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of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationWed, 14 Apr 2010 10:52:35 +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/Apr/14/t1271242390gzfn5u0ttbxmfzf.htm/, Retrieved Thu, 28 Mar 2024 18:12:47 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=74630, Retrieved Thu, 28 Mar 2024 18:12:47 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsKDGP1W52
Estimated Impact237
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [] [2010-04-14 10:52:35] [ba71a47f11e8062985d77fe3913d8d26] [Current]
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Dataseries X:
268
250
231
295
258
288
292
253
272
251
274
302
325
307
246
299
305
280
272
252
235
220
274
301
305
320
248
278
264
263
261
267
255
222
276
277
281
284
218
281
298
288
270
245
250
227
238
262
272
264
212
294
280
273
239
242
201
239
266
276
288
271
220
274
273
289
270
243
225
222
234
254




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

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 3 seconds \tabularnewline
R Server & 'RServer@AstonUniversity' @ vre.aston.ac.uk \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=74630&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]3 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'RServer@AstonUniversity' @ vre.aston.ac.uk[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=74630&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=74630&T=0

As an alternative you can also use a QR Code:  

The GUIDs for individual cells are displayed in the table below:

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







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean264.5694444444443.1875900299592882.9998343443884
Geometric Mean263.177602060977
Harmonic Mean261.756688076777
Quadratic Mean265.929319139086
Winsorized Mean ( 1 / 24 )264.6527777777783.1300802038041484.5514365593994
Winsorized Mean ( 2 / 24 )264.4583333333333.0111255297947287.8270702156221
Winsorized Mean ( 3 / 24 )264.4583333333332.9770205918113688.8332227397945
Winsorized Mean ( 4 / 24 )264.4583333333332.9770205918113688.8332227397945
Winsorized Mean ( 5 / 24 )264.3888888888892.9091993985753590.8802913331968
Winsorized Mean ( 6 / 24 )264.3055555555562.8941713921770691.3233944160918
Winsorized Mean ( 7 / 24 )264.4027777777782.800951361559394.3974898695076
Winsorized Mean ( 8 / 24 )264.5138888888892.7382551198797396.5994318675854
Winsorized Mean ( 9 / 24 )264.6388888888892.58064797242332102.547457738059
Winsorized Mean ( 10 / 24 )264.9166666666672.48286380537804106.698025921857
Winsorized Mean ( 11 / 24 )264.7638888888892.40658761522365110.016309904546
Winsorized Mean ( 12 / 24 )264.7638888888892.24301149561615118.039470331007
Winsorized Mean ( 13 / 24 )264.7638888888892.18558847226374121.140778444287
Winsorized Mean ( 14 / 24 )264.7638888888892.18558847226374121.140778444287
Winsorized Mean ( 15 / 24 )265.3888888888892.08425383941562127.330406628061
Winsorized Mean ( 16 / 24 )264.7222222222221.91793917976302138.024304949509
Winsorized Mean ( 17 / 24 )264.4861111111111.74566230302297151.510467203823
Winsorized Mean ( 18 / 24 )264.7361111111111.70667852470246155.117737335603
Winsorized Mean ( 19 / 24 )2651.59088266953651166.574194989003
Winsorized Mean ( 20 / 24 )265.5555555555561.50869790277912176.016388082985
Winsorized Mean ( 21 / 24 )264.9722222222221.43194225298819185.04393013704
Winsorized Mean ( 22 / 24 )264.9722222222221.34835612866027196.515013051856
Winsorized Mean ( 23 / 24 )264.9722222222221.26218198898827209.93186761809
Winsorized Mean ( 24 / 24 )265.3055555555561.21426041699677218.491479951011
Trimmed Mean ( 1 / 24 )264.6142857142863.0267470773839987.4253047740583
Trimmed Mean ( 2 / 24 )264.5735294117652.9036560902223991.117377950741
Trimmed Mean ( 3 / 24 )264.6363636363642.8335022324787793.3955020761913
Trimmed Mean ( 4 / 24 )264.7031252.7648121731731895.7400027272739
Trimmed Mean ( 5 / 24 )264.7741935483872.6817260985621898.732750406668
Trimmed Mean ( 6 / 24 )264.8666666666672.60285226716201101.760161346176
Trimmed Mean ( 7 / 24 )264.982758620692.51065381218042105.543327931206
Trimmed Mean ( 8 / 24 )265.0892857142862.42300618071076109.405121548854
Trimmed Mean ( 9 / 24 )265.1851851851852.3307973751412113.774448183905
Trimmed Mean ( 10 / 24 )265.2692307692312.25539664262122117.615334596284
Trimmed Mean ( 11 / 24 )265.322.18406847466851121.479707746008
Trimmed Mean ( 12 / 24 )265.3958333333332.11121196062153125.707810624189
Trimmed Mean ( 13 / 24 )265.4782608695652.05568356237837129.143544136926
Trimmed Mean ( 14 / 24 )265.5681818181821.99613731835623133.041038497728
Trimmed Mean ( 15 / 24 )265.6666666666671.91717788465878138.57173546207
Trimmed Mean ( 16 / 24 )265.71.83805917708368144.554649443642
Trimmed Mean ( 17 / 24 )265.8157894736841.77298169793722149.925850776096
Trimmed Mean ( 18 / 24 )265.9722222222221.72630723925475154.070038156732
Trimmed Mean ( 19 / 24 )266.1176470588241.67010236212292159.342117641552
Trimmed Mean ( 20 / 24 )266.251.62142907894996164.206997059917
Trimmed Mean ( 21 / 24 )266.3333333333331.57373071155469169.23691669601
Trimmed Mean ( 22 / 24 )266.51.5218861869856175.111649135772
Trimmed Mean ( 23 / 24 )266.6923076923081.46735683958421181.750137729196
Trimmed Mean ( 24 / 24 )266.9166666666671.40897314169208189.440564030992
Median269
Midrange263
Midmean - Weighted Average at Xnp265.815789473684
Midmean - Weighted Average at X(n+1)p266.378378378378
Midmean - Empirical Distribution Function265.815789473684
Midmean - Empirical Distribution Function - Averaging266.378378378378
Midmean - Empirical Distribution Function - Interpolation266.378378378378
Midmean - Closest Observation265.815789473684
Midmean - True Basic - Statistics Graphics Toolkit266.378378378378
Midmean - MS Excel (old versions)265.815789473684
Number of observations72

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 264.569444444444 & 3.18759002995928 & 82.9998343443884 \tabularnewline
Geometric Mean & 263.177602060977 &  &  \tabularnewline
Harmonic Mean & 261.756688076777 &  &  \tabularnewline
Quadratic Mean & 265.929319139086 &  &  \tabularnewline
Winsorized Mean ( 1 / 24 ) & 264.652777777778 & 3.13008020380414 & 84.5514365593994 \tabularnewline
Winsorized Mean ( 2 / 24 ) & 264.458333333333 & 3.01112552979472 & 87.8270702156221 \tabularnewline
Winsorized Mean ( 3 / 24 ) & 264.458333333333 & 2.97702059181136 & 88.8332227397945 \tabularnewline
Winsorized Mean ( 4 / 24 ) & 264.458333333333 & 2.97702059181136 & 88.8332227397945 \tabularnewline
Winsorized Mean ( 5 / 24 ) & 264.388888888889 & 2.90919939857535 & 90.8802913331968 \tabularnewline
Winsorized Mean ( 6 / 24 ) & 264.305555555556 & 2.89417139217706 & 91.3233944160918 \tabularnewline
Winsorized Mean ( 7 / 24 ) & 264.402777777778 & 2.8009513615593 & 94.3974898695076 \tabularnewline
Winsorized Mean ( 8 / 24 ) & 264.513888888889 & 2.73825511987973 & 96.5994318675854 \tabularnewline
Winsorized Mean ( 9 / 24 ) & 264.638888888889 & 2.58064797242332 & 102.547457738059 \tabularnewline
Winsorized Mean ( 10 / 24 ) & 264.916666666667 & 2.48286380537804 & 106.698025921857 \tabularnewline
Winsorized Mean ( 11 / 24 ) & 264.763888888889 & 2.40658761522365 & 110.016309904546 \tabularnewline
Winsorized Mean ( 12 / 24 ) & 264.763888888889 & 2.24301149561615 & 118.039470331007 \tabularnewline
Winsorized Mean ( 13 / 24 ) & 264.763888888889 & 2.18558847226374 & 121.140778444287 \tabularnewline
Winsorized Mean ( 14 / 24 ) & 264.763888888889 & 2.18558847226374 & 121.140778444287 \tabularnewline
Winsorized Mean ( 15 / 24 ) & 265.388888888889 & 2.08425383941562 & 127.330406628061 \tabularnewline
Winsorized Mean ( 16 / 24 ) & 264.722222222222 & 1.91793917976302 & 138.024304949509 \tabularnewline
Winsorized Mean ( 17 / 24 ) & 264.486111111111 & 1.74566230302297 & 151.510467203823 \tabularnewline
Winsorized Mean ( 18 / 24 ) & 264.736111111111 & 1.70667852470246 & 155.117737335603 \tabularnewline
Winsorized Mean ( 19 / 24 ) & 265 & 1.59088266953651 & 166.574194989003 \tabularnewline
Winsorized Mean ( 20 / 24 ) & 265.555555555556 & 1.50869790277912 & 176.016388082985 \tabularnewline
Winsorized Mean ( 21 / 24 ) & 264.972222222222 & 1.43194225298819 & 185.04393013704 \tabularnewline
Winsorized Mean ( 22 / 24 ) & 264.972222222222 & 1.34835612866027 & 196.515013051856 \tabularnewline
Winsorized Mean ( 23 / 24 ) & 264.972222222222 & 1.26218198898827 & 209.93186761809 \tabularnewline
Winsorized Mean ( 24 / 24 ) & 265.305555555556 & 1.21426041699677 & 218.491479951011 \tabularnewline
Trimmed Mean ( 1 / 24 ) & 264.614285714286 & 3.02674707738399 & 87.4253047740583 \tabularnewline
Trimmed Mean ( 2 / 24 ) & 264.573529411765 & 2.90365609022239 & 91.117377950741 \tabularnewline
Trimmed Mean ( 3 / 24 ) & 264.636363636364 & 2.83350223247877 & 93.3955020761913 \tabularnewline
Trimmed Mean ( 4 / 24 ) & 264.703125 & 2.76481217317318 & 95.7400027272739 \tabularnewline
Trimmed Mean ( 5 / 24 ) & 264.774193548387 & 2.68172609856218 & 98.732750406668 \tabularnewline
Trimmed Mean ( 6 / 24 ) & 264.866666666667 & 2.60285226716201 & 101.760161346176 \tabularnewline
Trimmed Mean ( 7 / 24 ) & 264.98275862069 & 2.51065381218042 & 105.543327931206 \tabularnewline
Trimmed Mean ( 8 / 24 ) & 265.089285714286 & 2.42300618071076 & 109.405121548854 \tabularnewline
Trimmed Mean ( 9 / 24 ) & 265.185185185185 & 2.3307973751412 & 113.774448183905 \tabularnewline
Trimmed Mean ( 10 / 24 ) & 265.269230769231 & 2.25539664262122 & 117.615334596284 \tabularnewline
Trimmed Mean ( 11 / 24 ) & 265.32 & 2.18406847466851 & 121.479707746008 \tabularnewline
Trimmed Mean ( 12 / 24 ) & 265.395833333333 & 2.11121196062153 & 125.707810624189 \tabularnewline
Trimmed Mean ( 13 / 24 ) & 265.478260869565 & 2.05568356237837 & 129.143544136926 \tabularnewline
Trimmed Mean ( 14 / 24 ) & 265.568181818182 & 1.99613731835623 & 133.041038497728 \tabularnewline
Trimmed Mean ( 15 / 24 ) & 265.666666666667 & 1.91717788465878 & 138.57173546207 \tabularnewline
Trimmed Mean ( 16 / 24 ) & 265.7 & 1.83805917708368 & 144.554649443642 \tabularnewline
Trimmed Mean ( 17 / 24 ) & 265.815789473684 & 1.77298169793722 & 149.925850776096 \tabularnewline
Trimmed Mean ( 18 / 24 ) & 265.972222222222 & 1.72630723925475 & 154.070038156732 \tabularnewline
Trimmed Mean ( 19 / 24 ) & 266.117647058824 & 1.67010236212292 & 159.342117641552 \tabularnewline
Trimmed Mean ( 20 / 24 ) & 266.25 & 1.62142907894996 & 164.206997059917 \tabularnewline
Trimmed Mean ( 21 / 24 ) & 266.333333333333 & 1.57373071155469 & 169.23691669601 \tabularnewline
Trimmed Mean ( 22 / 24 ) & 266.5 & 1.5218861869856 & 175.111649135772 \tabularnewline
Trimmed Mean ( 23 / 24 ) & 266.692307692308 & 1.46735683958421 & 181.750137729196 \tabularnewline
Trimmed Mean ( 24 / 24 ) & 266.916666666667 & 1.40897314169208 & 189.440564030992 \tabularnewline
Median & 269 &  &  \tabularnewline
Midrange & 263 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 265.815789473684 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 266.378378378378 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 265.815789473684 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 266.378378378378 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 266.378378378378 &  &  \tabularnewline
Midmean - Closest Observation & 265.815789473684 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 266.378378378378 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 265.815789473684 &  &  \tabularnewline
Number of observations & 72 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=74630&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]264.569444444444[/C][C]3.18759002995928[/C][C]82.9998343443884[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]263.177602060977[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]261.756688076777[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]265.929319139086[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 24 )[/C][C]264.652777777778[/C][C]3.13008020380414[/C][C]84.5514365593994[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 24 )[/C][C]264.458333333333[/C][C]3.01112552979472[/C][C]87.8270702156221[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 24 )[/C][C]264.458333333333[/C][C]2.97702059181136[/C][C]88.8332227397945[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 24 )[/C][C]264.458333333333[/C][C]2.97702059181136[/C][C]88.8332227397945[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 24 )[/C][C]264.388888888889[/C][C]2.90919939857535[/C][C]90.8802913331968[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 24 )[/C][C]264.305555555556[/C][C]2.89417139217706[/C][C]91.3233944160918[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 24 )[/C][C]264.402777777778[/C][C]2.8009513615593[/C][C]94.3974898695076[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 24 )[/C][C]264.513888888889[/C][C]2.73825511987973[/C][C]96.5994318675854[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 24 )[/C][C]264.638888888889[/C][C]2.58064797242332[/C][C]102.547457738059[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 24 )[/C][C]264.916666666667[/C][C]2.48286380537804[/C][C]106.698025921857[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 24 )[/C][C]264.763888888889[/C][C]2.40658761522365[/C][C]110.016309904546[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 24 )[/C][C]264.763888888889[/C][C]2.24301149561615[/C][C]118.039470331007[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 24 )[/C][C]264.763888888889[/C][C]2.18558847226374[/C][C]121.140778444287[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 24 )[/C][C]264.763888888889[/C][C]2.18558847226374[/C][C]121.140778444287[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 24 )[/C][C]265.388888888889[/C][C]2.08425383941562[/C][C]127.330406628061[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 24 )[/C][C]264.722222222222[/C][C]1.91793917976302[/C][C]138.024304949509[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 24 )[/C][C]264.486111111111[/C][C]1.74566230302297[/C][C]151.510467203823[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 24 )[/C][C]264.736111111111[/C][C]1.70667852470246[/C][C]155.117737335603[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 24 )[/C][C]265[/C][C]1.59088266953651[/C][C]166.574194989003[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 24 )[/C][C]265.555555555556[/C][C]1.50869790277912[/C][C]176.016388082985[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 24 )[/C][C]264.972222222222[/C][C]1.43194225298819[/C][C]185.04393013704[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 24 )[/C][C]264.972222222222[/C][C]1.34835612866027[/C][C]196.515013051856[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 24 )[/C][C]264.972222222222[/C][C]1.26218198898827[/C][C]209.93186761809[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 24 )[/C][C]265.305555555556[/C][C]1.21426041699677[/C][C]218.491479951011[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 24 )[/C][C]264.614285714286[/C][C]3.02674707738399[/C][C]87.4253047740583[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 24 )[/C][C]264.573529411765[/C][C]2.90365609022239[/C][C]91.117377950741[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 24 )[/C][C]264.636363636364[/C][C]2.83350223247877[/C][C]93.3955020761913[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 24 )[/C][C]264.703125[/C][C]2.76481217317318[/C][C]95.7400027272739[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 24 )[/C][C]264.774193548387[/C][C]2.68172609856218[/C][C]98.732750406668[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 24 )[/C][C]264.866666666667[/C][C]2.60285226716201[/C][C]101.760161346176[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 24 )[/C][C]264.98275862069[/C][C]2.51065381218042[/C][C]105.543327931206[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 24 )[/C][C]265.089285714286[/C][C]2.42300618071076[/C][C]109.405121548854[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 24 )[/C][C]265.185185185185[/C][C]2.3307973751412[/C][C]113.774448183905[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 24 )[/C][C]265.269230769231[/C][C]2.25539664262122[/C][C]117.615334596284[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 24 )[/C][C]265.32[/C][C]2.18406847466851[/C][C]121.479707746008[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 24 )[/C][C]265.395833333333[/C][C]2.11121196062153[/C][C]125.707810624189[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 24 )[/C][C]265.478260869565[/C][C]2.05568356237837[/C][C]129.143544136926[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 24 )[/C][C]265.568181818182[/C][C]1.99613731835623[/C][C]133.041038497728[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 24 )[/C][C]265.666666666667[/C][C]1.91717788465878[/C][C]138.57173546207[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 24 )[/C][C]265.7[/C][C]1.83805917708368[/C][C]144.554649443642[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 24 )[/C][C]265.815789473684[/C][C]1.77298169793722[/C][C]149.925850776096[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 24 )[/C][C]265.972222222222[/C][C]1.72630723925475[/C][C]154.070038156732[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 24 )[/C][C]266.117647058824[/C][C]1.67010236212292[/C][C]159.342117641552[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 24 )[/C][C]266.25[/C][C]1.62142907894996[/C][C]164.206997059917[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 24 )[/C][C]266.333333333333[/C][C]1.57373071155469[/C][C]169.23691669601[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 24 )[/C][C]266.5[/C][C]1.5218861869856[/C][C]175.111649135772[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 24 )[/C][C]266.692307692308[/C][C]1.46735683958421[/C][C]181.750137729196[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 24 )[/C][C]266.916666666667[/C][C]1.40897314169208[/C][C]189.440564030992[/C][/ROW]
[ROW][C]Median[/C][C]269[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]263[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]265.815789473684[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]266.378378378378[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]265.815789473684[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]266.378378378378[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]266.378378378378[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]265.815789473684[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]266.378378378378[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]265.815789473684[/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=74630&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=74630&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 Mean264.5694444444443.1875900299592882.9998343443884
Geometric Mean263.177602060977
Harmonic Mean261.756688076777
Quadratic Mean265.929319139086
Winsorized Mean ( 1 / 24 )264.6527777777783.1300802038041484.5514365593994
Winsorized Mean ( 2 / 24 )264.4583333333333.0111255297947287.8270702156221
Winsorized Mean ( 3 / 24 )264.4583333333332.9770205918113688.8332227397945
Winsorized Mean ( 4 / 24 )264.4583333333332.9770205918113688.8332227397945
Winsorized Mean ( 5 / 24 )264.3888888888892.9091993985753590.8802913331968
Winsorized Mean ( 6 / 24 )264.3055555555562.8941713921770691.3233944160918
Winsorized Mean ( 7 / 24 )264.4027777777782.800951361559394.3974898695076
Winsorized Mean ( 8 / 24 )264.5138888888892.7382551198797396.5994318675854
Winsorized Mean ( 9 / 24 )264.6388888888892.58064797242332102.547457738059
Winsorized Mean ( 10 / 24 )264.9166666666672.48286380537804106.698025921857
Winsorized Mean ( 11 / 24 )264.7638888888892.40658761522365110.016309904546
Winsorized Mean ( 12 / 24 )264.7638888888892.24301149561615118.039470331007
Winsorized Mean ( 13 / 24 )264.7638888888892.18558847226374121.140778444287
Winsorized Mean ( 14 / 24 )264.7638888888892.18558847226374121.140778444287
Winsorized Mean ( 15 / 24 )265.3888888888892.08425383941562127.330406628061
Winsorized Mean ( 16 / 24 )264.7222222222221.91793917976302138.024304949509
Winsorized Mean ( 17 / 24 )264.4861111111111.74566230302297151.510467203823
Winsorized Mean ( 18 / 24 )264.7361111111111.70667852470246155.117737335603
Winsorized Mean ( 19 / 24 )2651.59088266953651166.574194989003
Winsorized Mean ( 20 / 24 )265.5555555555561.50869790277912176.016388082985
Winsorized Mean ( 21 / 24 )264.9722222222221.43194225298819185.04393013704
Winsorized Mean ( 22 / 24 )264.9722222222221.34835612866027196.515013051856
Winsorized Mean ( 23 / 24 )264.9722222222221.26218198898827209.93186761809
Winsorized Mean ( 24 / 24 )265.3055555555561.21426041699677218.491479951011
Trimmed Mean ( 1 / 24 )264.6142857142863.0267470773839987.4253047740583
Trimmed Mean ( 2 / 24 )264.5735294117652.9036560902223991.117377950741
Trimmed Mean ( 3 / 24 )264.6363636363642.8335022324787793.3955020761913
Trimmed Mean ( 4 / 24 )264.7031252.7648121731731895.7400027272739
Trimmed Mean ( 5 / 24 )264.7741935483872.6817260985621898.732750406668
Trimmed Mean ( 6 / 24 )264.8666666666672.60285226716201101.760161346176
Trimmed Mean ( 7 / 24 )264.982758620692.51065381218042105.543327931206
Trimmed Mean ( 8 / 24 )265.0892857142862.42300618071076109.405121548854
Trimmed Mean ( 9 / 24 )265.1851851851852.3307973751412113.774448183905
Trimmed Mean ( 10 / 24 )265.2692307692312.25539664262122117.615334596284
Trimmed Mean ( 11 / 24 )265.322.18406847466851121.479707746008
Trimmed Mean ( 12 / 24 )265.3958333333332.11121196062153125.707810624189
Trimmed Mean ( 13 / 24 )265.4782608695652.05568356237837129.143544136926
Trimmed Mean ( 14 / 24 )265.5681818181821.99613731835623133.041038497728
Trimmed Mean ( 15 / 24 )265.6666666666671.91717788465878138.57173546207
Trimmed Mean ( 16 / 24 )265.71.83805917708368144.554649443642
Trimmed Mean ( 17 / 24 )265.8157894736841.77298169793722149.925850776096
Trimmed Mean ( 18 / 24 )265.9722222222221.72630723925475154.070038156732
Trimmed Mean ( 19 / 24 )266.1176470588241.67010236212292159.342117641552
Trimmed Mean ( 20 / 24 )266.251.62142907894996164.206997059917
Trimmed Mean ( 21 / 24 )266.3333333333331.57373071155469169.23691669601
Trimmed Mean ( 22 / 24 )266.51.5218861869856175.111649135772
Trimmed Mean ( 23 / 24 )266.6923076923081.46735683958421181.750137729196
Trimmed Mean ( 24 / 24 )266.9166666666671.40897314169208189.440564030992
Median269
Midrange263
Midmean - Weighted Average at Xnp265.815789473684
Midmean - Weighted Average at X(n+1)p266.378378378378
Midmean - Empirical Distribution Function265.815789473684
Midmean - Empirical Distribution Function - Averaging266.378378378378
Midmean - Empirical Distribution Function - Interpolation266.378378378378
Midmean - Closest Observation265.815789473684
Midmean - True Basic - Statistics Graphics Toolkit266.378378378378
Midmean - MS Excel (old versions)265.815789473684
Number of observations72



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')