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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, 11 Dec 2008 03:05:39 -0700
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2008/Dec/11/t1228990000dqlhohbgeekobhb.htm/, Retrieved Sun, 19 May 2024 06:00:48 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=32152, Retrieved Sun, 19 May 2024 06:00:48 +0000
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Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsjulie govaerts
Estimated Impact175
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [paper julie] [2008-12-11 10:05:39] [ff1af8c6f1c2f1c0e8def9bfc9355be9] [Current]
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Dataseries X:
345
334
345
333
336
324
320
330
313
301
288
294
302
294
293
290
283
286
293
334
329
411
416
418
408
402
401
400
389
371
364
350
332
323
316
312
315
314
313
314
317
308
312
306
304
297
284
278
273
265
259
252
245
235
232
229
219
218
215
211




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time5 seconds
R Server'Sir Ronald Aylmer Fisher' @ 193.190.124.24

\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 & 5 seconds \tabularnewline
R Server & 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=32152&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]5 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Sir Ronald Aylmer Fisher' @ 193.190.124.24[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=32152&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=32152&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 time5 seconds
R Server'Sir Ronald Aylmer Fisher' @ 193.190.124.24







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean311.5833333333336.7509485279007546.1540081435374
Geometric Mean307.210560582279
Harmonic Mean302.762877475470
Quadratic Mean315.868828260509
Winsorized Mean ( 1 / 20 )311.6166666666676.7255769360264246.3330759027455
Winsorized Mean ( 2 / 20 )311.556.6584734257622446.7900042665312
Winsorized Mean ( 3 / 20 )311.456.6090344346350747.124886862115
Winsorized Mean ( 4 / 20 )311.7166666666676.3587251176954149.0218810999086
Winsorized Mean ( 5 / 20 )311.8833333333336.2841874765998749.6298581948229
Winsorized Mean ( 6 / 20 )312.0833333333336.1961940052470250.3669402651138
Winsorized Mean ( 7 / 20 )311.9666666666675.6530061332665855.1859770380963
Winsorized Mean ( 8 / 20 )310.54.9373189732959162.8883816661182
Winsorized Mean ( 9 / 20 )310.54.5156038318370868.7615680124179
Winsorized Mean ( 10 / 20 )309.1666666666673.8779520679160879.7242104214056
Winsorized Mean ( 11 / 20 )309.7166666666673.4416928290000389.9896307006148
Winsorized Mean ( 12 / 20 )310.7166666666673.2662537211610195.1293724224892
Winsorized Mean ( 13 / 20 )309.852.75269000432068112.562620387204
Winsorized Mean ( 14 / 20 )309.6166666666672.64009626458058117.274764113896
Winsorized Mean ( 15 / 20 )310.1166666666672.55903094152820121.185196174874
Winsorized Mean ( 16 / 20 )310.3833333333332.43272088105529127.586907215879
Winsorized Mean ( 17 / 20 )310.6666666666672.30078182077687135.026565257617
Winsorized Mean ( 18 / 20 )310.9666666666672.07214055467836150.070257524078
Winsorized Mean ( 19 / 20 )310.652.02314642794993153.547956642359
Winsorized Mean ( 20 / 20 )309.3166666666671.72444892805249179.371311979644
Trimmed Mean ( 1 / 20 )311.4827586206906.5050234848152447.8834179996103
Trimmed Mean ( 2 / 20 )311.3392857142866.2330433242223449.9498029324431
Trimmed Mean ( 3 / 20 )311.2222222222225.9409901991954952.385580818559
Trimmed Mean ( 4 / 20 )311.1346153846155.5992369690082355.5673241026849
Trimmed Mean ( 5 / 20 )310.965.2737284955615658.9639759160352
Trimmed Mean ( 6 / 20 )310.7291666666674.8831868503070663.6324548275533
Trimmed Mean ( 7 / 20 )310.4347826086964.4006644397212470.5427070981944
Trimmed Mean ( 8 / 20 )310.1363636363643.9573026280470578.3706460654027
Trimmed Mean ( 9 / 20 )310.0714285714293.6183159141724585.6949575234493
Trimmed Mean ( 10 / 20 )3103.3038439151062593.8300985051318
Trimmed Mean ( 11 / 20 )310.1315789473683.08743404917591100.449620625952
Trimmed Mean ( 12 / 20 )310.1944444444442.92873542363557105.914123188153
Trimmed Mean ( 13 / 20 )310.1176470588242.76203079137107112.278852222672
Trimmed Mean ( 14 / 20 )310.156252.68550070983048115.492894440374
Trimmed Mean ( 15 / 20 )310.2333333333332.60445389220626119.116462096601
Trimmed Mean ( 16 / 20 )310.252.50640713364304123.782762918112
Trimmed Mean ( 17 / 20 )310.2307692307692.39763196784962129.390487527161
Trimmed Mean ( 18 / 20 )310.1666666666672.27356155087208136.423254759782
Trimmed Mean ( 19 / 20 )310.0454545454552.16472834316114143.226033661433
Trimmed Mean ( 20 / 20 )309.951.99667486745233155.23308529219
Median312.5
Midrange314.5
Midmean - Weighted Average at Xnp310.15625
Midmean - Weighted Average at X(n+1)p311
Midmean - Empirical Distribution Function310.15625
Midmean - Empirical Distribution Function - Averaging311
Midmean - Empirical Distribution Function - Interpolation311
Midmean - Closest Observation310.15625
Midmean - True Basic - Statistics Graphics Toolkit311
Midmean - MS Excel (old versions)310.15625
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 311.583333333333 & 6.75094852790075 & 46.1540081435374 \tabularnewline
Geometric Mean & 307.210560582279 &  &  \tabularnewline
Harmonic Mean & 302.762877475470 &  &  \tabularnewline
Quadratic Mean & 315.868828260509 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 311.616666666667 & 6.72557693602642 & 46.3330759027455 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 311.55 & 6.65847342576224 & 46.7900042665312 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 311.45 & 6.60903443463507 & 47.124886862115 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 311.716666666667 & 6.35872511769541 & 49.0218810999086 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 311.883333333333 & 6.28418747659987 & 49.6298581948229 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 312.083333333333 & 6.19619400524702 & 50.3669402651138 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 311.966666666667 & 5.65300613326658 & 55.1859770380963 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 310.5 & 4.93731897329591 & 62.8883816661182 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 310.5 & 4.51560383183708 & 68.7615680124179 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 309.166666666667 & 3.87795206791608 & 79.7242104214056 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 309.716666666667 & 3.44169282900003 & 89.9896307006148 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 310.716666666667 & 3.26625372116101 & 95.1293724224892 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 309.85 & 2.75269000432068 & 112.562620387204 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 309.616666666667 & 2.64009626458058 & 117.274764113896 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 310.116666666667 & 2.55903094152820 & 121.185196174874 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 310.383333333333 & 2.43272088105529 & 127.586907215879 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 310.666666666667 & 2.30078182077687 & 135.026565257617 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 310.966666666667 & 2.07214055467836 & 150.070257524078 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 310.65 & 2.02314642794993 & 153.547956642359 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 309.316666666667 & 1.72444892805249 & 179.371311979644 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 311.482758620690 & 6.50502348481524 & 47.8834179996103 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 311.339285714286 & 6.23304332422234 & 49.9498029324431 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 311.222222222222 & 5.94099019919549 & 52.385580818559 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 311.134615384615 & 5.59923696900823 & 55.5673241026849 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 310.96 & 5.27372849556156 & 58.9639759160352 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 310.729166666667 & 4.88318685030706 & 63.6324548275533 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 310.434782608696 & 4.40066443972124 & 70.5427070981944 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 310.136363636364 & 3.95730262804705 & 78.3706460654027 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 310.071428571429 & 3.61831591417245 & 85.6949575234493 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 310 & 3.30384391510625 & 93.8300985051318 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 310.131578947368 & 3.08743404917591 & 100.449620625952 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 310.194444444444 & 2.92873542363557 & 105.914123188153 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 310.117647058824 & 2.76203079137107 & 112.278852222672 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 310.15625 & 2.68550070983048 & 115.492894440374 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 310.233333333333 & 2.60445389220626 & 119.116462096601 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 310.25 & 2.50640713364304 & 123.782762918112 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 310.230769230769 & 2.39763196784962 & 129.390487527161 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 310.166666666667 & 2.27356155087208 & 136.423254759782 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 310.045454545455 & 2.16472834316114 & 143.226033661433 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 309.95 & 1.99667486745233 & 155.23308529219 \tabularnewline
Median & 312.5 &  &  \tabularnewline
Midrange & 314.5 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 310.15625 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 311 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 310.15625 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 311 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 311 &  &  \tabularnewline
Midmean - Closest Observation & 310.15625 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 311 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 310.15625 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=32152&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]311.583333333333[/C][C]6.75094852790075[/C][C]46.1540081435374[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]307.210560582279[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]302.762877475470[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]315.868828260509[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]311.616666666667[/C][C]6.72557693602642[/C][C]46.3330759027455[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]311.55[/C][C]6.65847342576224[/C][C]46.7900042665312[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]311.45[/C][C]6.60903443463507[/C][C]47.124886862115[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]311.716666666667[/C][C]6.35872511769541[/C][C]49.0218810999086[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]311.883333333333[/C][C]6.28418747659987[/C][C]49.6298581948229[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]312.083333333333[/C][C]6.19619400524702[/C][C]50.3669402651138[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]311.966666666667[/C][C]5.65300613326658[/C][C]55.1859770380963[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]310.5[/C][C]4.93731897329591[/C][C]62.8883816661182[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]310.5[/C][C]4.51560383183708[/C][C]68.7615680124179[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]309.166666666667[/C][C]3.87795206791608[/C][C]79.7242104214056[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]309.716666666667[/C][C]3.44169282900003[/C][C]89.9896307006148[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]310.716666666667[/C][C]3.26625372116101[/C][C]95.1293724224892[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]309.85[/C][C]2.75269000432068[/C][C]112.562620387204[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]309.616666666667[/C][C]2.64009626458058[/C][C]117.274764113896[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]310.116666666667[/C][C]2.55903094152820[/C][C]121.185196174874[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]310.383333333333[/C][C]2.43272088105529[/C][C]127.586907215879[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]310.666666666667[/C][C]2.30078182077687[/C][C]135.026565257617[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]310.966666666667[/C][C]2.07214055467836[/C][C]150.070257524078[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]310.65[/C][C]2.02314642794993[/C][C]153.547956642359[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]309.316666666667[/C][C]1.72444892805249[/C][C]179.371311979644[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]311.482758620690[/C][C]6.50502348481524[/C][C]47.8834179996103[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]311.339285714286[/C][C]6.23304332422234[/C][C]49.9498029324431[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]311.222222222222[/C][C]5.94099019919549[/C][C]52.385580818559[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]311.134615384615[/C][C]5.59923696900823[/C][C]55.5673241026849[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]310.96[/C][C]5.27372849556156[/C][C]58.9639759160352[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]310.729166666667[/C][C]4.88318685030706[/C][C]63.6324548275533[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]310.434782608696[/C][C]4.40066443972124[/C][C]70.5427070981944[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]310.136363636364[/C][C]3.95730262804705[/C][C]78.3706460654027[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]310.071428571429[/C][C]3.61831591417245[/C][C]85.6949575234493[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]310[/C][C]3.30384391510625[/C][C]93.8300985051318[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]310.131578947368[/C][C]3.08743404917591[/C][C]100.449620625952[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]310.194444444444[/C][C]2.92873542363557[/C][C]105.914123188153[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]310.117647058824[/C][C]2.76203079137107[/C][C]112.278852222672[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]310.15625[/C][C]2.68550070983048[/C][C]115.492894440374[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]310.233333333333[/C][C]2.60445389220626[/C][C]119.116462096601[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]310.25[/C][C]2.50640713364304[/C][C]123.782762918112[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]310.230769230769[/C][C]2.39763196784962[/C][C]129.390487527161[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]310.166666666667[/C][C]2.27356155087208[/C][C]136.423254759782[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]310.045454545455[/C][C]2.16472834316114[/C][C]143.226033661433[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]309.95[/C][C]1.99667486745233[/C][C]155.23308529219[/C][/ROW]
[ROW][C]Median[/C][C]312.5[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]314.5[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]310.15625[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]311[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]310.15625[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]311[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]311[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]310.15625[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]311[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]310.15625[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]60[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=32152&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=32152&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 Mean311.5833333333336.7509485279007546.1540081435374
Geometric Mean307.210560582279
Harmonic Mean302.762877475470
Quadratic Mean315.868828260509
Winsorized Mean ( 1 / 20 )311.6166666666676.7255769360264246.3330759027455
Winsorized Mean ( 2 / 20 )311.556.6584734257622446.7900042665312
Winsorized Mean ( 3 / 20 )311.456.6090344346350747.124886862115
Winsorized Mean ( 4 / 20 )311.7166666666676.3587251176954149.0218810999086
Winsorized Mean ( 5 / 20 )311.8833333333336.2841874765998749.6298581948229
Winsorized Mean ( 6 / 20 )312.0833333333336.1961940052470250.3669402651138
Winsorized Mean ( 7 / 20 )311.9666666666675.6530061332665855.1859770380963
Winsorized Mean ( 8 / 20 )310.54.9373189732959162.8883816661182
Winsorized Mean ( 9 / 20 )310.54.5156038318370868.7615680124179
Winsorized Mean ( 10 / 20 )309.1666666666673.8779520679160879.7242104214056
Winsorized Mean ( 11 / 20 )309.7166666666673.4416928290000389.9896307006148
Winsorized Mean ( 12 / 20 )310.7166666666673.2662537211610195.1293724224892
Winsorized Mean ( 13 / 20 )309.852.75269000432068112.562620387204
Winsorized Mean ( 14 / 20 )309.6166666666672.64009626458058117.274764113896
Winsorized Mean ( 15 / 20 )310.1166666666672.55903094152820121.185196174874
Winsorized Mean ( 16 / 20 )310.3833333333332.43272088105529127.586907215879
Winsorized Mean ( 17 / 20 )310.6666666666672.30078182077687135.026565257617
Winsorized Mean ( 18 / 20 )310.9666666666672.07214055467836150.070257524078
Winsorized Mean ( 19 / 20 )310.652.02314642794993153.547956642359
Winsorized Mean ( 20 / 20 )309.3166666666671.72444892805249179.371311979644
Trimmed Mean ( 1 / 20 )311.4827586206906.5050234848152447.8834179996103
Trimmed Mean ( 2 / 20 )311.3392857142866.2330433242223449.9498029324431
Trimmed Mean ( 3 / 20 )311.2222222222225.9409901991954952.385580818559
Trimmed Mean ( 4 / 20 )311.1346153846155.5992369690082355.5673241026849
Trimmed Mean ( 5 / 20 )310.965.2737284955615658.9639759160352
Trimmed Mean ( 6 / 20 )310.7291666666674.8831868503070663.6324548275533
Trimmed Mean ( 7 / 20 )310.4347826086964.4006644397212470.5427070981944
Trimmed Mean ( 8 / 20 )310.1363636363643.9573026280470578.3706460654027
Trimmed Mean ( 9 / 20 )310.0714285714293.6183159141724585.6949575234493
Trimmed Mean ( 10 / 20 )3103.3038439151062593.8300985051318
Trimmed Mean ( 11 / 20 )310.1315789473683.08743404917591100.449620625952
Trimmed Mean ( 12 / 20 )310.1944444444442.92873542363557105.914123188153
Trimmed Mean ( 13 / 20 )310.1176470588242.76203079137107112.278852222672
Trimmed Mean ( 14 / 20 )310.156252.68550070983048115.492894440374
Trimmed Mean ( 15 / 20 )310.2333333333332.60445389220626119.116462096601
Trimmed Mean ( 16 / 20 )310.252.50640713364304123.782762918112
Trimmed Mean ( 17 / 20 )310.2307692307692.39763196784962129.390487527161
Trimmed Mean ( 18 / 20 )310.1666666666672.27356155087208136.423254759782
Trimmed Mean ( 19 / 20 )310.0454545454552.16472834316114143.226033661433
Trimmed Mean ( 20 / 20 )309.951.99667486745233155.23308529219
Median312.5
Midrange314.5
Midmean - Weighted Average at Xnp310.15625
Midmean - Weighted Average at X(n+1)p311
Midmean - Empirical Distribution Function310.15625
Midmean - Empirical Distribution Function - Averaging311
Midmean - Empirical Distribution Function - Interpolation311
Midmean - Closest Observation310.15625
Midmean - True Basic - Statistics Graphics Toolkit311
Midmean - MS Excel (old versions)310.15625
Number of observations60



Parameters (Session):
Parameters (R input):
R code (references can be found in the software module):
geomean <- function(x) {
return(exp(mean(log(x))))
}
harmean <- function(x) {
return(1/mean(1/x))
}
quamean <- function(x) {
return(sqrt(mean(x*x)))
}
winmean <- function(x) {
x <-sort(x[!is.na(x)])
n<-length(x)
denom <- 3
nodenom <- n/denom
if (nodenom>40) denom <- n/40
sqrtn = sqrt(n)
roundnodenom = floor(nodenom)
win <- array(NA,dim=c(roundnodenom,2))
for (j in 1:roundnodenom) {
win[j,1] <- (j*x[j+1]+sum(x[(j+1):(n-j)])+j*x[n-j])/n
win[j,2] <- sd(c(rep(x[j+1],j),x[(j+1):(n-j)],rep(x[n-j],j)))/sqrtn
}
return(win)
}
trimean <- function(x) {
x <-sort(x[!is.na(x)])
n<-length(x)
denom <- 3
nodenom <- n/denom
if (nodenom>40) denom <- n/40
sqrtn = sqrt(n)
roundnodenom = floor(nodenom)
tri <- array(NA,dim=c(roundnodenom,2))
for (j in 1:roundnodenom) {
tri[j,1] <- mean(x,trim=j/n)
tri[j,2] <- sd(x[(j+1):(n-j)]) / sqrt(n-j*2)
}
return(tri)
}
midrange <- function(x) {
return((max(x)+min(x))/2)
}
q1 <- function(data,n,p,i,f) {
np <- n*p;
i <<- floor(np)
f <<- np - i
qvalue <- (1-f)*data[i] + f*data[i+1]
}
q2 <- function(data,n,p,i,f) {
np <- (n+1)*p
i <<- floor(np)
f <<- np - i
qvalue <- (1-f)*data[i] + f*data[i+1]
}
q3 <- function(data,n,p,i,f) {
np <- n*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- data[i]
} else {
qvalue <- data[i+1]
}
}
q4 <- function(data,n,p,i,f) {
np <- n*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- (data[i]+data[i+1])/2
} else {
qvalue <- data[i+1]
}
}
q5 <- function(data,n,p,i,f) {
np <- (n-1)*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- data[i+1]
} else {
qvalue <- data[i+1] + f*(data[i+2]-data[i+1])
}
}
q6 <- function(data,n,p,i,f) {
np <- n*p+0.5
i <<- floor(np)
f <<- np - i
qvalue <- data[i]
}
q7 <- function(data,n,p,i,f) {
np <- (n+1)*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- data[i]
} else {
qvalue <- f*data[i] + (1-f)*data[i+1]
}
}
q8 <- function(data,n,p,i,f) {
np <- (n+1)*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- data[i]
} else {
if (f == 0.5) {
qvalue <- (data[i]+data[i+1])/2
} else {
if (f < 0.5) {
qvalue <- data[i]
} else {
qvalue <- data[i+1]
}
}
}
}
midmean <- function(x,def) {
x <-sort(x[!is.na(x)])
n<-length(x)
if (def==1) {
qvalue1 <- q1(x,n,0.25,i,f)
qvalue3 <- q1(x,n,0.75,i,f)
}
if (def==2) {
qvalue1 <- q2(x,n,0.25,i,f)
qvalue3 <- q2(x,n,0.75,i,f)
}
if (def==3) {
qvalue1 <- q3(x,n,0.25,i,f)
qvalue3 <- q3(x,n,0.75,i,f)
}
if (def==4) {
qvalue1 <- q4(x,n,0.25,i,f)
qvalue3 <- q4(x,n,0.75,i,f)
}
if (def==5) {
qvalue1 <- q5(x,n,0.25,i,f)
qvalue3 <- q5(x,n,0.75,i,f)
}
if (def==6) {
qvalue1 <- q6(x,n,0.25,i,f)
qvalue3 <- q6(x,n,0.75,i,f)
}
if (def==7) {
qvalue1 <- q7(x,n,0.25,i,f)
qvalue3 <- q7(x,n,0.75,i,f)
}
if (def==8) {
qvalue1 <- q8(x,n,0.25,i,f)
qvalue3 <- q8(x,n,0.75,i,f)
}
midm <- 0
myn <- 0
roundno4 <- round(n/4)
round3no4 <- round(3*n/4)
for (i in 1:n) {
if ((x[i]>=qvalue1) & (x[i]<=qvalue3)){
midm = midm + x[i]
myn = myn + 1
}
}
midm = midm / myn
return(midm)
}
(arm <- mean(x))
sqrtn <- sqrt(length(x))
(armse <- sd(x) / sqrtn)
(armose <- arm / armse)
(geo <- geomean(x))
(har <- harmean(x))
(qua <- quamean(x))
(win <- winmean(x))
(tri <- trimean(x))
(midr <- midrange(x))
midm <- array(NA,dim=8)
for (j in 1:8) midm[j] <- midmean(x,j)
midm
bitmap(file='test1.png')
lb <- win[,1] - 2*win[,2]
ub <- win[,1] + 2*win[,2]
if ((ylimmin == '') | (ylimmax == '')) plot(win[,1],type='b',main=main, xlab='j', pch=19, ylab='Winsorized Mean(j/n)', ylim=c(min(lb),max(ub))) else plot(win[,1],type='l',main=main, xlab='j', pch=19, ylab='Winsorized Mean(j/n)', ylim=c(ylimmin,ylimmax))
lines(ub,lty=3)
lines(lb,lty=3)
grid()
dev.off()
bitmap(file='test2.png')
lb <- tri[,1] - 2*tri[,2]
ub <- tri[,1] + 2*tri[,2]
if ((ylimmin == '') | (ylimmax == '')) plot(tri[,1],type='b',main=main, xlab='j', pch=19, ylab='Trimmed Mean(j/n)', ylim=c(min(lb),max(ub))) else plot(tri[,1],type='l',main=main, xlab='j', pch=19, ylab='Trimmed Mean(j/n)', ylim=c(ylimmin,ylimmax))
lines(ub,lty=3)
lines(lb,lty=3)
grid()
dev.off()
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Central Tendency - Ungrouped Data',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Measure',header=TRUE)
a<-table.element(a,'Value',header=TRUE)
a<-table.element(a,'S.E.',header=TRUE)
a<-table.element(a,'Value/S.E.',header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('arithmetic_mean.htm', 'Arithmetic Mean', 'click to view the definition of the Arithmetic Mean'),header=TRUE)
a<-table.element(a,arm)
a<-table.element(a,hyperlink('arithmetic_mean_standard_error.htm', armse, 'click to view the definition of the Standard Error of the Arithmetic Mean'))
a<-table.element(a,armose)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('geometric_mean.htm', 'Geometric Mean', 'click to view the definition of the Geometric Mean'),header=TRUE)
a<-table.element(a,geo)
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('harmonic_mean.htm', 'Harmonic Mean', 'click to view the definition of the Harmonic Mean'),header=TRUE)
a<-table.element(a,har)
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('quadratic_mean.htm', 'Quadratic Mean', 'click to view the definition of the Quadratic Mean'),header=TRUE)
a<-table.element(a,qua)
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
for (j in 1:length(win[,1])) {
a<-table.row.start(a)
mylabel <- paste('Winsorized Mean (',j)
mylabel <- paste(mylabel,'/')
mylabel <- paste(mylabel,length(win[,1]))
mylabel <- paste(mylabel,')')
a<-table.element(a,hyperlink('winsorized_mean.htm', mylabel, 'click to view the definition of the Winsorized Mean'),header=TRUE)
a<-table.element(a,win[j,1])
a<-table.element(a,win[j,2])
a<-table.element(a,win[j,1]/win[j,2])
a<-table.row.end(a)
}
for (j in 1:length(tri[,1])) {
a<-table.row.start(a)
mylabel <- paste('Trimmed Mean (',j)
mylabel <- paste(mylabel,'/')
mylabel <- paste(mylabel,length(tri[,1]))
mylabel <- paste(mylabel,')')
a<-table.element(a,hyperlink('arithmetic_mean.htm', mylabel, 'click to view the definition of the Trimmed Mean'),header=TRUE)
a<-table.element(a,tri[j,1])
a<-table.element(a,tri[j,2])
a<-table.element(a,tri[j,1]/tri[j,2])
a<-table.row.end(a)
}
a<-table.row.start(a)
a<-table.element(a,hyperlink('median_1.htm', 'Median', 'click to view the definition of the Median'),header=TRUE)
a<-table.element(a,median(x))
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('midrange.htm', 'Midrange', 'click to view the definition of the Midrange'),header=TRUE)
a<-table.element(a,midr)
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_1.htm','Weighted Average at Xnp',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[1])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_2.htm','Weighted Average at X(n+1)p',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[2])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_3.htm','Empirical Distribution Function',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[3])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_4.htm','Empirical Distribution Function - Averaging',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[4])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_5.htm','Empirical Distribution Function - Interpolation',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[5])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_6.htm','Closest Observation',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[6])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_7.htm','True Basic - Statistics Graphics Toolkit',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[7])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_8.htm','MS Excel (old versions)',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[8])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Number of observations',header=TRUE)
a<-table.element(a,length(x))
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable.tab')