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Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationThu, 17 Dec 2009 02:27:52 -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/2009/Dec/17/t1261042135ffk3jff19ypxv8y.htm/, Retrieved Tue, 30 Apr 2024 00:52:08 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=68658, Retrieved Tue, 30 Apr 2024 00:52:08 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsSHW Paper: Central tendency: uitvoer
Estimated Impact123
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Bivariate Data Series] [Bivariate dataset] [2008-01-05 23:51:08] [74be16979710d4c4e7c6647856088456]
F RMPD  [Univariate Explorative Data Analysis] [Colombia Coffee] [2008-01-07 14:21:11] [74be16979710d4c4e7c6647856088456]
F RMPD    [Univariate Data Series] [] [2009-10-14 08:30:28] [74be16979710d4c4e7c6647856088456]
- RMPD      [Univariate Explorative Data Analysis] [WS 3 - Vraag 1 (1)] [2009-10-21 15:37:29] [b103a1dc147def8132c7f643ad8c8f84]
- RMP         [Central Tendency] [WS 3 - Vraag 1 (2)] [2009-10-21 15:45:10] [b103a1dc147def8132c7f643ad8c8f84]
-    D          [Central Tendency] [WS 3 - Vraag 2 (1)] [2009-10-21 15:49:21] [b103a1dc147def8132c7f643ad8c8f84]
-  M D              [Central Tendency] [Paper: Central te...] [2009-12-17 09:27:52] [a45cc820faa25ce30779915639528ec2] [Current]
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Dataseries X:
15.5
15.1
11.7
16.3
16.7
15
14.9
14.6
15.3
17.9
16.4
15.4
17.9
15.9
13.9
17.8
17.9
17.4
16.7
16
16.6
19.1
17.8
17.2
18.6
16.3
15.1
19.2
17.7
19.1
18
17.5
17.8
21.1
17.2
19.4
19.8
17.6
16.2
19.5
19.9
20
17.3
18.9
18.6
21.4
18.6
19.8
20.8
19.6
17.7
19.8
22.2
20.7
17.9
20.9
21.2
21.4
23
21.3
23.9
22.4
18.3
22.8
22.3
17.8
16.4
16
16.4
17.7
16.6
16.2
18.3




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135

\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 & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=68658&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]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=68658&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=68658&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'Gwilym Jenkins' @ 72.249.127.135







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean18.15342465753420.27946651035522164.9574241810226
Geometric Mean17.9979334775636
Harmonic Mean17.8408922323676
Quadratic Mean18.3076524160336
Winsorized Mean ( 1 / 24 )18.17123287671230.26795834040385767.8136491266714
Winsorized Mean ( 2 / 24 )18.18493150684930.26266019416437269.2336787639366
Winsorized Mean ( 3 / 24 )18.18082191780820.25651078654874370.8774167450205
Winsorized Mean ( 4 / 24 )18.18082191780820.25430582337923671.4919606488754
Winsorized Mean ( 5 / 24 )18.18082191780820.25159806992680372.261372764495
Winsorized Mean ( 6 / 24 )18.11506849315070.23797304274827776.1223552211854
Winsorized Mean ( 7 / 24 )18.13424657534250.23467665486087577.2733299189607
Winsorized Mean ( 8 / 24 )18.13424657534250.23075235279066078.5874828838428
Winsorized Mean ( 9 / 24 )18.13424657534250.22640747988651480.0956160301425
Winsorized Mean ( 10 / 24 )18.17534246575340.21537002972299584.391233493027
Winsorized Mean ( 11 / 24 )18.16027397260270.20756928136850287.4901808826058
Winsorized Mean ( 12 / 24 )18.14383561643840.20458022416119788.6881207156272
Winsorized Mean ( 13 / 24 )18.16164383561640.19630946332737292.5153761198433
Winsorized Mean ( 14 / 24 )18.02739726027400.173570046852213103.862374800322
Winsorized Mean ( 15 / 24 )18.02739726027400.167375891388696107.706056772591
Winsorized Mean ( 16 / 24 )18.00547945205480.164007211239336109.784681514884
Winsorized Mean ( 17 / 24 )18.02876712328770.160685833327559112.198858791341
Winsorized Mean ( 18 / 24 )18.02876712328770.160685833327559112.198858791341
Winsorized Mean ( 19 / 24 )17.97671232876710.152858612808324117.603529160041
Winsorized Mean ( 20 / 24 )18.00410958904110.141104017735220127.594592117324
Winsorized Mean ( 21 / 24 )17.97534246575340.136906750112899131.296246904775
Winsorized Mean ( 22 / 24 )17.94520547945210.124110857426294144.590133785106
Winsorized Mean ( 23 / 24 )17.9136986301370.119730085020877149.617354961482
Winsorized Mean ( 24 / 24 )18.07808219178080.0977728896879098184.898720386458
Trimmed Mean ( 1 / 24 )18.16338028169010.25994303227176369.8744648892949
Trimmed Mean ( 2 / 24 )18.15507246376810.25042620304365472.4966966040824
Trimmed Mean ( 3 / 24 )18.13880597014930.24248967976734774.802383291331
Trimmed Mean ( 4 / 24 )18.12307692307690.2358267905644576.8491013243213
Trimmed Mean ( 5 / 24 )18.10634920634920.22861000556293979.2019105277713
Trimmed Mean ( 6 / 24 )18.08852459016390.22073026291229781.948548203157
Trimmed Mean ( 7 / 24 )18.08305084745760.21516378905709984.0431883389953
Trimmed Mean ( 8 / 24 )18.07368421052630.20918037802351286.4023881269343
Trimmed Mean ( 9 / 24 )18.06363636363640.2027647894503289.086652631384
Trimmed Mean ( 10 / 24 )18.05283018867920.19583107434134292.1857281812811
Trimmed Mean ( 11 / 24 )18.03529411764710.18969166993425295.0768904290746
Trimmed Mean ( 12 / 24 )18.01836734693880.18372731636996298.0712487557165
Trimmed Mean ( 13 / 24 )18.00212765957450.176786228531918101.829920854521
Trimmed Mean ( 14 / 24 )17.98222222222220.169708272831835105.959608934568
Trimmed Mean ( 15 / 24 )17.97674418604650.166017691398142108.282099544047
Trimmed Mean ( 16 / 24 )17.97073170731710.162422360531042110.641980873579
Trimmed Mean ( 17 / 24 )17.96666666666670.158277389079543113.513792280446
Trimmed Mean ( 18 / 24 )17.95945945945950.153314700173144117.141144581551
Trimmed Mean ( 19 / 24 )17.95142857142860.146348922793716122.661842866665
Trimmed Mean ( 20 / 24 )17.94848484848480.138861797174086129.254303298290
Trimmed Mean ( 21 / 24 )17.94193548387100.131719332889878136.213379541415
Trimmed Mean ( 22 / 24 )17.93793103448280.122616566948487146.292882608749
Trimmed Mean ( 23 / 24 )17.93703703703700.113748378799148157.690485142733
Trimmed Mean ( 24 / 24 )17.940.101653004546513176.482732409462
Median17.8
Midrange17.8
Midmean - Weighted Average at Xnp17.8675675675676
Midmean - Weighted Average at X(n+1)p18.0125
Midmean - Empirical Distribution Function18.0125
Midmean - Empirical Distribution Function - Averaging18.0125
Midmean - Empirical Distribution Function - Interpolation18.0125
Midmean - Closest Observation18.0125
Midmean - True Basic - Statistics Graphics Toolkit18.0125
Midmean - MS Excel (old versions)18.0125
Number of observations73

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 18.1534246575342 & 0.279466510355221 & 64.9574241810226 \tabularnewline
Geometric Mean & 17.9979334775636 &  &  \tabularnewline
Harmonic Mean & 17.8408922323676 &  &  \tabularnewline
Quadratic Mean & 18.3076524160336 &  &  \tabularnewline
Winsorized Mean ( 1 / 24 ) & 18.1712328767123 & 0.267958340403857 & 67.8136491266714 \tabularnewline
Winsorized Mean ( 2 / 24 ) & 18.1849315068493 & 0.262660194164372 & 69.2336787639366 \tabularnewline
Winsorized Mean ( 3 / 24 ) & 18.1808219178082 & 0.256510786548743 & 70.8774167450205 \tabularnewline
Winsorized Mean ( 4 / 24 ) & 18.1808219178082 & 0.254305823379236 & 71.4919606488754 \tabularnewline
Winsorized Mean ( 5 / 24 ) & 18.1808219178082 & 0.251598069926803 & 72.261372764495 \tabularnewline
Winsorized Mean ( 6 / 24 ) & 18.1150684931507 & 0.237973042748277 & 76.1223552211854 \tabularnewline
Winsorized Mean ( 7 / 24 ) & 18.1342465753425 & 0.234676654860875 & 77.2733299189607 \tabularnewline
Winsorized Mean ( 8 / 24 ) & 18.1342465753425 & 0.230752352790660 & 78.5874828838428 \tabularnewline
Winsorized Mean ( 9 / 24 ) & 18.1342465753425 & 0.226407479886514 & 80.0956160301425 \tabularnewline
Winsorized Mean ( 10 / 24 ) & 18.1753424657534 & 0.215370029722995 & 84.391233493027 \tabularnewline
Winsorized Mean ( 11 / 24 ) & 18.1602739726027 & 0.207569281368502 & 87.4901808826058 \tabularnewline
Winsorized Mean ( 12 / 24 ) & 18.1438356164384 & 0.204580224161197 & 88.6881207156272 \tabularnewline
Winsorized Mean ( 13 / 24 ) & 18.1616438356164 & 0.196309463327372 & 92.5153761198433 \tabularnewline
Winsorized Mean ( 14 / 24 ) & 18.0273972602740 & 0.173570046852213 & 103.862374800322 \tabularnewline
Winsorized Mean ( 15 / 24 ) & 18.0273972602740 & 0.167375891388696 & 107.706056772591 \tabularnewline
Winsorized Mean ( 16 / 24 ) & 18.0054794520548 & 0.164007211239336 & 109.784681514884 \tabularnewline
Winsorized Mean ( 17 / 24 ) & 18.0287671232877 & 0.160685833327559 & 112.198858791341 \tabularnewline
Winsorized Mean ( 18 / 24 ) & 18.0287671232877 & 0.160685833327559 & 112.198858791341 \tabularnewline
Winsorized Mean ( 19 / 24 ) & 17.9767123287671 & 0.152858612808324 & 117.603529160041 \tabularnewline
Winsorized Mean ( 20 / 24 ) & 18.0041095890411 & 0.141104017735220 & 127.594592117324 \tabularnewline
Winsorized Mean ( 21 / 24 ) & 17.9753424657534 & 0.136906750112899 & 131.296246904775 \tabularnewline
Winsorized Mean ( 22 / 24 ) & 17.9452054794521 & 0.124110857426294 & 144.590133785106 \tabularnewline
Winsorized Mean ( 23 / 24 ) & 17.913698630137 & 0.119730085020877 & 149.617354961482 \tabularnewline
Winsorized Mean ( 24 / 24 ) & 18.0780821917808 & 0.0977728896879098 & 184.898720386458 \tabularnewline
Trimmed Mean ( 1 / 24 ) & 18.1633802816901 & 0.259943032271763 & 69.8744648892949 \tabularnewline
Trimmed Mean ( 2 / 24 ) & 18.1550724637681 & 0.250426203043654 & 72.4966966040824 \tabularnewline
Trimmed Mean ( 3 / 24 ) & 18.1388059701493 & 0.242489679767347 & 74.802383291331 \tabularnewline
Trimmed Mean ( 4 / 24 ) & 18.1230769230769 & 0.23582679056445 & 76.8491013243213 \tabularnewline
Trimmed Mean ( 5 / 24 ) & 18.1063492063492 & 0.228610005562939 & 79.2019105277713 \tabularnewline
Trimmed Mean ( 6 / 24 ) & 18.0885245901639 & 0.220730262912297 & 81.948548203157 \tabularnewline
Trimmed Mean ( 7 / 24 ) & 18.0830508474576 & 0.215163789057099 & 84.0431883389953 \tabularnewline
Trimmed Mean ( 8 / 24 ) & 18.0736842105263 & 0.209180378023512 & 86.4023881269343 \tabularnewline
Trimmed Mean ( 9 / 24 ) & 18.0636363636364 & 0.20276478945032 & 89.086652631384 \tabularnewline
Trimmed Mean ( 10 / 24 ) & 18.0528301886792 & 0.195831074341342 & 92.1857281812811 \tabularnewline
Trimmed Mean ( 11 / 24 ) & 18.0352941176471 & 0.189691669934252 & 95.0768904290746 \tabularnewline
Trimmed Mean ( 12 / 24 ) & 18.0183673469388 & 0.183727316369962 & 98.0712487557165 \tabularnewline
Trimmed Mean ( 13 / 24 ) & 18.0021276595745 & 0.176786228531918 & 101.829920854521 \tabularnewline
Trimmed Mean ( 14 / 24 ) & 17.9822222222222 & 0.169708272831835 & 105.959608934568 \tabularnewline
Trimmed Mean ( 15 / 24 ) & 17.9767441860465 & 0.166017691398142 & 108.282099544047 \tabularnewline
Trimmed Mean ( 16 / 24 ) & 17.9707317073171 & 0.162422360531042 & 110.641980873579 \tabularnewline
Trimmed Mean ( 17 / 24 ) & 17.9666666666667 & 0.158277389079543 & 113.513792280446 \tabularnewline
Trimmed Mean ( 18 / 24 ) & 17.9594594594595 & 0.153314700173144 & 117.141144581551 \tabularnewline
Trimmed Mean ( 19 / 24 ) & 17.9514285714286 & 0.146348922793716 & 122.661842866665 \tabularnewline
Trimmed Mean ( 20 / 24 ) & 17.9484848484848 & 0.138861797174086 & 129.254303298290 \tabularnewline
Trimmed Mean ( 21 / 24 ) & 17.9419354838710 & 0.131719332889878 & 136.213379541415 \tabularnewline
Trimmed Mean ( 22 / 24 ) & 17.9379310344828 & 0.122616566948487 & 146.292882608749 \tabularnewline
Trimmed Mean ( 23 / 24 ) & 17.9370370370370 & 0.113748378799148 & 157.690485142733 \tabularnewline
Trimmed Mean ( 24 / 24 ) & 17.94 & 0.101653004546513 & 176.482732409462 \tabularnewline
Median & 17.8 &  &  \tabularnewline
Midrange & 17.8 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 17.8675675675676 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 18.0125 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 18.0125 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 18.0125 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 18.0125 &  &  \tabularnewline
Midmean - Closest Observation & 18.0125 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 18.0125 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 18.0125 &  &  \tabularnewline
Number of observations & 73 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=68658&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]18.1534246575342[/C][C]0.279466510355221[/C][C]64.9574241810226[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]17.9979334775636[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]17.8408922323676[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]18.3076524160336[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 24 )[/C][C]18.1712328767123[/C][C]0.267958340403857[/C][C]67.8136491266714[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 24 )[/C][C]18.1849315068493[/C][C]0.262660194164372[/C][C]69.2336787639366[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 24 )[/C][C]18.1808219178082[/C][C]0.256510786548743[/C][C]70.8774167450205[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 24 )[/C][C]18.1808219178082[/C][C]0.254305823379236[/C][C]71.4919606488754[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 24 )[/C][C]18.1808219178082[/C][C]0.251598069926803[/C][C]72.261372764495[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 24 )[/C][C]18.1150684931507[/C][C]0.237973042748277[/C][C]76.1223552211854[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 24 )[/C][C]18.1342465753425[/C][C]0.234676654860875[/C][C]77.2733299189607[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 24 )[/C][C]18.1342465753425[/C][C]0.230752352790660[/C][C]78.5874828838428[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 24 )[/C][C]18.1342465753425[/C][C]0.226407479886514[/C][C]80.0956160301425[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 24 )[/C][C]18.1753424657534[/C][C]0.215370029722995[/C][C]84.391233493027[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 24 )[/C][C]18.1602739726027[/C][C]0.207569281368502[/C][C]87.4901808826058[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 24 )[/C][C]18.1438356164384[/C][C]0.204580224161197[/C][C]88.6881207156272[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 24 )[/C][C]18.1616438356164[/C][C]0.196309463327372[/C][C]92.5153761198433[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 24 )[/C][C]18.0273972602740[/C][C]0.173570046852213[/C][C]103.862374800322[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 24 )[/C][C]18.0273972602740[/C][C]0.167375891388696[/C][C]107.706056772591[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 24 )[/C][C]18.0054794520548[/C][C]0.164007211239336[/C][C]109.784681514884[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 24 )[/C][C]18.0287671232877[/C][C]0.160685833327559[/C][C]112.198858791341[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 24 )[/C][C]18.0287671232877[/C][C]0.160685833327559[/C][C]112.198858791341[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 24 )[/C][C]17.9767123287671[/C][C]0.152858612808324[/C][C]117.603529160041[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 24 )[/C][C]18.0041095890411[/C][C]0.141104017735220[/C][C]127.594592117324[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 24 )[/C][C]17.9753424657534[/C][C]0.136906750112899[/C][C]131.296246904775[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 24 )[/C][C]17.9452054794521[/C][C]0.124110857426294[/C][C]144.590133785106[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 24 )[/C][C]17.913698630137[/C][C]0.119730085020877[/C][C]149.617354961482[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 24 )[/C][C]18.0780821917808[/C][C]0.0977728896879098[/C][C]184.898720386458[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 24 )[/C][C]18.1633802816901[/C][C]0.259943032271763[/C][C]69.8744648892949[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 24 )[/C][C]18.1550724637681[/C][C]0.250426203043654[/C][C]72.4966966040824[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 24 )[/C][C]18.1388059701493[/C][C]0.242489679767347[/C][C]74.802383291331[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 24 )[/C][C]18.1230769230769[/C][C]0.23582679056445[/C][C]76.8491013243213[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 24 )[/C][C]18.1063492063492[/C][C]0.228610005562939[/C][C]79.2019105277713[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 24 )[/C][C]18.0885245901639[/C][C]0.220730262912297[/C][C]81.948548203157[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 24 )[/C][C]18.0830508474576[/C][C]0.215163789057099[/C][C]84.0431883389953[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 24 )[/C][C]18.0736842105263[/C][C]0.209180378023512[/C][C]86.4023881269343[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 24 )[/C][C]18.0636363636364[/C][C]0.20276478945032[/C][C]89.086652631384[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 24 )[/C][C]18.0528301886792[/C][C]0.195831074341342[/C][C]92.1857281812811[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 24 )[/C][C]18.0352941176471[/C][C]0.189691669934252[/C][C]95.0768904290746[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 24 )[/C][C]18.0183673469388[/C][C]0.183727316369962[/C][C]98.0712487557165[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 24 )[/C][C]18.0021276595745[/C][C]0.176786228531918[/C][C]101.829920854521[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 24 )[/C][C]17.9822222222222[/C][C]0.169708272831835[/C][C]105.959608934568[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 24 )[/C][C]17.9767441860465[/C][C]0.166017691398142[/C][C]108.282099544047[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 24 )[/C][C]17.9707317073171[/C][C]0.162422360531042[/C][C]110.641980873579[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 24 )[/C][C]17.9666666666667[/C][C]0.158277389079543[/C][C]113.513792280446[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 24 )[/C][C]17.9594594594595[/C][C]0.153314700173144[/C][C]117.141144581551[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 24 )[/C][C]17.9514285714286[/C][C]0.146348922793716[/C][C]122.661842866665[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 24 )[/C][C]17.9484848484848[/C][C]0.138861797174086[/C][C]129.254303298290[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 24 )[/C][C]17.9419354838710[/C][C]0.131719332889878[/C][C]136.213379541415[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 24 )[/C][C]17.9379310344828[/C][C]0.122616566948487[/C][C]146.292882608749[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 24 )[/C][C]17.9370370370370[/C][C]0.113748378799148[/C][C]157.690485142733[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 24 )[/C][C]17.94[/C][C]0.101653004546513[/C][C]176.482732409462[/C][/ROW]
[ROW][C]Median[/C][C]17.8[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]17.8[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]17.8675675675676[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]18.0125[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]18.0125[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]18.0125[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]18.0125[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]18.0125[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]18.0125[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]18.0125[/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=68658&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=68658&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 Mean18.15342465753420.27946651035522164.9574241810226
Geometric Mean17.9979334775636
Harmonic Mean17.8408922323676
Quadratic Mean18.3076524160336
Winsorized Mean ( 1 / 24 )18.17123287671230.26795834040385767.8136491266714
Winsorized Mean ( 2 / 24 )18.18493150684930.26266019416437269.2336787639366
Winsorized Mean ( 3 / 24 )18.18082191780820.25651078654874370.8774167450205
Winsorized Mean ( 4 / 24 )18.18082191780820.25430582337923671.4919606488754
Winsorized Mean ( 5 / 24 )18.18082191780820.25159806992680372.261372764495
Winsorized Mean ( 6 / 24 )18.11506849315070.23797304274827776.1223552211854
Winsorized Mean ( 7 / 24 )18.13424657534250.23467665486087577.2733299189607
Winsorized Mean ( 8 / 24 )18.13424657534250.23075235279066078.5874828838428
Winsorized Mean ( 9 / 24 )18.13424657534250.22640747988651480.0956160301425
Winsorized Mean ( 10 / 24 )18.17534246575340.21537002972299584.391233493027
Winsorized Mean ( 11 / 24 )18.16027397260270.20756928136850287.4901808826058
Winsorized Mean ( 12 / 24 )18.14383561643840.20458022416119788.6881207156272
Winsorized Mean ( 13 / 24 )18.16164383561640.19630946332737292.5153761198433
Winsorized Mean ( 14 / 24 )18.02739726027400.173570046852213103.862374800322
Winsorized Mean ( 15 / 24 )18.02739726027400.167375891388696107.706056772591
Winsorized Mean ( 16 / 24 )18.00547945205480.164007211239336109.784681514884
Winsorized Mean ( 17 / 24 )18.02876712328770.160685833327559112.198858791341
Winsorized Mean ( 18 / 24 )18.02876712328770.160685833327559112.198858791341
Winsorized Mean ( 19 / 24 )17.97671232876710.152858612808324117.603529160041
Winsorized Mean ( 20 / 24 )18.00410958904110.141104017735220127.594592117324
Winsorized Mean ( 21 / 24 )17.97534246575340.136906750112899131.296246904775
Winsorized Mean ( 22 / 24 )17.94520547945210.124110857426294144.590133785106
Winsorized Mean ( 23 / 24 )17.9136986301370.119730085020877149.617354961482
Winsorized Mean ( 24 / 24 )18.07808219178080.0977728896879098184.898720386458
Trimmed Mean ( 1 / 24 )18.16338028169010.25994303227176369.8744648892949
Trimmed Mean ( 2 / 24 )18.15507246376810.25042620304365472.4966966040824
Trimmed Mean ( 3 / 24 )18.13880597014930.24248967976734774.802383291331
Trimmed Mean ( 4 / 24 )18.12307692307690.2358267905644576.8491013243213
Trimmed Mean ( 5 / 24 )18.10634920634920.22861000556293979.2019105277713
Trimmed Mean ( 6 / 24 )18.08852459016390.22073026291229781.948548203157
Trimmed Mean ( 7 / 24 )18.08305084745760.21516378905709984.0431883389953
Trimmed Mean ( 8 / 24 )18.07368421052630.20918037802351286.4023881269343
Trimmed Mean ( 9 / 24 )18.06363636363640.2027647894503289.086652631384
Trimmed Mean ( 10 / 24 )18.05283018867920.19583107434134292.1857281812811
Trimmed Mean ( 11 / 24 )18.03529411764710.18969166993425295.0768904290746
Trimmed Mean ( 12 / 24 )18.01836734693880.18372731636996298.0712487557165
Trimmed Mean ( 13 / 24 )18.00212765957450.176786228531918101.829920854521
Trimmed Mean ( 14 / 24 )17.98222222222220.169708272831835105.959608934568
Trimmed Mean ( 15 / 24 )17.97674418604650.166017691398142108.282099544047
Trimmed Mean ( 16 / 24 )17.97073170731710.162422360531042110.641980873579
Trimmed Mean ( 17 / 24 )17.96666666666670.158277389079543113.513792280446
Trimmed Mean ( 18 / 24 )17.95945945945950.153314700173144117.141144581551
Trimmed Mean ( 19 / 24 )17.95142857142860.146348922793716122.661842866665
Trimmed Mean ( 20 / 24 )17.94848484848480.138861797174086129.254303298290
Trimmed Mean ( 21 / 24 )17.94193548387100.131719332889878136.213379541415
Trimmed Mean ( 22 / 24 )17.93793103448280.122616566948487146.292882608749
Trimmed Mean ( 23 / 24 )17.93703703703700.113748378799148157.690485142733
Trimmed Mean ( 24 / 24 )17.940.101653004546513176.482732409462
Median17.8
Midrange17.8
Midmean - Weighted Average at Xnp17.8675675675676
Midmean - Weighted Average at X(n+1)p18.0125
Midmean - Empirical Distribution Function18.0125
Midmean - Empirical Distribution Function - Averaging18.0125
Midmean - Empirical Distribution Function - Interpolation18.0125
Midmean - Closest Observation18.0125
Midmean - True Basic - Statistics Graphics Toolkit18.0125
Midmean - MS Excel (old versions)18.0125
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')