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Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationMon, 21 Nov 2011 12:37:44 -0500
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2011/Nov/21/t1321897090838oil17fvnma7x.htm/, Retrieved Tue, 23 Apr 2024 16:07:09 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=145850, Retrieved Tue, 23 Apr 2024 16:07:09 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact75
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Central Tendency] [Arabica Price in ...] [2008-01-06 21:28:17] [74be16979710d4c4e7c6647856088456]
- RM D    [Central Tendency] [] [2011-11-21 17:37:44] [d41d8cd98f00b204e9800998ecf8427e] [Current]
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Dataseries X:
129,99
59,99
49,99
84,99
179,99
329,99
25,99
499,99
89,99
119,99
79,99
199,99
449,99
549,99
529,99
639,99
749,99
399,99
169,99
189,99
199,99
69,99
69,99
109,99
159,99
159,99
199,99
75
349,99
439,99
309,99
379,99
349,99
169,99
239,99
229,99
69,99
99,99
29,99
39,99
21,99
499,99
29,99
29,99
49,99
49,99
55,99
59,99
79,99
139,99
159,99
169,99
229,99
249,99
309,99
499,99
65,99
89,99
89,99
449,99




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'George Udny Yule' @ yule.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 & 'George Udny Yule' @ yule.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=145850&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]'George Udny Yule' @ yule.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=145850&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=145850&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'George Udny Yule' @ yule.wessa.net







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean210.323522.81956135516399.21680731397605
Geometric Mean144.570381736265
Harmonic Mean96.3621439960425
Quadratic Mean273.786751137328
Winsorized Mean ( 1 / 20 )208.55683333333322.13905758268069.42031215892801
Winsorized Mean ( 2 / 20 )205.69016666666721.21047328241259.6975755292185
Winsorized Mean ( 3 / 20 )204.69016666666720.9412279957819.77450638080563
Winsorized Mean ( 4 / 20 )202.69016666666720.43110267520959.92066702854002
Winsorized Mean ( 5 / 20 )203.523520.314548812032210.0186079387327
Winsorized Mean ( 6 / 20 )204.523520.181425304837810.1342445793942
Winsorized Mean ( 7 / 20 )198.69016666666718.794443568973410.5717504185478
Winsorized Mean ( 8 / 20 )198.69016666666718.794443568973410.5717504185477
Winsorized Mean ( 9 / 20 )198.09016666666718.337289799829210.8025869051005
Winsorized Mean ( 10 / 20 )192.09016666666716.80276963061211.4320538155037
Winsorized Mean ( 11 / 20 )188.423516.04703947531511.7419478084946
Winsorized Mean ( 12 / 20 )183.623514.700433914624712.4910258477012
Winsorized Mean ( 13 / 20 )184.49016666666714.583994110276112.650181100709
Winsorized Mean ( 14 / 20 )179.823513.701274599095913.1245818554623
Winsorized Mean ( 15 / 20 )174.823512.788438643085613.67043349694
Winsorized Mean ( 16 / 20 )176.159512.604746862604513.9756475810415
Winsorized Mean ( 17 / 20 )160.5733333333339.497317244355116.9072306633511
Winsorized Mean ( 18 / 20 )157.5733333333339.0256161398727517.4584572278913
Winsorized Mean ( 19 / 20 )155.998.3113835217247518.7682351069789
Winsorized Mean ( 20 / 20 )157.6566666666678.0722957433891319.5305860536367
Trimmed Mean ( 1 / 20 )204.26603448275921.40381063587089.54344242517394
Trimmed Mean ( 2 / 20 )199.6687520.47911290068169.7498730032078
Trimmed Mean ( 3 / 20 )196.32351851851919.95464435633129.83848747252814
Trimmed Mean ( 4 / 20 )193.10557692307719.41911858122319.94409587208538
Trimmed Mean ( 5 / 20 )190.230218.940043049947810.0438103281145
Trimmed Mean ( 6 / 20 )186.90687518.352143337626110.1844711847252
Trimmed Mean ( 7 / 20 )183.07717391304317.616163670888210.3925677198146
Trimmed Mean ( 8 / 20 )180.03568181818217.096601053706910.5304955793623
Trimmed Mean ( 9 / 20 )176.70452380952416.393225018413610.7791190330787
Trimmed Mean ( 10 / 20 )173.1402515.573793263073811.1174103235674
Trimmed Mean ( 11 / 20 )170.14815789473714.938545271546711.3898746365093
Trimmed Mean ( 12 / 20 )167.37916666666714.290598193434411.712537460018
Trimmed Mean ( 13 / 20 )164.99029411764713.794332198389211.9607308092024
Trimmed Mean ( 14 / 20 )162.177812513.090685995221112.3887940295264
Trimmed Mean ( 15 / 20 )159.65712.37094173233512.9058080988847
Trimmed Mean ( 16 / 20 )157.49035714285711.636772931295613.5338515302044
Trimmed Mean ( 17 / 20 )154.79769230769210.533758074476414.6953908769531
Trimmed Mean ( 18 / 20 )153.94833333333310.201676326919415.0904937972896
Trimmed Mean ( 19 / 20 )153.3990909090919.8219339070740615.6180129453537
Trimmed Mean ( 20 / 20 )152.999.4618346946812416.1691685531137
Median159.99
Midrange385.99
Midmean - Weighted Average at Xnp154.0528125
Midmean - Weighted Average at X(n+1)p154.0528125
Midmean - Empirical Distribution Function154.0528125
Midmean - Empirical Distribution Function - Averaging154.0528125
Midmean - Empirical Distribution Function - Interpolation154.0528125
Midmean - Closest Observation154.0528125
Midmean - True Basic - Statistics Graphics Toolkit154.0528125
Midmean - MS Excel (old versions)159.384242424242
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 210.3235 & 22.8195613551639 & 9.21680731397605 \tabularnewline
Geometric Mean & 144.570381736265 &  &  \tabularnewline
Harmonic Mean & 96.3621439960425 &  &  \tabularnewline
Quadratic Mean & 273.786751137328 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 208.556833333333 & 22.1390575826806 & 9.42031215892801 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 205.690166666667 & 21.2104732824125 & 9.6975755292185 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 204.690166666667 & 20.941227995781 & 9.77450638080563 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 202.690166666667 & 20.4311026752095 & 9.92066702854002 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 203.5235 & 20.3145488120322 & 10.0186079387327 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 204.5235 & 20.1814253048378 & 10.1342445793942 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 198.690166666667 & 18.7944435689734 & 10.5717504185478 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 198.690166666667 & 18.7944435689734 & 10.5717504185477 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 198.090166666667 & 18.3372897998292 & 10.8025869051005 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 192.090166666667 & 16.802769630612 & 11.4320538155037 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 188.4235 & 16.047039475315 & 11.7419478084946 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 183.6235 & 14.7004339146247 & 12.4910258477012 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 184.490166666667 & 14.5839941102761 & 12.650181100709 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 179.8235 & 13.7012745990959 & 13.1245818554623 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 174.8235 & 12.7884386430856 & 13.67043349694 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 176.1595 & 12.6047468626045 & 13.9756475810415 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 160.573333333333 & 9.4973172443551 & 16.9072306633511 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 157.573333333333 & 9.02561613987275 & 17.4584572278913 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 155.99 & 8.31138352172475 & 18.7682351069789 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 157.656666666667 & 8.07229574338913 & 19.5305860536367 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 204.266034482759 & 21.4038106358708 & 9.54344242517394 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 199.66875 & 20.4791129006816 & 9.7498730032078 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 196.323518518519 & 19.9546443563312 & 9.83848747252814 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 193.105576923077 & 19.4191185812231 & 9.94409587208538 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 190.2302 & 18.9400430499478 & 10.0438103281145 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 186.906875 & 18.3521433376261 & 10.1844711847252 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 183.077173913043 & 17.6161636708882 & 10.3925677198146 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 180.035681818182 & 17.0966010537069 & 10.5304955793623 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 176.704523809524 & 16.3932250184136 & 10.7791190330787 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 173.14025 & 15.5737932630738 & 11.1174103235674 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 170.148157894737 & 14.9385452715467 & 11.3898746365093 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 167.379166666667 & 14.2905981934344 & 11.712537460018 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 164.990294117647 & 13.7943321983892 & 11.9607308092024 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 162.1778125 & 13.0906859952211 & 12.3887940295264 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 159.657 & 12.370941732335 & 12.9058080988847 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 157.490357142857 & 11.6367729312956 & 13.5338515302044 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 154.797692307692 & 10.5337580744764 & 14.6953908769531 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 153.948333333333 & 10.2016763269194 & 15.0904937972896 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 153.399090909091 & 9.82193390707406 & 15.6180129453537 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 152.99 & 9.46183469468124 & 16.1691685531137 \tabularnewline
Median & 159.99 &  &  \tabularnewline
Midrange & 385.99 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 154.0528125 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 154.0528125 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 154.0528125 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 154.0528125 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 154.0528125 &  &  \tabularnewline
Midmean - Closest Observation & 154.0528125 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 154.0528125 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 159.384242424242 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=145850&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]210.3235[/C][C]22.8195613551639[/C][C]9.21680731397605[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]144.570381736265[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]96.3621439960425[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]273.786751137328[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]208.556833333333[/C][C]22.1390575826806[/C][C]9.42031215892801[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]205.690166666667[/C][C]21.2104732824125[/C][C]9.6975755292185[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]204.690166666667[/C][C]20.941227995781[/C][C]9.77450638080563[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]202.690166666667[/C][C]20.4311026752095[/C][C]9.92066702854002[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]203.5235[/C][C]20.3145488120322[/C][C]10.0186079387327[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]204.5235[/C][C]20.1814253048378[/C][C]10.1342445793942[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]198.690166666667[/C][C]18.7944435689734[/C][C]10.5717504185478[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]198.690166666667[/C][C]18.7944435689734[/C][C]10.5717504185477[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]198.090166666667[/C][C]18.3372897998292[/C][C]10.8025869051005[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]192.090166666667[/C][C]16.802769630612[/C][C]11.4320538155037[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]188.4235[/C][C]16.047039475315[/C][C]11.7419478084946[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]183.6235[/C][C]14.7004339146247[/C][C]12.4910258477012[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]184.490166666667[/C][C]14.5839941102761[/C][C]12.650181100709[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]179.8235[/C][C]13.7012745990959[/C][C]13.1245818554623[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]174.8235[/C][C]12.7884386430856[/C][C]13.67043349694[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]176.1595[/C][C]12.6047468626045[/C][C]13.9756475810415[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]160.573333333333[/C][C]9.4973172443551[/C][C]16.9072306633511[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]157.573333333333[/C][C]9.02561613987275[/C][C]17.4584572278913[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]155.99[/C][C]8.31138352172475[/C][C]18.7682351069789[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]157.656666666667[/C][C]8.07229574338913[/C][C]19.5305860536367[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]204.266034482759[/C][C]21.4038106358708[/C][C]9.54344242517394[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]199.66875[/C][C]20.4791129006816[/C][C]9.7498730032078[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]196.323518518519[/C][C]19.9546443563312[/C][C]9.83848747252814[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]193.105576923077[/C][C]19.4191185812231[/C][C]9.94409587208538[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]190.2302[/C][C]18.9400430499478[/C][C]10.0438103281145[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]186.906875[/C][C]18.3521433376261[/C][C]10.1844711847252[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]183.077173913043[/C][C]17.6161636708882[/C][C]10.3925677198146[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]180.035681818182[/C][C]17.0966010537069[/C][C]10.5304955793623[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]176.704523809524[/C][C]16.3932250184136[/C][C]10.7791190330787[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]173.14025[/C][C]15.5737932630738[/C][C]11.1174103235674[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]170.148157894737[/C][C]14.9385452715467[/C][C]11.3898746365093[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]167.379166666667[/C][C]14.2905981934344[/C][C]11.712537460018[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]164.990294117647[/C][C]13.7943321983892[/C][C]11.9607308092024[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]162.1778125[/C][C]13.0906859952211[/C][C]12.3887940295264[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]159.657[/C][C]12.370941732335[/C][C]12.9058080988847[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]157.490357142857[/C][C]11.6367729312956[/C][C]13.5338515302044[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]154.797692307692[/C][C]10.5337580744764[/C][C]14.6953908769531[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]153.948333333333[/C][C]10.2016763269194[/C][C]15.0904937972896[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]153.399090909091[/C][C]9.82193390707406[/C][C]15.6180129453537[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]152.99[/C][C]9.46183469468124[/C][C]16.1691685531137[/C][/ROW]
[ROW][C]Median[/C][C]159.99[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]385.99[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]154.0528125[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]154.0528125[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]154.0528125[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]154.0528125[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]154.0528125[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]154.0528125[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]154.0528125[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]159.384242424242[/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=145850&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=145850&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 Mean210.323522.81956135516399.21680731397605
Geometric Mean144.570381736265
Harmonic Mean96.3621439960425
Quadratic Mean273.786751137328
Winsorized Mean ( 1 / 20 )208.55683333333322.13905758268069.42031215892801
Winsorized Mean ( 2 / 20 )205.69016666666721.21047328241259.6975755292185
Winsorized Mean ( 3 / 20 )204.69016666666720.9412279957819.77450638080563
Winsorized Mean ( 4 / 20 )202.69016666666720.43110267520959.92066702854002
Winsorized Mean ( 5 / 20 )203.523520.314548812032210.0186079387327
Winsorized Mean ( 6 / 20 )204.523520.181425304837810.1342445793942
Winsorized Mean ( 7 / 20 )198.69016666666718.794443568973410.5717504185478
Winsorized Mean ( 8 / 20 )198.69016666666718.794443568973410.5717504185477
Winsorized Mean ( 9 / 20 )198.09016666666718.337289799829210.8025869051005
Winsorized Mean ( 10 / 20 )192.09016666666716.80276963061211.4320538155037
Winsorized Mean ( 11 / 20 )188.423516.04703947531511.7419478084946
Winsorized Mean ( 12 / 20 )183.623514.700433914624712.4910258477012
Winsorized Mean ( 13 / 20 )184.49016666666714.583994110276112.650181100709
Winsorized Mean ( 14 / 20 )179.823513.701274599095913.1245818554623
Winsorized Mean ( 15 / 20 )174.823512.788438643085613.67043349694
Winsorized Mean ( 16 / 20 )176.159512.604746862604513.9756475810415
Winsorized Mean ( 17 / 20 )160.5733333333339.497317244355116.9072306633511
Winsorized Mean ( 18 / 20 )157.5733333333339.0256161398727517.4584572278913
Winsorized Mean ( 19 / 20 )155.998.3113835217247518.7682351069789
Winsorized Mean ( 20 / 20 )157.6566666666678.0722957433891319.5305860536367
Trimmed Mean ( 1 / 20 )204.26603448275921.40381063587089.54344242517394
Trimmed Mean ( 2 / 20 )199.6687520.47911290068169.7498730032078
Trimmed Mean ( 3 / 20 )196.32351851851919.95464435633129.83848747252814
Trimmed Mean ( 4 / 20 )193.10557692307719.41911858122319.94409587208538
Trimmed Mean ( 5 / 20 )190.230218.940043049947810.0438103281145
Trimmed Mean ( 6 / 20 )186.90687518.352143337626110.1844711847252
Trimmed Mean ( 7 / 20 )183.07717391304317.616163670888210.3925677198146
Trimmed Mean ( 8 / 20 )180.03568181818217.096601053706910.5304955793623
Trimmed Mean ( 9 / 20 )176.70452380952416.393225018413610.7791190330787
Trimmed Mean ( 10 / 20 )173.1402515.573793263073811.1174103235674
Trimmed Mean ( 11 / 20 )170.14815789473714.938545271546711.3898746365093
Trimmed Mean ( 12 / 20 )167.37916666666714.290598193434411.712537460018
Trimmed Mean ( 13 / 20 )164.99029411764713.794332198389211.9607308092024
Trimmed Mean ( 14 / 20 )162.177812513.090685995221112.3887940295264
Trimmed Mean ( 15 / 20 )159.65712.37094173233512.9058080988847
Trimmed Mean ( 16 / 20 )157.49035714285711.636772931295613.5338515302044
Trimmed Mean ( 17 / 20 )154.79769230769210.533758074476414.6953908769531
Trimmed Mean ( 18 / 20 )153.94833333333310.201676326919415.0904937972896
Trimmed Mean ( 19 / 20 )153.3990909090919.8219339070740615.6180129453537
Trimmed Mean ( 20 / 20 )152.999.4618346946812416.1691685531137
Median159.99
Midrange385.99
Midmean - Weighted Average at Xnp154.0528125
Midmean - Weighted Average at X(n+1)p154.0528125
Midmean - Empirical Distribution Function154.0528125
Midmean - Empirical Distribution Function - Averaging154.0528125
Midmean - Empirical Distribution Function - Interpolation154.0528125
Midmean - Closest Observation154.0528125
Midmean - True Basic - Statistics Graphics Toolkit154.0528125
Midmean - MS Excel (old versions)159.384242424242
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')