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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 computationTue, 15 Dec 2015 19:36:24 +0000
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2015/Dec/15/t1450208216dt23ezjjd2cc6qe.htm/, Retrieved Fri, 24 May 2024 18:44:58 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=286578, Retrieved Fri, 24 May 2024 18:44:58 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact77
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [] [2015-12-15 19:36:24] [9d441e5437781f0cd4d5053adc3d2c6c] [Current]
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Dataseries X:
55954
52044
49975
50398
48751
46908
44938
42372
43522
58434
62713
59266
53411
50215
48474
50250
49409
46751
44869
43023
44638
57810
65000
61665
56119
52162
51069
51744
50816
48578
47144
44839
45879
60730
65037
63281
57300
53335
51813
52597
50744
48008
45326
42661
43627
58156
61772
59879
54417
50575
48798
48819
47606
45345
42484
39735
40959
53249
57028
55763
50547




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Sir Maurice George Kendall' @ kendall.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 & 1 seconds \tabularnewline
R Server & 'Sir Maurice George Kendall' @ kendall.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=286578&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]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Sir Maurice George Kendall' @ kendall.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=286578&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=286578&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 time1 seconds
R Server'Sir Maurice George Kendall' @ kendall.wessa.net







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean51290.6721311475817.83347327658762.7153006169525
Geometric Mean50906.9422040902
Harmonic Mean50531.329744374
Quadratic Mean51680.4038593505
Winsorized Mean ( 1 / 20 )51310.131147541813.17158086834263.0987756516893
Winsorized Mean ( 2 / 20 )51300.0983606557788.82712640849265.0333851907751
Winsorized Mean ( 3 / 20 )51277.6721311475780.84527049840965.6694406286374
Winsorized Mean ( 4 / 20 )51227.5737704918764.03979578320867.0483056683965
Winsorized Mean ( 5 / 20 )51248.4754098361756.56366596560967.738483508096
Winsorized Mean ( 6 / 20 )51205.5901639344727.192712176970.415433634706
Winsorized Mean ( 7 / 20 )51119.9836065574704.27513194129772.5852458621503
Winsorized Mean ( 8 / 20 )51172.1803278689665.15018621590976.9332721967521
Winsorized Mean ( 9 / 20 )51079.0819672131636.00655360367280.3121943913853
Winsorized Mean ( 10 / 20 )51038.4262295082626.4937321519681.4667786925736
Winsorized Mean ( 11 / 20 )50988.4754098361612.75209537470983.2122416140506
Winsorized Mean ( 12 / 20 )50964.4754098361581.88911333875587.5845143714974
Winsorized Mean ( 13 / 20 )50910.5573770492570.79572323530189.1922544347133
Winsorized Mean ( 14 / 20 )50824.4918032787514.44896066305398.7940411771325
Winsorized Mean ( 15 / 20 )50998.3442622951474.207953901925107.54426163177
Winsorized Mean ( 16 / 20 )50989.4262295082459.383482946257110.995340760811
Winsorized Mean ( 17 / 20 )50680.0819672131386.621536815466131.084477043509
Winsorized Mean ( 18 / 20 )50519.5573770492319.417751990495158.16139542098
Winsorized Mean ( 19 / 20 )50621.0983606557297.124042379718170.370253296309
Winsorized Mean ( 20 / 20 )50745.6885245902270.909644103522187.315917425217
Trimmed Mean ( 1 / 20 )51253.5423728814788.10198066242765.0341499329832
Trimmed Mean ( 2 / 20 )51192.9824561404757.22680396207267.6058773781924
Trimmed Mean ( 3 / 20 )51133.5818181818735.38388275152869.5331826241001
Trimmed Mean ( 4 / 20 )51078.3018867925711.98646076196571.7405522460759
Trimmed Mean ( 5 / 20 )51033.6666666667689.35228801641374.0313299220551
Trimmed Mean ( 6 / 20 )50980.1836734694663.18411647248176.8718405751879
Trimmed Mean ( 7 / 20 )50931.4255319149639.30951980514879.6663023998736
Trimmed Mean ( 8 / 20 )50894.9111111111615.52790172357382.6849781603685
Trimmed Mean ( 9 / 20 )50845.7441860465595.68571196070785.3566623558707
Trimmed Mean ( 10 / 20 )50807.1707317073577.58965295276687.9641289832147
Trimmed Mean ( 11 / 20 )50771555.79507189549691.3484170106968
Trimmed Mean ( 12 / 20 )50738.4054054054530.02293063242695.7286986524604
Trimmed Mean ( 13 / 20 )50705.5714285714503.604477132357100.685307083251
Trimmed Mean ( 14 / 20 )50676.4242424242469.795978506658107.869003909973
Trimmed Mean ( 15 / 20 )50655.6129032258440.451365939409115.008413687595
Trimmed Mean ( 16 / 20 )50607.5517241379410.801950851222123.192092002665
Trimmed Mean ( 17 / 20 )50553.6296296296371.122610298896136.218134456736
Trimmed Mean ( 18 / 20 )50535.48341.878190393401147.817209228376
Trimmed Mean ( 19 / 20 )50537.8260869565324.487505025515155.746601345968
Trimmed Mean ( 20 / 20 )50525.0952380952304.92082426475165.699064207653
Median50547
Midrange52386
Midmean - Weighted Average at Xnp50479
Midmean - Weighted Average at X(n+1)p50655.6129032258
Midmean - Empirical Distribution Function50655.6129032258
Midmean - Empirical Distribution Function - Averaging50655.6129032258
Midmean - Empirical Distribution Function - Interpolation50655.6129032258
Midmean - Closest Observation50506.34375
Midmean - True Basic - Statistics Graphics Toolkit50655.6129032258
Midmean - MS Excel (old versions)50655.6129032258
Number of observations61

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 51290.6721311475 & 817.833473276587 & 62.7153006169525 \tabularnewline
Geometric Mean & 50906.9422040902 &  &  \tabularnewline
Harmonic Mean & 50531.329744374 &  &  \tabularnewline
Quadratic Mean & 51680.4038593505 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 51310.131147541 & 813.171580868342 & 63.0987756516893 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 51300.0983606557 & 788.827126408492 & 65.0333851907751 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 51277.6721311475 & 780.845270498409 & 65.6694406286374 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 51227.5737704918 & 764.039795783208 & 67.0483056683965 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 51248.4754098361 & 756.563665965609 & 67.738483508096 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 51205.5901639344 & 727.1927121769 & 70.415433634706 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 51119.9836065574 & 704.275131941297 & 72.5852458621503 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 51172.1803278689 & 665.150186215909 & 76.9332721967521 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 51079.0819672131 & 636.006553603672 & 80.3121943913853 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 51038.4262295082 & 626.49373215196 & 81.4667786925736 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 50988.4754098361 & 612.752095374709 & 83.2122416140506 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 50964.4754098361 & 581.889113338755 & 87.5845143714974 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 50910.5573770492 & 570.795723235301 & 89.1922544347133 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 50824.4918032787 & 514.448960663053 & 98.7940411771325 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 50998.3442622951 & 474.207953901925 & 107.54426163177 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 50989.4262295082 & 459.383482946257 & 110.995340760811 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 50680.0819672131 & 386.621536815466 & 131.084477043509 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 50519.5573770492 & 319.417751990495 & 158.16139542098 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 50621.0983606557 & 297.124042379718 & 170.370253296309 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 50745.6885245902 & 270.909644103522 & 187.315917425217 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 51253.5423728814 & 788.101980662427 & 65.0341499329832 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 51192.9824561404 & 757.226803962072 & 67.6058773781924 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 51133.5818181818 & 735.383882751528 & 69.5331826241001 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 51078.3018867925 & 711.986460761965 & 71.7405522460759 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 51033.6666666667 & 689.352288016413 & 74.0313299220551 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 50980.1836734694 & 663.184116472481 & 76.8718405751879 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 50931.4255319149 & 639.309519805148 & 79.6663023998736 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 50894.9111111111 & 615.527901723573 & 82.6849781603685 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 50845.7441860465 & 595.685711960707 & 85.3566623558707 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 50807.1707317073 & 577.589652952766 & 87.9641289832147 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 50771 & 555.795071895496 & 91.3484170106968 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 50738.4054054054 & 530.022930632426 & 95.7286986524604 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 50705.5714285714 & 503.604477132357 & 100.685307083251 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 50676.4242424242 & 469.795978506658 & 107.869003909973 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 50655.6129032258 & 440.451365939409 & 115.008413687595 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 50607.5517241379 & 410.801950851222 & 123.192092002665 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 50553.6296296296 & 371.122610298896 & 136.218134456736 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 50535.48 & 341.878190393401 & 147.817209228376 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 50537.8260869565 & 324.487505025515 & 155.746601345968 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 50525.0952380952 & 304.92082426475 & 165.699064207653 \tabularnewline
Median & 50547 &  &  \tabularnewline
Midrange & 52386 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 50479 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 50655.6129032258 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 50655.6129032258 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 50655.6129032258 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 50655.6129032258 &  &  \tabularnewline
Midmean - Closest Observation & 50506.34375 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 50655.6129032258 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 50655.6129032258 &  &  \tabularnewline
Number of observations & 61 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=286578&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]51290.6721311475[/C][C]817.833473276587[/C][C]62.7153006169525[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]50906.9422040902[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]50531.329744374[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]51680.4038593505[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]51310.131147541[/C][C]813.171580868342[/C][C]63.0987756516893[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]51300.0983606557[/C][C]788.827126408492[/C][C]65.0333851907751[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]51277.6721311475[/C][C]780.845270498409[/C][C]65.6694406286374[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]51227.5737704918[/C][C]764.039795783208[/C][C]67.0483056683965[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]51248.4754098361[/C][C]756.563665965609[/C][C]67.738483508096[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]51205.5901639344[/C][C]727.1927121769[/C][C]70.415433634706[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]51119.9836065574[/C][C]704.275131941297[/C][C]72.5852458621503[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]51172.1803278689[/C][C]665.150186215909[/C][C]76.9332721967521[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]51079.0819672131[/C][C]636.006553603672[/C][C]80.3121943913853[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]51038.4262295082[/C][C]626.49373215196[/C][C]81.4667786925736[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]50988.4754098361[/C][C]612.752095374709[/C][C]83.2122416140506[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]50964.4754098361[/C][C]581.889113338755[/C][C]87.5845143714974[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]50910.5573770492[/C][C]570.795723235301[/C][C]89.1922544347133[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]50824.4918032787[/C][C]514.448960663053[/C][C]98.7940411771325[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]50998.3442622951[/C][C]474.207953901925[/C][C]107.54426163177[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]50989.4262295082[/C][C]459.383482946257[/C][C]110.995340760811[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]50680.0819672131[/C][C]386.621536815466[/C][C]131.084477043509[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]50519.5573770492[/C][C]319.417751990495[/C][C]158.16139542098[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]50621.0983606557[/C][C]297.124042379718[/C][C]170.370253296309[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]50745.6885245902[/C][C]270.909644103522[/C][C]187.315917425217[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]51253.5423728814[/C][C]788.101980662427[/C][C]65.0341499329832[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]51192.9824561404[/C][C]757.226803962072[/C][C]67.6058773781924[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]51133.5818181818[/C][C]735.383882751528[/C][C]69.5331826241001[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]51078.3018867925[/C][C]711.986460761965[/C][C]71.7405522460759[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]51033.6666666667[/C][C]689.352288016413[/C][C]74.0313299220551[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]50980.1836734694[/C][C]663.184116472481[/C][C]76.8718405751879[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]50931.4255319149[/C][C]639.309519805148[/C][C]79.6663023998736[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]50894.9111111111[/C][C]615.527901723573[/C][C]82.6849781603685[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]50845.7441860465[/C][C]595.685711960707[/C][C]85.3566623558707[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]50807.1707317073[/C][C]577.589652952766[/C][C]87.9641289832147[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]50771[/C][C]555.795071895496[/C][C]91.3484170106968[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]50738.4054054054[/C][C]530.022930632426[/C][C]95.7286986524604[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]50705.5714285714[/C][C]503.604477132357[/C][C]100.685307083251[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]50676.4242424242[/C][C]469.795978506658[/C][C]107.869003909973[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]50655.6129032258[/C][C]440.451365939409[/C][C]115.008413687595[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]50607.5517241379[/C][C]410.801950851222[/C][C]123.192092002665[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]50553.6296296296[/C][C]371.122610298896[/C][C]136.218134456736[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]50535.48[/C][C]341.878190393401[/C][C]147.817209228376[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]50537.8260869565[/C][C]324.487505025515[/C][C]155.746601345968[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]50525.0952380952[/C][C]304.92082426475[/C][C]165.699064207653[/C][/ROW]
[ROW][C]Median[/C][C]50547[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]52386[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]50479[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]50655.6129032258[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]50655.6129032258[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]50655.6129032258[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]50655.6129032258[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]50506.34375[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]50655.6129032258[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]50655.6129032258[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]61[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=286578&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=286578&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 Mean51290.6721311475817.83347327658762.7153006169525
Geometric Mean50906.9422040902
Harmonic Mean50531.329744374
Quadratic Mean51680.4038593505
Winsorized Mean ( 1 / 20 )51310.131147541813.17158086834263.0987756516893
Winsorized Mean ( 2 / 20 )51300.0983606557788.82712640849265.0333851907751
Winsorized Mean ( 3 / 20 )51277.6721311475780.84527049840965.6694406286374
Winsorized Mean ( 4 / 20 )51227.5737704918764.03979578320867.0483056683965
Winsorized Mean ( 5 / 20 )51248.4754098361756.56366596560967.738483508096
Winsorized Mean ( 6 / 20 )51205.5901639344727.192712176970.415433634706
Winsorized Mean ( 7 / 20 )51119.9836065574704.27513194129772.5852458621503
Winsorized Mean ( 8 / 20 )51172.1803278689665.15018621590976.9332721967521
Winsorized Mean ( 9 / 20 )51079.0819672131636.00655360367280.3121943913853
Winsorized Mean ( 10 / 20 )51038.4262295082626.4937321519681.4667786925736
Winsorized Mean ( 11 / 20 )50988.4754098361612.75209537470983.2122416140506
Winsorized Mean ( 12 / 20 )50964.4754098361581.88911333875587.5845143714974
Winsorized Mean ( 13 / 20 )50910.5573770492570.79572323530189.1922544347133
Winsorized Mean ( 14 / 20 )50824.4918032787514.44896066305398.7940411771325
Winsorized Mean ( 15 / 20 )50998.3442622951474.207953901925107.54426163177
Winsorized Mean ( 16 / 20 )50989.4262295082459.383482946257110.995340760811
Winsorized Mean ( 17 / 20 )50680.0819672131386.621536815466131.084477043509
Winsorized Mean ( 18 / 20 )50519.5573770492319.417751990495158.16139542098
Winsorized Mean ( 19 / 20 )50621.0983606557297.124042379718170.370253296309
Winsorized Mean ( 20 / 20 )50745.6885245902270.909644103522187.315917425217
Trimmed Mean ( 1 / 20 )51253.5423728814788.10198066242765.0341499329832
Trimmed Mean ( 2 / 20 )51192.9824561404757.22680396207267.6058773781924
Trimmed Mean ( 3 / 20 )51133.5818181818735.38388275152869.5331826241001
Trimmed Mean ( 4 / 20 )51078.3018867925711.98646076196571.7405522460759
Trimmed Mean ( 5 / 20 )51033.6666666667689.35228801641374.0313299220551
Trimmed Mean ( 6 / 20 )50980.1836734694663.18411647248176.8718405751879
Trimmed Mean ( 7 / 20 )50931.4255319149639.30951980514879.6663023998736
Trimmed Mean ( 8 / 20 )50894.9111111111615.52790172357382.6849781603685
Trimmed Mean ( 9 / 20 )50845.7441860465595.68571196070785.3566623558707
Trimmed Mean ( 10 / 20 )50807.1707317073577.58965295276687.9641289832147
Trimmed Mean ( 11 / 20 )50771555.79507189549691.3484170106968
Trimmed Mean ( 12 / 20 )50738.4054054054530.02293063242695.7286986524604
Trimmed Mean ( 13 / 20 )50705.5714285714503.604477132357100.685307083251
Trimmed Mean ( 14 / 20 )50676.4242424242469.795978506658107.869003909973
Trimmed Mean ( 15 / 20 )50655.6129032258440.451365939409115.008413687595
Trimmed Mean ( 16 / 20 )50607.5517241379410.801950851222123.192092002665
Trimmed Mean ( 17 / 20 )50553.6296296296371.122610298896136.218134456736
Trimmed Mean ( 18 / 20 )50535.48341.878190393401147.817209228376
Trimmed Mean ( 19 / 20 )50537.8260869565324.487505025515155.746601345968
Trimmed Mean ( 20 / 20 )50525.0952380952304.92082426475165.699064207653
Median50547
Midrange52386
Midmean - Weighted Average at Xnp50479
Midmean - Weighted Average at X(n+1)p50655.6129032258
Midmean - Empirical Distribution Function50655.6129032258
Midmean - Empirical Distribution Function - Averaging50655.6129032258
Midmean - Empirical Distribution Function - Interpolation50655.6129032258
Midmean - Closest Observation50506.34375
Midmean - True Basic - Statistics Graphics Toolkit50655.6129032258
Midmean - MS Excel (old versions)50655.6129032258
Number of observations61



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')