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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 computationTue, 15 Nov 2011 16:24:49 -0500
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2011/Nov/15/t13213923036yq2ee2zcz0xv0r.htm/, Retrieved Fri, 29 Mar 2024 14:31:16 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=143569, Retrieved Fri, 29 Mar 2024 14:31:16 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact79
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Univariate Data Series] [Arabica Price in ...] [2008-01-05 23:14:31] [74be16979710d4c4e7c6647856088456]
- RMPD  [Univariate Data Series] [Workshop 6 - Mini...] [2011-11-15 16:41:21] [74be16979710d4c4e7c6647856088456]
-   PD    [Univariate Data Series] [tut1] [2011-11-15 20:44:36] [f7a862281046b7153543b12c78921b36]
- RM D        [Central Tendency] [tut6] [2011-11-15 21:24:49] [47995d3a8fac585eeb070a274b466f8c] [Current]
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Dataseries X:
0.3
0.3
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0.3
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0.3
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0.3
0.3
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0.4
0.45
0.45
0.45
0.45
0.45
0.5
0.5
0.5
0.5
0.5
0.45
0.45
0.45
0.45
0.45
0.45
0.45
0.4
0.4
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0.4
0.4
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0.4




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gertrude Mary Cox' @ cox.wessa.net

\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 & 'Gertrude Mary Cox' @ cox.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=143569&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]'Gertrude Mary Cox' @ cox.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=143569&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=143569&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 time1 seconds
R Server'Gertrude Mary Cox' @ cox.wessa.net







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean0.3888888888888890.0071468925680006554.4137029049649
Geometric Mean0.384012471740246
Harmonic Mean0.378947368421053
Quadratic Mean0.39352396510392
Winsorized Mean ( 1 / 24 )0.3888888888888890.0071468925680006554.4137029049649
Winsorized Mean ( 2 / 24 )0.3888888888888890.0071468925680006554.4137029049649
Winsorized Mean ( 3 / 24 )0.3888888888888890.0071468925680006554.4137029049649
Winsorized Mean ( 4 / 24 )0.3888888888888890.0071468925680006554.4137029049649
Winsorized Mean ( 5 / 24 )0.3854166666666670.0065181145804504859.1300846141355
Winsorized Mean ( 6 / 24 )0.3854166666666670.0065181145804504859.1300846141355
Winsorized Mean ( 7 / 24 )0.3854166666666670.0065181145804504859.1300846141355
Winsorized Mean ( 8 / 24 )0.3854166666666670.0065181145804504859.1300846141355
Winsorized Mean ( 9 / 24 )0.3854166666666670.0065181145804504859.1300846141355
Winsorized Mean ( 10 / 24 )0.3854166666666670.0065181145804504859.1300846141355
Winsorized Mean ( 11 / 24 )0.3854166666666670.0065181145804504859.1300846141355
Winsorized Mean ( 12 / 24 )0.3854166666666670.0065181145804504859.1300846141355
Winsorized Mean ( 13 / 24 )0.3854166666666670.0065181145804504859.1300846141355
Winsorized Mean ( 14 / 24 )0.3854166666666670.0065181145804504859.1300846141355
Winsorized Mean ( 15 / 24 )0.3854166666666670.0065181145804504859.1300846141355
Winsorized Mean ( 16 / 24 )0.3854166666666670.0065181145804504859.1300846141355
Winsorized Mean ( 17 / 24 )0.3736111111111110.0052306187285139871.4277087478051
Winsorized Mean ( 18 / 24 )0.3736111111111110.0052306187285139871.4277087478051
Winsorized Mean ( 19 / 24 )0.40Inf
Winsorized Mean ( 20 / 24 )0.40Inf
Winsorized Mean ( 21 / 24 )0.40Inf
Winsorized Mean ( 22 / 24 )0.40Inf
Winsorized Mean ( 23 / 24 )0.40Inf
Winsorized Mean ( 24 / 24 )0.40Inf
Trimmed Mean ( 1 / 24 )0.3885714285714290.0070616501812998655.0255844732177
Trimmed Mean ( 2 / 24 )0.3882352941176470.0069582385795203555.7950535441987
Trimmed Mean ( 3 / 24 )0.3878787878787880.0068330581041228856.765035796308
Trimmed Mean ( 4 / 24 )0.38750.0066815310478106157.9956894949961
Trimmed Mean ( 5 / 24 )0.3870967741935480.0064977199628574559.574247029156
Trimmed Mean ( 6 / 24 )0.38750.0064686335758785359.9044597988953
Trimmed Mean ( 7 / 24 )0.3879310344827590.0064268352848006460.3611291237242
Trimmed Mean ( 8 / 24 )0.3883928571428570.0063694521860422460.9774350758085
Trimmed Mean ( 9 / 24 )0.3888888888888890.0062928012661650561.7990100815444
Trimmed Mean ( 10 / 24 )0.3894230769230770.0061920828491261462.8904823161458
Trimmed Mean ( 11 / 24 )0.390.0060609152673132764.3467170879758
Trimmed Mean ( 12 / 24 )0.3906250.0058905972225486566.3133100502483
Trimmed Mean ( 13 / 24 )0.3913043478260870.0056688716566979669.0268489962633
Trimmed Mean ( 14 / 24 )0.3920454545454550.0053776959457013672.9021236053397
Trimmed Mean ( 15 / 24 )0.3928571428571430.0049887878269255678.7480158480199
Trimmed Mean ( 16 / 24 )0.393750.0044532831449651688.4179126236719
Trimmed Mean ( 17 / 24 )0.3947368421052630.00367097806559429107.529065838033
Trimmed Mean ( 18 / 24 )0.3972222222222220.00277777777777778143
Trimmed Mean ( 19 / 24 )0.40Inf
Trimmed Mean ( 20 / 24 )0.40Inf
Trimmed Mean ( 21 / 24 )0.40Inf
Trimmed Mean ( 22 / 24 )0.40Inf
Trimmed Mean ( 23 / 24 )0.40Inf
Trimmed Mean ( 24 / 24 )0.40Inf
Median0.4
Midrange0.4
Midmean - Weighted Average at Xnp0.365454545454545
Midmean - Weighted Average at X(n+1)p0.365454545454545
Midmean - Empirical Distribution Function0.365454545454545
Midmean - Empirical Distribution Function - Averaging0.365454545454545
Midmean - Empirical Distribution Function - Interpolation0.365454545454545
Midmean - Closest Observation0.365454545454545
Midmean - True Basic - Statistics Graphics Toolkit0.365454545454545
Midmean - MS Excel (old versions)0.365454545454545
Number of observations72

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 0.388888888888889 & 0.00714689256800065 & 54.4137029049649 \tabularnewline
Geometric Mean & 0.384012471740246 &  &  \tabularnewline
Harmonic Mean & 0.378947368421053 &  &  \tabularnewline
Quadratic Mean & 0.39352396510392 &  &  \tabularnewline
Winsorized Mean ( 1 / 24 ) & 0.388888888888889 & 0.00714689256800065 & 54.4137029049649 \tabularnewline
Winsorized Mean ( 2 / 24 ) & 0.388888888888889 & 0.00714689256800065 & 54.4137029049649 \tabularnewline
Winsorized Mean ( 3 / 24 ) & 0.388888888888889 & 0.00714689256800065 & 54.4137029049649 \tabularnewline
Winsorized Mean ( 4 / 24 ) & 0.388888888888889 & 0.00714689256800065 & 54.4137029049649 \tabularnewline
Winsorized Mean ( 5 / 24 ) & 0.385416666666667 & 0.00651811458045048 & 59.1300846141355 \tabularnewline
Winsorized Mean ( 6 / 24 ) & 0.385416666666667 & 0.00651811458045048 & 59.1300846141355 \tabularnewline
Winsorized Mean ( 7 / 24 ) & 0.385416666666667 & 0.00651811458045048 & 59.1300846141355 \tabularnewline
Winsorized Mean ( 8 / 24 ) & 0.385416666666667 & 0.00651811458045048 & 59.1300846141355 \tabularnewline
Winsorized Mean ( 9 / 24 ) & 0.385416666666667 & 0.00651811458045048 & 59.1300846141355 \tabularnewline
Winsorized Mean ( 10 / 24 ) & 0.385416666666667 & 0.00651811458045048 & 59.1300846141355 \tabularnewline
Winsorized Mean ( 11 / 24 ) & 0.385416666666667 & 0.00651811458045048 & 59.1300846141355 \tabularnewline
Winsorized Mean ( 12 / 24 ) & 0.385416666666667 & 0.00651811458045048 & 59.1300846141355 \tabularnewline
Winsorized Mean ( 13 / 24 ) & 0.385416666666667 & 0.00651811458045048 & 59.1300846141355 \tabularnewline
Winsorized Mean ( 14 / 24 ) & 0.385416666666667 & 0.00651811458045048 & 59.1300846141355 \tabularnewline
Winsorized Mean ( 15 / 24 ) & 0.385416666666667 & 0.00651811458045048 & 59.1300846141355 \tabularnewline
Winsorized Mean ( 16 / 24 ) & 0.385416666666667 & 0.00651811458045048 & 59.1300846141355 \tabularnewline
Winsorized Mean ( 17 / 24 ) & 0.373611111111111 & 0.00523061872851398 & 71.4277087478051 \tabularnewline
Winsorized Mean ( 18 / 24 ) & 0.373611111111111 & 0.00523061872851398 & 71.4277087478051 \tabularnewline
Winsorized Mean ( 19 / 24 ) & 0.4 & 0 & Inf \tabularnewline
Winsorized Mean ( 20 / 24 ) & 0.4 & 0 & Inf \tabularnewline
Winsorized Mean ( 21 / 24 ) & 0.4 & 0 & Inf \tabularnewline
Winsorized Mean ( 22 / 24 ) & 0.4 & 0 & Inf \tabularnewline
Winsorized Mean ( 23 / 24 ) & 0.4 & 0 & Inf \tabularnewline
Winsorized Mean ( 24 / 24 ) & 0.4 & 0 & Inf \tabularnewline
Trimmed Mean ( 1 / 24 ) & 0.388571428571429 & 0.00706165018129986 & 55.0255844732177 \tabularnewline
Trimmed Mean ( 2 / 24 ) & 0.388235294117647 & 0.00695823857952035 & 55.7950535441987 \tabularnewline
Trimmed Mean ( 3 / 24 ) & 0.387878787878788 & 0.00683305810412288 & 56.765035796308 \tabularnewline
Trimmed Mean ( 4 / 24 ) & 0.3875 & 0.00668153104781061 & 57.9956894949961 \tabularnewline
Trimmed Mean ( 5 / 24 ) & 0.387096774193548 & 0.00649771996285745 & 59.574247029156 \tabularnewline
Trimmed Mean ( 6 / 24 ) & 0.3875 & 0.00646863357587853 & 59.9044597988953 \tabularnewline
Trimmed Mean ( 7 / 24 ) & 0.387931034482759 & 0.00642683528480064 & 60.3611291237242 \tabularnewline
Trimmed Mean ( 8 / 24 ) & 0.388392857142857 & 0.00636945218604224 & 60.9774350758085 \tabularnewline
Trimmed Mean ( 9 / 24 ) & 0.388888888888889 & 0.00629280126616505 & 61.7990100815444 \tabularnewline
Trimmed Mean ( 10 / 24 ) & 0.389423076923077 & 0.00619208284912614 & 62.8904823161458 \tabularnewline
Trimmed Mean ( 11 / 24 ) & 0.39 & 0.00606091526731327 & 64.3467170879758 \tabularnewline
Trimmed Mean ( 12 / 24 ) & 0.390625 & 0.00589059722254865 & 66.3133100502483 \tabularnewline
Trimmed Mean ( 13 / 24 ) & 0.391304347826087 & 0.00566887165669796 & 69.0268489962633 \tabularnewline
Trimmed Mean ( 14 / 24 ) & 0.392045454545455 & 0.00537769594570136 & 72.9021236053397 \tabularnewline
Trimmed Mean ( 15 / 24 ) & 0.392857142857143 & 0.00498878782692556 & 78.7480158480199 \tabularnewline
Trimmed Mean ( 16 / 24 ) & 0.39375 & 0.00445328314496516 & 88.4179126236719 \tabularnewline
Trimmed Mean ( 17 / 24 ) & 0.394736842105263 & 0.00367097806559429 & 107.529065838033 \tabularnewline
Trimmed Mean ( 18 / 24 ) & 0.397222222222222 & 0.00277777777777778 & 143 \tabularnewline
Trimmed Mean ( 19 / 24 ) & 0.4 & 0 & Inf \tabularnewline
Trimmed Mean ( 20 / 24 ) & 0.4 & 0 & Inf \tabularnewline
Trimmed Mean ( 21 / 24 ) & 0.4 & 0 & Inf \tabularnewline
Trimmed Mean ( 22 / 24 ) & 0.4 & 0 & Inf \tabularnewline
Trimmed Mean ( 23 / 24 ) & 0.4 & 0 & Inf \tabularnewline
Trimmed Mean ( 24 / 24 ) & 0.4 & 0 & Inf \tabularnewline
Median & 0.4 &  &  \tabularnewline
Midrange & 0.4 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 0.365454545454545 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 0.365454545454545 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 0.365454545454545 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 0.365454545454545 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 0.365454545454545 &  &  \tabularnewline
Midmean - Closest Observation & 0.365454545454545 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 0.365454545454545 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 0.365454545454545 &  &  \tabularnewline
Number of observations & 72 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=143569&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]0.388888888888889[/C][C]0.00714689256800065[/C][C]54.4137029049649[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]0.384012471740246[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]0.378947368421053[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]0.39352396510392[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 24 )[/C][C]0.388888888888889[/C][C]0.00714689256800065[/C][C]54.4137029049649[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 24 )[/C][C]0.388888888888889[/C][C]0.00714689256800065[/C][C]54.4137029049649[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 24 )[/C][C]0.388888888888889[/C][C]0.00714689256800065[/C][C]54.4137029049649[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 24 )[/C][C]0.388888888888889[/C][C]0.00714689256800065[/C][C]54.4137029049649[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 24 )[/C][C]0.385416666666667[/C][C]0.00651811458045048[/C][C]59.1300846141355[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 24 )[/C][C]0.385416666666667[/C][C]0.00651811458045048[/C][C]59.1300846141355[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 24 )[/C][C]0.385416666666667[/C][C]0.00651811458045048[/C][C]59.1300846141355[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 24 )[/C][C]0.385416666666667[/C][C]0.00651811458045048[/C][C]59.1300846141355[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 24 )[/C][C]0.385416666666667[/C][C]0.00651811458045048[/C][C]59.1300846141355[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 24 )[/C][C]0.385416666666667[/C][C]0.00651811458045048[/C][C]59.1300846141355[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 24 )[/C][C]0.385416666666667[/C][C]0.00651811458045048[/C][C]59.1300846141355[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 24 )[/C][C]0.385416666666667[/C][C]0.00651811458045048[/C][C]59.1300846141355[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 24 )[/C][C]0.385416666666667[/C][C]0.00651811458045048[/C][C]59.1300846141355[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 24 )[/C][C]0.385416666666667[/C][C]0.00651811458045048[/C][C]59.1300846141355[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 24 )[/C][C]0.385416666666667[/C][C]0.00651811458045048[/C][C]59.1300846141355[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 24 )[/C][C]0.385416666666667[/C][C]0.00651811458045048[/C][C]59.1300846141355[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 24 )[/C][C]0.373611111111111[/C][C]0.00523061872851398[/C][C]71.4277087478051[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 24 )[/C][C]0.373611111111111[/C][C]0.00523061872851398[/C][C]71.4277087478051[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 24 )[/C][C]0.4[/C][C]0[/C][C]Inf[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 24 )[/C][C]0.4[/C][C]0[/C][C]Inf[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 24 )[/C][C]0.4[/C][C]0[/C][C]Inf[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 24 )[/C][C]0.4[/C][C]0[/C][C]Inf[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 24 )[/C][C]0.4[/C][C]0[/C][C]Inf[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 24 )[/C][C]0.4[/C][C]0[/C][C]Inf[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 24 )[/C][C]0.388571428571429[/C][C]0.00706165018129986[/C][C]55.0255844732177[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 24 )[/C][C]0.388235294117647[/C][C]0.00695823857952035[/C][C]55.7950535441987[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 24 )[/C][C]0.387878787878788[/C][C]0.00683305810412288[/C][C]56.765035796308[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 24 )[/C][C]0.3875[/C][C]0.00668153104781061[/C][C]57.9956894949961[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 24 )[/C][C]0.387096774193548[/C][C]0.00649771996285745[/C][C]59.574247029156[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 24 )[/C][C]0.3875[/C][C]0.00646863357587853[/C][C]59.9044597988953[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 24 )[/C][C]0.387931034482759[/C][C]0.00642683528480064[/C][C]60.3611291237242[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 24 )[/C][C]0.388392857142857[/C][C]0.00636945218604224[/C][C]60.9774350758085[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 24 )[/C][C]0.388888888888889[/C][C]0.00629280126616505[/C][C]61.7990100815444[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 24 )[/C][C]0.389423076923077[/C][C]0.00619208284912614[/C][C]62.8904823161458[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 24 )[/C][C]0.39[/C][C]0.00606091526731327[/C][C]64.3467170879758[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 24 )[/C][C]0.390625[/C][C]0.00589059722254865[/C][C]66.3133100502483[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 24 )[/C][C]0.391304347826087[/C][C]0.00566887165669796[/C][C]69.0268489962633[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 24 )[/C][C]0.392045454545455[/C][C]0.00537769594570136[/C][C]72.9021236053397[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 24 )[/C][C]0.392857142857143[/C][C]0.00498878782692556[/C][C]78.7480158480199[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 24 )[/C][C]0.39375[/C][C]0.00445328314496516[/C][C]88.4179126236719[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 24 )[/C][C]0.394736842105263[/C][C]0.00367097806559429[/C][C]107.529065838033[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 24 )[/C][C]0.397222222222222[/C][C]0.00277777777777778[/C][C]143[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 24 )[/C][C]0.4[/C][C]0[/C][C]Inf[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 24 )[/C][C]0.4[/C][C]0[/C][C]Inf[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 24 )[/C][C]0.4[/C][C]0[/C][C]Inf[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 24 )[/C][C]0.4[/C][C]0[/C][C]Inf[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 24 )[/C][C]0.4[/C][C]0[/C][C]Inf[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 24 )[/C][C]0.4[/C][C]0[/C][C]Inf[/C][/ROW]
[ROW][C]Median[/C][C]0.4[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]0.4[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]0.365454545454545[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]0.365454545454545[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]0.365454545454545[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]0.365454545454545[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]0.365454545454545[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]0.365454545454545[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]0.365454545454545[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]0.365454545454545[/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=143569&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=143569&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 Mean0.3888888888888890.0071468925680006554.4137029049649
Geometric Mean0.384012471740246
Harmonic Mean0.378947368421053
Quadratic Mean0.39352396510392
Winsorized Mean ( 1 / 24 )0.3888888888888890.0071468925680006554.4137029049649
Winsorized Mean ( 2 / 24 )0.3888888888888890.0071468925680006554.4137029049649
Winsorized Mean ( 3 / 24 )0.3888888888888890.0071468925680006554.4137029049649
Winsorized Mean ( 4 / 24 )0.3888888888888890.0071468925680006554.4137029049649
Winsorized Mean ( 5 / 24 )0.3854166666666670.0065181145804504859.1300846141355
Winsorized Mean ( 6 / 24 )0.3854166666666670.0065181145804504859.1300846141355
Winsorized Mean ( 7 / 24 )0.3854166666666670.0065181145804504859.1300846141355
Winsorized Mean ( 8 / 24 )0.3854166666666670.0065181145804504859.1300846141355
Winsorized Mean ( 9 / 24 )0.3854166666666670.0065181145804504859.1300846141355
Winsorized Mean ( 10 / 24 )0.3854166666666670.0065181145804504859.1300846141355
Winsorized Mean ( 11 / 24 )0.3854166666666670.0065181145804504859.1300846141355
Winsorized Mean ( 12 / 24 )0.3854166666666670.0065181145804504859.1300846141355
Winsorized Mean ( 13 / 24 )0.3854166666666670.0065181145804504859.1300846141355
Winsorized Mean ( 14 / 24 )0.3854166666666670.0065181145804504859.1300846141355
Winsorized Mean ( 15 / 24 )0.3854166666666670.0065181145804504859.1300846141355
Winsorized Mean ( 16 / 24 )0.3854166666666670.0065181145804504859.1300846141355
Winsorized Mean ( 17 / 24 )0.3736111111111110.0052306187285139871.4277087478051
Winsorized Mean ( 18 / 24 )0.3736111111111110.0052306187285139871.4277087478051
Winsorized Mean ( 19 / 24 )0.40Inf
Winsorized Mean ( 20 / 24 )0.40Inf
Winsorized Mean ( 21 / 24 )0.40Inf
Winsorized Mean ( 22 / 24 )0.40Inf
Winsorized Mean ( 23 / 24 )0.40Inf
Winsorized Mean ( 24 / 24 )0.40Inf
Trimmed Mean ( 1 / 24 )0.3885714285714290.0070616501812998655.0255844732177
Trimmed Mean ( 2 / 24 )0.3882352941176470.0069582385795203555.7950535441987
Trimmed Mean ( 3 / 24 )0.3878787878787880.0068330581041228856.765035796308
Trimmed Mean ( 4 / 24 )0.38750.0066815310478106157.9956894949961
Trimmed Mean ( 5 / 24 )0.3870967741935480.0064977199628574559.574247029156
Trimmed Mean ( 6 / 24 )0.38750.0064686335758785359.9044597988953
Trimmed Mean ( 7 / 24 )0.3879310344827590.0064268352848006460.3611291237242
Trimmed Mean ( 8 / 24 )0.3883928571428570.0063694521860422460.9774350758085
Trimmed Mean ( 9 / 24 )0.3888888888888890.0062928012661650561.7990100815444
Trimmed Mean ( 10 / 24 )0.3894230769230770.0061920828491261462.8904823161458
Trimmed Mean ( 11 / 24 )0.390.0060609152673132764.3467170879758
Trimmed Mean ( 12 / 24 )0.3906250.0058905972225486566.3133100502483
Trimmed Mean ( 13 / 24 )0.3913043478260870.0056688716566979669.0268489962633
Trimmed Mean ( 14 / 24 )0.3920454545454550.0053776959457013672.9021236053397
Trimmed Mean ( 15 / 24 )0.3928571428571430.0049887878269255678.7480158480199
Trimmed Mean ( 16 / 24 )0.393750.0044532831449651688.4179126236719
Trimmed Mean ( 17 / 24 )0.3947368421052630.00367097806559429107.529065838033
Trimmed Mean ( 18 / 24 )0.3972222222222220.00277777777777778143
Trimmed Mean ( 19 / 24 )0.40Inf
Trimmed Mean ( 20 / 24 )0.40Inf
Trimmed Mean ( 21 / 24 )0.40Inf
Trimmed Mean ( 22 / 24 )0.40Inf
Trimmed Mean ( 23 / 24 )0.40Inf
Trimmed Mean ( 24 / 24 )0.40Inf
Median0.4
Midrange0.4
Midmean - Weighted Average at Xnp0.365454545454545
Midmean - Weighted Average at X(n+1)p0.365454545454545
Midmean - Empirical Distribution Function0.365454545454545
Midmean - Empirical Distribution Function - Averaging0.365454545454545
Midmean - Empirical Distribution Function - Interpolation0.365454545454545
Midmean - Closest Observation0.365454545454545
Midmean - True Basic - Statistics Graphics Toolkit0.365454545454545
Midmean - MS Excel (old versions)0.365454545454545
Number of observations72



Parameters (Session):
par1 = 500 ; par2 = 12 ;
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')