Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationSun, 19 Oct 2008 11:23:45 -0600
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/Oct/19/t1224437078bf1shjlq8tnzcok.htm/, Retrieved Sun, 19 May 2024 22:01:09 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=16978, Retrieved Sun, 19 May 2024 22:01:09 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsq9, central tendency
Estimated Impact156
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Central Tendency] [Investigating Ass...] [2007-10-22 10:34:53] [b9964c45117f7aac638ab9056d451faa]
F    D    [Central Tendency] [Investigating ass...] [2008-10-19 17:23:45] [c577d4c76516de948d1234ed72fcf120] [Current]
Feedback Forum
2008-10-25 13:00:08 [Bob Leysen] [reply
Vanboven staat 'unverified author'. Bij de winsorized mean zien we dat er een aantal outliers zijn.
2008-10-26 15:19:14 [Stijn Loomans] [reply
Goed gekozen en berekende berekening.
2008-10-27 20:36:17 [Jeroen Michel] [reply
De berekeningen zijn correct uitgevoerd. Het is belangrijk te kijken naar de trimmed mean. Daar bij de winsorized mean enkele outliers waar te nemen zijn.

Post a new message
Dataseries X:
97.3
101
113.2
101
105.7
113.9
86.4
96.5
103.3
114.9
105.8
94.2
98.4
99.4
108.8
112.6
104.4
112.2
81.1
97.1
112.6
113.8
107.8
103.2
103.3
101.2
107.7
110.4
101.9
115.9
89.9
88.6
117.2
123.9
100
103.6
94.1
98.7
119.5
112.7
104.4
124.7
89.1
97
121.6
118.8
114
111.5
97.2
102.5
113.4
109.8
104.9
126.1
80
96.8
117.2
112.3
117.3
111.1
102.2
104.3
122.9
107.6
121.3
131.5
89
104.4
128.9
135.9
133.3
121.3




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'Herman Ole Andreas Wold' @ 193.190.124.10:1001

\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 & 'Herman Ole Andreas Wold' @ 193.190.124.10:1001 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=16978&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]'Herman Ole Andreas Wold' @ 193.190.124.10:1001[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=16978&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=16978&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'Herman Ole Andreas Wold' @ 193.190.124.10:1001







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean107.5763888888891.4092133304445076.3379018384367
Geometric Mean106.915063547619
Harmonic Mean106.246111074420
Quadratic Mean108.229742138348
Winsorized Mean ( 1 / 24 )107.5555555555561.3952620600841377.0862754980024
Winsorized Mean ( 2 / 24 )107.6527777777781.3464422665239979.9535044719722
Winsorized Mean ( 3 / 24 )107.6361111111111.3007917198451482.7466145955523
Winsorized Mean ( 4 / 24 )107.5027777777781.2621320056228185.175542097698
Winsorized Mean ( 5 / 24 )107.41251.2410634188567586.5487600133654
Winsorized Mean ( 6 / 24 )107.41251.2144489684413988.4454619265328
Winsorized Mean ( 7 / 24 )107.7236111111111.1191330988844096.2562998257262
Winsorized Mean ( 8 / 24 )107.5902777777781.0903459554254498.6753582589278
Winsorized Mean ( 9 / 24 )107.8402777777781.03643835272877104.048907003347
Winsorized Mean ( 10 / 24 )107.8819444444441.03007081207595104.732551568008
Winsorized Mean ( 11 / 24 )107.63750.97661714831445110.214632403058
Winsorized Mean ( 12 / 24 )107.53750.954376783556775112.678243910365
Winsorized Mean ( 13 / 24 )107.2847222222220.907992807174357118.155916406528
Winsorized Mean ( 14 / 24 )107.2847222222220.901940309162391118.948805294948
Winsorized Mean ( 15 / 24 )107.5138888888890.867093849116173123.993370496720
Winsorized Mean ( 16 / 24 )107.2916666666670.812889487721933131.988011023914
Winsorized Mean ( 17 / 24 )107.2208333333330.753935780287766142.214809452880
Winsorized Mean ( 18 / 24 )107.1458333333330.700530587811906152.949543099897
Winsorized Mean ( 19 / 24 )107.3833333333330.659915938118948162.722745626395
Winsorized Mean ( 20 / 24 )107.3555555555560.656062640409582163.636136160006
Winsorized Mean ( 21 / 24 )107.2972222222220.632115125104475169.743165383819
Winsorized Mean ( 22 / 24 )107.450.595214352309836180.523200730999
Winsorized Mean ( 23 / 24 )107.3861111111110.561159045195318191.364840379137
Winsorized Mean ( 24 / 24 )107.4527777777780.543790427497973197.599612542239
Trimmed Mean ( 1 / 24 )107.5657142857141.3335251710559180.6626801056495
Trimmed Mean ( 2 / 24 )107.5764705882351.2594195006813685.417504278785
Trimmed Mean ( 3 / 24 )107.5348484848481.2027115681645989.4103385477142
Trimmed Mean ( 4 / 24 )107.4968751.1562523460937292.970081628952
Trimmed Mean ( 5 / 24 )107.4951612903231.1150440594277596.4044069662051
Trimmed Mean ( 6 / 24 )107.5151.07196378480441100.297231608078
Trimmed Mean ( 7 / 24 )107.5362068965521.02731213635599104.677247635754
Trimmed Mean ( 8 / 24 )107.5017857142860.998767068093446107.634491713365
Trimmed Mean ( 9 / 24 )107.4870370370370.970692283943213110.732349288279
Trimmed Mean ( 10 / 24 )107.4326923076920.948332350503986113.28590894384
Trimmed Mean ( 11 / 24 )107.3680.921283222201623116.541794545459
Trimmed Mean ( 12 / 24 )107.331250.899350416928284119.343081383770
Trimmed Mean ( 13 / 24 )107.3043478260870.87600298083526122.493130929501
Trimmed Mean ( 14 / 24 )107.3068181818180.856040578947138125.352490081483
Trimmed Mean ( 15 / 24 )107.3095238095240.830758923731184129.170473821172
Trimmed Mean ( 16 / 24 )107.2850.805124214019179133.252730612129
Trimmed Mean ( 17 / 24 )107.2842105263160.783593559514077136.913083605288
Trimmed Mean ( 18 / 24 )107.2916666666670.767984116485883139.705580315396
Trimmed Mean ( 19 / 24 )107.3088235294120.758180198211514141.534721933578
Trimmed Mean ( 20 / 24 )107.30.75249584716462142.592149052121
Trimmed Mean ( 21 / 24 )107.2933333333330.742610080594632144.481385503709
Trimmed Mean ( 22 / 24 )107.2928571428570.732248992178022146.525100463057
Trimmed Mean ( 23 / 24 )107.2730769230770.724697447582468148.024637427565
Trimmed Mean ( 24 / 24 )107.2583333333330.720027089533328148.964302722069
Median106.7
Midrange107.95
Midmean - Weighted Average at Xnp107.078378378378
Midmean - Weighted Average at X(n+1)p107.291666666667
Midmean - Empirical Distribution Function107.078378378378
Midmean - Empirical Distribution Function - Averaging107.291666666667
Midmean - Empirical Distribution Function - Interpolation107.291666666667
Midmean - Closest Observation107.078378378378
Midmean - True Basic - Statistics Graphics Toolkit107.291666666667
Midmean - MS Excel (old versions)107.284210526316
Number of observations72

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 107.576388888889 & 1.40921333044450 & 76.3379018384367 \tabularnewline
Geometric Mean & 106.915063547619 &  &  \tabularnewline
Harmonic Mean & 106.246111074420 &  &  \tabularnewline
Quadratic Mean & 108.229742138348 &  &  \tabularnewline
Winsorized Mean ( 1 / 24 ) & 107.555555555556 & 1.39526206008413 & 77.0862754980024 \tabularnewline
Winsorized Mean ( 2 / 24 ) & 107.652777777778 & 1.34644226652399 & 79.9535044719722 \tabularnewline
Winsorized Mean ( 3 / 24 ) & 107.636111111111 & 1.30079171984514 & 82.7466145955523 \tabularnewline
Winsorized Mean ( 4 / 24 ) & 107.502777777778 & 1.26213200562281 & 85.175542097698 \tabularnewline
Winsorized Mean ( 5 / 24 ) & 107.4125 & 1.24106341885675 & 86.5487600133654 \tabularnewline
Winsorized Mean ( 6 / 24 ) & 107.4125 & 1.21444896844139 & 88.4454619265328 \tabularnewline
Winsorized Mean ( 7 / 24 ) & 107.723611111111 & 1.11913309888440 & 96.2562998257262 \tabularnewline
Winsorized Mean ( 8 / 24 ) & 107.590277777778 & 1.09034595542544 & 98.6753582589278 \tabularnewline
Winsorized Mean ( 9 / 24 ) & 107.840277777778 & 1.03643835272877 & 104.048907003347 \tabularnewline
Winsorized Mean ( 10 / 24 ) & 107.881944444444 & 1.03007081207595 & 104.732551568008 \tabularnewline
Winsorized Mean ( 11 / 24 ) & 107.6375 & 0.97661714831445 & 110.214632403058 \tabularnewline
Winsorized Mean ( 12 / 24 ) & 107.5375 & 0.954376783556775 & 112.678243910365 \tabularnewline
Winsorized Mean ( 13 / 24 ) & 107.284722222222 & 0.907992807174357 & 118.155916406528 \tabularnewline
Winsorized Mean ( 14 / 24 ) & 107.284722222222 & 0.901940309162391 & 118.948805294948 \tabularnewline
Winsorized Mean ( 15 / 24 ) & 107.513888888889 & 0.867093849116173 & 123.993370496720 \tabularnewline
Winsorized Mean ( 16 / 24 ) & 107.291666666667 & 0.812889487721933 & 131.988011023914 \tabularnewline
Winsorized Mean ( 17 / 24 ) & 107.220833333333 & 0.753935780287766 & 142.214809452880 \tabularnewline
Winsorized Mean ( 18 / 24 ) & 107.145833333333 & 0.700530587811906 & 152.949543099897 \tabularnewline
Winsorized Mean ( 19 / 24 ) & 107.383333333333 & 0.659915938118948 & 162.722745626395 \tabularnewline
Winsorized Mean ( 20 / 24 ) & 107.355555555556 & 0.656062640409582 & 163.636136160006 \tabularnewline
Winsorized Mean ( 21 / 24 ) & 107.297222222222 & 0.632115125104475 & 169.743165383819 \tabularnewline
Winsorized Mean ( 22 / 24 ) & 107.45 & 0.595214352309836 & 180.523200730999 \tabularnewline
Winsorized Mean ( 23 / 24 ) & 107.386111111111 & 0.561159045195318 & 191.364840379137 \tabularnewline
Winsorized Mean ( 24 / 24 ) & 107.452777777778 & 0.543790427497973 & 197.599612542239 \tabularnewline
Trimmed Mean ( 1 / 24 ) & 107.565714285714 & 1.33352517105591 & 80.6626801056495 \tabularnewline
Trimmed Mean ( 2 / 24 ) & 107.576470588235 & 1.25941950068136 & 85.417504278785 \tabularnewline
Trimmed Mean ( 3 / 24 ) & 107.534848484848 & 1.20271156816459 & 89.4103385477142 \tabularnewline
Trimmed Mean ( 4 / 24 ) & 107.496875 & 1.15625234609372 & 92.970081628952 \tabularnewline
Trimmed Mean ( 5 / 24 ) & 107.495161290323 & 1.11504405942775 & 96.4044069662051 \tabularnewline
Trimmed Mean ( 6 / 24 ) & 107.515 & 1.07196378480441 & 100.297231608078 \tabularnewline
Trimmed Mean ( 7 / 24 ) & 107.536206896552 & 1.02731213635599 & 104.677247635754 \tabularnewline
Trimmed Mean ( 8 / 24 ) & 107.501785714286 & 0.998767068093446 & 107.634491713365 \tabularnewline
Trimmed Mean ( 9 / 24 ) & 107.487037037037 & 0.970692283943213 & 110.732349288279 \tabularnewline
Trimmed Mean ( 10 / 24 ) & 107.432692307692 & 0.948332350503986 & 113.28590894384 \tabularnewline
Trimmed Mean ( 11 / 24 ) & 107.368 & 0.921283222201623 & 116.541794545459 \tabularnewline
Trimmed Mean ( 12 / 24 ) & 107.33125 & 0.899350416928284 & 119.343081383770 \tabularnewline
Trimmed Mean ( 13 / 24 ) & 107.304347826087 & 0.87600298083526 & 122.493130929501 \tabularnewline
Trimmed Mean ( 14 / 24 ) & 107.306818181818 & 0.856040578947138 & 125.352490081483 \tabularnewline
Trimmed Mean ( 15 / 24 ) & 107.309523809524 & 0.830758923731184 & 129.170473821172 \tabularnewline
Trimmed Mean ( 16 / 24 ) & 107.285 & 0.805124214019179 & 133.252730612129 \tabularnewline
Trimmed Mean ( 17 / 24 ) & 107.284210526316 & 0.783593559514077 & 136.913083605288 \tabularnewline
Trimmed Mean ( 18 / 24 ) & 107.291666666667 & 0.767984116485883 & 139.705580315396 \tabularnewline
Trimmed Mean ( 19 / 24 ) & 107.308823529412 & 0.758180198211514 & 141.534721933578 \tabularnewline
Trimmed Mean ( 20 / 24 ) & 107.3 & 0.75249584716462 & 142.592149052121 \tabularnewline
Trimmed Mean ( 21 / 24 ) & 107.293333333333 & 0.742610080594632 & 144.481385503709 \tabularnewline
Trimmed Mean ( 22 / 24 ) & 107.292857142857 & 0.732248992178022 & 146.525100463057 \tabularnewline
Trimmed Mean ( 23 / 24 ) & 107.273076923077 & 0.724697447582468 & 148.024637427565 \tabularnewline
Trimmed Mean ( 24 / 24 ) & 107.258333333333 & 0.720027089533328 & 148.964302722069 \tabularnewline
Median & 106.7 &  &  \tabularnewline
Midrange & 107.95 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 107.078378378378 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 107.291666666667 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 107.078378378378 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 107.291666666667 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 107.291666666667 &  &  \tabularnewline
Midmean - Closest Observation & 107.078378378378 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 107.291666666667 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 107.284210526316 &  &  \tabularnewline
Number of observations & 72 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=16978&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]107.576388888889[/C][C]1.40921333044450[/C][C]76.3379018384367[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]106.915063547619[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]106.246111074420[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]108.229742138348[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 24 )[/C][C]107.555555555556[/C][C]1.39526206008413[/C][C]77.0862754980024[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 24 )[/C][C]107.652777777778[/C][C]1.34644226652399[/C][C]79.9535044719722[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 24 )[/C][C]107.636111111111[/C][C]1.30079171984514[/C][C]82.7466145955523[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 24 )[/C][C]107.502777777778[/C][C]1.26213200562281[/C][C]85.175542097698[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 24 )[/C][C]107.4125[/C][C]1.24106341885675[/C][C]86.5487600133654[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 24 )[/C][C]107.4125[/C][C]1.21444896844139[/C][C]88.4454619265328[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 24 )[/C][C]107.723611111111[/C][C]1.11913309888440[/C][C]96.2562998257262[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 24 )[/C][C]107.590277777778[/C][C]1.09034595542544[/C][C]98.6753582589278[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 24 )[/C][C]107.840277777778[/C][C]1.03643835272877[/C][C]104.048907003347[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 24 )[/C][C]107.881944444444[/C][C]1.03007081207595[/C][C]104.732551568008[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 24 )[/C][C]107.6375[/C][C]0.97661714831445[/C][C]110.214632403058[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 24 )[/C][C]107.5375[/C][C]0.954376783556775[/C][C]112.678243910365[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 24 )[/C][C]107.284722222222[/C][C]0.907992807174357[/C][C]118.155916406528[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 24 )[/C][C]107.284722222222[/C][C]0.901940309162391[/C][C]118.948805294948[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 24 )[/C][C]107.513888888889[/C][C]0.867093849116173[/C][C]123.993370496720[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 24 )[/C][C]107.291666666667[/C][C]0.812889487721933[/C][C]131.988011023914[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 24 )[/C][C]107.220833333333[/C][C]0.753935780287766[/C][C]142.214809452880[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 24 )[/C][C]107.145833333333[/C][C]0.700530587811906[/C][C]152.949543099897[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 24 )[/C][C]107.383333333333[/C][C]0.659915938118948[/C][C]162.722745626395[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 24 )[/C][C]107.355555555556[/C][C]0.656062640409582[/C][C]163.636136160006[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 24 )[/C][C]107.297222222222[/C][C]0.632115125104475[/C][C]169.743165383819[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 24 )[/C][C]107.45[/C][C]0.595214352309836[/C][C]180.523200730999[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 24 )[/C][C]107.386111111111[/C][C]0.561159045195318[/C][C]191.364840379137[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 24 )[/C][C]107.452777777778[/C][C]0.543790427497973[/C][C]197.599612542239[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 24 )[/C][C]107.565714285714[/C][C]1.33352517105591[/C][C]80.6626801056495[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 24 )[/C][C]107.576470588235[/C][C]1.25941950068136[/C][C]85.417504278785[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 24 )[/C][C]107.534848484848[/C][C]1.20271156816459[/C][C]89.4103385477142[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 24 )[/C][C]107.496875[/C][C]1.15625234609372[/C][C]92.970081628952[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 24 )[/C][C]107.495161290323[/C][C]1.11504405942775[/C][C]96.4044069662051[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 24 )[/C][C]107.515[/C][C]1.07196378480441[/C][C]100.297231608078[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 24 )[/C][C]107.536206896552[/C][C]1.02731213635599[/C][C]104.677247635754[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 24 )[/C][C]107.501785714286[/C][C]0.998767068093446[/C][C]107.634491713365[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 24 )[/C][C]107.487037037037[/C][C]0.970692283943213[/C][C]110.732349288279[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 24 )[/C][C]107.432692307692[/C][C]0.948332350503986[/C][C]113.28590894384[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 24 )[/C][C]107.368[/C][C]0.921283222201623[/C][C]116.541794545459[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 24 )[/C][C]107.33125[/C][C]0.899350416928284[/C][C]119.343081383770[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 24 )[/C][C]107.304347826087[/C][C]0.87600298083526[/C][C]122.493130929501[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 24 )[/C][C]107.306818181818[/C][C]0.856040578947138[/C][C]125.352490081483[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 24 )[/C][C]107.309523809524[/C][C]0.830758923731184[/C][C]129.170473821172[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 24 )[/C][C]107.285[/C][C]0.805124214019179[/C][C]133.252730612129[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 24 )[/C][C]107.284210526316[/C][C]0.783593559514077[/C][C]136.913083605288[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 24 )[/C][C]107.291666666667[/C][C]0.767984116485883[/C][C]139.705580315396[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 24 )[/C][C]107.308823529412[/C][C]0.758180198211514[/C][C]141.534721933578[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 24 )[/C][C]107.3[/C][C]0.75249584716462[/C][C]142.592149052121[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 24 )[/C][C]107.293333333333[/C][C]0.742610080594632[/C][C]144.481385503709[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 24 )[/C][C]107.292857142857[/C][C]0.732248992178022[/C][C]146.525100463057[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 24 )[/C][C]107.273076923077[/C][C]0.724697447582468[/C][C]148.024637427565[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 24 )[/C][C]107.258333333333[/C][C]0.720027089533328[/C][C]148.964302722069[/C][/ROW]
[ROW][C]Median[/C][C]106.7[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]107.95[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]107.078378378378[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]107.291666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]107.078378378378[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]107.291666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]107.291666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]107.078378378378[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]107.291666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]107.284210526316[/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=16978&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=16978&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 Mean107.5763888888891.4092133304445076.3379018384367
Geometric Mean106.915063547619
Harmonic Mean106.246111074420
Quadratic Mean108.229742138348
Winsorized Mean ( 1 / 24 )107.5555555555561.3952620600841377.0862754980024
Winsorized Mean ( 2 / 24 )107.6527777777781.3464422665239979.9535044719722
Winsorized Mean ( 3 / 24 )107.6361111111111.3007917198451482.7466145955523
Winsorized Mean ( 4 / 24 )107.5027777777781.2621320056228185.175542097698
Winsorized Mean ( 5 / 24 )107.41251.2410634188567586.5487600133654
Winsorized Mean ( 6 / 24 )107.41251.2144489684413988.4454619265328
Winsorized Mean ( 7 / 24 )107.7236111111111.1191330988844096.2562998257262
Winsorized Mean ( 8 / 24 )107.5902777777781.0903459554254498.6753582589278
Winsorized Mean ( 9 / 24 )107.8402777777781.03643835272877104.048907003347
Winsorized Mean ( 10 / 24 )107.8819444444441.03007081207595104.732551568008
Winsorized Mean ( 11 / 24 )107.63750.97661714831445110.214632403058
Winsorized Mean ( 12 / 24 )107.53750.954376783556775112.678243910365
Winsorized Mean ( 13 / 24 )107.2847222222220.907992807174357118.155916406528
Winsorized Mean ( 14 / 24 )107.2847222222220.901940309162391118.948805294948
Winsorized Mean ( 15 / 24 )107.5138888888890.867093849116173123.993370496720
Winsorized Mean ( 16 / 24 )107.2916666666670.812889487721933131.988011023914
Winsorized Mean ( 17 / 24 )107.2208333333330.753935780287766142.214809452880
Winsorized Mean ( 18 / 24 )107.1458333333330.700530587811906152.949543099897
Winsorized Mean ( 19 / 24 )107.3833333333330.659915938118948162.722745626395
Winsorized Mean ( 20 / 24 )107.3555555555560.656062640409582163.636136160006
Winsorized Mean ( 21 / 24 )107.2972222222220.632115125104475169.743165383819
Winsorized Mean ( 22 / 24 )107.450.595214352309836180.523200730999
Winsorized Mean ( 23 / 24 )107.3861111111110.561159045195318191.364840379137
Winsorized Mean ( 24 / 24 )107.4527777777780.543790427497973197.599612542239
Trimmed Mean ( 1 / 24 )107.5657142857141.3335251710559180.6626801056495
Trimmed Mean ( 2 / 24 )107.5764705882351.2594195006813685.417504278785
Trimmed Mean ( 3 / 24 )107.5348484848481.2027115681645989.4103385477142
Trimmed Mean ( 4 / 24 )107.4968751.1562523460937292.970081628952
Trimmed Mean ( 5 / 24 )107.4951612903231.1150440594277596.4044069662051
Trimmed Mean ( 6 / 24 )107.5151.07196378480441100.297231608078
Trimmed Mean ( 7 / 24 )107.5362068965521.02731213635599104.677247635754
Trimmed Mean ( 8 / 24 )107.5017857142860.998767068093446107.634491713365
Trimmed Mean ( 9 / 24 )107.4870370370370.970692283943213110.732349288279
Trimmed Mean ( 10 / 24 )107.4326923076920.948332350503986113.28590894384
Trimmed Mean ( 11 / 24 )107.3680.921283222201623116.541794545459
Trimmed Mean ( 12 / 24 )107.331250.899350416928284119.343081383770
Trimmed Mean ( 13 / 24 )107.3043478260870.87600298083526122.493130929501
Trimmed Mean ( 14 / 24 )107.3068181818180.856040578947138125.352490081483
Trimmed Mean ( 15 / 24 )107.3095238095240.830758923731184129.170473821172
Trimmed Mean ( 16 / 24 )107.2850.805124214019179133.252730612129
Trimmed Mean ( 17 / 24 )107.2842105263160.783593559514077136.913083605288
Trimmed Mean ( 18 / 24 )107.2916666666670.767984116485883139.705580315396
Trimmed Mean ( 19 / 24 )107.3088235294120.758180198211514141.534721933578
Trimmed Mean ( 20 / 24 )107.30.75249584716462142.592149052121
Trimmed Mean ( 21 / 24 )107.2933333333330.742610080594632144.481385503709
Trimmed Mean ( 22 / 24 )107.2928571428570.732248992178022146.525100463057
Trimmed Mean ( 23 / 24 )107.2730769230770.724697447582468148.024637427565
Trimmed Mean ( 24 / 24 )107.2583333333330.720027089533328148.964302722069
Median106.7
Midrange107.95
Midmean - Weighted Average at Xnp107.078378378378
Midmean - Weighted Average at X(n+1)p107.291666666667
Midmean - Empirical Distribution Function107.078378378378
Midmean - Empirical Distribution Function - Averaging107.291666666667
Midmean - Empirical Distribution Function - Interpolation107.291666666667
Midmean - Closest Observation107.078378378378
Midmean - True Basic - Statistics Graphics Toolkit107.291666666667
Midmean - MS Excel (old versions)107.284210526316
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')