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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 computationMon, 22 Oct 2007 01:52:36 -0700
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2007/Oct/22/b9gwqhue6bg49n11193042924.htm/, Retrieved Sun, 05 May 2024 22:25:57 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=1415, Retrieved Sun, 05 May 2024 22:25:57 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsgroep 1, ws1, deel1, vraag 8
Estimated Impact187
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [vraag 8, mannen j...] [2007-10-22 08:52:36] [234bcf6fb77cd83fa17f2489a043102b] [Current]
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Dataseries X:
16,8
18,7
18,7
18,7
16,8
16,8
16,8
16,0
16,0
16,0
18,0
18,0
18,0
18,0
18,0
18,0
21,6
21,6
21,6
20,1
20,1
20,1
22,9
22,9
22,9
24,0
24,0
24,0
20,3
20,3
20,3
15,8
15,8
15,8
23,2
23,2
23,2
20,9
20,9
20,9
19,8
19,8
19,8
20,6
20,6
20,6
21,1
21,1
21,1
22,4
22,4
22,4
20,5
20,5
20,5
18,4
18,4
18,4
17,6
17,6
17,6
18,5
18,5
18,5
17,3
17,3
17,3
16,2
16,2
16,2
18,0
18,0
18,0




Summary of compuational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135

\begin{tabular}{lllllllll}
\hline
Summary of compuational 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' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=1415&T=0

[TABLE]
[ROW][C]Summary of compuational 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' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=1415&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=1415&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 compuational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean19.40958904109590.27296475583546871.1065755785527
Geometric Mean19.2726145924944
Harmonic Mean19.1373519258611
Quadratic Mean19.5472977496908
Winsorized Mean ( 1 / 24 )19.40958904109590.27296475583546871.1065755785527
Winsorized Mean ( 2 / 24 )19.40958904109590.27296475583546871.1065755785527
Winsorized Mean ( 3 / 24 )19.38493150684930.26433535179255473.3346159542908
Winsorized Mean ( 4 / 24 )19.38493150684930.26433535179255473.3346159542908
Winsorized Mean ( 5 / 24 )19.38493150684930.26433535179255473.3346159542908
Winsorized Mean ( 6 / 24 )19.37671232876710.25663583213309775.5027548870026
Winsorized Mean ( 7 / 24 )19.37671232876710.25663583213309775.5027548870026
Winsorized Mean ( 8 / 24 )19.37671232876710.25663583213309775.5027548870026
Winsorized Mean ( 9 / 24 )19.38904109589040.23311765671334483.172769361406
Winsorized Mean ( 10 / 24 )19.38904109589040.23311765671334483.172769361406
Winsorized Mean ( 11 / 24 )19.38904109589040.23311765671334483.172769361406
Winsorized Mean ( 12 / 24 )19.25753424657530.21110636487692591.2219499293756
Winsorized Mean ( 13 / 24 )19.34657534246580.19747340718199897.9705349623878
Winsorized Mean ( 14 / 24 )19.34657534246580.19747340718199897.9705349623878
Winsorized Mean ( 15 / 24 )19.24383561643840.182020896961396105.723221551423
Winsorized Mean ( 16 / 24 )19.30958904109590.172612705372955111.866556980117
Winsorized Mean ( 17 / 24 )19.30958904109590.172612705372955111.866556980117
Winsorized Mean ( 18 / 24 )19.26027397260270.165667550116019116.258579058570
Winsorized Mean ( 19 / 24 )19.36438356164380.151895304895230127.485069897324
Winsorized Mean ( 20 / 24 )19.36438356164380.151895304895230127.485069897324
Winsorized Mean ( 21 / 24 )19.27808219178080.140167959904535137.535583773286
Winsorized Mean ( 22 / 24 )19.27808219178080.140167959904535137.535583773286
Winsorized Mean ( 23 / 24 )19.27808219178080.140167959904535137.535583773286
Winsorized Mean ( 24 / 24 )19.24520547945210.135906129412030141.606604225375
Trimmed Mean ( 1 / 24 )19.39577464788730.26820392718642872.3172656394602
Trimmed Mean ( 2 / 24 )19.38115942028990.26252329383367273.8264370268386
Trimmed Mean ( 3 / 24 )19.36567164179100.25573080811280475.7267838971077
Trimmed Mean ( 4 / 24 )19.35846153846150.25151361321633576.9678479463086
Trimmed Mean ( 5 / 24 )19.35079365079370.24638578494383878.5385961093678
Trimmed Mean ( 6 / 24 )19.34262295081970.24014407124259780.5459108389957
Trimmed Mean ( 7 / 24 )19.3355932203390.2347233435228282.3760983042538
Trimmed Mean ( 8 / 24 )19.32807017543860.22804270125630384.756363913245
Trimmed Mean ( 9 / 24 )19.320.21977031168697487.9099631415096
Trimmed Mean ( 10 / 24 )19.30943396226420.21517644143874789.7376768253735
Trimmed Mean ( 11 / 24 )19.29803921568630.20934051809972792.1849214421688
Trimmed Mean ( 12 / 24 )19.28571428571430.20190420035860895.5191335864254
Trimmed Mean ( 13 / 24 )19.28936170212770.19751541919348697.6600296872611
Trimmed Mean ( 14 / 24 )19.28222222222220.19468412356577799.0436295936964
Trimmed Mean ( 15 / 24 )19.27441860465120.190792861747083101.022744919050
Trimmed Mean ( 16 / 24 )19.27804878048780.188883503751101102.063168024939
Trimmed Mean ( 17 / 24 )19.27435897435900.187990221007834102.528519148641
Trimmed Mean ( 18 / 24 )19.27027027027030.186313407082345103.429326810353
Trimmed Mean ( 19 / 24 )19.27142857142860.185144568930773104.088543794305
Trimmed Mean ( 20 / 24 )19.26060606060610.185962860515955103.572326254648
Trimmed Mean ( 21 / 24 )19.24838709677420.186182415333448103.384560041832
Trimmed Mean ( 22 / 24 )19.24482758620690.188498487985505102.095394991639
Trimmed Mean ( 23 / 24 )19.24074074074070.190460475089949101.022223806036
Trimmed Mean ( 24 / 24 )19.2360.191822834928483100.280031869885
Median18.7
Midrange19.9
Midmean - Weighted Average at Xnp19.1846153846154
Midmean - Weighted Average at X(n+1)p19.1846153846154
Midmean - Empirical Distribution Function19.1846153846154
Midmean - Empirical Distribution Function - Averaging19.1846153846154
Midmean - Empirical Distribution Function - Interpolation19.1846153846154
Midmean - Closest Observation19.1846153846154
Midmean - True Basic - Statistics Graphics Toolkit19.1846153846154
Midmean - MS Excel (old versions)19.1846153846154
Number of observations73

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 19.4095890410959 & 0.272964755835468 & 71.1065755785527 \tabularnewline
Geometric Mean & 19.2726145924944 &  &  \tabularnewline
Harmonic Mean & 19.1373519258611 &  &  \tabularnewline
Quadratic Mean & 19.5472977496908 &  &  \tabularnewline
Winsorized Mean ( 1 / 24 ) & 19.4095890410959 & 0.272964755835468 & 71.1065755785527 \tabularnewline
Winsorized Mean ( 2 / 24 ) & 19.4095890410959 & 0.272964755835468 & 71.1065755785527 \tabularnewline
Winsorized Mean ( 3 / 24 ) & 19.3849315068493 & 0.264335351792554 & 73.3346159542908 \tabularnewline
Winsorized Mean ( 4 / 24 ) & 19.3849315068493 & 0.264335351792554 & 73.3346159542908 \tabularnewline
Winsorized Mean ( 5 / 24 ) & 19.3849315068493 & 0.264335351792554 & 73.3346159542908 \tabularnewline
Winsorized Mean ( 6 / 24 ) & 19.3767123287671 & 0.256635832133097 & 75.5027548870026 \tabularnewline
Winsorized Mean ( 7 / 24 ) & 19.3767123287671 & 0.256635832133097 & 75.5027548870026 \tabularnewline
Winsorized Mean ( 8 / 24 ) & 19.3767123287671 & 0.256635832133097 & 75.5027548870026 \tabularnewline
Winsorized Mean ( 9 / 24 ) & 19.3890410958904 & 0.233117656713344 & 83.172769361406 \tabularnewline
Winsorized Mean ( 10 / 24 ) & 19.3890410958904 & 0.233117656713344 & 83.172769361406 \tabularnewline
Winsorized Mean ( 11 / 24 ) & 19.3890410958904 & 0.233117656713344 & 83.172769361406 \tabularnewline
Winsorized Mean ( 12 / 24 ) & 19.2575342465753 & 0.211106364876925 & 91.2219499293756 \tabularnewline
Winsorized Mean ( 13 / 24 ) & 19.3465753424658 & 0.197473407181998 & 97.9705349623878 \tabularnewline
Winsorized Mean ( 14 / 24 ) & 19.3465753424658 & 0.197473407181998 & 97.9705349623878 \tabularnewline
Winsorized Mean ( 15 / 24 ) & 19.2438356164384 & 0.182020896961396 & 105.723221551423 \tabularnewline
Winsorized Mean ( 16 / 24 ) & 19.3095890410959 & 0.172612705372955 & 111.866556980117 \tabularnewline
Winsorized Mean ( 17 / 24 ) & 19.3095890410959 & 0.172612705372955 & 111.866556980117 \tabularnewline
Winsorized Mean ( 18 / 24 ) & 19.2602739726027 & 0.165667550116019 & 116.258579058570 \tabularnewline
Winsorized Mean ( 19 / 24 ) & 19.3643835616438 & 0.151895304895230 & 127.485069897324 \tabularnewline
Winsorized Mean ( 20 / 24 ) & 19.3643835616438 & 0.151895304895230 & 127.485069897324 \tabularnewline
Winsorized Mean ( 21 / 24 ) & 19.2780821917808 & 0.140167959904535 & 137.535583773286 \tabularnewline
Winsorized Mean ( 22 / 24 ) & 19.2780821917808 & 0.140167959904535 & 137.535583773286 \tabularnewline
Winsorized Mean ( 23 / 24 ) & 19.2780821917808 & 0.140167959904535 & 137.535583773286 \tabularnewline
Winsorized Mean ( 24 / 24 ) & 19.2452054794521 & 0.135906129412030 & 141.606604225375 \tabularnewline
Trimmed Mean ( 1 / 24 ) & 19.3957746478873 & 0.268203927186428 & 72.3172656394602 \tabularnewline
Trimmed Mean ( 2 / 24 ) & 19.3811594202899 & 0.262523293833672 & 73.8264370268386 \tabularnewline
Trimmed Mean ( 3 / 24 ) & 19.3656716417910 & 0.255730808112804 & 75.7267838971077 \tabularnewline
Trimmed Mean ( 4 / 24 ) & 19.3584615384615 & 0.251513613216335 & 76.9678479463086 \tabularnewline
Trimmed Mean ( 5 / 24 ) & 19.3507936507937 & 0.246385784943838 & 78.5385961093678 \tabularnewline
Trimmed Mean ( 6 / 24 ) & 19.3426229508197 & 0.240144071242597 & 80.5459108389957 \tabularnewline
Trimmed Mean ( 7 / 24 ) & 19.335593220339 & 0.23472334352282 & 82.3760983042538 \tabularnewline
Trimmed Mean ( 8 / 24 ) & 19.3280701754386 & 0.228042701256303 & 84.756363913245 \tabularnewline
Trimmed Mean ( 9 / 24 ) & 19.32 & 0.219770311686974 & 87.9099631415096 \tabularnewline
Trimmed Mean ( 10 / 24 ) & 19.3094339622642 & 0.215176441438747 & 89.7376768253735 \tabularnewline
Trimmed Mean ( 11 / 24 ) & 19.2980392156863 & 0.209340518099727 & 92.1849214421688 \tabularnewline
Trimmed Mean ( 12 / 24 ) & 19.2857142857143 & 0.201904200358608 & 95.5191335864254 \tabularnewline
Trimmed Mean ( 13 / 24 ) & 19.2893617021277 & 0.197515419193486 & 97.6600296872611 \tabularnewline
Trimmed Mean ( 14 / 24 ) & 19.2822222222222 & 0.194684123565777 & 99.0436295936964 \tabularnewline
Trimmed Mean ( 15 / 24 ) & 19.2744186046512 & 0.190792861747083 & 101.022744919050 \tabularnewline
Trimmed Mean ( 16 / 24 ) & 19.2780487804878 & 0.188883503751101 & 102.063168024939 \tabularnewline
Trimmed Mean ( 17 / 24 ) & 19.2743589743590 & 0.187990221007834 & 102.528519148641 \tabularnewline
Trimmed Mean ( 18 / 24 ) & 19.2702702702703 & 0.186313407082345 & 103.429326810353 \tabularnewline
Trimmed Mean ( 19 / 24 ) & 19.2714285714286 & 0.185144568930773 & 104.088543794305 \tabularnewline
Trimmed Mean ( 20 / 24 ) & 19.2606060606061 & 0.185962860515955 & 103.572326254648 \tabularnewline
Trimmed Mean ( 21 / 24 ) & 19.2483870967742 & 0.186182415333448 & 103.384560041832 \tabularnewline
Trimmed Mean ( 22 / 24 ) & 19.2448275862069 & 0.188498487985505 & 102.095394991639 \tabularnewline
Trimmed Mean ( 23 / 24 ) & 19.2407407407407 & 0.190460475089949 & 101.022223806036 \tabularnewline
Trimmed Mean ( 24 / 24 ) & 19.236 & 0.191822834928483 & 100.280031869885 \tabularnewline
Median & 18.7 &  &  \tabularnewline
Midrange & 19.9 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 19.1846153846154 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 19.1846153846154 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 19.1846153846154 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 19.1846153846154 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 19.1846153846154 &  &  \tabularnewline
Midmean - Closest Observation & 19.1846153846154 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 19.1846153846154 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 19.1846153846154 &  &  \tabularnewline
Number of observations & 73 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=1415&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]19.4095890410959[/C][C]0.272964755835468[/C][C]71.1065755785527[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]19.2726145924944[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]19.1373519258611[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]19.5472977496908[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 24 )[/C][C]19.4095890410959[/C][C]0.272964755835468[/C][C]71.1065755785527[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 24 )[/C][C]19.4095890410959[/C][C]0.272964755835468[/C][C]71.1065755785527[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 24 )[/C][C]19.3849315068493[/C][C]0.264335351792554[/C][C]73.3346159542908[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 24 )[/C][C]19.3849315068493[/C][C]0.264335351792554[/C][C]73.3346159542908[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 24 )[/C][C]19.3849315068493[/C][C]0.264335351792554[/C][C]73.3346159542908[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 24 )[/C][C]19.3767123287671[/C][C]0.256635832133097[/C][C]75.5027548870026[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 24 )[/C][C]19.3767123287671[/C][C]0.256635832133097[/C][C]75.5027548870026[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 24 )[/C][C]19.3767123287671[/C][C]0.256635832133097[/C][C]75.5027548870026[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 24 )[/C][C]19.3890410958904[/C][C]0.233117656713344[/C][C]83.172769361406[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 24 )[/C][C]19.3890410958904[/C][C]0.233117656713344[/C][C]83.172769361406[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 24 )[/C][C]19.3890410958904[/C][C]0.233117656713344[/C][C]83.172769361406[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 24 )[/C][C]19.2575342465753[/C][C]0.211106364876925[/C][C]91.2219499293756[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 24 )[/C][C]19.3465753424658[/C][C]0.197473407181998[/C][C]97.9705349623878[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 24 )[/C][C]19.3465753424658[/C][C]0.197473407181998[/C][C]97.9705349623878[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 24 )[/C][C]19.2438356164384[/C][C]0.182020896961396[/C][C]105.723221551423[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 24 )[/C][C]19.3095890410959[/C][C]0.172612705372955[/C][C]111.866556980117[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 24 )[/C][C]19.3095890410959[/C][C]0.172612705372955[/C][C]111.866556980117[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 24 )[/C][C]19.2602739726027[/C][C]0.165667550116019[/C][C]116.258579058570[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 24 )[/C][C]19.3643835616438[/C][C]0.151895304895230[/C][C]127.485069897324[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 24 )[/C][C]19.3643835616438[/C][C]0.151895304895230[/C][C]127.485069897324[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 24 )[/C][C]19.2780821917808[/C][C]0.140167959904535[/C][C]137.535583773286[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 24 )[/C][C]19.2780821917808[/C][C]0.140167959904535[/C][C]137.535583773286[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 24 )[/C][C]19.2780821917808[/C][C]0.140167959904535[/C][C]137.535583773286[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 24 )[/C][C]19.2452054794521[/C][C]0.135906129412030[/C][C]141.606604225375[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 24 )[/C][C]19.3957746478873[/C][C]0.268203927186428[/C][C]72.3172656394602[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 24 )[/C][C]19.3811594202899[/C][C]0.262523293833672[/C][C]73.8264370268386[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 24 )[/C][C]19.3656716417910[/C][C]0.255730808112804[/C][C]75.7267838971077[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 24 )[/C][C]19.3584615384615[/C][C]0.251513613216335[/C][C]76.9678479463086[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 24 )[/C][C]19.3507936507937[/C][C]0.246385784943838[/C][C]78.5385961093678[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 24 )[/C][C]19.3426229508197[/C][C]0.240144071242597[/C][C]80.5459108389957[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 24 )[/C][C]19.335593220339[/C][C]0.23472334352282[/C][C]82.3760983042538[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 24 )[/C][C]19.3280701754386[/C][C]0.228042701256303[/C][C]84.756363913245[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 24 )[/C][C]19.32[/C][C]0.219770311686974[/C][C]87.9099631415096[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 24 )[/C][C]19.3094339622642[/C][C]0.215176441438747[/C][C]89.7376768253735[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 24 )[/C][C]19.2980392156863[/C][C]0.209340518099727[/C][C]92.1849214421688[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 24 )[/C][C]19.2857142857143[/C][C]0.201904200358608[/C][C]95.5191335864254[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 24 )[/C][C]19.2893617021277[/C][C]0.197515419193486[/C][C]97.6600296872611[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 24 )[/C][C]19.2822222222222[/C][C]0.194684123565777[/C][C]99.0436295936964[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 24 )[/C][C]19.2744186046512[/C][C]0.190792861747083[/C][C]101.022744919050[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 24 )[/C][C]19.2780487804878[/C][C]0.188883503751101[/C][C]102.063168024939[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 24 )[/C][C]19.2743589743590[/C][C]0.187990221007834[/C][C]102.528519148641[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 24 )[/C][C]19.2702702702703[/C][C]0.186313407082345[/C][C]103.429326810353[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 24 )[/C][C]19.2714285714286[/C][C]0.185144568930773[/C][C]104.088543794305[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 24 )[/C][C]19.2606060606061[/C][C]0.185962860515955[/C][C]103.572326254648[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 24 )[/C][C]19.2483870967742[/C][C]0.186182415333448[/C][C]103.384560041832[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 24 )[/C][C]19.2448275862069[/C][C]0.188498487985505[/C][C]102.095394991639[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 24 )[/C][C]19.2407407407407[/C][C]0.190460475089949[/C][C]101.022223806036[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 24 )[/C][C]19.236[/C][C]0.191822834928483[/C][C]100.280031869885[/C][/ROW]
[ROW][C]Median[/C][C]18.7[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]19.9[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]19.1846153846154[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]19.1846153846154[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]19.1846153846154[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]19.1846153846154[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]19.1846153846154[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]19.1846153846154[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]19.1846153846154[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]19.1846153846154[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]73[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=1415&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=1415&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 Mean19.40958904109590.27296475583546871.1065755785527
Geometric Mean19.2726145924944
Harmonic Mean19.1373519258611
Quadratic Mean19.5472977496908
Winsorized Mean ( 1 / 24 )19.40958904109590.27296475583546871.1065755785527
Winsorized Mean ( 2 / 24 )19.40958904109590.27296475583546871.1065755785527
Winsorized Mean ( 3 / 24 )19.38493150684930.26433535179255473.3346159542908
Winsorized Mean ( 4 / 24 )19.38493150684930.26433535179255473.3346159542908
Winsorized Mean ( 5 / 24 )19.38493150684930.26433535179255473.3346159542908
Winsorized Mean ( 6 / 24 )19.37671232876710.25663583213309775.5027548870026
Winsorized Mean ( 7 / 24 )19.37671232876710.25663583213309775.5027548870026
Winsorized Mean ( 8 / 24 )19.37671232876710.25663583213309775.5027548870026
Winsorized Mean ( 9 / 24 )19.38904109589040.23311765671334483.172769361406
Winsorized Mean ( 10 / 24 )19.38904109589040.23311765671334483.172769361406
Winsorized Mean ( 11 / 24 )19.38904109589040.23311765671334483.172769361406
Winsorized Mean ( 12 / 24 )19.25753424657530.21110636487692591.2219499293756
Winsorized Mean ( 13 / 24 )19.34657534246580.19747340718199897.9705349623878
Winsorized Mean ( 14 / 24 )19.34657534246580.19747340718199897.9705349623878
Winsorized Mean ( 15 / 24 )19.24383561643840.182020896961396105.723221551423
Winsorized Mean ( 16 / 24 )19.30958904109590.172612705372955111.866556980117
Winsorized Mean ( 17 / 24 )19.30958904109590.172612705372955111.866556980117
Winsorized Mean ( 18 / 24 )19.26027397260270.165667550116019116.258579058570
Winsorized Mean ( 19 / 24 )19.36438356164380.151895304895230127.485069897324
Winsorized Mean ( 20 / 24 )19.36438356164380.151895304895230127.485069897324
Winsorized Mean ( 21 / 24 )19.27808219178080.140167959904535137.535583773286
Winsorized Mean ( 22 / 24 )19.27808219178080.140167959904535137.535583773286
Winsorized Mean ( 23 / 24 )19.27808219178080.140167959904535137.535583773286
Winsorized Mean ( 24 / 24 )19.24520547945210.135906129412030141.606604225375
Trimmed Mean ( 1 / 24 )19.39577464788730.26820392718642872.3172656394602
Trimmed Mean ( 2 / 24 )19.38115942028990.26252329383367273.8264370268386
Trimmed Mean ( 3 / 24 )19.36567164179100.25573080811280475.7267838971077
Trimmed Mean ( 4 / 24 )19.35846153846150.25151361321633576.9678479463086
Trimmed Mean ( 5 / 24 )19.35079365079370.24638578494383878.5385961093678
Trimmed Mean ( 6 / 24 )19.34262295081970.24014407124259780.5459108389957
Trimmed Mean ( 7 / 24 )19.3355932203390.2347233435228282.3760983042538
Trimmed Mean ( 8 / 24 )19.32807017543860.22804270125630384.756363913245
Trimmed Mean ( 9 / 24 )19.320.21977031168697487.9099631415096
Trimmed Mean ( 10 / 24 )19.30943396226420.21517644143874789.7376768253735
Trimmed Mean ( 11 / 24 )19.29803921568630.20934051809972792.1849214421688
Trimmed Mean ( 12 / 24 )19.28571428571430.20190420035860895.5191335864254
Trimmed Mean ( 13 / 24 )19.28936170212770.19751541919348697.6600296872611
Trimmed Mean ( 14 / 24 )19.28222222222220.19468412356577799.0436295936964
Trimmed Mean ( 15 / 24 )19.27441860465120.190792861747083101.022744919050
Trimmed Mean ( 16 / 24 )19.27804878048780.188883503751101102.063168024939
Trimmed Mean ( 17 / 24 )19.27435897435900.187990221007834102.528519148641
Trimmed Mean ( 18 / 24 )19.27027027027030.186313407082345103.429326810353
Trimmed Mean ( 19 / 24 )19.27142857142860.185144568930773104.088543794305
Trimmed Mean ( 20 / 24 )19.26060606060610.185962860515955103.572326254648
Trimmed Mean ( 21 / 24 )19.24838709677420.186182415333448103.384560041832
Trimmed Mean ( 22 / 24 )19.24482758620690.188498487985505102.095394991639
Trimmed Mean ( 23 / 24 )19.24074074074070.190460475089949101.022223806036
Trimmed Mean ( 24 / 24 )19.2360.191822834928483100.280031869885
Median18.7
Midrange19.9
Midmean - Weighted Average at Xnp19.1846153846154
Midmean - Weighted Average at X(n+1)p19.1846153846154
Midmean - Empirical Distribution Function19.1846153846154
Midmean - Empirical Distribution Function - Averaging19.1846153846154
Midmean - Empirical Distribution Function - Interpolation19.1846153846154
Midmean - Closest Observation19.1846153846154
Midmean - True Basic - Statistics Graphics Toolkit19.1846153846154
Midmean - MS Excel (old versions)19.1846153846154
Number of observations73



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')