Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationSat, 10 Oct 2015 10:55:54 +0100
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2015/Oct/10/t1444470989eof763e8p0ums9h.htm/, Retrieved Tue, 14 May 2024 01:51:24 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=282101, Retrieved Tue, 14 May 2024 01:51:24 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact119
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [OPGAVE 5 OEF 2 ce...] [2015-10-10 09:55:54] [48da048a5e5e3f4e8c34faa6148f9354] [Current]
Feedback Forum

Post a new message
Dataseries X:
78,46
78,59
81,37
83,61
84,65
84,56
83,85
84,08
85,41
85,75
86,38
88,87
90,37
92,21
95,75
97,29
98,29
99,51
99,04
98,9
100,74
100,3
101,68
101,3
103,13
104,17
105,98
106,25
104,01
101,68
101,93
104,41
105,51
104,71
103,14
102,66
102,68
101,89
101,37
101,16
99,34
99,35
99,88
99,31
99,91
98,39
98,02
98,7
98,01
98,42
98,2
93,5
93,17
93,42
93,13
92,31
92,09
92,62
91,43
89,38




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 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 & 2 seconds \tabularnewline
R Server & 'George Udny Yule' @ yule.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=282101&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]'George Udny Yule' @ yule.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=282101&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=282101&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'George Udny Yule' @ yule.wessa.net







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean95.90366666666670.954135896427351100.513634405504
Geometric Mean95.6114385356741
Harmonic Mean95.3068994236585
Quadratic Mean96.1832907699322
Winsorized Mean ( 1 / 20 )95.90133333333330.952649545377969100.668009341551
Winsorized Mean ( 2 / 20 )95.97833333333330.923146889128551103.968647312387
Winsorized Mean ( 3 / 20 )96.05033333333330.887986739818879108.166404999386
Winsorized Mean ( 4 / 20 )96.04633333333330.880947614039412109.026157517962
Winsorized Mean ( 5 / 20 )96.04550.873287069924418109.981589454099
Winsorized Mean ( 6 / 20 )96.07750.85975057560893111.750434051122
Winsorized Mean ( 7 / 20 )95.98650.842110907822388113.983204716124
Winsorized Mean ( 8 / 20 )96.08650.819159512242381117.298888145694
Winsorized Mean ( 9 / 20 )96.070.798280815181604120.346121531362
Winsorized Mean ( 10 / 20 )96.17166666666670.775061476208224124.082630370381
Winsorized Mean ( 11 / 20 )96.49433333333330.662510179717833145.649585904372
Winsorized Mean ( 12 / 20 )96.58833333333330.641732742947559150.511773623535
Winsorized Mean ( 13 / 20 )96.75733333333330.595405519440354162.506611333196
Winsorized Mean ( 14 / 20 )97.00466666666670.551690082627287175.831811593759
Winsorized Mean ( 15 / 20 )97.09216666666670.512856853392409189.316309267251
Winsorized Mean ( 16 / 20 )97.10550.50494892201272192.30756967049
Winsorized Mean ( 17 / 20 )97.09416666666670.494743801282766196.25140611145
Winsorized Mean ( 18 / 20 )97.06116666666670.462266529355044209.967974108112
Winsorized Mean ( 19 / 20 )97.08333333333330.417645652164761232.453834560773
Winsorized Mean ( 20 / 20 )96.96666666666670.398877922410876243.098605409359
Trimmed Mean ( 1 / 20 )96.02603448275860.922025307600462104.146853336014
Trimmed Mean ( 2 / 20 )96.15964285714290.883917562570826108.788021563309
Trimmed Mean ( 3 / 20 )96.26037037037040.856537524749611112.383132774609
Trimmed Mean ( 4 / 20 )96.34115384615380.83926041445816114.79292027416
Trimmed Mean ( 5 / 20 )96.42960.819763826616283117.630952805066
Trimmed Mean ( 6 / 20 )96.5256250.797147558032691121.088779646041
Trimmed Mean ( 7 / 20 )96.62304347826090.772077182542913125.146870886695
Trimmed Mean ( 8 / 20 )96.74704545454550.744050580496198130.027511557112
Trimmed Mean ( 9 / 20 )96.8650.71388154360811135.687777429325
Trimmed Mean ( 10 / 20 )96.99750.679138665460211142.824293377952
Trimmed Mean ( 11 / 20 )97.12789473684210.638987258580314152.002866148909
Trimmed Mean ( 12 / 20 )97.22388888888890.618813287964594157.113447270466
Trimmed Mean ( 13 / 20 )97.31735294117650.596256490052165163.213909726437
Trimmed Mean ( 14 / 20 )97.3981250.577979907686691168.514724655095
Trimmed Mean ( 15 / 20 )97.45433333333330.564608028683298172.605291427759
Trimmed Mean ( 16 / 20 )97.50607142857140.555345676058485175.577258691581
Trimmed Mean ( 17 / 20 )97.56384615384620.541547661635137180.157450702056
Trimmed Mean ( 18 / 20 )97.63291666666670.521248320181725187.305959341276
Trimmed Mean ( 19 / 20 )97.71954545454550.49898142018899195.838044265324
Trimmed Mean ( 20 / 20 )97.820.478774202356503204.313431088256
Median98.405
Midrange92.355
Midmean - Weighted Average at Xnp97.26
Midmean - Weighted Average at X(n+1)p97.4543333333333
Midmean - Empirical Distribution Function97.26
Midmean - Empirical Distribution Function - Averaging97.4543333333333
Midmean - Empirical Distribution Function - Interpolation97.4543333333333
Midmean - Closest Observation97.26
Midmean - True Basic - Statistics Graphics Toolkit97.4543333333333
Midmean - MS Excel (old versions)97.5278787878788
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 95.9036666666667 & 0.954135896427351 & 100.513634405504 \tabularnewline
Geometric Mean & 95.6114385356741 &  &  \tabularnewline
Harmonic Mean & 95.3068994236585 &  &  \tabularnewline
Quadratic Mean & 96.1832907699322 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 95.9013333333333 & 0.952649545377969 & 100.668009341551 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 95.9783333333333 & 0.923146889128551 & 103.968647312387 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 96.0503333333333 & 0.887986739818879 & 108.166404999386 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 96.0463333333333 & 0.880947614039412 & 109.026157517962 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 96.0455 & 0.873287069924418 & 109.981589454099 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 96.0775 & 0.85975057560893 & 111.750434051122 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 95.9865 & 0.842110907822388 & 113.983204716124 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 96.0865 & 0.819159512242381 & 117.298888145694 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 96.07 & 0.798280815181604 & 120.346121531362 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 96.1716666666667 & 0.775061476208224 & 124.082630370381 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 96.4943333333333 & 0.662510179717833 & 145.649585904372 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 96.5883333333333 & 0.641732742947559 & 150.511773623535 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 96.7573333333333 & 0.595405519440354 & 162.506611333196 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 97.0046666666667 & 0.551690082627287 & 175.831811593759 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 97.0921666666667 & 0.512856853392409 & 189.316309267251 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 97.1055 & 0.50494892201272 & 192.30756967049 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 97.0941666666667 & 0.494743801282766 & 196.25140611145 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 97.0611666666667 & 0.462266529355044 & 209.967974108112 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 97.0833333333333 & 0.417645652164761 & 232.453834560773 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 96.9666666666667 & 0.398877922410876 & 243.098605409359 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 96.0260344827586 & 0.922025307600462 & 104.146853336014 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 96.1596428571429 & 0.883917562570826 & 108.788021563309 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 96.2603703703704 & 0.856537524749611 & 112.383132774609 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 96.3411538461538 & 0.83926041445816 & 114.79292027416 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 96.4296 & 0.819763826616283 & 117.630952805066 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 96.525625 & 0.797147558032691 & 121.088779646041 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 96.6230434782609 & 0.772077182542913 & 125.146870886695 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 96.7470454545455 & 0.744050580496198 & 130.027511557112 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 96.865 & 0.71388154360811 & 135.687777429325 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 96.9975 & 0.679138665460211 & 142.824293377952 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 97.1278947368421 & 0.638987258580314 & 152.002866148909 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 97.2238888888889 & 0.618813287964594 & 157.113447270466 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 97.3173529411765 & 0.596256490052165 & 163.213909726437 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 97.398125 & 0.577979907686691 & 168.514724655095 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 97.4543333333333 & 0.564608028683298 & 172.605291427759 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 97.5060714285714 & 0.555345676058485 & 175.577258691581 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 97.5638461538462 & 0.541547661635137 & 180.157450702056 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 97.6329166666667 & 0.521248320181725 & 187.305959341276 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 97.7195454545455 & 0.49898142018899 & 195.838044265324 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 97.82 & 0.478774202356503 & 204.313431088256 \tabularnewline
Median & 98.405 &  &  \tabularnewline
Midrange & 92.355 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 97.26 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 97.4543333333333 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 97.26 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 97.4543333333333 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 97.4543333333333 &  &  \tabularnewline
Midmean - Closest Observation & 97.26 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 97.4543333333333 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 97.5278787878788 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=282101&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]95.9036666666667[/C][C]0.954135896427351[/C][C]100.513634405504[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]95.6114385356741[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]95.3068994236585[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]96.1832907699322[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]95.9013333333333[/C][C]0.952649545377969[/C][C]100.668009341551[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]95.9783333333333[/C][C]0.923146889128551[/C][C]103.968647312387[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]96.0503333333333[/C][C]0.887986739818879[/C][C]108.166404999386[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]96.0463333333333[/C][C]0.880947614039412[/C][C]109.026157517962[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]96.0455[/C][C]0.873287069924418[/C][C]109.981589454099[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]96.0775[/C][C]0.85975057560893[/C][C]111.750434051122[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]95.9865[/C][C]0.842110907822388[/C][C]113.983204716124[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]96.0865[/C][C]0.819159512242381[/C][C]117.298888145694[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]96.07[/C][C]0.798280815181604[/C][C]120.346121531362[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]96.1716666666667[/C][C]0.775061476208224[/C][C]124.082630370381[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]96.4943333333333[/C][C]0.662510179717833[/C][C]145.649585904372[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]96.5883333333333[/C][C]0.641732742947559[/C][C]150.511773623535[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]96.7573333333333[/C][C]0.595405519440354[/C][C]162.506611333196[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]97.0046666666667[/C][C]0.551690082627287[/C][C]175.831811593759[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]97.0921666666667[/C][C]0.512856853392409[/C][C]189.316309267251[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]97.1055[/C][C]0.50494892201272[/C][C]192.30756967049[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]97.0941666666667[/C][C]0.494743801282766[/C][C]196.25140611145[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]97.0611666666667[/C][C]0.462266529355044[/C][C]209.967974108112[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]97.0833333333333[/C][C]0.417645652164761[/C][C]232.453834560773[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]96.9666666666667[/C][C]0.398877922410876[/C][C]243.098605409359[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]96.0260344827586[/C][C]0.922025307600462[/C][C]104.146853336014[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]96.1596428571429[/C][C]0.883917562570826[/C][C]108.788021563309[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]96.2603703703704[/C][C]0.856537524749611[/C][C]112.383132774609[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]96.3411538461538[/C][C]0.83926041445816[/C][C]114.79292027416[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]96.4296[/C][C]0.819763826616283[/C][C]117.630952805066[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]96.525625[/C][C]0.797147558032691[/C][C]121.088779646041[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]96.6230434782609[/C][C]0.772077182542913[/C][C]125.146870886695[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]96.7470454545455[/C][C]0.744050580496198[/C][C]130.027511557112[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]96.865[/C][C]0.71388154360811[/C][C]135.687777429325[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]96.9975[/C][C]0.679138665460211[/C][C]142.824293377952[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]97.1278947368421[/C][C]0.638987258580314[/C][C]152.002866148909[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]97.2238888888889[/C][C]0.618813287964594[/C][C]157.113447270466[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]97.3173529411765[/C][C]0.596256490052165[/C][C]163.213909726437[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]97.398125[/C][C]0.577979907686691[/C][C]168.514724655095[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]97.4543333333333[/C][C]0.564608028683298[/C][C]172.605291427759[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]97.5060714285714[/C][C]0.555345676058485[/C][C]175.577258691581[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]97.5638461538462[/C][C]0.541547661635137[/C][C]180.157450702056[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]97.6329166666667[/C][C]0.521248320181725[/C][C]187.305959341276[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]97.7195454545455[/C][C]0.49898142018899[/C][C]195.838044265324[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]97.82[/C][C]0.478774202356503[/C][C]204.313431088256[/C][/ROW]
[ROW][C]Median[/C][C]98.405[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]92.355[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]97.26[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]97.4543333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]97.26[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]97.4543333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]97.4543333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]97.26[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]97.4543333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]97.5278787878788[/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=282101&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=282101&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 Mean95.90366666666670.954135896427351100.513634405504
Geometric Mean95.6114385356741
Harmonic Mean95.3068994236585
Quadratic Mean96.1832907699322
Winsorized Mean ( 1 / 20 )95.90133333333330.952649545377969100.668009341551
Winsorized Mean ( 2 / 20 )95.97833333333330.923146889128551103.968647312387
Winsorized Mean ( 3 / 20 )96.05033333333330.887986739818879108.166404999386
Winsorized Mean ( 4 / 20 )96.04633333333330.880947614039412109.026157517962
Winsorized Mean ( 5 / 20 )96.04550.873287069924418109.981589454099
Winsorized Mean ( 6 / 20 )96.07750.85975057560893111.750434051122
Winsorized Mean ( 7 / 20 )95.98650.842110907822388113.983204716124
Winsorized Mean ( 8 / 20 )96.08650.819159512242381117.298888145694
Winsorized Mean ( 9 / 20 )96.070.798280815181604120.346121531362
Winsorized Mean ( 10 / 20 )96.17166666666670.775061476208224124.082630370381
Winsorized Mean ( 11 / 20 )96.49433333333330.662510179717833145.649585904372
Winsorized Mean ( 12 / 20 )96.58833333333330.641732742947559150.511773623535
Winsorized Mean ( 13 / 20 )96.75733333333330.595405519440354162.506611333196
Winsorized Mean ( 14 / 20 )97.00466666666670.551690082627287175.831811593759
Winsorized Mean ( 15 / 20 )97.09216666666670.512856853392409189.316309267251
Winsorized Mean ( 16 / 20 )97.10550.50494892201272192.30756967049
Winsorized Mean ( 17 / 20 )97.09416666666670.494743801282766196.25140611145
Winsorized Mean ( 18 / 20 )97.06116666666670.462266529355044209.967974108112
Winsorized Mean ( 19 / 20 )97.08333333333330.417645652164761232.453834560773
Winsorized Mean ( 20 / 20 )96.96666666666670.398877922410876243.098605409359
Trimmed Mean ( 1 / 20 )96.02603448275860.922025307600462104.146853336014
Trimmed Mean ( 2 / 20 )96.15964285714290.883917562570826108.788021563309
Trimmed Mean ( 3 / 20 )96.26037037037040.856537524749611112.383132774609
Trimmed Mean ( 4 / 20 )96.34115384615380.83926041445816114.79292027416
Trimmed Mean ( 5 / 20 )96.42960.819763826616283117.630952805066
Trimmed Mean ( 6 / 20 )96.5256250.797147558032691121.088779646041
Trimmed Mean ( 7 / 20 )96.62304347826090.772077182542913125.146870886695
Trimmed Mean ( 8 / 20 )96.74704545454550.744050580496198130.027511557112
Trimmed Mean ( 9 / 20 )96.8650.71388154360811135.687777429325
Trimmed Mean ( 10 / 20 )96.99750.679138665460211142.824293377952
Trimmed Mean ( 11 / 20 )97.12789473684210.638987258580314152.002866148909
Trimmed Mean ( 12 / 20 )97.22388888888890.618813287964594157.113447270466
Trimmed Mean ( 13 / 20 )97.31735294117650.596256490052165163.213909726437
Trimmed Mean ( 14 / 20 )97.3981250.577979907686691168.514724655095
Trimmed Mean ( 15 / 20 )97.45433333333330.564608028683298172.605291427759
Trimmed Mean ( 16 / 20 )97.50607142857140.555345676058485175.577258691581
Trimmed Mean ( 17 / 20 )97.56384615384620.541547661635137180.157450702056
Trimmed Mean ( 18 / 20 )97.63291666666670.521248320181725187.305959341276
Trimmed Mean ( 19 / 20 )97.71954545454550.49898142018899195.838044265324
Trimmed Mean ( 20 / 20 )97.820.478774202356503204.313431088256
Median98.405
Midrange92.355
Midmean - Weighted Average at Xnp97.26
Midmean - Weighted Average at X(n+1)p97.4543333333333
Midmean - Empirical Distribution Function97.26
Midmean - Empirical Distribution Function - Averaging97.4543333333333
Midmean - Empirical Distribution Function - Interpolation97.4543333333333
Midmean - Closest Observation97.26
Midmean - True Basic - Statistics Graphics Toolkit97.4543333333333
Midmean - MS Excel (old versions)97.5278787878788
Number of observations60



Parameters (Session):
par1 = 0,01 ; par2 = 0,9 ; par3 = 0,1 ;
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')