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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 computationSat, 17 Oct 2009 03:42:58 -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/17/t1255772611k4ab1iflbc225vq.htm/, Retrieved Mon, 06 May 2024 08:07:39 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=47092, Retrieved Mon, 06 May 2024 08:07:39 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact174
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]
-   PD      [Univariate Data Series] [WS 3Yt] [2009-10-17 09:25:12] [6e4e01d7eb22a9f33d58ebb35753a195]
-   PD        [Univariate Data Series] [WS3 YT-XT] [2009-10-17 09:36:45] [6e4e01d7eb22a9f33d58ebb35753a195]
-   PD          [Univariate Data Series] [Yt/Xt CT] [2009-10-17 09:39:32] [6e4e01d7eb22a9f33d58ebb35753a195]
- RMPD              [Central Tendency] [Yt/Xt CT1] [2009-10-17 09:42:58] [2e4ef2c1b76db9b31c0a03b96e94ad77] [Current]
- RM                  [Harrell-Davis Quantiles] [WS 3 3] [2009-10-17 12:16:24] [6e4e01d7eb22a9f33d58ebb35753a195]
- RMP                   [Univariate Explorative Data Analysis] [ws3 3] [2009-10-19 07:04:35] [6e4e01d7eb22a9f33d58ebb35753a195]
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Dataseries X:
1.03
1.05
1.09
1.11
1.13
1.17
1.20
1.23
1.26
1.29
1.28
1.28
1.26
1.25
1.21
1.22
1.21
1.18
1.17
1.19
1.19
1.19
1.16
1.15
1.11
1.07
1.06
1.07
1.05
1.06
1.05
1.04
1.03
0.97
0.95
0.93
0.87
0.83
0.82
0.83
0.86
0.86
0.83
0.83
0.83
0.81
0.79
0.79
0.74
0.72
0.71
0.72
0.75
0.76
0.76
0.73
0.72
0.71
0.70
0.67




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'RServer@AstonUniversity' @ vre.aston.ac.uk

\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 & 3 seconds \tabularnewline
R Server & 'RServer@AstonUniversity' @ vre.aston.ac.uk \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=47092&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]3 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'RServer@AstonUniversity' @ vre.aston.ac.uk[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=47092&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=47092&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 time3 seconds
R Server'RServer@AstonUniversity' @ vre.aston.ac.uk







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean0.9921666666666670.025346292775054839.144449070798
Geometric Mean0.97237033336433
Harmonic Mean0.952253488522075
Quadratic Mean1.01108769814163
Winsorized Mean ( 1 / 20 )0.99250.025210554018075539.3684327321166
Winsorized Mean ( 2 / 20 )0.9928333333333330.025146004913077439.4827463354627
Winsorized Mean ( 3 / 20 )0.9918333333333330.024958147641801939.7398616102476
Winsorized Mean ( 4 / 20 )0.99250.024832347457016439.9680296725056
Winsorized Mean ( 5 / 20 )0.9916666666666670.024682351098383640.1771558436185
Winsorized Mean ( 6 / 20 )0.9896666666666670.024337512217595740.6642494030738
Winsorized Mean ( 7 / 20 )0.9896666666666670.023927818321823341.3605057241697
Winsorized Mean ( 8 / 20 )0.9896666666666670.023470099581977642.1671268675237
Winsorized Mean ( 9 / 20 )0.9911666666666670.023202731753580842.7176712291088
Winsorized Mean ( 10 / 20 )0.9911666666666670.022648245671907343.7635073826536
Winsorized Mean ( 11 / 20 )0.9893333333333330.022365564060489944.2346694524484
Winsorized Mean ( 12 / 20 )0.9953333333333330.021354509264166546.6099839158343
Winsorized Mean ( 13 / 20 )0.9953333333333330.021354509264166546.6099839158343
Winsorized Mean ( 14 / 20 )0.9976666666666670.020248968260898749.2700000223313
Winsorized Mean ( 15 / 20 )0.9976666666666670.019481073919438251.2120979979034
Winsorized Mean ( 16 / 20 )1.000333333333330.019073107442031952.4473181086829
Winsorized Mean ( 17 / 20 )0.99750.018650252569441453.4845303722274
Winsorized Mean ( 18 / 20 )0.99450.018211601505044354.6080474978843
Winsorized Mean ( 19 / 20 )0.9881666666666670.017313153724901557.0760638049084
Winsorized Mean ( 20 / 20 )0.98150.016407289615971759.8209712251655
Trimmed Mean ( 1 / 20 )0.9925862068965520.025093365096353639.5557233191011
Trimmed Mean ( 2 / 20 )0.9926785714285710.024925201182515439.8263012667243
Trimmed Mean ( 3 / 20 )0.9925925925925930.024735053347304640.1289853171373
Trimmed Mean ( 4 / 20 )0.9928846153846150.024559983729411440.4269248027067
Trimmed Mean ( 5 / 20 )0.9930.024359970510353840.7635961454856
Trimmed Mean ( 6 / 20 )0.9933333333333330.024127199369362941.1706853384187
Trimmed Mean ( 7 / 20 )0.9941304347826090.023901116920430941.5934718905465
Trimmed Mean ( 8 / 20 )0.9950.023688651710748542.0032348041373
Trimmed Mean ( 9 / 20 )0.9959523809523810.023493047687370442.3934942032997
Trimmed Mean ( 10 / 20 )0.996750.023261025783761642.8506467971772
Trimmed Mean ( 11 / 20 )0.9976315789473680.023044993440923843.2905993878806
Trimmed Mean ( 12 / 20 )0.9988888888888890.022767903395879343.8726777569548
Trimmed Mean ( 13 / 20 )0.9994117647058820.022598334046742544.2250195363381
Trimmed Mean ( 14 / 20 )10.022288431832419044.8663238185057
Trimmed Mean ( 15 / 20 )1.000333333333330.022083870086732145.2970122267803
Trimmed Mean ( 16 / 20 )1.000714285714290.021912093321069645.6694972520972
Trimmed Mean ( 17 / 20 )1.000769230769230.021668290031735546.1858886558883
Trimmed Mean ( 18 / 20 )1.001250.021309592485171046.9858820949650
Trimmed Mean ( 19 / 20 )1.002272727272730.020763894510188248.2699778108072
Trimmed Mean ( 20 / 20 )1.00450.020071910196774250.0450624854546
Median1.045
Midrange0.98
Midmean - Weighted Average at Xnp0.994193548387097
Midmean - Weighted Average at X(n+1)p1.00033333333333
Midmean - Empirical Distribution Function0.994193548387097
Midmean - Empirical Distribution Function - Averaging1.00033333333333
Midmean - Empirical Distribution Function - Interpolation1.00033333333333
Midmean - Closest Observation0.994193548387097
Midmean - True Basic - Statistics Graphics Toolkit1.00033333333333
Midmean - MS Excel (old versions)1
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 0.992166666666667 & 0.0253462927750548 & 39.144449070798 \tabularnewline
Geometric Mean & 0.97237033336433 &  &  \tabularnewline
Harmonic Mean & 0.952253488522075 &  &  \tabularnewline
Quadratic Mean & 1.01108769814163 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 0.9925 & 0.0252105540180755 & 39.3684327321166 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 0.992833333333333 & 0.0251460049130774 & 39.4827463354627 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 0.991833333333333 & 0.0249581476418019 & 39.7398616102476 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 0.9925 & 0.0248323474570164 & 39.9680296725056 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 0.991666666666667 & 0.0246823510983836 & 40.1771558436185 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 0.989666666666667 & 0.0243375122175957 & 40.6642494030738 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 0.989666666666667 & 0.0239278183218233 & 41.3605057241697 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 0.989666666666667 & 0.0234700995819776 & 42.1671268675237 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 0.991166666666667 & 0.0232027317535808 & 42.7176712291088 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 0.991166666666667 & 0.0226482456719073 & 43.7635073826536 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 0.989333333333333 & 0.0223655640604899 & 44.2346694524484 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 0.995333333333333 & 0.0213545092641665 & 46.6099839158343 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 0.995333333333333 & 0.0213545092641665 & 46.6099839158343 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 0.997666666666667 & 0.0202489682608987 & 49.2700000223313 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 0.997666666666667 & 0.0194810739194382 & 51.2120979979034 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 1.00033333333333 & 0.0190731074420319 & 52.4473181086829 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 0.9975 & 0.0186502525694414 & 53.4845303722274 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 0.9945 & 0.0182116015050443 & 54.6080474978843 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 0.988166666666667 & 0.0173131537249015 & 57.0760638049084 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 0.9815 & 0.0164072896159717 & 59.8209712251655 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 0.992586206896552 & 0.0250933650963536 & 39.5557233191011 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 0.992678571428571 & 0.0249252011825154 & 39.8263012667243 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 0.992592592592593 & 0.0247350533473046 & 40.1289853171373 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 0.992884615384615 & 0.0245599837294114 & 40.4269248027067 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 0.993 & 0.0243599705103538 & 40.7635961454856 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 0.993333333333333 & 0.0241271993693629 & 41.1706853384187 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 0.994130434782609 & 0.0239011169204309 & 41.5934718905465 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 0.995 & 0.0236886517107485 & 42.0032348041373 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 0.995952380952381 & 0.0234930476873704 & 42.3934942032997 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 0.99675 & 0.0232610257837616 & 42.8506467971772 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 0.997631578947368 & 0.0230449934409238 & 43.2905993878806 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 0.998888888888889 & 0.0227679033958793 & 43.8726777569548 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 0.999411764705882 & 0.0225983340467425 & 44.2250195363381 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 1 & 0.0222884318324190 & 44.8663238185057 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 1.00033333333333 & 0.0220838700867321 & 45.2970122267803 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 1.00071428571429 & 0.0219120933210696 & 45.6694972520972 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 1.00076923076923 & 0.0216682900317355 & 46.1858886558883 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 1.00125 & 0.0213095924851710 & 46.9858820949650 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 1.00227272727273 & 0.0207638945101882 & 48.2699778108072 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 1.0045 & 0.0200719101967742 & 50.0450624854546 \tabularnewline
Median & 1.045 &  &  \tabularnewline
Midrange & 0.98 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 0.994193548387097 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 1.00033333333333 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 0.994193548387097 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 1.00033333333333 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 1.00033333333333 &  &  \tabularnewline
Midmean - Closest Observation & 0.994193548387097 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 1.00033333333333 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 1 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=47092&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]0.992166666666667[/C][C]0.0253462927750548[/C][C]39.144449070798[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]0.97237033336433[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]0.952253488522075[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]1.01108769814163[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]0.9925[/C][C]0.0252105540180755[/C][C]39.3684327321166[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]0.992833333333333[/C][C]0.0251460049130774[/C][C]39.4827463354627[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]0.991833333333333[/C][C]0.0249581476418019[/C][C]39.7398616102476[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]0.9925[/C][C]0.0248323474570164[/C][C]39.9680296725056[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]0.991666666666667[/C][C]0.0246823510983836[/C][C]40.1771558436185[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]0.989666666666667[/C][C]0.0243375122175957[/C][C]40.6642494030738[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]0.989666666666667[/C][C]0.0239278183218233[/C][C]41.3605057241697[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]0.989666666666667[/C][C]0.0234700995819776[/C][C]42.1671268675237[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]0.991166666666667[/C][C]0.0232027317535808[/C][C]42.7176712291088[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]0.991166666666667[/C][C]0.0226482456719073[/C][C]43.7635073826536[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]0.989333333333333[/C][C]0.0223655640604899[/C][C]44.2346694524484[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]0.995333333333333[/C][C]0.0213545092641665[/C][C]46.6099839158343[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]0.995333333333333[/C][C]0.0213545092641665[/C][C]46.6099839158343[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]0.997666666666667[/C][C]0.0202489682608987[/C][C]49.2700000223313[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]0.997666666666667[/C][C]0.0194810739194382[/C][C]51.2120979979034[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]1.00033333333333[/C][C]0.0190731074420319[/C][C]52.4473181086829[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]0.9975[/C][C]0.0186502525694414[/C][C]53.4845303722274[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]0.9945[/C][C]0.0182116015050443[/C][C]54.6080474978843[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]0.988166666666667[/C][C]0.0173131537249015[/C][C]57.0760638049084[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]0.9815[/C][C]0.0164072896159717[/C][C]59.8209712251655[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]0.992586206896552[/C][C]0.0250933650963536[/C][C]39.5557233191011[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]0.992678571428571[/C][C]0.0249252011825154[/C][C]39.8263012667243[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]0.992592592592593[/C][C]0.0247350533473046[/C][C]40.1289853171373[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]0.992884615384615[/C][C]0.0245599837294114[/C][C]40.4269248027067[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]0.993[/C][C]0.0243599705103538[/C][C]40.7635961454856[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]0.993333333333333[/C][C]0.0241271993693629[/C][C]41.1706853384187[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]0.994130434782609[/C][C]0.0239011169204309[/C][C]41.5934718905465[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]0.995[/C][C]0.0236886517107485[/C][C]42.0032348041373[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]0.995952380952381[/C][C]0.0234930476873704[/C][C]42.3934942032997[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]0.99675[/C][C]0.0232610257837616[/C][C]42.8506467971772[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]0.997631578947368[/C][C]0.0230449934409238[/C][C]43.2905993878806[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]0.998888888888889[/C][C]0.0227679033958793[/C][C]43.8726777569548[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]0.999411764705882[/C][C]0.0225983340467425[/C][C]44.2250195363381[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]1[/C][C]0.0222884318324190[/C][C]44.8663238185057[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]1.00033333333333[/C][C]0.0220838700867321[/C][C]45.2970122267803[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]1.00071428571429[/C][C]0.0219120933210696[/C][C]45.6694972520972[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]1.00076923076923[/C][C]0.0216682900317355[/C][C]46.1858886558883[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]1.00125[/C][C]0.0213095924851710[/C][C]46.9858820949650[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]1.00227272727273[/C][C]0.0207638945101882[/C][C]48.2699778108072[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]1.0045[/C][C]0.0200719101967742[/C][C]50.0450624854546[/C][/ROW]
[ROW][C]Median[/C][C]1.045[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]0.98[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]0.994193548387097[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]1.00033333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]0.994193548387097[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]1.00033333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]1.00033333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]0.994193548387097[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]1.00033333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]1[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]60[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=47092&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=47092&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 Mean0.9921666666666670.025346292775054839.144449070798
Geometric Mean0.97237033336433
Harmonic Mean0.952253488522075
Quadratic Mean1.01108769814163
Winsorized Mean ( 1 / 20 )0.99250.025210554018075539.3684327321166
Winsorized Mean ( 2 / 20 )0.9928333333333330.025146004913077439.4827463354627
Winsorized Mean ( 3 / 20 )0.9918333333333330.024958147641801939.7398616102476
Winsorized Mean ( 4 / 20 )0.99250.024832347457016439.9680296725056
Winsorized Mean ( 5 / 20 )0.9916666666666670.024682351098383640.1771558436185
Winsorized Mean ( 6 / 20 )0.9896666666666670.024337512217595740.6642494030738
Winsorized Mean ( 7 / 20 )0.9896666666666670.023927818321823341.3605057241697
Winsorized Mean ( 8 / 20 )0.9896666666666670.023470099581977642.1671268675237
Winsorized Mean ( 9 / 20 )0.9911666666666670.023202731753580842.7176712291088
Winsorized Mean ( 10 / 20 )0.9911666666666670.022648245671907343.7635073826536
Winsorized Mean ( 11 / 20 )0.9893333333333330.022365564060489944.2346694524484
Winsorized Mean ( 12 / 20 )0.9953333333333330.021354509264166546.6099839158343
Winsorized Mean ( 13 / 20 )0.9953333333333330.021354509264166546.6099839158343
Winsorized Mean ( 14 / 20 )0.9976666666666670.020248968260898749.2700000223313
Winsorized Mean ( 15 / 20 )0.9976666666666670.019481073919438251.2120979979034
Winsorized Mean ( 16 / 20 )1.000333333333330.019073107442031952.4473181086829
Winsorized Mean ( 17 / 20 )0.99750.018650252569441453.4845303722274
Winsorized Mean ( 18 / 20 )0.99450.018211601505044354.6080474978843
Winsorized Mean ( 19 / 20 )0.9881666666666670.017313153724901557.0760638049084
Winsorized Mean ( 20 / 20 )0.98150.016407289615971759.8209712251655
Trimmed Mean ( 1 / 20 )0.9925862068965520.025093365096353639.5557233191011
Trimmed Mean ( 2 / 20 )0.9926785714285710.024925201182515439.8263012667243
Trimmed Mean ( 3 / 20 )0.9925925925925930.024735053347304640.1289853171373
Trimmed Mean ( 4 / 20 )0.9928846153846150.024559983729411440.4269248027067
Trimmed Mean ( 5 / 20 )0.9930.024359970510353840.7635961454856
Trimmed Mean ( 6 / 20 )0.9933333333333330.024127199369362941.1706853384187
Trimmed Mean ( 7 / 20 )0.9941304347826090.023901116920430941.5934718905465
Trimmed Mean ( 8 / 20 )0.9950.023688651710748542.0032348041373
Trimmed Mean ( 9 / 20 )0.9959523809523810.023493047687370442.3934942032997
Trimmed Mean ( 10 / 20 )0.996750.023261025783761642.8506467971772
Trimmed Mean ( 11 / 20 )0.9976315789473680.023044993440923843.2905993878806
Trimmed Mean ( 12 / 20 )0.9988888888888890.022767903395879343.8726777569548
Trimmed Mean ( 13 / 20 )0.9994117647058820.022598334046742544.2250195363381
Trimmed Mean ( 14 / 20 )10.022288431832419044.8663238185057
Trimmed Mean ( 15 / 20 )1.000333333333330.022083870086732145.2970122267803
Trimmed Mean ( 16 / 20 )1.000714285714290.021912093321069645.6694972520972
Trimmed Mean ( 17 / 20 )1.000769230769230.021668290031735546.1858886558883
Trimmed Mean ( 18 / 20 )1.001250.021309592485171046.9858820949650
Trimmed Mean ( 19 / 20 )1.002272727272730.020763894510188248.2699778108072
Trimmed Mean ( 20 / 20 )1.00450.020071910196774250.0450624854546
Median1.045
Midrange0.98
Midmean - Weighted Average at Xnp0.994193548387097
Midmean - Weighted Average at X(n+1)p1.00033333333333
Midmean - Empirical Distribution Function0.994193548387097
Midmean - Empirical Distribution Function - Averaging1.00033333333333
Midmean - Empirical Distribution Function - Interpolation1.00033333333333
Midmean - Closest Observation0.994193548387097
Midmean - True Basic - Statistics Graphics Toolkit1.00033333333333
Midmean - MS Excel (old versions)1
Number of observations60



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')