57081523635[/C][C]68.273888820556[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 44 )[/C][C]84216.0977443609[/C][C]1224.43845094338[/C][C]68.779363862247[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 44 )[/C][C]84253.090225564[/C][C]1206.94486351325[/C][C]69.8069089753733[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 44 )[/C][C]84286.2481203007[/C][C]1195.33679466409[/C][C]70.5125521916075[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 44 )[/C][C]84217.7518796993[/C][C]1176.52585623340[/C][C]71.5817263458356[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 44 )[/C][C]84291.2781954887[/C][C]1159.17497222803[/C][C]72.7166132939138[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 44 )[/C][C]84410.6466165414[/C][C]1134.72737097834[/C][C]74.3884820049452[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 44 )[/C][C]84381.9097744361[/C][C]1129.37702697801[/C][C]74.7154473296002[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 44 )[/C][C]84450.6466165414[/C][C]1120.10932547889[/C][C]75.3950035907748[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 44 )[/C][C]84388.6165413534[/C][C]1111.84586123825[/C][C]75.8995643940884[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 44 )[/C][C]84576.4060150376[/C][C]1085.25023872859[/C][C]77.9326306475838[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 44 )[/C][C]84511.0902255639[/C][C]1060.28405126263[/C][C]79.7060845392562[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 44 )[/C][C]84568.4736842105[/C][C]1051.4205094943[/C][C]80.4325889789665[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 44 )[/C][C]84489.6165413534[/C][C]1037.79819525146[/C][C]81.4123756698973[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 44 )[/C][C]84430.6691729323[/C][C]1028.96258898839[/C][C]82.0541680295096[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 44 )[/C][C]84329.1428571429[/C][C]1010.13814377450[/C][C]83.4827824064116[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 44 )[/C][C]84397.1278195489[/C][C]989.580616228057[/C][C]85.285752808338[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 44 )[/C][C]84317.5789473684[/C][C]969.308240943795[/C][C]86.9873744860254[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 44 )[/C][C]84277.3383458647[/C][C]964.445481091405[/C][C]87.3842430683516[/C][/ROW]
[ROW][C]Winsorized Mean ( 25 / 44 )[/C][C]84257.7894736842[/C][C]958.26228863148[/C][C]87.927690021085[/C][/ROW]
[ROW][C]Winsorized Mean ( 26 / 44 )[/C][C]84238.045112782[/C][C]937.94805657416[/C][C]89.8109916880259[/C][/ROW]
[ROW][C]Winsorized Mean ( 27 / 44 )[/C][C]84264.030075188[/C][C]934.496195515346[/C][C]90.1705437427907[/C][/ROW]
[ROW][C]Winsorized Mean ( 28 / 44 )[/C][C]84270.7669172932[/C][C]929.616822607479[/C][C]90.6510778074373[/C][/ROW]
[ROW][C]Winsorized Mean ( 29 / 44 )[/C][C]84279.92481203[/C][C]923.646996018528[/C][C]91.2468997087925[/C][/ROW]
[ROW][C]Winsorized Mean ( 30 / 44 )[/C][C]84073.7593984962[/C][C]884.271903997523[/C][C]95.0768185876137[/C][/ROW]
[ROW][C]Winsorized Mean ( 31 / 44 )[/C][C]83969.8045112782[/C][C]862.178927757971[/C][C]97.392550209543[/C][/ROW]
[ROW][C]Winsorized Mean ( 32 / 44 )[/C][C]83893.5338345865[/C][C]846.713787963425[/C][C]99.0813366065209[/C][/ROW]
[ROW][C]Winsorized Mean ( 33 / 44 )[/C][C]84137.1879699248[/C][C]810.395128018912[/C][C]103.822425704367[/C][/ROW]
[ROW][C]Winsorized Mean ( 34 / 44 )[/C][C]84266.5413533835[/C][C]787.766697382282[/C][C]106.968905430247[/C][/ROW]
[ROW][C]Winsorized Mean ( 35 / 44 )[/C][C]84356.015037594[/C][C]774.336529518084[/C][C]108.939733335445[/C][/ROW]
[ROW][C]Winsorized Mean ( 36 / 44 )[/C][C]84416.6466165414[/C][C]764.420086100049[/C][C]110.432271667823[/C][/ROW]
[ROW][C]Winsorized Mean ( 37 / 44 )[/C][C]84705.969924812[/C][C]730.288527450953[/C][C]115.989731100494[/C][/ROW]
[ROW][C]Winsorized Mean ( 38 / 44 )[/C][C]84459.969924812[/C][C]684.305909934227[/C][C]123.424288317092[/C][/ROW]
[ROW][C]Winsorized Mean ( 39 / 44 )[/C][C]84481.0827067669[/C][C]632.618221880623[/C][C]133.541968575652[/C][/ROW]
[ROW][C]Winsorized Mean ( 40 / 44 )[/C][C]84418.5263157895[/C][C]617.671324006357[/C][C]136.672244662795[/C][/ROW]
[ROW][C]Winsorized Mean ( 41 / 44 )[/C][C]84354.7142857143[/C][C]601.67995442095[/C][C]140.198644920614[/C][/ROW]
[ROW][C]Winsorized Mean ( 42 / 44 )[/C][C]84355.977443609[/C][C]587.768356851024[/C][C]143.519086150788[/C][/ROW]
[ROW][C]Winsorized Mean ( 43 / 44 )[/C][C]84595.5488721805[/C][C]552.424668329837[/C][C]153.134995089812[/C][/ROW]
[ROW][C]Winsorized Mean ( 44 / 44 )[/C][C]84440.060150376[/C][C]529.875440269587[/C][C]159.358320339239[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 44 )[/C][C]84214.0610687023[/C][C]1275.90454822373[/C][C]66.0034178778828[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 44 )[/C][C]84248.3953488372[/C][C]1243.84319824450[/C][C]67.7323278912817[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 44 )[/C][C]84265.9606299213[/C][C]1215.92976653693[/C][C]69.301667702336[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 44 )[/C][C]84260.128[/C][C]1196.59397738188[/C][C]70.416640558696[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 44 )[/C][C]84259.4715447154[/C][C]1176.7273919511[/C][C]71.6049206647659[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 44 )[/C][C]84281.090909091[/C][C]1159.06782419079[/C][C]72.7145462500713[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 44 )[/C][C]84292.3445378151[/C][C]1141.75649964947[/C][C]73.8269014134746[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 44 )[/C][C]84304.7264957265[/C][C]1124.44286427927[/C][C]74.9746644973043[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 44 )[/C][C]84312.1913043478[/C][C]1108.46704420329[/C][C]76.0619738270591[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 44 )[/C][C]84315.5840707965[/C][C]1092.68879269490[/C][C]77.1634015416672[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 44 )[/C][C]84327.3063063063[/C][C]1078.1004073917[/C][C]78.2184161402215[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 44 )[/C][C]84331.3027522936[/C][C]1064.40977277262[/C][C]79.2282304329314[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 44 )[/C][C]84323.0841121495[/C][C]1052.53043865860[/C][C]80.1146275822822[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 44 )[/C][C]84317.3523809524[/C][C]1039.90376984890[/C][C]81.0818797139312[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 44 )[/C][C]84305.0582524272[/C][C]1026.90204571955[/C][C]82.0964946012496[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 44 )[/C][C]84297.7227722772[/C][C]1013.30472082748[/C][C]83.1908911896105[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 44 )[/C][C]84274.3232323232[/C][C]1001.22046486256[/C][C]84.1715947584952[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 44 )[/C][C]84255.2268041237[/C][C]990.523823711704[/C][C]85.061282512521[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 44 )[/C][C]84230.8631578947[/C][C]979.34600782781[/C][C]86.007256357453[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 44 )[/C][C]84211.3870967742[/C][C]968.172788018555[/C][C]86.979708724431[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 44 )[/C][C]84195.3626373626[/C][C]956.394553649626[/C][C]88.034130177834[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 44 )[/C][C]84185.8426966292[/C][C]945.048283634833[/C][C]89.0809963410914[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 44 )[/C][C]84171.1609195402[/C][C]934.294908567831[/C][C]90.0905700626852[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 44 )[/C][C]84161.2[/C][C]924.135523486847[/C][C]91.0701924783199[/C][/ROW]
[ROW][C]Trimmed Mean ( 25 / 44 )[/C][C]84153.4457831325[/C][C]912.844129314229[/C][C]92.1881875346588[/C][/ROW]
[ROW][C]Trimmed Mean ( 26 / 44 )[/C][C]84146.5925925926[/C][C]900.38415408725[/C][C]93.4563232933557[/C][/ROW]
[ROW][C]Trimmed Mean ( 27 / 44 )[/C][C]84140.670886076[/C][C]888.205153616684[/C][C]94.7311221326103[/C][/ROW]
[ROW][C]Trimmed Mean ( 28 / 44 )[/C][C]84132.7792207792[/C][C]874.311768906992[/C][C]96.2274353529022[/C][/ROW]
[ROW][C]Trimmed Mean ( 29 / 44 )[/C][C]84124.04[/C][C]858.577747782568[/C][C]97.9806898295064[/C][/ROW]
[ROW][C]Trimmed Mean ( 30 / 44 )[/C][C]84114.2465753425[/C][C]840.800883603183[/C][C]100.040625807715[/C][/ROW]
[ROW][C]Trimmed Mean ( 31 / 44 )[/C][C]84116.7746478873[/C][C]824.910050872857[/C][C]101.970844650130[/C][/ROW]
[ROW][C]Trimmed Mean ( 32 / 44 )[/C][C]84125.9130434783[/C][C]808.889849401698[/C][C]104.001692079215[/C][/ROW]
[ROW][C]Trimmed Mean ( 33 / 44 )[/C][C]84140.328358209[/C][C]791.800601697493[/C][C]106.264542080198[/C][/ROW]
[ROW][C]Trimmed Mean ( 34 / 44 )[/C][C]84140.5230769231[/C][C]776.300104324901[/C][C]108.386592515139[/C][/ROW]
[ROW][C]Trimmed Mean ( 35 / 44 )[/C][C]84132.6984126984[/C][C]760.693133824597[/C][C]110.600049706901[/C][/ROW]
[ROW][C]Trimmed Mean ( 36 / 44 )[/C][C]84118.7868852459[/C][C]743.614214905253[/C][C]113.121542325497[/C][/ROW]
[ROW][C]Trimmed Mean ( 37 / 44 )[/C][C]84100.1355932203[/C][C]724.205485149759[/C][C]116.127449070383[/C][/ROW]
[ROW][C]Trimmed Mean ( 38 / 44 )[/C][C]84061.9298245614[/C][C]705.509782032567[/C][C]119.150622663771[/C][/ROW]
[ROW][C]Trimmed Mean ( 39 / 44 )[/C][C]84036.6[/C][C]689.917002571839[/C][C]121.806825584429[/C][/ROW]
[ROW][C]Trimmed Mean ( 40 / 44 )[/C][C]84008[/C][C]678.578961589406[/C][C]123.799888819470[/C][/ROW]
[ROW][C]Trimmed Mean ( 41 / 44 )[/C][C]83981.2352941177[/C][C]666.490643970774[/C][C]126.005122583237[/C][/ROW]
[ROW][C]Trimmed Mean ( 42 / 44 )[/C][C]83956.5102040816[/C][C]653.63501845374[/C][C]128.445551162011[/C][/ROW]
[ROW][C]Trimmed Mean ( 43 / 44 )[/C][C]83929.5957446808[/C][C]639.38148351451[/C][C]131.266853840280[/C][/ROW]
[ROW][C]Trimmed Mean ( 44 / 44 )[/C][C]83883.8222222222[/C][C]626.976516958219[/C][C]133.791011231466[/C][/ROW]
[ROW][C]Median[/C][C]84165[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]78875[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]83965.893939394[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]84140.328358209[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]84140.328358209[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]84140.328358209[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]84140.328358209[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]83953.7647058823[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]84140.328358209[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]84140.328358209[/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=74186&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=74186&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 Mean84133.77443609021321.9302307346363.6446406020497
Geometric Mean82688.6538048968
Harmonic Mean81150.6940789484
Quadratic Mean85493.6368361628
Winsorized Mean ( 1 / 44 )84180.75939849621305.0501613692764.5038496529308
Winsorized Mean ( 2 / 44 )84214.84962406021292.3560058044865.1638165070753
Winsorized Mean ( 3 / 44 )84282.40601503761264.1183650859466.6728752171144
Winsorized Mean ( 4 / 44 )84262.55639097751259.5704276740066.897852267445
Winsorized Mean ( 5 / 44 )84161.12781954891243.2668226401367.6935363245913
Winsorized Mean ( 6 / 44 )84220.67669172931233.5708152363568.273888820556
Winsorized Mean ( 7 / 44 )84216.09774436091224.4384509433868.779363862247
Winsorized Mean ( 8 / 44 )84253.0902255641206.9448635132569.8069089753733
Winsorized Mean ( 9 / 44 )84286.24812030071195.3367946640970.5125521916075
Winsorized Mean ( 10 / 44 )84217.75187969931176.5258562334071.5817263458356
Winsorized Mean ( 11 / 44 )84291.27819548871159.1749722280372.7166132939138
Winsorized Mean ( 12 / 44 )84410.64661654141134.7273709783474.3884820049452
Winsorized Mean ( 13 / 44 )84381.90977443611129.3770269780174.7154473296002
Winsorized Mean ( 14 / 44 )84450.64661654141120.1093254788975.3950035907748
Winsorized Mean ( 15 / 44 )84388.61654135341111.8458612382575.8995643940884
Winsorized Mean ( 16 / 44 )84576.40601503761085.2502387285977.9326306475838
Winsorized Mean ( 17 / 44 )84511.09022556391060.2840512626379.7060845392562
Winsorized Mean ( 18 / 44 )84568.47368421051051.420509494380.4325889789665
Winsorized Mean ( 19 / 44 )84489.61654135341037.7981952514681.4123756698973
Winsorized Mean ( 20 / 44 )84430.66917293231028.9625889883982.0541680295096
Winsorized Mean ( 21 / 44 )84329.14285714291010.1381437745083.4827824064116
Winsorized Mean ( 22 / 44 )84397.1278195489989.58061622805785.285752808338
Winsorized Mean ( 23 / 44 )84317.5789473684969.30824094379586.9873744860254
Winsorized Mean ( 24 / 44 )84277.3383458647964.44548109140587.3842430683516
Winsorized Mean ( 25 / 44 )84257.7894736842958.2622886314887.927690021085
Winsorized Mean ( 26 / 44 )84238.045112782937.9480565741689.8109916880259
Winsorized Mean ( 27 / 44 )84264.030075188934.49619551534690.1705437427907
Winsorized Mean ( 28 / 44 )84270.7669172932929.61682260747990.6510778074373
Winsorized Mean ( 29 / 44 )84279.92481203923.64699601852891.2468997087925
Winsorized Mean ( 30 / 44 )84073.7593984962884.27190399752395.0768185876137
Winsorized Mean ( 31 / 44 )83969.8045112782862.17892775797197.392550209543
Winsorized Mean ( 32 / 44 )83893.5338345865846.71378796342599.0813366065209
Winsorized Mean ( 33 / 44 )84137.1879699248810.395128018912103.822425704367
Winsorized Mean ( 34 / 44 )84266.5413533835787.766697382282106.968905430247
Winsorized Mean ( 35 / 44 )84356.015037594774.336529518084108.939733335445
Winsorized Mean ( 36 / 44 )84416.6466165414764.420086100049110.432271667823
Winsorized Mean ( 37 / 44 )84705.969924812730.288527450953115.989731100494
Winsorized Mean ( 38 / 44 )84459.969924812684.305909934227123.424288317092
Winsorized Mean ( 39 / 44 )84481.0827067669632.618221880623133.541968575652
Winsorized Mean ( 40 / 44 )84418.5263157895617.671324006357136.672244662795
Winsorized Mean ( 41 / 44 )84354.7142857143601.67995442095140.198644920614
Winsorized Mean ( 42 / 44 )84355.977443609587.768356851024143.519086150788
Winsorized Mean ( 43 / 44 )84595.5488721805552.424668329837153.134995089812
Winsorized Mean ( 44 / 44 )84440.060150376529.875440269587159.358320339239
Trimmed Mean ( 1 / 44 )84214.06106870231275.9045482237366.0034178778828
Trimmed Mean ( 2 / 44 )84248.39534883721243.8431982445067.7323278912817
Trimmed Mean ( 3 / 44 )84265.96062992131215.9297665369369.301667702336
Trimmed Mean ( 4 / 44 )84260.1281196.5939773818870.416640558696
Trimmed Mean ( 5 / 44 )84259.47154471541176.727391951171.6049206647659
Trimmed Mean ( 6 / 44 )84281.0909090911159.0678241907972.7145462500713
Trimmed Mean ( 7 / 44 )84292.34453781511141.7564996494773.8269014134746
Trimmed Mean ( 8 / 44 )84304.72649572651124.4428642792774.9746644973043
Trimmed Mean ( 9 / 44 )84312.19130434781108.4670442032976.0619738270591
Trimmed Mean ( 10 / 44 )84315.58407079651092.6887926949077.1634015416672
Trimmed Mean ( 11 / 44 )84327.30630630631078.100407391778.2184161402215
Trimmed Mean ( 12 / 44 )84331.30275229361064.4097727726279.2282304329314
Trimmed Mean ( 13 / 44 )84323.08411214951052.5304386586080.1146275822822
Trimmed Mean ( 14 / 44 )84317.35238095241039.9037698489081.0818797139312
Trimmed Mean ( 15 / 44 )84305.05825242721026.9020457195582.0964946012496
Trimmed Mean ( 16 / 44 )84297.72277227721013.3047208274883.1908911896105
Trimmed Mean ( 17 / 44 )84274.32323232321001.2204648625684.1715947584952
Trimmed Mean ( 18 / 44 )84255.2268041237990.52382371170485.061282512521
Trimmed Mean ( 19 / 44 )84230.8631578947979.3460078278186.007256357453
Trimmed Mean ( 20 / 44 )84211.3870967742968.17278801855586.979708724431
Trimmed Mean ( 21 / 44 )84195.3626373626956.39455364962688.034130177834
Trimmed Mean ( 22 / 44 )84185.8426966292945.04828363483389.0809963410914
Trimmed Mean ( 23 / 44 )84171.1609195402934.29490856783190.0905700626852
Trimmed Mean ( 24 / 44 )84161.2924.13552348684791.0701924783199
Trimmed Mean ( 25 / 44 )84153.4457831325912.84412931422992.1881875346588
Trimmed Mean ( 26 / 44 )84146.5925925926900.3841540872593.4563232933557
Trimmed Mean ( 27 / 44 )84140.670886076888.20515361668494.7311221326103
Trimmed Mean ( 28 / 44 )84132.7792207792874.31176890699296.2274353529022
Trimmed Mean ( 29 / 44 )84124.04858.57774778256897.9806898295064
Trimmed Mean ( 30 / 44 )84114.2465753425840.800883603183100.040625807715
Trimmed Mean ( 31 / 44 )84116.7746478873824.910050872857101.970844650130
Trimmed Mean ( 32 / 44 )84125.9130434783808.889849401698104.001692079215
Trimmed Mean ( 33 / 44 )84140.328358209791.800601697493106.264542080198
Trimmed Mean ( 34 / 44 )84140.5230769231776.300104324901108.386592515139
Trimmed Mean ( 35 / 44 )84132.6984126984760.693133824597110.600049706901
Trimmed Mean ( 36 / 44 )84118.7868852459743.614214905253113.121542325497
Trimmed Mean ( 37 / 44 )84100.1355932203724.205485149759116.127449070383
Trimmed Mean ( 38 / 44 )84061.9298245614705.509782032567119.150622663771
Trimmed Mean ( 39 / 44 )84036.6689.917002571839121.806825584429
Trimmed Mean ( 40 / 44 )84008678.578961589406123.799888819470
Trimmed Mean ( 41 / 44 )83981.2352941177666.490643970774126.005122583237
Trimmed Mean ( 42 / 44 )83956.5102040816653.63501845374128.445551162011
Trimmed Mean ( 43 / 44 )83929.5957446808639.38148351451131.266853840280
Trimmed Mean ( 44 / 44 )83883.8222222222626.976516958219133.791011231466
Median84165
Midrange78875
Midmean - Weighted Average at Xnp83965.893939394
Midmean - Weighted Average at X(n+1)p84140.328358209
Midmean - Empirical Distribution Function84140.328358209
Midmean - Empirical Distribution Function - Averaging84140.328358209
Midmean - Empirical Distribution Function - Interpolation84140.328358209
Midmean - Closest Observation83953.7647058823
Midmean - True Basic - Statistics Graphics Toolkit84140.328358209
Midmean - MS Excel (old versions)84140.328358209
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')