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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 computationFri, 01 Mar 2013 09:51:25 -0500
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2013/Mar/01/t136214952927hot5dd6ppbsmo.htm/, Retrieved Thu, 02 May 2024 07:57:18 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=207225, Retrieved Thu, 02 May 2024 07:57:18 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact152
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [robuustheid gemid...] [2013-03-01 14:51:25] [a7b46db3730015db727d65b06ff3f02a] [Current]
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Dataseries X:
10,92
10,98
11,15
11,19
11,33
11,38
11,4
11,45
11,56
11,61
11,82
11,77
11,85
11,82
11,92
11,86
11,87
11,94
11,86
11,92
11,83
11,91
11,93
11,99
11,96
12,12
11,85
12,01
12,1
12,21
12,31
12,31
12,39
12,35
12,41
12,51
12,27
12,51
12,44
12,47
12,51
12,58
12,5
12,52
12,59
12,51
12,67
12,64
12,54
12,6
12,67
12,62
12,72
12,85
12,85
12,82
12,79
12,94
12,71
12,56
12,64
12,7
12,74
12,85
12,84
12,83
12,88
13,07
12,99
13,2
13,23
13,18




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 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 & 2 seconds \tabularnewline
R Server & 'George Udny Yule' @ yule.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=207225&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]2 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=207225&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=207225&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 time2 seconds
R Server'George Udny Yule' @ yule.wessa.net







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean12.27527777777780.0653020465658577187.976922980477
Geometric Mean12.2627327541129
Harmonic Mean12.2499734852942
Quadratic Mean12.2876040743869
Winsorized Mean ( 1 / 24 )12.27569444444440.0649785766997495188.919103309503
Winsorized Mean ( 2 / 24 )12.27986111111110.0636130138749526193.040077227755
Winsorized Mean ( 3 / 24 )12.27694444444440.0623319772419361196.960612957817
Winsorized Mean ( 4 / 24 )12.28027777777780.059733030284531205.586050452859
Winsorized Mean ( 5 / 24 )12.28027777777780.0584000196362482210.278658368046
Winsorized Mean ( 6 / 24 )12.27694444444440.0572705460903513214.367511444296
Winsorized Mean ( 7 / 24 )12.27888888888890.0558111880809403220.00765995308
Winsorized Mean ( 8 / 24 )12.29111111111110.0533511397635244230.381415759639
Winsorized Mean ( 9 / 24 )12.29736111111110.0521677927609321235.727073358574
Winsorized Mean ( 10 / 24 )12.31819444444440.0481014050094646256.088038218856
Winsorized Mean ( 11 / 24 )12.32430555555560.0466733003286842264.054726551689
Winsorized Mean ( 12 / 24 )12.32263888888890.0464203733129276265.457556875294
Winsorized Mean ( 13 / 24 )12.31902777777780.0453404612087499271.700539636338
Winsorized Mean ( 14 / 24 )12.31319444444440.0433666477163106283.932355689401
Winsorized Mean ( 15 / 24 )12.30902777777780.0427960368679734287.620739643518
Winsorized Mean ( 16 / 24 )12.30902777777780.0421623843704195291.943350965075
Winsorized Mean ( 17 / 24 )12.30666666666670.0418479623898408294.080427429706
Winsorized Mean ( 18 / 24 )12.30166666666670.0404952710776915303.780326425412
Winsorized Mean ( 19 / 24 )12.31222222222220.038934469152582316.22935897678
Winsorized Mean ( 20 / 24 )12.30666666666670.0374688185437878328.450886496048
Winsorized Mean ( 21 / 24 )12.30666666666670.0374688185437878328.450886496048
Winsorized Mean ( 22 / 24 )12.30361111111110.0362666536973725339.25410416353
Winsorized Mean ( 23 / 24 )12.30041666666670.0350259447210118351.180154158347
Winsorized Mean ( 24 / 24 )12.303750.0336629463267709365.498310236002
Trimmed Mean ( 1 / 24 )12.2810.0628001364875678195.556899823477
Trimmed Mean ( 2 / 24 )12.28661764705880.0601970754856089204.106554146408
Trimmed Mean ( 3 / 24 )12.2903030303030.0579739390437663211.997032339388
Trimmed Mean ( 4 / 24 )12.29531250.0558981361451701219.959257104181
Trimmed Mean ( 5 / 24 )12.29967741935480.0543768932780941226.193088237901
Trimmed Mean ( 6 / 24 )12.30433333333330.0529515110600301232.369824524633
Trimmed Mean ( 7 / 24 )12.310.0515183848799752238.943826144379
Trimmed Mean ( 8 / 24 )12.31571428571430.0501347904859355245.652054518294
Trimmed Mean ( 9 / 24 )12.31981481481480.0490443193948241251.197589584962
Trimmed Mean ( 10 / 24 )12.32326923076920.0479541645425276256.980167381302
Trimmed Mean ( 11 / 24 )12.3240.0474896336701227259.509266498163
Trimmed Mean ( 12 / 24 )12.32395833333330.0471499227071309261.378123775153
Trimmed Mean ( 13 / 24 )12.32413043478260.0467045147627385263.874499015564
Trimmed Mean ( 14 / 24 )12.32477272727270.046289931777556266.251693489176
Trimmed Mean ( 15 / 24 )12.32619047619050.046078446947017267.504468854249
Trimmed Mean ( 16 / 24 )12.328250.0458130083138974269.099333436705
Trimmed Mean ( 17 / 24 )12.33052631578950.0454860699111625271.083572176533
Trimmed Mean ( 18 / 24 )12.33333333333330.0449938267370585274.111677706559
Trimmed Mean ( 19 / 24 )12.33705882352940.04450466019734277.208246705517
Trimmed Mean ( 20 / 24 )12.340.0440948391391745279.851344077973
Trimmed Mean ( 21 / 24 )12.3440.0437064397264661282.429776418626
Trimmed Mean ( 22 / 24 )12.34857142857140.0429399552645956287.577650057613
Trimmed Mean ( 23 / 24 )12.35423076923080.041956655571501294.452229353151
Trimmed Mean ( 24 / 24 )12.361250.0406260451370578304.269095313057
Median12.425
Midrange12.075
Midmean - Weighted Average at Xnp12.3084210526316
Midmean - Weighted Average at X(n+1)p12.3333333333333
Midmean - Empirical Distribution Function12.3084210526316
Midmean - Empirical Distribution Function - Averaging12.3333333333333
Midmean - Empirical Distribution Function - Interpolation12.3333333333333
Midmean - Closest Observation12.3084210526316
Midmean - True Basic - Statistics Graphics Toolkit12.3333333333333
Midmean - MS Excel (old versions)12.3184615384615
Number of observations72

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 12.2752777777778 & 0.0653020465658577 & 187.976922980477 \tabularnewline
Geometric Mean & 12.2627327541129 &  &  \tabularnewline
Harmonic Mean & 12.2499734852942 &  &  \tabularnewline
Quadratic Mean & 12.2876040743869 &  &  \tabularnewline
Winsorized Mean ( 1 / 24 ) & 12.2756944444444 & 0.0649785766997495 & 188.919103309503 \tabularnewline
Winsorized Mean ( 2 / 24 ) & 12.2798611111111 & 0.0636130138749526 & 193.040077227755 \tabularnewline
Winsorized Mean ( 3 / 24 ) & 12.2769444444444 & 0.0623319772419361 & 196.960612957817 \tabularnewline
Winsorized Mean ( 4 / 24 ) & 12.2802777777778 & 0.059733030284531 & 205.586050452859 \tabularnewline
Winsorized Mean ( 5 / 24 ) & 12.2802777777778 & 0.0584000196362482 & 210.278658368046 \tabularnewline
Winsorized Mean ( 6 / 24 ) & 12.2769444444444 & 0.0572705460903513 & 214.367511444296 \tabularnewline
Winsorized Mean ( 7 / 24 ) & 12.2788888888889 & 0.0558111880809403 & 220.00765995308 \tabularnewline
Winsorized Mean ( 8 / 24 ) & 12.2911111111111 & 0.0533511397635244 & 230.381415759639 \tabularnewline
Winsorized Mean ( 9 / 24 ) & 12.2973611111111 & 0.0521677927609321 & 235.727073358574 \tabularnewline
Winsorized Mean ( 10 / 24 ) & 12.3181944444444 & 0.0481014050094646 & 256.088038218856 \tabularnewline
Winsorized Mean ( 11 / 24 ) & 12.3243055555556 & 0.0466733003286842 & 264.054726551689 \tabularnewline
Winsorized Mean ( 12 / 24 ) & 12.3226388888889 & 0.0464203733129276 & 265.457556875294 \tabularnewline
Winsorized Mean ( 13 / 24 ) & 12.3190277777778 & 0.0453404612087499 & 271.700539636338 \tabularnewline
Winsorized Mean ( 14 / 24 ) & 12.3131944444444 & 0.0433666477163106 & 283.932355689401 \tabularnewline
Winsorized Mean ( 15 / 24 ) & 12.3090277777778 & 0.0427960368679734 & 287.620739643518 \tabularnewline
Winsorized Mean ( 16 / 24 ) & 12.3090277777778 & 0.0421623843704195 & 291.943350965075 \tabularnewline
Winsorized Mean ( 17 / 24 ) & 12.3066666666667 & 0.0418479623898408 & 294.080427429706 \tabularnewline
Winsorized Mean ( 18 / 24 ) & 12.3016666666667 & 0.0404952710776915 & 303.780326425412 \tabularnewline
Winsorized Mean ( 19 / 24 ) & 12.3122222222222 & 0.038934469152582 & 316.22935897678 \tabularnewline
Winsorized Mean ( 20 / 24 ) & 12.3066666666667 & 0.0374688185437878 & 328.450886496048 \tabularnewline
Winsorized Mean ( 21 / 24 ) & 12.3066666666667 & 0.0374688185437878 & 328.450886496048 \tabularnewline
Winsorized Mean ( 22 / 24 ) & 12.3036111111111 & 0.0362666536973725 & 339.25410416353 \tabularnewline
Winsorized Mean ( 23 / 24 ) & 12.3004166666667 & 0.0350259447210118 & 351.180154158347 \tabularnewline
Winsorized Mean ( 24 / 24 ) & 12.30375 & 0.0336629463267709 & 365.498310236002 \tabularnewline
Trimmed Mean ( 1 / 24 ) & 12.281 & 0.0628001364875678 & 195.556899823477 \tabularnewline
Trimmed Mean ( 2 / 24 ) & 12.2866176470588 & 0.0601970754856089 & 204.106554146408 \tabularnewline
Trimmed Mean ( 3 / 24 ) & 12.290303030303 & 0.0579739390437663 & 211.997032339388 \tabularnewline
Trimmed Mean ( 4 / 24 ) & 12.2953125 & 0.0558981361451701 & 219.959257104181 \tabularnewline
Trimmed Mean ( 5 / 24 ) & 12.2996774193548 & 0.0543768932780941 & 226.193088237901 \tabularnewline
Trimmed Mean ( 6 / 24 ) & 12.3043333333333 & 0.0529515110600301 & 232.369824524633 \tabularnewline
Trimmed Mean ( 7 / 24 ) & 12.31 & 0.0515183848799752 & 238.943826144379 \tabularnewline
Trimmed Mean ( 8 / 24 ) & 12.3157142857143 & 0.0501347904859355 & 245.652054518294 \tabularnewline
Trimmed Mean ( 9 / 24 ) & 12.3198148148148 & 0.0490443193948241 & 251.197589584962 \tabularnewline
Trimmed Mean ( 10 / 24 ) & 12.3232692307692 & 0.0479541645425276 & 256.980167381302 \tabularnewline
Trimmed Mean ( 11 / 24 ) & 12.324 & 0.0474896336701227 & 259.509266498163 \tabularnewline
Trimmed Mean ( 12 / 24 ) & 12.3239583333333 & 0.0471499227071309 & 261.378123775153 \tabularnewline
Trimmed Mean ( 13 / 24 ) & 12.3241304347826 & 0.0467045147627385 & 263.874499015564 \tabularnewline
Trimmed Mean ( 14 / 24 ) & 12.3247727272727 & 0.046289931777556 & 266.251693489176 \tabularnewline
Trimmed Mean ( 15 / 24 ) & 12.3261904761905 & 0.046078446947017 & 267.504468854249 \tabularnewline
Trimmed Mean ( 16 / 24 ) & 12.32825 & 0.0458130083138974 & 269.099333436705 \tabularnewline
Trimmed Mean ( 17 / 24 ) & 12.3305263157895 & 0.0454860699111625 & 271.083572176533 \tabularnewline
Trimmed Mean ( 18 / 24 ) & 12.3333333333333 & 0.0449938267370585 & 274.111677706559 \tabularnewline
Trimmed Mean ( 19 / 24 ) & 12.3370588235294 & 0.04450466019734 & 277.208246705517 \tabularnewline
Trimmed Mean ( 20 / 24 ) & 12.34 & 0.0440948391391745 & 279.851344077973 \tabularnewline
Trimmed Mean ( 21 / 24 ) & 12.344 & 0.0437064397264661 & 282.429776418626 \tabularnewline
Trimmed Mean ( 22 / 24 ) & 12.3485714285714 & 0.0429399552645956 & 287.577650057613 \tabularnewline
Trimmed Mean ( 23 / 24 ) & 12.3542307692308 & 0.041956655571501 & 294.452229353151 \tabularnewline
Trimmed Mean ( 24 / 24 ) & 12.36125 & 0.0406260451370578 & 304.269095313057 \tabularnewline
Median & 12.425 &  &  \tabularnewline
Midrange & 12.075 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 12.3084210526316 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 12.3333333333333 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 12.3084210526316 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 12.3333333333333 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 12.3333333333333 &  &  \tabularnewline
Midmean - Closest Observation & 12.3084210526316 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 12.3333333333333 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 12.3184615384615 &  &  \tabularnewline
Number of observations & 72 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=207225&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]12.2752777777778[/C][C]0.0653020465658577[/C][C]187.976922980477[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]12.2627327541129[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]12.2499734852942[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]12.2876040743869[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 24 )[/C][C]12.2756944444444[/C][C]0.0649785766997495[/C][C]188.919103309503[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 24 )[/C][C]12.2798611111111[/C][C]0.0636130138749526[/C][C]193.040077227755[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 24 )[/C][C]12.2769444444444[/C][C]0.0623319772419361[/C][C]196.960612957817[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 24 )[/C][C]12.2802777777778[/C][C]0.059733030284531[/C][C]205.586050452859[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 24 )[/C][C]12.2802777777778[/C][C]0.0584000196362482[/C][C]210.278658368046[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 24 )[/C][C]12.2769444444444[/C][C]0.0572705460903513[/C][C]214.367511444296[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 24 )[/C][C]12.2788888888889[/C][C]0.0558111880809403[/C][C]220.00765995308[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 24 )[/C][C]12.2911111111111[/C][C]0.0533511397635244[/C][C]230.381415759639[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 24 )[/C][C]12.2973611111111[/C][C]0.0521677927609321[/C][C]235.727073358574[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 24 )[/C][C]12.3181944444444[/C][C]0.0481014050094646[/C][C]256.088038218856[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 24 )[/C][C]12.3243055555556[/C][C]0.0466733003286842[/C][C]264.054726551689[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 24 )[/C][C]12.3226388888889[/C][C]0.0464203733129276[/C][C]265.457556875294[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 24 )[/C][C]12.3190277777778[/C][C]0.0453404612087499[/C][C]271.700539636338[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 24 )[/C][C]12.3131944444444[/C][C]0.0433666477163106[/C][C]283.932355689401[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 24 )[/C][C]12.3090277777778[/C][C]0.0427960368679734[/C][C]287.620739643518[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 24 )[/C][C]12.3090277777778[/C][C]0.0421623843704195[/C][C]291.943350965075[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 24 )[/C][C]12.3066666666667[/C][C]0.0418479623898408[/C][C]294.080427429706[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 24 )[/C][C]12.3016666666667[/C][C]0.0404952710776915[/C][C]303.780326425412[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 24 )[/C][C]12.3122222222222[/C][C]0.038934469152582[/C][C]316.22935897678[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 24 )[/C][C]12.3066666666667[/C][C]0.0374688185437878[/C][C]328.450886496048[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 24 )[/C][C]12.3066666666667[/C][C]0.0374688185437878[/C][C]328.450886496048[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 24 )[/C][C]12.3036111111111[/C][C]0.0362666536973725[/C][C]339.25410416353[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 24 )[/C][C]12.3004166666667[/C][C]0.0350259447210118[/C][C]351.180154158347[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 24 )[/C][C]12.30375[/C][C]0.0336629463267709[/C][C]365.498310236002[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 24 )[/C][C]12.281[/C][C]0.0628001364875678[/C][C]195.556899823477[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 24 )[/C][C]12.2866176470588[/C][C]0.0601970754856089[/C][C]204.106554146408[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 24 )[/C][C]12.290303030303[/C][C]0.0579739390437663[/C][C]211.997032339388[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 24 )[/C][C]12.2953125[/C][C]0.0558981361451701[/C][C]219.959257104181[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 24 )[/C][C]12.2996774193548[/C][C]0.0543768932780941[/C][C]226.193088237901[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 24 )[/C][C]12.3043333333333[/C][C]0.0529515110600301[/C][C]232.369824524633[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 24 )[/C][C]12.31[/C][C]0.0515183848799752[/C][C]238.943826144379[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 24 )[/C][C]12.3157142857143[/C][C]0.0501347904859355[/C][C]245.652054518294[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 24 )[/C][C]12.3198148148148[/C][C]0.0490443193948241[/C][C]251.197589584962[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 24 )[/C][C]12.3232692307692[/C][C]0.0479541645425276[/C][C]256.980167381302[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 24 )[/C][C]12.324[/C][C]0.0474896336701227[/C][C]259.509266498163[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 24 )[/C][C]12.3239583333333[/C][C]0.0471499227071309[/C][C]261.378123775153[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 24 )[/C][C]12.3241304347826[/C][C]0.0467045147627385[/C][C]263.874499015564[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 24 )[/C][C]12.3247727272727[/C][C]0.046289931777556[/C][C]266.251693489176[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 24 )[/C][C]12.3261904761905[/C][C]0.046078446947017[/C][C]267.504468854249[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 24 )[/C][C]12.32825[/C][C]0.0458130083138974[/C][C]269.099333436705[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 24 )[/C][C]12.3305263157895[/C][C]0.0454860699111625[/C][C]271.083572176533[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 24 )[/C][C]12.3333333333333[/C][C]0.0449938267370585[/C][C]274.111677706559[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 24 )[/C][C]12.3370588235294[/C][C]0.04450466019734[/C][C]277.208246705517[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 24 )[/C][C]12.34[/C][C]0.0440948391391745[/C][C]279.851344077973[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 24 )[/C][C]12.344[/C][C]0.0437064397264661[/C][C]282.429776418626[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 24 )[/C][C]12.3485714285714[/C][C]0.0429399552645956[/C][C]287.577650057613[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 24 )[/C][C]12.3542307692308[/C][C]0.041956655571501[/C][C]294.452229353151[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 24 )[/C][C]12.36125[/C][C]0.0406260451370578[/C][C]304.269095313057[/C][/ROW]
[ROW][C]Median[/C][C]12.425[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]12.075[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]12.3084210526316[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]12.3333333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]12.3084210526316[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]12.3333333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]12.3333333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]12.3084210526316[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]12.3333333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]12.3184615384615[/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=207225&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=207225&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 Mean12.27527777777780.0653020465658577187.976922980477
Geometric Mean12.2627327541129
Harmonic Mean12.2499734852942
Quadratic Mean12.2876040743869
Winsorized Mean ( 1 / 24 )12.27569444444440.0649785766997495188.919103309503
Winsorized Mean ( 2 / 24 )12.27986111111110.0636130138749526193.040077227755
Winsorized Mean ( 3 / 24 )12.27694444444440.0623319772419361196.960612957817
Winsorized Mean ( 4 / 24 )12.28027777777780.059733030284531205.586050452859
Winsorized Mean ( 5 / 24 )12.28027777777780.0584000196362482210.278658368046
Winsorized Mean ( 6 / 24 )12.27694444444440.0572705460903513214.367511444296
Winsorized Mean ( 7 / 24 )12.27888888888890.0558111880809403220.00765995308
Winsorized Mean ( 8 / 24 )12.29111111111110.0533511397635244230.381415759639
Winsorized Mean ( 9 / 24 )12.29736111111110.0521677927609321235.727073358574
Winsorized Mean ( 10 / 24 )12.31819444444440.0481014050094646256.088038218856
Winsorized Mean ( 11 / 24 )12.32430555555560.0466733003286842264.054726551689
Winsorized Mean ( 12 / 24 )12.32263888888890.0464203733129276265.457556875294
Winsorized Mean ( 13 / 24 )12.31902777777780.0453404612087499271.700539636338
Winsorized Mean ( 14 / 24 )12.31319444444440.0433666477163106283.932355689401
Winsorized Mean ( 15 / 24 )12.30902777777780.0427960368679734287.620739643518
Winsorized Mean ( 16 / 24 )12.30902777777780.0421623843704195291.943350965075
Winsorized Mean ( 17 / 24 )12.30666666666670.0418479623898408294.080427429706
Winsorized Mean ( 18 / 24 )12.30166666666670.0404952710776915303.780326425412
Winsorized Mean ( 19 / 24 )12.31222222222220.038934469152582316.22935897678
Winsorized Mean ( 20 / 24 )12.30666666666670.0374688185437878328.450886496048
Winsorized Mean ( 21 / 24 )12.30666666666670.0374688185437878328.450886496048
Winsorized Mean ( 22 / 24 )12.30361111111110.0362666536973725339.25410416353
Winsorized Mean ( 23 / 24 )12.30041666666670.0350259447210118351.180154158347
Winsorized Mean ( 24 / 24 )12.303750.0336629463267709365.498310236002
Trimmed Mean ( 1 / 24 )12.2810.0628001364875678195.556899823477
Trimmed Mean ( 2 / 24 )12.28661764705880.0601970754856089204.106554146408
Trimmed Mean ( 3 / 24 )12.2903030303030.0579739390437663211.997032339388
Trimmed Mean ( 4 / 24 )12.29531250.0558981361451701219.959257104181
Trimmed Mean ( 5 / 24 )12.29967741935480.0543768932780941226.193088237901
Trimmed Mean ( 6 / 24 )12.30433333333330.0529515110600301232.369824524633
Trimmed Mean ( 7 / 24 )12.310.0515183848799752238.943826144379
Trimmed Mean ( 8 / 24 )12.31571428571430.0501347904859355245.652054518294
Trimmed Mean ( 9 / 24 )12.31981481481480.0490443193948241251.197589584962
Trimmed Mean ( 10 / 24 )12.32326923076920.0479541645425276256.980167381302
Trimmed Mean ( 11 / 24 )12.3240.0474896336701227259.509266498163
Trimmed Mean ( 12 / 24 )12.32395833333330.0471499227071309261.378123775153
Trimmed Mean ( 13 / 24 )12.32413043478260.0467045147627385263.874499015564
Trimmed Mean ( 14 / 24 )12.32477272727270.046289931777556266.251693489176
Trimmed Mean ( 15 / 24 )12.32619047619050.046078446947017267.504468854249
Trimmed Mean ( 16 / 24 )12.328250.0458130083138974269.099333436705
Trimmed Mean ( 17 / 24 )12.33052631578950.0454860699111625271.083572176533
Trimmed Mean ( 18 / 24 )12.33333333333330.0449938267370585274.111677706559
Trimmed Mean ( 19 / 24 )12.33705882352940.04450466019734277.208246705517
Trimmed Mean ( 20 / 24 )12.340.0440948391391745279.851344077973
Trimmed Mean ( 21 / 24 )12.3440.0437064397264661282.429776418626
Trimmed Mean ( 22 / 24 )12.34857142857140.0429399552645956287.577650057613
Trimmed Mean ( 23 / 24 )12.35423076923080.041956655571501294.452229353151
Trimmed Mean ( 24 / 24 )12.361250.0406260451370578304.269095313057
Median12.425
Midrange12.075
Midmean - Weighted Average at Xnp12.3084210526316
Midmean - Weighted Average at X(n+1)p12.3333333333333
Midmean - Empirical Distribution Function12.3084210526316
Midmean - Empirical Distribution Function - Averaging12.3333333333333
Midmean - Empirical Distribution Function - Interpolation12.3333333333333
Midmean - Closest Observation12.3084210526316
Midmean - True Basic - Statistics Graphics Toolkit12.3333333333333
Midmean - MS Excel (old versions)12.3184615384615
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')