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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 computationSun, 19 Dec 2010 21:05:11 +0000
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2010/Dec/19/t12927925822518lf3972ynkag.htm/, Retrieved Sun, 05 May 2024 07:37:52 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=112744, Retrieved Sun, 05 May 2024 07:37:52 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact113
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Central Tendency] [Arabica Price in ...] [2008-01-06 21:28:17] [74be16979710d4c4e7c6647856088456]
-  M D  [Central Tendency] [Robustness of Cen...] [2010-12-18 14:20:59] [1afa3497b02a8d7c9f6727c1b17b89b2]
-         [Central Tendency] [Central tendency ...] [2010-12-19 18:22:32] [1afa3497b02a8d7c9f6727c1b17b89b2]
-    D        [Central Tendency] [Central tendency ...] [2010-12-19 21:05:11] [214713b86cef2e1efaaf6d85aa84ff3c] [Current]
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Dataseries X:
35.16   
41.54   
45.07   
46.84   
45.20   
46.65   
52.55   
55.05   
60.75   
55.99   
53.39   
49.42   
55.12   
59.84   
55.98   
61.27   
66.94   
64.67   
67.74   
69.79   
64.49   
54.92   
53.32   
56.13   
54.63   
52.11   
57.83   
64.93   
63.40   
65.37   
69.91   
73.81   
71.42   
75.57   
86.02   
85.91   
92.93   
88.71   
98.01   
98.39   
110.21   
121.36   
137.11   
121.29   
106.41   
93.38   
58.66   
43.12   
34.57   
41.77   
42.85   
48.09   
48.91   
65.62   
68.47   
71.52   
68.07   
65.00   
76.34   
76.18   




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=112744&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=112744&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=112744&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 Mean66.92833333333332.8339315005005323.6167787829425
Geometric Mean63.8394607687197
Harmonic Mean61.1191544826577
Quadratic Mean70.3792632811683
Winsorized Mean ( 1 / 20 )66.67566666666672.732210497290924.4035614140193
Winsorized Mean ( 2 / 20 )66.8862.693640839412624.8310758514434
Winsorized Mean ( 3 / 20 )66.34352.5146028634228626.3832913598506
Winsorized Mean ( 4 / 20 )66.16216666666672.4297370075962727.2301761300993
Winsorized Mean ( 5 / 20 )65.51633333333332.2489761005714629.1316271954538
Winsorized Mean ( 6 / 20 )65.67333333333332.2076630365303829.7478973224770
Winsorized Mean ( 7 / 20 )65.14833333333332.0757712904109131.385121103798
Winsorized Mean ( 8 / 20 )65.28166666666672.0311521342496832.1402151842171
Winsorized Mean ( 9 / 20 )64.67716666666671.8850689881075134.3102385507909
Winsorized Mean ( 10 / 20 )64.43716666666671.7567441972781436.6798801820459
Winsorized Mean ( 11 / 20 )64.56733333333331.7291413215758837.3406918958417
Winsorized Mean ( 12 / 20 )62.75533333333331.3441504461352446.6877301672369
Winsorized Mean ( 13 / 20 )63.30351.2445415924844550.864913139326
Winsorized Mean ( 14 / 20 )63.26383333333331.2041640814782752.5375522376224
Winsorized Mean ( 15 / 20 )63.01633333333331.1005220119024157.2604024742771
Winsorized Mean ( 16 / 20 )62.42433333333330.99968114596454562.4442439325021
Winsorized Mean ( 17 / 20 )62.74733333333330.94270610198880766.5608647286325
Winsorized Mean ( 18 / 20 )62.38133333333330.86100497930496772.4517683784938
Winsorized Mean ( 19 / 20 )62.38450.84934522553958873.4501097128876
Winsorized Mean ( 20 / 20 )61.96783333333330.78234281978221379.208029736355
Trimmed Mean ( 1 / 20 )66.27620689655172.6049153224470825.4427490695903
Trimmed Mean ( 2 / 20 )65.84821428571432.4455392482537526.9258464499122
Trimmed Mean ( 3 / 20 )65.27166666666672.2692463392694728.763587953029
Trimmed Mean ( 4 / 20 )64.85942307692312.1410649056311530.2930672051737
Trimmed Mean ( 5 / 20 )64.46862.0141020384341232.0086066990536
Trimmed Mean ( 6 / 20 )64.20666666666671.9214367715695133.4159664354814
Trimmed Mean ( 7 / 20 )63.88782608695651.8145169014923235.2092758322686
Trimmed Mean ( 8 / 20 )63.64227272727271.7194540366979137.0130700611766
Trimmed Mean ( 9 / 20 )63.34952380952381.6063954987905039.435820043832
Trimmed Mean ( 10 / 20 )63.128251.5034054457447241.9901698365401
Trimmed Mean ( 11 / 20 )62.92157894736841.4046638697418544.794758591557
Trimmed Mean ( 12 / 20 )62.67222222222221.2746368988797949.1686866097329
Trimmed Mean ( 13 / 20 )62.661.2253583273079951.1360624917439
Trimmed Mean ( 14 / 20 )62.56718751.1838623600637052.8500521772085
Trimmed Mean ( 15 / 20 )62.46766666666671.1349229234382455.0413295710175
Trimmed Mean ( 16 / 20 )62.38928571428571.0959902782863856.9250356963325
Trimmed Mean ( 17 / 20 )62.38423076923081.0696839465758758.3202458716211
Trimmed Mean ( 18 / 20 )62.33083333333331.0442247864274159.6910111151305
Trimmed Mean ( 19 / 20 )62.32318181818181.0293719739547460.544859773812
Trimmed Mean ( 20 / 20 )62.31351.0011622916443362.2411576225619
Median63.945
Midrange85.84
Midmean - Weighted Average at Xnp62.1477419354839
Midmean - Weighted Average at X(n+1)p62.4676666666667
Midmean - Empirical Distribution Function62.1477419354839
Midmean - Empirical Distribution Function - Averaging62.4676666666667
Midmean - Empirical Distribution Function - Interpolation62.4676666666667
Midmean - Closest Observation62.1477419354839
Midmean - True Basic - Statistics Graphics Toolkit62.4676666666667
Midmean - MS Excel (old versions)62.5671875
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 66.9283333333333 & 2.83393150050053 & 23.6167787829425 \tabularnewline
Geometric Mean & 63.8394607687197 &  &  \tabularnewline
Harmonic Mean & 61.1191544826577 &  &  \tabularnewline
Quadratic Mean & 70.3792632811683 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 66.6756666666667 & 2.7322104972909 & 24.4035614140193 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 66.886 & 2.6936408394126 & 24.8310758514434 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 66.3435 & 2.51460286342286 & 26.3832913598506 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 66.1621666666667 & 2.42973700759627 & 27.2301761300993 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 65.5163333333333 & 2.24897610057146 & 29.1316271954538 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 65.6733333333333 & 2.20766303653038 & 29.7478973224770 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 65.1483333333333 & 2.07577129041091 & 31.385121103798 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 65.2816666666667 & 2.03115213424968 & 32.1402151842171 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 64.6771666666667 & 1.88506898810751 & 34.3102385507909 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 64.4371666666667 & 1.75674419727814 & 36.6798801820459 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 64.5673333333333 & 1.72914132157588 & 37.3406918958417 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 62.7553333333333 & 1.34415044613524 & 46.6877301672369 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 63.3035 & 1.24454159248445 & 50.864913139326 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 63.2638333333333 & 1.20416408147827 & 52.5375522376224 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 63.0163333333333 & 1.10052201190241 & 57.2604024742771 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 62.4243333333333 & 0.999681145964545 & 62.4442439325021 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 62.7473333333333 & 0.942706101988807 & 66.5608647286325 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 62.3813333333333 & 0.861004979304967 & 72.4517683784938 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 62.3845 & 0.849345225539588 & 73.4501097128876 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 61.9678333333333 & 0.782342819782213 & 79.208029736355 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 66.2762068965517 & 2.60491532244708 & 25.4427490695903 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 65.8482142857143 & 2.44553924825375 & 26.9258464499122 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 65.2716666666667 & 2.26924633926947 & 28.763587953029 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 64.8594230769231 & 2.14106490563115 & 30.2930672051737 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 64.4686 & 2.01410203843412 & 32.0086066990536 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 64.2066666666667 & 1.92143677156951 & 33.4159664354814 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 63.8878260869565 & 1.81451690149232 & 35.2092758322686 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 63.6422727272727 & 1.71945403669791 & 37.0130700611766 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 63.3495238095238 & 1.60639549879050 & 39.435820043832 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 63.12825 & 1.50340544574472 & 41.9901698365401 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 62.9215789473684 & 1.40466386974185 & 44.794758591557 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 62.6722222222222 & 1.27463689887979 & 49.1686866097329 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 62.66 & 1.22535832730799 & 51.1360624917439 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 62.5671875 & 1.18386236006370 & 52.8500521772085 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 62.4676666666667 & 1.13492292343824 & 55.0413295710175 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 62.3892857142857 & 1.09599027828638 & 56.9250356963325 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 62.3842307692308 & 1.06968394657587 & 58.3202458716211 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 62.3308333333333 & 1.04422478642741 & 59.6910111151305 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 62.3231818181818 & 1.02937197395474 & 60.544859773812 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 62.3135 & 1.00116229164433 & 62.2411576225619 \tabularnewline
Median & 63.945 &  &  \tabularnewline
Midrange & 85.84 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 62.1477419354839 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 62.4676666666667 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 62.1477419354839 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 62.4676666666667 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 62.4676666666667 &  &  \tabularnewline
Midmean - Closest Observation & 62.1477419354839 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 62.4676666666667 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 62.5671875 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=112744&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]66.9283333333333[/C][C]2.83393150050053[/C][C]23.6167787829425[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]63.8394607687197[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]61.1191544826577[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]70.3792632811683[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]66.6756666666667[/C][C]2.7322104972909[/C][C]24.4035614140193[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]66.886[/C][C]2.6936408394126[/C][C]24.8310758514434[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]66.3435[/C][C]2.51460286342286[/C][C]26.3832913598506[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]66.1621666666667[/C][C]2.42973700759627[/C][C]27.2301761300993[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]65.5163333333333[/C][C]2.24897610057146[/C][C]29.1316271954538[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]65.6733333333333[/C][C]2.20766303653038[/C][C]29.7478973224770[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]65.1483333333333[/C][C]2.07577129041091[/C][C]31.385121103798[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]65.2816666666667[/C][C]2.03115213424968[/C][C]32.1402151842171[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]64.6771666666667[/C][C]1.88506898810751[/C][C]34.3102385507909[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]64.4371666666667[/C][C]1.75674419727814[/C][C]36.6798801820459[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]64.5673333333333[/C][C]1.72914132157588[/C][C]37.3406918958417[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]62.7553333333333[/C][C]1.34415044613524[/C][C]46.6877301672369[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]63.3035[/C][C]1.24454159248445[/C][C]50.864913139326[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]63.2638333333333[/C][C]1.20416408147827[/C][C]52.5375522376224[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]63.0163333333333[/C][C]1.10052201190241[/C][C]57.2604024742771[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]62.4243333333333[/C][C]0.999681145964545[/C][C]62.4442439325021[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]62.7473333333333[/C][C]0.942706101988807[/C][C]66.5608647286325[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]62.3813333333333[/C][C]0.861004979304967[/C][C]72.4517683784938[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]62.3845[/C][C]0.849345225539588[/C][C]73.4501097128876[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]61.9678333333333[/C][C]0.782342819782213[/C][C]79.208029736355[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]66.2762068965517[/C][C]2.60491532244708[/C][C]25.4427490695903[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]65.8482142857143[/C][C]2.44553924825375[/C][C]26.9258464499122[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]65.2716666666667[/C][C]2.26924633926947[/C][C]28.763587953029[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]64.8594230769231[/C][C]2.14106490563115[/C][C]30.2930672051737[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]64.4686[/C][C]2.01410203843412[/C][C]32.0086066990536[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]64.2066666666667[/C][C]1.92143677156951[/C][C]33.4159664354814[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]63.8878260869565[/C][C]1.81451690149232[/C][C]35.2092758322686[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]63.6422727272727[/C][C]1.71945403669791[/C][C]37.0130700611766[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]63.3495238095238[/C][C]1.60639549879050[/C][C]39.435820043832[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]63.12825[/C][C]1.50340544574472[/C][C]41.9901698365401[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]62.9215789473684[/C][C]1.40466386974185[/C][C]44.794758591557[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]62.6722222222222[/C][C]1.27463689887979[/C][C]49.1686866097329[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]62.66[/C][C]1.22535832730799[/C][C]51.1360624917439[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]62.5671875[/C][C]1.18386236006370[/C][C]52.8500521772085[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]62.4676666666667[/C][C]1.13492292343824[/C][C]55.0413295710175[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]62.3892857142857[/C][C]1.09599027828638[/C][C]56.9250356963325[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]62.3842307692308[/C][C]1.06968394657587[/C][C]58.3202458716211[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]62.3308333333333[/C][C]1.04422478642741[/C][C]59.6910111151305[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]62.3231818181818[/C][C]1.02937197395474[/C][C]60.544859773812[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]62.3135[/C][C]1.00116229164433[/C][C]62.2411576225619[/C][/ROW]
[ROW][C]Median[/C][C]63.945[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]85.84[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]62.1477419354839[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]62.4676666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]62.1477419354839[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]62.4676666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]62.4676666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]62.1477419354839[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]62.4676666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]62.5671875[/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=112744&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=112744&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 Mean66.92833333333332.8339315005005323.6167787829425
Geometric Mean63.8394607687197
Harmonic Mean61.1191544826577
Quadratic Mean70.3792632811683
Winsorized Mean ( 1 / 20 )66.67566666666672.732210497290924.4035614140193
Winsorized Mean ( 2 / 20 )66.8862.693640839412624.8310758514434
Winsorized Mean ( 3 / 20 )66.34352.5146028634228626.3832913598506
Winsorized Mean ( 4 / 20 )66.16216666666672.4297370075962727.2301761300993
Winsorized Mean ( 5 / 20 )65.51633333333332.2489761005714629.1316271954538
Winsorized Mean ( 6 / 20 )65.67333333333332.2076630365303829.7478973224770
Winsorized Mean ( 7 / 20 )65.14833333333332.0757712904109131.385121103798
Winsorized Mean ( 8 / 20 )65.28166666666672.0311521342496832.1402151842171
Winsorized Mean ( 9 / 20 )64.67716666666671.8850689881075134.3102385507909
Winsorized Mean ( 10 / 20 )64.43716666666671.7567441972781436.6798801820459
Winsorized Mean ( 11 / 20 )64.56733333333331.7291413215758837.3406918958417
Winsorized Mean ( 12 / 20 )62.75533333333331.3441504461352446.6877301672369
Winsorized Mean ( 13 / 20 )63.30351.2445415924844550.864913139326
Winsorized Mean ( 14 / 20 )63.26383333333331.2041640814782752.5375522376224
Winsorized Mean ( 15 / 20 )63.01633333333331.1005220119024157.2604024742771
Winsorized Mean ( 16 / 20 )62.42433333333330.99968114596454562.4442439325021
Winsorized Mean ( 17 / 20 )62.74733333333330.94270610198880766.5608647286325
Winsorized Mean ( 18 / 20 )62.38133333333330.86100497930496772.4517683784938
Winsorized Mean ( 19 / 20 )62.38450.84934522553958873.4501097128876
Winsorized Mean ( 20 / 20 )61.96783333333330.78234281978221379.208029736355
Trimmed Mean ( 1 / 20 )66.27620689655172.6049153224470825.4427490695903
Trimmed Mean ( 2 / 20 )65.84821428571432.4455392482537526.9258464499122
Trimmed Mean ( 3 / 20 )65.27166666666672.2692463392694728.763587953029
Trimmed Mean ( 4 / 20 )64.85942307692312.1410649056311530.2930672051737
Trimmed Mean ( 5 / 20 )64.46862.0141020384341232.0086066990536
Trimmed Mean ( 6 / 20 )64.20666666666671.9214367715695133.4159664354814
Trimmed Mean ( 7 / 20 )63.88782608695651.8145169014923235.2092758322686
Trimmed Mean ( 8 / 20 )63.64227272727271.7194540366979137.0130700611766
Trimmed Mean ( 9 / 20 )63.34952380952381.6063954987905039.435820043832
Trimmed Mean ( 10 / 20 )63.128251.5034054457447241.9901698365401
Trimmed Mean ( 11 / 20 )62.92157894736841.4046638697418544.794758591557
Trimmed Mean ( 12 / 20 )62.67222222222221.2746368988797949.1686866097329
Trimmed Mean ( 13 / 20 )62.661.2253583273079951.1360624917439
Trimmed Mean ( 14 / 20 )62.56718751.1838623600637052.8500521772085
Trimmed Mean ( 15 / 20 )62.46766666666671.1349229234382455.0413295710175
Trimmed Mean ( 16 / 20 )62.38928571428571.0959902782863856.9250356963325
Trimmed Mean ( 17 / 20 )62.38423076923081.0696839465758758.3202458716211
Trimmed Mean ( 18 / 20 )62.33083333333331.0442247864274159.6910111151305
Trimmed Mean ( 19 / 20 )62.32318181818181.0293719739547460.544859773812
Trimmed Mean ( 20 / 20 )62.31351.0011622916443362.2411576225619
Median63.945
Midrange85.84
Midmean - Weighted Average at Xnp62.1477419354839
Midmean - Weighted Average at X(n+1)p62.4676666666667
Midmean - Empirical Distribution Function62.1477419354839
Midmean - Empirical Distribution Function - Averaging62.4676666666667
Midmean - Empirical Distribution Function - Interpolation62.4676666666667
Midmean - Closest Observation62.1477419354839
Midmean - True Basic - Statistics Graphics Toolkit62.4676666666667
Midmean - MS Excel (old versions)62.5671875
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')