Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationMon, 10 Oct 2016 15:50:52 +0100
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2016/Oct/10/t1476111067gfp1fm47y8hof1d.htm/, Retrieved Thu, 09 May 2024 02:59:02 +0200
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=, Retrieved Thu, 09 May 2024 02:59:02 +0200
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact0
Dataseries X:
154
156
152
150
152
138
140
138
141
152
158
146
166
167
163
169
168
158
159
161
166
177
186
182
203
213
215
216
219
217
216
222
224
234
237
233
253
257
254
258
253
241
238
240
240
245
249
247
263
265
261
257
252
245
235
240
243
255
252
240




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Herman Ole Andreas Wold' @ wold.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 & 'Herman Ole Andreas Wold' @ wold.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&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]'Herman Ole Andreas Wold' @ wold.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&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'Herman Ole Andreas Wold' @ wold.wessa.net







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean207.1833333333335.5446055458556937.3666497318628
Geometric Mean202.537049757637
Harmonic Mean197.72902528868
Quadratic Mean211.51536587208
Winsorized Mean ( 1 / 20 )207.155.5388114432060137.3997205220072
Winsorized Mean ( 2 / 20 )207.155.513661768887837.5703132841581
Winsorized Mean ( 3 / 20 )207.055.4791554155541737.7886707524719
Winsorized Mean ( 4 / 20 )207.3166666666675.4025779401362438.3736558664878
Winsorized Mean ( 5 / 20 )207.655.3400112676831538.8856857394033
Winsorized Mean ( 6 / 20 )207.655.2729361775203939.3803363077396
Winsorized Mean ( 7 / 20 )207.5333333333335.2553156660213339.4901746197963
Winsorized Mean ( 8 / 20 )207.45.2354830231675639.6143009312099
Winsorized Mean ( 9 / 20 )207.75.1822327932237740.0792492903032
Winsorized Mean ( 10 / 20 )207.8666666666675.0996547277977140.7609294671669
Winsorized Mean ( 11 / 20 )208.2333333333335.0370585234577441.3402648318625
Winsorized Mean ( 12 / 20 )207.6333333333334.9503733047997341.9429648127785
Winsorized Mean ( 13 / 20 )207.4166666666674.8529967249943642.7399148238468
Winsorized Mean ( 14 / 20 )207.4166666666674.7107457196716644.0305376281536
Winsorized Mean ( 15 / 20 )207.9166666666674.6278627827507944.9271459477201
Winsorized Mean ( 16 / 20 )208.1833333333334.4256246433687147.0404406404578
Winsorized Mean ( 17 / 20 )207.6166666666674.3509912934186547.7170954078234
Winsorized Mean ( 18 / 20 )207.6166666666674.2636349354187848.6947568943949
Winsorized Mean ( 19 / 20 )207.9333333333334.212630099361849.3595042595444
Winsorized Mean ( 20 / 20 )208.2666666666674.1591819780974150.0739490994661
Trimmed Mean ( 1 / 20 )207.3793103448285.5189728075702537.5757079397764
Trimmed Mean ( 2 / 20 )207.6255.4886874510273337.827805254449
Trimmed Mean ( 3 / 20 )207.8888888888895.4612968120939938.0658470033199
Trimmed Mean ( 4 / 20 )208.2115384615385.4361324350154338.3014102306261
Trimmed Mean ( 5 / 20 )208.485.4254306703877138.4264425565135
Trimmed Mean ( 6 / 20 )208.68755.4227453276267638.4837360767837
Trimmed Mean ( 7 / 20 )208.9130434782615.4275933125227438.490916958765
Trimmed Mean ( 8 / 20 )209.1818181818185.4260619937787838.5513137191677
Trimmed Mean ( 9 / 20 )209.55.4159451855787838.6820753943084
Trimmed Mean ( 10 / 20 )209.85.4026584149581438.8327345328986
Trimmed Mean ( 11 / 20 )210.1052631578955.3905493236710738.9765959909275
Trimmed Mean ( 12 / 20 )210.3888888888895.3735504177136739.1526779381005
Trimmed Mean ( 13 / 20 )210.7941176470595.3522579924849439.3841473903226
Trimmed Mean ( 14 / 20 )211.281255.3261062713874739.6689887948782
Trimmed Mean ( 15 / 20 )211.8333333333335.3030208986332539.9457851255931
Trimmed Mean ( 16 / 20 )212.3928571428575.2670331612773740.3249515693855
Trimmed Mean ( 17 / 20 )2135.2438975522469540.6186425035577
Trimmed Mean ( 18 / 20 )213.7916666666675.1895167344559241.1968353907006
Trimmed Mean ( 19 / 20 )214.7272727272735.0901746532694842.1846571785805
Trimmed Mean ( 20 / 20 )215.84.9003759254292244.037437797407
Median218
Midrange201.5
Midmean - Weighted Average at Xnp211.28125
Midmean - Weighted Average at X(n+1)p212.903225806452
Midmean - Empirical Distribution Function211.28125
Midmean - Empirical Distribution Function - Averaging212.903225806452
Midmean - Empirical Distribution Function - Interpolation212.903225806452
Midmean - Closest Observation211.28125
Midmean - True Basic - Statistics Graphics Toolkit212.903225806452
Midmean - MS Excel (old versions)211.28125
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 207.183333333333 & 5.54460554585569 & 37.3666497318628 \tabularnewline
Geometric Mean & 202.537049757637 &  &  \tabularnewline
Harmonic Mean & 197.72902528868 &  &  \tabularnewline
Quadratic Mean & 211.51536587208 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 207.15 & 5.53881144320601 & 37.3997205220072 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 207.15 & 5.5136617688878 & 37.5703132841581 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 207.05 & 5.47915541555417 & 37.7886707524719 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 207.316666666667 & 5.40257794013624 & 38.3736558664878 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 207.65 & 5.34001126768315 & 38.8856857394033 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 207.65 & 5.27293617752039 & 39.3803363077396 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 207.533333333333 & 5.25531566602133 & 39.4901746197963 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 207.4 & 5.23548302316756 & 39.6143009312099 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 207.7 & 5.18223279322377 & 40.0792492903032 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 207.866666666667 & 5.09965472779771 & 40.7609294671669 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 208.233333333333 & 5.03705852345774 & 41.3402648318625 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 207.633333333333 & 4.95037330479973 & 41.9429648127785 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 207.416666666667 & 4.85299672499436 & 42.7399148238468 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 207.416666666667 & 4.71074571967166 & 44.0305376281536 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 207.916666666667 & 4.62786278275079 & 44.9271459477201 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 208.183333333333 & 4.42562464336871 & 47.0404406404578 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 207.616666666667 & 4.35099129341865 & 47.7170954078234 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 207.616666666667 & 4.26363493541878 & 48.6947568943949 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 207.933333333333 & 4.2126300993618 & 49.3595042595444 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 208.266666666667 & 4.15918197809741 & 50.0739490994661 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 207.379310344828 & 5.51897280757025 & 37.5757079397764 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 207.625 & 5.48868745102733 & 37.827805254449 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 207.888888888889 & 5.46129681209399 & 38.0658470033199 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 208.211538461538 & 5.43613243501543 & 38.3014102306261 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 208.48 & 5.42543067038771 & 38.4264425565135 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 208.6875 & 5.42274532762676 & 38.4837360767837 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 208.913043478261 & 5.42759331252274 & 38.490916958765 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 209.181818181818 & 5.42606199377878 & 38.5513137191677 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 209.5 & 5.41594518557878 & 38.6820753943084 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 209.8 & 5.40265841495814 & 38.8327345328986 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 210.105263157895 & 5.39054932367107 & 38.9765959909275 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 210.388888888889 & 5.37355041771367 & 39.1526779381005 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 210.794117647059 & 5.35225799248494 & 39.3841473903226 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 211.28125 & 5.32610627138747 & 39.6689887948782 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 211.833333333333 & 5.30302089863325 & 39.9457851255931 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 212.392857142857 & 5.26703316127737 & 40.3249515693855 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 213 & 5.24389755224695 & 40.6186425035577 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 213.791666666667 & 5.18951673445592 & 41.1968353907006 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 214.727272727273 & 5.09017465326948 & 42.1846571785805 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 215.8 & 4.90037592542922 & 44.037437797407 \tabularnewline
Median & 218 &  &  \tabularnewline
Midrange & 201.5 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 211.28125 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 212.903225806452 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 211.28125 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 212.903225806452 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 212.903225806452 &  &  \tabularnewline
Midmean - Closest Observation & 211.28125 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 212.903225806452 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 211.28125 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&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]207.183333333333[/C][C]5.54460554585569[/C][C]37.3666497318628[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]202.537049757637[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]197.72902528868[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]211.51536587208[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]207.15[/C][C]5.53881144320601[/C][C]37.3997205220072[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]207.15[/C][C]5.5136617688878[/C][C]37.5703132841581[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]207.05[/C][C]5.47915541555417[/C][C]37.7886707524719[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]207.316666666667[/C][C]5.40257794013624[/C][C]38.3736558664878[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]207.65[/C][C]5.34001126768315[/C][C]38.8856857394033[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]207.65[/C][C]5.27293617752039[/C][C]39.3803363077396[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]207.533333333333[/C][C]5.25531566602133[/C][C]39.4901746197963[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]207.4[/C][C]5.23548302316756[/C][C]39.6143009312099[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]207.7[/C][C]5.18223279322377[/C][C]40.0792492903032[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]207.866666666667[/C][C]5.09965472779771[/C][C]40.7609294671669[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]208.233333333333[/C][C]5.03705852345774[/C][C]41.3402648318625[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]207.633333333333[/C][C]4.95037330479973[/C][C]41.9429648127785[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]207.416666666667[/C][C]4.85299672499436[/C][C]42.7399148238468[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]207.416666666667[/C][C]4.71074571967166[/C][C]44.0305376281536[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]207.916666666667[/C][C]4.62786278275079[/C][C]44.9271459477201[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]208.183333333333[/C][C]4.42562464336871[/C][C]47.0404406404578[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]207.616666666667[/C][C]4.35099129341865[/C][C]47.7170954078234[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]207.616666666667[/C][C]4.26363493541878[/C][C]48.6947568943949[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]207.933333333333[/C][C]4.2126300993618[/C][C]49.3595042595444[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]208.266666666667[/C][C]4.15918197809741[/C][C]50.0739490994661[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]207.379310344828[/C][C]5.51897280757025[/C][C]37.5757079397764[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]207.625[/C][C]5.48868745102733[/C][C]37.827805254449[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]207.888888888889[/C][C]5.46129681209399[/C][C]38.0658470033199[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]208.211538461538[/C][C]5.43613243501543[/C][C]38.3014102306261[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]208.48[/C][C]5.42543067038771[/C][C]38.4264425565135[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]208.6875[/C][C]5.42274532762676[/C][C]38.4837360767837[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]208.913043478261[/C][C]5.42759331252274[/C][C]38.490916958765[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]209.181818181818[/C][C]5.42606199377878[/C][C]38.5513137191677[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]209.5[/C][C]5.41594518557878[/C][C]38.6820753943084[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]209.8[/C][C]5.40265841495814[/C][C]38.8327345328986[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]210.105263157895[/C][C]5.39054932367107[/C][C]38.9765959909275[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]210.388888888889[/C][C]5.37355041771367[/C][C]39.1526779381005[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]210.794117647059[/C][C]5.35225799248494[/C][C]39.3841473903226[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]211.28125[/C][C]5.32610627138747[/C][C]39.6689887948782[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]211.833333333333[/C][C]5.30302089863325[/C][C]39.9457851255931[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]212.392857142857[/C][C]5.26703316127737[/C][C]40.3249515693855[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]213[/C][C]5.24389755224695[/C][C]40.6186425035577[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]213.791666666667[/C][C]5.18951673445592[/C][C]41.1968353907006[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]214.727272727273[/C][C]5.09017465326948[/C][C]42.1846571785805[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]215.8[/C][C]4.90037592542922[/C][C]44.037437797407[/C][/ROW]
[ROW][C]Median[/C][C]218[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]201.5[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]211.28125[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]212.903225806452[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]211.28125[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]212.903225806452[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]212.903225806452[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]211.28125[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]212.903225806452[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]211.28125[/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=&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&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 Mean207.1833333333335.5446055458556937.3666497318628
Geometric Mean202.537049757637
Harmonic Mean197.72902528868
Quadratic Mean211.51536587208
Winsorized Mean ( 1 / 20 )207.155.5388114432060137.3997205220072
Winsorized Mean ( 2 / 20 )207.155.513661768887837.5703132841581
Winsorized Mean ( 3 / 20 )207.055.4791554155541737.7886707524719
Winsorized Mean ( 4 / 20 )207.3166666666675.4025779401362438.3736558664878
Winsorized Mean ( 5 / 20 )207.655.3400112676831538.8856857394033
Winsorized Mean ( 6 / 20 )207.655.2729361775203939.3803363077396
Winsorized Mean ( 7 / 20 )207.5333333333335.2553156660213339.4901746197963
Winsorized Mean ( 8 / 20 )207.45.2354830231675639.6143009312099
Winsorized Mean ( 9 / 20 )207.75.1822327932237740.0792492903032
Winsorized Mean ( 10 / 20 )207.8666666666675.0996547277977140.7609294671669
Winsorized Mean ( 11 / 20 )208.2333333333335.0370585234577441.3402648318625
Winsorized Mean ( 12 / 20 )207.6333333333334.9503733047997341.9429648127785
Winsorized Mean ( 13 / 20 )207.4166666666674.8529967249943642.7399148238468
Winsorized Mean ( 14 / 20 )207.4166666666674.7107457196716644.0305376281536
Winsorized Mean ( 15 / 20 )207.9166666666674.6278627827507944.9271459477201
Winsorized Mean ( 16 / 20 )208.1833333333334.4256246433687147.0404406404578
Winsorized Mean ( 17 / 20 )207.6166666666674.3509912934186547.7170954078234
Winsorized Mean ( 18 / 20 )207.6166666666674.2636349354187848.6947568943949
Winsorized Mean ( 19 / 20 )207.9333333333334.212630099361849.3595042595444
Winsorized Mean ( 20 / 20 )208.2666666666674.1591819780974150.0739490994661
Trimmed Mean ( 1 / 20 )207.3793103448285.5189728075702537.5757079397764
Trimmed Mean ( 2 / 20 )207.6255.4886874510273337.827805254449
Trimmed Mean ( 3 / 20 )207.8888888888895.4612968120939938.0658470033199
Trimmed Mean ( 4 / 20 )208.2115384615385.4361324350154338.3014102306261
Trimmed Mean ( 5 / 20 )208.485.4254306703877138.4264425565135
Trimmed Mean ( 6 / 20 )208.68755.4227453276267638.4837360767837
Trimmed Mean ( 7 / 20 )208.9130434782615.4275933125227438.490916958765
Trimmed Mean ( 8 / 20 )209.1818181818185.4260619937787838.5513137191677
Trimmed Mean ( 9 / 20 )209.55.4159451855787838.6820753943084
Trimmed Mean ( 10 / 20 )209.85.4026584149581438.8327345328986
Trimmed Mean ( 11 / 20 )210.1052631578955.3905493236710738.9765959909275
Trimmed Mean ( 12 / 20 )210.3888888888895.3735504177136739.1526779381005
Trimmed Mean ( 13 / 20 )210.7941176470595.3522579924849439.3841473903226
Trimmed Mean ( 14 / 20 )211.281255.3261062713874739.6689887948782
Trimmed Mean ( 15 / 20 )211.8333333333335.3030208986332539.9457851255931
Trimmed Mean ( 16 / 20 )212.3928571428575.2670331612773740.3249515693855
Trimmed Mean ( 17 / 20 )2135.2438975522469540.6186425035577
Trimmed Mean ( 18 / 20 )213.7916666666675.1895167344559241.1968353907006
Trimmed Mean ( 19 / 20 )214.7272727272735.0901746532694842.1846571785805
Trimmed Mean ( 20 / 20 )215.84.9003759254292244.037437797407
Median218
Midrange201.5
Midmean - Weighted Average at Xnp211.28125
Midmean - Weighted Average at X(n+1)p212.903225806452
Midmean - Empirical Distribution Function211.28125
Midmean - Empirical Distribution Function - Averaging212.903225806452
Midmean - Empirical Distribution Function - Interpolation212.903225806452
Midmean - Closest Observation211.28125
Midmean - True Basic - Statistics Graphics Toolkit212.903225806452
Midmean - MS Excel (old versions)211.28125
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')