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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, 19 Mar 2009 11:21:56 -0600
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2009/Mar/19/t1237483379f3430o01ni5fjxy.htm/, Retrieved Thu, 06 Oct 2022 23:57:01 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=39129, Retrieved Thu, 06 Oct 2022 23:57:01 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact183
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [Robustness Brutos...] [2009-03-19 17:21:56] [1f24ecf252e89ff3a946a11432983a6a] [Current]
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Dataseries X:
260288
261544
259886
257006
259670
258873
264416
263596
262586
260237
261690
259295
264170
264451
265538
261723
266189
265073
267007
266376
267406
262742
260300
263074
265940
264771
268403
264264
264118
266817
269296
269001
266707
267507
267510
267420
270845
270671
273653
271567
268372
268160
267879
271142
271323
269478
271008
269145
271684
273582
279475
276188
278422
281084
278618
280738
288897
282129
286406
284288
286139
288275
287670
286864
288798
288316
286915
288006
293338
303730
306248
305700
314849




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

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 1 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=39129&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=39129&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=39129&T=0

As an alternative you can also use a QR Code:  

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

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







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean273075.2328767121463.91488799207186.537643080649
Geometric Mean272802.666303081
Harmonic Mean272539.657049444
Quadratic Mean273357.608601296
Winsorized Mean ( 1 / 24 )272982.986301371417.57966960243192.569766733413
Winsorized Mean ( 2 / 24 )272979.5342465751411.13762305569193.446429169299
Winsorized Mean ( 3 / 24 )272913.986301371383.51122398221197.261851997002
Winsorized Mean ( 4 / 24 )272356.3972602741224.83702154736222.361336625995
Winsorized Mean ( 5 / 24 )272076.2602739731154.29859457777235.707001249096
Winsorized Mean ( 6 / 24 )272072.3150684931152.05845979188236.161900254300
Winsorized Mean ( 7 / 24 )272027.2465753421142.65912713049238.065088806031
Winsorized Mean ( 8 / 24 )272159.0821917811123.09548800293242.329423543255
Winsorized Mean ( 9 / 24 )272143.9178082191114.15736442694244.259856369746
Winsorized Mean ( 10 / 24 )272102.4109589041104.51191790853246.355341709801
Winsorized Mean ( 11 / 24 )272118.6849315071065.83527975030255.310262384314
Winsorized Mean ( 12 / 24 )272135.9452054791061.04951953767256.478081554627
Winsorized Mean ( 13 / 24 )272113.5068493151038.17861397825262.106638670382
Winsorized Mean ( 14 / 24 )272162.4109589041016.47959332004267.749999849936
Winsorized Mean ( 15 / 24 )271889.328767123932.504043893524291.569061332852
Winsorized Mean ( 16 / 24 )271427.520547945845.791767678697320.915301993169
Winsorized Mean ( 17 / 24 )271206.054794521800.930214726857338.613839018435
Winsorized Mean ( 18 / 24 )271158.219178082781.863041422753346.810380862429
Winsorized Mean ( 19 / 24 )270838.602739726725.589488143475373.266987966854
Winsorized Mean ( 20 / 24 )270691.479452055676.373299461436400.210179301273
Winsorized Mean ( 21 / 24 )270721.972602740656.721910840739412.232283001126
Winsorized Mean ( 22 / 24 )270188.849315069532.106997868694507.771651937083
Winsorized Mean ( 23 / 24 )269516.808219178395.262689685618681.867566183757
Winsorized Mean ( 24 / 24 )269575.328767123381.674833941245706.295791062351
Trimmed Mean ( 1 / 24 )272713.1971830991364.34034541114199.886485876013
Trimmed Mean ( 2 / 24 )272427.7681159421300.00366271779209.559231199705
Trimmed Mean ( 3 / 24 )272127.1791044781225.75630091714222.007571081516
Trimmed Mean ( 4 / 24 )271832.6307692311148.20104393477236.746545568089
Trimmed Mean ( 5 / 24 )271680.9047619051117.48976352783243.117130580443
Trimmed Mean ( 6 / 24 )271586.2786885251102.63528818925246.306536347593
Trimmed Mean ( 7 / 24 )271486.0508474581084.58159938205250.314085175461
Trimmed Mean ( 8 / 24 )271387.0350877191064.40822421311254.965180570969
Trimmed Mean ( 9 / 24 )271258.9454545451043.40687397520259.974274868532
Trimmed Mean ( 10 / 24 )271123.5094339621018.77014867754266.128242750247
Trimmed Mean ( 11 / 24 )270983.392156863989.60773495417273.829096707103
Trimmed Mean ( 12 / 24 )270829.632653061960.925376302096281.842523188729
Trimmed Mean ( 13 / 24 )270660.553191489924.516949556428292.758887028895
Trimmed Mean ( 14 / 24 )270479.244444444882.196390762453306.597541405353
Trimmed Mean ( 15 / 24 )270275.139534884830.808092109824325.315968996551
Trimmed Mean ( 16 / 24 )270083.536585366785.07472154672344.022714237008
Trimmed Mean ( 17 / 24 )269926.307692308748.265733209178360.735893296412
Trimmed Mean ( 18 / 24 )269777.783783784710.497309375153379.702752176556
Trimmed Mean ( 19 / 24 )269617.828571429662.711261366801406.840571888515
Trimmed Mean ( 20 / 24 )269475.696969697613.997863121912438.887027390503
Trimmed Mean ( 21 / 24 )269332.548387097560.101651370707480.863692738583
Trimmed Mean ( 22 / 24 )269166483.964022295922556.169441528068
Trimmed Mean ( 23 / 24 )269040.296296296425.822628747368631.81305579679
Trimmed Mean ( 24 / 24 )268979.8400.644730403384671.3673726076
Median268403
Midrange285927.5
Midmean - Weighted Average at Xnp269473.333333333
Midmean - Weighted Average at X(n+1)p269777.783783784
Midmean - Empirical Distribution Function269777.783783784
Midmean - Empirical Distribution Function - Averaging269777.783783784
Midmean - Empirical Distribution Function - Interpolation269777.783783784
Midmean - Closest Observation269632.684210526
Midmean - True Basic - Statistics Graphics Toolkit269777.783783784
Midmean - MS Excel (old versions)269777.783783784
Number of observations73

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 273075.232876712 & 1463.91488799207 & 186.537643080649 \tabularnewline
Geometric Mean & 272802.666303081 &  &  \tabularnewline
Harmonic Mean & 272539.657049444 &  &  \tabularnewline
Quadratic Mean & 273357.608601296 &  &  \tabularnewline
Winsorized Mean ( 1 / 24 ) & 272982.98630137 & 1417.57966960243 & 192.569766733413 \tabularnewline
Winsorized Mean ( 2 / 24 ) & 272979.534246575 & 1411.13762305569 & 193.446429169299 \tabularnewline
Winsorized Mean ( 3 / 24 ) & 272913.98630137 & 1383.51122398221 & 197.261851997002 \tabularnewline
Winsorized Mean ( 4 / 24 ) & 272356.397260274 & 1224.83702154736 & 222.361336625995 \tabularnewline
Winsorized Mean ( 5 / 24 ) & 272076.260273973 & 1154.29859457777 & 235.707001249096 \tabularnewline
Winsorized Mean ( 6 / 24 ) & 272072.315068493 & 1152.05845979188 & 236.161900254300 \tabularnewline
Winsorized Mean ( 7 / 24 ) & 272027.246575342 & 1142.65912713049 & 238.065088806031 \tabularnewline
Winsorized Mean ( 8 / 24 ) & 272159.082191781 & 1123.09548800293 & 242.329423543255 \tabularnewline
Winsorized Mean ( 9 / 24 ) & 272143.917808219 & 1114.15736442694 & 244.259856369746 \tabularnewline
Winsorized Mean ( 10 / 24 ) & 272102.410958904 & 1104.51191790853 & 246.355341709801 \tabularnewline
Winsorized Mean ( 11 / 24 ) & 272118.684931507 & 1065.83527975030 & 255.310262384314 \tabularnewline
Winsorized Mean ( 12 / 24 ) & 272135.945205479 & 1061.04951953767 & 256.478081554627 \tabularnewline
Winsorized Mean ( 13 / 24 ) & 272113.506849315 & 1038.17861397825 & 262.106638670382 \tabularnewline
Winsorized Mean ( 14 / 24 ) & 272162.410958904 & 1016.47959332004 & 267.749999849936 \tabularnewline
Winsorized Mean ( 15 / 24 ) & 271889.328767123 & 932.504043893524 & 291.569061332852 \tabularnewline
Winsorized Mean ( 16 / 24 ) & 271427.520547945 & 845.791767678697 & 320.915301993169 \tabularnewline
Winsorized Mean ( 17 / 24 ) & 271206.054794521 & 800.930214726857 & 338.613839018435 \tabularnewline
Winsorized Mean ( 18 / 24 ) & 271158.219178082 & 781.863041422753 & 346.810380862429 \tabularnewline
Winsorized Mean ( 19 / 24 ) & 270838.602739726 & 725.589488143475 & 373.266987966854 \tabularnewline
Winsorized Mean ( 20 / 24 ) & 270691.479452055 & 676.373299461436 & 400.210179301273 \tabularnewline
Winsorized Mean ( 21 / 24 ) & 270721.972602740 & 656.721910840739 & 412.232283001126 \tabularnewline
Winsorized Mean ( 22 / 24 ) & 270188.849315069 & 532.106997868694 & 507.771651937083 \tabularnewline
Winsorized Mean ( 23 / 24 ) & 269516.808219178 & 395.262689685618 & 681.867566183757 \tabularnewline
Winsorized Mean ( 24 / 24 ) & 269575.328767123 & 381.674833941245 & 706.295791062351 \tabularnewline
Trimmed Mean ( 1 / 24 ) & 272713.197183099 & 1364.34034541114 & 199.886485876013 \tabularnewline
Trimmed Mean ( 2 / 24 ) & 272427.768115942 & 1300.00366271779 & 209.559231199705 \tabularnewline
Trimmed Mean ( 3 / 24 ) & 272127.179104478 & 1225.75630091714 & 222.007571081516 \tabularnewline
Trimmed Mean ( 4 / 24 ) & 271832.630769231 & 1148.20104393477 & 236.746545568089 \tabularnewline
Trimmed Mean ( 5 / 24 ) & 271680.904761905 & 1117.48976352783 & 243.117130580443 \tabularnewline
Trimmed Mean ( 6 / 24 ) & 271586.278688525 & 1102.63528818925 & 246.306536347593 \tabularnewline
Trimmed Mean ( 7 / 24 ) & 271486.050847458 & 1084.58159938205 & 250.314085175461 \tabularnewline
Trimmed Mean ( 8 / 24 ) & 271387.035087719 & 1064.40822421311 & 254.965180570969 \tabularnewline
Trimmed Mean ( 9 / 24 ) & 271258.945454545 & 1043.40687397520 & 259.974274868532 \tabularnewline
Trimmed Mean ( 10 / 24 ) & 271123.509433962 & 1018.77014867754 & 266.128242750247 \tabularnewline
Trimmed Mean ( 11 / 24 ) & 270983.392156863 & 989.60773495417 & 273.829096707103 \tabularnewline
Trimmed Mean ( 12 / 24 ) & 270829.632653061 & 960.925376302096 & 281.842523188729 \tabularnewline
Trimmed Mean ( 13 / 24 ) & 270660.553191489 & 924.516949556428 & 292.758887028895 \tabularnewline
Trimmed Mean ( 14 / 24 ) & 270479.244444444 & 882.196390762453 & 306.597541405353 \tabularnewline
Trimmed Mean ( 15 / 24 ) & 270275.139534884 & 830.808092109824 & 325.315968996551 \tabularnewline
Trimmed Mean ( 16 / 24 ) & 270083.536585366 & 785.07472154672 & 344.022714237008 \tabularnewline
Trimmed Mean ( 17 / 24 ) & 269926.307692308 & 748.265733209178 & 360.735893296412 \tabularnewline
Trimmed Mean ( 18 / 24 ) & 269777.783783784 & 710.497309375153 & 379.702752176556 \tabularnewline
Trimmed Mean ( 19 / 24 ) & 269617.828571429 & 662.711261366801 & 406.840571888515 \tabularnewline
Trimmed Mean ( 20 / 24 ) & 269475.696969697 & 613.997863121912 & 438.887027390503 \tabularnewline
Trimmed Mean ( 21 / 24 ) & 269332.548387097 & 560.101651370707 & 480.863692738583 \tabularnewline
Trimmed Mean ( 22 / 24 ) & 269166 & 483.964022295922 & 556.169441528068 \tabularnewline
Trimmed Mean ( 23 / 24 ) & 269040.296296296 & 425.822628747368 & 631.81305579679 \tabularnewline
Trimmed Mean ( 24 / 24 ) & 268979.8 & 400.644730403384 & 671.3673726076 \tabularnewline
Median & 268403 &  &  \tabularnewline
Midrange & 285927.5 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 269473.333333333 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 269777.783783784 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 269777.783783784 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 269777.783783784 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 269777.783783784 &  &  \tabularnewline
Midmean - Closest Observation & 269632.684210526 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 269777.783783784 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 269777.783783784 &  &  \tabularnewline
Number of observations & 73 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=39129&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]273075.232876712[/C][C]1463.91488799207[/C][C]186.537643080649[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]272802.666303081[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]272539.657049444[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]273357.608601296[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 24 )[/C][C]272982.98630137[/C][C]1417.57966960243[/C][C]192.569766733413[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 24 )[/C][C]272979.534246575[/C][C]1411.13762305569[/C][C]193.446429169299[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 24 )[/C][C]272913.98630137[/C][C]1383.51122398221[/C][C]197.261851997002[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 24 )[/C][C]272356.397260274[/C][C]1224.83702154736[/C][C]222.361336625995[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 24 )[/C][C]272076.260273973[/C][C]1154.29859457777[/C][C]235.707001249096[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 24 )[/C][C]272072.315068493[/C][C]1152.05845979188[/C][C]236.161900254300[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 24 )[/C][C]272027.246575342[/C][C]1142.65912713049[/C][C]238.065088806031[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 24 )[/C][C]272159.082191781[/C][C]1123.09548800293[/C][C]242.329423543255[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 24 )[/C][C]272143.917808219[/C][C]1114.15736442694[/C][C]244.259856369746[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 24 )[/C][C]272102.410958904[/C][C]1104.51191790853[/C][C]246.355341709801[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 24 )[/C][C]272118.684931507[/C][C]1065.83527975030[/C][C]255.310262384314[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 24 )[/C][C]272135.945205479[/C][C]1061.04951953767[/C][C]256.478081554627[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 24 )[/C][C]272113.506849315[/C][C]1038.17861397825[/C][C]262.106638670382[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 24 )[/C][C]272162.410958904[/C][C]1016.47959332004[/C][C]267.749999849936[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 24 )[/C][C]271889.328767123[/C][C]932.504043893524[/C][C]291.569061332852[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 24 )[/C][C]271427.520547945[/C][C]845.791767678697[/C][C]320.915301993169[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 24 )[/C][C]271206.054794521[/C][C]800.930214726857[/C][C]338.613839018435[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 24 )[/C][C]271158.219178082[/C][C]781.863041422753[/C][C]346.810380862429[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 24 )[/C][C]270838.602739726[/C][C]725.589488143475[/C][C]373.266987966854[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 24 )[/C][C]270691.479452055[/C][C]676.373299461436[/C][C]400.210179301273[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 24 )[/C][C]270721.972602740[/C][C]656.721910840739[/C][C]412.232283001126[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 24 )[/C][C]270188.849315069[/C][C]532.106997868694[/C][C]507.771651937083[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 24 )[/C][C]269516.808219178[/C][C]395.262689685618[/C][C]681.867566183757[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 24 )[/C][C]269575.328767123[/C][C]381.674833941245[/C][C]706.295791062351[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 24 )[/C][C]272713.197183099[/C][C]1364.34034541114[/C][C]199.886485876013[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 24 )[/C][C]272427.768115942[/C][C]1300.00366271779[/C][C]209.559231199705[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 24 )[/C][C]272127.179104478[/C][C]1225.75630091714[/C][C]222.007571081516[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 24 )[/C][C]271832.630769231[/C][C]1148.20104393477[/C][C]236.746545568089[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 24 )[/C][C]271680.904761905[/C][C]1117.48976352783[/C][C]243.117130580443[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 24 )[/C][C]271586.278688525[/C][C]1102.63528818925[/C][C]246.306536347593[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 24 )[/C][C]271486.050847458[/C][C]1084.58159938205[/C][C]250.314085175461[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 24 )[/C][C]271387.035087719[/C][C]1064.40822421311[/C][C]254.965180570969[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 24 )[/C][C]271258.945454545[/C][C]1043.40687397520[/C][C]259.974274868532[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 24 )[/C][C]271123.509433962[/C][C]1018.77014867754[/C][C]266.128242750247[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 24 )[/C][C]270983.392156863[/C][C]989.60773495417[/C][C]273.829096707103[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 24 )[/C][C]270829.632653061[/C][C]960.925376302096[/C][C]281.842523188729[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 24 )[/C][C]270660.553191489[/C][C]924.516949556428[/C][C]292.758887028895[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 24 )[/C][C]270479.244444444[/C][C]882.196390762453[/C][C]306.597541405353[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 24 )[/C][C]270275.139534884[/C][C]830.808092109824[/C][C]325.315968996551[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 24 )[/C][C]270083.536585366[/C][C]785.07472154672[/C][C]344.022714237008[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 24 )[/C][C]269926.307692308[/C][C]748.265733209178[/C][C]360.735893296412[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 24 )[/C][C]269777.783783784[/C][C]710.497309375153[/C][C]379.702752176556[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 24 )[/C][C]269617.828571429[/C][C]662.711261366801[/C][C]406.840571888515[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 24 )[/C][C]269475.696969697[/C][C]613.997863121912[/C][C]438.887027390503[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 24 )[/C][C]269332.548387097[/C][C]560.101651370707[/C][C]480.863692738583[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 24 )[/C][C]269166[/C][C]483.964022295922[/C][C]556.169441528068[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 24 )[/C][C]269040.296296296[/C][C]425.822628747368[/C][C]631.81305579679[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 24 )[/C][C]268979.8[/C][C]400.644730403384[/C][C]671.3673726076[/C][/ROW]
[ROW][C]Median[/C][C]268403[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]285927.5[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]269473.333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]269777.783783784[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]269777.783783784[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]269777.783783784[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]269777.783783784[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]269632.684210526[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]269777.783783784[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]269777.783783784[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]73[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=39129&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=39129&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 Mean273075.2328767121463.91488799207186.537643080649
Geometric Mean272802.666303081
Harmonic Mean272539.657049444
Quadratic Mean273357.608601296
Winsorized Mean ( 1 / 24 )272982.986301371417.57966960243192.569766733413
Winsorized Mean ( 2 / 24 )272979.5342465751411.13762305569193.446429169299
Winsorized Mean ( 3 / 24 )272913.986301371383.51122398221197.261851997002
Winsorized Mean ( 4 / 24 )272356.3972602741224.83702154736222.361336625995
Winsorized Mean ( 5 / 24 )272076.2602739731154.29859457777235.707001249096
Winsorized Mean ( 6 / 24 )272072.3150684931152.05845979188236.161900254300
Winsorized Mean ( 7 / 24 )272027.2465753421142.65912713049238.065088806031
Winsorized Mean ( 8 / 24 )272159.0821917811123.09548800293242.329423543255
Winsorized Mean ( 9 / 24 )272143.9178082191114.15736442694244.259856369746
Winsorized Mean ( 10 / 24 )272102.4109589041104.51191790853246.355341709801
Winsorized Mean ( 11 / 24 )272118.6849315071065.83527975030255.310262384314
Winsorized Mean ( 12 / 24 )272135.9452054791061.04951953767256.478081554627
Winsorized Mean ( 13 / 24 )272113.5068493151038.17861397825262.106638670382
Winsorized Mean ( 14 / 24 )272162.4109589041016.47959332004267.749999849936
Winsorized Mean ( 15 / 24 )271889.328767123932.504043893524291.569061332852
Winsorized Mean ( 16 / 24 )271427.520547945845.791767678697320.915301993169
Winsorized Mean ( 17 / 24 )271206.054794521800.930214726857338.613839018435
Winsorized Mean ( 18 / 24 )271158.219178082781.863041422753346.810380862429
Winsorized Mean ( 19 / 24 )270838.602739726725.589488143475373.266987966854
Winsorized Mean ( 20 / 24 )270691.479452055676.373299461436400.210179301273
Winsorized Mean ( 21 / 24 )270721.972602740656.721910840739412.232283001126
Winsorized Mean ( 22 / 24 )270188.849315069532.106997868694507.771651937083
Winsorized Mean ( 23 / 24 )269516.808219178395.262689685618681.867566183757
Winsorized Mean ( 24 / 24 )269575.328767123381.674833941245706.295791062351
Trimmed Mean ( 1 / 24 )272713.1971830991364.34034541114199.886485876013
Trimmed Mean ( 2 / 24 )272427.7681159421300.00366271779209.559231199705
Trimmed Mean ( 3 / 24 )272127.1791044781225.75630091714222.007571081516
Trimmed Mean ( 4 / 24 )271832.6307692311148.20104393477236.746545568089
Trimmed Mean ( 5 / 24 )271680.9047619051117.48976352783243.117130580443
Trimmed Mean ( 6 / 24 )271586.2786885251102.63528818925246.306536347593
Trimmed Mean ( 7 / 24 )271486.0508474581084.58159938205250.314085175461
Trimmed Mean ( 8 / 24 )271387.0350877191064.40822421311254.965180570969
Trimmed Mean ( 9 / 24 )271258.9454545451043.40687397520259.974274868532
Trimmed Mean ( 10 / 24 )271123.5094339621018.77014867754266.128242750247
Trimmed Mean ( 11 / 24 )270983.392156863989.60773495417273.829096707103
Trimmed Mean ( 12 / 24 )270829.632653061960.925376302096281.842523188729
Trimmed Mean ( 13 / 24 )270660.553191489924.516949556428292.758887028895
Trimmed Mean ( 14 / 24 )270479.244444444882.196390762453306.597541405353
Trimmed Mean ( 15 / 24 )270275.139534884830.808092109824325.315968996551
Trimmed Mean ( 16 / 24 )270083.536585366785.07472154672344.022714237008
Trimmed Mean ( 17 / 24 )269926.307692308748.265733209178360.735893296412
Trimmed Mean ( 18 / 24 )269777.783783784710.497309375153379.702752176556
Trimmed Mean ( 19 / 24 )269617.828571429662.711261366801406.840571888515
Trimmed Mean ( 20 / 24 )269475.696969697613.997863121912438.887027390503
Trimmed Mean ( 21 / 24 )269332.548387097560.101651370707480.863692738583
Trimmed Mean ( 22 / 24 )269166483.964022295922556.169441528068
Trimmed Mean ( 23 / 24 )269040.296296296425.822628747368631.81305579679
Trimmed Mean ( 24 / 24 )268979.8400.644730403384671.3673726076
Median268403
Midrange285927.5
Midmean - Weighted Average at Xnp269473.333333333
Midmean - Weighted Average at X(n+1)p269777.783783784
Midmean - Empirical Distribution Function269777.783783784
Midmean - Empirical Distribution Function - Averaging269777.783783784
Midmean - Empirical Distribution Function - Interpolation269777.783783784
Midmean - Closest Observation269632.684210526
Midmean - True Basic - Statistics Graphics Toolkit269777.783783784
Midmean - MS Excel (old versions)269777.783783784
Number of observations73



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')