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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 computationWed, 21 Oct 2009 09:49:21 -0600
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2009/Oct/21/t12561402082tyaayy4cvjbjly.htm/, Retrieved Sat, 04 May 2024 09:10:34 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=49450, Retrieved Sat, 04 May 2024 09:10:34 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsSHW WS 3 - Vraag 2 (1)
Estimated Impact136
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] [a45cc820faa25ce30779915639528ec2] [Current]
-  M D              [Central Tendency] [Paper: Central te...] [2009-12-17 09:27:52] [b103a1dc147def8132c7f643ad8c8f84]
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Dataseries X:
14.2
13.5
11.9
14.6
15.6
14.1
14.9
14.2
14.6
17.2
15.4
14.3
17.5
14.5
14.4
16.6
16.7
16.6
16.9
15.7
16.4
18.4
16.9
16.5
18.3
15.1
15.7
18.1
16.8
18.9
19
18.1
17.8
21.5
17.1
18.7
19
16.4
16.9
18.6
19.3
19.4
17.6
18.6
18.1
20.4
18.1
19.6
19.9
19.2
17.8
19.2
22
21.1
19.5
22.2
20.9
22.2
23.5
21.5
24.3
22.8
20.3
23.7
23.3
19.6
18
17.3
16.8
18.2
16.5
16
18.4




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'George Udny Yule' @ 72.249.76.132

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 2 seconds \tabularnewline
R Server & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=49450&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'George Udny Yule' @ 72.249.76.132[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=49450&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=49450&T=0

As an alternative you can also use a QR Code:  

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

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'George Udny Yule' @ 72.249.76.132







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean17.98493150684930.31249761784709557.552219536116
Geometric Mean17.7909972690593
Harmonic Mean17.5980950099908
Quadratic Mean18.1793537869086
Winsorized Mean ( 1 / 24 )17.99863013698630.30505939955239959.0004116031008
Winsorized Mean ( 2 / 24 )18.00958904109590.30048264311124159.9355385543138
Winsorized Mean ( 3 / 24 )18.00547945205480.29768826724562760.4843436345384
Winsorized Mean ( 4 / 24 )17.97808219178080.29115085880865461.7483398996123
Winsorized Mean ( 5 / 24 )17.94383561643840.28085801824610163.8893478224115
Winsorized Mean ( 6 / 24 )17.95205479452050.27939179969368764.2540504560349
Winsorized Mean ( 7 / 24 )17.94246575342470.2737078248699765.5533533319647
Winsorized Mean ( 8 / 24 )17.89863013698630.26088548686209068.6072282221199
Winsorized Mean ( 9 / 24 )17.89863013698630.26088548686209068.6072282221199
Winsorized Mean ( 10 / 24 )17.88493150684930.2434895916696173.4525504117535
Winsorized Mean ( 11 / 24 )17.88493150684930.23294709743030776.7767948351453
Winsorized Mean ( 12 / 24 )17.85205479452050.21053954741033484.7919310842229
Winsorized Mean ( 13 / 24 )17.86986301369860.20189065386204788.5125817954366
Winsorized Mean ( 14 / 24 )17.81232876712330.18649153156390695.512802204745
Winsorized Mean ( 15 / 24 )17.75068493150690.177224106416842100.159539751077
Winsorized Mean ( 16 / 24 )17.81643835616440.166963362611241106.708669959220
Winsorized Mean ( 17 / 24 )17.8863013698630.150016679292016119.228751458005
Winsorized Mean ( 18 / 24 )17.86164383561640.146374633204535122.026907562991
Winsorized Mean ( 19 / 24 )17.86164383561640.139028348906961128.474832478731
Winsorized Mean ( 20 / 24 )17.83424657534250.135136482929583131.972108410099
Winsorized Mean ( 21 / 24 )17.86301369863010.131240812526378136.108679569778
Winsorized Mean ( 22 / 24 )17.80273972602740.12289278040087144.863999886370
Winsorized Mean ( 23 / 24 )17.83424657534250.118659098478620150.298180282871
Winsorized Mean ( 24 / 24 )17.83424657534250.109867416605959162.325165424661
Trimmed Mean ( 1 / 24 )17.98169014084510.29631071474833360.6852511429348
Trimmed Mean ( 2 / 24 )17.96376811594200.28591525323264262.8289953503297
Trimmed Mean ( 3 / 24 )17.93880597014930.27644571035352664.890882000696
Trimmed Mean ( 4 / 24 )17.91384615384620.26637593557462167.250242088133
Trimmed Mean ( 5 / 24 )17.89523809523810.25675142307002369.6986909800206
Trimmed Mean ( 6 / 24 )17.88360655737700.24850570166265071.964572393008
Trimmed Mean ( 7 / 24 )17.86949152542370.23886364327302574.8104285799518
Trimmed Mean ( 8 / 24 )17.85614035087720.22860886834468578.1078200516466
Trimmed Mean ( 9 / 24 )17.84909090909090.21937887107135881.3619416579323
Trimmed Mean ( 10 / 24 )17.84150943396230.20783691346795285.8437951962435
Trimmed Mean ( 11 / 24 )17.83529411764710.19780805767627690.164649141015
Trimmed Mean ( 12 / 24 )17.82857142857140.18774077511147194.9637680891951
Trimmed Mean ( 13 / 24 )17.82553191489360.18043702946278698.790874400701
Trimmed Mean ( 14 / 24 )17.820.173076733143296102.960112987840
Trimmed Mean ( 15 / 24 )17.82093023255810.167204827920425106.581433408366
Trimmed Mean ( 16 / 24 )17.82926829268290.161594339373473110.333495355158
Trimmed Mean ( 17 / 24 )17.83076923076920.156598192439187113.863186752258
Trimmed Mean ( 18 / 24 )17.82432432432430.153800961690420115.892151313086
Trimmed Mean ( 19 / 24 )17.820.150617775463968118.312728661054
Trimmed Mean ( 20 / 24 )17.81515151515150.147781652772714120.550495822042
Trimmed Mean ( 21 / 24 )17.81290322580650.144485883931847123.284730252325
Trimmed Mean ( 22 / 24 )17.80689655172410.140454139780032126.780859429362
Trimmed Mean ( 23 / 24 )17.80740740740740.136805841781219130.16554830959
Trimmed Mean ( 24 / 24 )17.8040.132222035480727134.652291013892
Median18
Midrange18.1
Midmean - Weighted Average at Xnp17.7432432432432
Midmean - Weighted Average at X(n+1)p17.7868421052632
Midmean - Empirical Distribution Function17.7868421052632
Midmean - Empirical Distribution Function - Averaging17.7868421052632
Midmean - Empirical Distribution Function - Interpolation17.7868421052632
Midmean - Closest Observation17.7868421052632
Midmean - True Basic - Statistics Graphics Toolkit17.7868421052632
Midmean - MS Excel (old versions)17.7868421052632
Number of observations73

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 17.9849315068493 & 0.312497617847095 & 57.552219536116 \tabularnewline
Geometric Mean & 17.7909972690593 &  &  \tabularnewline
Harmonic Mean & 17.5980950099908 &  &  \tabularnewline
Quadratic Mean & 18.1793537869086 &  &  \tabularnewline
Winsorized Mean ( 1 / 24 ) & 17.9986301369863 & 0.305059399552399 & 59.0004116031008 \tabularnewline
Winsorized Mean ( 2 / 24 ) & 18.0095890410959 & 0.300482643111241 & 59.9355385543138 \tabularnewline
Winsorized Mean ( 3 / 24 ) & 18.0054794520548 & 0.297688267245627 & 60.4843436345384 \tabularnewline
Winsorized Mean ( 4 / 24 ) & 17.9780821917808 & 0.291150858808654 & 61.7483398996123 \tabularnewline
Winsorized Mean ( 5 / 24 ) & 17.9438356164384 & 0.280858018246101 & 63.8893478224115 \tabularnewline
Winsorized Mean ( 6 / 24 ) & 17.9520547945205 & 0.279391799693687 & 64.2540504560349 \tabularnewline
Winsorized Mean ( 7 / 24 ) & 17.9424657534247 & 0.27370782486997 & 65.5533533319647 \tabularnewline
Winsorized Mean ( 8 / 24 ) & 17.8986301369863 & 0.260885486862090 & 68.6072282221199 \tabularnewline
Winsorized Mean ( 9 / 24 ) & 17.8986301369863 & 0.260885486862090 & 68.6072282221199 \tabularnewline
Winsorized Mean ( 10 / 24 ) & 17.8849315068493 & 0.24348959166961 & 73.4525504117535 \tabularnewline
Winsorized Mean ( 11 / 24 ) & 17.8849315068493 & 0.232947097430307 & 76.7767948351453 \tabularnewline
Winsorized Mean ( 12 / 24 ) & 17.8520547945205 & 0.210539547410334 & 84.7919310842229 \tabularnewline
Winsorized Mean ( 13 / 24 ) & 17.8698630136986 & 0.201890653862047 & 88.5125817954366 \tabularnewline
Winsorized Mean ( 14 / 24 ) & 17.8123287671233 & 0.186491531563906 & 95.512802204745 \tabularnewline
Winsorized Mean ( 15 / 24 ) & 17.7506849315069 & 0.177224106416842 & 100.159539751077 \tabularnewline
Winsorized Mean ( 16 / 24 ) & 17.8164383561644 & 0.166963362611241 & 106.708669959220 \tabularnewline
Winsorized Mean ( 17 / 24 ) & 17.886301369863 & 0.150016679292016 & 119.228751458005 \tabularnewline
Winsorized Mean ( 18 / 24 ) & 17.8616438356164 & 0.146374633204535 & 122.026907562991 \tabularnewline
Winsorized Mean ( 19 / 24 ) & 17.8616438356164 & 0.139028348906961 & 128.474832478731 \tabularnewline
Winsorized Mean ( 20 / 24 ) & 17.8342465753425 & 0.135136482929583 & 131.972108410099 \tabularnewline
Winsorized Mean ( 21 / 24 ) & 17.8630136986301 & 0.131240812526378 & 136.108679569778 \tabularnewline
Winsorized Mean ( 22 / 24 ) & 17.8027397260274 & 0.12289278040087 & 144.863999886370 \tabularnewline
Winsorized Mean ( 23 / 24 ) & 17.8342465753425 & 0.118659098478620 & 150.298180282871 \tabularnewline
Winsorized Mean ( 24 / 24 ) & 17.8342465753425 & 0.109867416605959 & 162.325165424661 \tabularnewline
Trimmed Mean ( 1 / 24 ) & 17.9816901408451 & 0.296310714748333 & 60.6852511429348 \tabularnewline
Trimmed Mean ( 2 / 24 ) & 17.9637681159420 & 0.285915253232642 & 62.8289953503297 \tabularnewline
Trimmed Mean ( 3 / 24 ) & 17.9388059701493 & 0.276445710353526 & 64.890882000696 \tabularnewline
Trimmed Mean ( 4 / 24 ) & 17.9138461538462 & 0.266375935574621 & 67.250242088133 \tabularnewline
Trimmed Mean ( 5 / 24 ) & 17.8952380952381 & 0.256751423070023 & 69.6986909800206 \tabularnewline
Trimmed Mean ( 6 / 24 ) & 17.8836065573770 & 0.248505701662650 & 71.964572393008 \tabularnewline
Trimmed Mean ( 7 / 24 ) & 17.8694915254237 & 0.238863643273025 & 74.8104285799518 \tabularnewline
Trimmed Mean ( 8 / 24 ) & 17.8561403508772 & 0.228608868344685 & 78.1078200516466 \tabularnewline
Trimmed Mean ( 9 / 24 ) & 17.8490909090909 & 0.219378871071358 & 81.3619416579323 \tabularnewline
Trimmed Mean ( 10 / 24 ) & 17.8415094339623 & 0.207836913467952 & 85.8437951962435 \tabularnewline
Trimmed Mean ( 11 / 24 ) & 17.8352941176471 & 0.197808057676276 & 90.164649141015 \tabularnewline
Trimmed Mean ( 12 / 24 ) & 17.8285714285714 & 0.187740775111471 & 94.9637680891951 \tabularnewline
Trimmed Mean ( 13 / 24 ) & 17.8255319148936 & 0.180437029462786 & 98.790874400701 \tabularnewline
Trimmed Mean ( 14 / 24 ) & 17.82 & 0.173076733143296 & 102.960112987840 \tabularnewline
Trimmed Mean ( 15 / 24 ) & 17.8209302325581 & 0.167204827920425 & 106.581433408366 \tabularnewline
Trimmed Mean ( 16 / 24 ) & 17.8292682926829 & 0.161594339373473 & 110.333495355158 \tabularnewline
Trimmed Mean ( 17 / 24 ) & 17.8307692307692 & 0.156598192439187 & 113.863186752258 \tabularnewline
Trimmed Mean ( 18 / 24 ) & 17.8243243243243 & 0.153800961690420 & 115.892151313086 \tabularnewline
Trimmed Mean ( 19 / 24 ) & 17.82 & 0.150617775463968 & 118.312728661054 \tabularnewline
Trimmed Mean ( 20 / 24 ) & 17.8151515151515 & 0.147781652772714 & 120.550495822042 \tabularnewline
Trimmed Mean ( 21 / 24 ) & 17.8129032258065 & 0.144485883931847 & 123.284730252325 \tabularnewline
Trimmed Mean ( 22 / 24 ) & 17.8068965517241 & 0.140454139780032 & 126.780859429362 \tabularnewline
Trimmed Mean ( 23 / 24 ) & 17.8074074074074 & 0.136805841781219 & 130.16554830959 \tabularnewline
Trimmed Mean ( 24 / 24 ) & 17.804 & 0.132222035480727 & 134.652291013892 \tabularnewline
Median & 18 &  &  \tabularnewline
Midrange & 18.1 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 17.7432432432432 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 17.7868421052632 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 17.7868421052632 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 17.7868421052632 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 17.7868421052632 &  &  \tabularnewline
Midmean - Closest Observation & 17.7868421052632 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 17.7868421052632 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 17.7868421052632 &  &  \tabularnewline
Number of observations & 73 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=49450&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]17.9849315068493[/C][C]0.312497617847095[/C][C]57.552219536116[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]17.7909972690593[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]17.5980950099908[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]18.1793537869086[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 24 )[/C][C]17.9986301369863[/C][C]0.305059399552399[/C][C]59.0004116031008[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 24 )[/C][C]18.0095890410959[/C][C]0.300482643111241[/C][C]59.9355385543138[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 24 )[/C][C]18.0054794520548[/C][C]0.297688267245627[/C][C]60.4843436345384[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 24 )[/C][C]17.9780821917808[/C][C]0.291150858808654[/C][C]61.7483398996123[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 24 )[/C][C]17.9438356164384[/C][C]0.280858018246101[/C][C]63.8893478224115[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 24 )[/C][C]17.9520547945205[/C][C]0.279391799693687[/C][C]64.2540504560349[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 24 )[/C][C]17.9424657534247[/C][C]0.27370782486997[/C][C]65.5533533319647[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 24 )[/C][C]17.8986301369863[/C][C]0.260885486862090[/C][C]68.6072282221199[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 24 )[/C][C]17.8986301369863[/C][C]0.260885486862090[/C][C]68.6072282221199[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 24 )[/C][C]17.8849315068493[/C][C]0.24348959166961[/C][C]73.4525504117535[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 24 )[/C][C]17.8849315068493[/C][C]0.232947097430307[/C][C]76.7767948351453[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 24 )[/C][C]17.8520547945205[/C][C]0.210539547410334[/C][C]84.7919310842229[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 24 )[/C][C]17.8698630136986[/C][C]0.201890653862047[/C][C]88.5125817954366[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 24 )[/C][C]17.8123287671233[/C][C]0.186491531563906[/C][C]95.512802204745[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 24 )[/C][C]17.7506849315069[/C][C]0.177224106416842[/C][C]100.159539751077[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 24 )[/C][C]17.8164383561644[/C][C]0.166963362611241[/C][C]106.708669959220[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 24 )[/C][C]17.886301369863[/C][C]0.150016679292016[/C][C]119.228751458005[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 24 )[/C][C]17.8616438356164[/C][C]0.146374633204535[/C][C]122.026907562991[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 24 )[/C][C]17.8616438356164[/C][C]0.139028348906961[/C][C]128.474832478731[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 24 )[/C][C]17.8342465753425[/C][C]0.135136482929583[/C][C]131.972108410099[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 24 )[/C][C]17.8630136986301[/C][C]0.131240812526378[/C][C]136.108679569778[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 24 )[/C][C]17.8027397260274[/C][C]0.12289278040087[/C][C]144.863999886370[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 24 )[/C][C]17.8342465753425[/C][C]0.118659098478620[/C][C]150.298180282871[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 24 )[/C][C]17.8342465753425[/C][C]0.109867416605959[/C][C]162.325165424661[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 24 )[/C][C]17.9816901408451[/C][C]0.296310714748333[/C][C]60.6852511429348[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 24 )[/C][C]17.9637681159420[/C][C]0.285915253232642[/C][C]62.8289953503297[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 24 )[/C][C]17.9388059701493[/C][C]0.276445710353526[/C][C]64.890882000696[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 24 )[/C][C]17.9138461538462[/C][C]0.266375935574621[/C][C]67.250242088133[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 24 )[/C][C]17.8952380952381[/C][C]0.256751423070023[/C][C]69.6986909800206[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 24 )[/C][C]17.8836065573770[/C][C]0.248505701662650[/C][C]71.964572393008[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 24 )[/C][C]17.8694915254237[/C][C]0.238863643273025[/C][C]74.8104285799518[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 24 )[/C][C]17.8561403508772[/C][C]0.228608868344685[/C][C]78.1078200516466[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 24 )[/C][C]17.8490909090909[/C][C]0.219378871071358[/C][C]81.3619416579323[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 24 )[/C][C]17.8415094339623[/C][C]0.207836913467952[/C][C]85.8437951962435[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 24 )[/C][C]17.8352941176471[/C][C]0.197808057676276[/C][C]90.164649141015[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 24 )[/C][C]17.8285714285714[/C][C]0.187740775111471[/C][C]94.9637680891951[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 24 )[/C][C]17.8255319148936[/C][C]0.180437029462786[/C][C]98.790874400701[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 24 )[/C][C]17.82[/C][C]0.173076733143296[/C][C]102.960112987840[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 24 )[/C][C]17.8209302325581[/C][C]0.167204827920425[/C][C]106.581433408366[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 24 )[/C][C]17.8292682926829[/C][C]0.161594339373473[/C][C]110.333495355158[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 24 )[/C][C]17.8307692307692[/C][C]0.156598192439187[/C][C]113.863186752258[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 24 )[/C][C]17.8243243243243[/C][C]0.153800961690420[/C][C]115.892151313086[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 24 )[/C][C]17.82[/C][C]0.150617775463968[/C][C]118.312728661054[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 24 )[/C][C]17.8151515151515[/C][C]0.147781652772714[/C][C]120.550495822042[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 24 )[/C][C]17.8129032258065[/C][C]0.144485883931847[/C][C]123.284730252325[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 24 )[/C][C]17.8068965517241[/C][C]0.140454139780032[/C][C]126.780859429362[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 24 )[/C][C]17.8074074074074[/C][C]0.136805841781219[/C][C]130.16554830959[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 24 )[/C][C]17.804[/C][C]0.132222035480727[/C][C]134.652291013892[/C][/ROW]
[ROW][C]Median[/C][C]18[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]18.1[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]17.7432432432432[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]17.7868421052632[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]17.7868421052632[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]17.7868421052632[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]17.7868421052632[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]17.7868421052632[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]17.7868421052632[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]17.7868421052632[/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=49450&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=49450&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 Mean17.98493150684930.31249761784709557.552219536116
Geometric Mean17.7909972690593
Harmonic Mean17.5980950099908
Quadratic Mean18.1793537869086
Winsorized Mean ( 1 / 24 )17.99863013698630.30505939955239959.0004116031008
Winsorized Mean ( 2 / 24 )18.00958904109590.30048264311124159.9355385543138
Winsorized Mean ( 3 / 24 )18.00547945205480.29768826724562760.4843436345384
Winsorized Mean ( 4 / 24 )17.97808219178080.29115085880865461.7483398996123
Winsorized Mean ( 5 / 24 )17.94383561643840.28085801824610163.8893478224115
Winsorized Mean ( 6 / 24 )17.95205479452050.27939179969368764.2540504560349
Winsorized Mean ( 7 / 24 )17.94246575342470.2737078248699765.5533533319647
Winsorized Mean ( 8 / 24 )17.89863013698630.26088548686209068.6072282221199
Winsorized Mean ( 9 / 24 )17.89863013698630.26088548686209068.6072282221199
Winsorized Mean ( 10 / 24 )17.88493150684930.2434895916696173.4525504117535
Winsorized Mean ( 11 / 24 )17.88493150684930.23294709743030776.7767948351453
Winsorized Mean ( 12 / 24 )17.85205479452050.21053954741033484.7919310842229
Winsorized Mean ( 13 / 24 )17.86986301369860.20189065386204788.5125817954366
Winsorized Mean ( 14 / 24 )17.81232876712330.18649153156390695.512802204745
Winsorized Mean ( 15 / 24 )17.75068493150690.177224106416842100.159539751077
Winsorized Mean ( 16 / 24 )17.81643835616440.166963362611241106.708669959220
Winsorized Mean ( 17 / 24 )17.8863013698630.150016679292016119.228751458005
Winsorized Mean ( 18 / 24 )17.86164383561640.146374633204535122.026907562991
Winsorized Mean ( 19 / 24 )17.86164383561640.139028348906961128.474832478731
Winsorized Mean ( 20 / 24 )17.83424657534250.135136482929583131.972108410099
Winsorized Mean ( 21 / 24 )17.86301369863010.131240812526378136.108679569778
Winsorized Mean ( 22 / 24 )17.80273972602740.12289278040087144.863999886370
Winsorized Mean ( 23 / 24 )17.83424657534250.118659098478620150.298180282871
Winsorized Mean ( 24 / 24 )17.83424657534250.109867416605959162.325165424661
Trimmed Mean ( 1 / 24 )17.98169014084510.29631071474833360.6852511429348
Trimmed Mean ( 2 / 24 )17.96376811594200.28591525323264262.8289953503297
Trimmed Mean ( 3 / 24 )17.93880597014930.27644571035352664.890882000696
Trimmed Mean ( 4 / 24 )17.91384615384620.26637593557462167.250242088133
Trimmed Mean ( 5 / 24 )17.89523809523810.25675142307002369.6986909800206
Trimmed Mean ( 6 / 24 )17.88360655737700.24850570166265071.964572393008
Trimmed Mean ( 7 / 24 )17.86949152542370.23886364327302574.8104285799518
Trimmed Mean ( 8 / 24 )17.85614035087720.22860886834468578.1078200516466
Trimmed Mean ( 9 / 24 )17.84909090909090.21937887107135881.3619416579323
Trimmed Mean ( 10 / 24 )17.84150943396230.20783691346795285.8437951962435
Trimmed Mean ( 11 / 24 )17.83529411764710.19780805767627690.164649141015
Trimmed Mean ( 12 / 24 )17.82857142857140.18774077511147194.9637680891951
Trimmed Mean ( 13 / 24 )17.82553191489360.18043702946278698.790874400701
Trimmed Mean ( 14 / 24 )17.820.173076733143296102.960112987840
Trimmed Mean ( 15 / 24 )17.82093023255810.167204827920425106.581433408366
Trimmed Mean ( 16 / 24 )17.82926829268290.161594339373473110.333495355158
Trimmed Mean ( 17 / 24 )17.83076923076920.156598192439187113.863186752258
Trimmed Mean ( 18 / 24 )17.82432432432430.153800961690420115.892151313086
Trimmed Mean ( 19 / 24 )17.820.150617775463968118.312728661054
Trimmed Mean ( 20 / 24 )17.81515151515150.147781652772714120.550495822042
Trimmed Mean ( 21 / 24 )17.81290322580650.144485883931847123.284730252325
Trimmed Mean ( 22 / 24 )17.80689655172410.140454139780032126.780859429362
Trimmed Mean ( 23 / 24 )17.80740740740740.136805841781219130.16554830959
Trimmed Mean ( 24 / 24 )17.8040.132222035480727134.652291013892
Median18
Midrange18.1
Midmean - Weighted Average at Xnp17.7432432432432
Midmean - Weighted Average at X(n+1)p17.7868421052632
Midmean - Empirical Distribution Function17.7868421052632
Midmean - Empirical Distribution Function - Averaging17.7868421052632
Midmean - Empirical Distribution Function - Interpolation17.7868421052632
Midmean - Closest Observation17.7868421052632
Midmean - True Basic - Statistics Graphics Toolkit17.7868421052632
Midmean - MS Excel (old versions)17.7868421052632
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')