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Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationTue, 04 Dec 2007 14:36:32 -0700
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2007/Dec/04/t1196803475yf6nfqssa4dzzah.htm/, Retrieved Thu, 02 May 2024 06:18:08 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=2451, Retrieved Thu, 02 May 2024 06:18:08 +0000
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Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact201
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Variance Reduction Matrix] [Variance reductio...] [2007-11-30 14:45:44] [6c50c82828af94f83a614a64264ea782]
- RMPD    [Central Tendency] [Residuals - Inves...] [2007-12-04 21:36:32] [014bfc073eb4f6c1ae65a07cc44c50c0] [Current]
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Dataseries X:
0.0693990238502622 
-0.202508887032611 
-18.0825455917289 
6.67897086412986 
14.9871942821514 
6.82249050901706 
1.20477848555194 
10.5148806187963 
5.85093740630802 
-3.73615484417776 
3.85281994413698 
-11.1861995804540 
15.0124189927225 
9.95856871162544 
0.786773718657626 
3.36539271347048 
4.44160405783372 
3.47164790709255 
2.04647133779179 
3.45954726421257 
-4.67092870856952 
-8.59891087939083 
1.58097343408977 
-2.66817988759935 
7.94842793846805 
4.84790432157784 
-8.81314797577659 
2.0741093430285 
-3.3862830219909 
4.06380375144544 
4.94898165578284 
4.04195671121746 
-11.9303577345720 
16.9273902622685 
3.70496204828917 
5.92386939768789 
-4.20185529239969 
-3.13453183583787 
5.59907406134631 
9.90828010787837 
2.64382629803101 
8.4400616431807 
-1.19528260174552 
0.314644633048942 
1.92084762279685 
3.51002162943734 
3.08440882152912 
8.05495974515165 
-1.55364513271137 




Summary of compuational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'Herman Ole Andreas Wold' @ 193.190.124.10:1001

\begin{tabular}{lllllllll}
\hline
Summary of compuational 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 & 'Herman Ole Andreas Wold' @ 193.190.124.10:1001 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=2451&T=0

[TABLE]
[ROW][C]Summary of compuational 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]'Herman Ole Andreas Wold' @ 193.190.124.10:1001[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=2451&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=2451&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 compuational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'Herman Ole Andreas Wold' @ 193.190.124.10:1001







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean2.218405454890150.9751083443533742.27503483867861
Geometric MeanNaN
Harmonic Mean2.66058113844271
Quadratic Mean7.11065850376814
Winsorized Mean ( 1 / 16 )2.304879262800580.915519991978372.51756300571865
Winsorized Mean ( 2 / 16 )2.334223484986160.9055768588565832.57760946755358
Winsorized Mean ( 3 / 16 )2.205697236495690.7913371596305182.78730400771973
Winsorized Mean ( 4 / 16 )2.177772762145890.7765632338433722.80437273777132
Winsorized Mean ( 5 / 16 )2.573455779194280.6715304457079363.83222502515327
Winsorized Mean ( 6 / 16 )2.451111487537810.6200159250274753.95330408235755
Winsorized Mean ( 7 / 16 )2.462625566136790.5944184735311464.14291559868177
Winsorized Mean ( 8 / 16 )2.502354548259770.5787477923932714.32373925421278
Winsorized Mean ( 9 / 16 )2.341789728062190.5303130285140394.41586308868178
Winsorized Mean ( 10 / 16 )2.407673871603280.5049442351460164.76819756325576
Winsorized Mean ( 11 / 16 )2.488362977172790.4245289602874345.86146814457134
Winsorized Mean ( 12 / 16 )2.558264333806090.4043117981672766.3274540723337
Winsorized Mean ( 13 / 16 )2.754832391087020.3436573388023288.01621871567713
Winsorized Mean ( 14 / 16 )2.646779678321140.2987101534004688.860695387119
Winsorized Mean ( 15 / 16 )2.690912823727360.2803665612927599.5978379565654
Winsorized Mean ( 16 / 16 )2.712407949234160.23248118600801511.6672148650371
Trimmed Mean ( 1 / 16 )2.218405454890150.8622032449313542.57294955444847
Trimmed Mean ( 2 / 16 )2.337383459980380.7923043472563172.9501080841908
Trimmed Mean ( 3 / 16 )2.394743410679760.705910545883473.39241767196248
Trimmed Mean ( 4 / 16 )2.394743410679760.6571192286617513.64430579144176
Trimmed Mean ( 5 / 16 )2.561860927794240.597584413347954.28702769110307
Trimmed Mean ( 6 / 16 )2.558789859045050.5634975629510134.54090670001263
Trimmed Mean ( 7 / 16 )2.583914812396730.5365870387785044.81546259163994
Trimmed Mean ( 8 / 16 )2.583914812396730.5082035976460375.08440873768947
Trimmed Mean ( 9 / 16 )2.630840923110790.4732254725084485.55938147024371
Trimmed Mean ( 10 / 16 )2.68510723942260.4402355141393356.09925177134337
Trimmed Mean ( 11 / 16 )2.735456258026850.4006662163240826.82726954901097
Trimmed Mean ( 12 / 16 )2.779483788069940.3743519489107997.42478781306473
Trimmed Mean ( 13 / 16 )2.818758256399390.3409344189500568.26774329526498
Trimmed Mean ( 14 / 16 )2.830232129660580.3160567343140718.95482305037085
Trimmed Mean ( 15 / 16 )2.864026002275740.2952924183815229.69894864884536
Trimmed Mean ( 16 / 16 )2.864026002275740.26684191645942910.7330438945906
Median3.36539271347048
Midrange-0.5775776647302
Midmean - Weighted Average at Xnp2.65150655397668
Midmean - Weighted Average at X(n+1)p2.77948378806994
Midmean - Empirical Distribution Function2.77948378806994
Midmean - Empirical Distribution Function - Averaging2.77948378806994
Midmean - Empirical Distribution Function - Interpolation2.77948378806994
Midmean - Closest Observation2.6128249834245
Midmean - True Basic - Statistics Graphics Toolkit2.77948378806994
Midmean - MS Excel (old versions)2.77948378806994
Number of observations49

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 2.21840545489015 & 0.975108344353374 & 2.27503483867861 \tabularnewline
Geometric Mean & NaN &  &  \tabularnewline
Harmonic Mean & 2.66058113844271 &  &  \tabularnewline
Quadratic Mean & 7.11065850376814 &  &  \tabularnewline
Winsorized Mean ( 1 / 16 ) & 2.30487926280058 & 0.91551999197837 & 2.51756300571865 \tabularnewline
Winsorized Mean ( 2 / 16 ) & 2.33422348498616 & 0.905576858856583 & 2.57760946755358 \tabularnewline
Winsorized Mean ( 3 / 16 ) & 2.20569723649569 & 0.791337159630518 & 2.78730400771973 \tabularnewline
Winsorized Mean ( 4 / 16 ) & 2.17777276214589 & 0.776563233843372 & 2.80437273777132 \tabularnewline
Winsorized Mean ( 5 / 16 ) & 2.57345577919428 & 0.671530445707936 & 3.83222502515327 \tabularnewline
Winsorized Mean ( 6 / 16 ) & 2.45111148753781 & 0.620015925027475 & 3.95330408235755 \tabularnewline
Winsorized Mean ( 7 / 16 ) & 2.46262556613679 & 0.594418473531146 & 4.14291559868177 \tabularnewline
Winsorized Mean ( 8 / 16 ) & 2.50235454825977 & 0.578747792393271 & 4.32373925421278 \tabularnewline
Winsorized Mean ( 9 / 16 ) & 2.34178972806219 & 0.530313028514039 & 4.41586308868178 \tabularnewline
Winsorized Mean ( 10 / 16 ) & 2.40767387160328 & 0.504944235146016 & 4.76819756325576 \tabularnewline
Winsorized Mean ( 11 / 16 ) & 2.48836297717279 & 0.424528960287434 & 5.86146814457134 \tabularnewline
Winsorized Mean ( 12 / 16 ) & 2.55826433380609 & 0.404311798167276 & 6.3274540723337 \tabularnewline
Winsorized Mean ( 13 / 16 ) & 2.75483239108702 & 0.343657338802328 & 8.01621871567713 \tabularnewline
Winsorized Mean ( 14 / 16 ) & 2.64677967832114 & 0.298710153400468 & 8.860695387119 \tabularnewline
Winsorized Mean ( 15 / 16 ) & 2.69091282372736 & 0.280366561292759 & 9.5978379565654 \tabularnewline
Winsorized Mean ( 16 / 16 ) & 2.71240794923416 & 0.232481186008015 & 11.6672148650371 \tabularnewline
Trimmed Mean ( 1 / 16 ) & 2.21840545489015 & 0.862203244931354 & 2.57294955444847 \tabularnewline
Trimmed Mean ( 2 / 16 ) & 2.33738345998038 & 0.792304347256317 & 2.9501080841908 \tabularnewline
Trimmed Mean ( 3 / 16 ) & 2.39474341067976 & 0.70591054588347 & 3.39241767196248 \tabularnewline
Trimmed Mean ( 4 / 16 ) & 2.39474341067976 & 0.657119228661751 & 3.64430579144176 \tabularnewline
Trimmed Mean ( 5 / 16 ) & 2.56186092779424 & 0.59758441334795 & 4.28702769110307 \tabularnewline
Trimmed Mean ( 6 / 16 ) & 2.55878985904505 & 0.563497562951013 & 4.54090670001263 \tabularnewline
Trimmed Mean ( 7 / 16 ) & 2.58391481239673 & 0.536587038778504 & 4.81546259163994 \tabularnewline
Trimmed Mean ( 8 / 16 ) & 2.58391481239673 & 0.508203597646037 & 5.08440873768947 \tabularnewline
Trimmed Mean ( 9 / 16 ) & 2.63084092311079 & 0.473225472508448 & 5.55938147024371 \tabularnewline
Trimmed Mean ( 10 / 16 ) & 2.6851072394226 & 0.440235514139335 & 6.09925177134337 \tabularnewline
Trimmed Mean ( 11 / 16 ) & 2.73545625802685 & 0.400666216324082 & 6.82726954901097 \tabularnewline
Trimmed Mean ( 12 / 16 ) & 2.77948378806994 & 0.374351948910799 & 7.42478781306473 \tabularnewline
Trimmed Mean ( 13 / 16 ) & 2.81875825639939 & 0.340934418950056 & 8.26774329526498 \tabularnewline
Trimmed Mean ( 14 / 16 ) & 2.83023212966058 & 0.316056734314071 & 8.95482305037085 \tabularnewline
Trimmed Mean ( 15 / 16 ) & 2.86402600227574 & 0.295292418381522 & 9.69894864884536 \tabularnewline
Trimmed Mean ( 16 / 16 ) & 2.86402600227574 & 0.266841916459429 & 10.7330438945906 \tabularnewline
Median & 3.36539271347048 &  &  \tabularnewline
Midrange & -0.5775776647302 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 2.65150655397668 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 2.77948378806994 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 2.77948378806994 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 2.77948378806994 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 2.77948378806994 &  &  \tabularnewline
Midmean - Closest Observation & 2.6128249834245 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 2.77948378806994 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 2.77948378806994 &  &  \tabularnewline
Number of observations & 49 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=2451&T=1

[TABLE]
[ROW][C]Central Tendency - Ungrouped Data[/C][/ROW]
[ROW][C]Measure[/C][C]Value[/C][C]S.E.[/C][C]Value/S.E.[/C][/ROW]
[ROW][C]Arithmetic Mean[/C][C]2.21840545489015[/C][C]0.975108344353374[/C][C]2.27503483867861[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]NaN[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]2.66058113844271[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]7.11065850376814[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 16 )[/C][C]2.30487926280058[/C][C]0.91551999197837[/C][C]2.51756300571865[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 16 )[/C][C]2.33422348498616[/C][C]0.905576858856583[/C][C]2.57760946755358[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 16 )[/C][C]2.20569723649569[/C][C]0.791337159630518[/C][C]2.78730400771973[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 16 )[/C][C]2.17777276214589[/C][C]0.776563233843372[/C][C]2.80437273777132[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 16 )[/C][C]2.57345577919428[/C][C]0.671530445707936[/C][C]3.83222502515327[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 16 )[/C][C]2.45111148753781[/C][C]0.620015925027475[/C][C]3.95330408235755[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 16 )[/C][C]2.46262556613679[/C][C]0.594418473531146[/C][C]4.14291559868177[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 16 )[/C][C]2.50235454825977[/C][C]0.578747792393271[/C][C]4.32373925421278[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 16 )[/C][C]2.34178972806219[/C][C]0.530313028514039[/C][C]4.41586308868178[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 16 )[/C][C]2.40767387160328[/C][C]0.504944235146016[/C][C]4.76819756325576[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 16 )[/C][C]2.48836297717279[/C][C]0.424528960287434[/C][C]5.86146814457134[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 16 )[/C][C]2.55826433380609[/C][C]0.404311798167276[/C][C]6.3274540723337[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 16 )[/C][C]2.75483239108702[/C][C]0.343657338802328[/C][C]8.01621871567713[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 16 )[/C][C]2.64677967832114[/C][C]0.298710153400468[/C][C]8.860695387119[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 16 )[/C][C]2.69091282372736[/C][C]0.280366561292759[/C][C]9.5978379565654[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 16 )[/C][C]2.71240794923416[/C][C]0.232481186008015[/C][C]11.6672148650371[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 16 )[/C][C]2.21840545489015[/C][C]0.862203244931354[/C][C]2.57294955444847[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 16 )[/C][C]2.33738345998038[/C][C]0.792304347256317[/C][C]2.9501080841908[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 16 )[/C][C]2.39474341067976[/C][C]0.70591054588347[/C][C]3.39241767196248[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 16 )[/C][C]2.39474341067976[/C][C]0.657119228661751[/C][C]3.64430579144176[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 16 )[/C][C]2.56186092779424[/C][C]0.59758441334795[/C][C]4.28702769110307[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 16 )[/C][C]2.55878985904505[/C][C]0.563497562951013[/C][C]4.54090670001263[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 16 )[/C][C]2.58391481239673[/C][C]0.536587038778504[/C][C]4.81546259163994[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 16 )[/C][C]2.58391481239673[/C][C]0.508203597646037[/C][C]5.08440873768947[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 16 )[/C][C]2.63084092311079[/C][C]0.473225472508448[/C][C]5.55938147024371[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 16 )[/C][C]2.6851072394226[/C][C]0.440235514139335[/C][C]6.09925177134337[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 16 )[/C][C]2.73545625802685[/C][C]0.400666216324082[/C][C]6.82726954901097[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 16 )[/C][C]2.77948378806994[/C][C]0.374351948910799[/C][C]7.42478781306473[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 16 )[/C][C]2.81875825639939[/C][C]0.340934418950056[/C][C]8.26774329526498[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 16 )[/C][C]2.83023212966058[/C][C]0.316056734314071[/C][C]8.95482305037085[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 16 )[/C][C]2.86402600227574[/C][C]0.295292418381522[/C][C]9.69894864884536[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 16 )[/C][C]2.86402600227574[/C][C]0.266841916459429[/C][C]10.7330438945906[/C][/ROW]
[ROW][C]Median[/C][C]3.36539271347048[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]-0.5775776647302[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]2.65150655397668[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]2.77948378806994[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]2.77948378806994[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]2.77948378806994[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]2.77948378806994[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]2.6128249834245[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]2.77948378806994[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]2.77948378806994[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]49[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=2451&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=2451&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 Mean2.218405454890150.9751083443533742.27503483867861
Geometric MeanNaN
Harmonic Mean2.66058113844271
Quadratic Mean7.11065850376814
Winsorized Mean ( 1 / 16 )2.304879262800580.915519991978372.51756300571865
Winsorized Mean ( 2 / 16 )2.334223484986160.9055768588565832.57760946755358
Winsorized Mean ( 3 / 16 )2.205697236495690.7913371596305182.78730400771973
Winsorized Mean ( 4 / 16 )2.177772762145890.7765632338433722.80437273777132
Winsorized Mean ( 5 / 16 )2.573455779194280.6715304457079363.83222502515327
Winsorized Mean ( 6 / 16 )2.451111487537810.6200159250274753.95330408235755
Winsorized Mean ( 7 / 16 )2.462625566136790.5944184735311464.14291559868177
Winsorized Mean ( 8 / 16 )2.502354548259770.5787477923932714.32373925421278
Winsorized Mean ( 9 / 16 )2.341789728062190.5303130285140394.41586308868178
Winsorized Mean ( 10 / 16 )2.407673871603280.5049442351460164.76819756325576
Winsorized Mean ( 11 / 16 )2.488362977172790.4245289602874345.86146814457134
Winsorized Mean ( 12 / 16 )2.558264333806090.4043117981672766.3274540723337
Winsorized Mean ( 13 / 16 )2.754832391087020.3436573388023288.01621871567713
Winsorized Mean ( 14 / 16 )2.646779678321140.2987101534004688.860695387119
Winsorized Mean ( 15 / 16 )2.690912823727360.2803665612927599.5978379565654
Winsorized Mean ( 16 / 16 )2.712407949234160.23248118600801511.6672148650371
Trimmed Mean ( 1 / 16 )2.218405454890150.8622032449313542.57294955444847
Trimmed Mean ( 2 / 16 )2.337383459980380.7923043472563172.9501080841908
Trimmed Mean ( 3 / 16 )2.394743410679760.705910545883473.39241767196248
Trimmed Mean ( 4 / 16 )2.394743410679760.6571192286617513.64430579144176
Trimmed Mean ( 5 / 16 )2.561860927794240.597584413347954.28702769110307
Trimmed Mean ( 6 / 16 )2.558789859045050.5634975629510134.54090670001263
Trimmed Mean ( 7 / 16 )2.583914812396730.5365870387785044.81546259163994
Trimmed Mean ( 8 / 16 )2.583914812396730.5082035976460375.08440873768947
Trimmed Mean ( 9 / 16 )2.630840923110790.4732254725084485.55938147024371
Trimmed Mean ( 10 / 16 )2.68510723942260.4402355141393356.09925177134337
Trimmed Mean ( 11 / 16 )2.735456258026850.4006662163240826.82726954901097
Trimmed Mean ( 12 / 16 )2.779483788069940.3743519489107997.42478781306473
Trimmed Mean ( 13 / 16 )2.818758256399390.3409344189500568.26774329526498
Trimmed Mean ( 14 / 16 )2.830232129660580.3160567343140718.95482305037085
Trimmed Mean ( 15 / 16 )2.864026002275740.2952924183815229.69894864884536
Trimmed Mean ( 16 / 16 )2.864026002275740.26684191645942910.7330438945906
Median3.36539271347048
Midrange-0.5775776647302
Midmean - Weighted Average at Xnp2.65150655397668
Midmean - Weighted Average at X(n+1)p2.77948378806994
Midmean - Empirical Distribution Function2.77948378806994
Midmean - Empirical Distribution Function - Averaging2.77948378806994
Midmean - Empirical Distribution Function - Interpolation2.77948378806994
Midmean - Closest Observation2.6128249834245
Midmean - True Basic - Statistics Graphics Toolkit2.77948378806994
Midmean - MS Excel (old versions)2.77948378806994
Number of observations49



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')