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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 computationSun, 21 Oct 2012 06:25:18 -0400
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2012/Oct/21/t1350815237jt7o0oszynflau6.htm/, Retrieved Sun, 28 Apr 2024 20:08:20 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=180735, Retrieved Sun, 28 Apr 2024 20:08:20 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact66
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [centrummaten prij...] [2012-10-21 10:25:18] [4b6fdd269237d5d28b13f97475f55381] [Current]
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Dataseries X:
104,42
104,42
104,42
104,42
104,42
104,42
104,42
104,44
104,44
104,44
105,19
105,19
105,19
106,38
106,38
106,38
106,38
106,38
106,38
106,72
106,73
106,72
108,6
108,6
109,65
109,65
109,65
109,65
109,65
109,65
109,65
109,65
112,27
112,27
112,27
112,27
112,27
114,98
114,98
114,98
114,98
114,98
114,98
116,04
116,59
116,59
116,59
116,59
118,75
118,75
118,75
118,75
118,75
118,75
118,75
119,31
119,31
119,31
119,31
119,31
121,19
121,19
121,19
121,19
121,19
122,91
122,91
122,91
122,91
122,91
122,91
122,91




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'George Udny Yule' @ yule.wessa.net

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 3 seconds \tabularnewline
R Server & 'George Udny Yule' @ yule.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=180735&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]'George Udny Yule' @ yule.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=180735&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=180735&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'George Udny Yule' @ yule.wessa.net







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean113.0615277777780.761944984123574148.385421695277
Geometric Mean112.879357083383
Harmonic Mean112.697587359832
Quadratic Mean113.24367017508
Winsorized Mean ( 1 / 24 )113.0615277777780.761944984123574148.385421695277
Winsorized Mean ( 2 / 24 )113.0615277777780.761944984123574148.385421695277
Winsorized Mean ( 3 / 24 )113.0615277777780.761944984123574148.385421695277
Winsorized Mean ( 4 / 24 )113.0615277777780.761944984123574148.385421695277
Winsorized Mean ( 5 / 24 )113.0615277777780.761944984123574148.385421695277
Winsorized Mean ( 6 / 24 )113.0615277777780.761944984123574148.385421695277
Winsorized Mean ( 7 / 24 )112.896250.733050186414296154.00889610605
Winsorized Mean ( 8 / 24 )112.896250.733050186414296154.00889610605
Winsorized Mean ( 9 / 24 )112.896250.733050186414296154.00889610605
Winsorized Mean ( 10 / 24 )113.0004166666670.716587162243052157.692493838369
Winsorized Mean ( 11 / 24 )113.0004166666670.716587162243052157.692493838369
Winsorized Mean ( 12 / 24 )112.6870833333330.669423216494387168.3345909684
Winsorized Mean ( 13 / 24 )112.9019444444440.636948099157767177.254543335217
Winsorized Mean ( 14 / 24 )112.9019444444440.636948099157767177.254543335217
Winsorized Mean ( 15 / 24 )112.9019444444440.636948099157767177.254543335217
Winsorized Mean ( 16 / 24 )112.9019444444440.636948099157767177.254543335217
Winsorized Mean ( 17 / 24 )112.7697222222220.618572773332724182.306313959869
Winsorized Mean ( 18 / 24 )112.7697222222220.618572773332724182.306313959869
Winsorized Mean ( 19 / 24 )112.8594444444440.60563953991128186.347549998101
Winsorized Mean ( 20 / 24 )112.8594444444440.60563953991128186.347549998101
Winsorized Mean ( 21 / 24 )112.8623611111110.605223205797902186.480557965913
Winsorized Mean ( 22 / 24 )113.433750.527297656327567215.122803294868
Winsorized Mean ( 23 / 24 )113.433750.527297656327567215.122803294868
Winsorized Mean ( 24 / 24 )113.063750.384338009690023294.177903692607
Trimmed Mean ( 1 / 24 )113.0442857142860.760861219880713148.574119380153
Trimmed Mean ( 2 / 24 )113.0260294117650.75896760951712148.920754976191
Trimmed Mean ( 3 / 24 )113.0066666666670.756112568342979149.457463607993
Trimmed Mean ( 4 / 24 )112.986093750.752111070494572150.225276800809
Trimmed Mean ( 5 / 24 )112.9641935483870.746735201424429151.277445248199
Trimmed Mean ( 6 / 24 )112.9408333333330.739701241098636152.684390748877
Trimmed Mean ( 7 / 24 )112.9158620689660.730651617886439154.54131532015
Trimmed Mean ( 8 / 24 )112.9194642857140.726272212018906155.478156009602
Trimmed Mean ( 9 / 24 )112.9233333333330.720156972949877156.803776919331
Trimmed Mean ( 10 / 24 )112.92750.711890546680098158.630425037441
Trimmed Mean ( 11 / 24 )112.9170.704463567806985160.287920000624
Trimmed Mean ( 12 / 24 )112.9056250.694361658112115162.603484338373
Trimmed Mean ( 13 / 24 )112.9341304347830.690557191262633163.540589923176
Trimmed Mean ( 14 / 24 )112.9381818181820.691044439841508163.431141771554
Trimmed Mean ( 15 / 24 )112.9426190476190.690023317581719163.679423825041
Trimmed Mean ( 16 / 24 )112.94750.687007235993692164.405109702567
Trimmed Mean ( 17 / 24 )112.9528947368420.681326096708581165.783895967741
Trimmed Mean ( 18 / 24 )112.9744444444440.676033300161826167.113727115811
Trimmed Mean ( 19 / 24 )112.9985294117650.666878103594653169.444054022275
Trimmed Mean ( 20 / 24 )113.0150.655678514606151172.363433424207
Trimmed Mean ( 21 / 24 )113.0336666666670.637836948741664177.21404645758
Trimmed Mean ( 22 / 24 )113.0546428571430.610232734278392185.264795719016
Trimmed Mean ( 23 / 24 )113.0069230769230.593791149305952190.314259835315
Trimmed Mean ( 24 / 24 )112.951250.565787674781612199.635402173789
Median112.27
Midrange113.665
Midmean - Weighted Average at Xnp112.326904761905
Midmean - Weighted Average at X(n+1)p112.326904761905
Midmean - Empirical Distribution Function112.326904761905
Midmean - Empirical Distribution Function - Averaging112.326904761905
Midmean - Empirical Distribution Function - Interpolation112.326904761905
Midmean - Closest Observation112.326904761905
Midmean - True Basic - Statistics Graphics Toolkit112.326904761905
Midmean - MS Excel (old versions)112.326904761905
Number of observations72

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 113.061527777778 & 0.761944984123574 & 148.385421695277 \tabularnewline
Geometric Mean & 112.879357083383 &  &  \tabularnewline
Harmonic Mean & 112.697587359832 &  &  \tabularnewline
Quadratic Mean & 113.24367017508 &  &  \tabularnewline
Winsorized Mean ( 1 / 24 ) & 113.061527777778 & 0.761944984123574 & 148.385421695277 \tabularnewline
Winsorized Mean ( 2 / 24 ) & 113.061527777778 & 0.761944984123574 & 148.385421695277 \tabularnewline
Winsorized Mean ( 3 / 24 ) & 113.061527777778 & 0.761944984123574 & 148.385421695277 \tabularnewline
Winsorized Mean ( 4 / 24 ) & 113.061527777778 & 0.761944984123574 & 148.385421695277 \tabularnewline
Winsorized Mean ( 5 / 24 ) & 113.061527777778 & 0.761944984123574 & 148.385421695277 \tabularnewline
Winsorized Mean ( 6 / 24 ) & 113.061527777778 & 0.761944984123574 & 148.385421695277 \tabularnewline
Winsorized Mean ( 7 / 24 ) & 112.89625 & 0.733050186414296 & 154.00889610605 \tabularnewline
Winsorized Mean ( 8 / 24 ) & 112.89625 & 0.733050186414296 & 154.00889610605 \tabularnewline
Winsorized Mean ( 9 / 24 ) & 112.89625 & 0.733050186414296 & 154.00889610605 \tabularnewline
Winsorized Mean ( 10 / 24 ) & 113.000416666667 & 0.716587162243052 & 157.692493838369 \tabularnewline
Winsorized Mean ( 11 / 24 ) & 113.000416666667 & 0.716587162243052 & 157.692493838369 \tabularnewline
Winsorized Mean ( 12 / 24 ) & 112.687083333333 & 0.669423216494387 & 168.3345909684 \tabularnewline
Winsorized Mean ( 13 / 24 ) & 112.901944444444 & 0.636948099157767 & 177.254543335217 \tabularnewline
Winsorized Mean ( 14 / 24 ) & 112.901944444444 & 0.636948099157767 & 177.254543335217 \tabularnewline
Winsorized Mean ( 15 / 24 ) & 112.901944444444 & 0.636948099157767 & 177.254543335217 \tabularnewline
Winsorized Mean ( 16 / 24 ) & 112.901944444444 & 0.636948099157767 & 177.254543335217 \tabularnewline
Winsorized Mean ( 17 / 24 ) & 112.769722222222 & 0.618572773332724 & 182.306313959869 \tabularnewline
Winsorized Mean ( 18 / 24 ) & 112.769722222222 & 0.618572773332724 & 182.306313959869 \tabularnewline
Winsorized Mean ( 19 / 24 ) & 112.859444444444 & 0.60563953991128 & 186.347549998101 \tabularnewline
Winsorized Mean ( 20 / 24 ) & 112.859444444444 & 0.60563953991128 & 186.347549998101 \tabularnewline
Winsorized Mean ( 21 / 24 ) & 112.862361111111 & 0.605223205797902 & 186.480557965913 \tabularnewline
Winsorized Mean ( 22 / 24 ) & 113.43375 & 0.527297656327567 & 215.122803294868 \tabularnewline
Winsorized Mean ( 23 / 24 ) & 113.43375 & 0.527297656327567 & 215.122803294868 \tabularnewline
Winsorized Mean ( 24 / 24 ) & 113.06375 & 0.384338009690023 & 294.177903692607 \tabularnewline
Trimmed Mean ( 1 / 24 ) & 113.044285714286 & 0.760861219880713 & 148.574119380153 \tabularnewline
Trimmed Mean ( 2 / 24 ) & 113.026029411765 & 0.75896760951712 & 148.920754976191 \tabularnewline
Trimmed Mean ( 3 / 24 ) & 113.006666666667 & 0.756112568342979 & 149.457463607993 \tabularnewline
Trimmed Mean ( 4 / 24 ) & 112.98609375 & 0.752111070494572 & 150.225276800809 \tabularnewline
Trimmed Mean ( 5 / 24 ) & 112.964193548387 & 0.746735201424429 & 151.277445248199 \tabularnewline
Trimmed Mean ( 6 / 24 ) & 112.940833333333 & 0.739701241098636 & 152.684390748877 \tabularnewline
Trimmed Mean ( 7 / 24 ) & 112.915862068966 & 0.730651617886439 & 154.54131532015 \tabularnewline
Trimmed Mean ( 8 / 24 ) & 112.919464285714 & 0.726272212018906 & 155.478156009602 \tabularnewline
Trimmed Mean ( 9 / 24 ) & 112.923333333333 & 0.720156972949877 & 156.803776919331 \tabularnewline
Trimmed Mean ( 10 / 24 ) & 112.9275 & 0.711890546680098 & 158.630425037441 \tabularnewline
Trimmed Mean ( 11 / 24 ) & 112.917 & 0.704463567806985 & 160.287920000624 \tabularnewline
Trimmed Mean ( 12 / 24 ) & 112.905625 & 0.694361658112115 & 162.603484338373 \tabularnewline
Trimmed Mean ( 13 / 24 ) & 112.934130434783 & 0.690557191262633 & 163.540589923176 \tabularnewline
Trimmed Mean ( 14 / 24 ) & 112.938181818182 & 0.691044439841508 & 163.431141771554 \tabularnewline
Trimmed Mean ( 15 / 24 ) & 112.942619047619 & 0.690023317581719 & 163.679423825041 \tabularnewline
Trimmed Mean ( 16 / 24 ) & 112.9475 & 0.687007235993692 & 164.405109702567 \tabularnewline
Trimmed Mean ( 17 / 24 ) & 112.952894736842 & 0.681326096708581 & 165.783895967741 \tabularnewline
Trimmed Mean ( 18 / 24 ) & 112.974444444444 & 0.676033300161826 & 167.113727115811 \tabularnewline
Trimmed Mean ( 19 / 24 ) & 112.998529411765 & 0.666878103594653 & 169.444054022275 \tabularnewline
Trimmed Mean ( 20 / 24 ) & 113.015 & 0.655678514606151 & 172.363433424207 \tabularnewline
Trimmed Mean ( 21 / 24 ) & 113.033666666667 & 0.637836948741664 & 177.21404645758 \tabularnewline
Trimmed Mean ( 22 / 24 ) & 113.054642857143 & 0.610232734278392 & 185.264795719016 \tabularnewline
Trimmed Mean ( 23 / 24 ) & 113.006923076923 & 0.593791149305952 & 190.314259835315 \tabularnewline
Trimmed Mean ( 24 / 24 ) & 112.95125 & 0.565787674781612 & 199.635402173789 \tabularnewline
Median & 112.27 &  &  \tabularnewline
Midrange & 113.665 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 112.326904761905 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 112.326904761905 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 112.326904761905 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 112.326904761905 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 112.326904761905 &  &  \tabularnewline
Midmean - Closest Observation & 112.326904761905 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 112.326904761905 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 112.326904761905 &  &  \tabularnewline
Number of observations & 72 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=180735&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]113.061527777778[/C][C]0.761944984123574[/C][C]148.385421695277[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]112.879357083383[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]112.697587359832[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]113.24367017508[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 24 )[/C][C]113.061527777778[/C][C]0.761944984123574[/C][C]148.385421695277[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 24 )[/C][C]113.061527777778[/C][C]0.761944984123574[/C][C]148.385421695277[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 24 )[/C][C]113.061527777778[/C][C]0.761944984123574[/C][C]148.385421695277[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 24 )[/C][C]113.061527777778[/C][C]0.761944984123574[/C][C]148.385421695277[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 24 )[/C][C]113.061527777778[/C][C]0.761944984123574[/C][C]148.385421695277[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 24 )[/C][C]113.061527777778[/C][C]0.761944984123574[/C][C]148.385421695277[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 24 )[/C][C]112.89625[/C][C]0.733050186414296[/C][C]154.00889610605[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 24 )[/C][C]112.89625[/C][C]0.733050186414296[/C][C]154.00889610605[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 24 )[/C][C]112.89625[/C][C]0.733050186414296[/C][C]154.00889610605[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 24 )[/C][C]113.000416666667[/C][C]0.716587162243052[/C][C]157.692493838369[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 24 )[/C][C]113.000416666667[/C][C]0.716587162243052[/C][C]157.692493838369[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 24 )[/C][C]112.687083333333[/C][C]0.669423216494387[/C][C]168.3345909684[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 24 )[/C][C]112.901944444444[/C][C]0.636948099157767[/C][C]177.254543335217[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 24 )[/C][C]112.901944444444[/C][C]0.636948099157767[/C][C]177.254543335217[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 24 )[/C][C]112.901944444444[/C][C]0.636948099157767[/C][C]177.254543335217[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 24 )[/C][C]112.901944444444[/C][C]0.636948099157767[/C][C]177.254543335217[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 24 )[/C][C]112.769722222222[/C][C]0.618572773332724[/C][C]182.306313959869[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 24 )[/C][C]112.769722222222[/C][C]0.618572773332724[/C][C]182.306313959869[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 24 )[/C][C]112.859444444444[/C][C]0.60563953991128[/C][C]186.347549998101[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 24 )[/C][C]112.859444444444[/C][C]0.60563953991128[/C][C]186.347549998101[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 24 )[/C][C]112.862361111111[/C][C]0.605223205797902[/C][C]186.480557965913[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 24 )[/C][C]113.43375[/C][C]0.527297656327567[/C][C]215.122803294868[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 24 )[/C][C]113.43375[/C][C]0.527297656327567[/C][C]215.122803294868[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 24 )[/C][C]113.06375[/C][C]0.384338009690023[/C][C]294.177903692607[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 24 )[/C][C]113.044285714286[/C][C]0.760861219880713[/C][C]148.574119380153[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 24 )[/C][C]113.026029411765[/C][C]0.75896760951712[/C][C]148.920754976191[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 24 )[/C][C]113.006666666667[/C][C]0.756112568342979[/C][C]149.457463607993[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 24 )[/C][C]112.98609375[/C][C]0.752111070494572[/C][C]150.225276800809[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 24 )[/C][C]112.964193548387[/C][C]0.746735201424429[/C][C]151.277445248199[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 24 )[/C][C]112.940833333333[/C][C]0.739701241098636[/C][C]152.684390748877[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 24 )[/C][C]112.915862068966[/C][C]0.730651617886439[/C][C]154.54131532015[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 24 )[/C][C]112.919464285714[/C][C]0.726272212018906[/C][C]155.478156009602[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 24 )[/C][C]112.923333333333[/C][C]0.720156972949877[/C][C]156.803776919331[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 24 )[/C][C]112.9275[/C][C]0.711890546680098[/C][C]158.630425037441[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 24 )[/C][C]112.917[/C][C]0.704463567806985[/C][C]160.287920000624[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 24 )[/C][C]112.905625[/C][C]0.694361658112115[/C][C]162.603484338373[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 24 )[/C][C]112.934130434783[/C][C]0.690557191262633[/C][C]163.540589923176[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 24 )[/C][C]112.938181818182[/C][C]0.691044439841508[/C][C]163.431141771554[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 24 )[/C][C]112.942619047619[/C][C]0.690023317581719[/C][C]163.679423825041[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 24 )[/C][C]112.9475[/C][C]0.687007235993692[/C][C]164.405109702567[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 24 )[/C][C]112.952894736842[/C][C]0.681326096708581[/C][C]165.783895967741[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 24 )[/C][C]112.974444444444[/C][C]0.676033300161826[/C][C]167.113727115811[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 24 )[/C][C]112.998529411765[/C][C]0.666878103594653[/C][C]169.444054022275[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 24 )[/C][C]113.015[/C][C]0.655678514606151[/C][C]172.363433424207[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 24 )[/C][C]113.033666666667[/C][C]0.637836948741664[/C][C]177.21404645758[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 24 )[/C][C]113.054642857143[/C][C]0.610232734278392[/C][C]185.264795719016[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 24 )[/C][C]113.006923076923[/C][C]0.593791149305952[/C][C]190.314259835315[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 24 )[/C][C]112.95125[/C][C]0.565787674781612[/C][C]199.635402173789[/C][/ROW]
[ROW][C]Median[/C][C]112.27[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]113.665[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]112.326904761905[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]112.326904761905[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]112.326904761905[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]112.326904761905[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]112.326904761905[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]112.326904761905[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]112.326904761905[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]112.326904761905[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]72[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=180735&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=180735&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 Mean113.0615277777780.761944984123574148.385421695277
Geometric Mean112.879357083383
Harmonic Mean112.697587359832
Quadratic Mean113.24367017508
Winsorized Mean ( 1 / 24 )113.0615277777780.761944984123574148.385421695277
Winsorized Mean ( 2 / 24 )113.0615277777780.761944984123574148.385421695277
Winsorized Mean ( 3 / 24 )113.0615277777780.761944984123574148.385421695277
Winsorized Mean ( 4 / 24 )113.0615277777780.761944984123574148.385421695277
Winsorized Mean ( 5 / 24 )113.0615277777780.761944984123574148.385421695277
Winsorized Mean ( 6 / 24 )113.0615277777780.761944984123574148.385421695277
Winsorized Mean ( 7 / 24 )112.896250.733050186414296154.00889610605
Winsorized Mean ( 8 / 24 )112.896250.733050186414296154.00889610605
Winsorized Mean ( 9 / 24 )112.896250.733050186414296154.00889610605
Winsorized Mean ( 10 / 24 )113.0004166666670.716587162243052157.692493838369
Winsorized Mean ( 11 / 24 )113.0004166666670.716587162243052157.692493838369
Winsorized Mean ( 12 / 24 )112.6870833333330.669423216494387168.3345909684
Winsorized Mean ( 13 / 24 )112.9019444444440.636948099157767177.254543335217
Winsorized Mean ( 14 / 24 )112.9019444444440.636948099157767177.254543335217
Winsorized Mean ( 15 / 24 )112.9019444444440.636948099157767177.254543335217
Winsorized Mean ( 16 / 24 )112.9019444444440.636948099157767177.254543335217
Winsorized Mean ( 17 / 24 )112.7697222222220.618572773332724182.306313959869
Winsorized Mean ( 18 / 24 )112.7697222222220.618572773332724182.306313959869
Winsorized Mean ( 19 / 24 )112.8594444444440.60563953991128186.347549998101
Winsorized Mean ( 20 / 24 )112.8594444444440.60563953991128186.347549998101
Winsorized Mean ( 21 / 24 )112.8623611111110.605223205797902186.480557965913
Winsorized Mean ( 22 / 24 )113.433750.527297656327567215.122803294868
Winsorized Mean ( 23 / 24 )113.433750.527297656327567215.122803294868
Winsorized Mean ( 24 / 24 )113.063750.384338009690023294.177903692607
Trimmed Mean ( 1 / 24 )113.0442857142860.760861219880713148.574119380153
Trimmed Mean ( 2 / 24 )113.0260294117650.75896760951712148.920754976191
Trimmed Mean ( 3 / 24 )113.0066666666670.756112568342979149.457463607993
Trimmed Mean ( 4 / 24 )112.986093750.752111070494572150.225276800809
Trimmed Mean ( 5 / 24 )112.9641935483870.746735201424429151.277445248199
Trimmed Mean ( 6 / 24 )112.9408333333330.739701241098636152.684390748877
Trimmed Mean ( 7 / 24 )112.9158620689660.730651617886439154.54131532015
Trimmed Mean ( 8 / 24 )112.9194642857140.726272212018906155.478156009602
Trimmed Mean ( 9 / 24 )112.9233333333330.720156972949877156.803776919331
Trimmed Mean ( 10 / 24 )112.92750.711890546680098158.630425037441
Trimmed Mean ( 11 / 24 )112.9170.704463567806985160.287920000624
Trimmed Mean ( 12 / 24 )112.9056250.694361658112115162.603484338373
Trimmed Mean ( 13 / 24 )112.9341304347830.690557191262633163.540589923176
Trimmed Mean ( 14 / 24 )112.9381818181820.691044439841508163.431141771554
Trimmed Mean ( 15 / 24 )112.9426190476190.690023317581719163.679423825041
Trimmed Mean ( 16 / 24 )112.94750.687007235993692164.405109702567
Trimmed Mean ( 17 / 24 )112.9528947368420.681326096708581165.783895967741
Trimmed Mean ( 18 / 24 )112.9744444444440.676033300161826167.113727115811
Trimmed Mean ( 19 / 24 )112.9985294117650.666878103594653169.444054022275
Trimmed Mean ( 20 / 24 )113.0150.655678514606151172.363433424207
Trimmed Mean ( 21 / 24 )113.0336666666670.637836948741664177.21404645758
Trimmed Mean ( 22 / 24 )113.0546428571430.610232734278392185.264795719016
Trimmed Mean ( 23 / 24 )113.0069230769230.593791149305952190.314259835315
Trimmed Mean ( 24 / 24 )112.951250.565787674781612199.635402173789
Median112.27
Midrange113.665
Midmean - Weighted Average at Xnp112.326904761905
Midmean - Weighted Average at X(n+1)p112.326904761905
Midmean - Empirical Distribution Function112.326904761905
Midmean - Empirical Distribution Function - Averaging112.326904761905
Midmean - Empirical Distribution Function - Interpolation112.326904761905
Midmean - Closest Observation112.326904761905
Midmean - True Basic - Statistics Graphics Toolkit112.326904761905
Midmean - MS Excel (old versions)112.326904761905
Number of observations72



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')