Free Statistics

of Irreproducible Research!

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, 21 Dec 2008 15:24:57 -0700
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2008/Dec/21/t1229898486wrqkwdone21j46j.htm/, Retrieved Sun, 19 May 2024 08:49:49 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=35886, Retrieved Sun, 19 May 2024 08:49:49 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact169
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Central Tendency] [Paper central ten...] [2007-11-09 08:56:17] [74be16979710d4c4e7c6647856088456]
-    D    [Central Tendency] [] [2008-12-21 22:24:57] [0e4dd4b7713a9edf1ca3fab1bbbafcc9] [Current]
Feedback Forum

Post a new message
Dataseries X:
3999
4864
5134
5410
4669
3546
5040
4850
4808
4441
4227
3620
3153
3936
4159
4209
4282
3174
4686
4131
4486
4625
3971
3397
3228
3441
3832
5267
3580
2617
3874
3431
4023
4151
3180
2916
2640
2700
3603
4348
3322
2312
3472
3592
3481
3451
2725
2574
2429
3160
3371
3448
3229
1986
2955
3000
8255
4191
3520
2497




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Sir Ronald Aylmer Fisher' @ 193.190.124.24

\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 & 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=35886&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]'Sir Ronald Aylmer Fisher' @ 193.190.124.24[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=35886&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=35886&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'Sir Ronald Aylmer Fisher' @ 193.190.124.24







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean3776.96666666667127.40319459286329.6457767698569
Geometric Mean3663.91825690969
Harmonic Mean3558.0623755996
Quadratic Mean3901.68426024796
Winsorized Mean ( 1 / 20 )3734.98333333333104.83589137116035.6269526064316
Winsorized Mean ( 2 / 20 )3734.11666666667102.71836624310936.3529600717065
Winsorized Mean ( 3 / 20 )3730.86666666667100.36844403217037.1717097205458
Winsorized Mean ( 4 / 20 )3729.7333333333397.865790340755538.1106954774176
Winsorized Mean ( 5 / 20 )3718.6593.969017087103739.5731499091135
Winsorized Mean ( 6 / 20 )3719.5593.226306952005839.8980729968728
Winsorized Mean ( 7 / 20 )3721.6590.872120444123640.9548053001405
Winsorized Mean ( 8 / 20 )3708.7166666666787.037280445693542.6106680686181
Winsorized Mean ( 9 / 20 )3734.8166666666781.348484829113245.9113242798843
Winsorized Mean ( 10 / 20 )3733.9833333333378.83328074794347.3655707070236
Winsorized Mean ( 11 / 20 )3716.7572.721613853578151.1092892889247
Winsorized Mean ( 12 / 20 )3738.3566.246355085747156.4310292266073
Winsorized Mean ( 13 / 20 )3719.7166666666762.486771895806659.5280657619679
Winsorized Mean ( 14 / 20 )3707.5833333333359.414969350009162.4015020775697
Winsorized Mean ( 15 / 20 )3695.3333333333356.971023790950864.863382952235
Winsorized Mean ( 16 / 20 )3703.3333333333354.280567772129968.2257663346476
Winsorized Mean ( 17 / 20 )3698.5166666666753.43745745915269.2120628960283
Winsorized Mean ( 18 / 20 )3716.8166666666747.903584261748277.5895316383372
Winsorized Mean ( 19 / 20 )3729.845.381545068104182.1875939746584
Winsorized Mean ( 20 / 20 )3731.843.184480106097186.415304545327
Trimmed Mean ( 1 / 20 )3730.63793103448101.52339243991136.7465846183437
Trimmed Mean ( 2 / 20 )3725.9821428571497.436184547309238.2402303637827
Trimmed Mean ( 3 / 20 )3721.4629629629693.803348996680239.6730287646198
Trimmed Mean ( 4 / 20 )3717.8461538461590.431516986147241.112283391372
Trimmed Mean ( 5 / 20 )3714.2887.202724353622642.5936233934382
Trimmed Mean ( 6 / 20 )3713.187584.490114702793143.9481886497812
Trimmed Mean ( 7 / 20 )3711.8043478260981.235844516829745.6917062892983
Trimmed Mean ( 8 / 20 )3709.8863636363677.742046600466247.7204617817987
Trimmed Mean ( 9 / 20 )3710.0952380952474.322794804513349.9186722976938
Trimmed Mean ( 10 / 20 )3705.97571.4383048107351.8765809157801
Trimmed Mean ( 11 / 20 )3701.5526315789568.264606265021354.2235989351281
Trimmed Mean ( 12 / 20 )3699.2565.733436866044256.2765340801907
Trimmed Mean ( 13 / 20 )3693.563.992315854433257.7178673827308
Trimmed Mean ( 14 / 20 )3689.7187562.549645353275758.9886438070231
Trimmed Mean ( 15 / 20 )3687.1666666666761.253197586406860.195496920228
Trimmed Mean ( 16 / 20 )368659.932987268806861.5020236429704
Trimmed Mean ( 17 / 20 )3683.558.599927802528462.8584392187778
Trimmed Mean ( 18 / 20 )3681.2916666666756.591354872065465.0504246627222
Trimmed Mean ( 19 / 20 )3675.9090909090955.24231975730666.5415411057741
Trimmed Mean ( 20 / 20 )3667.453.5518145547468.4832069742703
Median3586
Midrange5120.5
Midmean - Weighted Average at Xnp3670.61290322581
Midmean - Weighted Average at X(n+1)p3687.16666666667
Midmean - Empirical Distribution Function3670.61290322581
Midmean - Empirical Distribution Function - Averaging3687.16666666667
Midmean - Empirical Distribution Function - Interpolation3687.16666666667
Midmean - Closest Observation3670.61290322581
Midmean - True Basic - Statistics Graphics Toolkit3687.16666666667
Midmean - MS Excel (old versions)3689.71875
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 3776.96666666667 & 127.403194592863 & 29.6457767698569 \tabularnewline
Geometric Mean & 3663.91825690969 &  &  \tabularnewline
Harmonic Mean & 3558.0623755996 &  &  \tabularnewline
Quadratic Mean & 3901.68426024796 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 3734.98333333333 & 104.835891371160 & 35.6269526064316 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 3734.11666666667 & 102.718366243109 & 36.3529600717065 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 3730.86666666667 & 100.368444032170 & 37.1717097205458 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 3729.73333333333 & 97.8657903407555 & 38.1106954774176 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 3718.65 & 93.9690170871037 & 39.5731499091135 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 3719.55 & 93.2263069520058 & 39.8980729968728 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 3721.65 & 90.8721204441236 & 40.9548053001405 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 3708.71666666667 & 87.0372804456935 & 42.6106680686181 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 3734.81666666667 & 81.3484848291132 & 45.9113242798843 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 3733.98333333333 & 78.833280747943 & 47.3655707070236 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 3716.75 & 72.7216138535781 & 51.1092892889247 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 3738.35 & 66.2463550857471 & 56.4310292266073 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 3719.71666666667 & 62.4867718958066 & 59.5280657619679 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 3707.58333333333 & 59.4149693500091 & 62.4015020775697 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 3695.33333333333 & 56.9710237909508 & 64.863382952235 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 3703.33333333333 & 54.2805677721299 & 68.2257663346476 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 3698.51666666667 & 53.437457459152 & 69.2120628960283 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 3716.81666666667 & 47.9035842617482 & 77.5895316383372 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 3729.8 & 45.3815450681041 & 82.1875939746584 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 3731.8 & 43.1844801060971 & 86.415304545327 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 3730.63793103448 & 101.523392439911 & 36.7465846183437 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 3725.98214285714 & 97.4361845473092 & 38.2402303637827 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 3721.46296296296 & 93.8033489966802 & 39.6730287646198 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 3717.84615384615 & 90.4315169861472 & 41.112283391372 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 3714.28 & 87.2027243536226 & 42.5936233934382 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 3713.1875 & 84.4901147027931 & 43.9481886497812 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 3711.80434782609 & 81.2358445168297 & 45.6917062892983 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 3709.88636363636 & 77.7420466004662 & 47.7204617817987 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 3710.09523809524 & 74.3227948045133 & 49.9186722976938 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 3705.975 & 71.43830481073 & 51.8765809157801 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 3701.55263157895 & 68.2646062650213 & 54.2235989351281 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 3699.25 & 65.7334368660442 & 56.2765340801907 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 3693.5 & 63.9923158544332 & 57.7178673827308 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 3689.71875 & 62.5496453532757 & 58.9886438070231 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 3687.16666666667 & 61.2531975864068 & 60.195496920228 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 3686 & 59.9329872688068 & 61.5020236429704 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 3683.5 & 58.5999278025284 & 62.8584392187778 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 3681.29166666667 & 56.5913548720654 & 65.0504246627222 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 3675.90909090909 & 55.242319757306 & 66.5415411057741 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 3667.4 & 53.55181455474 & 68.4832069742703 \tabularnewline
Median & 3586 &  &  \tabularnewline
Midrange & 5120.5 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 3670.61290322581 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 3687.16666666667 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 3670.61290322581 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 3687.16666666667 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 3687.16666666667 &  &  \tabularnewline
Midmean - Closest Observation & 3670.61290322581 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 3687.16666666667 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 3689.71875 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=35886&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]3776.96666666667[/C][C]127.403194592863[/C][C]29.6457767698569[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]3663.91825690969[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]3558.0623755996[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]3901.68426024796[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]3734.98333333333[/C][C]104.835891371160[/C][C]35.6269526064316[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]3734.11666666667[/C][C]102.718366243109[/C][C]36.3529600717065[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]3730.86666666667[/C][C]100.368444032170[/C][C]37.1717097205458[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]3729.73333333333[/C][C]97.8657903407555[/C][C]38.1106954774176[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]3718.65[/C][C]93.9690170871037[/C][C]39.5731499091135[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]3719.55[/C][C]93.2263069520058[/C][C]39.8980729968728[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]3721.65[/C][C]90.8721204441236[/C][C]40.9548053001405[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]3708.71666666667[/C][C]87.0372804456935[/C][C]42.6106680686181[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]3734.81666666667[/C][C]81.3484848291132[/C][C]45.9113242798843[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]3733.98333333333[/C][C]78.833280747943[/C][C]47.3655707070236[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]3716.75[/C][C]72.7216138535781[/C][C]51.1092892889247[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]3738.35[/C][C]66.2463550857471[/C][C]56.4310292266073[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]3719.71666666667[/C][C]62.4867718958066[/C][C]59.5280657619679[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]3707.58333333333[/C][C]59.4149693500091[/C][C]62.4015020775697[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]3695.33333333333[/C][C]56.9710237909508[/C][C]64.863382952235[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]3703.33333333333[/C][C]54.2805677721299[/C][C]68.2257663346476[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]3698.51666666667[/C][C]53.437457459152[/C][C]69.2120628960283[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]3716.81666666667[/C][C]47.9035842617482[/C][C]77.5895316383372[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]3729.8[/C][C]45.3815450681041[/C][C]82.1875939746584[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]3731.8[/C][C]43.1844801060971[/C][C]86.415304545327[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]3730.63793103448[/C][C]101.523392439911[/C][C]36.7465846183437[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]3725.98214285714[/C][C]97.4361845473092[/C][C]38.2402303637827[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]3721.46296296296[/C][C]93.8033489966802[/C][C]39.6730287646198[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]3717.84615384615[/C][C]90.4315169861472[/C][C]41.112283391372[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]3714.28[/C][C]87.2027243536226[/C][C]42.5936233934382[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]3713.1875[/C][C]84.4901147027931[/C][C]43.9481886497812[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]3711.80434782609[/C][C]81.2358445168297[/C][C]45.6917062892983[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]3709.88636363636[/C][C]77.7420466004662[/C][C]47.7204617817987[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]3710.09523809524[/C][C]74.3227948045133[/C][C]49.9186722976938[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]3705.975[/C][C]71.43830481073[/C][C]51.8765809157801[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]3701.55263157895[/C][C]68.2646062650213[/C][C]54.2235989351281[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]3699.25[/C][C]65.7334368660442[/C][C]56.2765340801907[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]3693.5[/C][C]63.9923158544332[/C][C]57.7178673827308[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]3689.71875[/C][C]62.5496453532757[/C][C]58.9886438070231[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]3687.16666666667[/C][C]61.2531975864068[/C][C]60.195496920228[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]3686[/C][C]59.9329872688068[/C][C]61.5020236429704[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]3683.5[/C][C]58.5999278025284[/C][C]62.8584392187778[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]3681.29166666667[/C][C]56.5913548720654[/C][C]65.0504246627222[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]3675.90909090909[/C][C]55.242319757306[/C][C]66.5415411057741[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]3667.4[/C][C]53.55181455474[/C][C]68.4832069742703[/C][/ROW]
[ROW][C]Median[/C][C]3586[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]5120.5[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]3670.61290322581[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]3687.16666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]3670.61290322581[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]3687.16666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]3687.16666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]3670.61290322581[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]3687.16666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]3689.71875[/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=35886&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=35886&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 Mean3776.96666666667127.40319459286329.6457767698569
Geometric Mean3663.91825690969
Harmonic Mean3558.0623755996
Quadratic Mean3901.68426024796
Winsorized Mean ( 1 / 20 )3734.98333333333104.83589137116035.6269526064316
Winsorized Mean ( 2 / 20 )3734.11666666667102.71836624310936.3529600717065
Winsorized Mean ( 3 / 20 )3730.86666666667100.36844403217037.1717097205458
Winsorized Mean ( 4 / 20 )3729.7333333333397.865790340755538.1106954774176
Winsorized Mean ( 5 / 20 )3718.6593.969017087103739.5731499091135
Winsorized Mean ( 6 / 20 )3719.5593.226306952005839.8980729968728
Winsorized Mean ( 7 / 20 )3721.6590.872120444123640.9548053001405
Winsorized Mean ( 8 / 20 )3708.7166666666787.037280445693542.6106680686181
Winsorized Mean ( 9 / 20 )3734.8166666666781.348484829113245.9113242798843
Winsorized Mean ( 10 / 20 )3733.9833333333378.83328074794347.3655707070236
Winsorized Mean ( 11 / 20 )3716.7572.721613853578151.1092892889247
Winsorized Mean ( 12 / 20 )3738.3566.246355085747156.4310292266073
Winsorized Mean ( 13 / 20 )3719.7166666666762.486771895806659.5280657619679
Winsorized Mean ( 14 / 20 )3707.5833333333359.414969350009162.4015020775697
Winsorized Mean ( 15 / 20 )3695.3333333333356.971023790950864.863382952235
Winsorized Mean ( 16 / 20 )3703.3333333333354.280567772129968.2257663346476
Winsorized Mean ( 17 / 20 )3698.5166666666753.43745745915269.2120628960283
Winsorized Mean ( 18 / 20 )3716.8166666666747.903584261748277.5895316383372
Winsorized Mean ( 19 / 20 )3729.845.381545068104182.1875939746584
Winsorized Mean ( 20 / 20 )3731.843.184480106097186.415304545327
Trimmed Mean ( 1 / 20 )3730.63793103448101.52339243991136.7465846183437
Trimmed Mean ( 2 / 20 )3725.9821428571497.436184547309238.2402303637827
Trimmed Mean ( 3 / 20 )3721.4629629629693.803348996680239.6730287646198
Trimmed Mean ( 4 / 20 )3717.8461538461590.431516986147241.112283391372
Trimmed Mean ( 5 / 20 )3714.2887.202724353622642.5936233934382
Trimmed Mean ( 6 / 20 )3713.187584.490114702793143.9481886497812
Trimmed Mean ( 7 / 20 )3711.8043478260981.235844516829745.6917062892983
Trimmed Mean ( 8 / 20 )3709.8863636363677.742046600466247.7204617817987
Trimmed Mean ( 9 / 20 )3710.0952380952474.322794804513349.9186722976938
Trimmed Mean ( 10 / 20 )3705.97571.4383048107351.8765809157801
Trimmed Mean ( 11 / 20 )3701.5526315789568.264606265021354.2235989351281
Trimmed Mean ( 12 / 20 )3699.2565.733436866044256.2765340801907
Trimmed Mean ( 13 / 20 )3693.563.992315854433257.7178673827308
Trimmed Mean ( 14 / 20 )3689.7187562.549645353275758.9886438070231
Trimmed Mean ( 15 / 20 )3687.1666666666761.253197586406860.195496920228
Trimmed Mean ( 16 / 20 )368659.932987268806861.5020236429704
Trimmed Mean ( 17 / 20 )3683.558.599927802528462.8584392187778
Trimmed Mean ( 18 / 20 )3681.2916666666756.591354872065465.0504246627222
Trimmed Mean ( 19 / 20 )3675.9090909090955.24231975730666.5415411057741
Trimmed Mean ( 20 / 20 )3667.453.5518145547468.4832069742703
Median3586
Midrange5120.5
Midmean - Weighted Average at Xnp3670.61290322581
Midmean - Weighted Average at X(n+1)p3687.16666666667
Midmean - Empirical Distribution Function3670.61290322581
Midmean - Empirical Distribution Function - Averaging3687.16666666667
Midmean - Empirical Distribution Function - Interpolation3687.16666666667
Midmean - Closest Observation3670.61290322581
Midmean - True Basic - Statistics Graphics Toolkit3687.16666666667
Midmean - MS Excel (old versions)3689.71875
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')