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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, 05 Dec 2008 02:27:45 -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/Dec/05/t122846930562xkpvf8lm789m9.htm/, Retrieved Thu, 16 May 2024 11:53:33 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=29082, Retrieved Thu, 16 May 2024 11:53:33 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact238
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Univariate Data Series] [Run sequence plot...] [2008-12-02 21:59:14] [ed2ba3b6182103c15c0ab511ae4e6284]
-   PD  [Univariate Data Series] [Run sequence plot...] [2008-12-05 09:24:52] [ed2ba3b6182103c15c0ab511ae4e6284]
- RMPD      [Central Tendency] [central tendency ...] [2008-12-05 09:27:45] [a8228479d4547a92e2d3f176a5299609] [Current]
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Dataseries X:
88.32
88.32
88.32
88.24
88.32
88.94
89.26
89.34
89.49
89.49
89.73
89.65
90.20
91.62
91.85
92.01
92.48
93.27
93.58
93.58
93.82
93.82
93.98
93.74
94.13
95.63
96.10
97.28
97.83
98.07
98.15
98.15
97.99
97.91
98.22
98.22
98.77
99.32
99.48
99.48
99.72
99.88
99.80
99.95
100.43
101.13
101.13
100.90
100.97
101.04
100.87
100.74
100.84
101.07
101.35
101.51
102.20
102.01
102.24
102.15
102.17




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'George Udny Yule' @ 72.249.76.132

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 1 seconds \tabularnewline
R Server & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=29082&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'George Udny Yule' @ 72.249.76.132[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=29082&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=29082&T=0

As an alternative you can also use a QR Code:  

The GUIDs for individual cells are displayed in the table below:

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'George Udny Yule' @ 72.249.76.132







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean96.20.610804539760757157.497192207642
Geometric Mean96.0819821381842
Harmonic Mean95.9624095865493
Quadratic Mean96.3162755257259
Winsorized Mean ( 1 / 20 )96.2006557377050.61041327346165157.599219938570
Winsorized Mean ( 2 / 20 )96.19967213114760.610252521735773157.639122666010
Winsorized Mean ( 3 / 20 )96.19868852459020.610092372984869157.678890581666
Winsorized Mean ( 4 / 20 )96.18950819672130.60861445377667158.046703623010
Winsorized Mean ( 5 / 20 )96.1993442622950.591603122987489162.607904732662
Winsorized Mean ( 6 / 20 )96.21508196721310.582921679399773165.056619726829
Winsorized Mean ( 7 / 20 )96.19901639344260.577450147112192166.592764543451
Winsorized Mean ( 8 / 20 )96.21868852459020.573579713013689167.751205876931
Winsorized Mean ( 9 / 20 )96.20983606557380.572321582755369168.104504468246
Winsorized Mean ( 10 / 20 )96.23114754098360.566519915023354169.863662316296
Winsorized Mean ( 11 / 20 )96.23295081967210.561952506805551171.247480266105
Winsorized Mean ( 12 / 20 )96.31163934426230.5424126521974177.561564897294
Winsorized Mean ( 13 / 20 )96.6078688524590.487119733418814198.324687391381
Winsorized Mean ( 14 / 20 )96.65377049180330.47718093874591202.551616470308
Winsorized Mean ( 15 / 20 )96.6685245901640.467025223459981206.987802230445
Winsorized Mean ( 16 / 20 )96.71049180327870.435075298189301222.284492375846
Winsorized Mean ( 17 / 20 )96.79688524590160.381448600766115253.761280160660
Winsorized Mean ( 18 / 20 )96.86770491803280.364679393098874265.624290133031
Winsorized Mean ( 19 / 20 )96.8427868852460.361264334988715268.066281406580
Winsorized Mean ( 20 / 20 )96.86901639344260.349834754505612276.89935075301
Trimmed Mean ( 1 / 20 )96.23254237288140.608140548349696158.240628147599
Trimmed Mean ( 2 / 20 )96.26666666666670.604724990486279159.190819266880
Trimmed Mean ( 3 / 20 )96.30381818181820.600004236287463160.505230392538
Trimmed Mean ( 4 / 20 )96.34415094339620.593631442763614162.296239725565
Trimmed Mean ( 5 / 20 )96.39039215686270.585649226527367164.587244020476
Trimmed Mean ( 6 / 20 )96.43795918367350.580574939322542166.107685075426
Trimmed Mean ( 7 / 20 )96.4861702127660.575888370021758167.543182386407
Trimmed Mean ( 8 / 20 )96.54177777777780.57041968325022169.246925750682
Trimmed Mean ( 9 / 20 )96.59906976744190.563434120540951171.446964686302
Trimmed Mean ( 10 / 20 )96.66341463414630.553608628351194174.606047817640
Trimmed Mean ( 11 / 20 )96.73102564102560.541222786448513178.726816503369
Trimmed Mean ( 12 / 20 )96.80567567567570.524848832882821184.444871762321
Trimmed Mean ( 13 / 20 )96.87742857142860.507376236986266190.938048551239
Trimmed Mean ( 14 / 20 )96.91575757575760.498779576912759194.305785685185
Trimmed Mean ( 15 / 20 )96.95258064516130.48814900945139198.612675162697
Trimmed Mean ( 16 / 20 )96.99241379310350.474457858923934204.427879038786
Trimmed Mean ( 17 / 20 )97.03222222222220.463124325155576209.516574603648
Trimmed Mean ( 18 / 20 )97.0660.461648495430597210.259539369803
Trimmed Mean ( 19 / 20 )97.09521739130430.461526025870072210.378639445652
Trimmed Mean ( 20 / 20 )97.13380952380950.457938692190329212.110946684188
Median97.99
Midrange95.24
Midmean - Weighted Average at Xnp96.8263333333333
Midmean - Weighted Average at X(n+1)p96.9525806451613
Midmean - Empirical Distribution Function96.9525806451613
Midmean - Empirical Distribution Function - Averaging96.9525806451613
Midmean - Empirical Distribution Function - Interpolation96.9525806451613
Midmean - Closest Observation96.793125
Midmean - True Basic - Statistics Graphics Toolkit96.9525806451613
Midmean - MS Excel (old versions)96.9525806451613
Number of observations61

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 96.2 & 0.610804539760757 & 157.497192207642 \tabularnewline
Geometric Mean & 96.0819821381842 &  &  \tabularnewline
Harmonic Mean & 95.9624095865493 &  &  \tabularnewline
Quadratic Mean & 96.3162755257259 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 96.200655737705 & 0.61041327346165 & 157.599219938570 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 96.1996721311476 & 0.610252521735773 & 157.639122666010 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 96.1986885245902 & 0.610092372984869 & 157.678890581666 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 96.1895081967213 & 0.60861445377667 & 158.046703623010 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 96.199344262295 & 0.591603122987489 & 162.607904732662 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 96.2150819672131 & 0.582921679399773 & 165.056619726829 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 96.1990163934426 & 0.577450147112192 & 166.592764543451 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 96.2186885245902 & 0.573579713013689 & 167.751205876931 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 96.2098360655738 & 0.572321582755369 & 168.104504468246 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 96.2311475409836 & 0.566519915023354 & 169.863662316296 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 96.2329508196721 & 0.561952506805551 & 171.247480266105 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 96.3116393442623 & 0.5424126521974 & 177.561564897294 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 96.607868852459 & 0.487119733418814 & 198.324687391381 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 96.6537704918033 & 0.47718093874591 & 202.551616470308 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 96.668524590164 & 0.467025223459981 & 206.987802230445 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 96.7104918032787 & 0.435075298189301 & 222.284492375846 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 96.7968852459016 & 0.381448600766115 & 253.761280160660 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 96.8677049180328 & 0.364679393098874 & 265.624290133031 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 96.842786885246 & 0.361264334988715 & 268.066281406580 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 96.8690163934426 & 0.349834754505612 & 276.89935075301 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 96.2325423728814 & 0.608140548349696 & 158.240628147599 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 96.2666666666667 & 0.604724990486279 & 159.190819266880 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 96.3038181818182 & 0.600004236287463 & 160.505230392538 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 96.3441509433962 & 0.593631442763614 & 162.296239725565 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 96.3903921568627 & 0.585649226527367 & 164.587244020476 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 96.4379591836735 & 0.580574939322542 & 166.107685075426 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 96.486170212766 & 0.575888370021758 & 167.543182386407 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 96.5417777777778 & 0.57041968325022 & 169.246925750682 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 96.5990697674419 & 0.563434120540951 & 171.446964686302 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 96.6634146341463 & 0.553608628351194 & 174.606047817640 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 96.7310256410256 & 0.541222786448513 & 178.726816503369 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 96.8056756756757 & 0.524848832882821 & 184.444871762321 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 96.8774285714286 & 0.507376236986266 & 190.938048551239 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 96.9157575757576 & 0.498779576912759 & 194.305785685185 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 96.9525806451613 & 0.48814900945139 & 198.612675162697 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 96.9924137931035 & 0.474457858923934 & 204.427879038786 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 97.0322222222222 & 0.463124325155576 & 209.516574603648 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 97.066 & 0.461648495430597 & 210.259539369803 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 97.0952173913043 & 0.461526025870072 & 210.378639445652 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 97.1338095238095 & 0.457938692190329 & 212.110946684188 \tabularnewline
Median & 97.99 &  &  \tabularnewline
Midrange & 95.24 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 96.8263333333333 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 96.9525806451613 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 96.9525806451613 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 96.9525806451613 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 96.9525806451613 &  &  \tabularnewline
Midmean - Closest Observation & 96.793125 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 96.9525806451613 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 96.9525806451613 &  &  \tabularnewline
Number of observations & 61 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=29082&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]96.2[/C][C]0.610804539760757[/C][C]157.497192207642[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]96.0819821381842[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]95.9624095865493[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]96.3162755257259[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]96.200655737705[/C][C]0.61041327346165[/C][C]157.599219938570[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]96.1996721311476[/C][C]0.610252521735773[/C][C]157.639122666010[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]96.1986885245902[/C][C]0.610092372984869[/C][C]157.678890581666[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]96.1895081967213[/C][C]0.60861445377667[/C][C]158.046703623010[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]96.199344262295[/C][C]0.591603122987489[/C][C]162.607904732662[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]96.2150819672131[/C][C]0.582921679399773[/C][C]165.056619726829[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]96.1990163934426[/C][C]0.577450147112192[/C][C]166.592764543451[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]96.2186885245902[/C][C]0.573579713013689[/C][C]167.751205876931[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]96.2098360655738[/C][C]0.572321582755369[/C][C]168.104504468246[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]96.2311475409836[/C][C]0.566519915023354[/C][C]169.863662316296[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]96.2329508196721[/C][C]0.561952506805551[/C][C]171.247480266105[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]96.3116393442623[/C][C]0.5424126521974[/C][C]177.561564897294[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]96.607868852459[/C][C]0.487119733418814[/C][C]198.324687391381[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]96.6537704918033[/C][C]0.47718093874591[/C][C]202.551616470308[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]96.668524590164[/C][C]0.467025223459981[/C][C]206.987802230445[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]96.7104918032787[/C][C]0.435075298189301[/C][C]222.284492375846[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]96.7968852459016[/C][C]0.381448600766115[/C][C]253.761280160660[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]96.8677049180328[/C][C]0.364679393098874[/C][C]265.624290133031[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]96.842786885246[/C][C]0.361264334988715[/C][C]268.066281406580[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]96.8690163934426[/C][C]0.349834754505612[/C][C]276.89935075301[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]96.2325423728814[/C][C]0.608140548349696[/C][C]158.240628147599[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]96.2666666666667[/C][C]0.604724990486279[/C][C]159.190819266880[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]96.3038181818182[/C][C]0.600004236287463[/C][C]160.505230392538[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]96.3441509433962[/C][C]0.593631442763614[/C][C]162.296239725565[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]96.3903921568627[/C][C]0.585649226527367[/C][C]164.587244020476[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]96.4379591836735[/C][C]0.580574939322542[/C][C]166.107685075426[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]96.486170212766[/C][C]0.575888370021758[/C][C]167.543182386407[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]96.5417777777778[/C][C]0.57041968325022[/C][C]169.246925750682[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]96.5990697674419[/C][C]0.563434120540951[/C][C]171.446964686302[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]96.6634146341463[/C][C]0.553608628351194[/C][C]174.606047817640[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]96.7310256410256[/C][C]0.541222786448513[/C][C]178.726816503369[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]96.8056756756757[/C][C]0.524848832882821[/C][C]184.444871762321[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]96.8774285714286[/C][C]0.507376236986266[/C][C]190.938048551239[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]96.9157575757576[/C][C]0.498779576912759[/C][C]194.305785685185[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]96.9525806451613[/C][C]0.48814900945139[/C][C]198.612675162697[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]96.9924137931035[/C][C]0.474457858923934[/C][C]204.427879038786[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]97.0322222222222[/C][C]0.463124325155576[/C][C]209.516574603648[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]97.066[/C][C]0.461648495430597[/C][C]210.259539369803[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]97.0952173913043[/C][C]0.461526025870072[/C][C]210.378639445652[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]97.1338095238095[/C][C]0.457938692190329[/C][C]212.110946684188[/C][/ROW]
[ROW][C]Median[/C][C]97.99[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]95.24[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]96.8263333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]96.9525806451613[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]96.9525806451613[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]96.9525806451613[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]96.9525806451613[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]96.793125[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]96.9525806451613[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]96.9525806451613[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]61[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=29082&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=29082&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 Mean96.20.610804539760757157.497192207642
Geometric Mean96.0819821381842
Harmonic Mean95.9624095865493
Quadratic Mean96.3162755257259
Winsorized Mean ( 1 / 20 )96.2006557377050.61041327346165157.599219938570
Winsorized Mean ( 2 / 20 )96.19967213114760.610252521735773157.639122666010
Winsorized Mean ( 3 / 20 )96.19868852459020.610092372984869157.678890581666
Winsorized Mean ( 4 / 20 )96.18950819672130.60861445377667158.046703623010
Winsorized Mean ( 5 / 20 )96.1993442622950.591603122987489162.607904732662
Winsorized Mean ( 6 / 20 )96.21508196721310.582921679399773165.056619726829
Winsorized Mean ( 7 / 20 )96.19901639344260.577450147112192166.592764543451
Winsorized Mean ( 8 / 20 )96.21868852459020.573579713013689167.751205876931
Winsorized Mean ( 9 / 20 )96.20983606557380.572321582755369168.104504468246
Winsorized Mean ( 10 / 20 )96.23114754098360.566519915023354169.863662316296
Winsorized Mean ( 11 / 20 )96.23295081967210.561952506805551171.247480266105
Winsorized Mean ( 12 / 20 )96.31163934426230.5424126521974177.561564897294
Winsorized Mean ( 13 / 20 )96.6078688524590.487119733418814198.324687391381
Winsorized Mean ( 14 / 20 )96.65377049180330.47718093874591202.551616470308
Winsorized Mean ( 15 / 20 )96.6685245901640.467025223459981206.987802230445
Winsorized Mean ( 16 / 20 )96.71049180327870.435075298189301222.284492375846
Winsorized Mean ( 17 / 20 )96.79688524590160.381448600766115253.761280160660
Winsorized Mean ( 18 / 20 )96.86770491803280.364679393098874265.624290133031
Winsorized Mean ( 19 / 20 )96.8427868852460.361264334988715268.066281406580
Winsorized Mean ( 20 / 20 )96.86901639344260.349834754505612276.89935075301
Trimmed Mean ( 1 / 20 )96.23254237288140.608140548349696158.240628147599
Trimmed Mean ( 2 / 20 )96.26666666666670.604724990486279159.190819266880
Trimmed Mean ( 3 / 20 )96.30381818181820.600004236287463160.505230392538
Trimmed Mean ( 4 / 20 )96.34415094339620.593631442763614162.296239725565
Trimmed Mean ( 5 / 20 )96.39039215686270.585649226527367164.587244020476
Trimmed Mean ( 6 / 20 )96.43795918367350.580574939322542166.107685075426
Trimmed Mean ( 7 / 20 )96.4861702127660.575888370021758167.543182386407
Trimmed Mean ( 8 / 20 )96.54177777777780.57041968325022169.246925750682
Trimmed Mean ( 9 / 20 )96.59906976744190.563434120540951171.446964686302
Trimmed Mean ( 10 / 20 )96.66341463414630.553608628351194174.606047817640
Trimmed Mean ( 11 / 20 )96.73102564102560.541222786448513178.726816503369
Trimmed Mean ( 12 / 20 )96.80567567567570.524848832882821184.444871762321
Trimmed Mean ( 13 / 20 )96.87742857142860.507376236986266190.938048551239
Trimmed Mean ( 14 / 20 )96.91575757575760.498779576912759194.305785685185
Trimmed Mean ( 15 / 20 )96.95258064516130.48814900945139198.612675162697
Trimmed Mean ( 16 / 20 )96.99241379310350.474457858923934204.427879038786
Trimmed Mean ( 17 / 20 )97.03222222222220.463124325155576209.516574603648
Trimmed Mean ( 18 / 20 )97.0660.461648495430597210.259539369803
Trimmed Mean ( 19 / 20 )97.09521739130430.461526025870072210.378639445652
Trimmed Mean ( 20 / 20 )97.13380952380950.457938692190329212.110946684188
Median97.99
Midrange95.24
Midmean - Weighted Average at Xnp96.8263333333333
Midmean - Weighted Average at X(n+1)p96.9525806451613
Midmean - Empirical Distribution Function96.9525806451613
Midmean - Empirical Distribution Function - Averaging96.9525806451613
Midmean - Empirical Distribution Function - Interpolation96.9525806451613
Midmean - Closest Observation96.793125
Midmean - True Basic - Statistics Graphics Toolkit96.9525806451613
Midmean - MS Excel (old versions)96.9525806451613
Number of observations61



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')