Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationSun, 21 Oct 2007 06:53:33 -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/21/6gemscazv7la0vq1192974606.htm/, Retrieved Thu, 09 May 2024 16:27:36 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=1209, Retrieved Thu, 09 May 2024 16:27:36 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsgroep 7, workshop2
Estimated Impact214
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [workshop 2: vraag...] [2007-10-21 13:53:33] [2cdb7403ed3391afb545b8c0d20da37e] [Current]
Feedback Forum

Post a new message
Dataseries X:
6,3
7,5
7,4
7,4
7,4
7,4
7,4
7,2
7,2
7,2
7,5
7,4
7,4
8
8,1
8,1
8,1
8,1
8,1
7,9
7,9
8
8,1
8,1
8,1
8,5
8,5
8,6
8,4
8,4
8,4
7,7
7,8
7,9
8,7
8,8
8,8
8,5
8,5
8,5
8,4
8,5
8,5
8,3
8,4
8,4
8,4
8,4
8,4
8,5
8,5
8,5
8,5
8,5
8,5
8,3
8,3
8,4
8,2
8,2
8,1
8,1
8
7,8
7,9
7,8
7,7
7,9
7,8
7,7
7,7
7,6
7,5




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=1209&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=1209&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=1209&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 Mean8.041095890410960.0553745932034203145.212730698928
Geometric Mean8.0268101364404
Harmonic Mean8.01191246462044
Quadratic Mean8.0548122262409
Winsorized Mean ( 1 / 24 )8.053424657534250.0512062335593077157.274302321155
Winsorized Mean ( 2 / 24 )8.050684931506850.0506849315068493158.837837837838
Winsorized Mean ( 3 / 24 )8.046575342465750.0500031274433181160.921441395582
Winsorized Mean ( 4 / 24 )8.052054794520550.0468615300906776171.826544693264
Winsorized Mean ( 5 / 24 )8.052054794520550.0468615300906776171.826544693264
Winsorized Mean ( 6 / 24 )8.052054794520550.0468615300906776171.826544693264
Winsorized Mean ( 7 / 24 )8.052054794520550.0468615300906776171.826544693264
Winsorized Mean ( 8 / 24 )8.052054794520550.0468615300906776171.826544693264
Winsorized Mean ( 9 / 24 )8.052054794520550.0468615300906776171.826544693264
Winsorized Mean ( 10 / 24 )8.052054794520550.0468615300906776171.826544693264
Winsorized Mean ( 11 / 24 )8.067123287671230.0440550538774861183.114593619731
Winsorized Mean ( 12 / 24 )8.067123287671230.0440550538774861183.114593619731
Winsorized Mean ( 13 / 24 )8.067123287671230.0440550538774861183.114593619731
Winsorized Mean ( 14 / 24 )8.086301369863010.0407462293636599198.455206681649
Winsorized Mean ( 15 / 24 )8.10684931506850.0374881395309498216.251044103577
Winsorized Mean ( 16 / 24 )8.10684931506850.0374881395309498216.251044103577
Winsorized Mean ( 17 / 24 )8.083561643835620.0342906869637143235.736357582730
Winsorized Mean ( 18 / 24 )8.083561643835620.0342906869637143235.736357582730
Winsorized Mean ( 19 / 24 )8.109589041095890.0304184654851623266.600859436898
Winsorized Mean ( 20 / 24 )8.109589041095890.0304184654851623266.600859436898
Winsorized Mean ( 21 / 24 )8.109589041095890.0304184654851623266.600859436898
Winsorized Mean ( 22 / 24 )8.109589041095890.0304184654851623266.600859436898
Winsorized Mean ( 23 / 24 )8.141095890410960.0261592430820137311.212976036318
Winsorized Mean ( 24 / 24 )8.141095890410960.0261592430820137311.212976036318
Trimmed Mean ( 1 / 24 )8.054929577464790.0501422015054018160.641721656299
Trimmed Mean ( 2 / 24 )8.056521739130440.0488782200562116164.828459994352
Trimmed Mean ( 3 / 24 )8.059701492537310.0476996720451846168.967650027081
Trimmed Mean ( 4 / 24 )8.064615384615380.0465869105724601173.109040404641
Trimmed Mean ( 5 / 24 )8.068253968253970.0463642492545388174.018863628297
Trimmed Mean ( 6 / 24 )8.072131147540980.0460536125886384175.276828327088
Trimmed Mean ( 7 / 24 )8.076271186440680.0456359045750951176.971865938385
Trimmed Mean ( 8 / 24 )8.080701754385960.0450868416091202179.225278728581
Trimmed Mean ( 9 / 24 )8.085454545454550.0443750606254193182.207177443786
Trimmed Mean ( 10 / 24 )8.090566037735850.0434592840281504186.164273495515
Trimmed Mean ( 11 / 24 )8.096078431372550.042283894334695191.469554986791
Trimmed Mean ( 12 / 24 )8.10.0414449885369743195.439793469209
Trimmed Mean ( 13 / 24 )8.104255319148940.0403451169612064200.87326371966
Trimmed Mean ( 14 / 24 )8.108888888888890.0389018737340819208.444686863109
Trimmed Mean ( 15 / 24 )8.111627906976740.037827097215921214.439608217219
Trimmed Mean ( 16 / 24 )8.112195121951220.0371541157407667218.339071196095
Trimmed Mean ( 17 / 24 )8.112820512820510.0362141417750097224.023547574968
Trimmed Mean ( 18 / 24 )8.116216216216220.0356226286842659227.838778776061
Trimmed Mean ( 19 / 24 )8.120.0347379142879309233.750360850570
Trimmed Mean ( 20 / 24 )8.121212121212120.0344759401605538235.56173039493
Trimmed Mean ( 21 / 24 )8.122580645161290.0339859798479121238.997983330479
Trimmed Mean ( 22 / 24 )8.124137931034480.0331644552787437244.965215401609
Trimmed Mean ( 23 / 24 )8.125925925925930.0318439001536706255.179983818322
Trimmed Mean ( 24 / 24 )8.1240.0312409987036266260.042903143712
Median8.1
Midrange7.55
Midmean - Weighted Average at Xnp8.09268292682926
Midmean - Weighted Average at X(n+1)p8.09268292682926
Midmean - Empirical Distribution Function8.09268292682926
Midmean - Empirical Distribution Function - Averaging8.09268292682926
Midmean - Empirical Distribution Function - Interpolation8.09268292682926
Midmean - Closest Observation8.09268292682926
Midmean - True Basic - Statistics Graphics Toolkit8.09268292682926
Midmean - MS Excel (old versions)8.09268292682926
Number of observations73

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 8.04109589041096 & 0.0553745932034203 & 145.212730698928 \tabularnewline
Geometric Mean & 8.0268101364404 &  &  \tabularnewline
Harmonic Mean & 8.01191246462044 &  &  \tabularnewline
Quadratic Mean & 8.0548122262409 &  &  \tabularnewline
Winsorized Mean ( 1 / 24 ) & 8.05342465753425 & 0.0512062335593077 & 157.274302321155 \tabularnewline
Winsorized Mean ( 2 / 24 ) & 8.05068493150685 & 0.0506849315068493 & 158.837837837838 \tabularnewline
Winsorized Mean ( 3 / 24 ) & 8.04657534246575 & 0.0500031274433181 & 160.921441395582 \tabularnewline
Winsorized Mean ( 4 / 24 ) & 8.05205479452055 & 0.0468615300906776 & 171.826544693264 \tabularnewline
Winsorized Mean ( 5 / 24 ) & 8.05205479452055 & 0.0468615300906776 & 171.826544693264 \tabularnewline
Winsorized Mean ( 6 / 24 ) & 8.05205479452055 & 0.0468615300906776 & 171.826544693264 \tabularnewline
Winsorized Mean ( 7 / 24 ) & 8.05205479452055 & 0.0468615300906776 & 171.826544693264 \tabularnewline
Winsorized Mean ( 8 / 24 ) & 8.05205479452055 & 0.0468615300906776 & 171.826544693264 \tabularnewline
Winsorized Mean ( 9 / 24 ) & 8.05205479452055 & 0.0468615300906776 & 171.826544693264 \tabularnewline
Winsorized Mean ( 10 / 24 ) & 8.05205479452055 & 0.0468615300906776 & 171.826544693264 \tabularnewline
Winsorized Mean ( 11 / 24 ) & 8.06712328767123 & 0.0440550538774861 & 183.114593619731 \tabularnewline
Winsorized Mean ( 12 / 24 ) & 8.06712328767123 & 0.0440550538774861 & 183.114593619731 \tabularnewline
Winsorized Mean ( 13 / 24 ) & 8.06712328767123 & 0.0440550538774861 & 183.114593619731 \tabularnewline
Winsorized Mean ( 14 / 24 ) & 8.08630136986301 & 0.0407462293636599 & 198.455206681649 \tabularnewline
Winsorized Mean ( 15 / 24 ) & 8.1068493150685 & 0.0374881395309498 & 216.251044103577 \tabularnewline
Winsorized Mean ( 16 / 24 ) & 8.1068493150685 & 0.0374881395309498 & 216.251044103577 \tabularnewline
Winsorized Mean ( 17 / 24 ) & 8.08356164383562 & 0.0342906869637143 & 235.736357582730 \tabularnewline
Winsorized Mean ( 18 / 24 ) & 8.08356164383562 & 0.0342906869637143 & 235.736357582730 \tabularnewline
Winsorized Mean ( 19 / 24 ) & 8.10958904109589 & 0.0304184654851623 & 266.600859436898 \tabularnewline
Winsorized Mean ( 20 / 24 ) & 8.10958904109589 & 0.0304184654851623 & 266.600859436898 \tabularnewline
Winsorized Mean ( 21 / 24 ) & 8.10958904109589 & 0.0304184654851623 & 266.600859436898 \tabularnewline
Winsorized Mean ( 22 / 24 ) & 8.10958904109589 & 0.0304184654851623 & 266.600859436898 \tabularnewline
Winsorized Mean ( 23 / 24 ) & 8.14109589041096 & 0.0261592430820137 & 311.212976036318 \tabularnewline
Winsorized Mean ( 24 / 24 ) & 8.14109589041096 & 0.0261592430820137 & 311.212976036318 \tabularnewline
Trimmed Mean ( 1 / 24 ) & 8.05492957746479 & 0.0501422015054018 & 160.641721656299 \tabularnewline
Trimmed Mean ( 2 / 24 ) & 8.05652173913044 & 0.0488782200562116 & 164.828459994352 \tabularnewline
Trimmed Mean ( 3 / 24 ) & 8.05970149253731 & 0.0476996720451846 & 168.967650027081 \tabularnewline
Trimmed Mean ( 4 / 24 ) & 8.06461538461538 & 0.0465869105724601 & 173.109040404641 \tabularnewline
Trimmed Mean ( 5 / 24 ) & 8.06825396825397 & 0.0463642492545388 & 174.018863628297 \tabularnewline
Trimmed Mean ( 6 / 24 ) & 8.07213114754098 & 0.0460536125886384 & 175.276828327088 \tabularnewline
Trimmed Mean ( 7 / 24 ) & 8.07627118644068 & 0.0456359045750951 & 176.971865938385 \tabularnewline
Trimmed Mean ( 8 / 24 ) & 8.08070175438596 & 0.0450868416091202 & 179.225278728581 \tabularnewline
Trimmed Mean ( 9 / 24 ) & 8.08545454545455 & 0.0443750606254193 & 182.207177443786 \tabularnewline
Trimmed Mean ( 10 / 24 ) & 8.09056603773585 & 0.0434592840281504 & 186.164273495515 \tabularnewline
Trimmed Mean ( 11 / 24 ) & 8.09607843137255 & 0.042283894334695 & 191.469554986791 \tabularnewline
Trimmed Mean ( 12 / 24 ) & 8.1 & 0.0414449885369743 & 195.439793469209 \tabularnewline
Trimmed Mean ( 13 / 24 ) & 8.10425531914894 & 0.0403451169612064 & 200.87326371966 \tabularnewline
Trimmed Mean ( 14 / 24 ) & 8.10888888888889 & 0.0389018737340819 & 208.444686863109 \tabularnewline
Trimmed Mean ( 15 / 24 ) & 8.11162790697674 & 0.037827097215921 & 214.439608217219 \tabularnewline
Trimmed Mean ( 16 / 24 ) & 8.11219512195122 & 0.0371541157407667 & 218.339071196095 \tabularnewline
Trimmed Mean ( 17 / 24 ) & 8.11282051282051 & 0.0362141417750097 & 224.023547574968 \tabularnewline
Trimmed Mean ( 18 / 24 ) & 8.11621621621622 & 0.0356226286842659 & 227.838778776061 \tabularnewline
Trimmed Mean ( 19 / 24 ) & 8.12 & 0.0347379142879309 & 233.750360850570 \tabularnewline
Trimmed Mean ( 20 / 24 ) & 8.12121212121212 & 0.0344759401605538 & 235.56173039493 \tabularnewline
Trimmed Mean ( 21 / 24 ) & 8.12258064516129 & 0.0339859798479121 & 238.997983330479 \tabularnewline
Trimmed Mean ( 22 / 24 ) & 8.12413793103448 & 0.0331644552787437 & 244.965215401609 \tabularnewline
Trimmed Mean ( 23 / 24 ) & 8.12592592592593 & 0.0318439001536706 & 255.179983818322 \tabularnewline
Trimmed Mean ( 24 / 24 ) & 8.124 & 0.0312409987036266 & 260.042903143712 \tabularnewline
Median & 8.1 &  &  \tabularnewline
Midrange & 7.55 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 8.09268292682926 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 8.09268292682926 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 8.09268292682926 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 8.09268292682926 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 8.09268292682926 &  &  \tabularnewline
Midmean - Closest Observation & 8.09268292682926 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 8.09268292682926 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 8.09268292682926 &  &  \tabularnewline
Number of observations & 73 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=1209&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]8.04109589041096[/C][C]0.0553745932034203[/C][C]145.212730698928[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]8.0268101364404[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]8.01191246462044[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]8.0548122262409[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 24 )[/C][C]8.05342465753425[/C][C]0.0512062335593077[/C][C]157.274302321155[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 24 )[/C][C]8.05068493150685[/C][C]0.0506849315068493[/C][C]158.837837837838[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 24 )[/C][C]8.04657534246575[/C][C]0.0500031274433181[/C][C]160.921441395582[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 24 )[/C][C]8.05205479452055[/C][C]0.0468615300906776[/C][C]171.826544693264[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 24 )[/C][C]8.05205479452055[/C][C]0.0468615300906776[/C][C]171.826544693264[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 24 )[/C][C]8.05205479452055[/C][C]0.0468615300906776[/C][C]171.826544693264[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 24 )[/C][C]8.05205479452055[/C][C]0.0468615300906776[/C][C]171.826544693264[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 24 )[/C][C]8.05205479452055[/C][C]0.0468615300906776[/C][C]171.826544693264[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 24 )[/C][C]8.05205479452055[/C][C]0.0468615300906776[/C][C]171.826544693264[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 24 )[/C][C]8.05205479452055[/C][C]0.0468615300906776[/C][C]171.826544693264[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 24 )[/C][C]8.06712328767123[/C][C]0.0440550538774861[/C][C]183.114593619731[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 24 )[/C][C]8.06712328767123[/C][C]0.0440550538774861[/C][C]183.114593619731[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 24 )[/C][C]8.06712328767123[/C][C]0.0440550538774861[/C][C]183.114593619731[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 24 )[/C][C]8.08630136986301[/C][C]0.0407462293636599[/C][C]198.455206681649[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 24 )[/C][C]8.1068493150685[/C][C]0.0374881395309498[/C][C]216.251044103577[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 24 )[/C][C]8.1068493150685[/C][C]0.0374881395309498[/C][C]216.251044103577[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 24 )[/C][C]8.08356164383562[/C][C]0.0342906869637143[/C][C]235.736357582730[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 24 )[/C][C]8.08356164383562[/C][C]0.0342906869637143[/C][C]235.736357582730[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 24 )[/C][C]8.10958904109589[/C][C]0.0304184654851623[/C][C]266.600859436898[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 24 )[/C][C]8.10958904109589[/C][C]0.0304184654851623[/C][C]266.600859436898[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 24 )[/C][C]8.10958904109589[/C][C]0.0304184654851623[/C][C]266.600859436898[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 24 )[/C][C]8.10958904109589[/C][C]0.0304184654851623[/C][C]266.600859436898[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 24 )[/C][C]8.14109589041096[/C][C]0.0261592430820137[/C][C]311.212976036318[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 24 )[/C][C]8.14109589041096[/C][C]0.0261592430820137[/C][C]311.212976036318[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 24 )[/C][C]8.05492957746479[/C][C]0.0501422015054018[/C][C]160.641721656299[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 24 )[/C][C]8.05652173913044[/C][C]0.0488782200562116[/C][C]164.828459994352[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 24 )[/C][C]8.05970149253731[/C][C]0.0476996720451846[/C][C]168.967650027081[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 24 )[/C][C]8.06461538461538[/C][C]0.0465869105724601[/C][C]173.109040404641[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 24 )[/C][C]8.06825396825397[/C][C]0.0463642492545388[/C][C]174.018863628297[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 24 )[/C][C]8.07213114754098[/C][C]0.0460536125886384[/C][C]175.276828327088[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 24 )[/C][C]8.07627118644068[/C][C]0.0456359045750951[/C][C]176.971865938385[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 24 )[/C][C]8.08070175438596[/C][C]0.0450868416091202[/C][C]179.225278728581[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 24 )[/C][C]8.08545454545455[/C][C]0.0443750606254193[/C][C]182.207177443786[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 24 )[/C][C]8.09056603773585[/C][C]0.0434592840281504[/C][C]186.164273495515[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 24 )[/C][C]8.09607843137255[/C][C]0.042283894334695[/C][C]191.469554986791[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 24 )[/C][C]8.1[/C][C]0.0414449885369743[/C][C]195.439793469209[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 24 )[/C][C]8.10425531914894[/C][C]0.0403451169612064[/C][C]200.87326371966[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 24 )[/C][C]8.10888888888889[/C][C]0.0389018737340819[/C][C]208.444686863109[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 24 )[/C][C]8.11162790697674[/C][C]0.037827097215921[/C][C]214.439608217219[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 24 )[/C][C]8.11219512195122[/C][C]0.0371541157407667[/C][C]218.339071196095[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 24 )[/C][C]8.11282051282051[/C][C]0.0362141417750097[/C][C]224.023547574968[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 24 )[/C][C]8.11621621621622[/C][C]0.0356226286842659[/C][C]227.838778776061[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 24 )[/C][C]8.12[/C][C]0.0347379142879309[/C][C]233.750360850570[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 24 )[/C][C]8.12121212121212[/C][C]0.0344759401605538[/C][C]235.56173039493[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 24 )[/C][C]8.12258064516129[/C][C]0.0339859798479121[/C][C]238.997983330479[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 24 )[/C][C]8.12413793103448[/C][C]0.0331644552787437[/C][C]244.965215401609[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 24 )[/C][C]8.12592592592593[/C][C]0.0318439001536706[/C][C]255.179983818322[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 24 )[/C][C]8.124[/C][C]0.0312409987036266[/C][C]260.042903143712[/C][/ROW]
[ROW][C]Median[/C][C]8.1[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]7.55[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]8.09268292682926[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]8.09268292682926[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]8.09268292682926[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]8.09268292682926[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]8.09268292682926[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]8.09268292682926[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]8.09268292682926[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]8.09268292682926[/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=1209&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=1209&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 Mean8.041095890410960.0553745932034203145.212730698928
Geometric Mean8.0268101364404
Harmonic Mean8.01191246462044
Quadratic Mean8.0548122262409
Winsorized Mean ( 1 / 24 )8.053424657534250.0512062335593077157.274302321155
Winsorized Mean ( 2 / 24 )8.050684931506850.0506849315068493158.837837837838
Winsorized Mean ( 3 / 24 )8.046575342465750.0500031274433181160.921441395582
Winsorized Mean ( 4 / 24 )8.052054794520550.0468615300906776171.826544693264
Winsorized Mean ( 5 / 24 )8.052054794520550.0468615300906776171.826544693264
Winsorized Mean ( 6 / 24 )8.052054794520550.0468615300906776171.826544693264
Winsorized Mean ( 7 / 24 )8.052054794520550.0468615300906776171.826544693264
Winsorized Mean ( 8 / 24 )8.052054794520550.0468615300906776171.826544693264
Winsorized Mean ( 9 / 24 )8.052054794520550.0468615300906776171.826544693264
Winsorized Mean ( 10 / 24 )8.052054794520550.0468615300906776171.826544693264
Winsorized Mean ( 11 / 24 )8.067123287671230.0440550538774861183.114593619731
Winsorized Mean ( 12 / 24 )8.067123287671230.0440550538774861183.114593619731
Winsorized Mean ( 13 / 24 )8.067123287671230.0440550538774861183.114593619731
Winsorized Mean ( 14 / 24 )8.086301369863010.0407462293636599198.455206681649
Winsorized Mean ( 15 / 24 )8.10684931506850.0374881395309498216.251044103577
Winsorized Mean ( 16 / 24 )8.10684931506850.0374881395309498216.251044103577
Winsorized Mean ( 17 / 24 )8.083561643835620.0342906869637143235.736357582730
Winsorized Mean ( 18 / 24 )8.083561643835620.0342906869637143235.736357582730
Winsorized Mean ( 19 / 24 )8.109589041095890.0304184654851623266.600859436898
Winsorized Mean ( 20 / 24 )8.109589041095890.0304184654851623266.600859436898
Winsorized Mean ( 21 / 24 )8.109589041095890.0304184654851623266.600859436898
Winsorized Mean ( 22 / 24 )8.109589041095890.0304184654851623266.600859436898
Winsorized Mean ( 23 / 24 )8.141095890410960.0261592430820137311.212976036318
Winsorized Mean ( 24 / 24 )8.141095890410960.0261592430820137311.212976036318
Trimmed Mean ( 1 / 24 )8.054929577464790.0501422015054018160.641721656299
Trimmed Mean ( 2 / 24 )8.056521739130440.0488782200562116164.828459994352
Trimmed Mean ( 3 / 24 )8.059701492537310.0476996720451846168.967650027081
Trimmed Mean ( 4 / 24 )8.064615384615380.0465869105724601173.109040404641
Trimmed Mean ( 5 / 24 )8.068253968253970.0463642492545388174.018863628297
Trimmed Mean ( 6 / 24 )8.072131147540980.0460536125886384175.276828327088
Trimmed Mean ( 7 / 24 )8.076271186440680.0456359045750951176.971865938385
Trimmed Mean ( 8 / 24 )8.080701754385960.0450868416091202179.225278728581
Trimmed Mean ( 9 / 24 )8.085454545454550.0443750606254193182.207177443786
Trimmed Mean ( 10 / 24 )8.090566037735850.0434592840281504186.164273495515
Trimmed Mean ( 11 / 24 )8.096078431372550.042283894334695191.469554986791
Trimmed Mean ( 12 / 24 )8.10.0414449885369743195.439793469209
Trimmed Mean ( 13 / 24 )8.104255319148940.0403451169612064200.87326371966
Trimmed Mean ( 14 / 24 )8.108888888888890.0389018737340819208.444686863109
Trimmed Mean ( 15 / 24 )8.111627906976740.037827097215921214.439608217219
Trimmed Mean ( 16 / 24 )8.112195121951220.0371541157407667218.339071196095
Trimmed Mean ( 17 / 24 )8.112820512820510.0362141417750097224.023547574968
Trimmed Mean ( 18 / 24 )8.116216216216220.0356226286842659227.838778776061
Trimmed Mean ( 19 / 24 )8.120.0347379142879309233.750360850570
Trimmed Mean ( 20 / 24 )8.121212121212120.0344759401605538235.56173039493
Trimmed Mean ( 21 / 24 )8.122580645161290.0339859798479121238.997983330479
Trimmed Mean ( 22 / 24 )8.124137931034480.0331644552787437244.965215401609
Trimmed Mean ( 23 / 24 )8.125925925925930.0318439001536706255.179983818322
Trimmed Mean ( 24 / 24 )8.1240.0312409987036266260.042903143712
Median8.1
Midrange7.55
Midmean - Weighted Average at Xnp8.09268292682926
Midmean - Weighted Average at X(n+1)p8.09268292682926
Midmean - Empirical Distribution Function8.09268292682926
Midmean - Empirical Distribution Function - Averaging8.09268292682926
Midmean - Empirical Distribution Function - Interpolation8.09268292682926
Midmean - Closest Observation8.09268292682926
Midmean - True Basic - Statistics Graphics Toolkit8.09268292682926
Midmean - MS Excel (old versions)8.09268292682926
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')