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R Software Module

rwasp_centraltendency.wasp

Title produced by software

Central Tendency

Date of computation

Mon, 20 Oct 2008 07:50:27 -0600

Cite this page as follows

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2008/Oct/20/t1224510684q6njxbxaz6rcer8.htm/, Retrieved Fri, 17 May 2024 05:05:29 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=17282, Retrieved Fri, 17 May 2024 05:05:29 +0000

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IsPrivate?

No (this computation is public)

User-defined keywords

central tendency prijzen uitvoer

Estimated Impact

137

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)

-     [Central Tendency] [Central Tendency:...] [2008-10-20 13:43:11] [9e54d1454d464f1bf9ee4a54d5d56945]
-    D    [Central Tendency] [Central Tendency ...] [2008-10-20 13:50:27] [8da7502cfecb272886bc60b3f290b8b8] [Current]

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Boxplots

-1,3
-1,4
-1,3
-1
-0,8
-0,7
-0,6
-0,8
-0,9
-1
-1,2
-1,3
-1,3
-1,4
-1,4
-1,8
-1,9
-2
-2,4
-2,5
-2,5
-2,3
-1,7
-1,1
-0,7
-0,2
0,3
1,1
1,6
2,2
3
3,8
4,6
5,1
5,3
5,5
5,7
5,9
6,1
6,1
6,3
6,5
6,7
6,6
6,5
6,4
6,3
6,3
6,3
6,2
6
5,6
5,3
5,1
4,5
4
3,5
3,5
3,3
3,1
2,9
2,5
2,6
2,8
2,8
2,9
3,1
3,3
3,5
3,4
3,5
3,7
3,8

Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	2 seconds
R Server	'Sir Ronald Aylmer Fisher' @ 193.190.124.24

\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 & 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=17282&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]'Sir Ronald Aylmer Fisher' @ 193.190.124.24[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=17282&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=17282&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 Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	2 seconds
R Server	'Sir Ronald Aylmer Fisher' @ 193.190.124.24

Central Tendency - Ungrouped Data
Measure	Value	S.E.	Value/S.E.
Arithmetic Mean	2.32328767123288	0.361643259074306	6.4242526659553
Geometric Mean	NaN
Harmonic Mean	-7.03944705628872
Quadratic Mean	3.84892797741689
Winsorized Mean ( 1 / 24 )	2.32191780821918	0.361415525114155	6.424510423247
Winsorized Mean ( 2 / 24 )	2.32191780821918	0.360466711759479	6.44142089261345
Winsorized Mean ( 3 / 24 )	2.32602739726027	0.359725856410680	6.46611122277731
Winsorized Mean ( 4 / 24 )	2.33698630136986	0.355990839935015	6.56473717637362
Winsorized Mean ( 5 / 24 )	2.33698630136986	0.353765926110537	6.60602429143968
Winsorized Mean ( 6 / 24 )	2.34520547945205	0.35241092387863	6.65474683259178
Winsorized Mean ( 7 / 24 )	2.35479452054794	0.350858053966370	6.71153047201718
Winsorized Mean ( 8 / 24 )	2.38767123287671	0.345717137906792	6.90643005820686
Winsorized Mean ( 9 / 24 )	2.37534246575342	0.343795743168813	6.90916776298498
Winsorized Mean ( 10 / 24 )	2.36164383561644	0.341696624908811	6.91152227870759
Winsorized Mean ( 11 / 24 )	2.37671232876712	0.339411033818917	7.00246041510587
Winsorized Mean ( 12 / 24 )	2.36027397260274	0.336925505894366	7.00532886739285
Winsorized Mean ( 13 / 24 )	2.34246575342466	0.334273319662633	7.00763601411205
Winsorized Mean ( 14 / 24 )	2.30410958904110	0.328685856901787	7.01006611832884
Winsorized Mean ( 15 / 24 )	2.30410958904110	0.322639173633454	7.14144399482861
Winsorized Mean ( 16 / 24 )	2.30410958904110	0.316254468303749	7.28561908199855
Winsorized Mean ( 17 / 24 )	2.28082191780822	0.306323869941962	7.44578578953171
Winsorized Mean ( 18 / 24 )	2.28082191780822	0.306323869941962	7.44578578953171
Winsorized Mean ( 19 / 24 )	2.25479452054794	0.295411646181621	7.63272047562296
Winsorized Mean ( 20 / 24 )	2.28219178082192	0.291367050712792	7.83270371594464
Winsorized Mean ( 21 / 24 )	2.13835616438356	0.272668127354456	7.84234000919292
Winsorized Mean ( 22 / 24 )	2.13835616438356	0.264407022562975	8.08736524338819
Winsorized Mean ( 23 / 24 )	1.98082191780822	0.245613399290707	8.06479582762392
Winsorized Mean ( 24 / 24 )	1.94794520547945	0.233244516601161	8.35151554199389
Trimmed Mean ( 1 / 24 )	2.32957746478873	0.360244687502860	6.46665320989707
Trimmed Mean ( 2 / 24 )	2.33768115942029	0.358617582589756	6.51859047885697
Trimmed Mean ( 3 / 24 )	2.34626865671642	0.357021248217692	6.5717899660857
Trimmed Mean ( 4 / 24 )	2.35384615384615	0.355181947706146	6.62715593809844
Trimmed Mean ( 5 / 24 )	2.35873015873016	0.353995806228864	6.66315848161545
Trimmed Mean ( 6 / 24 )	2.36393442622951	0.352896157940251	6.6986686395995
Trimmed Mean ( 7 / 24 )	2.36779661016949	0.351571912045558	6.73488560673944
Trimmed Mean ( 8 / 24 )	2.37017543859649	0.349972832030793	6.772455521313
Trimmed Mean ( 9 / 24 )	2.36727272727273	0.348783885750603	6.78721931828421
Trimmed Mean ( 10 / 24 )	2.36603773584906	0.347298755002961	6.8126870648554
Trimmed Mean ( 11 / 24 )	2.36666666666667	0.345442786803037	6.85111039246011
Trimmed Mean ( 12 / 24 )	2.36530612244898	0.343124288537584	6.89343832967947
Trimmed Mean ( 13 / 24 )	2.36595744680851	0.340230054885524	6.95399307860845
Trimmed Mean ( 14 / 24 )	2.36888888888889	0.336602487465410	7.03764522575706
Trimmed Mean ( 15 / 24 )	2.37674418604651	0.332593373750116	7.14609602484807
Trimmed Mean ( 16 / 24 )	2.38536585365854	0.328142610572430	7.2692962657223
Trimmed Mean ( 17 / 24 )	2.39487179487179	0.32312886500608	7.41150684519234
Trimmed Mean ( 18 / 24 )	2.40810810810811	0.318083090604018	7.57068885219669
Trimmed Mean ( 19 / 24 )	2.42285714285714	0.310572410379344	7.80126328638716
Trimmed Mean ( 20 / 24 )	2.44242424242424	0.302390422897985	8.07705554632668
Trimmed Mean ( 21 / 24 )	2.46129032258065	0.291406578451174	8.44624145296377
Trimmed Mean ( 22 / 24 )	2.5	0.280130159754249	8.92442285469436
Trimmed Mean ( 23 / 24 )	2.54444444444444	0.265345731216886	9.5891666799218
Trimmed Mean ( 24 / 24 )	2.616	0.247162564587223	10.5841271082815
Median	3
Midrange	2.1
Midmean - Weighted Average at Xnp	2.23783783783784
Midmean - Weighted Average at X(n+1)p	2.39487179487179
Midmean - Empirical Distribution Function	2.39487179487179
Midmean - Empirical Distribution Function - Averaging	2.39487179487179
Midmean - Empirical Distribution Function - Interpolation	2.39487179487179
Midmean - Closest Observation	2.39487179487179
Midmean - True Basic - Statistics Graphics Toolkit	2.39487179487179
Midmean - MS Excel (old versions)	2.39487179487179
Number of observations	73

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 2.32328767123288 & 0.361643259074306 & 6.4242526659553 \tabularnewline
Geometric Mean & NaN &  &  \tabularnewline
Harmonic Mean & -7.03944705628872 &  &  \tabularnewline
Quadratic Mean & 3.84892797741689 &  &  \tabularnewline
Winsorized Mean ( 1 / 24 ) & 2.32191780821918 & 0.361415525114155 & 6.424510423247 \tabularnewline
Winsorized Mean ( 2 / 24 ) & 2.32191780821918 & 0.360466711759479 & 6.44142089261345 \tabularnewline
Winsorized Mean ( 3 / 24 ) & 2.32602739726027 & 0.359725856410680 & 6.46611122277731 \tabularnewline
Winsorized Mean ( 4 / 24 ) & 2.33698630136986 & 0.355990839935015 & 6.56473717637362 \tabularnewline
Winsorized Mean ( 5 / 24 ) & 2.33698630136986 & 0.353765926110537 & 6.60602429143968 \tabularnewline
Winsorized Mean ( 6 / 24 ) & 2.34520547945205 & 0.35241092387863 & 6.65474683259178 \tabularnewline
Winsorized Mean ( 7 / 24 ) & 2.35479452054794 & 0.350858053966370 & 6.71153047201718 \tabularnewline
Winsorized Mean ( 8 / 24 ) & 2.38767123287671 & 0.345717137906792 & 6.90643005820686 \tabularnewline
Winsorized Mean ( 9 / 24 ) & 2.37534246575342 & 0.343795743168813 & 6.90916776298498 \tabularnewline
Winsorized Mean ( 10 / 24 ) & 2.36164383561644 & 0.341696624908811 & 6.91152227870759 \tabularnewline
Winsorized Mean ( 11 / 24 ) & 2.37671232876712 & 0.339411033818917 & 7.00246041510587 \tabularnewline
Winsorized Mean ( 12 / 24 ) & 2.36027397260274 & 0.336925505894366 & 7.00532886739285 \tabularnewline
Winsorized Mean ( 13 / 24 ) & 2.34246575342466 & 0.334273319662633 & 7.00763601411205 \tabularnewline
Winsorized Mean ( 14 / 24 ) & 2.30410958904110 & 0.328685856901787 & 7.01006611832884 \tabularnewline
Winsorized Mean ( 15 / 24 ) & 2.30410958904110 & 0.322639173633454 & 7.14144399482861 \tabularnewline
Winsorized Mean ( 16 / 24 ) & 2.30410958904110 & 0.316254468303749 & 7.28561908199855 \tabularnewline
Winsorized Mean ( 17 / 24 ) & 2.28082191780822 & 0.306323869941962 & 7.44578578953171 \tabularnewline
Winsorized Mean ( 18 / 24 ) & 2.28082191780822 & 0.306323869941962 & 7.44578578953171 \tabularnewline
Winsorized Mean ( 19 / 24 ) & 2.25479452054794 & 0.295411646181621 & 7.63272047562296 \tabularnewline
Winsorized Mean ( 20 / 24 ) & 2.28219178082192 & 0.291367050712792 & 7.83270371594464 \tabularnewline
Winsorized Mean ( 21 / 24 ) & 2.13835616438356 & 0.272668127354456 & 7.84234000919292 \tabularnewline
Winsorized Mean ( 22 / 24 ) & 2.13835616438356 & 0.264407022562975 & 8.08736524338819 \tabularnewline
Winsorized Mean ( 23 / 24 ) & 1.98082191780822 & 0.245613399290707 & 8.06479582762392 \tabularnewline
Winsorized Mean ( 24 / 24 ) & 1.94794520547945 & 0.233244516601161 & 8.35151554199389 \tabularnewline
Trimmed Mean ( 1 / 24 ) & 2.32957746478873 & 0.360244687502860 & 6.46665320989707 \tabularnewline
Trimmed Mean ( 2 / 24 ) & 2.33768115942029 & 0.358617582589756 & 6.51859047885697 \tabularnewline
Trimmed Mean ( 3 / 24 ) & 2.34626865671642 & 0.357021248217692 & 6.5717899660857 \tabularnewline
Trimmed Mean ( 4 / 24 ) & 2.35384615384615 & 0.355181947706146 & 6.62715593809844 \tabularnewline
Trimmed Mean ( 5 / 24 ) & 2.35873015873016 & 0.353995806228864 & 6.66315848161545 \tabularnewline
Trimmed Mean ( 6 / 24 ) & 2.36393442622951 & 0.352896157940251 & 6.6986686395995 \tabularnewline
Trimmed Mean ( 7 / 24 ) & 2.36779661016949 & 0.351571912045558 & 6.73488560673944 \tabularnewline
Trimmed Mean ( 8 / 24 ) & 2.37017543859649 & 0.349972832030793 & 6.772455521313 \tabularnewline
Trimmed Mean ( 9 / 24 ) & 2.36727272727273 & 0.348783885750603 & 6.78721931828421 \tabularnewline
Trimmed Mean ( 10 / 24 ) & 2.36603773584906 & 0.347298755002961 & 6.8126870648554 \tabularnewline
Trimmed Mean ( 11 / 24 ) & 2.36666666666667 & 0.345442786803037 & 6.85111039246011 \tabularnewline
Trimmed Mean ( 12 / 24 ) & 2.36530612244898 & 0.343124288537584 & 6.89343832967947 \tabularnewline
Trimmed Mean ( 13 / 24 ) & 2.36595744680851 & 0.340230054885524 & 6.95399307860845 \tabularnewline
Trimmed Mean ( 14 / 24 ) & 2.36888888888889 & 0.336602487465410 & 7.03764522575706 \tabularnewline
Trimmed Mean ( 15 / 24 ) & 2.37674418604651 & 0.332593373750116 & 7.14609602484807 \tabularnewline
Trimmed Mean ( 16 / 24 ) & 2.38536585365854 & 0.328142610572430 & 7.2692962657223 \tabularnewline
Trimmed Mean ( 17 / 24 ) & 2.39487179487179 & 0.32312886500608 & 7.41150684519234 \tabularnewline
Trimmed Mean ( 18 / 24 ) & 2.40810810810811 & 0.318083090604018 & 7.57068885219669 \tabularnewline
Trimmed Mean ( 19 / 24 ) & 2.42285714285714 & 0.310572410379344 & 7.80126328638716 \tabularnewline
Trimmed Mean ( 20 / 24 ) & 2.44242424242424 & 0.302390422897985 & 8.07705554632668 \tabularnewline
Trimmed Mean ( 21 / 24 ) & 2.46129032258065 & 0.291406578451174 & 8.44624145296377 \tabularnewline
Trimmed Mean ( 22 / 24 ) & 2.5 & 0.280130159754249 & 8.92442285469436 \tabularnewline
Trimmed Mean ( 23 / 24 ) & 2.54444444444444 & 0.265345731216886 & 9.5891666799218 \tabularnewline
Trimmed Mean ( 24 / 24 ) & 2.616 & 0.247162564587223 & 10.5841271082815 \tabularnewline
Median & 3 &  &  \tabularnewline
Midrange & 2.1 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 2.23783783783784 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 2.39487179487179 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 2.39487179487179 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 2.39487179487179 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 2.39487179487179 &  &  \tabularnewline
Midmean - Closest Observation & 2.39487179487179 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 2.39487179487179 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 2.39487179487179 &  &  \tabularnewline
Number of observations & 73 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=17282&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]2.32328767123288[/C][C]0.361643259074306[/C][C]6.4242526659553[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]NaN[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]-7.03944705628872[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]3.84892797741689[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 24 )[/C][C]2.32191780821918[/C][C]0.361415525114155[/C][C]6.424510423247[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 24 )[/C][C]2.32191780821918[/C][C]0.360466711759479[/C][C]6.44142089261345[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 24 )[/C][C]2.32602739726027[/C][C]0.359725856410680[/C][C]6.46611122277731[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 24 )[/C][C]2.33698630136986[/C][C]0.355990839935015[/C][C]6.56473717637362[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 24 )[/C][C]2.33698630136986[/C][C]0.353765926110537[/C][C]6.60602429143968[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 24 )[/C][C]2.34520547945205[/C][C]0.35241092387863[/C][C]6.65474683259178[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 24 )[/C][C]2.35479452054794[/C][C]0.350858053966370[/C][C]6.71153047201718[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 24 )[/C][C]2.38767123287671[/C][C]0.345717137906792[/C][C]6.90643005820686[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 24 )[/C][C]2.37534246575342[/C][C]0.343795743168813[/C][C]6.90916776298498[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 24 )[/C][C]2.36164383561644[/C][C]0.341696624908811[/C][C]6.91152227870759[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 24 )[/C][C]2.37671232876712[/C][C]0.339411033818917[/C][C]7.00246041510587[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 24 )[/C][C]2.36027397260274[/C][C]0.336925505894366[/C][C]7.00532886739285[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 24 )[/C][C]2.34246575342466[/C][C]0.334273319662633[/C][C]7.00763601411205[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 24 )[/C][C]2.30410958904110[/C][C]0.328685856901787[/C][C]7.01006611832884[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 24 )[/C][C]2.30410958904110[/C][C]0.322639173633454[/C][C]7.14144399482861[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 24 )[/C][C]2.30410958904110[/C][C]0.316254468303749[/C][C]7.28561908199855[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 24 )[/C][C]2.28082191780822[/C][C]0.306323869941962[/C][C]7.44578578953171[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 24 )[/C][C]2.28082191780822[/C][C]0.306323869941962[/C][C]7.44578578953171[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 24 )[/C][C]2.25479452054794[/C][C]0.295411646181621[/C][C]7.63272047562296[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 24 )[/C][C]2.28219178082192[/C][C]0.291367050712792[/C][C]7.83270371594464[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 24 )[/C][C]2.13835616438356[/C][C]0.272668127354456[/C][C]7.84234000919292[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 24 )[/C][C]2.13835616438356[/C][C]0.264407022562975[/C][C]8.08736524338819[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 24 )[/C][C]1.98082191780822[/C][C]0.245613399290707[/C][C]8.06479582762392[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 24 )[/C][C]1.94794520547945[/C][C]0.233244516601161[/C][C]8.35151554199389[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 24 )[/C][C]2.32957746478873[/C][C]0.360244687502860[/C][C]6.46665320989707[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 24 )[/C][C]2.33768115942029[/C][C]0.358617582589756[/C][C]6.51859047885697[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 24 )[/C][C]2.34626865671642[/C][C]0.357021248217692[/C][C]6.5717899660857[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 24 )[/C][C]2.35384615384615[/C][C]0.355181947706146[/C][C]6.62715593809844[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 24 )[/C][C]2.35873015873016[/C][C]0.353995806228864[/C][C]6.66315848161545[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 24 )[/C][C]2.36393442622951[/C][C]0.352896157940251[/C][C]6.6986686395995[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 24 )[/C][C]2.36779661016949[/C][C]0.351571912045558[/C][C]6.73488560673944[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 24 )[/C][C]2.37017543859649[/C][C]0.349972832030793[/C][C]6.772455521313[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 24 )[/C][C]2.36727272727273[/C][C]0.348783885750603[/C][C]6.78721931828421[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 24 )[/C][C]2.36603773584906[/C][C]0.347298755002961[/C][C]6.8126870648554[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 24 )[/C][C]2.36666666666667[/C][C]0.345442786803037[/C][C]6.85111039246011[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 24 )[/C][C]2.36530612244898[/C][C]0.343124288537584[/C][C]6.89343832967947[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 24 )[/C][C]2.36595744680851[/C][C]0.340230054885524[/C][C]6.95399307860845[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 24 )[/C][C]2.36888888888889[/C][C]0.336602487465410[/C][C]7.03764522575706[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 24 )[/C][C]2.37674418604651[/C][C]0.332593373750116[/C][C]7.14609602484807[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 24 )[/C][C]2.38536585365854[/C][C]0.328142610572430[/C][C]7.2692962657223[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 24 )[/C][C]2.39487179487179[/C][C]0.32312886500608[/C][C]7.41150684519234[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 24 )[/C][C]2.40810810810811[/C][C]0.318083090604018[/C][C]7.57068885219669[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 24 )[/C][C]2.42285714285714[/C][C]0.310572410379344[/C][C]7.80126328638716[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 24 )[/C][C]2.44242424242424[/C][C]0.302390422897985[/C][C]8.07705554632668[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 24 )[/C][C]2.46129032258065[/C][C]0.291406578451174[/C][C]8.44624145296377[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 24 )[/C][C]2.5[/C][C]0.280130159754249[/C][C]8.92442285469436[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 24 )[/C][C]2.54444444444444[/C][C]0.265345731216886[/C][C]9.5891666799218[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 24 )[/C][C]2.616[/C][C]0.247162564587223[/C][C]10.5841271082815[/C][/ROW]
[ROW][C]Median[/C][C]3[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]2.1[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]2.23783783783784[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]2.39487179487179[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]2.39487179487179[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]2.39487179487179[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]2.39487179487179[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]2.39487179487179[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]2.39487179487179[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]2.39487179487179[/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=17282&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=17282&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
Measure	Value	S.E.	Value/S.E.
Arithmetic Mean	2.32328767123288	0.361643259074306	6.4242526659553
Geometric Mean	NaN
Harmonic Mean	-7.03944705628872
Quadratic Mean	3.84892797741689
Winsorized Mean ( 1 / 24 )	2.32191780821918	0.361415525114155	6.424510423247
Winsorized Mean ( 2 / 24 )	2.32191780821918	0.360466711759479	6.44142089261345
Winsorized Mean ( 3 / 24 )	2.32602739726027	0.359725856410680	6.46611122277731
Winsorized Mean ( 4 / 24 )	2.33698630136986	0.355990839935015	6.56473717637362
Winsorized Mean ( 5 / 24 )	2.33698630136986	0.353765926110537	6.60602429143968
Winsorized Mean ( 6 / 24 )	2.34520547945205	0.35241092387863	6.65474683259178
Winsorized Mean ( 7 / 24 )	2.35479452054794	0.350858053966370	6.71153047201718
Winsorized Mean ( 8 / 24 )	2.38767123287671	0.345717137906792	6.90643005820686
Winsorized Mean ( 9 / 24 )	2.37534246575342	0.343795743168813	6.90916776298498
Winsorized Mean ( 10 / 24 )	2.36164383561644	0.341696624908811	6.91152227870759
Winsorized Mean ( 11 / 24 )	2.37671232876712	0.339411033818917	7.00246041510587
Winsorized Mean ( 12 / 24 )	2.36027397260274	0.336925505894366	7.00532886739285
Winsorized Mean ( 13 / 24 )	2.34246575342466	0.334273319662633	7.00763601411205
Winsorized Mean ( 14 / 24 )	2.30410958904110	0.328685856901787	7.01006611832884
Winsorized Mean ( 15 / 24 )	2.30410958904110	0.322639173633454	7.14144399482861
Winsorized Mean ( 16 / 24 )	2.30410958904110	0.316254468303749	7.28561908199855
Winsorized Mean ( 17 / 24 )	2.28082191780822	0.306323869941962	7.44578578953171
Winsorized Mean ( 18 / 24 )	2.28082191780822	0.306323869941962	7.44578578953171
Winsorized Mean ( 19 / 24 )	2.25479452054794	0.295411646181621	7.63272047562296
Winsorized Mean ( 20 / 24 )	2.28219178082192	0.291367050712792	7.83270371594464
Winsorized Mean ( 21 / 24 )	2.13835616438356	0.272668127354456	7.84234000919292
Winsorized Mean ( 22 / 24 )	2.13835616438356	0.264407022562975	8.08736524338819
Winsorized Mean ( 23 / 24 )	1.98082191780822	0.245613399290707	8.06479582762392
Winsorized Mean ( 24 / 24 )	1.94794520547945	0.233244516601161	8.35151554199389
Trimmed Mean ( 1 / 24 )	2.32957746478873	0.360244687502860	6.46665320989707
Trimmed Mean ( 2 / 24 )	2.33768115942029	0.358617582589756	6.51859047885697
Trimmed Mean ( 3 / 24 )	2.34626865671642	0.357021248217692	6.5717899660857
Trimmed Mean ( 4 / 24 )	2.35384615384615	0.355181947706146	6.62715593809844
Trimmed Mean ( 5 / 24 )	2.35873015873016	0.353995806228864	6.66315848161545
Trimmed Mean ( 6 / 24 )	2.36393442622951	0.352896157940251	6.6986686395995
Trimmed Mean ( 7 / 24 )	2.36779661016949	0.351571912045558	6.73488560673944
Trimmed Mean ( 8 / 24 )	2.37017543859649	0.349972832030793	6.772455521313
Trimmed Mean ( 9 / 24 )	2.36727272727273	0.348783885750603	6.78721931828421
Trimmed Mean ( 10 / 24 )	2.36603773584906	0.347298755002961	6.8126870648554
Trimmed Mean ( 11 / 24 )	2.36666666666667	0.345442786803037	6.85111039246011
Trimmed Mean ( 12 / 24 )	2.36530612244898	0.343124288537584	6.89343832967947
Trimmed Mean ( 13 / 24 )	2.36595744680851	0.340230054885524	6.95399307860845
Trimmed Mean ( 14 / 24 )	2.36888888888889	0.336602487465410	7.03764522575706
Trimmed Mean ( 15 / 24 )	2.37674418604651	0.332593373750116	7.14609602484807
Trimmed Mean ( 16 / 24 )	2.38536585365854	0.328142610572430	7.2692962657223
Trimmed Mean ( 17 / 24 )	2.39487179487179	0.32312886500608	7.41150684519234
Trimmed Mean ( 18 / 24 )	2.40810810810811	0.318083090604018	7.57068885219669
Trimmed Mean ( 19 / 24 )	2.42285714285714	0.310572410379344	7.80126328638716
Trimmed Mean ( 20 / 24 )	2.44242424242424	0.302390422897985	8.07705554632668
Trimmed Mean ( 21 / 24 )	2.46129032258065	0.291406578451174	8.44624145296377
Trimmed Mean ( 22 / 24 )	2.5	0.280130159754249	8.92442285469436
Trimmed Mean ( 23 / 24 )	2.54444444444444	0.265345731216886	9.5891666799218
Trimmed Mean ( 24 / 24 )	2.616	0.247162564587223	10.5841271082815
Median	3
Midrange	2.1
Midmean - Weighted Average at Xnp	2.23783783783784
Midmean - Weighted Average at X(n+1)p	2.39487179487179
Midmean - Empirical Distribution Function	2.39487179487179
Midmean - Empirical Distribution Function - Averaging	2.39487179487179
Midmean - Empirical Distribution Function - Interpolation	2.39487179487179
Midmean - Closest Observation	2.39487179487179
Midmean - True Basic - Statistics Graphics Toolkit	2.39487179487179
Midmean - MS Excel (old versions)	2.39487179487179
Number of observations	73

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

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')

Free Statistics

Description of Statistical Computation

Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code