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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 computationMon, 15 Nov 2010 19:55:26 +0000
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2010/Nov/15/t128985082411uffps5azarpp2.htm/, Retrieved Sat, 27 Apr 2024 21:44:22 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=95036, Retrieved Sat, 27 Apr 2024 21:44:22 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact149
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Central Tendency] [Arabica Price in ...] [2008-01-06 21:28:17] [74be16979710d4c4e7c6647856088456]
-  M D    [Central Tendency] [Blog 1 - Olie] [2010-11-15 19:55:26] [47bfda5353cd53c1cf7ea7aa9038654a] [Current]
-    D      [Central Tendency] [Blog 5 - Vervoer] [2010-11-16 17:33:01] [1aa8d85d6b335d32b1f6be940e33a166]
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Dataseries X:
288,6
269,1
268,7
264,3
264,3
267,6
298,1
279,8
263,2
272,5
263,7
273,7
261,4
241,1
253,4
228,6
244,9
206,1
177
165,1
148,1
152,9
146,5
188
252
351,6
403
468,8
464
435,4
382,2
360,6
329,5
320,2
315
322,7
289,7
270,3
247,8
259,6
241
230
230,3
214
202,9
188,5
215,6
205,6
203,7
218,2
253
255,4
240,7
242,2
240,2
215,2
211,1
219,3




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135

\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 & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=95036&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]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=95036&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=95036&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'Gwilym Jenkins' @ 72.249.127.135







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean261.8275862068979.2313967515044528.362727034154
Geometric Mean253.413093915403
Harmonic Mean245.595116186522
Quadratic Mean270.944920601956
Winsorized Mean ( 1 / 19 )261.7724137931039.1931353414025528.4747699312307
Winsorized Mean ( 2 / 19 )260.9517241379318.7950380064707529.6703350168517
Winsorized Mean ( 3 / 19 )259.9068965517248.1099215755579132.048016017201
Winsorized Mean ( 4 / 19 )259.2931034482767.5184225693593334.4877001866059
Winsorized Mean ( 5 / 19 )258.3793103448286.8287858026991237.8367864815296
Winsorized Mean ( 6 / 19 )257.56.5802087357047139.13249721134
Winsorized Mean ( 7 / 19 )256.5706896551725.634092172436145.5389585052236
Winsorized Mean ( 8 / 19 )255.7431034482765.4070813017453347.2978098860332
Winsorized Mean ( 9 / 19 )255.655.2738458252269548.475061363592
Winsorized Mean ( 10 / 19 )254.8396551724145.0697607363768950.2666039728209
Winsorized Mean ( 11 / 19 )252.582758620694.273070288569259.1103683214312
Winsorized Mean ( 12 / 19 )251.4448275862073.8566942550863365.1969824298603
Winsorized Mean ( 13 / 19 )251.4672413793103.7683123258863166.7320592435673
Winsorized Mean ( 14 / 19 )249.4396551724143.4009197180091573.3447643152341
Winsorized Mean ( 15 / 19 )248.5344827586213.0450653819621581.6187672786429
Winsorized Mean ( 16 / 19 )248.5068965517242.9444780129451384.3976064549257
Winsorized Mean ( 17 / 19 )250.5879310344832.39317323784072104.709482402778
Winsorized Mean ( 18 / 19 )250.652.27000783516001110.418121082094
Winsorized Mean ( 19 / 19 )250.6172413793102.23569207265780112.098282426424
Trimmed Mean ( 1 / 19 )260.1910714285718.5554904816571130.412174729949
Trimmed Mean ( 2 / 19 )258.4925925925937.7339291915368333.4231910056093
Trimmed Mean ( 3 / 19 )257.1211538461546.9647590266775736.9174515387088
Trimmed Mean ( 4 / 19 )256.0446.3514845830060340.3124650077982
Trimmed Mean ( 5 / 19 )255.06255.8280165423045943.7648895037522
Trimmed Mean ( 6 / 19 )254.2260869565225.4266772021962846.8474680700801
Trimmed Mean ( 7 / 19 )253.5068181818184.9912559881869250.7901856329963
Trimmed Mean ( 8 / 19 )252.9023809523814.745763424075953.2901365604052
Trimmed Mean ( 9 / 19 )252.38754.4921700933330556.1838698794097
Trimmed Mean ( 10 / 19 )251.8342105263164.1897495253980460.1072233554083
Trimmed Mean ( 11 / 19 )251.353.8411876057050765.435491780377
Trimmed Mean ( 12 / 19 )251.1588235294123.6299509620074269.1906932512711
Trimmed Mean ( 13 / 19 )251.1156253.4661121817901472.4487875260593
Trimmed Mean ( 14 / 19 )251.0633333333333.25589291858977.1104393206322
Trimmed Mean ( 15 / 19 )251.3035714285713.0726799315013781.786446044115
Trimmed Mean ( 16 / 19 )251.7153846153852.9183277208686786.2532959596665
Trimmed Mean ( 17 / 19 )252.22.7078187917022293.1376947278881
Trimmed Mean ( 18 / 19 )252.452.6159165660470796.5053714925928
Trimmed Mean ( 19 / 19 )252.742.50187718996841101.02014639783
Median253.2
Midrange307.65
Midmean - Weighted Average at Xnp250.072413793103
Midmean - Weighted Average at X(n+1)p251.063333333333
Midmean - Empirical Distribution Function251.063333333333
Midmean - Empirical Distribution Function - Averaging251.063333333333
Midmean - Empirical Distribution Function - Interpolation251.303571428571
Midmean - Closest Observation251.063333333333
Midmean - True Basic - Statistics Graphics Toolkit251.063333333333
Midmean - MS Excel (old versions)251.063333333333
Number of observations58

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 261.827586206897 & 9.23139675150445 & 28.362727034154 \tabularnewline
Geometric Mean & 253.413093915403 &  &  \tabularnewline
Harmonic Mean & 245.595116186522 &  &  \tabularnewline
Quadratic Mean & 270.944920601956 &  &  \tabularnewline
Winsorized Mean ( 1 / 19 ) & 261.772413793103 & 9.19313534140255 & 28.4747699312307 \tabularnewline
Winsorized Mean ( 2 / 19 ) & 260.951724137931 & 8.79503800647075 & 29.6703350168517 \tabularnewline
Winsorized Mean ( 3 / 19 ) & 259.906896551724 & 8.10992157555791 & 32.048016017201 \tabularnewline
Winsorized Mean ( 4 / 19 ) & 259.293103448276 & 7.51842256935933 & 34.4877001866059 \tabularnewline
Winsorized Mean ( 5 / 19 ) & 258.379310344828 & 6.82878580269912 & 37.8367864815296 \tabularnewline
Winsorized Mean ( 6 / 19 ) & 257.5 & 6.58020873570471 & 39.13249721134 \tabularnewline
Winsorized Mean ( 7 / 19 ) & 256.570689655172 & 5.6340921724361 & 45.5389585052236 \tabularnewline
Winsorized Mean ( 8 / 19 ) & 255.743103448276 & 5.40708130174533 & 47.2978098860332 \tabularnewline
Winsorized Mean ( 9 / 19 ) & 255.65 & 5.27384582522695 & 48.475061363592 \tabularnewline
Winsorized Mean ( 10 / 19 ) & 254.839655172414 & 5.06976073637689 & 50.2666039728209 \tabularnewline
Winsorized Mean ( 11 / 19 ) & 252.58275862069 & 4.2730702885692 & 59.1103683214312 \tabularnewline
Winsorized Mean ( 12 / 19 ) & 251.444827586207 & 3.85669425508633 & 65.1969824298603 \tabularnewline
Winsorized Mean ( 13 / 19 ) & 251.467241379310 & 3.76831232588631 & 66.7320592435673 \tabularnewline
Winsorized Mean ( 14 / 19 ) & 249.439655172414 & 3.40091971800915 & 73.3447643152341 \tabularnewline
Winsorized Mean ( 15 / 19 ) & 248.534482758621 & 3.04506538196215 & 81.6187672786429 \tabularnewline
Winsorized Mean ( 16 / 19 ) & 248.506896551724 & 2.94447801294513 & 84.3976064549257 \tabularnewline
Winsorized Mean ( 17 / 19 ) & 250.587931034483 & 2.39317323784072 & 104.709482402778 \tabularnewline
Winsorized Mean ( 18 / 19 ) & 250.65 & 2.27000783516001 & 110.418121082094 \tabularnewline
Winsorized Mean ( 19 / 19 ) & 250.617241379310 & 2.23569207265780 & 112.098282426424 \tabularnewline
Trimmed Mean ( 1 / 19 ) & 260.191071428571 & 8.55549048165711 & 30.412174729949 \tabularnewline
Trimmed Mean ( 2 / 19 ) & 258.492592592593 & 7.73392919153683 & 33.4231910056093 \tabularnewline
Trimmed Mean ( 3 / 19 ) & 257.121153846154 & 6.96475902667757 & 36.9174515387088 \tabularnewline
Trimmed Mean ( 4 / 19 ) & 256.044 & 6.35148458300603 & 40.3124650077982 \tabularnewline
Trimmed Mean ( 5 / 19 ) & 255.0625 & 5.82801654230459 & 43.7648895037522 \tabularnewline
Trimmed Mean ( 6 / 19 ) & 254.226086956522 & 5.42667720219628 & 46.8474680700801 \tabularnewline
Trimmed Mean ( 7 / 19 ) & 253.506818181818 & 4.99125598818692 & 50.7901856329963 \tabularnewline
Trimmed Mean ( 8 / 19 ) & 252.902380952381 & 4.7457634240759 & 53.2901365604052 \tabularnewline
Trimmed Mean ( 9 / 19 ) & 252.3875 & 4.49217009333305 & 56.1838698794097 \tabularnewline
Trimmed Mean ( 10 / 19 ) & 251.834210526316 & 4.18974952539804 & 60.1072233554083 \tabularnewline
Trimmed Mean ( 11 / 19 ) & 251.35 & 3.84118760570507 & 65.435491780377 \tabularnewline
Trimmed Mean ( 12 / 19 ) & 251.158823529412 & 3.62995096200742 & 69.1906932512711 \tabularnewline
Trimmed Mean ( 13 / 19 ) & 251.115625 & 3.46611218179014 & 72.4487875260593 \tabularnewline
Trimmed Mean ( 14 / 19 ) & 251.063333333333 & 3.255892918589 & 77.1104393206322 \tabularnewline
Trimmed Mean ( 15 / 19 ) & 251.303571428571 & 3.07267993150137 & 81.786446044115 \tabularnewline
Trimmed Mean ( 16 / 19 ) & 251.715384615385 & 2.91832772086867 & 86.2532959596665 \tabularnewline
Trimmed Mean ( 17 / 19 ) & 252.2 & 2.70781879170222 & 93.1376947278881 \tabularnewline
Trimmed Mean ( 18 / 19 ) & 252.45 & 2.61591656604707 & 96.5053714925928 \tabularnewline
Trimmed Mean ( 19 / 19 ) & 252.74 & 2.50187718996841 & 101.02014639783 \tabularnewline
Median & 253.2 &  &  \tabularnewline
Midrange & 307.65 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 250.072413793103 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 251.063333333333 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 251.063333333333 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 251.063333333333 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 251.303571428571 &  &  \tabularnewline
Midmean - Closest Observation & 251.063333333333 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 251.063333333333 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 251.063333333333 &  &  \tabularnewline
Number of observations & 58 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=95036&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]261.827586206897[/C][C]9.23139675150445[/C][C]28.362727034154[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]253.413093915403[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]245.595116186522[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]270.944920601956[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 19 )[/C][C]261.772413793103[/C][C]9.19313534140255[/C][C]28.4747699312307[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 19 )[/C][C]260.951724137931[/C][C]8.79503800647075[/C][C]29.6703350168517[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 19 )[/C][C]259.906896551724[/C][C]8.10992157555791[/C][C]32.048016017201[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 19 )[/C][C]259.293103448276[/C][C]7.51842256935933[/C][C]34.4877001866059[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 19 )[/C][C]258.379310344828[/C][C]6.82878580269912[/C][C]37.8367864815296[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 19 )[/C][C]257.5[/C][C]6.58020873570471[/C][C]39.13249721134[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 19 )[/C][C]256.570689655172[/C][C]5.6340921724361[/C][C]45.5389585052236[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 19 )[/C][C]255.743103448276[/C][C]5.40708130174533[/C][C]47.2978098860332[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 19 )[/C][C]255.65[/C][C]5.27384582522695[/C][C]48.475061363592[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 19 )[/C][C]254.839655172414[/C][C]5.06976073637689[/C][C]50.2666039728209[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 19 )[/C][C]252.58275862069[/C][C]4.2730702885692[/C][C]59.1103683214312[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 19 )[/C][C]251.444827586207[/C][C]3.85669425508633[/C][C]65.1969824298603[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 19 )[/C][C]251.467241379310[/C][C]3.76831232588631[/C][C]66.7320592435673[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 19 )[/C][C]249.439655172414[/C][C]3.40091971800915[/C][C]73.3447643152341[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 19 )[/C][C]248.534482758621[/C][C]3.04506538196215[/C][C]81.6187672786429[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 19 )[/C][C]248.506896551724[/C][C]2.94447801294513[/C][C]84.3976064549257[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 19 )[/C][C]250.587931034483[/C][C]2.39317323784072[/C][C]104.709482402778[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 19 )[/C][C]250.65[/C][C]2.27000783516001[/C][C]110.418121082094[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 19 )[/C][C]250.617241379310[/C][C]2.23569207265780[/C][C]112.098282426424[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 19 )[/C][C]260.191071428571[/C][C]8.55549048165711[/C][C]30.412174729949[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 19 )[/C][C]258.492592592593[/C][C]7.73392919153683[/C][C]33.4231910056093[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 19 )[/C][C]257.121153846154[/C][C]6.96475902667757[/C][C]36.9174515387088[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 19 )[/C][C]256.044[/C][C]6.35148458300603[/C][C]40.3124650077982[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 19 )[/C][C]255.0625[/C][C]5.82801654230459[/C][C]43.7648895037522[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 19 )[/C][C]254.226086956522[/C][C]5.42667720219628[/C][C]46.8474680700801[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 19 )[/C][C]253.506818181818[/C][C]4.99125598818692[/C][C]50.7901856329963[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 19 )[/C][C]252.902380952381[/C][C]4.7457634240759[/C][C]53.2901365604052[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 19 )[/C][C]252.3875[/C][C]4.49217009333305[/C][C]56.1838698794097[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 19 )[/C][C]251.834210526316[/C][C]4.18974952539804[/C][C]60.1072233554083[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 19 )[/C][C]251.35[/C][C]3.84118760570507[/C][C]65.435491780377[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 19 )[/C][C]251.158823529412[/C][C]3.62995096200742[/C][C]69.1906932512711[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 19 )[/C][C]251.115625[/C][C]3.46611218179014[/C][C]72.4487875260593[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 19 )[/C][C]251.063333333333[/C][C]3.255892918589[/C][C]77.1104393206322[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 19 )[/C][C]251.303571428571[/C][C]3.07267993150137[/C][C]81.786446044115[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 19 )[/C][C]251.715384615385[/C][C]2.91832772086867[/C][C]86.2532959596665[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 19 )[/C][C]252.2[/C][C]2.70781879170222[/C][C]93.1376947278881[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 19 )[/C][C]252.45[/C][C]2.61591656604707[/C][C]96.5053714925928[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 19 )[/C][C]252.74[/C][C]2.50187718996841[/C][C]101.02014639783[/C][/ROW]
[ROW][C]Median[/C][C]253.2[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]307.65[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]250.072413793103[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]251.063333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]251.063333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]251.063333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]251.303571428571[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]251.063333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]251.063333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]251.063333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]58[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=95036&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=95036&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 Mean261.8275862068979.2313967515044528.362727034154
Geometric Mean253.413093915403
Harmonic Mean245.595116186522
Quadratic Mean270.944920601956
Winsorized Mean ( 1 / 19 )261.7724137931039.1931353414025528.4747699312307
Winsorized Mean ( 2 / 19 )260.9517241379318.7950380064707529.6703350168517
Winsorized Mean ( 3 / 19 )259.9068965517248.1099215755579132.048016017201
Winsorized Mean ( 4 / 19 )259.2931034482767.5184225693593334.4877001866059
Winsorized Mean ( 5 / 19 )258.3793103448286.8287858026991237.8367864815296
Winsorized Mean ( 6 / 19 )257.56.5802087357047139.13249721134
Winsorized Mean ( 7 / 19 )256.5706896551725.634092172436145.5389585052236
Winsorized Mean ( 8 / 19 )255.7431034482765.4070813017453347.2978098860332
Winsorized Mean ( 9 / 19 )255.655.2738458252269548.475061363592
Winsorized Mean ( 10 / 19 )254.8396551724145.0697607363768950.2666039728209
Winsorized Mean ( 11 / 19 )252.582758620694.273070288569259.1103683214312
Winsorized Mean ( 12 / 19 )251.4448275862073.8566942550863365.1969824298603
Winsorized Mean ( 13 / 19 )251.4672413793103.7683123258863166.7320592435673
Winsorized Mean ( 14 / 19 )249.4396551724143.4009197180091573.3447643152341
Winsorized Mean ( 15 / 19 )248.5344827586213.0450653819621581.6187672786429
Winsorized Mean ( 16 / 19 )248.5068965517242.9444780129451384.3976064549257
Winsorized Mean ( 17 / 19 )250.5879310344832.39317323784072104.709482402778
Winsorized Mean ( 18 / 19 )250.652.27000783516001110.418121082094
Winsorized Mean ( 19 / 19 )250.6172413793102.23569207265780112.098282426424
Trimmed Mean ( 1 / 19 )260.1910714285718.5554904816571130.412174729949
Trimmed Mean ( 2 / 19 )258.4925925925937.7339291915368333.4231910056093
Trimmed Mean ( 3 / 19 )257.1211538461546.9647590266775736.9174515387088
Trimmed Mean ( 4 / 19 )256.0446.3514845830060340.3124650077982
Trimmed Mean ( 5 / 19 )255.06255.8280165423045943.7648895037522
Trimmed Mean ( 6 / 19 )254.2260869565225.4266772021962846.8474680700801
Trimmed Mean ( 7 / 19 )253.5068181818184.9912559881869250.7901856329963
Trimmed Mean ( 8 / 19 )252.9023809523814.745763424075953.2901365604052
Trimmed Mean ( 9 / 19 )252.38754.4921700933330556.1838698794097
Trimmed Mean ( 10 / 19 )251.8342105263164.1897495253980460.1072233554083
Trimmed Mean ( 11 / 19 )251.353.8411876057050765.435491780377
Trimmed Mean ( 12 / 19 )251.1588235294123.6299509620074269.1906932512711
Trimmed Mean ( 13 / 19 )251.1156253.4661121817901472.4487875260593
Trimmed Mean ( 14 / 19 )251.0633333333333.25589291858977.1104393206322
Trimmed Mean ( 15 / 19 )251.3035714285713.0726799315013781.786446044115
Trimmed Mean ( 16 / 19 )251.7153846153852.9183277208686786.2532959596665
Trimmed Mean ( 17 / 19 )252.22.7078187917022293.1376947278881
Trimmed Mean ( 18 / 19 )252.452.6159165660470796.5053714925928
Trimmed Mean ( 19 / 19 )252.742.50187718996841101.02014639783
Median253.2
Midrange307.65
Midmean - Weighted Average at Xnp250.072413793103
Midmean - Weighted Average at X(n+1)p251.063333333333
Midmean - Empirical Distribution Function251.063333333333
Midmean - Empirical Distribution Function - Averaging251.063333333333
Midmean - Empirical Distribution Function - Interpolation251.303571428571
Midmean - Closest Observation251.063333333333
Midmean - True Basic - Statistics Graphics Toolkit251.063333333333
Midmean - MS Excel (old versions)251.063333333333
Number of observations58



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')