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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 computationThu, 08 Jul 2010 14:03:44 +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/Jul/08/t1278597818krnfsah98afupcu.htm/, Retrieved Wed, 08 May 2024 11:49:10 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=77964, Retrieved Wed, 08 May 2024 11:49:10 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact184
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [Kelly Janbroers -...] [2010-07-08 14:03:44] [413e0fefcf22560c5655fbc122c1a3c2] [Current]
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Dataseries X:
268
267
266
264
262
261
262
264
265
265
266
268
260
264
265
262
258
265
273
273
270
263
260
257
248
248
237
228
225
231
243
250
246
240
236
235
225
230
225
221
231
234
249
257
253
252
245
239
229
232
222
218
223
221
230
234
237
226
215
211
203
202
187
179
181
172
182
180
175
163
160
151
145
140
125
122
124
108
115
116
104
98
101
91




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 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 & 2 seconds \tabularnewline
R Server & 'RServer@AstonUniversity' @ vre.aston.ac.uk \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=77964&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]2 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=77964&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=77964&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 time2 seconds
R Server'RServer@AstonUniversity' @ vre.aston.ac.uk







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean217.8333333333335.5737848752127239.0817618925452
Geometric Mean210.266968625264
Harmonic Mean200.745752612892
Quadratic Mean223.673710058712
Winsorized Mean ( 1 / 28 )217.9166666666675.551516628030139.2535375948234
Winsorized Mean ( 2 / 28 )217.9166666666675.5247891872183939.443435628425
Winsorized Mean ( 3 / 28 )217.9523809523815.4897522211637139.7016790871082
Winsorized Mean ( 4 / 28 )218.1428571428575.4427111501118840.0798152109125
Winsorized Mean ( 5 / 28 )218.55.3366715384761340.9431231479522
Winsorized Mean ( 6 / 28 )218.55.3122656541070141.1312261522678
Winsorized Mean ( 7 / 28 )2195.1979187326168642.1322477832865
Winsorized Mean ( 8 / 28 )219.0952380952385.1449895708682342.5841947932783
Winsorized Mean ( 9 / 28 )219.2023809523815.1211871271129942.8030406840364
Winsorized Mean ( 10 / 28 )220.9880952380954.7389238572899646.6325482098949
Winsorized Mean ( 11 / 28 )221.6428571428574.6058545788956848.1219833032591
Winsorized Mean ( 12 / 28 )222.3571428571434.4203164600233750.3034443049734
Winsorized Mean ( 13 / 28 )223.754.1559486359711953.8384902217909
Winsorized Mean ( 14 / 28 )224.254.064344598657755.1749475362059
Winsorized Mean ( 15 / 28 )225.6785714285713.7586832233915960.0419237311873
Winsorized Mean ( 16 / 28 )226.0595238095243.6384725975244662.130335669789
Winsorized Mean ( 17 / 28 )226.8690476190483.5033702223803964.7573716787773
Winsorized Mean ( 18 / 28 )227.0833333333333.468206896134265.4757170301603
Winsorized Mean ( 19 / 28 )227.0833333333333.4039651684252566.7114150989938
Winsorized Mean ( 20 / 28 )227.0833333333333.3367255401476368.055742254212
Winsorized Mean ( 21 / 28 )228.3333333333333.1356469040662672.818573110778
Winsorized Mean ( 22 / 28 )231.7380952380952.4703705492280293.8070182671635
Winsorized Mean ( 23 / 28 )231.7380952380952.3957985221419196.7268712691728
Winsorized Mean ( 24 / 28 )234.023809523812.07711184796041112.667890154113
Winsorized Mean ( 25 / 28 )234.023809523811.76339852325817132.711809858734
Winsorized Mean ( 26 / 28 )234.6428571428571.60469789160893146.222449951371
Winsorized Mean ( 27 / 28 )234.9642857142861.40305854214376167.46577470337
Winsorized Mean ( 28 / 28 )234.6309523809521.36032417438287172.481645771969
Trimmed Mean ( 1 / 28 )218.7073170731715.4516982760979940.1172819912016
Trimmed Mean ( 2 / 28 )219.53755.3342974265417741.1558416123651
Trimmed Mean ( 3 / 28 )220.4102564102565.212386816308142.2858594685748
Trimmed Mean ( 4 / 28 )221.3157894736845.0834858369870243.5362262373997
Trimmed Mean ( 5 / 28 )222.2162162162164.9473073267551144.9165983714955
Trimmed Mean ( 6 / 28 )223.0833333333334.8179596035857446.3024499348863
Trimmed Mean ( 7 / 28 )2244.6690913547150647.9750733028161
Trimmed Mean ( 8 / 28 )224.8823529411764.51985811600749.754294752032
Trimmed Mean ( 9 / 28 )225.803030303034.3514710797646251.8911940729811
Trimmed Mean ( 10 / 28 )226.7656254.1510267296737954.6288038520582
Trimmed Mean ( 11 / 28 )227.5483870967743.9978628227235556.9175074750956
Trimmed Mean ( 12 / 28 )228.33.8398961261845459.454733278644
Trimmed Mean ( 13 / 28 )229.017241379313.6859875422622262.1318544225884
Trimmed Mean ( 14 / 28 )229.6253.554269656653564.6053963773255
Trimmed Mean ( 15 / 28 )230.2222222222223.4094728343473967.5242870108656
Trimmed Mean ( 16 / 28 )230.7115384615383.2949910038238670.0188674851603
Trimmed Mean ( 17 / 28 )231.23.1750301300193472.8182066097722
Trimmed Mean ( 18 / 28 )231.6458333333333.0520731216395475.897864861408
Trimmed Mean ( 19 / 28 )232.1086956521742.9006459818377180.0196566921692
Trimmed Mean ( 20 / 28 )232.6136363636362.7161750071063785.6401504892158
Trimmed Mean ( 21 / 28 )233.1666666666672.4850112034713793.829221510531
Trimmed Mean ( 22 / 28 )233.652.23220886349293104.672104757432
Trimmed Mean ( 23 / 28 )233.8421052631582.09603239491999111.564165625448
Trimmed Mean ( 24 / 28 )234.0555555555561.92887188201119121.343235773395
Trimmed Mean ( 25 / 28 )234.0588235294121.79866318772329130.129323336893
Trimmed Mean ( 26 / 28 )234.06251.71211144638388136.709850573313
Trimmed Mean ( 27 / 28 )2341.63580624432282143.048726468745
Trimmed Mean ( 28 / 28 )233.8928571428571.5864332942572147.433149562315
Median233
Midrange182
Midmean - Weighted Average at Xnp232.613636363636
Midmean - Weighted Average at X(n+1)p233.790697674419
Midmean - Empirical Distribution Function232.613636363636
Midmean - Empirical Distribution Function - Averaging233.790697674419
Midmean - Empirical Distribution Function - Interpolation233.790697674419
Midmean - Closest Observation232.613636363636
Midmean - True Basic - Statistics Graphics Toolkit233.790697674419
Midmean - MS Excel (old versions)232.613636363636
Number of observations84

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 217.833333333333 & 5.57378487521272 & 39.0817618925452 \tabularnewline
Geometric Mean & 210.266968625264 &  &  \tabularnewline
Harmonic Mean & 200.745752612892 &  &  \tabularnewline
Quadratic Mean & 223.673710058712 &  &  \tabularnewline
Winsorized Mean ( 1 / 28 ) & 217.916666666667 & 5.5515166280301 & 39.2535375948234 \tabularnewline
Winsorized Mean ( 2 / 28 ) & 217.916666666667 & 5.52478918721839 & 39.443435628425 \tabularnewline
Winsorized Mean ( 3 / 28 ) & 217.952380952381 & 5.48975222116371 & 39.7016790871082 \tabularnewline
Winsorized Mean ( 4 / 28 ) & 218.142857142857 & 5.44271115011188 & 40.0798152109125 \tabularnewline
Winsorized Mean ( 5 / 28 ) & 218.5 & 5.33667153847613 & 40.9431231479522 \tabularnewline
Winsorized Mean ( 6 / 28 ) & 218.5 & 5.31226565410701 & 41.1312261522678 \tabularnewline
Winsorized Mean ( 7 / 28 ) & 219 & 5.19791873261686 & 42.1322477832865 \tabularnewline
Winsorized Mean ( 8 / 28 ) & 219.095238095238 & 5.14498957086823 & 42.5841947932783 \tabularnewline
Winsorized Mean ( 9 / 28 ) & 219.202380952381 & 5.12118712711299 & 42.8030406840364 \tabularnewline
Winsorized Mean ( 10 / 28 ) & 220.988095238095 & 4.73892385728996 & 46.6325482098949 \tabularnewline
Winsorized Mean ( 11 / 28 ) & 221.642857142857 & 4.60585457889568 & 48.1219833032591 \tabularnewline
Winsorized Mean ( 12 / 28 ) & 222.357142857143 & 4.42031646002337 & 50.3034443049734 \tabularnewline
Winsorized Mean ( 13 / 28 ) & 223.75 & 4.15594863597119 & 53.8384902217909 \tabularnewline
Winsorized Mean ( 14 / 28 ) & 224.25 & 4.0643445986577 & 55.1749475362059 \tabularnewline
Winsorized Mean ( 15 / 28 ) & 225.678571428571 & 3.75868322339159 & 60.0419237311873 \tabularnewline
Winsorized Mean ( 16 / 28 ) & 226.059523809524 & 3.63847259752446 & 62.130335669789 \tabularnewline
Winsorized Mean ( 17 / 28 ) & 226.869047619048 & 3.50337022238039 & 64.7573716787773 \tabularnewline
Winsorized Mean ( 18 / 28 ) & 227.083333333333 & 3.4682068961342 & 65.4757170301603 \tabularnewline
Winsorized Mean ( 19 / 28 ) & 227.083333333333 & 3.40396516842525 & 66.7114150989938 \tabularnewline
Winsorized Mean ( 20 / 28 ) & 227.083333333333 & 3.33672554014763 & 68.055742254212 \tabularnewline
Winsorized Mean ( 21 / 28 ) & 228.333333333333 & 3.13564690406626 & 72.818573110778 \tabularnewline
Winsorized Mean ( 22 / 28 ) & 231.738095238095 & 2.47037054922802 & 93.8070182671635 \tabularnewline
Winsorized Mean ( 23 / 28 ) & 231.738095238095 & 2.39579852214191 & 96.7268712691728 \tabularnewline
Winsorized Mean ( 24 / 28 ) & 234.02380952381 & 2.07711184796041 & 112.667890154113 \tabularnewline
Winsorized Mean ( 25 / 28 ) & 234.02380952381 & 1.76339852325817 & 132.711809858734 \tabularnewline
Winsorized Mean ( 26 / 28 ) & 234.642857142857 & 1.60469789160893 & 146.222449951371 \tabularnewline
Winsorized Mean ( 27 / 28 ) & 234.964285714286 & 1.40305854214376 & 167.46577470337 \tabularnewline
Winsorized Mean ( 28 / 28 ) & 234.630952380952 & 1.36032417438287 & 172.481645771969 \tabularnewline
Trimmed Mean ( 1 / 28 ) & 218.707317073171 & 5.45169827609799 & 40.1172819912016 \tabularnewline
Trimmed Mean ( 2 / 28 ) & 219.5375 & 5.33429742654177 & 41.1558416123651 \tabularnewline
Trimmed Mean ( 3 / 28 ) & 220.410256410256 & 5.2123868163081 & 42.2858594685748 \tabularnewline
Trimmed Mean ( 4 / 28 ) & 221.315789473684 & 5.08348583698702 & 43.5362262373997 \tabularnewline
Trimmed Mean ( 5 / 28 ) & 222.216216216216 & 4.94730732675511 & 44.9165983714955 \tabularnewline
Trimmed Mean ( 6 / 28 ) & 223.083333333333 & 4.81795960358574 & 46.3024499348863 \tabularnewline
Trimmed Mean ( 7 / 28 ) & 224 & 4.66909135471506 & 47.9750733028161 \tabularnewline
Trimmed Mean ( 8 / 28 ) & 224.882352941176 & 4.519858116007 & 49.754294752032 \tabularnewline
Trimmed Mean ( 9 / 28 ) & 225.80303030303 & 4.35147107976462 & 51.8911940729811 \tabularnewline
Trimmed Mean ( 10 / 28 ) & 226.765625 & 4.15102672967379 & 54.6288038520582 \tabularnewline
Trimmed Mean ( 11 / 28 ) & 227.548387096774 & 3.99786282272355 & 56.9175074750956 \tabularnewline
Trimmed Mean ( 12 / 28 ) & 228.3 & 3.83989612618454 & 59.454733278644 \tabularnewline
Trimmed Mean ( 13 / 28 ) & 229.01724137931 & 3.68598754226222 & 62.1318544225884 \tabularnewline
Trimmed Mean ( 14 / 28 ) & 229.625 & 3.5542696566535 & 64.6053963773255 \tabularnewline
Trimmed Mean ( 15 / 28 ) & 230.222222222222 & 3.40947283434739 & 67.5242870108656 \tabularnewline
Trimmed Mean ( 16 / 28 ) & 230.711538461538 & 3.29499100382386 & 70.0188674851603 \tabularnewline
Trimmed Mean ( 17 / 28 ) & 231.2 & 3.17503013001934 & 72.8182066097722 \tabularnewline
Trimmed Mean ( 18 / 28 ) & 231.645833333333 & 3.05207312163954 & 75.897864861408 \tabularnewline
Trimmed Mean ( 19 / 28 ) & 232.108695652174 & 2.90064598183771 & 80.0196566921692 \tabularnewline
Trimmed Mean ( 20 / 28 ) & 232.613636363636 & 2.71617500710637 & 85.6401504892158 \tabularnewline
Trimmed Mean ( 21 / 28 ) & 233.166666666667 & 2.48501120347137 & 93.829221510531 \tabularnewline
Trimmed Mean ( 22 / 28 ) & 233.65 & 2.23220886349293 & 104.672104757432 \tabularnewline
Trimmed Mean ( 23 / 28 ) & 233.842105263158 & 2.09603239491999 & 111.564165625448 \tabularnewline
Trimmed Mean ( 24 / 28 ) & 234.055555555556 & 1.92887188201119 & 121.343235773395 \tabularnewline
Trimmed Mean ( 25 / 28 ) & 234.058823529412 & 1.79866318772329 & 130.129323336893 \tabularnewline
Trimmed Mean ( 26 / 28 ) & 234.0625 & 1.71211144638388 & 136.709850573313 \tabularnewline
Trimmed Mean ( 27 / 28 ) & 234 & 1.63580624432282 & 143.048726468745 \tabularnewline
Trimmed Mean ( 28 / 28 ) & 233.892857142857 & 1.5864332942572 & 147.433149562315 \tabularnewline
Median & 233 &  &  \tabularnewline
Midrange & 182 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 232.613636363636 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 233.790697674419 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 232.613636363636 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 233.790697674419 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 233.790697674419 &  &  \tabularnewline
Midmean - Closest Observation & 232.613636363636 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 233.790697674419 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 232.613636363636 &  &  \tabularnewline
Number of observations & 84 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=77964&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]217.833333333333[/C][C]5.57378487521272[/C][C]39.0817618925452[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]210.266968625264[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]200.745752612892[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]223.673710058712[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 28 )[/C][C]217.916666666667[/C][C]5.5515166280301[/C][C]39.2535375948234[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 28 )[/C][C]217.916666666667[/C][C]5.52478918721839[/C][C]39.443435628425[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 28 )[/C][C]217.952380952381[/C][C]5.48975222116371[/C][C]39.7016790871082[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 28 )[/C][C]218.142857142857[/C][C]5.44271115011188[/C][C]40.0798152109125[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 28 )[/C][C]218.5[/C][C]5.33667153847613[/C][C]40.9431231479522[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 28 )[/C][C]218.5[/C][C]5.31226565410701[/C][C]41.1312261522678[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 28 )[/C][C]219[/C][C]5.19791873261686[/C][C]42.1322477832865[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 28 )[/C][C]219.095238095238[/C][C]5.14498957086823[/C][C]42.5841947932783[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 28 )[/C][C]219.202380952381[/C][C]5.12118712711299[/C][C]42.8030406840364[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 28 )[/C][C]220.988095238095[/C][C]4.73892385728996[/C][C]46.6325482098949[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 28 )[/C][C]221.642857142857[/C][C]4.60585457889568[/C][C]48.1219833032591[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 28 )[/C][C]222.357142857143[/C][C]4.42031646002337[/C][C]50.3034443049734[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 28 )[/C][C]223.75[/C][C]4.15594863597119[/C][C]53.8384902217909[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 28 )[/C][C]224.25[/C][C]4.0643445986577[/C][C]55.1749475362059[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 28 )[/C][C]225.678571428571[/C][C]3.75868322339159[/C][C]60.0419237311873[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 28 )[/C][C]226.059523809524[/C][C]3.63847259752446[/C][C]62.130335669789[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 28 )[/C][C]226.869047619048[/C][C]3.50337022238039[/C][C]64.7573716787773[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 28 )[/C][C]227.083333333333[/C][C]3.4682068961342[/C][C]65.4757170301603[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 28 )[/C][C]227.083333333333[/C][C]3.40396516842525[/C][C]66.7114150989938[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 28 )[/C][C]227.083333333333[/C][C]3.33672554014763[/C][C]68.055742254212[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 28 )[/C][C]228.333333333333[/C][C]3.13564690406626[/C][C]72.818573110778[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 28 )[/C][C]231.738095238095[/C][C]2.47037054922802[/C][C]93.8070182671635[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 28 )[/C][C]231.738095238095[/C][C]2.39579852214191[/C][C]96.7268712691728[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 28 )[/C][C]234.02380952381[/C][C]2.07711184796041[/C][C]112.667890154113[/C][/ROW]
[ROW][C]Winsorized Mean ( 25 / 28 )[/C][C]234.02380952381[/C][C]1.76339852325817[/C][C]132.711809858734[/C][/ROW]
[ROW][C]Winsorized Mean ( 26 / 28 )[/C][C]234.642857142857[/C][C]1.60469789160893[/C][C]146.222449951371[/C][/ROW]
[ROW][C]Winsorized Mean ( 27 / 28 )[/C][C]234.964285714286[/C][C]1.40305854214376[/C][C]167.46577470337[/C][/ROW]
[ROW][C]Winsorized Mean ( 28 / 28 )[/C][C]234.630952380952[/C][C]1.36032417438287[/C][C]172.481645771969[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 28 )[/C][C]218.707317073171[/C][C]5.45169827609799[/C][C]40.1172819912016[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 28 )[/C][C]219.5375[/C][C]5.33429742654177[/C][C]41.1558416123651[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 28 )[/C][C]220.410256410256[/C][C]5.2123868163081[/C][C]42.2858594685748[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 28 )[/C][C]221.315789473684[/C][C]5.08348583698702[/C][C]43.5362262373997[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 28 )[/C][C]222.216216216216[/C][C]4.94730732675511[/C][C]44.9165983714955[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 28 )[/C][C]223.083333333333[/C][C]4.81795960358574[/C][C]46.3024499348863[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 28 )[/C][C]224[/C][C]4.66909135471506[/C][C]47.9750733028161[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 28 )[/C][C]224.882352941176[/C][C]4.519858116007[/C][C]49.754294752032[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 28 )[/C][C]225.80303030303[/C][C]4.35147107976462[/C][C]51.8911940729811[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 28 )[/C][C]226.765625[/C][C]4.15102672967379[/C][C]54.6288038520582[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 28 )[/C][C]227.548387096774[/C][C]3.99786282272355[/C][C]56.9175074750956[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 28 )[/C][C]228.3[/C][C]3.83989612618454[/C][C]59.454733278644[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 28 )[/C][C]229.01724137931[/C][C]3.68598754226222[/C][C]62.1318544225884[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 28 )[/C][C]229.625[/C][C]3.5542696566535[/C][C]64.6053963773255[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 28 )[/C][C]230.222222222222[/C][C]3.40947283434739[/C][C]67.5242870108656[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 28 )[/C][C]230.711538461538[/C][C]3.29499100382386[/C][C]70.0188674851603[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 28 )[/C][C]231.2[/C][C]3.17503013001934[/C][C]72.8182066097722[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 28 )[/C][C]231.645833333333[/C][C]3.05207312163954[/C][C]75.897864861408[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 28 )[/C][C]232.108695652174[/C][C]2.90064598183771[/C][C]80.0196566921692[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 28 )[/C][C]232.613636363636[/C][C]2.71617500710637[/C][C]85.6401504892158[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 28 )[/C][C]233.166666666667[/C][C]2.48501120347137[/C][C]93.829221510531[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 28 )[/C][C]233.65[/C][C]2.23220886349293[/C][C]104.672104757432[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 28 )[/C][C]233.842105263158[/C][C]2.09603239491999[/C][C]111.564165625448[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 28 )[/C][C]234.055555555556[/C][C]1.92887188201119[/C][C]121.343235773395[/C][/ROW]
[ROW][C]Trimmed Mean ( 25 / 28 )[/C][C]234.058823529412[/C][C]1.79866318772329[/C][C]130.129323336893[/C][/ROW]
[ROW][C]Trimmed Mean ( 26 / 28 )[/C][C]234.0625[/C][C]1.71211144638388[/C][C]136.709850573313[/C][/ROW]
[ROW][C]Trimmed Mean ( 27 / 28 )[/C][C]234[/C][C]1.63580624432282[/C][C]143.048726468745[/C][/ROW]
[ROW][C]Trimmed Mean ( 28 / 28 )[/C][C]233.892857142857[/C][C]1.5864332942572[/C][C]147.433149562315[/C][/ROW]
[ROW][C]Median[/C][C]233[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]182[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]232.613636363636[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]233.790697674419[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]232.613636363636[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]233.790697674419[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]233.790697674419[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]232.613636363636[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]233.790697674419[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]232.613636363636[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]84[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=77964&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=77964&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 Mean217.8333333333335.5737848752127239.0817618925452
Geometric Mean210.266968625264
Harmonic Mean200.745752612892
Quadratic Mean223.673710058712
Winsorized Mean ( 1 / 28 )217.9166666666675.551516628030139.2535375948234
Winsorized Mean ( 2 / 28 )217.9166666666675.5247891872183939.443435628425
Winsorized Mean ( 3 / 28 )217.9523809523815.4897522211637139.7016790871082
Winsorized Mean ( 4 / 28 )218.1428571428575.4427111501118840.0798152109125
Winsorized Mean ( 5 / 28 )218.55.3366715384761340.9431231479522
Winsorized Mean ( 6 / 28 )218.55.3122656541070141.1312261522678
Winsorized Mean ( 7 / 28 )2195.1979187326168642.1322477832865
Winsorized Mean ( 8 / 28 )219.0952380952385.1449895708682342.5841947932783
Winsorized Mean ( 9 / 28 )219.2023809523815.1211871271129942.8030406840364
Winsorized Mean ( 10 / 28 )220.9880952380954.7389238572899646.6325482098949
Winsorized Mean ( 11 / 28 )221.6428571428574.6058545788956848.1219833032591
Winsorized Mean ( 12 / 28 )222.3571428571434.4203164600233750.3034443049734
Winsorized Mean ( 13 / 28 )223.754.1559486359711953.8384902217909
Winsorized Mean ( 14 / 28 )224.254.064344598657755.1749475362059
Winsorized Mean ( 15 / 28 )225.6785714285713.7586832233915960.0419237311873
Winsorized Mean ( 16 / 28 )226.0595238095243.6384725975244662.130335669789
Winsorized Mean ( 17 / 28 )226.8690476190483.5033702223803964.7573716787773
Winsorized Mean ( 18 / 28 )227.0833333333333.468206896134265.4757170301603
Winsorized Mean ( 19 / 28 )227.0833333333333.4039651684252566.7114150989938
Winsorized Mean ( 20 / 28 )227.0833333333333.3367255401476368.055742254212
Winsorized Mean ( 21 / 28 )228.3333333333333.1356469040662672.818573110778
Winsorized Mean ( 22 / 28 )231.7380952380952.4703705492280293.8070182671635
Winsorized Mean ( 23 / 28 )231.7380952380952.3957985221419196.7268712691728
Winsorized Mean ( 24 / 28 )234.023809523812.07711184796041112.667890154113
Winsorized Mean ( 25 / 28 )234.023809523811.76339852325817132.711809858734
Winsorized Mean ( 26 / 28 )234.6428571428571.60469789160893146.222449951371
Winsorized Mean ( 27 / 28 )234.9642857142861.40305854214376167.46577470337
Winsorized Mean ( 28 / 28 )234.6309523809521.36032417438287172.481645771969
Trimmed Mean ( 1 / 28 )218.7073170731715.4516982760979940.1172819912016
Trimmed Mean ( 2 / 28 )219.53755.3342974265417741.1558416123651
Trimmed Mean ( 3 / 28 )220.4102564102565.212386816308142.2858594685748
Trimmed Mean ( 4 / 28 )221.3157894736845.0834858369870243.5362262373997
Trimmed Mean ( 5 / 28 )222.2162162162164.9473073267551144.9165983714955
Trimmed Mean ( 6 / 28 )223.0833333333334.8179596035857446.3024499348863
Trimmed Mean ( 7 / 28 )2244.6690913547150647.9750733028161
Trimmed Mean ( 8 / 28 )224.8823529411764.51985811600749.754294752032
Trimmed Mean ( 9 / 28 )225.803030303034.3514710797646251.8911940729811
Trimmed Mean ( 10 / 28 )226.7656254.1510267296737954.6288038520582
Trimmed Mean ( 11 / 28 )227.5483870967743.9978628227235556.9175074750956
Trimmed Mean ( 12 / 28 )228.33.8398961261845459.454733278644
Trimmed Mean ( 13 / 28 )229.017241379313.6859875422622262.1318544225884
Trimmed Mean ( 14 / 28 )229.6253.554269656653564.6053963773255
Trimmed Mean ( 15 / 28 )230.2222222222223.4094728343473967.5242870108656
Trimmed Mean ( 16 / 28 )230.7115384615383.2949910038238670.0188674851603
Trimmed Mean ( 17 / 28 )231.23.1750301300193472.8182066097722
Trimmed Mean ( 18 / 28 )231.6458333333333.0520731216395475.897864861408
Trimmed Mean ( 19 / 28 )232.1086956521742.9006459818377180.0196566921692
Trimmed Mean ( 20 / 28 )232.6136363636362.7161750071063785.6401504892158
Trimmed Mean ( 21 / 28 )233.1666666666672.4850112034713793.829221510531
Trimmed Mean ( 22 / 28 )233.652.23220886349293104.672104757432
Trimmed Mean ( 23 / 28 )233.8421052631582.09603239491999111.564165625448
Trimmed Mean ( 24 / 28 )234.0555555555561.92887188201119121.343235773395
Trimmed Mean ( 25 / 28 )234.0588235294121.79866318772329130.129323336893
Trimmed Mean ( 26 / 28 )234.06251.71211144638388136.709850573313
Trimmed Mean ( 27 / 28 )2341.63580624432282143.048726468745
Trimmed Mean ( 28 / 28 )233.8928571428571.5864332942572147.433149562315
Median233
Midrange182
Midmean - Weighted Average at Xnp232.613636363636
Midmean - Weighted Average at X(n+1)p233.790697674419
Midmean - Empirical Distribution Function232.613636363636
Midmean - Empirical Distribution Function - Averaging233.790697674419
Midmean - Empirical Distribution Function - Interpolation233.790697674419
Midmean - Closest Observation232.613636363636
Midmean - True Basic - Statistics Graphics Toolkit233.790697674419
Midmean - MS Excel (old versions)232.613636363636
Number of observations84



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')