Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationTue, 15 Oct 2013 09:14:45 -0400
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2013/Oct/15/t1381842894buk4tcj5of81ov6.htm/, Retrieved Wed, 01 May 2024 15:01:59 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=215883, Retrieved Wed, 01 May 2024 15:01:59 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact75
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [] [2013-10-15 13:14:45] [f6b0814d1ccce07ea30140b42d9cb647] [Current]
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Dataseries X:
58608
46865
51378
46235
47206
45382
41227
33795
31295
42625
33625
21538
56421
53152
53536
52408
41454
38271
35306
26414
31917
38030
27534
18387
50556
43901
48572
43899
37532
40357
35489
29027
34485
42598
30306
26451
47460
50104
61465
53726
39477
43895
31481
29896
33842
39120
33702
25094
51442
45594
52518
48564
41745
49585
32747
33379
35645
37034
35681
20972
58552
54955
65540
51570
51145
46641
35704
33253
35193
41668
34865
21210
56126
49231
59723
48103
47472
50497
40059
34149
36860
46356
36577
23872
57276
56389
57657
62300
48929
51168
39636
33213
38127
43291
30600
21956
48033
46148
50736
48114
38390
44112
36287
30333
35908
40005
35263
26591
49771
47882
64830
57846
48188
54400
39778
37772
37214
43829
40701
29450
53597
53588
64172
53955
55509
48908
35331
38073
41776
42717
40736
49020
45099
44114
60487
48760
41281
48346
37025
31514
33977
42060
36036
22012




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

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 2 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=215883&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' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=215883&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=215883&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' @ jenkins.wessa.net







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean42426.9930555556856.62398119193549.5281406860934
Geometric Mean41100.0168903946
Harmonic Mean39663.9780561291
Quadratic Mean43646.1201482223
Winsorized Mean ( 1 / 48 )42440.0138888889852.36313747263549.7910010687803
Winsorized Mean ( 2 / 48 )42434.1805555556850.12700309546249.915107273437
Winsorized Mean ( 3 / 48 )42402.0138888889842.22888472687250.3450008160662
Winsorized Mean ( 4 / 48 )42390.4305555556836.46571696269950.6780250474341
Winsorized Mean ( 5 / 48 )42358.4166666667830.83434735964450.982986923061
Winsorized Mean ( 6 / 48 )42404.0833333333813.21842295198752.143535041184
Winsorized Mean ( 7 / 48 )42409.2847222222796.07088295327953.2732519557699
Winsorized Mean ( 8 / 48 )42479.5069444444784.79831987241554.1279279896399
Winsorized Mean ( 9 / 48 )42437.6944444444778.25198903569354.5295033515142
Winsorized Mean ( 10 / 48 )42434.2916666667775.04883852902254.7504744955213
Winsorized Mean ( 11 / 48 )42477.2222222222760.97449526518255.8195083889374
Winsorized Mean ( 12 / 48 )42530.3888888889734.87261918303457.8745047490957
Winsorized Mean ( 13 / 48 )42565.6875729.636475120658.3382121802017
Winsorized Mean ( 14 / 48 )42583.4791666667720.86893487468459.0724292676995
Winsorized Mean ( 15 / 48 )42561.9166666667707.31660373800560.1737841890559
Winsorized Mean ( 16 / 48 )42503.3611111111699.17897882165960.7903875810782
Winsorized Mean ( 17 / 48 )42469.3611111111687.29951287437261.7916356924202
Winsorized Mean ( 18 / 48 )42500.6111111111670.27287176307163.4079237002662
Winsorized Mean ( 19 / 48 )42494.9375663.82156147835564.0156029360695
Winsorized Mean ( 20 / 48 )42481.6041666667661.17676183771564.251508248098
Winsorized Mean ( 21 / 48 )42539.0625654.27689331753865.0169109355275
Winsorized Mean ( 22 / 48 )42657.9236111111639.2592716441866.7302384232841
Winsorized Mean ( 23 / 48 )42671.0208333333624.02725517163368.3800594921083
Winsorized Mean ( 24 / 48 )42572.0208333333611.09785018827869.6648185232807
Winsorized Mean ( 25 / 48 )42574.7986111111606.60273872780770.1856353309594
Winsorized Mean ( 26 / 48 )42467.9097222222585.08878111815372.5837019829068
Winsorized Mean ( 27 / 48 )42458.3472222222580.96184407374473.082849855511
Winsorized Mean ( 28 / 48 )42463.9861111111577.71583234621873.503241098061
Winsorized Mean ( 29 / 48 )42431.1597222222572.18273754631774.1566582455443
Winsorized Mean ( 30 / 48 )42454.4930555556568.72883363506374.6480405858891
Winsorized Mean ( 31 / 48 )42403.4722222222555.55241500180776.3266814744821
Winsorized Mean ( 32 / 48 )42438.1388888889543.66741954444678.0590069650466
Winsorized Mean ( 33 / 48 )42511.7013888889533.43395649699979.6944042858809
Winsorized Mean ( 34 / 48 )42496.3541666667516.07862020884982.3447290830785
Winsorized Mean ( 35 / 48 )42432.4305555556506.1182570676783.8389644376772
Winsorized Mean ( 36 / 48 )42396.6805555556500.35978078047684.7323909396234
Winsorized Mean ( 37 / 48 )42312.1458333333490.66752178596686.2338425810671
Winsorized Mean ( 38 / 48 )42298.1597222222481.06386799634887.9262869988467
Winsorized Mean ( 39 / 48 )42315.7638888889474.49073771503889.1814329035485
Winsorized Mean ( 40 / 48 )42319.9305555556472.93995128210989.4826720407718
Winsorized Mean ( 41 / 48 )42284.3402777778468.20640769452990.3113233455901
Winsorized Mean ( 42 / 48 )42289.0069444444457.09072204066292.5177539278133
Winsorized Mean ( 43 / 48 )42324.8402777778453.140417125293.4033661051331
Winsorized Mean ( 44 / 48 )42334.9236111111439.33292479755696.361827720103
Winsorized Mean ( 45 / 48 )42376.1736111111425.93804237368799.4890556733445
Winsorized Mean ( 46 / 48 )42442.9375415.12575130406102.241157930269
Winsorized Mean ( 47 / 48 )42493.2013888889409.736836769614103.708521117865
Winsorized Mean ( 48 / 48 )42472.8680555556407.225805144916104.298076199864
Trimmed Mean ( 1 / 48 )42433.5211267606836.15146837517350.7486056434467
Trimmed Mean ( 2 / 48 )42426.8428571429818.47128472096651.8366907296046
Trimmed Mean ( 3 / 48 )42423.0144927536800.43998875874252.9996190701814
Trimmed Mean ( 4 / 48 )42430.4264705882783.88825043856754.1281572301274
Trimmed Mean ( 5 / 48 )42441.171641791767.57947169906955.292218208814
Trimmed Mean ( 6 / 48 )42459.2272727273751.17644955176656.5236400822511
Trimmed Mean ( 7 / 48 )42469.4076923077737.19448929724657.6095023889734
Trimmed Mean ( 8 / 48 )42479.0703125725.28933934036158.5684471126158
Trimmed Mean ( 9 / 48 )42479.0079365079714.25200670271959.4734176983394
Trimmed Mean ( 10 / 48 )42484.3387096774703.1974702210260.415943613
Trimmed Mean ( 11 / 48 )42490.2459016393691.51567382984761.445094463751
Trimmed Mean ( 12 / 48 )42491.6666666667680.70602531770562.4229330816259
Trimmed Mean ( 13 / 48 )42487.7288135593672.37157537352563.1908462072567
Trimmed Mean ( 14 / 48 )42480.2844827586663.81248298342763.9944044014297
Trimmed Mean ( 15 / 48 )42470.9736842105655.4117978944364.8004412197833
Trimmed Mean ( 16 / 48 )42463.1785714286647.71576512362765.5583526878087
Trimmed Mean ( 17 / 48 )42459.8909090909640.08964868696866.3342876989027
Trimmed Mean ( 18 / 48 )42459.1481481481632.92443730619167.0840714080496
Trimmed Mean ( 19 / 48 )42456.0188679245626.78050599235167.7366613384154
Trimmed Mean ( 20 / 48 )42453.1826923077620.54976299875368.4122132077794
Trimmed Mean ( 21 / 48 )42451.1764705882613.78929737719869.1624579509413
Trimmed Mean ( 22 / 48 )42445.15606.87528354080169.9404822558512
Trimmed Mean ( 23 / 48 )42430.9387755102600.60505624097770.6469889565597
Trimmed Mean ( 24 / 48 )42415.28125595.03891895108471.2815244501458
Trimmed Mean ( 25 / 48 )42405.2765957447590.00178960526771.8731321545912
Trimmed Mean ( 26 / 48 )42394.6630434783584.63873880860272.5142899867902
Trimmed Mean ( 27 / 48 )42390.1555555556580.63576651897473.0064491371121
Trimmed Mean ( 28 / 48 )42386.0227272727576.33733082920673.5437745569765
Trimmed Mean ( 29 / 48 )42381.3604651163571.60224227057874.1448464176148
Trimmed Mean ( 30 / 48 )42378.4166666667566.60044655644474.7941815510818
Trimmed Mean ( 31 / 48 )42373.9634146341561.06013357342875.5248161097308
Trimmed Mean ( 32 / 48 )42372.25555.93050161560976.2186098385689
Trimmed Mean ( 33 / 48 )42368.4487179487551.0966760343876.8802472604744
Trimmed Mean ( 34 / 48 )42360.2236842105546.38963239203577.5275026701404
Trimmed Mean ( 35 / 48 )42352.4324324324542.58619977293678.0565971824501
Trimmed Mean ( 36 / 48 )42347.8611111111538.9832289504178.5699050294705
Trimmed Mean ( 37 / 48 )42345.0714285714535.11988568783679.1319339107379
Trimmed Mean ( 38 / 48 )42346.9558823529531.38399748245379.6918162439607
Trimmed Mean ( 39 / 48 )42349.7575757576527.76331359783880.2438450809573
Trimmed Mean ( 40 / 48 )42351.71875523.900706368480.8392091004719
Trimmed Mean ( 41 / 48 )42353.564516129519.11820121517281.5875159395031
Trimmed Mean ( 42 / 48 )42357.6166666667513.63534025965782.4663206493029
Trimmed Mean ( 43 / 48 )42361.6724137931508.16390146182183.3622228811067
Trimmed Mean ( 44 / 48 )42363.875501.69418497266884.441630517021
Trimmed Mean ( 45 / 48 )42365.6296296296495.44131997119385.5108928582964
Trimmed Mean ( 46 / 48 )42364.9807692308489.36821822564286.5707644906698
Trimmed Mean ( 47 / 48 )42360.1483.07985417548187.6875730458685
Trimmed Mean ( 48 / 48 )42351.6041666667475.60124297811389.0485565207316
Median41918
Midrange41963.5
Midmean - Weighted Average at Xnp42250.8082191781
Midmean - Weighted Average at X(n+1)p42347.8611111111
Midmean - Empirical Distribution Function42250.8082191781
Midmean - Empirical Distribution Function - Averaging42347.8611111111
Midmean - Empirical Distribution Function - Interpolation42347.8611111111
Midmean - Closest Observation42250.8082191781
Midmean - True Basic - Statistics Graphics Toolkit42347.8611111111
Midmean - MS Excel (old versions)42352.4324324324
Number of observations144

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 42426.9930555556 & 856.623981191935 & 49.5281406860934 \tabularnewline
Geometric Mean & 41100.0168903946 &  &  \tabularnewline
Harmonic Mean & 39663.9780561291 &  &  \tabularnewline
Quadratic Mean & 43646.1201482223 &  &  \tabularnewline
Winsorized Mean ( 1 / 48 ) & 42440.0138888889 & 852.363137472635 & 49.7910010687803 \tabularnewline
Winsorized Mean ( 2 / 48 ) & 42434.1805555556 & 850.127003095462 & 49.915107273437 \tabularnewline
Winsorized Mean ( 3 / 48 ) & 42402.0138888889 & 842.228884726872 & 50.3450008160662 \tabularnewline
Winsorized Mean ( 4 / 48 ) & 42390.4305555556 & 836.465716962699 & 50.6780250474341 \tabularnewline
Winsorized Mean ( 5 / 48 ) & 42358.4166666667 & 830.834347359644 & 50.982986923061 \tabularnewline
Winsorized Mean ( 6 / 48 ) & 42404.0833333333 & 813.218422951987 & 52.143535041184 \tabularnewline
Winsorized Mean ( 7 / 48 ) & 42409.2847222222 & 796.070882953279 & 53.2732519557699 \tabularnewline
Winsorized Mean ( 8 / 48 ) & 42479.5069444444 & 784.798319872415 & 54.1279279896399 \tabularnewline
Winsorized Mean ( 9 / 48 ) & 42437.6944444444 & 778.251989035693 & 54.5295033515142 \tabularnewline
Winsorized Mean ( 10 / 48 ) & 42434.2916666667 & 775.048838529022 & 54.7504744955213 \tabularnewline
Winsorized Mean ( 11 / 48 ) & 42477.2222222222 & 760.974495265182 & 55.8195083889374 \tabularnewline
Winsorized Mean ( 12 / 48 ) & 42530.3888888889 & 734.872619183034 & 57.8745047490957 \tabularnewline
Winsorized Mean ( 13 / 48 ) & 42565.6875 & 729.6364751206 & 58.3382121802017 \tabularnewline
Winsorized Mean ( 14 / 48 ) & 42583.4791666667 & 720.868934874684 & 59.0724292676995 \tabularnewline
Winsorized Mean ( 15 / 48 ) & 42561.9166666667 & 707.316603738005 & 60.1737841890559 \tabularnewline
Winsorized Mean ( 16 / 48 ) & 42503.3611111111 & 699.178978821659 & 60.7903875810782 \tabularnewline
Winsorized Mean ( 17 / 48 ) & 42469.3611111111 & 687.299512874372 & 61.7916356924202 \tabularnewline
Winsorized Mean ( 18 / 48 ) & 42500.6111111111 & 670.272871763071 & 63.4079237002662 \tabularnewline
Winsorized Mean ( 19 / 48 ) & 42494.9375 & 663.821561478355 & 64.0156029360695 \tabularnewline
Winsorized Mean ( 20 / 48 ) & 42481.6041666667 & 661.176761837715 & 64.251508248098 \tabularnewline
Winsorized Mean ( 21 / 48 ) & 42539.0625 & 654.276893317538 & 65.0169109355275 \tabularnewline
Winsorized Mean ( 22 / 48 ) & 42657.9236111111 & 639.25927164418 & 66.7302384232841 \tabularnewline
Winsorized Mean ( 23 / 48 ) & 42671.0208333333 & 624.027255171633 & 68.3800594921083 \tabularnewline
Winsorized Mean ( 24 / 48 ) & 42572.0208333333 & 611.097850188278 & 69.6648185232807 \tabularnewline
Winsorized Mean ( 25 / 48 ) & 42574.7986111111 & 606.602738727807 & 70.1856353309594 \tabularnewline
Winsorized Mean ( 26 / 48 ) & 42467.9097222222 & 585.088781118153 & 72.5837019829068 \tabularnewline
Winsorized Mean ( 27 / 48 ) & 42458.3472222222 & 580.961844073744 & 73.082849855511 \tabularnewline
Winsorized Mean ( 28 / 48 ) & 42463.9861111111 & 577.715832346218 & 73.503241098061 \tabularnewline
Winsorized Mean ( 29 / 48 ) & 42431.1597222222 & 572.182737546317 & 74.1566582455443 \tabularnewline
Winsorized Mean ( 30 / 48 ) & 42454.4930555556 & 568.728833635063 & 74.6480405858891 \tabularnewline
Winsorized Mean ( 31 / 48 ) & 42403.4722222222 & 555.552415001807 & 76.3266814744821 \tabularnewline
Winsorized Mean ( 32 / 48 ) & 42438.1388888889 & 543.667419544446 & 78.0590069650466 \tabularnewline
Winsorized Mean ( 33 / 48 ) & 42511.7013888889 & 533.433956496999 & 79.6944042858809 \tabularnewline
Winsorized Mean ( 34 / 48 ) & 42496.3541666667 & 516.078620208849 & 82.3447290830785 \tabularnewline
Winsorized Mean ( 35 / 48 ) & 42432.4305555556 & 506.11825706767 & 83.8389644376772 \tabularnewline
Winsorized Mean ( 36 / 48 ) & 42396.6805555556 & 500.359780780476 & 84.7323909396234 \tabularnewline
Winsorized Mean ( 37 / 48 ) & 42312.1458333333 & 490.667521785966 & 86.2338425810671 \tabularnewline
Winsorized Mean ( 38 / 48 ) & 42298.1597222222 & 481.063867996348 & 87.9262869988467 \tabularnewline
Winsorized Mean ( 39 / 48 ) & 42315.7638888889 & 474.490737715038 & 89.1814329035485 \tabularnewline
Winsorized Mean ( 40 / 48 ) & 42319.9305555556 & 472.939951282109 & 89.4826720407718 \tabularnewline
Winsorized Mean ( 41 / 48 ) & 42284.3402777778 & 468.206407694529 & 90.3113233455901 \tabularnewline
Winsorized Mean ( 42 / 48 ) & 42289.0069444444 & 457.090722040662 & 92.5177539278133 \tabularnewline
Winsorized Mean ( 43 / 48 ) & 42324.8402777778 & 453.1404171252 & 93.4033661051331 \tabularnewline
Winsorized Mean ( 44 / 48 ) & 42334.9236111111 & 439.332924797556 & 96.361827720103 \tabularnewline
Winsorized Mean ( 45 / 48 ) & 42376.1736111111 & 425.938042373687 & 99.4890556733445 \tabularnewline
Winsorized Mean ( 46 / 48 ) & 42442.9375 & 415.12575130406 & 102.241157930269 \tabularnewline
Winsorized Mean ( 47 / 48 ) & 42493.2013888889 & 409.736836769614 & 103.708521117865 \tabularnewline
Winsorized Mean ( 48 / 48 ) & 42472.8680555556 & 407.225805144916 & 104.298076199864 \tabularnewline
Trimmed Mean ( 1 / 48 ) & 42433.5211267606 & 836.151468375173 & 50.7486056434467 \tabularnewline
Trimmed Mean ( 2 / 48 ) & 42426.8428571429 & 818.471284720966 & 51.8366907296046 \tabularnewline
Trimmed Mean ( 3 / 48 ) & 42423.0144927536 & 800.439988758742 & 52.9996190701814 \tabularnewline
Trimmed Mean ( 4 / 48 ) & 42430.4264705882 & 783.888250438567 & 54.1281572301274 \tabularnewline
Trimmed Mean ( 5 / 48 ) & 42441.171641791 & 767.579471699069 & 55.292218208814 \tabularnewline
Trimmed Mean ( 6 / 48 ) & 42459.2272727273 & 751.176449551766 & 56.5236400822511 \tabularnewline
Trimmed Mean ( 7 / 48 ) & 42469.4076923077 & 737.194489297246 & 57.6095023889734 \tabularnewline
Trimmed Mean ( 8 / 48 ) & 42479.0703125 & 725.289339340361 & 58.5684471126158 \tabularnewline
Trimmed Mean ( 9 / 48 ) & 42479.0079365079 & 714.252006702719 & 59.4734176983394 \tabularnewline
Trimmed Mean ( 10 / 48 ) & 42484.3387096774 & 703.19747022102 & 60.415943613 \tabularnewline
Trimmed Mean ( 11 / 48 ) & 42490.2459016393 & 691.515673829847 & 61.445094463751 \tabularnewline
Trimmed Mean ( 12 / 48 ) & 42491.6666666667 & 680.706025317705 & 62.4229330816259 \tabularnewline
Trimmed Mean ( 13 / 48 ) & 42487.7288135593 & 672.371575373525 & 63.1908462072567 \tabularnewline
Trimmed Mean ( 14 / 48 ) & 42480.2844827586 & 663.812482983427 & 63.9944044014297 \tabularnewline
Trimmed Mean ( 15 / 48 ) & 42470.9736842105 & 655.41179789443 & 64.8004412197833 \tabularnewline
Trimmed Mean ( 16 / 48 ) & 42463.1785714286 & 647.715765123627 & 65.5583526878087 \tabularnewline
Trimmed Mean ( 17 / 48 ) & 42459.8909090909 & 640.089648686968 & 66.3342876989027 \tabularnewline
Trimmed Mean ( 18 / 48 ) & 42459.1481481481 & 632.924437306191 & 67.0840714080496 \tabularnewline
Trimmed Mean ( 19 / 48 ) & 42456.0188679245 & 626.780505992351 & 67.7366613384154 \tabularnewline
Trimmed Mean ( 20 / 48 ) & 42453.1826923077 & 620.549762998753 & 68.4122132077794 \tabularnewline
Trimmed Mean ( 21 / 48 ) & 42451.1764705882 & 613.789297377198 & 69.1624579509413 \tabularnewline
Trimmed Mean ( 22 / 48 ) & 42445.15 & 606.875283540801 & 69.9404822558512 \tabularnewline
Trimmed Mean ( 23 / 48 ) & 42430.9387755102 & 600.605056240977 & 70.6469889565597 \tabularnewline
Trimmed Mean ( 24 / 48 ) & 42415.28125 & 595.038918951084 & 71.2815244501458 \tabularnewline
Trimmed Mean ( 25 / 48 ) & 42405.2765957447 & 590.001789605267 & 71.8731321545912 \tabularnewline
Trimmed Mean ( 26 / 48 ) & 42394.6630434783 & 584.638738808602 & 72.5142899867902 \tabularnewline
Trimmed Mean ( 27 / 48 ) & 42390.1555555556 & 580.635766518974 & 73.0064491371121 \tabularnewline
Trimmed Mean ( 28 / 48 ) & 42386.0227272727 & 576.337330829206 & 73.5437745569765 \tabularnewline
Trimmed Mean ( 29 / 48 ) & 42381.3604651163 & 571.602242270578 & 74.1448464176148 \tabularnewline
Trimmed Mean ( 30 / 48 ) & 42378.4166666667 & 566.600446556444 & 74.7941815510818 \tabularnewline
Trimmed Mean ( 31 / 48 ) & 42373.9634146341 & 561.060133573428 & 75.5248161097308 \tabularnewline
Trimmed Mean ( 32 / 48 ) & 42372.25 & 555.930501615609 & 76.2186098385689 \tabularnewline
Trimmed Mean ( 33 / 48 ) & 42368.4487179487 & 551.09667603438 & 76.8802472604744 \tabularnewline
Trimmed Mean ( 34 / 48 ) & 42360.2236842105 & 546.389632392035 & 77.5275026701404 \tabularnewline
Trimmed Mean ( 35 / 48 ) & 42352.4324324324 & 542.586199772936 & 78.0565971824501 \tabularnewline
Trimmed Mean ( 36 / 48 ) & 42347.8611111111 & 538.98322895041 & 78.5699050294705 \tabularnewline
Trimmed Mean ( 37 / 48 ) & 42345.0714285714 & 535.119885687836 & 79.1319339107379 \tabularnewline
Trimmed Mean ( 38 / 48 ) & 42346.9558823529 & 531.383997482453 & 79.6918162439607 \tabularnewline
Trimmed Mean ( 39 / 48 ) & 42349.7575757576 & 527.763313597838 & 80.2438450809573 \tabularnewline
Trimmed Mean ( 40 / 48 ) & 42351.71875 & 523.9007063684 & 80.8392091004719 \tabularnewline
Trimmed Mean ( 41 / 48 ) & 42353.564516129 & 519.118201215172 & 81.5875159395031 \tabularnewline
Trimmed Mean ( 42 / 48 ) & 42357.6166666667 & 513.635340259657 & 82.4663206493029 \tabularnewline
Trimmed Mean ( 43 / 48 ) & 42361.6724137931 & 508.163901461821 & 83.3622228811067 \tabularnewline
Trimmed Mean ( 44 / 48 ) & 42363.875 & 501.694184972668 & 84.441630517021 \tabularnewline
Trimmed Mean ( 45 / 48 ) & 42365.6296296296 & 495.441319971193 & 85.5108928582964 \tabularnewline
Trimmed Mean ( 46 / 48 ) & 42364.9807692308 & 489.368218225642 & 86.5707644906698 \tabularnewline
Trimmed Mean ( 47 / 48 ) & 42360.1 & 483.079854175481 & 87.6875730458685 \tabularnewline
Trimmed Mean ( 48 / 48 ) & 42351.6041666667 & 475.601242978113 & 89.0485565207316 \tabularnewline
Median & 41918 &  &  \tabularnewline
Midrange & 41963.5 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 42250.8082191781 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 42347.8611111111 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 42250.8082191781 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 42347.8611111111 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 42347.8611111111 &  &  \tabularnewline
Midmean - Closest Observation & 42250.8082191781 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 42347.8611111111 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 42352.4324324324 &  &  \tabularnewline
Number of observations & 144 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=215883&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]42426.9930555556[/C][C]856.623981191935[/C][C]49.5281406860934[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]41100.0168903946[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]39663.9780561291[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]43646.1201482223[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 48 )[/C][C]42440.0138888889[/C][C]852.363137472635[/C][C]49.7910010687803[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 48 )[/C][C]42434.1805555556[/C][C]850.127003095462[/C][C]49.915107273437[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 48 )[/C][C]42402.0138888889[/C][C]842.228884726872[/C][C]50.3450008160662[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 48 )[/C][C]42390.4305555556[/C][C]836.465716962699[/C][C]50.6780250474341[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 48 )[/C][C]42358.4166666667[/C][C]830.834347359644[/C][C]50.982986923061[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 48 )[/C][C]42404.0833333333[/C][C]813.218422951987[/C][C]52.143535041184[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 48 )[/C][C]42409.2847222222[/C][C]796.070882953279[/C][C]53.2732519557699[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 48 )[/C][C]42479.5069444444[/C][C]784.798319872415[/C][C]54.1279279896399[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 48 )[/C][C]42437.6944444444[/C][C]778.251989035693[/C][C]54.5295033515142[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 48 )[/C][C]42434.2916666667[/C][C]775.048838529022[/C][C]54.7504744955213[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 48 )[/C][C]42477.2222222222[/C][C]760.974495265182[/C][C]55.8195083889374[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 48 )[/C][C]42530.3888888889[/C][C]734.872619183034[/C][C]57.8745047490957[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 48 )[/C][C]42565.6875[/C][C]729.6364751206[/C][C]58.3382121802017[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 48 )[/C][C]42583.4791666667[/C][C]720.868934874684[/C][C]59.0724292676995[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 48 )[/C][C]42561.9166666667[/C][C]707.316603738005[/C][C]60.1737841890559[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 48 )[/C][C]42503.3611111111[/C][C]699.178978821659[/C][C]60.7903875810782[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 48 )[/C][C]42469.3611111111[/C][C]687.299512874372[/C][C]61.7916356924202[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 48 )[/C][C]42500.6111111111[/C][C]670.272871763071[/C][C]63.4079237002662[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 48 )[/C][C]42494.9375[/C][C]663.821561478355[/C][C]64.0156029360695[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 48 )[/C][C]42481.6041666667[/C][C]661.176761837715[/C][C]64.251508248098[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 48 )[/C][C]42539.0625[/C][C]654.276893317538[/C][C]65.0169109355275[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 48 )[/C][C]42657.9236111111[/C][C]639.25927164418[/C][C]66.7302384232841[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 48 )[/C][C]42671.0208333333[/C][C]624.027255171633[/C][C]68.3800594921083[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 48 )[/C][C]42572.0208333333[/C][C]611.097850188278[/C][C]69.6648185232807[/C][/ROW]
[ROW][C]Winsorized Mean ( 25 / 48 )[/C][C]42574.7986111111[/C][C]606.602738727807[/C][C]70.1856353309594[/C][/ROW]
[ROW][C]Winsorized Mean ( 26 / 48 )[/C][C]42467.9097222222[/C][C]585.088781118153[/C][C]72.5837019829068[/C][/ROW]
[ROW][C]Winsorized Mean ( 27 / 48 )[/C][C]42458.3472222222[/C][C]580.961844073744[/C][C]73.082849855511[/C][/ROW]
[ROW][C]Winsorized Mean ( 28 / 48 )[/C][C]42463.9861111111[/C][C]577.715832346218[/C][C]73.503241098061[/C][/ROW]
[ROW][C]Winsorized Mean ( 29 / 48 )[/C][C]42431.1597222222[/C][C]572.182737546317[/C][C]74.1566582455443[/C][/ROW]
[ROW][C]Winsorized Mean ( 30 / 48 )[/C][C]42454.4930555556[/C][C]568.728833635063[/C][C]74.6480405858891[/C][/ROW]
[ROW][C]Winsorized Mean ( 31 / 48 )[/C][C]42403.4722222222[/C][C]555.552415001807[/C][C]76.3266814744821[/C][/ROW]
[ROW][C]Winsorized Mean ( 32 / 48 )[/C][C]42438.1388888889[/C][C]543.667419544446[/C][C]78.0590069650466[/C][/ROW]
[ROW][C]Winsorized Mean ( 33 / 48 )[/C][C]42511.7013888889[/C][C]533.433956496999[/C][C]79.6944042858809[/C][/ROW]
[ROW][C]Winsorized Mean ( 34 / 48 )[/C][C]42496.3541666667[/C][C]516.078620208849[/C][C]82.3447290830785[/C][/ROW]
[ROW][C]Winsorized Mean ( 35 / 48 )[/C][C]42432.4305555556[/C][C]506.11825706767[/C][C]83.8389644376772[/C][/ROW]
[ROW][C]Winsorized Mean ( 36 / 48 )[/C][C]42396.6805555556[/C][C]500.359780780476[/C][C]84.7323909396234[/C][/ROW]
[ROW][C]Winsorized Mean ( 37 / 48 )[/C][C]42312.1458333333[/C][C]490.667521785966[/C][C]86.2338425810671[/C][/ROW]
[ROW][C]Winsorized Mean ( 38 / 48 )[/C][C]42298.1597222222[/C][C]481.063867996348[/C][C]87.9262869988467[/C][/ROW]
[ROW][C]Winsorized Mean ( 39 / 48 )[/C][C]42315.7638888889[/C][C]474.490737715038[/C][C]89.1814329035485[/C][/ROW]
[ROW][C]Winsorized Mean ( 40 / 48 )[/C][C]42319.9305555556[/C][C]472.939951282109[/C][C]89.4826720407718[/C][/ROW]
[ROW][C]Winsorized Mean ( 41 / 48 )[/C][C]42284.3402777778[/C][C]468.206407694529[/C][C]90.3113233455901[/C][/ROW]
[ROW][C]Winsorized Mean ( 42 / 48 )[/C][C]42289.0069444444[/C][C]457.090722040662[/C][C]92.5177539278133[/C][/ROW]
[ROW][C]Winsorized Mean ( 43 / 48 )[/C][C]42324.8402777778[/C][C]453.1404171252[/C][C]93.4033661051331[/C][/ROW]
[ROW][C]Winsorized Mean ( 44 / 48 )[/C][C]42334.9236111111[/C][C]439.332924797556[/C][C]96.361827720103[/C][/ROW]
[ROW][C]Winsorized Mean ( 45 / 48 )[/C][C]42376.1736111111[/C][C]425.938042373687[/C][C]99.4890556733445[/C][/ROW]
[ROW][C]Winsorized Mean ( 46 / 48 )[/C][C]42442.9375[/C][C]415.12575130406[/C][C]102.241157930269[/C][/ROW]
[ROW][C]Winsorized Mean ( 47 / 48 )[/C][C]42493.2013888889[/C][C]409.736836769614[/C][C]103.708521117865[/C][/ROW]
[ROW][C]Winsorized Mean ( 48 / 48 )[/C][C]42472.8680555556[/C][C]407.225805144916[/C][C]104.298076199864[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 48 )[/C][C]42433.5211267606[/C][C]836.151468375173[/C][C]50.7486056434467[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 48 )[/C][C]42426.8428571429[/C][C]818.471284720966[/C][C]51.8366907296046[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 48 )[/C][C]42423.0144927536[/C][C]800.439988758742[/C][C]52.9996190701814[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 48 )[/C][C]42430.4264705882[/C][C]783.888250438567[/C][C]54.1281572301274[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 48 )[/C][C]42441.171641791[/C][C]767.579471699069[/C][C]55.292218208814[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 48 )[/C][C]42459.2272727273[/C][C]751.176449551766[/C][C]56.5236400822511[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 48 )[/C][C]42469.4076923077[/C][C]737.194489297246[/C][C]57.6095023889734[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 48 )[/C][C]42479.0703125[/C][C]725.289339340361[/C][C]58.5684471126158[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 48 )[/C][C]42479.0079365079[/C][C]714.252006702719[/C][C]59.4734176983394[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 48 )[/C][C]42484.3387096774[/C][C]703.19747022102[/C][C]60.415943613[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 48 )[/C][C]42490.2459016393[/C][C]691.515673829847[/C][C]61.445094463751[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 48 )[/C][C]42491.6666666667[/C][C]680.706025317705[/C][C]62.4229330816259[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 48 )[/C][C]42487.7288135593[/C][C]672.371575373525[/C][C]63.1908462072567[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 48 )[/C][C]42480.2844827586[/C][C]663.812482983427[/C][C]63.9944044014297[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 48 )[/C][C]42470.9736842105[/C][C]655.41179789443[/C][C]64.8004412197833[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 48 )[/C][C]42463.1785714286[/C][C]647.715765123627[/C][C]65.5583526878087[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 48 )[/C][C]42459.8909090909[/C][C]640.089648686968[/C][C]66.3342876989027[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 48 )[/C][C]42459.1481481481[/C][C]632.924437306191[/C][C]67.0840714080496[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 48 )[/C][C]42456.0188679245[/C][C]626.780505992351[/C][C]67.7366613384154[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 48 )[/C][C]42453.1826923077[/C][C]620.549762998753[/C][C]68.4122132077794[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 48 )[/C][C]42451.1764705882[/C][C]613.789297377198[/C][C]69.1624579509413[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 48 )[/C][C]42445.15[/C][C]606.875283540801[/C][C]69.9404822558512[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 48 )[/C][C]42430.9387755102[/C][C]600.605056240977[/C][C]70.6469889565597[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 48 )[/C][C]42415.28125[/C][C]595.038918951084[/C][C]71.2815244501458[/C][/ROW]
[ROW][C]Trimmed Mean ( 25 / 48 )[/C][C]42405.2765957447[/C][C]590.001789605267[/C][C]71.8731321545912[/C][/ROW]
[ROW][C]Trimmed Mean ( 26 / 48 )[/C][C]42394.6630434783[/C][C]584.638738808602[/C][C]72.5142899867902[/C][/ROW]
[ROW][C]Trimmed Mean ( 27 / 48 )[/C][C]42390.1555555556[/C][C]580.635766518974[/C][C]73.0064491371121[/C][/ROW]
[ROW][C]Trimmed Mean ( 28 / 48 )[/C][C]42386.0227272727[/C][C]576.337330829206[/C][C]73.5437745569765[/C][/ROW]
[ROW][C]Trimmed Mean ( 29 / 48 )[/C][C]42381.3604651163[/C][C]571.602242270578[/C][C]74.1448464176148[/C][/ROW]
[ROW][C]Trimmed Mean ( 30 / 48 )[/C][C]42378.4166666667[/C][C]566.600446556444[/C][C]74.7941815510818[/C][/ROW]
[ROW][C]Trimmed Mean ( 31 / 48 )[/C][C]42373.9634146341[/C][C]561.060133573428[/C][C]75.5248161097308[/C][/ROW]
[ROW][C]Trimmed Mean ( 32 / 48 )[/C][C]42372.25[/C][C]555.930501615609[/C][C]76.2186098385689[/C][/ROW]
[ROW][C]Trimmed Mean ( 33 / 48 )[/C][C]42368.4487179487[/C][C]551.09667603438[/C][C]76.8802472604744[/C][/ROW]
[ROW][C]Trimmed Mean ( 34 / 48 )[/C][C]42360.2236842105[/C][C]546.389632392035[/C][C]77.5275026701404[/C][/ROW]
[ROW][C]Trimmed Mean ( 35 / 48 )[/C][C]42352.4324324324[/C][C]542.586199772936[/C][C]78.0565971824501[/C][/ROW]
[ROW][C]Trimmed Mean ( 36 / 48 )[/C][C]42347.8611111111[/C][C]538.98322895041[/C][C]78.5699050294705[/C][/ROW]
[ROW][C]Trimmed Mean ( 37 / 48 )[/C][C]42345.0714285714[/C][C]535.119885687836[/C][C]79.1319339107379[/C][/ROW]
[ROW][C]Trimmed Mean ( 38 / 48 )[/C][C]42346.9558823529[/C][C]531.383997482453[/C][C]79.6918162439607[/C][/ROW]
[ROW][C]Trimmed Mean ( 39 / 48 )[/C][C]42349.7575757576[/C][C]527.763313597838[/C][C]80.2438450809573[/C][/ROW]
[ROW][C]Trimmed Mean ( 40 / 48 )[/C][C]42351.71875[/C][C]523.9007063684[/C][C]80.8392091004719[/C][/ROW]
[ROW][C]Trimmed Mean ( 41 / 48 )[/C][C]42353.564516129[/C][C]519.118201215172[/C][C]81.5875159395031[/C][/ROW]
[ROW][C]Trimmed Mean ( 42 / 48 )[/C][C]42357.6166666667[/C][C]513.635340259657[/C][C]82.4663206493029[/C][/ROW]
[ROW][C]Trimmed Mean ( 43 / 48 )[/C][C]42361.6724137931[/C][C]508.163901461821[/C][C]83.3622228811067[/C][/ROW]
[ROW][C]Trimmed Mean ( 44 / 48 )[/C][C]42363.875[/C][C]501.694184972668[/C][C]84.441630517021[/C][/ROW]
[ROW][C]Trimmed Mean ( 45 / 48 )[/C][C]42365.6296296296[/C][C]495.441319971193[/C][C]85.5108928582964[/C][/ROW]
[ROW][C]Trimmed Mean ( 46 / 48 )[/C][C]42364.9807692308[/C][C]489.368218225642[/C][C]86.5707644906698[/C][/ROW]
[ROW][C]Trimmed Mean ( 47 / 48 )[/C][C]42360.1[/C][C]483.079854175481[/C][C]87.6875730458685[/C][/ROW]
[ROW][C]Trimmed Mean ( 48 / 48 )[/C][C]42351.6041666667[/C][C]475.601242978113[/C][C]89.0485565207316[/C][/ROW]
[ROW][C]Median[/C][C]41918[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]41963.5[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]42250.8082191781[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]42347.8611111111[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]42250.8082191781[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]42347.8611111111[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]42347.8611111111[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]42250.8082191781[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]42347.8611111111[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]42352.4324324324[/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=215883&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=215883&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 Mean42426.9930555556856.62398119193549.5281406860934
Geometric Mean41100.0168903946
Harmonic Mean39663.9780561291
Quadratic Mean43646.1201482223
Winsorized Mean ( 1 / 48 )42440.0138888889852.36313747263549.7910010687803
Winsorized Mean ( 2 / 48 )42434.1805555556850.12700309546249.915107273437
Winsorized Mean ( 3 / 48 )42402.0138888889842.22888472687250.3450008160662
Winsorized Mean ( 4 / 48 )42390.4305555556836.46571696269950.6780250474341
Winsorized Mean ( 5 / 48 )42358.4166666667830.83434735964450.982986923061
Winsorized Mean ( 6 / 48 )42404.0833333333813.21842295198752.143535041184
Winsorized Mean ( 7 / 48 )42409.2847222222796.07088295327953.2732519557699
Winsorized Mean ( 8 / 48 )42479.5069444444784.79831987241554.1279279896399
Winsorized Mean ( 9 / 48 )42437.6944444444778.25198903569354.5295033515142
Winsorized Mean ( 10 / 48 )42434.2916666667775.04883852902254.7504744955213
Winsorized Mean ( 11 / 48 )42477.2222222222760.97449526518255.8195083889374
Winsorized Mean ( 12 / 48 )42530.3888888889734.87261918303457.8745047490957
Winsorized Mean ( 13 / 48 )42565.6875729.636475120658.3382121802017
Winsorized Mean ( 14 / 48 )42583.4791666667720.86893487468459.0724292676995
Winsorized Mean ( 15 / 48 )42561.9166666667707.31660373800560.1737841890559
Winsorized Mean ( 16 / 48 )42503.3611111111699.17897882165960.7903875810782
Winsorized Mean ( 17 / 48 )42469.3611111111687.29951287437261.7916356924202
Winsorized Mean ( 18 / 48 )42500.6111111111670.27287176307163.4079237002662
Winsorized Mean ( 19 / 48 )42494.9375663.82156147835564.0156029360695
Winsorized Mean ( 20 / 48 )42481.6041666667661.17676183771564.251508248098
Winsorized Mean ( 21 / 48 )42539.0625654.27689331753865.0169109355275
Winsorized Mean ( 22 / 48 )42657.9236111111639.2592716441866.7302384232841
Winsorized Mean ( 23 / 48 )42671.0208333333624.02725517163368.3800594921083
Winsorized Mean ( 24 / 48 )42572.0208333333611.09785018827869.6648185232807
Winsorized Mean ( 25 / 48 )42574.7986111111606.60273872780770.1856353309594
Winsorized Mean ( 26 / 48 )42467.9097222222585.08878111815372.5837019829068
Winsorized Mean ( 27 / 48 )42458.3472222222580.96184407374473.082849855511
Winsorized Mean ( 28 / 48 )42463.9861111111577.71583234621873.503241098061
Winsorized Mean ( 29 / 48 )42431.1597222222572.18273754631774.1566582455443
Winsorized Mean ( 30 / 48 )42454.4930555556568.72883363506374.6480405858891
Winsorized Mean ( 31 / 48 )42403.4722222222555.55241500180776.3266814744821
Winsorized Mean ( 32 / 48 )42438.1388888889543.66741954444678.0590069650466
Winsorized Mean ( 33 / 48 )42511.7013888889533.43395649699979.6944042858809
Winsorized Mean ( 34 / 48 )42496.3541666667516.07862020884982.3447290830785
Winsorized Mean ( 35 / 48 )42432.4305555556506.1182570676783.8389644376772
Winsorized Mean ( 36 / 48 )42396.6805555556500.35978078047684.7323909396234
Winsorized Mean ( 37 / 48 )42312.1458333333490.66752178596686.2338425810671
Winsorized Mean ( 38 / 48 )42298.1597222222481.06386799634887.9262869988467
Winsorized Mean ( 39 / 48 )42315.7638888889474.49073771503889.1814329035485
Winsorized Mean ( 40 / 48 )42319.9305555556472.93995128210989.4826720407718
Winsorized Mean ( 41 / 48 )42284.3402777778468.20640769452990.3113233455901
Winsorized Mean ( 42 / 48 )42289.0069444444457.09072204066292.5177539278133
Winsorized Mean ( 43 / 48 )42324.8402777778453.140417125293.4033661051331
Winsorized Mean ( 44 / 48 )42334.9236111111439.33292479755696.361827720103
Winsorized Mean ( 45 / 48 )42376.1736111111425.93804237368799.4890556733445
Winsorized Mean ( 46 / 48 )42442.9375415.12575130406102.241157930269
Winsorized Mean ( 47 / 48 )42493.2013888889409.736836769614103.708521117865
Winsorized Mean ( 48 / 48 )42472.8680555556407.225805144916104.298076199864
Trimmed Mean ( 1 / 48 )42433.5211267606836.15146837517350.7486056434467
Trimmed Mean ( 2 / 48 )42426.8428571429818.47128472096651.8366907296046
Trimmed Mean ( 3 / 48 )42423.0144927536800.43998875874252.9996190701814
Trimmed Mean ( 4 / 48 )42430.4264705882783.88825043856754.1281572301274
Trimmed Mean ( 5 / 48 )42441.171641791767.57947169906955.292218208814
Trimmed Mean ( 6 / 48 )42459.2272727273751.17644955176656.5236400822511
Trimmed Mean ( 7 / 48 )42469.4076923077737.19448929724657.6095023889734
Trimmed Mean ( 8 / 48 )42479.0703125725.28933934036158.5684471126158
Trimmed Mean ( 9 / 48 )42479.0079365079714.25200670271959.4734176983394
Trimmed Mean ( 10 / 48 )42484.3387096774703.1974702210260.415943613
Trimmed Mean ( 11 / 48 )42490.2459016393691.51567382984761.445094463751
Trimmed Mean ( 12 / 48 )42491.6666666667680.70602531770562.4229330816259
Trimmed Mean ( 13 / 48 )42487.7288135593672.37157537352563.1908462072567
Trimmed Mean ( 14 / 48 )42480.2844827586663.81248298342763.9944044014297
Trimmed Mean ( 15 / 48 )42470.9736842105655.4117978944364.8004412197833
Trimmed Mean ( 16 / 48 )42463.1785714286647.71576512362765.5583526878087
Trimmed Mean ( 17 / 48 )42459.8909090909640.08964868696866.3342876989027
Trimmed Mean ( 18 / 48 )42459.1481481481632.92443730619167.0840714080496
Trimmed Mean ( 19 / 48 )42456.0188679245626.78050599235167.7366613384154
Trimmed Mean ( 20 / 48 )42453.1826923077620.54976299875368.4122132077794
Trimmed Mean ( 21 / 48 )42451.1764705882613.78929737719869.1624579509413
Trimmed Mean ( 22 / 48 )42445.15606.87528354080169.9404822558512
Trimmed Mean ( 23 / 48 )42430.9387755102600.60505624097770.6469889565597
Trimmed Mean ( 24 / 48 )42415.28125595.03891895108471.2815244501458
Trimmed Mean ( 25 / 48 )42405.2765957447590.00178960526771.8731321545912
Trimmed Mean ( 26 / 48 )42394.6630434783584.63873880860272.5142899867902
Trimmed Mean ( 27 / 48 )42390.1555555556580.63576651897473.0064491371121
Trimmed Mean ( 28 / 48 )42386.0227272727576.33733082920673.5437745569765
Trimmed Mean ( 29 / 48 )42381.3604651163571.60224227057874.1448464176148
Trimmed Mean ( 30 / 48 )42378.4166666667566.60044655644474.7941815510818
Trimmed Mean ( 31 / 48 )42373.9634146341561.06013357342875.5248161097308
Trimmed Mean ( 32 / 48 )42372.25555.93050161560976.2186098385689
Trimmed Mean ( 33 / 48 )42368.4487179487551.0966760343876.8802472604744
Trimmed Mean ( 34 / 48 )42360.2236842105546.38963239203577.5275026701404
Trimmed Mean ( 35 / 48 )42352.4324324324542.58619977293678.0565971824501
Trimmed Mean ( 36 / 48 )42347.8611111111538.9832289504178.5699050294705
Trimmed Mean ( 37 / 48 )42345.0714285714535.11988568783679.1319339107379
Trimmed Mean ( 38 / 48 )42346.9558823529531.38399748245379.6918162439607
Trimmed Mean ( 39 / 48 )42349.7575757576527.76331359783880.2438450809573
Trimmed Mean ( 40 / 48 )42351.71875523.900706368480.8392091004719
Trimmed Mean ( 41 / 48 )42353.564516129519.11820121517281.5875159395031
Trimmed Mean ( 42 / 48 )42357.6166666667513.63534025965782.4663206493029
Trimmed Mean ( 43 / 48 )42361.6724137931508.16390146182183.3622228811067
Trimmed Mean ( 44 / 48 )42363.875501.69418497266884.441630517021
Trimmed Mean ( 45 / 48 )42365.6296296296495.44131997119385.5108928582964
Trimmed Mean ( 46 / 48 )42364.9807692308489.36821822564286.5707644906698
Trimmed Mean ( 47 / 48 )42360.1483.07985417548187.6875730458685
Trimmed Mean ( 48 / 48 )42351.6041666667475.60124297811389.0485565207316
Median41918
Midrange41963.5
Midmean - Weighted Average at Xnp42250.8082191781
Midmean - Weighted Average at X(n+1)p42347.8611111111
Midmean - Empirical Distribution Function42250.8082191781
Midmean - Empirical Distribution Function - Averaging42347.8611111111
Midmean - Empirical Distribution Function - Interpolation42347.8611111111
Midmean - Closest Observation42250.8082191781
Midmean - True Basic - Statistics Graphics Toolkit42347.8611111111
Midmean - MS Excel (old versions)42352.4324324324
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')