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Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationThu, 08 Oct 2015 21:08:13 +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/08/t1444335006hqjywtnagf71lex.htm/, Retrieved Wed, 15 May 2024 22:53:46 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=281662, Retrieved Wed, 15 May 2024 22:53:46 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact58
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [] [2015-10-08 20:08:13] [64c14b596f7fde091cf1a84a44b2a252] [Current]
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Dataseries X:
107,64
107,64
107,58
107,42
107,35
107,31
107,24
107
106,62
105,37
103,23
102,38
102,35
102,28
101,77
101,37
100,18
99,3
99,2
99,13
98,71
98,6
98,6
98,51
98,48
98,46
98,46
98,4
97,97
97,88
97,57
96,71
94,89
94,57
94,5
94,38
94,38
94,36
94,31
94,3
94,18
94,1
93,89
93,38
92,88
92,82
92,82
92,81
92,81
92,81
92,81
92,81
92,81
92,79
92,72
92,68
91,38
91,17
91,17
91,16




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=281662&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=281662&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=281662&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 Mean97.840.679361157206463144.017653882831
Geometric Mean97.7036592078096
Harmonic Mean97.5702079459527
Quadratic Mean97.9790587999973
Winsorized Mean ( 1 / 20 )97.84016666666670.679333400905393144.023783515235
Winsorized Mean ( 2 / 20 )97.83816666666670.678845667443754144.124314787312
Winsorized Mean ( 3 / 20 )97.84066666666670.675185258806782144.909364341833
Winsorized Mean ( 4 / 20 )97.92266666666670.661196222345866148.099253076864
Winsorized Mean ( 5 / 20 )97.92266666666670.659944950052511148.380053001201
Winsorized Mean ( 6 / 20 )97.92266666666670.65732937966517148.970470050413
Winsorized Mean ( 7 / 20 )97.8970.650335215604512150.53313683621
Winsorized Mean ( 8 / 20 )97.84633333333330.638423197344615153.262496946076
Winsorized Mean ( 9 / 20 )97.65883333333330.595983168707219163.861730433043
Winsorized Mean ( 10 / 20 )97.30216666666670.52225040488725186.31324314181
Winsorized Mean ( 11 / 20 )97.14633333333330.49321927411046196.96378149159
Winsorized Mean ( 12 / 20 )97.14033333333330.492141461833631197.382949551549
Winsorized Mean ( 13 / 20 )97.12733333333330.489103519057111198.582364568905
Winsorized Mean ( 14 / 20 )97.00833333333330.468215277558689207.187458382696
Winsorized Mean ( 15 / 20 )96.92333333333330.448915810477223215.905368158672
Winsorized Mean ( 16 / 20 )96.73933333333330.377324723904098256.38217483443
Winsorized Mean ( 17 / 20 )96.63450.31877913514791303.13935055744
Winsorized Mean ( 18 / 20 )96.66750.305458590589579316.466791172636
Winsorized Mean ( 19 / 20 )96.67066666666670.298760137209915323.572841977723
Winsorized Mean ( 20 / 20 )96.57066666666670.274075731489194352.35030165549
Trimmed Mean ( 1 / 20 )97.78620689655170.672012347007346145.512515256632
Trimmed Mean ( 2 / 20 )97.72839285714290.66252492120663147.50900642221
Trimmed Mean ( 3 / 20 )97.66740740740740.650663650089301150.104293353414
Trimmed Mean ( 4 / 20 )97.60076923076920.637204362949935153.170277709536
Trimmed Mean ( 5 / 20 )97.50420.625010111918199156.00419599733
Trimmed Mean ( 6 / 20 )97.39958333333330.609286363045056159.858465970837
Trimmed Mean ( 7 / 20 )97.28586956521740.58928340795209165.091818728294
Trimmed Mean ( 8 / 20 )97.16681818181820.564917043127565172.001923758347
Trimmed Mean ( 9 / 20 )97.04547619047620.536059438430935181.034917460892
Trimmed Mean ( 10 / 20 )96.943250.51089318311295189.752482914941
Trimmed Mean ( 11 / 20 )96.88657894736840.499252254007622194.063378121252
Trimmed Mean ( 12 / 20 )96.84722222222220.490867002824677197.298293967446
Trimmed Mean ( 13 / 20 )96.80411764705880.478554924726377202.284236657701
Trimmed Mean ( 14 / 20 )96.75750.461224920639979209.783764211489
Trimmed Mean ( 15 / 20 )96.72166666666670.442509843603308218.575175365757
Trimmed Mean ( 16 / 20 )96.69285714285710.420962570802475229.69466610424
Trimmed Mean ( 17 / 20 )96.68615384615380.412933251049713234.144752451804
Trimmed Mean ( 18 / 20 )96.693750.417423868134545231.644037108184
Trimmed Mean ( 19 / 20 )96.69772727272730.424296684068786227.901208997077
Trimmed Mean ( 20 / 20 )96.7020.432001218321869223.846590932414
Median97.725
Midrange99.4
Midmean - Weighted Average at Xnp96.4778125
Midmean - Weighted Average at X(n+1)p96.7216666666666
Midmean - Empirical Distribution Function96.4778125
Midmean - Empirical Distribution Function - Averaging96.7216666666666
Midmean - Empirical Distribution Function - Interpolation96.7216666666666
Midmean - Closest Observation96.4778125
Midmean - True Basic - Statistics Graphics Toolkit96.7216666666666
Midmean - MS Excel (old versions)96.6381818181818
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 97.84 & 0.679361157206463 & 144.017653882831 \tabularnewline
Geometric Mean & 97.7036592078096 &  &  \tabularnewline
Harmonic Mean & 97.5702079459527 &  &  \tabularnewline
Quadratic Mean & 97.9790587999973 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 97.8401666666667 & 0.679333400905393 & 144.023783515235 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 97.8381666666667 & 0.678845667443754 & 144.124314787312 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 97.8406666666667 & 0.675185258806782 & 144.909364341833 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 97.9226666666667 & 0.661196222345866 & 148.099253076864 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 97.9226666666667 & 0.659944950052511 & 148.380053001201 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 97.9226666666667 & 0.65732937966517 & 148.970470050413 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 97.897 & 0.650335215604512 & 150.53313683621 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 97.8463333333333 & 0.638423197344615 & 153.262496946076 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 97.6588333333333 & 0.595983168707219 & 163.861730433043 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 97.3021666666667 & 0.52225040488725 & 186.31324314181 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 97.1463333333333 & 0.49321927411046 & 196.96378149159 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 97.1403333333333 & 0.492141461833631 & 197.382949551549 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 97.1273333333333 & 0.489103519057111 & 198.582364568905 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 97.0083333333333 & 0.468215277558689 & 207.187458382696 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 96.9233333333333 & 0.448915810477223 & 215.905368158672 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 96.7393333333333 & 0.377324723904098 & 256.38217483443 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 96.6345 & 0.31877913514791 & 303.13935055744 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 96.6675 & 0.305458590589579 & 316.466791172636 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 96.6706666666667 & 0.298760137209915 & 323.572841977723 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 96.5706666666667 & 0.274075731489194 & 352.35030165549 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 97.7862068965517 & 0.672012347007346 & 145.512515256632 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 97.7283928571429 & 0.66252492120663 & 147.50900642221 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 97.6674074074074 & 0.650663650089301 & 150.104293353414 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 97.6007692307692 & 0.637204362949935 & 153.170277709536 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 97.5042 & 0.625010111918199 & 156.00419599733 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 97.3995833333333 & 0.609286363045056 & 159.858465970837 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 97.2858695652174 & 0.58928340795209 & 165.091818728294 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 97.1668181818182 & 0.564917043127565 & 172.001923758347 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 97.0454761904762 & 0.536059438430935 & 181.034917460892 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 96.94325 & 0.51089318311295 & 189.752482914941 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 96.8865789473684 & 0.499252254007622 & 194.063378121252 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 96.8472222222222 & 0.490867002824677 & 197.298293967446 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 96.8041176470588 & 0.478554924726377 & 202.284236657701 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 96.7575 & 0.461224920639979 & 209.783764211489 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 96.7216666666667 & 0.442509843603308 & 218.575175365757 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 96.6928571428571 & 0.420962570802475 & 229.69466610424 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 96.6861538461538 & 0.412933251049713 & 234.144752451804 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 96.69375 & 0.417423868134545 & 231.644037108184 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 96.6977272727273 & 0.424296684068786 & 227.901208997077 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 96.702 & 0.432001218321869 & 223.846590932414 \tabularnewline
Median & 97.725 &  &  \tabularnewline
Midrange & 99.4 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 96.4778125 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 96.7216666666666 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 96.4778125 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 96.7216666666666 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 96.7216666666666 &  &  \tabularnewline
Midmean - Closest Observation & 96.4778125 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 96.7216666666666 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 96.6381818181818 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=281662&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]97.84[/C][C]0.679361157206463[/C][C]144.017653882831[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]97.7036592078096[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]97.5702079459527[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]97.9790587999973[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]97.8401666666667[/C][C]0.679333400905393[/C][C]144.023783515235[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]97.8381666666667[/C][C]0.678845667443754[/C][C]144.124314787312[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]97.8406666666667[/C][C]0.675185258806782[/C][C]144.909364341833[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]97.9226666666667[/C][C]0.661196222345866[/C][C]148.099253076864[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]97.9226666666667[/C][C]0.659944950052511[/C][C]148.380053001201[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]97.9226666666667[/C][C]0.65732937966517[/C][C]148.970470050413[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]97.897[/C][C]0.650335215604512[/C][C]150.53313683621[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]97.8463333333333[/C][C]0.638423197344615[/C][C]153.262496946076[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]97.6588333333333[/C][C]0.595983168707219[/C][C]163.861730433043[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]97.3021666666667[/C][C]0.52225040488725[/C][C]186.31324314181[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]97.1463333333333[/C][C]0.49321927411046[/C][C]196.96378149159[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]97.1403333333333[/C][C]0.492141461833631[/C][C]197.382949551549[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]97.1273333333333[/C][C]0.489103519057111[/C][C]198.582364568905[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]97.0083333333333[/C][C]0.468215277558689[/C][C]207.187458382696[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]96.9233333333333[/C][C]0.448915810477223[/C][C]215.905368158672[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]96.7393333333333[/C][C]0.377324723904098[/C][C]256.38217483443[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]96.6345[/C][C]0.31877913514791[/C][C]303.13935055744[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]96.6675[/C][C]0.305458590589579[/C][C]316.466791172636[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]96.6706666666667[/C][C]0.298760137209915[/C][C]323.572841977723[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]96.5706666666667[/C][C]0.274075731489194[/C][C]352.35030165549[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]97.7862068965517[/C][C]0.672012347007346[/C][C]145.512515256632[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]97.7283928571429[/C][C]0.66252492120663[/C][C]147.50900642221[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]97.6674074074074[/C][C]0.650663650089301[/C][C]150.104293353414[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]97.6007692307692[/C][C]0.637204362949935[/C][C]153.170277709536[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]97.5042[/C][C]0.625010111918199[/C][C]156.00419599733[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]97.3995833333333[/C][C]0.609286363045056[/C][C]159.858465970837[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]97.2858695652174[/C][C]0.58928340795209[/C][C]165.091818728294[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]97.1668181818182[/C][C]0.564917043127565[/C][C]172.001923758347[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]97.0454761904762[/C][C]0.536059438430935[/C][C]181.034917460892[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]96.94325[/C][C]0.51089318311295[/C][C]189.752482914941[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]96.8865789473684[/C][C]0.499252254007622[/C][C]194.063378121252[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]96.8472222222222[/C][C]0.490867002824677[/C][C]197.298293967446[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]96.8041176470588[/C][C]0.478554924726377[/C][C]202.284236657701[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]96.7575[/C][C]0.461224920639979[/C][C]209.783764211489[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]96.7216666666667[/C][C]0.442509843603308[/C][C]218.575175365757[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]96.6928571428571[/C][C]0.420962570802475[/C][C]229.69466610424[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]96.6861538461538[/C][C]0.412933251049713[/C][C]234.144752451804[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]96.69375[/C][C]0.417423868134545[/C][C]231.644037108184[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]96.6977272727273[/C][C]0.424296684068786[/C][C]227.901208997077[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]96.702[/C][C]0.432001218321869[/C][C]223.846590932414[/C][/ROW]
[ROW][C]Median[/C][C]97.725[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]99.4[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]96.4778125[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]96.7216666666666[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]96.4778125[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]96.7216666666666[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]96.7216666666666[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]96.4778125[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]96.7216666666666[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]96.6381818181818[/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=281662&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=281662&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 Mean97.840.679361157206463144.017653882831
Geometric Mean97.7036592078096
Harmonic Mean97.5702079459527
Quadratic Mean97.9790587999973
Winsorized Mean ( 1 / 20 )97.84016666666670.679333400905393144.023783515235
Winsorized Mean ( 2 / 20 )97.83816666666670.678845667443754144.124314787312
Winsorized Mean ( 3 / 20 )97.84066666666670.675185258806782144.909364341833
Winsorized Mean ( 4 / 20 )97.92266666666670.661196222345866148.099253076864
Winsorized Mean ( 5 / 20 )97.92266666666670.659944950052511148.380053001201
Winsorized Mean ( 6 / 20 )97.92266666666670.65732937966517148.970470050413
Winsorized Mean ( 7 / 20 )97.8970.650335215604512150.53313683621
Winsorized Mean ( 8 / 20 )97.84633333333330.638423197344615153.262496946076
Winsorized Mean ( 9 / 20 )97.65883333333330.595983168707219163.861730433043
Winsorized Mean ( 10 / 20 )97.30216666666670.52225040488725186.31324314181
Winsorized Mean ( 11 / 20 )97.14633333333330.49321927411046196.96378149159
Winsorized Mean ( 12 / 20 )97.14033333333330.492141461833631197.382949551549
Winsorized Mean ( 13 / 20 )97.12733333333330.489103519057111198.582364568905
Winsorized Mean ( 14 / 20 )97.00833333333330.468215277558689207.187458382696
Winsorized Mean ( 15 / 20 )96.92333333333330.448915810477223215.905368158672
Winsorized Mean ( 16 / 20 )96.73933333333330.377324723904098256.38217483443
Winsorized Mean ( 17 / 20 )96.63450.31877913514791303.13935055744
Winsorized Mean ( 18 / 20 )96.66750.305458590589579316.466791172636
Winsorized Mean ( 19 / 20 )96.67066666666670.298760137209915323.572841977723
Winsorized Mean ( 20 / 20 )96.57066666666670.274075731489194352.35030165549
Trimmed Mean ( 1 / 20 )97.78620689655170.672012347007346145.512515256632
Trimmed Mean ( 2 / 20 )97.72839285714290.66252492120663147.50900642221
Trimmed Mean ( 3 / 20 )97.66740740740740.650663650089301150.104293353414
Trimmed Mean ( 4 / 20 )97.60076923076920.637204362949935153.170277709536
Trimmed Mean ( 5 / 20 )97.50420.625010111918199156.00419599733
Trimmed Mean ( 6 / 20 )97.39958333333330.609286363045056159.858465970837
Trimmed Mean ( 7 / 20 )97.28586956521740.58928340795209165.091818728294
Trimmed Mean ( 8 / 20 )97.16681818181820.564917043127565172.001923758347
Trimmed Mean ( 9 / 20 )97.04547619047620.536059438430935181.034917460892
Trimmed Mean ( 10 / 20 )96.943250.51089318311295189.752482914941
Trimmed Mean ( 11 / 20 )96.88657894736840.499252254007622194.063378121252
Trimmed Mean ( 12 / 20 )96.84722222222220.490867002824677197.298293967446
Trimmed Mean ( 13 / 20 )96.80411764705880.478554924726377202.284236657701
Trimmed Mean ( 14 / 20 )96.75750.461224920639979209.783764211489
Trimmed Mean ( 15 / 20 )96.72166666666670.442509843603308218.575175365757
Trimmed Mean ( 16 / 20 )96.69285714285710.420962570802475229.69466610424
Trimmed Mean ( 17 / 20 )96.68615384615380.412933251049713234.144752451804
Trimmed Mean ( 18 / 20 )96.693750.417423868134545231.644037108184
Trimmed Mean ( 19 / 20 )96.69772727272730.424296684068786227.901208997077
Trimmed Mean ( 20 / 20 )96.7020.432001218321869223.846590932414
Median97.725
Midrange99.4
Midmean - Weighted Average at Xnp96.4778125
Midmean - Weighted Average at X(n+1)p96.7216666666666
Midmean - Empirical Distribution Function96.4778125
Midmean - Empirical Distribution Function - Averaging96.7216666666666
Midmean - Empirical Distribution Function - Interpolation96.7216666666666
Midmean - Closest Observation96.4778125
Midmean - True Basic - Statistics Graphics Toolkit96.7216666666666
Midmean - MS Excel (old versions)96.6381818181818
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')