Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationTue, 16 Mar 2010 12:01:34 -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/2010/Mar/16/t12687630937l46pbx148sa2cw.htm/, Retrieved Fri, 21 Jan 2022 12:08:29 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=74475, Retrieved Fri, 21 Jan 2022 12:08:29 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsKDGP1W52
Estimated Impact151
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [IKO - Opgave 5 - ...] [2010-03-16 18:01:34] [8b7f9564fd63910ef0a86e3a376c4af8] [Current]
-    D    [Central Tendency] [Katleen van den A...] [2010-05-02 12:59:53] [b39c10f74e49ba87352399c34734b08b]
- RM D    [Mean versus Median] [Katleen van den A...] [2010-05-02 13:15:49] [b39c10f74e49ba87352399c34734b08b]
-           [Mean versus Median] [Katleen van den A...] [2010-05-07 09:09:38] [b39c10f74e49ba87352399c34734b08b]
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Dataseries X:
5714837
6015267
3415340
115612
615159
9714993
2414534
6614721
8414518
9513816
7713310
9212714
411919
3611400
710617
2410172
529569
269509
508895
308560
198397
977631
717793
57435
667628
57696
577284
677273
447200
327096
207113
616966
276765
866845
6725
576898
187085
966784
586883
476728
406853
217097
827154
526998
456977
427122
867075
157185
87059
657279
87566
67453
297553
227345
97406
187524
337651
397672
797737
717980
717784
897934
297932
108061
187927
887990
998136
288286
768212
988170
508491
438167




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 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 & 2 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=74475&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]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=74475&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=74475&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'Gwilym Jenkins' @ 72.249.127.135







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean1425603.65277778286767.3043597394.97129076817422
Geometric Mean551536.487744222
Harmonic Mean191008.242936065
Quadratic Mean2805541.89794872
Winsorized Mean ( 1 / 24 )1423513.83333333285592.8156213494.98441751847387
Winsorized Mean ( 2 / 24 )1415157.13888889282296.5747407955.01301562085296
Winsorized Mean ( 3 / 24 )1382305.51388889269683.9291459895.12565030577183
Winsorized Mean ( 4 / 24 )1344438.73611111255611.2416062735.25970112919368
Winsorized Mean ( 5 / 24 )1268183.04166667229668.1501137245.52180631506242
Winsorized Mean ( 6 / 24 )1219048.54166667213505.4646286895.70968309306152
Winsorized Mean ( 7 / 24 )1190875.97222222204250.3854179425.83047111409568
Winsorized Mean ( 8 / 24 )957999.75134422.0694117677.12680405972188
Winsorized Mean ( 9 / 24 )938688.875127199.3165343007.37966917256885
Winsorized Mean ( 10 / 24 )803840.81944444489976.942948178.9338534196198
Winsorized Mean ( 11 / 24 )803241.47222222289802.47724381318.94453579539267
Winsorized Mean ( 12 / 24 )567969.30555555636211.904738456215.6846017810376
Winsorized Mean ( 13 / 24 )568060.30555555635634.132176118515.9414659727917
Winsorized Mean ( 14 / 24 )567705.83333333335048.581349340416.1976836572878
Winsorized Mean ( 15 / 24 )567526.04166666734377.585658249916.5086067214982
Winsorized Mean ( 16 / 24 )554503.37531623.417593053517.5345809278313
Winsorized Mean ( 17 / 24 )562110.87529849.731432230118.8313545224418
Winsorized Mean ( 18 / 24 )558696.12528803.090539236919.3970894977023
Winsorized Mean ( 19 / 24 )561675.69444444428378.061092526119.7926029059249
Winsorized Mean ( 20 / 24 )553224.58333333326385.736321779420.9668048140347
Winsorized Mean ( 21 / 24 )544755.16666666725134.645745869321.6734770075760
Winsorized Mean ( 22 / 24 )538981.08333333323423.281930311023.0104852486902
Winsorized Mean ( 23 / 24 )528855.97222222220446.445582174525.8654234104770
Winsorized Mean ( 24 / 24 )532311.97222222219952.042967306326.6795722670844
Trimmed Mean ( 1 / 24 )1327453.5268800.8316685144.93842780083739
Trimmed Mean ( 2 / 24 )1225742.55882353247752.5533184384.94744672620216
Trimmed Mean ( 3 / 24 )1122425.51515152223237.8664718185.02793514779095
Trimmed Mean ( 4 / 24 )1024970.515625198517.1678448865.16313287536861
Trimmed Mean ( 5 / 24 )932221.677419355172662.6374406835.3990932331241
Trimmed Mean ( 6 / 24 )851590.95149723.0254766465.6877754593119
Trimmed Mean ( 7 / 24 )775565.24137931125159.9637724556.19659208905903
Trimmed Mean ( 8 / 24 )699283.67857142992968.22549862437.52174923013644
Trimmed Mean ( 9 / 24 )656164.33333333378639.78377975958.343923416308
Trimmed Mean ( 10 / 24 )612699.01923076960599.550212556610.1106199151923
Trimmed Mean ( 11 / 24 )585174.650601.757954410411.5643136455301
Trimmed Mean ( 12 / 24 )555438.20833333334863.794124928915.9316626969230
Trimmed Mean ( 13 / 24 )553803.71739130434127.945586629216.2272796639794
Trimmed Mean ( 14 / 24 )552009.18181818233282.646698690416.5854953428299
Trimmed Mean ( 15 / 24 )550087.14285714332291.242728587117.035180326775
Trimmed Mean ( 16 / 24 )547994.47531120.912524686917.6085606283331
Trimmed Mean ( 17 / 24 )547223.68421052630238.280036390718.0970506110785
Trimmed Mean ( 18 / 24 )545472.2529442.216400360818.5268745593934
Trimmed Mean ( 19 / 24 )543916.528580.644995342919.0309385980837
Trimmed Mean ( 20 / 24 )541813.437527436.47476859419.7479246903907
Trimmed Mean ( 21 / 24 )540444.126383.541893034320.4841375047786
Trimmed Mean ( 22 / 24 )539916.21428571425212.846793755521.4143297146213
Trimmed Mean ( 23 / 24 )540033.92307692324017.136015188622.4853589010530
Trimmed Mean ( 24 / 24 )541491.91666666723229.964535377923.3100621329837
Median528283.5
Midrange4860859
Midmean - Weighted Average at Xnp538013.783783784
Midmean - Weighted Average at X(n+1)p545472.25
Midmean - Empirical Distribution Function538013.783783784
Midmean - Empirical Distribution Function - Averaging545472.25
Midmean - Empirical Distribution Function - Interpolation545472.25
Midmean - Closest Observation538013.783783784
Midmean - True Basic - Statistics Graphics Toolkit545472.25
Midmean - MS Excel (old versions)547223.684210526
Number of observations72

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 1425603.65277778 & 286767.304359739 & 4.97129076817422 \tabularnewline
Geometric Mean & 551536.487744222 &  &  \tabularnewline
Harmonic Mean & 191008.242936065 &  &  \tabularnewline
Quadratic Mean & 2805541.89794872 &  &  \tabularnewline
Winsorized Mean ( 1 / 24 ) & 1423513.83333333 & 285592.815621349 & 4.98441751847387 \tabularnewline
Winsorized Mean ( 2 / 24 ) & 1415157.13888889 & 282296.574740795 & 5.01301562085296 \tabularnewline
Winsorized Mean ( 3 / 24 ) & 1382305.51388889 & 269683.929145989 & 5.12565030577183 \tabularnewline
Winsorized Mean ( 4 / 24 ) & 1344438.73611111 & 255611.241606273 & 5.25970112919368 \tabularnewline
Winsorized Mean ( 5 / 24 ) & 1268183.04166667 & 229668.150113724 & 5.52180631506242 \tabularnewline
Winsorized Mean ( 6 / 24 ) & 1219048.54166667 & 213505.464628689 & 5.70968309306152 \tabularnewline
Winsorized Mean ( 7 / 24 ) & 1190875.97222222 & 204250.385417942 & 5.83047111409568 \tabularnewline
Winsorized Mean ( 8 / 24 ) & 957999.75 & 134422.069411767 & 7.12680405972188 \tabularnewline
Winsorized Mean ( 9 / 24 ) & 938688.875 & 127199.316534300 & 7.37966917256885 \tabularnewline
Winsorized Mean ( 10 / 24 ) & 803840.819444444 & 89976.94294817 & 8.9338534196198 \tabularnewline
Winsorized Mean ( 11 / 24 ) & 803241.472222222 & 89802.4772438131 & 8.94453579539267 \tabularnewline
Winsorized Mean ( 12 / 24 ) & 567969.305555556 & 36211.9047384562 & 15.6846017810376 \tabularnewline
Winsorized Mean ( 13 / 24 ) & 568060.305555556 & 35634.1321761185 & 15.9414659727917 \tabularnewline
Winsorized Mean ( 14 / 24 ) & 567705.833333333 & 35048.5813493404 & 16.1976836572878 \tabularnewline
Winsorized Mean ( 15 / 24 ) & 567526.041666667 & 34377.5856582499 & 16.5086067214982 \tabularnewline
Winsorized Mean ( 16 / 24 ) & 554503.375 & 31623.4175930535 & 17.5345809278313 \tabularnewline
Winsorized Mean ( 17 / 24 ) & 562110.875 & 29849.7314322301 & 18.8313545224418 \tabularnewline
Winsorized Mean ( 18 / 24 ) & 558696.125 & 28803.0905392369 & 19.3970894977023 \tabularnewline
Winsorized Mean ( 19 / 24 ) & 561675.694444444 & 28378.0610925261 & 19.7926029059249 \tabularnewline
Winsorized Mean ( 20 / 24 ) & 553224.583333333 & 26385.7363217794 & 20.9668048140347 \tabularnewline
Winsorized Mean ( 21 / 24 ) & 544755.166666667 & 25134.6457458693 & 21.6734770075760 \tabularnewline
Winsorized Mean ( 22 / 24 ) & 538981.083333333 & 23423.2819303110 & 23.0104852486902 \tabularnewline
Winsorized Mean ( 23 / 24 ) & 528855.972222222 & 20446.4455821745 & 25.8654234104770 \tabularnewline
Winsorized Mean ( 24 / 24 ) & 532311.972222222 & 19952.0429673063 & 26.6795722670844 \tabularnewline
Trimmed Mean ( 1 / 24 ) & 1327453.5 & 268800.831668514 & 4.93842780083739 \tabularnewline
Trimmed Mean ( 2 / 24 ) & 1225742.55882353 & 247752.553318438 & 4.94744672620216 \tabularnewline
Trimmed Mean ( 3 / 24 ) & 1122425.51515152 & 223237.866471818 & 5.02793514779095 \tabularnewline
Trimmed Mean ( 4 / 24 ) & 1024970.515625 & 198517.167844886 & 5.16313287536861 \tabularnewline
Trimmed Mean ( 5 / 24 ) & 932221.677419355 & 172662.637440683 & 5.3990932331241 \tabularnewline
Trimmed Mean ( 6 / 24 ) & 851590.95 & 149723.025476646 & 5.6877754593119 \tabularnewline
Trimmed Mean ( 7 / 24 ) & 775565.24137931 & 125159.963772455 & 6.19659208905903 \tabularnewline
Trimmed Mean ( 8 / 24 ) & 699283.678571429 & 92968.2254986243 & 7.52174923013644 \tabularnewline
Trimmed Mean ( 9 / 24 ) & 656164.333333333 & 78639.7837797595 & 8.343923416308 \tabularnewline
Trimmed Mean ( 10 / 24 ) & 612699.019230769 & 60599.5502125566 & 10.1106199151923 \tabularnewline
Trimmed Mean ( 11 / 24 ) & 585174.6 & 50601.7579544104 & 11.5643136455301 \tabularnewline
Trimmed Mean ( 12 / 24 ) & 555438.208333333 & 34863.7941249289 & 15.9316626969230 \tabularnewline
Trimmed Mean ( 13 / 24 ) & 553803.717391304 & 34127.9455866292 & 16.2272796639794 \tabularnewline
Trimmed Mean ( 14 / 24 ) & 552009.181818182 & 33282.6466986904 & 16.5854953428299 \tabularnewline
Trimmed Mean ( 15 / 24 ) & 550087.142857143 & 32291.2427285871 & 17.035180326775 \tabularnewline
Trimmed Mean ( 16 / 24 ) & 547994.475 & 31120.9125246869 & 17.6085606283331 \tabularnewline
Trimmed Mean ( 17 / 24 ) & 547223.684210526 & 30238.2800363907 & 18.0970506110785 \tabularnewline
Trimmed Mean ( 18 / 24 ) & 545472.25 & 29442.2164003608 & 18.5268745593934 \tabularnewline
Trimmed Mean ( 19 / 24 ) & 543916.5 & 28580.6449953429 & 19.0309385980837 \tabularnewline
Trimmed Mean ( 20 / 24 ) & 541813.4375 & 27436.474768594 & 19.7479246903907 \tabularnewline
Trimmed Mean ( 21 / 24 ) & 540444.1 & 26383.5418930343 & 20.4841375047786 \tabularnewline
Trimmed Mean ( 22 / 24 ) & 539916.214285714 & 25212.8467937555 & 21.4143297146213 \tabularnewline
Trimmed Mean ( 23 / 24 ) & 540033.923076923 & 24017.1360151886 & 22.4853589010530 \tabularnewline
Trimmed Mean ( 24 / 24 ) & 541491.916666667 & 23229.9645353779 & 23.3100621329837 \tabularnewline
Median & 528283.5 &  &  \tabularnewline
Midrange & 4860859 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 538013.783783784 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 545472.25 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 538013.783783784 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 545472.25 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 545472.25 &  &  \tabularnewline
Midmean - Closest Observation & 538013.783783784 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 545472.25 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 547223.684210526 &  &  \tabularnewline
Number of observations & 72 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=74475&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]1425603.65277778[/C][C]286767.304359739[/C][C]4.97129076817422[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]551536.487744222[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]191008.242936065[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]2805541.89794872[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 24 )[/C][C]1423513.83333333[/C][C]285592.815621349[/C][C]4.98441751847387[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 24 )[/C][C]1415157.13888889[/C][C]282296.574740795[/C][C]5.01301562085296[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 24 )[/C][C]1382305.51388889[/C][C]269683.929145989[/C][C]5.12565030577183[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 24 )[/C][C]1344438.73611111[/C][C]255611.241606273[/C][C]5.25970112919368[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 24 )[/C][C]1268183.04166667[/C][C]229668.150113724[/C][C]5.52180631506242[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 24 )[/C][C]1219048.54166667[/C][C]213505.464628689[/C][C]5.70968309306152[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 24 )[/C][C]1190875.97222222[/C][C]204250.385417942[/C][C]5.83047111409568[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 24 )[/C][C]957999.75[/C][C]134422.069411767[/C][C]7.12680405972188[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 24 )[/C][C]938688.875[/C][C]127199.316534300[/C][C]7.37966917256885[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 24 )[/C][C]803840.819444444[/C][C]89976.94294817[/C][C]8.9338534196198[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 24 )[/C][C]803241.472222222[/C][C]89802.4772438131[/C][C]8.94453579539267[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 24 )[/C][C]567969.305555556[/C][C]36211.9047384562[/C][C]15.6846017810376[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 24 )[/C][C]568060.305555556[/C][C]35634.1321761185[/C][C]15.9414659727917[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 24 )[/C][C]567705.833333333[/C][C]35048.5813493404[/C][C]16.1976836572878[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 24 )[/C][C]567526.041666667[/C][C]34377.5856582499[/C][C]16.5086067214982[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 24 )[/C][C]554503.375[/C][C]31623.4175930535[/C][C]17.5345809278313[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 24 )[/C][C]562110.875[/C][C]29849.7314322301[/C][C]18.8313545224418[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 24 )[/C][C]558696.125[/C][C]28803.0905392369[/C][C]19.3970894977023[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 24 )[/C][C]561675.694444444[/C][C]28378.0610925261[/C][C]19.7926029059249[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 24 )[/C][C]553224.583333333[/C][C]26385.7363217794[/C][C]20.9668048140347[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 24 )[/C][C]544755.166666667[/C][C]25134.6457458693[/C][C]21.6734770075760[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 24 )[/C][C]538981.083333333[/C][C]23423.2819303110[/C][C]23.0104852486902[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 24 )[/C][C]528855.972222222[/C][C]20446.4455821745[/C][C]25.8654234104770[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 24 )[/C][C]532311.972222222[/C][C]19952.0429673063[/C][C]26.6795722670844[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 24 )[/C][C]1327453.5[/C][C]268800.831668514[/C][C]4.93842780083739[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 24 )[/C][C]1225742.55882353[/C][C]247752.553318438[/C][C]4.94744672620216[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 24 )[/C][C]1122425.51515152[/C][C]223237.866471818[/C][C]5.02793514779095[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 24 )[/C][C]1024970.515625[/C][C]198517.167844886[/C][C]5.16313287536861[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 24 )[/C][C]932221.677419355[/C][C]172662.637440683[/C][C]5.3990932331241[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 24 )[/C][C]851590.95[/C][C]149723.025476646[/C][C]5.6877754593119[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 24 )[/C][C]775565.24137931[/C][C]125159.963772455[/C][C]6.19659208905903[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 24 )[/C][C]699283.678571429[/C][C]92968.2254986243[/C][C]7.52174923013644[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 24 )[/C][C]656164.333333333[/C][C]78639.7837797595[/C][C]8.343923416308[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 24 )[/C][C]612699.019230769[/C][C]60599.5502125566[/C][C]10.1106199151923[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 24 )[/C][C]585174.6[/C][C]50601.7579544104[/C][C]11.5643136455301[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 24 )[/C][C]555438.208333333[/C][C]34863.7941249289[/C][C]15.9316626969230[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 24 )[/C][C]553803.717391304[/C][C]34127.9455866292[/C][C]16.2272796639794[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 24 )[/C][C]552009.181818182[/C][C]33282.6466986904[/C][C]16.5854953428299[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 24 )[/C][C]550087.142857143[/C][C]32291.2427285871[/C][C]17.035180326775[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 24 )[/C][C]547994.475[/C][C]31120.9125246869[/C][C]17.6085606283331[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 24 )[/C][C]547223.684210526[/C][C]30238.2800363907[/C][C]18.0970506110785[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 24 )[/C][C]545472.25[/C][C]29442.2164003608[/C][C]18.5268745593934[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 24 )[/C][C]543916.5[/C][C]28580.6449953429[/C][C]19.0309385980837[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 24 )[/C][C]541813.4375[/C][C]27436.474768594[/C][C]19.7479246903907[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 24 )[/C][C]540444.1[/C][C]26383.5418930343[/C][C]20.4841375047786[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 24 )[/C][C]539916.214285714[/C][C]25212.8467937555[/C][C]21.4143297146213[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 24 )[/C][C]540033.923076923[/C][C]24017.1360151886[/C][C]22.4853589010530[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 24 )[/C][C]541491.916666667[/C][C]23229.9645353779[/C][C]23.3100621329837[/C][/ROW]
[ROW][C]Median[/C][C]528283.5[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]4860859[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]538013.783783784[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]545472.25[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]538013.783783784[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]545472.25[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]545472.25[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]538013.783783784[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]545472.25[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]547223.684210526[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]72[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=74475&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=74475&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 Mean1425603.65277778286767.3043597394.97129076817422
Geometric Mean551536.487744222
Harmonic Mean191008.242936065
Quadratic Mean2805541.89794872
Winsorized Mean ( 1 / 24 )1423513.83333333285592.8156213494.98441751847387
Winsorized Mean ( 2 / 24 )1415157.13888889282296.5747407955.01301562085296
Winsorized Mean ( 3 / 24 )1382305.51388889269683.9291459895.12565030577183
Winsorized Mean ( 4 / 24 )1344438.73611111255611.2416062735.25970112919368
Winsorized Mean ( 5 / 24 )1268183.04166667229668.1501137245.52180631506242
Winsorized Mean ( 6 / 24 )1219048.54166667213505.4646286895.70968309306152
Winsorized Mean ( 7 / 24 )1190875.97222222204250.3854179425.83047111409568
Winsorized Mean ( 8 / 24 )957999.75134422.0694117677.12680405972188
Winsorized Mean ( 9 / 24 )938688.875127199.3165343007.37966917256885
Winsorized Mean ( 10 / 24 )803840.81944444489976.942948178.9338534196198
Winsorized Mean ( 11 / 24 )803241.47222222289802.47724381318.94453579539267
Winsorized Mean ( 12 / 24 )567969.30555555636211.904738456215.6846017810376
Winsorized Mean ( 13 / 24 )568060.30555555635634.132176118515.9414659727917
Winsorized Mean ( 14 / 24 )567705.83333333335048.581349340416.1976836572878
Winsorized Mean ( 15 / 24 )567526.04166666734377.585658249916.5086067214982
Winsorized Mean ( 16 / 24 )554503.37531623.417593053517.5345809278313
Winsorized Mean ( 17 / 24 )562110.87529849.731432230118.8313545224418
Winsorized Mean ( 18 / 24 )558696.12528803.090539236919.3970894977023
Winsorized Mean ( 19 / 24 )561675.69444444428378.061092526119.7926029059249
Winsorized Mean ( 20 / 24 )553224.58333333326385.736321779420.9668048140347
Winsorized Mean ( 21 / 24 )544755.16666666725134.645745869321.6734770075760
Winsorized Mean ( 22 / 24 )538981.08333333323423.281930311023.0104852486902
Winsorized Mean ( 23 / 24 )528855.97222222220446.445582174525.8654234104770
Winsorized Mean ( 24 / 24 )532311.97222222219952.042967306326.6795722670844
Trimmed Mean ( 1 / 24 )1327453.5268800.8316685144.93842780083739
Trimmed Mean ( 2 / 24 )1225742.55882353247752.5533184384.94744672620216
Trimmed Mean ( 3 / 24 )1122425.51515152223237.8664718185.02793514779095
Trimmed Mean ( 4 / 24 )1024970.515625198517.1678448865.16313287536861
Trimmed Mean ( 5 / 24 )932221.677419355172662.6374406835.3990932331241
Trimmed Mean ( 6 / 24 )851590.95149723.0254766465.6877754593119
Trimmed Mean ( 7 / 24 )775565.24137931125159.9637724556.19659208905903
Trimmed Mean ( 8 / 24 )699283.67857142992968.22549862437.52174923013644
Trimmed Mean ( 9 / 24 )656164.33333333378639.78377975958.343923416308
Trimmed Mean ( 10 / 24 )612699.01923076960599.550212556610.1106199151923
Trimmed Mean ( 11 / 24 )585174.650601.757954410411.5643136455301
Trimmed Mean ( 12 / 24 )555438.20833333334863.794124928915.9316626969230
Trimmed Mean ( 13 / 24 )553803.71739130434127.945586629216.2272796639794
Trimmed Mean ( 14 / 24 )552009.18181818233282.646698690416.5854953428299
Trimmed Mean ( 15 / 24 )550087.14285714332291.242728587117.035180326775
Trimmed Mean ( 16 / 24 )547994.47531120.912524686917.6085606283331
Trimmed Mean ( 17 / 24 )547223.68421052630238.280036390718.0970506110785
Trimmed Mean ( 18 / 24 )545472.2529442.216400360818.5268745593934
Trimmed Mean ( 19 / 24 )543916.528580.644995342919.0309385980837
Trimmed Mean ( 20 / 24 )541813.437527436.47476859419.7479246903907
Trimmed Mean ( 21 / 24 )540444.126383.541893034320.4841375047786
Trimmed Mean ( 22 / 24 )539916.21428571425212.846793755521.4143297146213
Trimmed Mean ( 23 / 24 )540033.92307692324017.136015188622.4853589010530
Trimmed Mean ( 24 / 24 )541491.91666666723229.964535377923.3100621329837
Median528283.5
Midrange4860859
Midmean - Weighted Average at Xnp538013.783783784
Midmean - Weighted Average at X(n+1)p545472.25
Midmean - Empirical Distribution Function538013.783783784
Midmean - Empirical Distribution Function - Averaging545472.25
Midmean - Empirical Distribution Function - Interpolation545472.25
Midmean - Closest Observation538013.783783784
Midmean - True Basic - Statistics Graphics Toolkit545472.25
Midmean - MS Excel (old versions)547223.684210526
Number of observations72



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