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Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationFri, 16 Oct 2009 05:07:08 -0600
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2009/Oct/16/t1255691309ymbv8reisso1l8m.htm/, Retrieved Tue, 30 Apr 2024 00:23:47 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=46958, Retrieved Tue, 30 Apr 2024 00:23:47 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsSHWWS3V2 Central Tendency Werkloosheidsgraad vrouwen
Estimated Impact164
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Bivariate Data Series] [Bivariate dataset] [2008-01-05 23:51:08] [74be16979710d4c4e7c6647856088456]
F RMPD  [Univariate Explorative Data Analysis] [Colombia Coffee] [2008-01-07 14:21:11] [74be16979710d4c4e7c6647856088456]
F RMPD    [Univariate Data Series] [] [2009-10-14 08:30:28] [74be16979710d4c4e7c6647856088456]
- RMP       [Histogram] [Histogram] [2009-10-16 09:23:58] [4395c69e961f9a13a0559fd2f0a72538]
- RMPD        [Quartiles] [Quartiles] [2009-10-16 09:37:48] [4395c69e961f9a13a0559fd2f0a72538]
- RM            [Percentiles] [Percentiles] [2009-10-16 09:44:59] [4395c69e961f9a13a0559fd2f0a72538]
- RMP             [Harrell-Davis Quantiles] [Harrell Davis Qua...] [2009-10-16 09:52:37] [4395c69e961f9a13a0559fd2f0a72538]
-   P               [Harrell-Davis Quantiles] [Harrell Davis Qua...] [2009-10-16 09:55:33] [4395c69e961f9a13a0559fd2f0a72538]
- RMPD                [Central Tendency] [Central Tendency ...] [2009-10-16 10:45:09] [4395c69e961f9a13a0559fd2f0a72538]
-    D                    [Central Tendency] [Central Tendency ...] [2009-10-16 11:07:08] [d1081bd6cdf1fed9ed45c42dbd523bf1] [Current]
- RM                        [Variability] [Variability Werkl...] [2009-10-16 11:13:10] [4395c69e961f9a13a0559fd2f0a72538]
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Dataseries X:
7.9
9.1
9.4
9.4
9.1
9
9.3
9.9
9.8
9.3
8.3
8
8.5
10.4
11.1
10.9
10
9.2
9.2
9.5
9.6
9.5
9.1
8.9
9
10.1
10.3
10.2
9.6
9.2
9.3
9.4
9.4
9.2
9
9
9
9.8
10
9.8
9.3
9
9
9.1
9.1
9.1
9.2
8.8
8.3
8.4
8.1
7.7
7.9
7.9
8
7.9
7.6
7.1
6.8
6.5
6.9
8.2
8.7
8.3
7.9
7.5
7.8
8.3
8.4
8.2
7.7
7.2
7.3




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 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=46958&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=46958&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=46958&T=0

As an alternative you can also use a QR Code:  

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

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Sir Ronald Aylmer Fisher' @ 193.190.124.24







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean8.820547945205480.11261657082672278.3237127578431
Geometric Mean8.76735822513928
Harmonic Mean8.71262970598255
Quadratic Mean8.8721590089139
Winsorized Mean ( 1 / 24 )8.821917808219180.11076471723891679.645558875852
Winsorized Mean ( 2 / 24 )8.810958904109590.10687126574667782.4446013860704
Winsorized Mean ( 3 / 24 )8.815068493150680.10407729011116084.6973291073948
Winsorized Mean ( 4 / 24 )8.815068493150680.10178526716654186.6045621192653
Winsorized Mean ( 5 / 24 )8.815068493150680.099037822227907289.007091380355
Winsorized Mean ( 6 / 24 )8.823287671232880.09423085556133993.6348037876979
Winsorized Mean ( 7 / 24 )8.832876712328770.09240682490016695.5868435245079
Winsorized Mean ( 8 / 24 )8.832876712328770.088537388041032899.7643696947007
Winsorized Mean ( 9 / 24 )8.820547945205480.0865357041794281101.929579574651
Winsorized Mean ( 10 / 24 )8.834246575342470.0841335817717486105.002620705124
Winsorized Mean ( 11 / 24 )8.849315068493150.0816292265233335108.408660052213
Winsorized Mean ( 12 / 24 )8.816438356164380.0766253039759015115.059097957212
Winsorized Mean ( 13 / 24 )8.816438356164380.0766253039759015115.059097957212
Winsorized Mean ( 14 / 24 )8.79726027397260.0739969095867224118.886860587907
Winsorized Mean ( 15 / 24 )8.79726027397260.0739969095867224118.886860587907
Winsorized Mean ( 16 / 24 )8.79726027397260.0675448045319042130.243330111605
Winsorized Mean ( 17 / 24 )8.79726027397260.0675448045319042130.243330111605
Winsorized Mean ( 18 / 24 )8.821917808219180.0635769938951907138.75959317552
Winsorized Mean ( 19 / 24 )8.847945205479450.0595553535876319148.566747949204
Winsorized Mean ( 20 / 24 )8.820547945205480.0561634554625029157.05137571342
Winsorized Mean ( 21 / 24 )8.849315068493150.0518355351861405170.719083669444
Winsorized Mean ( 22 / 24 )8.849315068493150.0518355351861405170.719083669444
Winsorized Mean ( 23 / 24 )8.849315068493150.0518355351861405170.719083669444
Winsorized Mean ( 24 / 24 )8.816438356164380.0480207059375933183.596600341987
Trimmed Mean ( 1 / 24 )8.821126760563380.10622317141141783.0433383164392
Trimmed Mean ( 2 / 24 )8.820289855072460.10079774956690987.5048291551152
Trimmed Mean ( 3 / 24 )8.825373134328360.096860329804015291.1144237500058
Trimmed Mean ( 4 / 24 )8.829230769230770.093457185716937794.4735356783872
Trimmed Mean ( 5 / 24 )8.833333333333330.090229269333996397.898757227386
Trimmed Mean ( 6 / 24 )8.837704918032790.087220715392537101.325755908544
Trimmed Mean ( 7 / 24 )8.84067796610170.0849629012472885104.053390789593
Trimmed Mean ( 8 / 24 )8.84210526315790.0826771421083214106.947398491027
Trimmed Mean ( 9 / 24 )8.843636363636360.0808108585381172109.436238193967
Trimmed Mean ( 10 / 24 )8.847169811320760.0789353951993342112.081149261103
Trimmed Mean ( 11 / 24 )8.849019607843140.077123407551214114.738441788466
Trimmed Mean ( 12 / 24 )8.848979591836730.075374487339306117.400196063718
Trimmed Mean ( 13 / 24 )8.85319148936170.0741807592931228119.346196692037
Trimmed Mean ( 14 / 24 )8.857777777777780.072577989323425122.044959640662
Trimmed Mean ( 15 / 24 )8.865116279069770.0709751505287792124.904508310625
Trimmed Mean ( 16 / 24 )8.873170731707320.0687895686792117128.990062041032
Trimmed Mean ( 17 / 24 )8.882051282051280.0673252017582725131.927585066017
Trimmed Mean ( 18 / 24 )8.89189189189190.065229829114309136.316345031499
Trimmed Mean ( 19 / 24 )8.90.0633782827369839140.426651143807
Trimmed Mean ( 20 / 24 )8.90606060606060.0618434291877532144.009811923952
Trimmed Mean ( 21 / 24 )8.916129032258060.0603033147314738147.854708683278
Trimmed Mean ( 22 / 24 )8.924137931034480.0592762532333485150.551653389823
Trimmed Mean ( 23 / 24 )8.933333333333330.0574877665668384155.395380040499
Trimmed Mean ( 24 / 24 )8.9440.0544915895651185164.135421105889
Median9
Midrange8.8
Midmean - Weighted Average at Xnp8.91794871794871
Midmean - Weighted Average at X(n+1)p8.91794871794871
Midmean - Empirical Distribution Function8.91794871794871
Midmean - Empirical Distribution Function - Averaging8.91794871794871
Midmean - Empirical Distribution Function - Interpolation8.91794871794871
Midmean - Closest Observation8.87317073170732
Midmean - True Basic - Statistics Graphics Toolkit8.91794871794871
Midmean - MS Excel (old versions)8.91794871794871
Number of observations73

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 8.82054794520548 & 0.112616570826722 & 78.3237127578431 \tabularnewline
Geometric Mean & 8.76735822513928 &  &  \tabularnewline
Harmonic Mean & 8.71262970598255 &  &  \tabularnewline
Quadratic Mean & 8.8721590089139 &  &  \tabularnewline
Winsorized Mean ( 1 / 24 ) & 8.82191780821918 & 0.110764717238916 & 79.645558875852 \tabularnewline
Winsorized Mean ( 2 / 24 ) & 8.81095890410959 & 0.106871265746677 & 82.4446013860704 \tabularnewline
Winsorized Mean ( 3 / 24 ) & 8.81506849315068 & 0.104077290111160 & 84.6973291073948 \tabularnewline
Winsorized Mean ( 4 / 24 ) & 8.81506849315068 & 0.101785267166541 & 86.6045621192653 \tabularnewline
Winsorized Mean ( 5 / 24 ) & 8.81506849315068 & 0.0990378222279072 & 89.007091380355 \tabularnewline
Winsorized Mean ( 6 / 24 ) & 8.82328767123288 & 0.094230855561339 & 93.6348037876979 \tabularnewline
Winsorized Mean ( 7 / 24 ) & 8.83287671232877 & 0.092406824900166 & 95.5868435245079 \tabularnewline
Winsorized Mean ( 8 / 24 ) & 8.83287671232877 & 0.0885373880410328 & 99.7643696947007 \tabularnewline
Winsorized Mean ( 9 / 24 ) & 8.82054794520548 & 0.0865357041794281 & 101.929579574651 \tabularnewline
Winsorized Mean ( 10 / 24 ) & 8.83424657534247 & 0.0841335817717486 & 105.002620705124 \tabularnewline
Winsorized Mean ( 11 / 24 ) & 8.84931506849315 & 0.0816292265233335 & 108.408660052213 \tabularnewline
Winsorized Mean ( 12 / 24 ) & 8.81643835616438 & 0.0766253039759015 & 115.059097957212 \tabularnewline
Winsorized Mean ( 13 / 24 ) & 8.81643835616438 & 0.0766253039759015 & 115.059097957212 \tabularnewline
Winsorized Mean ( 14 / 24 ) & 8.7972602739726 & 0.0739969095867224 & 118.886860587907 \tabularnewline
Winsorized Mean ( 15 / 24 ) & 8.7972602739726 & 0.0739969095867224 & 118.886860587907 \tabularnewline
Winsorized Mean ( 16 / 24 ) & 8.7972602739726 & 0.0675448045319042 & 130.243330111605 \tabularnewline
Winsorized Mean ( 17 / 24 ) & 8.7972602739726 & 0.0675448045319042 & 130.243330111605 \tabularnewline
Winsorized Mean ( 18 / 24 ) & 8.82191780821918 & 0.0635769938951907 & 138.75959317552 \tabularnewline
Winsorized Mean ( 19 / 24 ) & 8.84794520547945 & 0.0595553535876319 & 148.566747949204 \tabularnewline
Winsorized Mean ( 20 / 24 ) & 8.82054794520548 & 0.0561634554625029 & 157.05137571342 \tabularnewline
Winsorized Mean ( 21 / 24 ) & 8.84931506849315 & 0.0518355351861405 & 170.719083669444 \tabularnewline
Winsorized Mean ( 22 / 24 ) & 8.84931506849315 & 0.0518355351861405 & 170.719083669444 \tabularnewline
Winsorized Mean ( 23 / 24 ) & 8.84931506849315 & 0.0518355351861405 & 170.719083669444 \tabularnewline
Winsorized Mean ( 24 / 24 ) & 8.81643835616438 & 0.0480207059375933 & 183.596600341987 \tabularnewline
Trimmed Mean ( 1 / 24 ) & 8.82112676056338 & 0.106223171411417 & 83.0433383164392 \tabularnewline
Trimmed Mean ( 2 / 24 ) & 8.82028985507246 & 0.100797749566909 & 87.5048291551152 \tabularnewline
Trimmed Mean ( 3 / 24 ) & 8.82537313432836 & 0.0968603298040152 & 91.1144237500058 \tabularnewline
Trimmed Mean ( 4 / 24 ) & 8.82923076923077 & 0.0934571857169377 & 94.4735356783872 \tabularnewline
Trimmed Mean ( 5 / 24 ) & 8.83333333333333 & 0.0902292693339963 & 97.898757227386 \tabularnewline
Trimmed Mean ( 6 / 24 ) & 8.83770491803279 & 0.087220715392537 & 101.325755908544 \tabularnewline
Trimmed Mean ( 7 / 24 ) & 8.8406779661017 & 0.0849629012472885 & 104.053390789593 \tabularnewline
Trimmed Mean ( 8 / 24 ) & 8.8421052631579 & 0.0826771421083214 & 106.947398491027 \tabularnewline
Trimmed Mean ( 9 / 24 ) & 8.84363636363636 & 0.0808108585381172 & 109.436238193967 \tabularnewline
Trimmed Mean ( 10 / 24 ) & 8.84716981132076 & 0.0789353951993342 & 112.081149261103 \tabularnewline
Trimmed Mean ( 11 / 24 ) & 8.84901960784314 & 0.077123407551214 & 114.738441788466 \tabularnewline
Trimmed Mean ( 12 / 24 ) & 8.84897959183673 & 0.075374487339306 & 117.400196063718 \tabularnewline
Trimmed Mean ( 13 / 24 ) & 8.8531914893617 & 0.0741807592931228 & 119.346196692037 \tabularnewline
Trimmed Mean ( 14 / 24 ) & 8.85777777777778 & 0.072577989323425 & 122.044959640662 \tabularnewline
Trimmed Mean ( 15 / 24 ) & 8.86511627906977 & 0.0709751505287792 & 124.904508310625 \tabularnewline
Trimmed Mean ( 16 / 24 ) & 8.87317073170732 & 0.0687895686792117 & 128.990062041032 \tabularnewline
Trimmed Mean ( 17 / 24 ) & 8.88205128205128 & 0.0673252017582725 & 131.927585066017 \tabularnewline
Trimmed Mean ( 18 / 24 ) & 8.8918918918919 & 0.065229829114309 & 136.316345031499 \tabularnewline
Trimmed Mean ( 19 / 24 ) & 8.9 & 0.0633782827369839 & 140.426651143807 \tabularnewline
Trimmed Mean ( 20 / 24 ) & 8.9060606060606 & 0.0618434291877532 & 144.009811923952 \tabularnewline
Trimmed Mean ( 21 / 24 ) & 8.91612903225806 & 0.0603033147314738 & 147.854708683278 \tabularnewline
Trimmed Mean ( 22 / 24 ) & 8.92413793103448 & 0.0592762532333485 & 150.551653389823 \tabularnewline
Trimmed Mean ( 23 / 24 ) & 8.93333333333333 & 0.0574877665668384 & 155.395380040499 \tabularnewline
Trimmed Mean ( 24 / 24 ) & 8.944 & 0.0544915895651185 & 164.135421105889 \tabularnewline
Median & 9 &  &  \tabularnewline
Midrange & 8.8 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 8.91794871794871 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 8.91794871794871 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 8.91794871794871 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 8.91794871794871 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 8.91794871794871 &  &  \tabularnewline
Midmean - Closest Observation & 8.87317073170732 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 8.91794871794871 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 8.91794871794871 &  &  \tabularnewline
Number of observations & 73 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=46958&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]8.82054794520548[/C][C]0.112616570826722[/C][C]78.3237127578431[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]8.76735822513928[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]8.71262970598255[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]8.8721590089139[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 24 )[/C][C]8.82191780821918[/C][C]0.110764717238916[/C][C]79.645558875852[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 24 )[/C][C]8.81095890410959[/C][C]0.106871265746677[/C][C]82.4446013860704[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 24 )[/C][C]8.81506849315068[/C][C]0.104077290111160[/C][C]84.6973291073948[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 24 )[/C][C]8.81506849315068[/C][C]0.101785267166541[/C][C]86.6045621192653[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 24 )[/C][C]8.81506849315068[/C][C]0.0990378222279072[/C][C]89.007091380355[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 24 )[/C][C]8.82328767123288[/C][C]0.094230855561339[/C][C]93.6348037876979[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 24 )[/C][C]8.83287671232877[/C][C]0.092406824900166[/C][C]95.5868435245079[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 24 )[/C][C]8.83287671232877[/C][C]0.0885373880410328[/C][C]99.7643696947007[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 24 )[/C][C]8.82054794520548[/C][C]0.0865357041794281[/C][C]101.929579574651[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 24 )[/C][C]8.83424657534247[/C][C]0.0841335817717486[/C][C]105.002620705124[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 24 )[/C][C]8.84931506849315[/C][C]0.0816292265233335[/C][C]108.408660052213[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 24 )[/C][C]8.81643835616438[/C][C]0.0766253039759015[/C][C]115.059097957212[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 24 )[/C][C]8.81643835616438[/C][C]0.0766253039759015[/C][C]115.059097957212[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 24 )[/C][C]8.7972602739726[/C][C]0.0739969095867224[/C][C]118.886860587907[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 24 )[/C][C]8.7972602739726[/C][C]0.0739969095867224[/C][C]118.886860587907[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 24 )[/C][C]8.7972602739726[/C][C]0.0675448045319042[/C][C]130.243330111605[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 24 )[/C][C]8.7972602739726[/C][C]0.0675448045319042[/C][C]130.243330111605[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 24 )[/C][C]8.82191780821918[/C][C]0.0635769938951907[/C][C]138.75959317552[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 24 )[/C][C]8.84794520547945[/C][C]0.0595553535876319[/C][C]148.566747949204[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 24 )[/C][C]8.82054794520548[/C][C]0.0561634554625029[/C][C]157.05137571342[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 24 )[/C][C]8.84931506849315[/C][C]0.0518355351861405[/C][C]170.719083669444[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 24 )[/C][C]8.84931506849315[/C][C]0.0518355351861405[/C][C]170.719083669444[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 24 )[/C][C]8.84931506849315[/C][C]0.0518355351861405[/C][C]170.719083669444[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 24 )[/C][C]8.81643835616438[/C][C]0.0480207059375933[/C][C]183.596600341987[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 24 )[/C][C]8.82112676056338[/C][C]0.106223171411417[/C][C]83.0433383164392[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 24 )[/C][C]8.82028985507246[/C][C]0.100797749566909[/C][C]87.5048291551152[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 24 )[/C][C]8.82537313432836[/C][C]0.0968603298040152[/C][C]91.1144237500058[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 24 )[/C][C]8.82923076923077[/C][C]0.0934571857169377[/C][C]94.4735356783872[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 24 )[/C][C]8.83333333333333[/C][C]0.0902292693339963[/C][C]97.898757227386[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 24 )[/C][C]8.83770491803279[/C][C]0.087220715392537[/C][C]101.325755908544[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 24 )[/C][C]8.8406779661017[/C][C]0.0849629012472885[/C][C]104.053390789593[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 24 )[/C][C]8.8421052631579[/C][C]0.0826771421083214[/C][C]106.947398491027[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 24 )[/C][C]8.84363636363636[/C][C]0.0808108585381172[/C][C]109.436238193967[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 24 )[/C][C]8.84716981132076[/C][C]0.0789353951993342[/C][C]112.081149261103[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 24 )[/C][C]8.84901960784314[/C][C]0.077123407551214[/C][C]114.738441788466[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 24 )[/C][C]8.84897959183673[/C][C]0.075374487339306[/C][C]117.400196063718[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 24 )[/C][C]8.8531914893617[/C][C]0.0741807592931228[/C][C]119.346196692037[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 24 )[/C][C]8.85777777777778[/C][C]0.072577989323425[/C][C]122.044959640662[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 24 )[/C][C]8.86511627906977[/C][C]0.0709751505287792[/C][C]124.904508310625[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 24 )[/C][C]8.87317073170732[/C][C]0.0687895686792117[/C][C]128.990062041032[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 24 )[/C][C]8.88205128205128[/C][C]0.0673252017582725[/C][C]131.927585066017[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 24 )[/C][C]8.8918918918919[/C][C]0.065229829114309[/C][C]136.316345031499[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 24 )[/C][C]8.9[/C][C]0.0633782827369839[/C][C]140.426651143807[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 24 )[/C][C]8.9060606060606[/C][C]0.0618434291877532[/C][C]144.009811923952[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 24 )[/C][C]8.91612903225806[/C][C]0.0603033147314738[/C][C]147.854708683278[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 24 )[/C][C]8.92413793103448[/C][C]0.0592762532333485[/C][C]150.551653389823[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 24 )[/C][C]8.93333333333333[/C][C]0.0574877665668384[/C][C]155.395380040499[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 24 )[/C][C]8.944[/C][C]0.0544915895651185[/C][C]164.135421105889[/C][/ROW]
[ROW][C]Median[/C][C]9[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]8.8[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]8.91794871794871[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]8.91794871794871[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]8.91794871794871[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]8.91794871794871[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]8.91794871794871[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]8.87317073170732[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]8.91794871794871[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]8.91794871794871[/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=46958&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=46958&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 Mean8.820547945205480.11261657082672278.3237127578431
Geometric Mean8.76735822513928
Harmonic Mean8.71262970598255
Quadratic Mean8.8721590089139
Winsorized Mean ( 1 / 24 )8.821917808219180.11076471723891679.645558875852
Winsorized Mean ( 2 / 24 )8.810958904109590.10687126574667782.4446013860704
Winsorized Mean ( 3 / 24 )8.815068493150680.10407729011116084.6973291073948
Winsorized Mean ( 4 / 24 )8.815068493150680.10178526716654186.6045621192653
Winsorized Mean ( 5 / 24 )8.815068493150680.099037822227907289.007091380355
Winsorized Mean ( 6 / 24 )8.823287671232880.09423085556133993.6348037876979
Winsorized Mean ( 7 / 24 )8.832876712328770.09240682490016695.5868435245079
Winsorized Mean ( 8 / 24 )8.832876712328770.088537388041032899.7643696947007
Winsorized Mean ( 9 / 24 )8.820547945205480.0865357041794281101.929579574651
Winsorized Mean ( 10 / 24 )8.834246575342470.0841335817717486105.002620705124
Winsorized Mean ( 11 / 24 )8.849315068493150.0816292265233335108.408660052213
Winsorized Mean ( 12 / 24 )8.816438356164380.0766253039759015115.059097957212
Winsorized Mean ( 13 / 24 )8.816438356164380.0766253039759015115.059097957212
Winsorized Mean ( 14 / 24 )8.79726027397260.0739969095867224118.886860587907
Winsorized Mean ( 15 / 24 )8.79726027397260.0739969095867224118.886860587907
Winsorized Mean ( 16 / 24 )8.79726027397260.0675448045319042130.243330111605
Winsorized Mean ( 17 / 24 )8.79726027397260.0675448045319042130.243330111605
Winsorized Mean ( 18 / 24 )8.821917808219180.0635769938951907138.75959317552
Winsorized Mean ( 19 / 24 )8.847945205479450.0595553535876319148.566747949204
Winsorized Mean ( 20 / 24 )8.820547945205480.0561634554625029157.05137571342
Winsorized Mean ( 21 / 24 )8.849315068493150.0518355351861405170.719083669444
Winsorized Mean ( 22 / 24 )8.849315068493150.0518355351861405170.719083669444
Winsorized Mean ( 23 / 24 )8.849315068493150.0518355351861405170.719083669444
Winsorized Mean ( 24 / 24 )8.816438356164380.0480207059375933183.596600341987
Trimmed Mean ( 1 / 24 )8.821126760563380.10622317141141783.0433383164392
Trimmed Mean ( 2 / 24 )8.820289855072460.10079774956690987.5048291551152
Trimmed Mean ( 3 / 24 )8.825373134328360.096860329804015291.1144237500058
Trimmed Mean ( 4 / 24 )8.829230769230770.093457185716937794.4735356783872
Trimmed Mean ( 5 / 24 )8.833333333333330.090229269333996397.898757227386
Trimmed Mean ( 6 / 24 )8.837704918032790.087220715392537101.325755908544
Trimmed Mean ( 7 / 24 )8.84067796610170.0849629012472885104.053390789593
Trimmed Mean ( 8 / 24 )8.84210526315790.0826771421083214106.947398491027
Trimmed Mean ( 9 / 24 )8.843636363636360.0808108585381172109.436238193967
Trimmed Mean ( 10 / 24 )8.847169811320760.0789353951993342112.081149261103
Trimmed Mean ( 11 / 24 )8.849019607843140.077123407551214114.738441788466
Trimmed Mean ( 12 / 24 )8.848979591836730.075374487339306117.400196063718
Trimmed Mean ( 13 / 24 )8.85319148936170.0741807592931228119.346196692037
Trimmed Mean ( 14 / 24 )8.857777777777780.072577989323425122.044959640662
Trimmed Mean ( 15 / 24 )8.865116279069770.0709751505287792124.904508310625
Trimmed Mean ( 16 / 24 )8.873170731707320.0687895686792117128.990062041032
Trimmed Mean ( 17 / 24 )8.882051282051280.0673252017582725131.927585066017
Trimmed Mean ( 18 / 24 )8.89189189189190.065229829114309136.316345031499
Trimmed Mean ( 19 / 24 )8.90.0633782827369839140.426651143807
Trimmed Mean ( 20 / 24 )8.90606060606060.0618434291877532144.009811923952
Trimmed Mean ( 21 / 24 )8.916129032258060.0603033147314738147.854708683278
Trimmed Mean ( 22 / 24 )8.924137931034480.0592762532333485150.551653389823
Trimmed Mean ( 23 / 24 )8.933333333333330.0574877665668384155.395380040499
Trimmed Mean ( 24 / 24 )8.9440.0544915895651185164.135421105889
Median9
Midrange8.8
Midmean - Weighted Average at Xnp8.91794871794871
Midmean - Weighted Average at X(n+1)p8.91794871794871
Midmean - Empirical Distribution Function8.91794871794871
Midmean - Empirical Distribution Function - Averaging8.91794871794871
Midmean - Empirical Distribution Function - Interpolation8.91794871794871
Midmean - Closest Observation8.87317073170732
Midmean - True Basic - Statistics Graphics Toolkit8.91794871794871
Midmean - MS Excel (old versions)8.91794871794871
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')