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Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationThu, 22 Oct 2009 09:10:32 -0600
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2009/Oct/22/t1256224596y2i072b65vu77oh.htm/, Retrieved Thu, 02 May 2024 16:26:12 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=49751, Retrieved Thu, 02 May 2024 16:26:12 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact123
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [] [2009-10-22 15:10:32] [60d430b39377ac0bf942b21543df0c0d] [Current]
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Dataseries X:
61321
58088
54623
53495
51824
50518
49050
47111
45264
44357
54862
57871
59070
56273
52837
51702
49447
48965
46922
46256
45200
44471
53119
55016
56641
51847
47990
45744
46390
44461
41582
40813
38096
35461
44375
46255
45610
43375
40167
40628
40590
39473
36735
36634
32806
32907
41076
42254
43215
41116
40373
42026
43701
44106
44700
44506
41579
42470
50656
52857




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=49751&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=49751&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=49751&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 Mean46347.95852.41112810284254.3727650566385
Geometric Mean45885.6560562825
Harmonic Mean45423.1415474409
Quadratic Mean46808.1419023443
Winsorized Mean ( 1 / 20 )46312.1166666667841.54766695535755.0320777838048
Winsorized Mean ( 2 / 20 )46364.5166666667812.12333485268257.0904869702791
Winsorized Mean ( 3 / 20 )46412.3166666667796.69442408148258.2561083192919
Winsorized Mean ( 4 / 20 )46337.05776.05661066186259.70833746327
Winsorized Mean ( 5 / 20 )46419.8746.54373286817362.1796124677896
Winsorized Mean ( 6 / 20 )46431.8694.53471756155266.8531015454747
Winsorized Mean ( 7 / 20 )46494.8677.48285478753968.6287478294649
Winsorized Mean ( 8 / 20 )46490.4666.54149497219969.7486958436685
Winsorized Mean ( 9 / 20 )46353.75627.63086222967473.8551157846623
Winsorized Mean ( 10 / 20 )46297.4166666667614.70531973319275.316440545466
Winsorized Mean ( 11 / 20 )46283.3600.46102358725877.0796074714318
Winsorized Mean ( 12 / 20 )46331.9591.69592067410278.3035650257914
Winsorized Mean ( 13 / 20 )46126.0666666667551.49540663589483.6381701672447
Winsorized Mean ( 14 / 20 )46228.7333333333534.25654286773886.5290915955668
Winsorized Mean ( 15 / 20 )46198.9833333333528.74853019879187.3742066308233
Winsorized Mean ( 16 / 20 )46038.45463.04513783770799.4254042165022
Winsorized Mean ( 17 / 20 )46063.95447.028050172741103.044876003195
Winsorized Mean ( 18 / 20 )45807.45384.588386192024119.107730874454
Winsorized Mean ( 19 / 20 )45917.65330.646117024516138.872491270162
Winsorized Mean ( 20 / 20 )45942.65318.758678025217144.129879960054
Trimmed Mean ( 1 / 20 )46323.275862069809.15975209598857.248615915555
Trimmed Mean ( 2 / 20 )46335.2321428571769.1463817035860.2424106061962
Trimmed Mean ( 3 / 20 )46318.962962963739.63714070092362.6239008482841
Trimmed Mean ( 4 / 20 )46283.0576923077710.39987433706465.1507121049233
Trimmed Mean ( 5 / 20 )46266.86682.10777591766767.8292516717835
Trimmed Mean ( 6 / 20 )46228.625656.71586174829770.3936476833847
Trimmed Mean ( 7 / 20 )46184.4565217391640.8071086068672.0723223906582
Trimmed Mean ( 8 / 20 )46124624.69506303147573.834423752563
Trimmed Mean ( 9 / 20 )46058.5714285714606.22721841876375.9757563322662
Trimmed Mean ( 10 / 20 )46009.375592.44828042958777.6597325367176
Trimmed Mean ( 11 / 20 )45963.8947368421576.91950594817879.6712440174814
Trimmed Mean ( 12 / 20 )45915.5559.07849989748282.1271073890688
Trimmed Mean ( 13 / 20 )45854.2647058823536.02920030609485.5443410166792
Trimmed Mean ( 14 / 20 )45815.0625515.84571559076388.8154366999658
Trimmed Mean ( 15 / 20 )45755.9666666667491.08337069501893.1735208258211
Trimmed Mean ( 16 / 20 )45692.6785714286455.597523386954100.291762412897
Trimmed Mean ( 17 / 20 )45642.8076923077427.47646995696106.772678498312
Trimmed Mean ( 18 / 20 )45580.875388.780405924472117.240669296629
Trimmed Mean ( 19 / 20 )45546.5454545455356.706068911903127.686488748231
Trimmed Mean ( 20 / 20 )45487.95328.495585767025138.473550242044
Median45232
Midrange47063.5
Midmean - Weighted Average at Xnp45621.2258064516
Midmean - Weighted Average at X(n+1)p45755.9666666667
Midmean - Empirical Distribution Function45621.2258064516
Midmean - Empirical Distribution Function - Averaging45755.9666666667
Midmean - Empirical Distribution Function - Interpolation45755.9666666667
Midmean - Closest Observation45621.2258064516
Midmean - True Basic - Statistics Graphics Toolkit45755.9666666667
Midmean - MS Excel (old versions)45815.0625
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 46347.95 & 852.411128102842 & 54.3727650566385 \tabularnewline
Geometric Mean & 45885.6560562825 &  &  \tabularnewline
Harmonic Mean & 45423.1415474409 &  &  \tabularnewline
Quadratic Mean & 46808.1419023443 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 46312.1166666667 & 841.547666955357 & 55.0320777838048 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 46364.5166666667 & 812.123334852682 & 57.0904869702791 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 46412.3166666667 & 796.694424081482 & 58.2561083192919 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 46337.05 & 776.056610661862 & 59.70833746327 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 46419.8 & 746.543732868173 & 62.1796124677896 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 46431.8 & 694.534717561552 & 66.8531015454747 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 46494.8 & 677.482854787539 & 68.6287478294649 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 46490.4 & 666.541494972199 & 69.7486958436685 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 46353.75 & 627.630862229674 & 73.8551157846623 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 46297.4166666667 & 614.705319733192 & 75.316440545466 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 46283.3 & 600.461023587258 & 77.0796074714318 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 46331.9 & 591.695920674102 & 78.3035650257914 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 46126.0666666667 & 551.495406635894 & 83.6381701672447 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 46228.7333333333 & 534.256542867738 & 86.5290915955668 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 46198.9833333333 & 528.748530198791 & 87.3742066308233 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 46038.45 & 463.045137837707 & 99.4254042165022 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 46063.95 & 447.028050172741 & 103.044876003195 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 45807.45 & 384.588386192024 & 119.107730874454 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 45917.65 & 330.646117024516 & 138.872491270162 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 45942.65 & 318.758678025217 & 144.129879960054 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 46323.275862069 & 809.159752095988 & 57.248615915555 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 46335.2321428571 & 769.14638170358 & 60.2424106061962 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 46318.962962963 & 739.637140700923 & 62.6239008482841 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 46283.0576923077 & 710.399874337064 & 65.1507121049233 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 46266.86 & 682.107775917667 & 67.8292516717835 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 46228.625 & 656.715861748297 & 70.3936476833847 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 46184.4565217391 & 640.80710860686 & 72.0723223906582 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 46124 & 624.695063031475 & 73.834423752563 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 46058.5714285714 & 606.227218418763 & 75.9757563322662 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 46009.375 & 592.448280429587 & 77.6597325367176 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 45963.8947368421 & 576.919505948178 & 79.6712440174814 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 45915.5 & 559.078499897482 & 82.1271073890688 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 45854.2647058823 & 536.029200306094 & 85.5443410166792 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 45815.0625 & 515.845715590763 & 88.8154366999658 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 45755.9666666667 & 491.083370695018 & 93.1735208258211 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 45692.6785714286 & 455.597523386954 & 100.291762412897 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 45642.8076923077 & 427.47646995696 & 106.772678498312 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 45580.875 & 388.780405924472 & 117.240669296629 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 45546.5454545455 & 356.706068911903 & 127.686488748231 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 45487.95 & 328.495585767025 & 138.473550242044 \tabularnewline
Median & 45232 &  &  \tabularnewline
Midrange & 47063.5 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 45621.2258064516 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 45755.9666666667 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 45621.2258064516 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 45755.9666666667 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 45755.9666666667 &  &  \tabularnewline
Midmean - Closest Observation & 45621.2258064516 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 45755.9666666667 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 45815.0625 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=49751&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]46347.95[/C][C]852.411128102842[/C][C]54.3727650566385[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]45885.6560562825[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]45423.1415474409[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]46808.1419023443[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]46312.1166666667[/C][C]841.547666955357[/C][C]55.0320777838048[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]46364.5166666667[/C][C]812.123334852682[/C][C]57.0904869702791[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]46412.3166666667[/C][C]796.694424081482[/C][C]58.2561083192919[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]46337.05[/C][C]776.056610661862[/C][C]59.70833746327[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]46419.8[/C][C]746.543732868173[/C][C]62.1796124677896[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]46431.8[/C][C]694.534717561552[/C][C]66.8531015454747[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]46494.8[/C][C]677.482854787539[/C][C]68.6287478294649[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]46490.4[/C][C]666.541494972199[/C][C]69.7486958436685[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]46353.75[/C][C]627.630862229674[/C][C]73.8551157846623[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]46297.4166666667[/C][C]614.705319733192[/C][C]75.316440545466[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]46283.3[/C][C]600.461023587258[/C][C]77.0796074714318[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]46331.9[/C][C]591.695920674102[/C][C]78.3035650257914[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]46126.0666666667[/C][C]551.495406635894[/C][C]83.6381701672447[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]46228.7333333333[/C][C]534.256542867738[/C][C]86.5290915955668[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]46198.9833333333[/C][C]528.748530198791[/C][C]87.3742066308233[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]46038.45[/C][C]463.045137837707[/C][C]99.4254042165022[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]46063.95[/C][C]447.028050172741[/C][C]103.044876003195[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]45807.45[/C][C]384.588386192024[/C][C]119.107730874454[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]45917.65[/C][C]330.646117024516[/C][C]138.872491270162[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]45942.65[/C][C]318.758678025217[/C][C]144.129879960054[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]46323.275862069[/C][C]809.159752095988[/C][C]57.248615915555[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]46335.2321428571[/C][C]769.14638170358[/C][C]60.2424106061962[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]46318.962962963[/C][C]739.637140700923[/C][C]62.6239008482841[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]46283.0576923077[/C][C]710.399874337064[/C][C]65.1507121049233[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]46266.86[/C][C]682.107775917667[/C][C]67.8292516717835[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]46228.625[/C][C]656.715861748297[/C][C]70.3936476833847[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]46184.4565217391[/C][C]640.80710860686[/C][C]72.0723223906582[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]46124[/C][C]624.695063031475[/C][C]73.834423752563[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]46058.5714285714[/C][C]606.227218418763[/C][C]75.9757563322662[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]46009.375[/C][C]592.448280429587[/C][C]77.6597325367176[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]45963.8947368421[/C][C]576.919505948178[/C][C]79.6712440174814[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]45915.5[/C][C]559.078499897482[/C][C]82.1271073890688[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]45854.2647058823[/C][C]536.029200306094[/C][C]85.5443410166792[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]45815.0625[/C][C]515.845715590763[/C][C]88.8154366999658[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]45755.9666666667[/C][C]491.083370695018[/C][C]93.1735208258211[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]45692.6785714286[/C][C]455.597523386954[/C][C]100.291762412897[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]45642.8076923077[/C][C]427.47646995696[/C][C]106.772678498312[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]45580.875[/C][C]388.780405924472[/C][C]117.240669296629[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]45546.5454545455[/C][C]356.706068911903[/C][C]127.686488748231[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]45487.95[/C][C]328.495585767025[/C][C]138.473550242044[/C][/ROW]
[ROW][C]Median[/C][C]45232[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]47063.5[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]45621.2258064516[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]45755.9666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]45621.2258064516[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]45755.9666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]45755.9666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]45621.2258064516[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]45755.9666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]45815.0625[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]60[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=49751&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=49751&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 Mean46347.95852.41112810284254.3727650566385
Geometric Mean45885.6560562825
Harmonic Mean45423.1415474409
Quadratic Mean46808.1419023443
Winsorized Mean ( 1 / 20 )46312.1166666667841.54766695535755.0320777838048
Winsorized Mean ( 2 / 20 )46364.5166666667812.12333485268257.0904869702791
Winsorized Mean ( 3 / 20 )46412.3166666667796.69442408148258.2561083192919
Winsorized Mean ( 4 / 20 )46337.05776.05661066186259.70833746327
Winsorized Mean ( 5 / 20 )46419.8746.54373286817362.1796124677896
Winsorized Mean ( 6 / 20 )46431.8694.53471756155266.8531015454747
Winsorized Mean ( 7 / 20 )46494.8677.48285478753968.6287478294649
Winsorized Mean ( 8 / 20 )46490.4666.54149497219969.7486958436685
Winsorized Mean ( 9 / 20 )46353.75627.63086222967473.8551157846623
Winsorized Mean ( 10 / 20 )46297.4166666667614.70531973319275.316440545466
Winsorized Mean ( 11 / 20 )46283.3600.46102358725877.0796074714318
Winsorized Mean ( 12 / 20 )46331.9591.69592067410278.3035650257914
Winsorized Mean ( 13 / 20 )46126.0666666667551.49540663589483.6381701672447
Winsorized Mean ( 14 / 20 )46228.7333333333534.25654286773886.5290915955668
Winsorized Mean ( 15 / 20 )46198.9833333333528.74853019879187.3742066308233
Winsorized Mean ( 16 / 20 )46038.45463.04513783770799.4254042165022
Winsorized Mean ( 17 / 20 )46063.95447.028050172741103.044876003195
Winsorized Mean ( 18 / 20 )45807.45384.588386192024119.107730874454
Winsorized Mean ( 19 / 20 )45917.65330.646117024516138.872491270162
Winsorized Mean ( 20 / 20 )45942.65318.758678025217144.129879960054
Trimmed Mean ( 1 / 20 )46323.275862069809.15975209598857.248615915555
Trimmed Mean ( 2 / 20 )46335.2321428571769.1463817035860.2424106061962
Trimmed Mean ( 3 / 20 )46318.962962963739.63714070092362.6239008482841
Trimmed Mean ( 4 / 20 )46283.0576923077710.39987433706465.1507121049233
Trimmed Mean ( 5 / 20 )46266.86682.10777591766767.8292516717835
Trimmed Mean ( 6 / 20 )46228.625656.71586174829770.3936476833847
Trimmed Mean ( 7 / 20 )46184.4565217391640.8071086068672.0723223906582
Trimmed Mean ( 8 / 20 )46124624.69506303147573.834423752563
Trimmed Mean ( 9 / 20 )46058.5714285714606.22721841876375.9757563322662
Trimmed Mean ( 10 / 20 )46009.375592.44828042958777.6597325367176
Trimmed Mean ( 11 / 20 )45963.8947368421576.91950594817879.6712440174814
Trimmed Mean ( 12 / 20 )45915.5559.07849989748282.1271073890688
Trimmed Mean ( 13 / 20 )45854.2647058823536.02920030609485.5443410166792
Trimmed Mean ( 14 / 20 )45815.0625515.84571559076388.8154366999658
Trimmed Mean ( 15 / 20 )45755.9666666667491.08337069501893.1735208258211
Trimmed Mean ( 16 / 20 )45692.6785714286455.597523386954100.291762412897
Trimmed Mean ( 17 / 20 )45642.8076923077427.47646995696106.772678498312
Trimmed Mean ( 18 / 20 )45580.875388.780405924472117.240669296629
Trimmed Mean ( 19 / 20 )45546.5454545455356.706068911903127.686488748231
Trimmed Mean ( 20 / 20 )45487.95328.495585767025138.473550242044
Median45232
Midrange47063.5
Midmean - Weighted Average at Xnp45621.2258064516
Midmean - Weighted Average at X(n+1)p45755.9666666667
Midmean - Empirical Distribution Function45621.2258064516
Midmean - Empirical Distribution Function - Averaging45755.9666666667
Midmean - Empirical Distribution Function - Interpolation45755.9666666667
Midmean - Closest Observation45621.2258064516
Midmean - True Basic - Statistics Graphics Toolkit45755.9666666667
Midmean - MS Excel (old versions)45815.0625
Number of observations60



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')