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of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationWed, 24 Oct 2007 12:38:01 -0700
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2007/Oct/24/2x11zqtwd47x64o1193254425.htm/, Retrieved Sun, 05 May 2024 07:34:25 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=1726, Retrieved Sun, 05 May 2024 07:34:25 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsGroep 1, WS3, Deel 1, Vraag 2, Central Tendancy
Estimated Impact275
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [WS3, Deel 1, Vraag 2] [2007-10-24 19:38:01] [443d2fe869025e720a9fee03b1da487c] [Current]
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Dataseries X:
109.20
88.60
94.30
98.30
86.40
80.60
104.10
108.20
93.40
71.90
94.10
94.90
96.40
91.10
84.40
86.40
88.00
75.10
109.70
103.00
82.10
68.00
96.40
94.30
90.00
88.00
76.10
82.50
81.40
66.50
97.20
94.10
80.70
70.50
87.80
89.50
99.60
84.20
75.10
92.00
80.80
73.10
99.80
90.00
83.10
72.40
78.80
87.30
91.00
80.10
73.60
86.40
74.50
71.20
92.40
81.50
85.30
69.90
84.20
90.70




Summary of compuational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135

\begin{tabular}{lllllllll}
\hline
Summary of compuational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 2 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=1726&T=0

[TABLE]
[ROW][C]Summary of compuational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=1726&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=1726&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 compuational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean86.671.3572015492172663.8593435514313
Geometric Mean86.0410518690387
Harmonic Mean85.4105137533196
Quadratic Mean87.2947115618504
Winsorized Mean ( 1 / 20 )86.68666666666671.3487396641800764.2723491930262
Winsorized Mean ( 2 / 20 )86.71666666666671.3251908862961665.4371136742685
Winsorized Mean ( 3 / 20 )86.54166666666671.2664004143303968.3367327484848
Winsorized Mean ( 4 / 20 )86.5151.2396186423780069.7916254583229
Winsorized Mean ( 5 / 20 )86.30666666666671.1712272443910173.6890873056341
Winsorized Mean ( 6 / 20 )86.33666666666661.1570148778193474.6201871054487
Winsorized Mean ( 7 / 20 )86.26666666666671.1118180425315577.590633868688
Winsorized Mean ( 8 / 20 )86.18666666666671.0722632136032280.3782742644374
Winsorized Mean ( 9 / 20 )86.20166666666671.0251980425095284.0829411414588
Winsorized Mean ( 10 / 20 )86.30166666666671.0060873805618585.77949424082
Winsorized Mean ( 11 / 20 )86.02666666666670.96113711687708589.505092620066
Winsorized Mean ( 12 / 20 )86.10666666666670.9044955727114595.198549627546
Winsorized Mean ( 13 / 20 )86.69166666666660.800403470526512108.309958488361
Winsorized Mean ( 14 / 20 )86.94833333333330.743766911374621116.902663998102
Winsorized Mean ( 15 / 20 )87.07333333333330.724544925038639120.176583016836
Winsorized Mean ( 16 / 20 )86.91333333333330.690273288492338125.911482860890
Winsorized Mean ( 17 / 20 )86.65833333333330.641838336416704135.015826286001
Winsorized Mean ( 18 / 20 )86.71833333333330.596186049842132145.455153397662
Winsorized Mean ( 19 / 20 )86.4650.549559787877513157.335019605313
Winsorized Mean ( 20 / 20 )86.63166666666670.514526229705167168.371720750385
Trimmed Mean ( 1 / 20 )86.62068965517241.2995549487636066.654118579275
Trimmed Mean ( 2 / 20 )86.551.2387781999096669.867228860107
Trimmed Mean ( 3 / 20 )86.45740740740741.1792629431604673.314783533941
Trimmed Mean ( 4 / 20 )86.4251.1346253227061876.1705192634598
Trimmed Mean ( 5 / 20 )86.3981.0893828621784779.309123541036
Trimmed Mean ( 6 / 20 )86.42083333333331.0564138719803681.8058486597952
Trimmed Mean ( 7 / 20 )86.43913043478261.0185310928300384.8664621465877
Trimmed Mean ( 8 / 20 )86.47272727272730.98314744407454787.9549937233733
Trimmed Mean ( 9 / 20 )86.52380952380950.94809430182581791.2607631510749
Trimmed Mean ( 10 / 20 )86.57750.9148524296020294.6354813067098
Trimmed Mean ( 11 / 20 )86.6210526315790.8753634310860598.9543880352752
Trimmed Mean ( 12 / 20 )86.71111111111110.833712083241274104.006062589376
Trimmed Mean ( 13 / 20 )86.80.792871538329088109.475489791100
Trimmed Mean ( 14 / 20 )86.8156250.76798476042035113.043421528940
Trimmed Mean ( 15 / 20 )86.79666666666670.748108470427186116.021499685873
Trimmed Mean ( 16 / 20 )86.75714285714290.72295009545195120.004331423329
Trimmed Mean ( 17 / 20 )86.73461538461540.695368022266291124.731958628089
Trimmed Mean ( 18 / 20 )86.74583333333330.668899679623908129.684369683219
Trimmed Mean ( 19 / 20 )86.750.642632235789795134.991672014997
Trimmed Mean ( 20 / 20 )86.7950.616162786077972140.863748933089
Median86.85
Midrange88.1
Midmean - Weighted Average at Xnp86.815625
Midmean - Weighted Average at X(n+1)p87.0322580645161
Midmean - Empirical Distribution Function86.815625
Midmean - Empirical Distribution Function - Averaging87.0322580645161
Midmean - Empirical Distribution Function - Interpolation87.0322580645161
Midmean - Closest Observation86.815625
Midmean - True Basic - Statistics Graphics Toolkit87.0322580645161
Midmean - MS Excel (old versions)86.815625
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 86.67 & 1.35720154921726 & 63.8593435514313 \tabularnewline
Geometric Mean & 86.0410518690387 &  &  \tabularnewline
Harmonic Mean & 85.4105137533196 &  &  \tabularnewline
Quadratic Mean & 87.2947115618504 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 86.6866666666667 & 1.34873966418007 & 64.2723491930262 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 86.7166666666667 & 1.32519088629616 & 65.4371136742685 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 86.5416666666667 & 1.26640041433039 & 68.3367327484848 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 86.515 & 1.23961864237800 & 69.7916254583229 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 86.3066666666667 & 1.17122724439101 & 73.6890873056341 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 86.3366666666666 & 1.15701487781934 & 74.6201871054487 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 86.2666666666667 & 1.11181804253155 & 77.590633868688 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 86.1866666666667 & 1.07226321360322 & 80.3782742644374 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 86.2016666666667 & 1.02519804250952 & 84.0829411414588 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 86.3016666666667 & 1.00608738056185 & 85.77949424082 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 86.0266666666667 & 0.961137116877085 & 89.505092620066 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 86.1066666666667 & 0.90449557271145 & 95.198549627546 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 86.6916666666666 & 0.800403470526512 & 108.309958488361 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 86.9483333333333 & 0.743766911374621 & 116.902663998102 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 87.0733333333333 & 0.724544925038639 & 120.176583016836 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 86.9133333333333 & 0.690273288492338 & 125.911482860890 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 86.6583333333333 & 0.641838336416704 & 135.015826286001 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 86.7183333333333 & 0.596186049842132 & 145.455153397662 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 86.465 & 0.549559787877513 & 157.335019605313 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 86.6316666666667 & 0.514526229705167 & 168.371720750385 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 86.6206896551724 & 1.29955494876360 & 66.654118579275 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 86.55 & 1.23877819990966 & 69.867228860107 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 86.4574074074074 & 1.17926294316046 & 73.314783533941 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 86.425 & 1.13462532270618 & 76.1705192634598 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 86.398 & 1.08938286217847 & 79.309123541036 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 86.4208333333333 & 1.05641387198036 & 81.8058486597952 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 86.4391304347826 & 1.01853109283003 & 84.8664621465877 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 86.4727272727273 & 0.983147444074547 & 87.9549937233733 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 86.5238095238095 & 0.948094301825817 & 91.2607631510749 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 86.5775 & 0.91485242960202 & 94.6354813067098 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 86.621052631579 & 0.87536343108605 & 98.9543880352752 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 86.7111111111111 & 0.833712083241274 & 104.006062589376 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 86.8 & 0.792871538329088 & 109.475489791100 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 86.815625 & 0.76798476042035 & 113.043421528940 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 86.7966666666667 & 0.748108470427186 & 116.021499685873 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 86.7571428571429 & 0.72295009545195 & 120.004331423329 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 86.7346153846154 & 0.695368022266291 & 124.731958628089 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 86.7458333333333 & 0.668899679623908 & 129.684369683219 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 86.75 & 0.642632235789795 & 134.991672014997 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 86.795 & 0.616162786077972 & 140.863748933089 \tabularnewline
Median & 86.85 &  &  \tabularnewline
Midrange & 88.1 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 86.815625 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 87.0322580645161 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 86.815625 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 87.0322580645161 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 87.0322580645161 &  &  \tabularnewline
Midmean - Closest Observation & 86.815625 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 87.0322580645161 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 86.815625 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=1726&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]86.67[/C][C]1.35720154921726[/C][C]63.8593435514313[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]86.0410518690387[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]85.4105137533196[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]87.2947115618504[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]86.6866666666667[/C][C]1.34873966418007[/C][C]64.2723491930262[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]86.7166666666667[/C][C]1.32519088629616[/C][C]65.4371136742685[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]86.5416666666667[/C][C]1.26640041433039[/C][C]68.3367327484848[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]86.515[/C][C]1.23961864237800[/C][C]69.7916254583229[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]86.3066666666667[/C][C]1.17122724439101[/C][C]73.6890873056341[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]86.3366666666666[/C][C]1.15701487781934[/C][C]74.6201871054487[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]86.2666666666667[/C][C]1.11181804253155[/C][C]77.590633868688[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]86.1866666666667[/C][C]1.07226321360322[/C][C]80.3782742644374[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]86.2016666666667[/C][C]1.02519804250952[/C][C]84.0829411414588[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]86.3016666666667[/C][C]1.00608738056185[/C][C]85.77949424082[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]86.0266666666667[/C][C]0.961137116877085[/C][C]89.505092620066[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]86.1066666666667[/C][C]0.90449557271145[/C][C]95.198549627546[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]86.6916666666666[/C][C]0.800403470526512[/C][C]108.309958488361[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]86.9483333333333[/C][C]0.743766911374621[/C][C]116.902663998102[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]87.0733333333333[/C][C]0.724544925038639[/C][C]120.176583016836[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]86.9133333333333[/C][C]0.690273288492338[/C][C]125.911482860890[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]86.6583333333333[/C][C]0.641838336416704[/C][C]135.015826286001[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]86.7183333333333[/C][C]0.596186049842132[/C][C]145.455153397662[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]86.465[/C][C]0.549559787877513[/C][C]157.335019605313[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]86.6316666666667[/C][C]0.514526229705167[/C][C]168.371720750385[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]86.6206896551724[/C][C]1.29955494876360[/C][C]66.654118579275[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]86.55[/C][C]1.23877819990966[/C][C]69.867228860107[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]86.4574074074074[/C][C]1.17926294316046[/C][C]73.314783533941[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]86.425[/C][C]1.13462532270618[/C][C]76.1705192634598[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]86.398[/C][C]1.08938286217847[/C][C]79.309123541036[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]86.4208333333333[/C][C]1.05641387198036[/C][C]81.8058486597952[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]86.4391304347826[/C][C]1.01853109283003[/C][C]84.8664621465877[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]86.4727272727273[/C][C]0.983147444074547[/C][C]87.9549937233733[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]86.5238095238095[/C][C]0.948094301825817[/C][C]91.2607631510749[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]86.5775[/C][C]0.91485242960202[/C][C]94.6354813067098[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]86.621052631579[/C][C]0.87536343108605[/C][C]98.9543880352752[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]86.7111111111111[/C][C]0.833712083241274[/C][C]104.006062589376[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]86.8[/C][C]0.792871538329088[/C][C]109.475489791100[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]86.815625[/C][C]0.76798476042035[/C][C]113.043421528940[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]86.7966666666667[/C][C]0.748108470427186[/C][C]116.021499685873[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]86.7571428571429[/C][C]0.72295009545195[/C][C]120.004331423329[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]86.7346153846154[/C][C]0.695368022266291[/C][C]124.731958628089[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]86.7458333333333[/C][C]0.668899679623908[/C][C]129.684369683219[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]86.75[/C][C]0.642632235789795[/C][C]134.991672014997[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]86.795[/C][C]0.616162786077972[/C][C]140.863748933089[/C][/ROW]
[ROW][C]Median[/C][C]86.85[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]88.1[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]86.815625[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]87.0322580645161[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]86.815625[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]87.0322580645161[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]87.0322580645161[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]86.815625[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]87.0322580645161[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]86.815625[/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=1726&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=1726&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 Mean86.671.3572015492172663.8593435514313
Geometric Mean86.0410518690387
Harmonic Mean85.4105137533196
Quadratic Mean87.2947115618504
Winsorized Mean ( 1 / 20 )86.68666666666671.3487396641800764.2723491930262
Winsorized Mean ( 2 / 20 )86.71666666666671.3251908862961665.4371136742685
Winsorized Mean ( 3 / 20 )86.54166666666671.2664004143303968.3367327484848
Winsorized Mean ( 4 / 20 )86.5151.2396186423780069.7916254583229
Winsorized Mean ( 5 / 20 )86.30666666666671.1712272443910173.6890873056341
Winsorized Mean ( 6 / 20 )86.33666666666661.1570148778193474.6201871054487
Winsorized Mean ( 7 / 20 )86.26666666666671.1118180425315577.590633868688
Winsorized Mean ( 8 / 20 )86.18666666666671.0722632136032280.3782742644374
Winsorized Mean ( 9 / 20 )86.20166666666671.0251980425095284.0829411414588
Winsorized Mean ( 10 / 20 )86.30166666666671.0060873805618585.77949424082
Winsorized Mean ( 11 / 20 )86.02666666666670.96113711687708589.505092620066
Winsorized Mean ( 12 / 20 )86.10666666666670.9044955727114595.198549627546
Winsorized Mean ( 13 / 20 )86.69166666666660.800403470526512108.309958488361
Winsorized Mean ( 14 / 20 )86.94833333333330.743766911374621116.902663998102
Winsorized Mean ( 15 / 20 )87.07333333333330.724544925038639120.176583016836
Winsorized Mean ( 16 / 20 )86.91333333333330.690273288492338125.911482860890
Winsorized Mean ( 17 / 20 )86.65833333333330.641838336416704135.015826286001
Winsorized Mean ( 18 / 20 )86.71833333333330.596186049842132145.455153397662
Winsorized Mean ( 19 / 20 )86.4650.549559787877513157.335019605313
Winsorized Mean ( 20 / 20 )86.63166666666670.514526229705167168.371720750385
Trimmed Mean ( 1 / 20 )86.62068965517241.2995549487636066.654118579275
Trimmed Mean ( 2 / 20 )86.551.2387781999096669.867228860107
Trimmed Mean ( 3 / 20 )86.45740740740741.1792629431604673.314783533941
Trimmed Mean ( 4 / 20 )86.4251.1346253227061876.1705192634598
Trimmed Mean ( 5 / 20 )86.3981.0893828621784779.309123541036
Trimmed Mean ( 6 / 20 )86.42083333333331.0564138719803681.8058486597952
Trimmed Mean ( 7 / 20 )86.43913043478261.0185310928300384.8664621465877
Trimmed Mean ( 8 / 20 )86.47272727272730.98314744407454787.9549937233733
Trimmed Mean ( 9 / 20 )86.52380952380950.94809430182581791.2607631510749
Trimmed Mean ( 10 / 20 )86.57750.9148524296020294.6354813067098
Trimmed Mean ( 11 / 20 )86.6210526315790.8753634310860598.9543880352752
Trimmed Mean ( 12 / 20 )86.71111111111110.833712083241274104.006062589376
Trimmed Mean ( 13 / 20 )86.80.792871538329088109.475489791100
Trimmed Mean ( 14 / 20 )86.8156250.76798476042035113.043421528940
Trimmed Mean ( 15 / 20 )86.79666666666670.748108470427186116.021499685873
Trimmed Mean ( 16 / 20 )86.75714285714290.72295009545195120.004331423329
Trimmed Mean ( 17 / 20 )86.73461538461540.695368022266291124.731958628089
Trimmed Mean ( 18 / 20 )86.74583333333330.668899679623908129.684369683219
Trimmed Mean ( 19 / 20 )86.750.642632235789795134.991672014997
Trimmed Mean ( 20 / 20 )86.7950.616162786077972140.863748933089
Median86.85
Midrange88.1
Midmean - Weighted Average at Xnp86.815625
Midmean - Weighted Average at X(n+1)p87.0322580645161
Midmean - Empirical Distribution Function86.815625
Midmean - Empirical Distribution Function - Averaging87.0322580645161
Midmean - Empirical Distribution Function - Interpolation87.0322580645161
Midmean - Closest Observation86.815625
Midmean - True Basic - Statistics Graphics Toolkit87.0322580645161
Midmean - MS Excel (old versions)86.815625
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')