Repository of Reproducible Computations

Free Statistics

of Irreproducible Research!

Author's title

Author

*Unverified author*

R Software Module

rwasp_centraltendency.wasp

Title produced by software

Central Tendency

Date of computation

Wed, 20 Oct 2010 07:35:23 +0000

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/2010/Oct/20/t1287560256q57f2uxvibpvdpk.htm/, Retrieved Fri, 03 May 2024 23:52:59 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=87138, Retrieved Fri, 03 May 2024 23:52:59 +0000

QR Codes:

Paste this QR Code to cite your computation.

Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

KDGP1W52

Estimated Impact

133

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

-       [Central Tendency] [] [2010-10-20 07:35:23] [5cd570406d143ae5f29e48ad26074e87] [Current]

Feedback Forum

Post a new message

Dataseries X:

Download CSV

Histogram

Boxplots

1,35
1,91
1,31
1,19
1,3
1,14
1,1
1,02
1,11
1,18
1,24
1,36
1,29
1,73
1,41
1,15
1,31
1,15
1,08
1,1
1,14
1,24
1,33
1,49
1,38
1,96
1,36
1,24
1,35
1,23
1,09
1,08
1,33
1,35
1,38
1,5
1,47
2,09
1,52
1,29
1,52
1,27
1,35
1,29
1,41
1,39
1,45
1,53
1,45
2,11
1,53
1,38
1,54
1,35
1,29
1,33
1,47
1,47
1,54
1,59
1,5
2
1,51
1,4
1,62
1,44
1,29
1,28
1,4
1,39
1,46
1,49

Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	1 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 1 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=87138&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]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=87138&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=87138&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	1 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

Central Tendency - Ungrouped Data
Measure	Value	S.E.	Value/S.E.
Arithmetic Mean	1.39291666666667	0.0265242953412335	52.5147472815724
Geometric Mean	1.37657764177029
Harmonic Mean	1.36151749723835
Quadratic Mean	1.41073316242143
Winsorized Mean ( 1 / 24 )	1.39347222222222	0.026266927415103	53.0504462970039
Winsorized Mean ( 2 / 24 )	1.39097222222222	0.0253767848591897	54.812783807737
Winsorized Mean ( 3 / 24 )	1.38972222222222	0.0247530622994647	56.1434462293691
Winsorized Mean ( 4 / 24 )	1.3875	0.0237774221888495	58.3536763985574
Winsorized Mean ( 5 / 24 )	1.375	0.0202700855776949	67.8339514024077
Winsorized Mean ( 6 / 24 )	1.36666666666667	0.0180581134579125	75.681586000216
Winsorized Mean ( 7 / 24 )	1.36666666666667	0.0169310023903056	80.71977282628
Winsorized Mean ( 8 / 24 )	1.36111111111111	0.0159745439559069	85.2050058435513
Winsorized Mean ( 9 / 24 )	1.36236111111111	0.0157338647951183	86.587823707104
Winsorized Mean ( 10 / 24 )	1.36097222222222	0.0155168641185783	87.7092311836859
Winsorized Mean ( 11 / 24 )	1.36555555555556	0.0146688657240777	93.092102773435
Winsorized Mean ( 12 / 24 )	1.36555555555556	0.0141142899331304	96.7498586202478
Winsorized Mean ( 13 / 24 )	1.37277777777778	0.0129163406322963	106.282252602200
Winsorized Mean ( 14 / 24 )	1.37277777777778	0.0123083464407580	111.532266692782
Winsorized Mean ( 15 / 24 )	1.37069444444444	0.0119864398947031	114.353757786761
Winsorized Mean ( 16 / 24 )	1.37069444444444	0.0119864398947031	114.353757786761
Winsorized Mean ( 17 / 24 )	1.37541666666667	0.0105834072674953	129.959722034980
Winsorized Mean ( 18 / 24 )	1.37791666666667	0.0102395744529021	134.567766756765
Winsorized Mean ( 19 / 24 )	1.37527777777778	0.00909214742755389	151.259951374081
Winsorized Mean ( 20 / 24 )	1.37527777777778	0.00909214742755389	151.259951374081
Winsorized Mean ( 21 / 24 )	1.37527777777778	0.00909214742755389	151.259951374081
Winsorized Mean ( 22 / 24 )	1.37222222222222	0.0086494552421979	158.648398517353
Winsorized Mean ( 23 / 24 )	1.36902777777778	0.0081988198180787	166.978639384051
Winsorized Mean ( 24 / 24 )	1.37236111111111	0.00775326942889719	177.004181745083
Trimmed Mean ( 1 / 24 )	1.388	0.0246781350990482	56.2441203287494
Trimmed Mean ( 2 / 24 )	1.38220588235294	0.0227188851645128	60.8395118133687
Trimmed Mean ( 3 / 24 )	1.37742424242424	0.0209175433069508	65.8501919757723
Trimmed Mean ( 4 / 24 )	1.3728125	0.0189878678240599	72.2994552479707
Trimmed Mean ( 5 / 24 )	1.36854838709677	0.0169733152531212	80.6294095577534
Trimmed Mean ( 6 / 24 )	1.367	0.0158262101134059	86.3757014600768
Trimmed Mean ( 7 / 24 )	1.36706896551724	0.0151280251796870	90.3666505891897
Trimmed Mean ( 8 / 24 )	1.36714285714286	0.0145867630033710	93.7248968004014
Trimmed Mean ( 9 / 24 )	1.36814814814815	0.0141596025650096	96.6233439015468
Trimmed Mean ( 10 / 24 )	1.36903846153846	0.0136848266630687	100.040613976726
Trimmed Mean ( 11 / 24 )	1.3702	0.013135059798812	104.316236163914
Trimmed Mean ( 12 / 24 )	1.37083333333333	0.0126492274500359	108.372889866048
Trimmed Mean ( 13 / 24 )	1.37152173913043	0.0121582456118433	112.805891813407
Trimmed Mean ( 14 / 24 )	1.37136363636364	0.0118106578749359	116.112383483217
Trimmed Mean ( 15 / 24 )	1.37119047619048	0.0114925738834264	119.310999441813
Trimmed Mean ( 16 / 24 )	1.37125	0.0111412118983575	123.079070078737
Trimmed Mean ( 17 / 24 )	1.37131578947368	0.0106620867017305	128.616079369447
Trimmed Mean ( 18 / 24 )	1.37083333333333	0.0103691774635137	132.202707317617
Trimmed Mean ( 19 / 24 )	1.37	0.0100355873010860	136.51418286718
Trimmed Mean ( 20 / 24 )	1.369375	0.0098674430047309	138.777087371415
Trimmed Mean ( 21 / 24 )	1.36866666666667	0.0095980521651002	142.598377579497
Trimmed Mean ( 22 / 24 )	1.36785714285714	0.00917722541753897	149.049094974062
Trimmed Mean ( 23 / 24 )	1.36730769230769	0.00869230769230768	157.300884955752
Trimmed Mean ( 24 / 24 )	1.36708333333333	0.008108842164948	168.591681219646
Median	1.36
Midrange	1.565
Midmean - Weighted Average at Xnp	1.37131578947368
Midmean - Weighted Average at X(n+1)p	1.37405405405405
Midmean - Empirical Distribution Function	1.37131578947368
Midmean - Empirical Distribution Function - Averaging	1.37405405405405
Midmean - Empirical Distribution Function - Interpolation	1.37405405405405
Midmean - Closest Observation	1.37131578947368
Midmean - True Basic - Statistics Graphics Toolkit	1.37405405405405
Midmean - MS Excel (old versions)	1.37131578947368
Number of observations	72

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 1.39291666666667 & 0.0265242953412335 & 52.5147472815724 \tabularnewline
Geometric Mean & 1.37657764177029 &  &  \tabularnewline
Harmonic Mean & 1.36151749723835 &  &  \tabularnewline
Quadratic Mean & 1.41073316242143 &  &  \tabularnewline
Winsorized Mean ( 1 / 24 ) & 1.39347222222222 & 0.026266927415103 & 53.0504462970039 \tabularnewline
Winsorized Mean ( 2 / 24 ) & 1.39097222222222 & 0.0253767848591897 & 54.812783807737 \tabularnewline
Winsorized Mean ( 3 / 24 ) & 1.38972222222222 & 0.0247530622994647 & 56.1434462293691 \tabularnewline
Winsorized Mean ( 4 / 24 ) & 1.3875 & 0.0237774221888495 & 58.3536763985574 \tabularnewline
Winsorized Mean ( 5 / 24 ) & 1.375 & 0.0202700855776949 & 67.8339514024077 \tabularnewline
Winsorized Mean ( 6 / 24 ) & 1.36666666666667 & 0.0180581134579125 & 75.681586000216 \tabularnewline
Winsorized Mean ( 7 / 24 ) & 1.36666666666667 & 0.0169310023903056 & 80.71977282628 \tabularnewline
Winsorized Mean ( 8 / 24 ) & 1.36111111111111 & 0.0159745439559069 & 85.2050058435513 \tabularnewline
Winsorized Mean ( 9 / 24 ) & 1.36236111111111 & 0.0157338647951183 & 86.587823707104 \tabularnewline
Winsorized Mean ( 10 / 24 ) & 1.36097222222222 & 0.0155168641185783 & 87.7092311836859 \tabularnewline
Winsorized Mean ( 11 / 24 ) & 1.36555555555556 & 0.0146688657240777 & 93.092102773435 \tabularnewline
Winsorized Mean ( 12 / 24 ) & 1.36555555555556 & 0.0141142899331304 & 96.7498586202478 \tabularnewline
Winsorized Mean ( 13 / 24 ) & 1.37277777777778 & 0.0129163406322963 & 106.282252602200 \tabularnewline
Winsorized Mean ( 14 / 24 ) & 1.37277777777778 & 0.0123083464407580 & 111.532266692782 \tabularnewline
Winsorized Mean ( 15 / 24 ) & 1.37069444444444 & 0.0119864398947031 & 114.353757786761 \tabularnewline
Winsorized Mean ( 16 / 24 ) & 1.37069444444444 & 0.0119864398947031 & 114.353757786761 \tabularnewline
Winsorized Mean ( 17 / 24 ) & 1.37541666666667 & 0.0105834072674953 & 129.959722034980 \tabularnewline
Winsorized Mean ( 18 / 24 ) & 1.37791666666667 & 0.0102395744529021 & 134.567766756765 \tabularnewline
Winsorized Mean ( 19 / 24 ) & 1.37527777777778 & 0.00909214742755389 & 151.259951374081 \tabularnewline
Winsorized Mean ( 20 / 24 ) & 1.37527777777778 & 0.00909214742755389 & 151.259951374081 \tabularnewline
Winsorized Mean ( 21 / 24 ) & 1.37527777777778 & 0.00909214742755389 & 151.259951374081 \tabularnewline
Winsorized Mean ( 22 / 24 ) & 1.37222222222222 & 0.0086494552421979 & 158.648398517353 \tabularnewline
Winsorized Mean ( 23 / 24 ) & 1.36902777777778 & 0.0081988198180787 & 166.978639384051 \tabularnewline
Winsorized Mean ( 24 / 24 ) & 1.37236111111111 & 0.00775326942889719 & 177.004181745083 \tabularnewline
Trimmed Mean ( 1 / 24 ) & 1.388 & 0.0246781350990482 & 56.2441203287494 \tabularnewline
Trimmed Mean ( 2 / 24 ) & 1.38220588235294 & 0.0227188851645128 & 60.8395118133687 \tabularnewline
Trimmed Mean ( 3 / 24 ) & 1.37742424242424 & 0.0209175433069508 & 65.8501919757723 \tabularnewline
Trimmed Mean ( 4 / 24 ) & 1.3728125 & 0.0189878678240599 & 72.2994552479707 \tabularnewline
Trimmed Mean ( 5 / 24 ) & 1.36854838709677 & 0.0169733152531212 & 80.6294095577534 \tabularnewline
Trimmed Mean ( 6 / 24 ) & 1.367 & 0.0158262101134059 & 86.3757014600768 \tabularnewline
Trimmed Mean ( 7 / 24 ) & 1.36706896551724 & 0.0151280251796870 & 90.3666505891897 \tabularnewline
Trimmed Mean ( 8 / 24 ) & 1.36714285714286 & 0.0145867630033710 & 93.7248968004014 \tabularnewline
Trimmed Mean ( 9 / 24 ) & 1.36814814814815 & 0.0141596025650096 & 96.6233439015468 \tabularnewline
Trimmed Mean ( 10 / 24 ) & 1.36903846153846 & 0.0136848266630687 & 100.040613976726 \tabularnewline
Trimmed Mean ( 11 / 24 ) & 1.3702 & 0.013135059798812 & 104.316236163914 \tabularnewline
Trimmed Mean ( 12 / 24 ) & 1.37083333333333 & 0.0126492274500359 & 108.372889866048 \tabularnewline
Trimmed Mean ( 13 / 24 ) & 1.37152173913043 & 0.0121582456118433 & 112.805891813407 \tabularnewline
Trimmed Mean ( 14 / 24 ) & 1.37136363636364 & 0.0118106578749359 & 116.112383483217 \tabularnewline
Trimmed Mean ( 15 / 24 ) & 1.37119047619048 & 0.0114925738834264 & 119.310999441813 \tabularnewline
Trimmed Mean ( 16 / 24 ) & 1.37125 & 0.0111412118983575 & 123.079070078737 \tabularnewline
Trimmed Mean ( 17 / 24 ) & 1.37131578947368 & 0.0106620867017305 & 128.616079369447 \tabularnewline
Trimmed Mean ( 18 / 24 ) & 1.37083333333333 & 0.0103691774635137 & 132.202707317617 \tabularnewline
Trimmed Mean ( 19 / 24 ) & 1.37 & 0.0100355873010860 & 136.51418286718 \tabularnewline
Trimmed Mean ( 20 / 24 ) & 1.369375 & 0.0098674430047309 & 138.777087371415 \tabularnewline
Trimmed Mean ( 21 / 24 ) & 1.36866666666667 & 0.0095980521651002 & 142.598377579497 \tabularnewline
Trimmed Mean ( 22 / 24 ) & 1.36785714285714 & 0.00917722541753897 & 149.049094974062 \tabularnewline
Trimmed Mean ( 23 / 24 ) & 1.36730769230769 & 0.00869230769230768 & 157.300884955752 \tabularnewline
Trimmed Mean ( 24 / 24 ) & 1.36708333333333 & 0.008108842164948 & 168.591681219646 \tabularnewline
Median & 1.36 &  &  \tabularnewline
Midrange & 1.565 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 1.37131578947368 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 1.37405405405405 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 1.37131578947368 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 1.37405405405405 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 1.37405405405405 &  &  \tabularnewline
Midmean - Closest Observation & 1.37131578947368 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 1.37405405405405 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 1.37131578947368 &  &  \tabularnewline
Number of observations & 72 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=87138&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]1.39291666666667[/C][C]0.0265242953412335[/C][C]52.5147472815724[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]1.37657764177029[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]1.36151749723835[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]1.41073316242143[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 24 )[/C][C]1.39347222222222[/C][C]0.026266927415103[/C][C]53.0504462970039[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 24 )[/C][C]1.39097222222222[/C][C]0.0253767848591897[/C][C]54.812783807737[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 24 )[/C][C]1.38972222222222[/C][C]0.0247530622994647[/C][C]56.1434462293691[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 24 )[/C][C]1.3875[/C][C]0.0237774221888495[/C][C]58.3536763985574[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 24 )[/C][C]1.375[/C][C]0.0202700855776949[/C][C]67.8339514024077[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 24 )[/C][C]1.36666666666667[/C][C]0.0180581134579125[/C][C]75.681586000216[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 24 )[/C][C]1.36666666666667[/C][C]0.0169310023903056[/C][C]80.71977282628[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 24 )[/C][C]1.36111111111111[/C][C]0.0159745439559069[/C][C]85.2050058435513[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 24 )[/C][C]1.36236111111111[/C][C]0.0157338647951183[/C][C]86.587823707104[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 24 )[/C][C]1.36097222222222[/C][C]0.0155168641185783[/C][C]87.7092311836859[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 24 )[/C][C]1.36555555555556[/C][C]0.0146688657240777[/C][C]93.092102773435[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 24 )[/C][C]1.36555555555556[/C][C]0.0141142899331304[/C][C]96.7498586202478[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 24 )[/C][C]1.37277777777778[/C][C]0.0129163406322963[/C][C]106.282252602200[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 24 )[/C][C]1.37277777777778[/C][C]0.0123083464407580[/C][C]111.532266692782[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 24 )[/C][C]1.37069444444444[/C][C]0.0119864398947031[/C][C]114.353757786761[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 24 )[/C][C]1.37069444444444[/C][C]0.0119864398947031[/C][C]114.353757786761[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 24 )[/C][C]1.37541666666667[/C][C]0.0105834072674953[/C][C]129.959722034980[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 24 )[/C][C]1.37791666666667[/C][C]0.0102395744529021[/C][C]134.567766756765[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 24 )[/C][C]1.37527777777778[/C][C]0.00909214742755389[/C][C]151.259951374081[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 24 )[/C][C]1.37527777777778[/C][C]0.00909214742755389[/C][C]151.259951374081[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 24 )[/C][C]1.37527777777778[/C][C]0.00909214742755389[/C][C]151.259951374081[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 24 )[/C][C]1.37222222222222[/C][C]0.0086494552421979[/C][C]158.648398517353[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 24 )[/C][C]1.36902777777778[/C][C]0.0081988198180787[/C][C]166.978639384051[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 24 )[/C][C]1.37236111111111[/C][C]0.00775326942889719[/C][C]177.004181745083[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 24 )[/C][C]1.388[/C][C]0.0246781350990482[/C][C]56.2441203287494[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 24 )[/C][C]1.38220588235294[/C][C]0.0227188851645128[/C][C]60.8395118133687[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 24 )[/C][C]1.37742424242424[/C][C]0.0209175433069508[/C][C]65.8501919757723[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 24 )[/C][C]1.3728125[/C][C]0.0189878678240599[/C][C]72.2994552479707[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 24 )[/C][C]1.36854838709677[/C][C]0.0169733152531212[/C][C]80.6294095577534[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 24 )[/C][C]1.367[/C][C]0.0158262101134059[/C][C]86.3757014600768[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 24 )[/C][C]1.36706896551724[/C][C]0.0151280251796870[/C][C]90.3666505891897[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 24 )[/C][C]1.36714285714286[/C][C]0.0145867630033710[/C][C]93.7248968004014[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 24 )[/C][C]1.36814814814815[/C][C]0.0141596025650096[/C][C]96.6233439015468[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 24 )[/C][C]1.36903846153846[/C][C]0.0136848266630687[/C][C]100.040613976726[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 24 )[/C][C]1.3702[/C][C]0.013135059798812[/C][C]104.316236163914[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 24 )[/C][C]1.37083333333333[/C][C]0.0126492274500359[/C][C]108.372889866048[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 24 )[/C][C]1.37152173913043[/C][C]0.0121582456118433[/C][C]112.805891813407[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 24 )[/C][C]1.37136363636364[/C][C]0.0118106578749359[/C][C]116.112383483217[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 24 )[/C][C]1.37119047619048[/C][C]0.0114925738834264[/C][C]119.310999441813[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 24 )[/C][C]1.37125[/C][C]0.0111412118983575[/C][C]123.079070078737[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 24 )[/C][C]1.37131578947368[/C][C]0.0106620867017305[/C][C]128.616079369447[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 24 )[/C][C]1.37083333333333[/C][C]0.0103691774635137[/C][C]132.202707317617[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 24 )[/C][C]1.37[/C][C]0.0100355873010860[/C][C]136.51418286718[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 24 )[/C][C]1.369375[/C][C]0.0098674430047309[/C][C]138.777087371415[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 24 )[/C][C]1.36866666666667[/C][C]0.0095980521651002[/C][C]142.598377579497[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 24 )[/C][C]1.36785714285714[/C][C]0.00917722541753897[/C][C]149.049094974062[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 24 )[/C][C]1.36730769230769[/C][C]0.00869230769230768[/C][C]157.300884955752[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 24 )[/C][C]1.36708333333333[/C][C]0.008108842164948[/C][C]168.591681219646[/C][/ROW]
[ROW][C]Median[/C][C]1.36[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]1.565[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]1.37131578947368[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]1.37405405405405[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]1.37131578947368[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]1.37405405405405[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]1.37405405405405[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]1.37131578947368[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]1.37405405405405[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]1.37131578947368[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]72[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=87138&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=87138&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	1.39291666666667	0.0265242953412335	52.5147472815724
Geometric Mean	1.37657764177029
Harmonic Mean	1.36151749723835
Quadratic Mean	1.41073316242143
Winsorized Mean ( 1 / 24 )	1.39347222222222	0.026266927415103	53.0504462970039
Winsorized Mean ( 2 / 24 )	1.39097222222222	0.0253767848591897	54.812783807737
Winsorized Mean ( 3 / 24 )	1.38972222222222	0.0247530622994647	56.1434462293691
Winsorized Mean ( 4 / 24 )	1.3875	0.0237774221888495	58.3536763985574
Winsorized Mean ( 5 / 24 )	1.375	0.0202700855776949	67.8339514024077
Winsorized Mean ( 6 / 24 )	1.36666666666667	0.0180581134579125	75.681586000216
Winsorized Mean ( 7 / 24 )	1.36666666666667	0.0169310023903056	80.71977282628
Winsorized Mean ( 8 / 24 )	1.36111111111111	0.0159745439559069	85.2050058435513
Winsorized Mean ( 9 / 24 )	1.36236111111111	0.0157338647951183	86.587823707104
Winsorized Mean ( 10 / 24 )	1.36097222222222	0.0155168641185783	87.7092311836859
Winsorized Mean ( 11 / 24 )	1.36555555555556	0.0146688657240777	93.092102773435
Winsorized Mean ( 12 / 24 )	1.36555555555556	0.0141142899331304	96.7498586202478
Winsorized Mean ( 13 / 24 )	1.37277777777778	0.0129163406322963	106.282252602200
Winsorized Mean ( 14 / 24 )	1.37277777777778	0.0123083464407580	111.532266692782
Winsorized Mean ( 15 / 24 )	1.37069444444444	0.0119864398947031	114.353757786761
Winsorized Mean ( 16 / 24 )	1.37069444444444	0.0119864398947031	114.353757786761
Winsorized Mean ( 17 / 24 )	1.37541666666667	0.0105834072674953	129.959722034980
Winsorized Mean ( 18 / 24 )	1.37791666666667	0.0102395744529021	134.567766756765
Winsorized Mean ( 19 / 24 )	1.37527777777778	0.00909214742755389	151.259951374081
Winsorized Mean ( 20 / 24 )	1.37527777777778	0.00909214742755389	151.259951374081
Winsorized Mean ( 21 / 24 )	1.37527777777778	0.00909214742755389	151.259951374081
Winsorized Mean ( 22 / 24 )	1.37222222222222	0.0086494552421979	158.648398517353
Winsorized Mean ( 23 / 24 )	1.36902777777778	0.0081988198180787	166.978639384051
Winsorized Mean ( 24 / 24 )	1.37236111111111	0.00775326942889719	177.004181745083
Trimmed Mean ( 1 / 24 )	1.388	0.0246781350990482	56.2441203287494
Trimmed Mean ( 2 / 24 )	1.38220588235294	0.0227188851645128	60.8395118133687
Trimmed Mean ( 3 / 24 )	1.37742424242424	0.0209175433069508	65.8501919757723
Trimmed Mean ( 4 / 24 )	1.3728125	0.0189878678240599	72.2994552479707
Trimmed Mean ( 5 / 24 )	1.36854838709677	0.0169733152531212	80.6294095577534
Trimmed Mean ( 6 / 24 )	1.367	0.0158262101134059	86.3757014600768
Trimmed Mean ( 7 / 24 )	1.36706896551724	0.0151280251796870	90.3666505891897
Trimmed Mean ( 8 / 24 )	1.36714285714286	0.0145867630033710	93.7248968004014
Trimmed Mean ( 9 / 24 )	1.36814814814815	0.0141596025650096	96.6233439015468
Trimmed Mean ( 10 / 24 )	1.36903846153846	0.0136848266630687	100.040613976726
Trimmed Mean ( 11 / 24 )	1.3702	0.013135059798812	104.316236163914
Trimmed Mean ( 12 / 24 )	1.37083333333333	0.0126492274500359	108.372889866048
Trimmed Mean ( 13 / 24 )	1.37152173913043	0.0121582456118433	112.805891813407
Trimmed Mean ( 14 / 24 )	1.37136363636364	0.0118106578749359	116.112383483217
Trimmed Mean ( 15 / 24 )	1.37119047619048	0.0114925738834264	119.310999441813
Trimmed Mean ( 16 / 24 )	1.37125	0.0111412118983575	123.079070078737
Trimmed Mean ( 17 / 24 )	1.37131578947368	0.0106620867017305	128.616079369447
Trimmed Mean ( 18 / 24 )	1.37083333333333	0.0103691774635137	132.202707317617
Trimmed Mean ( 19 / 24 )	1.37	0.0100355873010860	136.51418286718
Trimmed Mean ( 20 / 24 )	1.369375	0.0098674430047309	138.777087371415
Trimmed Mean ( 21 / 24 )	1.36866666666667	0.0095980521651002	142.598377579497
Trimmed Mean ( 22 / 24 )	1.36785714285714	0.00917722541753897	149.049094974062
Trimmed Mean ( 23 / 24 )	1.36730769230769	0.00869230769230768	157.300884955752
Trimmed Mean ( 24 / 24 )	1.36708333333333	0.008108842164948	168.591681219646
Median	1.36
Midrange	1.565
Midmean - Weighted Average at Xnp	1.37131578947368
Midmean - Weighted Average at X(n+1)p	1.37405405405405
Midmean - Empirical Distribution Function	1.37131578947368
Midmean - Empirical Distribution Function - Averaging	1.37405405405405
Midmean - Empirical Distribution Function - Interpolation	1.37405405405405
Midmean - Closest Observation	1.37131578947368
Midmean - True Basic - Statistics Graphics Toolkit	1.37405405405405
Midmean - MS Excel (old versions)	1.37131578947368
Number of observations	72

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