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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, 15 Oct 2011 09:33:37 -0400
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2011/Oct/15/t13186856985fgzd50wop3hmj0.htm/, Retrieved Wed, 15 May 2024 03:22:35 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=129805, Retrieved Wed, 15 May 2024 03:22:35 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsKDG2011W52a
Estimated Impact84
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [Robuustheid Expor...] [2011-10-15 13:33:37] [b59b09b8e0844ceffdb892999921d72c] [Current]
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Dataseries X:
14,5
15,1
17,4
16,2
15,6
17,2
14,9
13,8
17,5
16,2
17,5
16,6
16,2
16,6
19,6
15,9
18
18,3
16,3
14,9
18,2
18,4
18,5
16
17,4
17,2
19,6
17,2
18,3
19,3
18,1
16,2
18,4
20,5
19
16,5
18,7
19
19,2
20,5
19,3
20,6
20,1
16,1
20,4
19,7
15,6
14,4
13,7
14,1
15
14,2
13,6
15,4
14,8
12,5
16,2
16,1
16
15,8
14,9
15,4
18,6
17,1
16,8
19,5
17,3
15,8
19,3
18,8
18,5
17,3




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gwilym Jenkins' @ jenkins.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 & 1 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=129805&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=129805&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=129805&T=0

As an alternative you can also use a QR Code:  

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

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gwilym Jenkins' @ jenkins.wessa.net







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean17.04722222222220.22915415861914974.391939142394
Geometric Mean16.9362269683173
Harmonic Mean16.8237143547688
Quadratic Mean17.1562265988507
Winsorized Mean ( 1 / 24 )17.06111111111110.2250591606760575.807228018898
Winsorized Mean ( 2 / 24 )17.06388888888890.22446515770797376.0202120593203
Winsorized Mean ( 3 / 24 )17.06388888888890.22270658285811776.6204962147887
Winsorized Mean ( 4 / 24 )17.06388888888890.21596406082833879.0126321177686
Winsorized Mean ( 5 / 24 )17.04305555555560.2093923916130981.3929074703312
Winsorized Mean ( 6 / 24 )17.05138888888890.20480336246081683.2573678674403
Winsorized Mean ( 7 / 24 )17.06111111111110.20305333175835284.0228080148671
Winsorized Mean ( 8 / 24 )17.08333333333330.19539895387055987.4279672175219
Winsorized Mean ( 9 / 24 )17.07083333333330.18910502397846790.271707087365
Winsorized Mean ( 10 / 24 )17.07083333333330.18910502397846790.271707087365
Winsorized Mean ( 11 / 24 )17.07083333333330.18910502397846790.271707087365
Winsorized Mean ( 12 / 24 )17.07083333333330.1836897676822992.9329572829503
Winsorized Mean ( 13 / 24 )17.05277777777780.17505836520815497.4119560496357
Winsorized Mean ( 14 / 24 )17.11111111111110.16623836464344102.931180463741
Winsorized Mean ( 15 / 24 )17.06944444444440.159721967067905106.869735940501
Winsorized Mean ( 16 / 24 )17.09166666666670.149957610077086113.976654188345
Winsorized Mean ( 17 / 24 )17.06805555555560.146434226675774116.557829020033
Winsorized Mean ( 18 / 24 )17.09305555555560.135881265325241125.794056411252
Winsorized Mean ( 19 / 24 )17.09305555555560.135881265325241125.794056411252
Winsorized Mean ( 20 / 24 )17.09305555555560.128176789909079133.355310018922
Winsorized Mean ( 21 / 24 )17.12222222222220.124411324678361137.625913609457
Winsorized Mean ( 22 / 24 )17.09166666666670.120034391263804142.38974752747
Winsorized Mean ( 23 / 24 )17.12361111111110.116002351703597147.614344533845
Winsorized Mean ( 24 / 24 )17.09027777777780.111280070090311153.578963096518
Trimmed Mean ( 1 / 24 )17.06142857142860.2206361296023277.3283532582833
Trimmed Mean ( 2 / 24 )17.06176470588240.21536694508434679.221835547699
Trimmed Mean ( 3 / 24 )17.06060606060610.20944903623074981.4546887759868
Trimmed Mean ( 4 / 24 )17.0593750.20315857475877383.9707357676437
Trimmed Mean ( 5 / 24 )17.0580645161290.19809441722010986.1107786655859
Trimmed Mean ( 6 / 24 )17.06166666666670.1940221267984287.9367057160079
Trimmed Mean ( 7 / 24 )17.06379310344830.19030809350336689.6640431277634
Trimmed Mean ( 8 / 24 )17.06428571428570.18615083556273791.6691330592212
Trimmed Mean ( 9 / 24 )17.06111111111110.18283077042069693.3164098792193
Trimmed Mean ( 10 / 24 )17.05961538461540.18006324545387794.7423520086734
Trimmed Mean ( 11 / 24 )17.0580.17647547092084796.6593255764756
Trimmed Mean ( 12 / 24 )17.056250.17184094601389599.2560294600615
Trimmed Mean ( 13 / 24 )17.0543478260870.167092398915263102.065371834991
Trimmed Mean ( 14 / 24 )17.05454545454550.162871125899404104.711902495714
Trimmed Mean ( 15 / 24 )17.0476190476190.159238828777576107.056923104045
Trimmed Mean ( 16 / 24 )17.0450.155824934642727109.385574517201
Trimmed Mean ( 17 / 24 )17.03947368421050.153319805117642111.136807610316
Trimmed Mean ( 18 / 24 )17.03611111111110.150509862450556113.189334132224
Trimmed Mean ( 19 / 24 )17.02941176470590.148883510419892114.380778077292
Trimmed Mean ( 20 / 24 )17.0218750.146169806729001116.45274342846
Trimmed Mean ( 21 / 24 )17.01333333333330.143977435439408118.166664668043
Trimmed Mean ( 22 / 24 )170.141234167066932120.367474479059
Trimmed Mean ( 23 / 24 )16.98846153846150.138044242972141123.065338855819
Trimmed Mean ( 24 / 24 )16.97083333333330.133714920452771126.918022879336
Median17.15
Midrange16.55
Midmean - Weighted Average at Xnp16.9605263157895
Midmean - Weighted Average at X(n+1)p17.0361111111111
Midmean - Empirical Distribution Function16.9605263157895
Midmean - Empirical Distribution Function - Averaging17.0361111111111
Midmean - Empirical Distribution Function - Interpolation17.0361111111111
Midmean - Closest Observation16.9605263157895
Midmean - True Basic - Statistics Graphics Toolkit17.0361111111111
Midmean - MS Excel (old versions)17.0025641025641
Number of observations72

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 17.0472222222222 & 0.229154158619149 & 74.391939142394 \tabularnewline
Geometric Mean & 16.9362269683173 &  &  \tabularnewline
Harmonic Mean & 16.8237143547688 &  &  \tabularnewline
Quadratic Mean & 17.1562265988507 &  &  \tabularnewline
Winsorized Mean ( 1 / 24 ) & 17.0611111111111 & 0.22505916067605 & 75.807228018898 \tabularnewline
Winsorized Mean ( 2 / 24 ) & 17.0638888888889 & 0.224465157707973 & 76.0202120593203 \tabularnewline
Winsorized Mean ( 3 / 24 ) & 17.0638888888889 & 0.222706582858117 & 76.6204962147887 \tabularnewline
Winsorized Mean ( 4 / 24 ) & 17.0638888888889 & 0.215964060828338 & 79.0126321177686 \tabularnewline
Winsorized Mean ( 5 / 24 ) & 17.0430555555556 & 0.20939239161309 & 81.3929074703312 \tabularnewline
Winsorized Mean ( 6 / 24 ) & 17.0513888888889 & 0.204803362460816 & 83.2573678674403 \tabularnewline
Winsorized Mean ( 7 / 24 ) & 17.0611111111111 & 0.203053331758352 & 84.0228080148671 \tabularnewline
Winsorized Mean ( 8 / 24 ) & 17.0833333333333 & 0.195398953870559 & 87.4279672175219 \tabularnewline
Winsorized Mean ( 9 / 24 ) & 17.0708333333333 & 0.189105023978467 & 90.271707087365 \tabularnewline
Winsorized Mean ( 10 / 24 ) & 17.0708333333333 & 0.189105023978467 & 90.271707087365 \tabularnewline
Winsorized Mean ( 11 / 24 ) & 17.0708333333333 & 0.189105023978467 & 90.271707087365 \tabularnewline
Winsorized Mean ( 12 / 24 ) & 17.0708333333333 & 0.18368976768229 & 92.9329572829503 \tabularnewline
Winsorized Mean ( 13 / 24 ) & 17.0527777777778 & 0.175058365208154 & 97.4119560496357 \tabularnewline
Winsorized Mean ( 14 / 24 ) & 17.1111111111111 & 0.16623836464344 & 102.931180463741 \tabularnewline
Winsorized Mean ( 15 / 24 ) & 17.0694444444444 & 0.159721967067905 & 106.869735940501 \tabularnewline
Winsorized Mean ( 16 / 24 ) & 17.0916666666667 & 0.149957610077086 & 113.976654188345 \tabularnewline
Winsorized Mean ( 17 / 24 ) & 17.0680555555556 & 0.146434226675774 & 116.557829020033 \tabularnewline
Winsorized Mean ( 18 / 24 ) & 17.0930555555556 & 0.135881265325241 & 125.794056411252 \tabularnewline
Winsorized Mean ( 19 / 24 ) & 17.0930555555556 & 0.135881265325241 & 125.794056411252 \tabularnewline
Winsorized Mean ( 20 / 24 ) & 17.0930555555556 & 0.128176789909079 & 133.355310018922 \tabularnewline
Winsorized Mean ( 21 / 24 ) & 17.1222222222222 & 0.124411324678361 & 137.625913609457 \tabularnewline
Winsorized Mean ( 22 / 24 ) & 17.0916666666667 & 0.120034391263804 & 142.38974752747 \tabularnewline
Winsorized Mean ( 23 / 24 ) & 17.1236111111111 & 0.116002351703597 & 147.614344533845 \tabularnewline
Winsorized Mean ( 24 / 24 ) & 17.0902777777778 & 0.111280070090311 & 153.578963096518 \tabularnewline
Trimmed Mean ( 1 / 24 ) & 17.0614285714286 & 0.22063612960232 & 77.3283532582833 \tabularnewline
Trimmed Mean ( 2 / 24 ) & 17.0617647058824 & 0.215366945084346 & 79.221835547699 \tabularnewline
Trimmed Mean ( 3 / 24 ) & 17.0606060606061 & 0.209449036230749 & 81.4546887759868 \tabularnewline
Trimmed Mean ( 4 / 24 ) & 17.059375 & 0.203158574758773 & 83.9707357676437 \tabularnewline
Trimmed Mean ( 5 / 24 ) & 17.058064516129 & 0.198094417220109 & 86.1107786655859 \tabularnewline
Trimmed Mean ( 6 / 24 ) & 17.0616666666667 & 0.19402212679842 & 87.9367057160079 \tabularnewline
Trimmed Mean ( 7 / 24 ) & 17.0637931034483 & 0.190308093503366 & 89.6640431277634 \tabularnewline
Trimmed Mean ( 8 / 24 ) & 17.0642857142857 & 0.186150835562737 & 91.6691330592212 \tabularnewline
Trimmed Mean ( 9 / 24 ) & 17.0611111111111 & 0.182830770420696 & 93.3164098792193 \tabularnewline
Trimmed Mean ( 10 / 24 ) & 17.0596153846154 & 0.180063245453877 & 94.7423520086734 \tabularnewline
Trimmed Mean ( 11 / 24 ) & 17.058 & 0.176475470920847 & 96.6593255764756 \tabularnewline
Trimmed Mean ( 12 / 24 ) & 17.05625 & 0.171840946013895 & 99.2560294600615 \tabularnewline
Trimmed Mean ( 13 / 24 ) & 17.054347826087 & 0.167092398915263 & 102.065371834991 \tabularnewline
Trimmed Mean ( 14 / 24 ) & 17.0545454545455 & 0.162871125899404 & 104.711902495714 \tabularnewline
Trimmed Mean ( 15 / 24 ) & 17.047619047619 & 0.159238828777576 & 107.056923104045 \tabularnewline
Trimmed Mean ( 16 / 24 ) & 17.045 & 0.155824934642727 & 109.385574517201 \tabularnewline
Trimmed Mean ( 17 / 24 ) & 17.0394736842105 & 0.153319805117642 & 111.136807610316 \tabularnewline
Trimmed Mean ( 18 / 24 ) & 17.0361111111111 & 0.150509862450556 & 113.189334132224 \tabularnewline
Trimmed Mean ( 19 / 24 ) & 17.0294117647059 & 0.148883510419892 & 114.380778077292 \tabularnewline
Trimmed Mean ( 20 / 24 ) & 17.021875 & 0.146169806729001 & 116.45274342846 \tabularnewline
Trimmed Mean ( 21 / 24 ) & 17.0133333333333 & 0.143977435439408 & 118.166664668043 \tabularnewline
Trimmed Mean ( 22 / 24 ) & 17 & 0.141234167066932 & 120.367474479059 \tabularnewline
Trimmed Mean ( 23 / 24 ) & 16.9884615384615 & 0.138044242972141 & 123.065338855819 \tabularnewline
Trimmed Mean ( 24 / 24 ) & 16.9708333333333 & 0.133714920452771 & 126.918022879336 \tabularnewline
Median & 17.15 &  &  \tabularnewline
Midrange & 16.55 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 16.9605263157895 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 17.0361111111111 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 16.9605263157895 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 17.0361111111111 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 17.0361111111111 &  &  \tabularnewline
Midmean - Closest Observation & 16.9605263157895 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 17.0361111111111 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 17.0025641025641 &  &  \tabularnewline
Number of observations & 72 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=129805&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]17.0472222222222[/C][C]0.229154158619149[/C][C]74.391939142394[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]16.9362269683173[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]16.8237143547688[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]17.1562265988507[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 24 )[/C][C]17.0611111111111[/C][C]0.22505916067605[/C][C]75.807228018898[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 24 )[/C][C]17.0638888888889[/C][C]0.224465157707973[/C][C]76.0202120593203[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 24 )[/C][C]17.0638888888889[/C][C]0.222706582858117[/C][C]76.6204962147887[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 24 )[/C][C]17.0638888888889[/C][C]0.215964060828338[/C][C]79.0126321177686[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 24 )[/C][C]17.0430555555556[/C][C]0.20939239161309[/C][C]81.3929074703312[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 24 )[/C][C]17.0513888888889[/C][C]0.204803362460816[/C][C]83.2573678674403[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 24 )[/C][C]17.0611111111111[/C][C]0.203053331758352[/C][C]84.0228080148671[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 24 )[/C][C]17.0833333333333[/C][C]0.195398953870559[/C][C]87.4279672175219[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 24 )[/C][C]17.0708333333333[/C][C]0.189105023978467[/C][C]90.271707087365[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 24 )[/C][C]17.0708333333333[/C][C]0.189105023978467[/C][C]90.271707087365[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 24 )[/C][C]17.0708333333333[/C][C]0.189105023978467[/C][C]90.271707087365[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 24 )[/C][C]17.0708333333333[/C][C]0.18368976768229[/C][C]92.9329572829503[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 24 )[/C][C]17.0527777777778[/C][C]0.175058365208154[/C][C]97.4119560496357[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 24 )[/C][C]17.1111111111111[/C][C]0.16623836464344[/C][C]102.931180463741[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 24 )[/C][C]17.0694444444444[/C][C]0.159721967067905[/C][C]106.869735940501[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 24 )[/C][C]17.0916666666667[/C][C]0.149957610077086[/C][C]113.976654188345[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 24 )[/C][C]17.0680555555556[/C][C]0.146434226675774[/C][C]116.557829020033[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 24 )[/C][C]17.0930555555556[/C][C]0.135881265325241[/C][C]125.794056411252[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 24 )[/C][C]17.0930555555556[/C][C]0.135881265325241[/C][C]125.794056411252[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 24 )[/C][C]17.0930555555556[/C][C]0.128176789909079[/C][C]133.355310018922[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 24 )[/C][C]17.1222222222222[/C][C]0.124411324678361[/C][C]137.625913609457[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 24 )[/C][C]17.0916666666667[/C][C]0.120034391263804[/C][C]142.38974752747[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 24 )[/C][C]17.1236111111111[/C][C]0.116002351703597[/C][C]147.614344533845[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 24 )[/C][C]17.0902777777778[/C][C]0.111280070090311[/C][C]153.578963096518[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 24 )[/C][C]17.0614285714286[/C][C]0.22063612960232[/C][C]77.3283532582833[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 24 )[/C][C]17.0617647058824[/C][C]0.215366945084346[/C][C]79.221835547699[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 24 )[/C][C]17.0606060606061[/C][C]0.209449036230749[/C][C]81.4546887759868[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 24 )[/C][C]17.059375[/C][C]0.203158574758773[/C][C]83.9707357676437[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 24 )[/C][C]17.058064516129[/C][C]0.198094417220109[/C][C]86.1107786655859[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 24 )[/C][C]17.0616666666667[/C][C]0.19402212679842[/C][C]87.9367057160079[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 24 )[/C][C]17.0637931034483[/C][C]0.190308093503366[/C][C]89.6640431277634[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 24 )[/C][C]17.0642857142857[/C][C]0.186150835562737[/C][C]91.6691330592212[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 24 )[/C][C]17.0611111111111[/C][C]0.182830770420696[/C][C]93.3164098792193[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 24 )[/C][C]17.0596153846154[/C][C]0.180063245453877[/C][C]94.7423520086734[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 24 )[/C][C]17.058[/C][C]0.176475470920847[/C][C]96.6593255764756[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 24 )[/C][C]17.05625[/C][C]0.171840946013895[/C][C]99.2560294600615[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 24 )[/C][C]17.054347826087[/C][C]0.167092398915263[/C][C]102.065371834991[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 24 )[/C][C]17.0545454545455[/C][C]0.162871125899404[/C][C]104.711902495714[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 24 )[/C][C]17.047619047619[/C][C]0.159238828777576[/C][C]107.056923104045[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 24 )[/C][C]17.045[/C][C]0.155824934642727[/C][C]109.385574517201[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 24 )[/C][C]17.0394736842105[/C][C]0.153319805117642[/C][C]111.136807610316[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 24 )[/C][C]17.0361111111111[/C][C]0.150509862450556[/C][C]113.189334132224[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 24 )[/C][C]17.0294117647059[/C][C]0.148883510419892[/C][C]114.380778077292[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 24 )[/C][C]17.021875[/C][C]0.146169806729001[/C][C]116.45274342846[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 24 )[/C][C]17.0133333333333[/C][C]0.143977435439408[/C][C]118.166664668043[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 24 )[/C][C]17[/C][C]0.141234167066932[/C][C]120.367474479059[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 24 )[/C][C]16.9884615384615[/C][C]0.138044242972141[/C][C]123.065338855819[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 24 )[/C][C]16.9708333333333[/C][C]0.133714920452771[/C][C]126.918022879336[/C][/ROW]
[ROW][C]Median[/C][C]17.15[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]16.55[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]16.9605263157895[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]17.0361111111111[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]16.9605263157895[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]17.0361111111111[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]17.0361111111111[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]16.9605263157895[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]17.0361111111111[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]17.0025641025641[/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=129805&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=129805&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 Mean17.04722222222220.22915415861914974.391939142394
Geometric Mean16.9362269683173
Harmonic Mean16.8237143547688
Quadratic Mean17.1562265988507
Winsorized Mean ( 1 / 24 )17.06111111111110.2250591606760575.807228018898
Winsorized Mean ( 2 / 24 )17.06388888888890.22446515770797376.0202120593203
Winsorized Mean ( 3 / 24 )17.06388888888890.22270658285811776.6204962147887
Winsorized Mean ( 4 / 24 )17.06388888888890.21596406082833879.0126321177686
Winsorized Mean ( 5 / 24 )17.04305555555560.2093923916130981.3929074703312
Winsorized Mean ( 6 / 24 )17.05138888888890.20480336246081683.2573678674403
Winsorized Mean ( 7 / 24 )17.06111111111110.20305333175835284.0228080148671
Winsorized Mean ( 8 / 24 )17.08333333333330.19539895387055987.4279672175219
Winsorized Mean ( 9 / 24 )17.07083333333330.18910502397846790.271707087365
Winsorized Mean ( 10 / 24 )17.07083333333330.18910502397846790.271707087365
Winsorized Mean ( 11 / 24 )17.07083333333330.18910502397846790.271707087365
Winsorized Mean ( 12 / 24 )17.07083333333330.1836897676822992.9329572829503
Winsorized Mean ( 13 / 24 )17.05277777777780.17505836520815497.4119560496357
Winsorized Mean ( 14 / 24 )17.11111111111110.16623836464344102.931180463741
Winsorized Mean ( 15 / 24 )17.06944444444440.159721967067905106.869735940501
Winsorized Mean ( 16 / 24 )17.09166666666670.149957610077086113.976654188345
Winsorized Mean ( 17 / 24 )17.06805555555560.146434226675774116.557829020033
Winsorized Mean ( 18 / 24 )17.09305555555560.135881265325241125.794056411252
Winsorized Mean ( 19 / 24 )17.09305555555560.135881265325241125.794056411252
Winsorized Mean ( 20 / 24 )17.09305555555560.128176789909079133.355310018922
Winsorized Mean ( 21 / 24 )17.12222222222220.124411324678361137.625913609457
Winsorized Mean ( 22 / 24 )17.09166666666670.120034391263804142.38974752747
Winsorized Mean ( 23 / 24 )17.12361111111110.116002351703597147.614344533845
Winsorized Mean ( 24 / 24 )17.09027777777780.111280070090311153.578963096518
Trimmed Mean ( 1 / 24 )17.06142857142860.2206361296023277.3283532582833
Trimmed Mean ( 2 / 24 )17.06176470588240.21536694508434679.221835547699
Trimmed Mean ( 3 / 24 )17.06060606060610.20944903623074981.4546887759868
Trimmed Mean ( 4 / 24 )17.0593750.20315857475877383.9707357676437
Trimmed Mean ( 5 / 24 )17.0580645161290.19809441722010986.1107786655859
Trimmed Mean ( 6 / 24 )17.06166666666670.1940221267984287.9367057160079
Trimmed Mean ( 7 / 24 )17.06379310344830.19030809350336689.6640431277634
Trimmed Mean ( 8 / 24 )17.06428571428570.18615083556273791.6691330592212
Trimmed Mean ( 9 / 24 )17.06111111111110.18283077042069693.3164098792193
Trimmed Mean ( 10 / 24 )17.05961538461540.18006324545387794.7423520086734
Trimmed Mean ( 11 / 24 )17.0580.17647547092084796.6593255764756
Trimmed Mean ( 12 / 24 )17.056250.17184094601389599.2560294600615
Trimmed Mean ( 13 / 24 )17.0543478260870.167092398915263102.065371834991
Trimmed Mean ( 14 / 24 )17.05454545454550.162871125899404104.711902495714
Trimmed Mean ( 15 / 24 )17.0476190476190.159238828777576107.056923104045
Trimmed Mean ( 16 / 24 )17.0450.155824934642727109.385574517201
Trimmed Mean ( 17 / 24 )17.03947368421050.153319805117642111.136807610316
Trimmed Mean ( 18 / 24 )17.03611111111110.150509862450556113.189334132224
Trimmed Mean ( 19 / 24 )17.02941176470590.148883510419892114.380778077292
Trimmed Mean ( 20 / 24 )17.0218750.146169806729001116.45274342846
Trimmed Mean ( 21 / 24 )17.01333333333330.143977435439408118.166664668043
Trimmed Mean ( 22 / 24 )170.141234167066932120.367474479059
Trimmed Mean ( 23 / 24 )16.98846153846150.138044242972141123.065338855819
Trimmed Mean ( 24 / 24 )16.97083333333330.133714920452771126.918022879336
Median17.15
Midrange16.55
Midmean - Weighted Average at Xnp16.9605263157895
Midmean - Weighted Average at X(n+1)p17.0361111111111
Midmean - Empirical Distribution Function16.9605263157895
Midmean - Empirical Distribution Function - Averaging17.0361111111111
Midmean - Empirical Distribution Function - Interpolation17.0361111111111
Midmean - Closest Observation16.9605263157895
Midmean - True Basic - Statistics Graphics Toolkit17.0361111111111
Midmean - MS Excel (old versions)17.0025641025641
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')