Free Statistics

of Irreproducible Research!

Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationFri, 21 Nov 2008 07:30:07 -0700
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2008/Nov/21/t1227277872gkgatjabubkwxgb.htm/, Retrieved Sun, 02 Jun 2024 18:26:15 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=25141, Retrieved Sun, 02 Jun 2024 18:26:15 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact176
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
F     [Exercise 1.13] [Exercise 1.13 (Wo...] [2008-10-01 13:28:34] [b98453cac15ba1066b407e146608df68]
F   P   [Exercise 1.13] [vraag 1 result 1 ...] [2008-10-10 13:06:35] [74be16979710d4c4e7c6647856088456]
- RMPD    [Central Tendency] [] [2008-11-21 14:16:19] [fad8a251ac01c156a8ae23a83577546f]
-    D        [Central Tendency] [] [2008-11-21 14:30:07] [fa8b44cd657c07c6ee11bb2476ca3f8d] [Current]
Feedback Forum

Post a new message
Dataseries X:
99,3
98,7
107,9
101,0
97,6
103,0
94,1
94,1
115,1
116,5
103,4
112,5
95,6
97,5
119,3
100,9
97,7
115,3
92,8
99,2
118,7
110,1
110,3
112,9
102,2
99,4
116,1
103,8
101,8
113,7
89,7
99,5
122,9
108,6
114,4
110,5
104,1
103,6
121,6
101,1
116,0
120,1
96,0
105,0
124,7
123,9
123,6
114,8
108,8
106,1
123,2
106,2
115,2
120,6
109,5
114,4
121,4
129,5
124,3
112,6




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'Sir Ronald Aylmer Fisher' @ 193.190.124.24

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 3 seconds \tabularnewline
R Server & 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=25141&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]3 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Sir Ronald Aylmer Fisher' @ 193.190.124.24[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=25141&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=25141&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 time3 seconds
R Server'Sir Ronald Aylmer Fisher' @ 193.190.124.24







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean109.041.2688648781868285.9350762043442
Geometric Mean108.603660682207
Harmonic Mean108.167476211050
Quadratic Mean109.474712452998
Winsorized Mean ( 1 / 20 )109.0116666666671.2368793693759988.1344368462249
Winsorized Mean ( 2 / 20 )109.0416666666671.2247432376285189.032266777652
Winsorized Mean ( 3 / 20 )109.0216666666671.2205655160243289.3206183816962
Winsorized Mean ( 4 / 20 )109.1016666666671.1965144569015491.182907182913
Winsorized Mean ( 5 / 20 )109.1016666666671.1834104972056192.192579772014
Winsorized Mean ( 6 / 20 )109.2216666666671.1503158290623294.9492860197347
Winsorized Mean ( 7 / 20 )109.0816666666671.1186136791084497.515048049124
Winsorized Mean ( 8 / 20 )109.0683333333331.1112610327292798.1482569090543
Winsorized Mean ( 9 / 20 )109.0983333333331.06352598630240102.581727892367
Winsorized Mean ( 10 / 20 )109.0983333333331.03471520049691105.438030948941
Winsorized Mean ( 11 / 20 )108.971.00574704505858108.347323052441
Winsorized Mean ( 12 / 20 )108.870.981853142389603110.882162820232
Winsorized Mean ( 13 / 20 )108.4150.901413908201058120.272162447951
Winsorized Mean ( 14 / 20 )108.6483333333330.834091717059367130.259456018073
Winsorized Mean ( 15 / 20 )108.6483333333330.826385129523488131.474211541031
Winsorized Mean ( 16 / 20 )108.4883333333330.794547420004958136.541042865203
Winsorized Mean ( 17 / 20 )108.6583333333330.759606245257551143.045602918248
Winsorized Mean ( 18 / 20 )108.7483333333330.737006050871168147.554193354028
Winsorized Mean ( 19 / 20 )108.9066666666670.685552549081242158.859691810088
Winsorized Mean ( 20 / 20 )108.9066666666670.646882426583823168.356199196508
Trimmed Mean ( 1 / 20 )109.0206896551721.2182811933481989.4872959136407
Trimmed Mean ( 2 / 20 )109.0303571428571.1949349806874491.2437571123177
Trimmed Mean ( 3 / 20 )109.0240740740741.1735732530140592.8992491896619
Trimmed Mean ( 4 / 20 )109.0251.1484361292585894.9334466431196
Trimmed Mean ( 5 / 20 )109.0021.1257740738292696.8240453692772
Trimmed Mean ( 6 / 20 )108.9770833333331.1009314221631498.986259397713
Trimmed Mean ( 7 / 20 )108.9239130434781.07871002216039100.976083290049
Trimmed Mean ( 8 / 20 )108.8931818181821.0584723011676102.877686735932
Trimmed Mean ( 9 / 20 )108.8619047619051.03312698314851105.371272396876
Trimmed Mean ( 10 / 20 )108.82251.01174821725971107.558874968658
Trimmed Mean ( 11 / 20 )108.7789473684210.989641643079681109.917512191494
Trimmed Mean ( 12 / 20 )108.750.966276604389487112.545413503735
Trimmed Mean ( 13 / 20 )108.7323529411760.939343273721884115.753586556654
Trimmed Mean ( 14 / 20 )108.7781250.922596423571157117.904342809985
Trimmed Mean ( 15 / 20 )108.7966666666670.91519087053025118.878662550066
Trimmed Mean ( 16 / 20 )108.8178571428570.902671718870363120.550865689063
Trimmed Mean ( 17 / 20 )108.8653846153850.889562421516977122.380826777435
Trimmed Mean ( 18 / 20 )108.8958333333330.876721477732186124.208013718352
Trimmed Mean ( 19 / 20 )108.9181818181820.859065140821541126.786871731312
Trimmed Mean ( 20 / 20 )108.920.845003892859299128.898814455682
Median109.15
Midrange109.6
Midmean - Weighted Average at Xnp108.541935483871
Midmean - Weighted Average at X(n+1)p108.796666666667
Midmean - Empirical Distribution Function108.541935483871
Midmean - Empirical Distribution Function - Averaging108.796666666667
Midmean - Empirical Distribution Function - Interpolation108.796666666667
Midmean - Closest Observation108.541935483871
Midmean - True Basic - Statistics Graphics Toolkit108.796666666667
Midmean - MS Excel (old versions)108.778125
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 109.04 & 1.26886487818682 & 85.9350762043442 \tabularnewline
Geometric Mean & 108.603660682207 &  &  \tabularnewline
Harmonic Mean & 108.167476211050 &  &  \tabularnewline
Quadratic Mean & 109.474712452998 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 109.011666666667 & 1.23687936937599 & 88.1344368462249 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 109.041666666667 & 1.22474323762851 & 89.032266777652 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 109.021666666667 & 1.22056551602432 & 89.3206183816962 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 109.101666666667 & 1.19651445690154 & 91.182907182913 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 109.101666666667 & 1.18341049720561 & 92.192579772014 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 109.221666666667 & 1.15031582906232 & 94.9492860197347 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 109.081666666667 & 1.11861367910844 & 97.515048049124 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 109.068333333333 & 1.11126103272927 & 98.1482569090543 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 109.098333333333 & 1.06352598630240 & 102.581727892367 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 109.098333333333 & 1.03471520049691 & 105.438030948941 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 108.97 & 1.00574704505858 & 108.347323052441 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 108.87 & 0.981853142389603 & 110.882162820232 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 108.415 & 0.901413908201058 & 120.272162447951 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 108.648333333333 & 0.834091717059367 & 130.259456018073 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 108.648333333333 & 0.826385129523488 & 131.474211541031 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 108.488333333333 & 0.794547420004958 & 136.541042865203 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 108.658333333333 & 0.759606245257551 & 143.045602918248 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 108.748333333333 & 0.737006050871168 & 147.554193354028 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 108.906666666667 & 0.685552549081242 & 158.859691810088 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 108.906666666667 & 0.646882426583823 & 168.356199196508 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 109.020689655172 & 1.21828119334819 & 89.4872959136407 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 109.030357142857 & 1.19493498068744 & 91.2437571123177 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 109.024074074074 & 1.17357325301405 & 92.8992491896619 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 109.025 & 1.14843612925858 & 94.9334466431196 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 109.002 & 1.12577407382926 & 96.8240453692772 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 108.977083333333 & 1.10093142216314 & 98.986259397713 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 108.923913043478 & 1.07871002216039 & 100.976083290049 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 108.893181818182 & 1.0584723011676 & 102.877686735932 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 108.861904761905 & 1.03312698314851 & 105.371272396876 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 108.8225 & 1.01174821725971 & 107.558874968658 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 108.778947368421 & 0.989641643079681 & 109.917512191494 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 108.75 & 0.966276604389487 & 112.545413503735 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 108.732352941176 & 0.939343273721884 & 115.753586556654 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 108.778125 & 0.922596423571157 & 117.904342809985 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 108.796666666667 & 0.91519087053025 & 118.878662550066 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 108.817857142857 & 0.902671718870363 & 120.550865689063 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 108.865384615385 & 0.889562421516977 & 122.380826777435 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 108.895833333333 & 0.876721477732186 & 124.208013718352 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 108.918181818182 & 0.859065140821541 & 126.786871731312 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 108.92 & 0.845003892859299 & 128.898814455682 \tabularnewline
Median & 109.15 &  &  \tabularnewline
Midrange & 109.6 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 108.541935483871 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 108.796666666667 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 108.541935483871 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 108.796666666667 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 108.796666666667 &  &  \tabularnewline
Midmean - Closest Observation & 108.541935483871 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 108.796666666667 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 108.778125 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=25141&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]109.04[/C][C]1.26886487818682[/C][C]85.9350762043442[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]108.603660682207[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]108.167476211050[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]109.474712452998[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]109.011666666667[/C][C]1.23687936937599[/C][C]88.1344368462249[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]109.041666666667[/C][C]1.22474323762851[/C][C]89.032266777652[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]109.021666666667[/C][C]1.22056551602432[/C][C]89.3206183816962[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]109.101666666667[/C][C]1.19651445690154[/C][C]91.182907182913[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]109.101666666667[/C][C]1.18341049720561[/C][C]92.192579772014[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]109.221666666667[/C][C]1.15031582906232[/C][C]94.9492860197347[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]109.081666666667[/C][C]1.11861367910844[/C][C]97.515048049124[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]109.068333333333[/C][C]1.11126103272927[/C][C]98.1482569090543[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]109.098333333333[/C][C]1.06352598630240[/C][C]102.581727892367[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]109.098333333333[/C][C]1.03471520049691[/C][C]105.438030948941[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]108.97[/C][C]1.00574704505858[/C][C]108.347323052441[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]108.87[/C][C]0.981853142389603[/C][C]110.882162820232[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]108.415[/C][C]0.901413908201058[/C][C]120.272162447951[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]108.648333333333[/C][C]0.834091717059367[/C][C]130.259456018073[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]108.648333333333[/C][C]0.826385129523488[/C][C]131.474211541031[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]108.488333333333[/C][C]0.794547420004958[/C][C]136.541042865203[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]108.658333333333[/C][C]0.759606245257551[/C][C]143.045602918248[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]108.748333333333[/C][C]0.737006050871168[/C][C]147.554193354028[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]108.906666666667[/C][C]0.685552549081242[/C][C]158.859691810088[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]108.906666666667[/C][C]0.646882426583823[/C][C]168.356199196508[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]109.020689655172[/C][C]1.21828119334819[/C][C]89.4872959136407[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]109.030357142857[/C][C]1.19493498068744[/C][C]91.2437571123177[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]109.024074074074[/C][C]1.17357325301405[/C][C]92.8992491896619[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]109.025[/C][C]1.14843612925858[/C][C]94.9334466431196[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]109.002[/C][C]1.12577407382926[/C][C]96.8240453692772[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]108.977083333333[/C][C]1.10093142216314[/C][C]98.986259397713[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]108.923913043478[/C][C]1.07871002216039[/C][C]100.976083290049[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]108.893181818182[/C][C]1.0584723011676[/C][C]102.877686735932[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]108.861904761905[/C][C]1.03312698314851[/C][C]105.371272396876[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]108.8225[/C][C]1.01174821725971[/C][C]107.558874968658[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]108.778947368421[/C][C]0.989641643079681[/C][C]109.917512191494[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]108.75[/C][C]0.966276604389487[/C][C]112.545413503735[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]108.732352941176[/C][C]0.939343273721884[/C][C]115.753586556654[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]108.778125[/C][C]0.922596423571157[/C][C]117.904342809985[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]108.796666666667[/C][C]0.91519087053025[/C][C]118.878662550066[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]108.817857142857[/C][C]0.902671718870363[/C][C]120.550865689063[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]108.865384615385[/C][C]0.889562421516977[/C][C]122.380826777435[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]108.895833333333[/C][C]0.876721477732186[/C][C]124.208013718352[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]108.918181818182[/C][C]0.859065140821541[/C][C]126.786871731312[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]108.92[/C][C]0.845003892859299[/C][C]128.898814455682[/C][/ROW]
[ROW][C]Median[/C][C]109.15[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]109.6[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]108.541935483871[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]108.796666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]108.541935483871[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]108.796666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]108.796666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]108.541935483871[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]108.796666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]108.778125[/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=25141&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=25141&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 Mean109.041.2688648781868285.9350762043442
Geometric Mean108.603660682207
Harmonic Mean108.167476211050
Quadratic Mean109.474712452998
Winsorized Mean ( 1 / 20 )109.0116666666671.2368793693759988.1344368462249
Winsorized Mean ( 2 / 20 )109.0416666666671.2247432376285189.032266777652
Winsorized Mean ( 3 / 20 )109.0216666666671.2205655160243289.3206183816962
Winsorized Mean ( 4 / 20 )109.1016666666671.1965144569015491.182907182913
Winsorized Mean ( 5 / 20 )109.1016666666671.1834104972056192.192579772014
Winsorized Mean ( 6 / 20 )109.2216666666671.1503158290623294.9492860197347
Winsorized Mean ( 7 / 20 )109.0816666666671.1186136791084497.515048049124
Winsorized Mean ( 8 / 20 )109.0683333333331.1112610327292798.1482569090543
Winsorized Mean ( 9 / 20 )109.0983333333331.06352598630240102.581727892367
Winsorized Mean ( 10 / 20 )109.0983333333331.03471520049691105.438030948941
Winsorized Mean ( 11 / 20 )108.971.00574704505858108.347323052441
Winsorized Mean ( 12 / 20 )108.870.981853142389603110.882162820232
Winsorized Mean ( 13 / 20 )108.4150.901413908201058120.272162447951
Winsorized Mean ( 14 / 20 )108.6483333333330.834091717059367130.259456018073
Winsorized Mean ( 15 / 20 )108.6483333333330.826385129523488131.474211541031
Winsorized Mean ( 16 / 20 )108.4883333333330.794547420004958136.541042865203
Winsorized Mean ( 17 / 20 )108.6583333333330.759606245257551143.045602918248
Winsorized Mean ( 18 / 20 )108.7483333333330.737006050871168147.554193354028
Winsorized Mean ( 19 / 20 )108.9066666666670.685552549081242158.859691810088
Winsorized Mean ( 20 / 20 )108.9066666666670.646882426583823168.356199196508
Trimmed Mean ( 1 / 20 )109.0206896551721.2182811933481989.4872959136407
Trimmed Mean ( 2 / 20 )109.0303571428571.1949349806874491.2437571123177
Trimmed Mean ( 3 / 20 )109.0240740740741.1735732530140592.8992491896619
Trimmed Mean ( 4 / 20 )109.0251.1484361292585894.9334466431196
Trimmed Mean ( 5 / 20 )109.0021.1257740738292696.8240453692772
Trimmed Mean ( 6 / 20 )108.9770833333331.1009314221631498.986259397713
Trimmed Mean ( 7 / 20 )108.9239130434781.07871002216039100.976083290049
Trimmed Mean ( 8 / 20 )108.8931818181821.0584723011676102.877686735932
Trimmed Mean ( 9 / 20 )108.8619047619051.03312698314851105.371272396876
Trimmed Mean ( 10 / 20 )108.82251.01174821725971107.558874968658
Trimmed Mean ( 11 / 20 )108.7789473684210.989641643079681109.917512191494
Trimmed Mean ( 12 / 20 )108.750.966276604389487112.545413503735
Trimmed Mean ( 13 / 20 )108.7323529411760.939343273721884115.753586556654
Trimmed Mean ( 14 / 20 )108.7781250.922596423571157117.904342809985
Trimmed Mean ( 15 / 20 )108.7966666666670.91519087053025118.878662550066
Trimmed Mean ( 16 / 20 )108.8178571428570.902671718870363120.550865689063
Trimmed Mean ( 17 / 20 )108.8653846153850.889562421516977122.380826777435
Trimmed Mean ( 18 / 20 )108.8958333333330.876721477732186124.208013718352
Trimmed Mean ( 19 / 20 )108.9181818181820.859065140821541126.786871731312
Trimmed Mean ( 20 / 20 )108.920.845003892859299128.898814455682
Median109.15
Midrange109.6
Midmean - Weighted Average at Xnp108.541935483871
Midmean - Weighted Average at X(n+1)p108.796666666667
Midmean - Empirical Distribution Function108.541935483871
Midmean - Empirical Distribution Function - Averaging108.796666666667
Midmean - Empirical Distribution Function - Interpolation108.796666666667
Midmean - Closest Observation108.541935483871
Midmean - True Basic - Statistics Graphics Toolkit108.796666666667
Midmean - MS Excel (old versions)108.778125
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')