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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 computationSat, 24 Oct 2009 08:02:41 -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/2009/Oct/24/t1256393333n28qvkvndzc2jjv.htm/, Retrieved Thu, 02 May 2024 01:45:26 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=50158, Retrieved Thu, 02 May 2024 01:45:26 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsKDGP1W52
Estimated Impact120
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Univariate Data Series] [Evolution of real...] [2009-09-28 22:40:28] [ae313ad3bd3ddca83679957b8289cb77]
- RMPD    [Central Tendency] [Opgave 5.2] [2009-10-24 14:02:41] [3f12ab8801f7554f488f56dad3cd0b03] [Current]
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Dataseries X:
46.5
47
47.5
48.3
49.1
50.1
51.1
52
53.2
53.9
54.5
55.2
55.6
55.7
56.1
56.8
57.5
58.3
58.9
59.4
59.8
60
60
60.3
60.1
59.7
59.5
59.4
59.3
59.2
59.1
59
59.3
59.5
59.5
59.5
59.7
59.7
60.5
60.7
61.3
61.4
61.8
62.4
62.4
62.9
63.2
63.4
63.9
64.5
65
65.4
66.3
67.7
69
70
71.4
72.5
73.4
74.6
75.2
75.9
76.8
77.9
79.2
80.5
82.6
84.4
85.9
87.6




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' @ 72.249.76.132

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 2 seconds \tabularnewline
R Server & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=50158&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' @ 72.249.76.132[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=50158&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=50158&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' @ 72.249.76.132







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean62.71.1349920877862955.2426758518568
Geometric Mean62.0274041652646
Harmonic Mean61.387564817268
Quadratic Mean63.4048601111483
Winsorized Mean ( 1 / 23 )62.68285714285711.1260421378370255.6665288416851
Winsorized Mean ( 2 / 23 )62.65428571428571.1107020996182656.4096221082316
Winsorized Mean ( 3 / 23 )62.61142857142861.0827549840643257.8260358926313
Winsorized Mean ( 4 / 23 )62.53714285714291.0430588307194959.9555279293359
Winsorized Mean ( 5 / 23 )62.51571428571431.0072647827171562.0648268046016
Winsorized Mean ( 6 / 23 )62.490.96601280806292464.6885832966405
Winsorized Mean ( 7 / 23 )62.470.92588126002228667.470854738432
Winsorized Mean ( 8 / 23 )62.50428571428570.88126211890240970.925873668703
Winsorized Mean ( 9 / 23 )62.50428571428570.84807524304423573.7013445763627
Winsorized Mean ( 10 / 23 )62.50428571428570.81719217228015976.4866427194034
Winsorized Mean ( 11 / 23 )62.42571428571430.7618890267526381.9354421624748
Winsorized Mean ( 12 / 23 )62.340.72065187881166586.5050127986857
Winsorized Mean ( 13 / 23 )62.15428571428570.67700376833263491.8078873731575
Winsorized Mean ( 14 / 23 )61.95428571428570.611469687671549101.320289400126
Winsorized Mean ( 15 / 23 )61.890.550486891583608112.42774523106
Winsorized Mean ( 16 / 23 )61.75285714285710.474490994264356130.145477763172
Winsorized Mean ( 17 / 23 )61.60714285714290.389134631726593158.318324390177
Winsorized Mean ( 18 / 23 )61.530.330802086909883186.002454140387
Winsorized Mean ( 19 / 23 )61.44857142857140.309442448297006198.578352022320
Winsorized Mean ( 20 / 23 )61.33428571428570.28268079074946216.973659765393
Winsorized Mean ( 21 / 23 )61.18428571428570.250462394033914244.28531856164
Winsorized Mean ( 22 / 23 )61.05857142857140.222506825048442274.412128325854
Winsorized Mean ( 23 / 23 )60.99285714285710.212549557524881286.958288001693
Trimmed Mean ( 1 / 23 )62.57205882352941.0824723870753857.8047621081463
Trimmed Mean ( 2 / 23 )62.45454545454551.0299572983616460.6379949478416
Trimmed Mean ( 3 / 23 )62.34531250.97651980065380663.8443915405076
Trimmed Mean ( 4 / 23 )62.24516129032260.92510858744731867.2841676479057
Trimmed Mean ( 5 / 23 )62.160.87821467589032770.77996042025
Trimmed Mean ( 6 / 23 )62.07413793103450.83300620443627374.5182179921966
Trimmed Mean ( 7 / 23 )61.98750.79010135179222278.4551245981177
Trimmed Mean ( 8 / 23 )61.89814814814810.74842714525810482.7043066787775
Trimmed Mean ( 9 / 23 )61.79615384615380.70840654331167787.2326130095688
Trimmed Mean ( 10 / 23 )61.6860.6664741830969192.5557231839998
Trimmed Mean ( 11 / 23 )61.56666666666670.62070034036526199.1890331982689
Trimmed Mean ( 12 / 23 )61.44782608695650.576493977078742106.588843127781
Trimmed Mean ( 13 / 23 )61.32954545454550.529764991830611115.767456136768
Trimmed Mean ( 14 / 23 )61.22380952380950.480403546052008127.442459629933
Trimmed Mean ( 15 / 23 )61.13250.433979609292938140.864913214702
Trimmed Mean ( 16 / 23 )61.03947368421050.38904887254716156.894102493026
Trimmed Mean ( 17 / 23 )60.95277777777780.351470518782433173.422163511554
Trimmed Mean ( 18 / 23 )60.87352941176470.326770750548564186.28818310566
Trimmed Mean ( 19 / 23 )60.793750.309817112414988196.224635644300
Trimmed Mean ( 20 / 23 )60.71333333333330.291872013099323208.013549119123
Trimmed Mean ( 21 / 23 )60.63571428571430.274595146226341220.818594643818
Trimmed Mean ( 22 / 23 )60.56538461538460.260646669632536232.365848759052
Trimmed Mean ( 23 / 23 )60.50.249709976700508242.281068619702
Median60
Midrange67.05
Midmean - Weighted Average at Xnp60.8
Midmean - Weighted Average at X(n+1)p60.9527777777778
Midmean - Empirical Distribution Function60.9527777777778
Midmean - Empirical Distribution Function - Averaging60.9527777777778
Midmean - Empirical Distribution Function - Interpolation60.8735294117647
Midmean - Closest Observation60.9527777777778
Midmean - True Basic - Statistics Graphics Toolkit60.9527777777778
Midmean - MS Excel (old versions)60.9527777777778
Number of observations70

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 62.7 & 1.13499208778629 & 55.2426758518568 \tabularnewline
Geometric Mean & 62.0274041652646 &  &  \tabularnewline
Harmonic Mean & 61.387564817268 &  &  \tabularnewline
Quadratic Mean & 63.4048601111483 &  &  \tabularnewline
Winsorized Mean ( 1 / 23 ) & 62.6828571428571 & 1.12604213783702 & 55.6665288416851 \tabularnewline
Winsorized Mean ( 2 / 23 ) & 62.6542857142857 & 1.11070209961826 & 56.4096221082316 \tabularnewline
Winsorized Mean ( 3 / 23 ) & 62.6114285714286 & 1.08275498406432 & 57.8260358926313 \tabularnewline
Winsorized Mean ( 4 / 23 ) & 62.5371428571429 & 1.04305883071949 & 59.9555279293359 \tabularnewline
Winsorized Mean ( 5 / 23 ) & 62.5157142857143 & 1.00726478271715 & 62.0648268046016 \tabularnewline
Winsorized Mean ( 6 / 23 ) & 62.49 & 0.966012808062924 & 64.6885832966405 \tabularnewline
Winsorized Mean ( 7 / 23 ) & 62.47 & 0.925881260022286 & 67.470854738432 \tabularnewline
Winsorized Mean ( 8 / 23 ) & 62.5042857142857 & 0.881262118902409 & 70.925873668703 \tabularnewline
Winsorized Mean ( 9 / 23 ) & 62.5042857142857 & 0.848075243044235 & 73.7013445763627 \tabularnewline
Winsorized Mean ( 10 / 23 ) & 62.5042857142857 & 0.817192172280159 & 76.4866427194034 \tabularnewline
Winsorized Mean ( 11 / 23 ) & 62.4257142857143 & 0.76188902675263 & 81.9354421624748 \tabularnewline
Winsorized Mean ( 12 / 23 ) & 62.34 & 0.720651878811665 & 86.5050127986857 \tabularnewline
Winsorized Mean ( 13 / 23 ) & 62.1542857142857 & 0.677003768332634 & 91.8078873731575 \tabularnewline
Winsorized Mean ( 14 / 23 ) & 61.9542857142857 & 0.611469687671549 & 101.320289400126 \tabularnewline
Winsorized Mean ( 15 / 23 ) & 61.89 & 0.550486891583608 & 112.42774523106 \tabularnewline
Winsorized Mean ( 16 / 23 ) & 61.7528571428571 & 0.474490994264356 & 130.145477763172 \tabularnewline
Winsorized Mean ( 17 / 23 ) & 61.6071428571429 & 0.389134631726593 & 158.318324390177 \tabularnewline
Winsorized Mean ( 18 / 23 ) & 61.53 & 0.330802086909883 & 186.002454140387 \tabularnewline
Winsorized Mean ( 19 / 23 ) & 61.4485714285714 & 0.309442448297006 & 198.578352022320 \tabularnewline
Winsorized Mean ( 20 / 23 ) & 61.3342857142857 & 0.28268079074946 & 216.973659765393 \tabularnewline
Winsorized Mean ( 21 / 23 ) & 61.1842857142857 & 0.250462394033914 & 244.28531856164 \tabularnewline
Winsorized Mean ( 22 / 23 ) & 61.0585714285714 & 0.222506825048442 & 274.412128325854 \tabularnewline
Winsorized Mean ( 23 / 23 ) & 60.9928571428571 & 0.212549557524881 & 286.958288001693 \tabularnewline
Trimmed Mean ( 1 / 23 ) & 62.5720588235294 & 1.08247238707538 & 57.8047621081463 \tabularnewline
Trimmed Mean ( 2 / 23 ) & 62.4545454545455 & 1.02995729836164 & 60.6379949478416 \tabularnewline
Trimmed Mean ( 3 / 23 ) & 62.3453125 & 0.976519800653806 & 63.8443915405076 \tabularnewline
Trimmed Mean ( 4 / 23 ) & 62.2451612903226 & 0.925108587447318 & 67.2841676479057 \tabularnewline
Trimmed Mean ( 5 / 23 ) & 62.16 & 0.878214675890327 & 70.77996042025 \tabularnewline
Trimmed Mean ( 6 / 23 ) & 62.0741379310345 & 0.833006204436273 & 74.5182179921966 \tabularnewline
Trimmed Mean ( 7 / 23 ) & 61.9875 & 0.790101351792222 & 78.4551245981177 \tabularnewline
Trimmed Mean ( 8 / 23 ) & 61.8981481481481 & 0.748427145258104 & 82.7043066787775 \tabularnewline
Trimmed Mean ( 9 / 23 ) & 61.7961538461538 & 0.708406543311677 & 87.2326130095688 \tabularnewline
Trimmed Mean ( 10 / 23 ) & 61.686 & 0.66647418309691 & 92.5557231839998 \tabularnewline
Trimmed Mean ( 11 / 23 ) & 61.5666666666667 & 0.620700340365261 & 99.1890331982689 \tabularnewline
Trimmed Mean ( 12 / 23 ) & 61.4478260869565 & 0.576493977078742 & 106.588843127781 \tabularnewline
Trimmed Mean ( 13 / 23 ) & 61.3295454545455 & 0.529764991830611 & 115.767456136768 \tabularnewline
Trimmed Mean ( 14 / 23 ) & 61.2238095238095 & 0.480403546052008 & 127.442459629933 \tabularnewline
Trimmed Mean ( 15 / 23 ) & 61.1325 & 0.433979609292938 & 140.864913214702 \tabularnewline
Trimmed Mean ( 16 / 23 ) & 61.0394736842105 & 0.38904887254716 & 156.894102493026 \tabularnewline
Trimmed Mean ( 17 / 23 ) & 60.9527777777778 & 0.351470518782433 & 173.422163511554 \tabularnewline
Trimmed Mean ( 18 / 23 ) & 60.8735294117647 & 0.326770750548564 & 186.28818310566 \tabularnewline
Trimmed Mean ( 19 / 23 ) & 60.79375 & 0.309817112414988 & 196.224635644300 \tabularnewline
Trimmed Mean ( 20 / 23 ) & 60.7133333333333 & 0.291872013099323 & 208.013549119123 \tabularnewline
Trimmed Mean ( 21 / 23 ) & 60.6357142857143 & 0.274595146226341 & 220.818594643818 \tabularnewline
Trimmed Mean ( 22 / 23 ) & 60.5653846153846 & 0.260646669632536 & 232.365848759052 \tabularnewline
Trimmed Mean ( 23 / 23 ) & 60.5 & 0.249709976700508 & 242.281068619702 \tabularnewline
Median & 60 &  &  \tabularnewline
Midrange & 67.05 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 60.8 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 60.9527777777778 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 60.9527777777778 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 60.9527777777778 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 60.8735294117647 &  &  \tabularnewline
Midmean - Closest Observation & 60.9527777777778 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 60.9527777777778 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 60.9527777777778 &  &  \tabularnewline
Number of observations & 70 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=50158&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]62.7[/C][C]1.13499208778629[/C][C]55.2426758518568[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]62.0274041652646[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]61.387564817268[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]63.4048601111483[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 23 )[/C][C]62.6828571428571[/C][C]1.12604213783702[/C][C]55.6665288416851[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 23 )[/C][C]62.6542857142857[/C][C]1.11070209961826[/C][C]56.4096221082316[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 23 )[/C][C]62.6114285714286[/C][C]1.08275498406432[/C][C]57.8260358926313[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 23 )[/C][C]62.5371428571429[/C][C]1.04305883071949[/C][C]59.9555279293359[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 23 )[/C][C]62.5157142857143[/C][C]1.00726478271715[/C][C]62.0648268046016[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 23 )[/C][C]62.49[/C][C]0.966012808062924[/C][C]64.6885832966405[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 23 )[/C][C]62.47[/C][C]0.925881260022286[/C][C]67.470854738432[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 23 )[/C][C]62.5042857142857[/C][C]0.881262118902409[/C][C]70.925873668703[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 23 )[/C][C]62.5042857142857[/C][C]0.848075243044235[/C][C]73.7013445763627[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 23 )[/C][C]62.5042857142857[/C][C]0.817192172280159[/C][C]76.4866427194034[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 23 )[/C][C]62.4257142857143[/C][C]0.76188902675263[/C][C]81.9354421624748[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 23 )[/C][C]62.34[/C][C]0.720651878811665[/C][C]86.5050127986857[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 23 )[/C][C]62.1542857142857[/C][C]0.677003768332634[/C][C]91.8078873731575[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 23 )[/C][C]61.9542857142857[/C][C]0.611469687671549[/C][C]101.320289400126[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 23 )[/C][C]61.89[/C][C]0.550486891583608[/C][C]112.42774523106[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 23 )[/C][C]61.7528571428571[/C][C]0.474490994264356[/C][C]130.145477763172[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 23 )[/C][C]61.6071428571429[/C][C]0.389134631726593[/C][C]158.318324390177[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 23 )[/C][C]61.53[/C][C]0.330802086909883[/C][C]186.002454140387[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 23 )[/C][C]61.4485714285714[/C][C]0.309442448297006[/C][C]198.578352022320[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 23 )[/C][C]61.3342857142857[/C][C]0.28268079074946[/C][C]216.973659765393[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 23 )[/C][C]61.1842857142857[/C][C]0.250462394033914[/C][C]244.28531856164[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 23 )[/C][C]61.0585714285714[/C][C]0.222506825048442[/C][C]274.412128325854[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 23 )[/C][C]60.9928571428571[/C][C]0.212549557524881[/C][C]286.958288001693[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 23 )[/C][C]62.5720588235294[/C][C]1.08247238707538[/C][C]57.8047621081463[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 23 )[/C][C]62.4545454545455[/C][C]1.02995729836164[/C][C]60.6379949478416[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 23 )[/C][C]62.3453125[/C][C]0.976519800653806[/C][C]63.8443915405076[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 23 )[/C][C]62.2451612903226[/C][C]0.925108587447318[/C][C]67.2841676479057[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 23 )[/C][C]62.16[/C][C]0.878214675890327[/C][C]70.77996042025[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 23 )[/C][C]62.0741379310345[/C][C]0.833006204436273[/C][C]74.5182179921966[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 23 )[/C][C]61.9875[/C][C]0.790101351792222[/C][C]78.4551245981177[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 23 )[/C][C]61.8981481481481[/C][C]0.748427145258104[/C][C]82.7043066787775[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 23 )[/C][C]61.7961538461538[/C][C]0.708406543311677[/C][C]87.2326130095688[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 23 )[/C][C]61.686[/C][C]0.66647418309691[/C][C]92.5557231839998[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 23 )[/C][C]61.5666666666667[/C][C]0.620700340365261[/C][C]99.1890331982689[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 23 )[/C][C]61.4478260869565[/C][C]0.576493977078742[/C][C]106.588843127781[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 23 )[/C][C]61.3295454545455[/C][C]0.529764991830611[/C][C]115.767456136768[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 23 )[/C][C]61.2238095238095[/C][C]0.480403546052008[/C][C]127.442459629933[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 23 )[/C][C]61.1325[/C][C]0.433979609292938[/C][C]140.864913214702[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 23 )[/C][C]61.0394736842105[/C][C]0.38904887254716[/C][C]156.894102493026[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 23 )[/C][C]60.9527777777778[/C][C]0.351470518782433[/C][C]173.422163511554[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 23 )[/C][C]60.8735294117647[/C][C]0.326770750548564[/C][C]186.28818310566[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 23 )[/C][C]60.79375[/C][C]0.309817112414988[/C][C]196.224635644300[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 23 )[/C][C]60.7133333333333[/C][C]0.291872013099323[/C][C]208.013549119123[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 23 )[/C][C]60.6357142857143[/C][C]0.274595146226341[/C][C]220.818594643818[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 23 )[/C][C]60.5653846153846[/C][C]0.260646669632536[/C][C]232.365848759052[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 23 )[/C][C]60.5[/C][C]0.249709976700508[/C][C]242.281068619702[/C][/ROW]
[ROW][C]Median[/C][C]60[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]67.05[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]60.8[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]60.9527777777778[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]60.9527777777778[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]60.9527777777778[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]60.8735294117647[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]60.9527777777778[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]60.9527777777778[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]60.9527777777778[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]70[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=50158&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=50158&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 Mean62.71.1349920877862955.2426758518568
Geometric Mean62.0274041652646
Harmonic Mean61.387564817268
Quadratic Mean63.4048601111483
Winsorized Mean ( 1 / 23 )62.68285714285711.1260421378370255.6665288416851
Winsorized Mean ( 2 / 23 )62.65428571428571.1107020996182656.4096221082316
Winsorized Mean ( 3 / 23 )62.61142857142861.0827549840643257.8260358926313
Winsorized Mean ( 4 / 23 )62.53714285714291.0430588307194959.9555279293359
Winsorized Mean ( 5 / 23 )62.51571428571431.0072647827171562.0648268046016
Winsorized Mean ( 6 / 23 )62.490.96601280806292464.6885832966405
Winsorized Mean ( 7 / 23 )62.470.92588126002228667.470854738432
Winsorized Mean ( 8 / 23 )62.50428571428570.88126211890240970.925873668703
Winsorized Mean ( 9 / 23 )62.50428571428570.84807524304423573.7013445763627
Winsorized Mean ( 10 / 23 )62.50428571428570.81719217228015976.4866427194034
Winsorized Mean ( 11 / 23 )62.42571428571430.7618890267526381.9354421624748
Winsorized Mean ( 12 / 23 )62.340.72065187881166586.5050127986857
Winsorized Mean ( 13 / 23 )62.15428571428570.67700376833263491.8078873731575
Winsorized Mean ( 14 / 23 )61.95428571428570.611469687671549101.320289400126
Winsorized Mean ( 15 / 23 )61.890.550486891583608112.42774523106
Winsorized Mean ( 16 / 23 )61.75285714285710.474490994264356130.145477763172
Winsorized Mean ( 17 / 23 )61.60714285714290.389134631726593158.318324390177
Winsorized Mean ( 18 / 23 )61.530.330802086909883186.002454140387
Winsorized Mean ( 19 / 23 )61.44857142857140.309442448297006198.578352022320
Winsorized Mean ( 20 / 23 )61.33428571428570.28268079074946216.973659765393
Winsorized Mean ( 21 / 23 )61.18428571428570.250462394033914244.28531856164
Winsorized Mean ( 22 / 23 )61.05857142857140.222506825048442274.412128325854
Winsorized Mean ( 23 / 23 )60.99285714285710.212549557524881286.958288001693
Trimmed Mean ( 1 / 23 )62.57205882352941.0824723870753857.8047621081463
Trimmed Mean ( 2 / 23 )62.45454545454551.0299572983616460.6379949478416
Trimmed Mean ( 3 / 23 )62.34531250.97651980065380663.8443915405076
Trimmed Mean ( 4 / 23 )62.24516129032260.92510858744731867.2841676479057
Trimmed Mean ( 5 / 23 )62.160.87821467589032770.77996042025
Trimmed Mean ( 6 / 23 )62.07413793103450.83300620443627374.5182179921966
Trimmed Mean ( 7 / 23 )61.98750.79010135179222278.4551245981177
Trimmed Mean ( 8 / 23 )61.89814814814810.74842714525810482.7043066787775
Trimmed Mean ( 9 / 23 )61.79615384615380.70840654331167787.2326130095688
Trimmed Mean ( 10 / 23 )61.6860.6664741830969192.5557231839998
Trimmed Mean ( 11 / 23 )61.56666666666670.62070034036526199.1890331982689
Trimmed Mean ( 12 / 23 )61.44782608695650.576493977078742106.588843127781
Trimmed Mean ( 13 / 23 )61.32954545454550.529764991830611115.767456136768
Trimmed Mean ( 14 / 23 )61.22380952380950.480403546052008127.442459629933
Trimmed Mean ( 15 / 23 )61.13250.433979609292938140.864913214702
Trimmed Mean ( 16 / 23 )61.03947368421050.38904887254716156.894102493026
Trimmed Mean ( 17 / 23 )60.95277777777780.351470518782433173.422163511554
Trimmed Mean ( 18 / 23 )60.87352941176470.326770750548564186.28818310566
Trimmed Mean ( 19 / 23 )60.793750.309817112414988196.224635644300
Trimmed Mean ( 20 / 23 )60.71333333333330.291872013099323208.013549119123
Trimmed Mean ( 21 / 23 )60.63571428571430.274595146226341220.818594643818
Trimmed Mean ( 22 / 23 )60.56538461538460.260646669632536232.365848759052
Trimmed Mean ( 23 / 23 )60.50.249709976700508242.281068619702
Median60
Midrange67.05
Midmean - Weighted Average at Xnp60.8
Midmean - Weighted Average at X(n+1)p60.9527777777778
Midmean - Empirical Distribution Function60.9527777777778
Midmean - Empirical Distribution Function - Averaging60.9527777777778
Midmean - Empirical Distribution Function - Interpolation60.8735294117647
Midmean - Closest Observation60.9527777777778
Midmean - True Basic - Statistics Graphics Toolkit60.9527777777778
Midmean - MS Excel (old versions)60.9527777777778
Number of observations70



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')