Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationMon, 13 Oct 2014 16:27:22 +0100
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2014/Oct/13/t1413214061hp7l2ap63iilfgb.htm/, Retrieved Fri, 10 May 2024 05:03:23 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=240784, Retrieved Fri, 10 May 2024 05:03:23 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsEline Van Loon
Estimated Impact87
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [] [2014-10-13 15:27:22] [9adebd9d8505f0d6c7bd6ecbde218cd8] [Current]
Feedback Forum

Post a new message
Dataseries X:
22943
21413
20631
19775
17506
20688
32631
34062
29159
25871
23719
25638
27596
28006
27662
26655
25213
28434
40388
42758
37956
33490
31578
34766
32324
32046
29565
28284
26366
27530
39728
41528
36458
32301
28985
29118
29249
28036
26326
24942
23280
23969
35948
37639
34327
30133
27549
27990
30437
30464
28471
26882
25806
26465
36416
42870
40489
36645
33841
33496
34504
34699
33322
32160
30173
30782
43062
46223
45191
40671
37251
36870




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Sir Ronald Aylmer Fisher' @ fisher.wessa.net

\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 & 'Sir Ronald Aylmer Fisher' @ fisher.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=240784&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]'Sir Ronald Aylmer Fisher' @ fisher.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=240784&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=240784&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'Sir Ronald Aylmer Fisher' @ fisher.wessa.net







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean31240.9583333333752.40123597019441.5216733303863
Geometric Mean30595.7672870544
Harmonic Mean29946.0939641531
Quadratic Mean31877.7527218783
Winsorized Mean ( 1 / 24 )31258.1388888889740.99736517073242.1838731932424
Winsorized Mean ( 2 / 24 )31222.7777777778721.26111115360243.2891463229445
Winsorized Mean ( 3 / 24 )31217.1527777778718.93260234971343.4215289107068
Winsorized Mean ( 4 / 24 )31251.2083333333709.42243610915444.0516210690085
Winsorized Mean ( 5 / 24 )31272.0416666667670.75448183169146.6221881682687
Winsorized Mean ( 6 / 24 )31228.7083333333650.89110082412647.9783919211572
Winsorized Mean ( 7 / 24 )31253.6944444444640.07564523820848.8281262956243
Winsorized Mean ( 8 / 24 )31270.25633.23897331104949.3814362633046
Winsorized Mean ( 9 / 24 )31309.375597.66218208594752.3864081390004
Winsorized Mean ( 10 / 24 )31100.9027777778545.67309734901856.9954848953921
Winsorized Mean ( 11 / 24 )31117.4027777778527.4836885906158.9921611811746
Winsorized Mean ( 12 / 24 )31080.7361111111512.28727253958560.6705217504881
Winsorized Mean ( 13 / 24 )31023.6805555556499.07093410823962.1628679117328
Winsorized Mean ( 14 / 24 )31068.4027777778479.27329071294564.8239811810958
Winsorized Mean ( 15 / 24 )31037.7777777778471.76676811590165.7905131845841
Winsorized Mean ( 16 / 24 )31050.4444444444467.20188326010466.4604436689692
Winsorized Mean ( 17 / 24 )30984.8055555556443.36159350734769.8860839759276
Winsorized Mean ( 18 / 24 )30746.0555555556390.68224047660878.6983701077564
Winsorized Mean ( 19 / 24 )30899.375365.05343169992584.6434311166792
Winsorized Mean ( 20 / 24 )30850.4861111111356.48569406854286.5406007153247
Winsorized Mean ( 21 / 24 )30812.5694444444347.29191247031488.7223927135886
Winsorized Mean ( 22 / 24 )30751.7638888889333.22247774792992.2859829166491
Winsorized Mean ( 23 / 24 )30785.9444444444309.87455996624899.3496995939186
Winsorized Mean ( 24 / 24 )30676.2777777778293.421453781435104.546812724294
Trimmed Mean ( 1 / 24 )31223.1428571429716.67643345043543.566582351284
Trimmed Mean ( 2 / 24 )31186.0882352941687.68084180258145.3496539958096
Trimmed Mean ( 3 / 24 )31166.0757575758665.86454774901546.8054289163375
Trimmed Mean ( 4 / 24 )31146.921875640.73175409580748.6114847217993
Trimmed Mean ( 5 / 24 )31116.6451612903613.97068079693550.6809952568107
Trimmed Mean ( 6 / 24 )31079.35594.31736173092152.2941983547021
Trimmed Mean ( 7 / 24 )31048.4482758621576.16749943061653.8878855654735
Trimmed Mean ( 8 / 24 )31010.75556.70793086878855.7038049585627
Trimmed Mean ( 9 / 24 )30967.5534.2709876971657.962159116065
Trimmed Mean ( 10 / 24 )30914.9038461538515.13595802329660.0130962800228
Trimmed Mean ( 11 / 24 )30888.12503.71011880619961.3212219623567
Trimmed Mean ( 12 / 24 )30856.8541666667493.05390242851362.5831253229774
Trimmed Mean ( 13 / 24 )30827.652173913482.54708485175763.8852728400247
Trimmed Mean ( 14 / 24 )30802.9772727273471.65862647105665.3077788552174
Trimmed Mean ( 15 / 24 )30770.4761904762461.45311467984466.6816957380918
Trimmed Mean ( 16 / 24 )30738.4449.28178126244968.4167515398184
Trimmed Mean ( 17 / 24 )30701.4473684211433.60233713304470.8055394060313
Trimmed Mean ( 18 / 24 )30668.1111111111418.23835912562173.3268731620567
Trimmed Mean ( 19 / 24 )30658.9411764706410.72215854181674.6464259082559
Trimmed Mean ( 20 / 24 )30630.46875405.52498576709375.5328767031685
Trimmed Mean ( 21 / 24 )30604.0666666667399.15759551039576.6716379968515
Trimmed Mean ( 22 / 24 )30578.5357142857391.18486908955378.1690145261867
Trimmed Mean ( 23 / 24 )30556.7307692308382.36971459446679.9140978035843
Trimmed Mean ( 24 / 24 )30526.8333333333375.03213710925481.3979131725457
Median30305
Midrange31864.5
Midmean - Weighted Average at Xnp30559.6486486487
Midmean - Weighted Average at X(n+1)p30668.1111111111
Midmean - Empirical Distribution Function30559.6486486487
Midmean - Empirical Distribution Function - Averaging30668.1111111111
Midmean - Empirical Distribution Function - Interpolation30668.1111111111
Midmean - Closest Observation30559.6486486487
Midmean - True Basic - Statistics Graphics Toolkit30668.1111111111
Midmean - MS Excel (old versions)30701.4473684211
Number of observations72

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 31240.9583333333 & 752.401235970194 & 41.5216733303863 \tabularnewline
Geometric Mean & 30595.7672870544 &  &  \tabularnewline
Harmonic Mean & 29946.0939641531 &  &  \tabularnewline
Quadratic Mean & 31877.7527218783 &  &  \tabularnewline
Winsorized Mean ( 1 / 24 ) & 31258.1388888889 & 740.997365170732 & 42.1838731932424 \tabularnewline
Winsorized Mean ( 2 / 24 ) & 31222.7777777778 & 721.261111153602 & 43.2891463229445 \tabularnewline
Winsorized Mean ( 3 / 24 ) & 31217.1527777778 & 718.932602349713 & 43.4215289107068 \tabularnewline
Winsorized Mean ( 4 / 24 ) & 31251.2083333333 & 709.422436109154 & 44.0516210690085 \tabularnewline
Winsorized Mean ( 5 / 24 ) & 31272.0416666667 & 670.754481831691 & 46.6221881682687 \tabularnewline
Winsorized Mean ( 6 / 24 ) & 31228.7083333333 & 650.891100824126 & 47.9783919211572 \tabularnewline
Winsorized Mean ( 7 / 24 ) & 31253.6944444444 & 640.075645238208 & 48.8281262956243 \tabularnewline
Winsorized Mean ( 8 / 24 ) & 31270.25 & 633.238973311049 & 49.3814362633046 \tabularnewline
Winsorized Mean ( 9 / 24 ) & 31309.375 & 597.662182085947 & 52.3864081390004 \tabularnewline
Winsorized Mean ( 10 / 24 ) & 31100.9027777778 & 545.673097349018 & 56.9954848953921 \tabularnewline
Winsorized Mean ( 11 / 24 ) & 31117.4027777778 & 527.48368859061 & 58.9921611811746 \tabularnewline
Winsorized Mean ( 12 / 24 ) & 31080.7361111111 & 512.287272539585 & 60.6705217504881 \tabularnewline
Winsorized Mean ( 13 / 24 ) & 31023.6805555556 & 499.070934108239 & 62.1628679117328 \tabularnewline
Winsorized Mean ( 14 / 24 ) & 31068.4027777778 & 479.273290712945 & 64.8239811810958 \tabularnewline
Winsorized Mean ( 15 / 24 ) & 31037.7777777778 & 471.766768115901 & 65.7905131845841 \tabularnewline
Winsorized Mean ( 16 / 24 ) & 31050.4444444444 & 467.201883260104 & 66.4604436689692 \tabularnewline
Winsorized Mean ( 17 / 24 ) & 30984.8055555556 & 443.361593507347 & 69.8860839759276 \tabularnewline
Winsorized Mean ( 18 / 24 ) & 30746.0555555556 & 390.682240476608 & 78.6983701077564 \tabularnewline
Winsorized Mean ( 19 / 24 ) & 30899.375 & 365.053431699925 & 84.6434311166792 \tabularnewline
Winsorized Mean ( 20 / 24 ) & 30850.4861111111 & 356.485694068542 & 86.5406007153247 \tabularnewline
Winsorized Mean ( 21 / 24 ) & 30812.5694444444 & 347.291912470314 & 88.7223927135886 \tabularnewline
Winsorized Mean ( 22 / 24 ) & 30751.7638888889 & 333.222477747929 & 92.2859829166491 \tabularnewline
Winsorized Mean ( 23 / 24 ) & 30785.9444444444 & 309.874559966248 & 99.3496995939186 \tabularnewline
Winsorized Mean ( 24 / 24 ) & 30676.2777777778 & 293.421453781435 & 104.546812724294 \tabularnewline
Trimmed Mean ( 1 / 24 ) & 31223.1428571429 & 716.676433450435 & 43.566582351284 \tabularnewline
Trimmed Mean ( 2 / 24 ) & 31186.0882352941 & 687.680841802581 & 45.3496539958096 \tabularnewline
Trimmed Mean ( 3 / 24 ) & 31166.0757575758 & 665.864547749015 & 46.8054289163375 \tabularnewline
Trimmed Mean ( 4 / 24 ) & 31146.921875 & 640.731754095807 & 48.6114847217993 \tabularnewline
Trimmed Mean ( 5 / 24 ) & 31116.6451612903 & 613.970680796935 & 50.6809952568107 \tabularnewline
Trimmed Mean ( 6 / 24 ) & 31079.35 & 594.317361730921 & 52.2941983547021 \tabularnewline
Trimmed Mean ( 7 / 24 ) & 31048.4482758621 & 576.167499430616 & 53.8878855654735 \tabularnewline
Trimmed Mean ( 8 / 24 ) & 31010.75 & 556.707930868788 & 55.7038049585627 \tabularnewline
Trimmed Mean ( 9 / 24 ) & 30967.5 & 534.27098769716 & 57.962159116065 \tabularnewline
Trimmed Mean ( 10 / 24 ) & 30914.9038461538 & 515.135958023296 & 60.0130962800228 \tabularnewline
Trimmed Mean ( 11 / 24 ) & 30888.12 & 503.710118806199 & 61.3212219623567 \tabularnewline
Trimmed Mean ( 12 / 24 ) & 30856.8541666667 & 493.053902428513 & 62.5831253229774 \tabularnewline
Trimmed Mean ( 13 / 24 ) & 30827.652173913 & 482.547084851757 & 63.8852728400247 \tabularnewline
Trimmed Mean ( 14 / 24 ) & 30802.9772727273 & 471.658626471056 & 65.3077788552174 \tabularnewline
Trimmed Mean ( 15 / 24 ) & 30770.4761904762 & 461.453114679844 & 66.6816957380918 \tabularnewline
Trimmed Mean ( 16 / 24 ) & 30738.4 & 449.281781262449 & 68.4167515398184 \tabularnewline
Trimmed Mean ( 17 / 24 ) & 30701.4473684211 & 433.602337133044 & 70.8055394060313 \tabularnewline
Trimmed Mean ( 18 / 24 ) & 30668.1111111111 & 418.238359125621 & 73.3268731620567 \tabularnewline
Trimmed Mean ( 19 / 24 ) & 30658.9411764706 & 410.722158541816 & 74.6464259082559 \tabularnewline
Trimmed Mean ( 20 / 24 ) & 30630.46875 & 405.524985767093 & 75.5328767031685 \tabularnewline
Trimmed Mean ( 21 / 24 ) & 30604.0666666667 & 399.157595510395 & 76.6716379968515 \tabularnewline
Trimmed Mean ( 22 / 24 ) & 30578.5357142857 & 391.184869089553 & 78.1690145261867 \tabularnewline
Trimmed Mean ( 23 / 24 ) & 30556.7307692308 & 382.369714594466 & 79.9140978035843 \tabularnewline
Trimmed Mean ( 24 / 24 ) & 30526.8333333333 & 375.032137109254 & 81.3979131725457 \tabularnewline
Median & 30305 &  &  \tabularnewline
Midrange & 31864.5 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 30559.6486486487 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 30668.1111111111 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 30559.6486486487 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 30668.1111111111 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 30668.1111111111 &  &  \tabularnewline
Midmean - Closest Observation & 30559.6486486487 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 30668.1111111111 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 30701.4473684211 &  &  \tabularnewline
Number of observations & 72 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=240784&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]31240.9583333333[/C][C]752.401235970194[/C][C]41.5216733303863[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]30595.7672870544[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]29946.0939641531[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]31877.7527218783[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 24 )[/C][C]31258.1388888889[/C][C]740.997365170732[/C][C]42.1838731932424[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 24 )[/C][C]31222.7777777778[/C][C]721.261111153602[/C][C]43.2891463229445[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 24 )[/C][C]31217.1527777778[/C][C]718.932602349713[/C][C]43.4215289107068[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 24 )[/C][C]31251.2083333333[/C][C]709.422436109154[/C][C]44.0516210690085[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 24 )[/C][C]31272.0416666667[/C][C]670.754481831691[/C][C]46.6221881682687[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 24 )[/C][C]31228.7083333333[/C][C]650.891100824126[/C][C]47.9783919211572[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 24 )[/C][C]31253.6944444444[/C][C]640.075645238208[/C][C]48.8281262956243[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 24 )[/C][C]31270.25[/C][C]633.238973311049[/C][C]49.3814362633046[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 24 )[/C][C]31309.375[/C][C]597.662182085947[/C][C]52.3864081390004[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 24 )[/C][C]31100.9027777778[/C][C]545.673097349018[/C][C]56.9954848953921[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 24 )[/C][C]31117.4027777778[/C][C]527.48368859061[/C][C]58.9921611811746[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 24 )[/C][C]31080.7361111111[/C][C]512.287272539585[/C][C]60.6705217504881[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 24 )[/C][C]31023.6805555556[/C][C]499.070934108239[/C][C]62.1628679117328[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 24 )[/C][C]31068.4027777778[/C][C]479.273290712945[/C][C]64.8239811810958[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 24 )[/C][C]31037.7777777778[/C][C]471.766768115901[/C][C]65.7905131845841[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 24 )[/C][C]31050.4444444444[/C][C]467.201883260104[/C][C]66.4604436689692[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 24 )[/C][C]30984.8055555556[/C][C]443.361593507347[/C][C]69.8860839759276[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 24 )[/C][C]30746.0555555556[/C][C]390.682240476608[/C][C]78.6983701077564[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 24 )[/C][C]30899.375[/C][C]365.053431699925[/C][C]84.6434311166792[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 24 )[/C][C]30850.4861111111[/C][C]356.485694068542[/C][C]86.5406007153247[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 24 )[/C][C]30812.5694444444[/C][C]347.291912470314[/C][C]88.7223927135886[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 24 )[/C][C]30751.7638888889[/C][C]333.222477747929[/C][C]92.2859829166491[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 24 )[/C][C]30785.9444444444[/C][C]309.874559966248[/C][C]99.3496995939186[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 24 )[/C][C]30676.2777777778[/C][C]293.421453781435[/C][C]104.546812724294[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 24 )[/C][C]31223.1428571429[/C][C]716.676433450435[/C][C]43.566582351284[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 24 )[/C][C]31186.0882352941[/C][C]687.680841802581[/C][C]45.3496539958096[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 24 )[/C][C]31166.0757575758[/C][C]665.864547749015[/C][C]46.8054289163375[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 24 )[/C][C]31146.921875[/C][C]640.731754095807[/C][C]48.6114847217993[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 24 )[/C][C]31116.6451612903[/C][C]613.970680796935[/C][C]50.6809952568107[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 24 )[/C][C]31079.35[/C][C]594.317361730921[/C][C]52.2941983547021[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 24 )[/C][C]31048.4482758621[/C][C]576.167499430616[/C][C]53.8878855654735[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 24 )[/C][C]31010.75[/C][C]556.707930868788[/C][C]55.7038049585627[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 24 )[/C][C]30967.5[/C][C]534.27098769716[/C][C]57.962159116065[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 24 )[/C][C]30914.9038461538[/C][C]515.135958023296[/C][C]60.0130962800228[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 24 )[/C][C]30888.12[/C][C]503.710118806199[/C][C]61.3212219623567[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 24 )[/C][C]30856.8541666667[/C][C]493.053902428513[/C][C]62.5831253229774[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 24 )[/C][C]30827.652173913[/C][C]482.547084851757[/C][C]63.8852728400247[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 24 )[/C][C]30802.9772727273[/C][C]471.658626471056[/C][C]65.3077788552174[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 24 )[/C][C]30770.4761904762[/C][C]461.453114679844[/C][C]66.6816957380918[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 24 )[/C][C]30738.4[/C][C]449.281781262449[/C][C]68.4167515398184[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 24 )[/C][C]30701.4473684211[/C][C]433.602337133044[/C][C]70.8055394060313[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 24 )[/C][C]30668.1111111111[/C][C]418.238359125621[/C][C]73.3268731620567[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 24 )[/C][C]30658.9411764706[/C][C]410.722158541816[/C][C]74.6464259082559[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 24 )[/C][C]30630.46875[/C][C]405.524985767093[/C][C]75.5328767031685[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 24 )[/C][C]30604.0666666667[/C][C]399.157595510395[/C][C]76.6716379968515[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 24 )[/C][C]30578.5357142857[/C][C]391.184869089553[/C][C]78.1690145261867[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 24 )[/C][C]30556.7307692308[/C][C]382.369714594466[/C][C]79.9140978035843[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 24 )[/C][C]30526.8333333333[/C][C]375.032137109254[/C][C]81.3979131725457[/C][/ROW]
[ROW][C]Median[/C][C]30305[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]31864.5[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]30559.6486486487[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]30668.1111111111[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]30559.6486486487[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]30668.1111111111[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]30668.1111111111[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]30559.6486486487[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]30668.1111111111[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]30701.4473684211[/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=240784&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=240784&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 Mean31240.9583333333752.40123597019441.5216733303863
Geometric Mean30595.7672870544
Harmonic Mean29946.0939641531
Quadratic Mean31877.7527218783
Winsorized Mean ( 1 / 24 )31258.1388888889740.99736517073242.1838731932424
Winsorized Mean ( 2 / 24 )31222.7777777778721.26111115360243.2891463229445
Winsorized Mean ( 3 / 24 )31217.1527777778718.93260234971343.4215289107068
Winsorized Mean ( 4 / 24 )31251.2083333333709.42243610915444.0516210690085
Winsorized Mean ( 5 / 24 )31272.0416666667670.75448183169146.6221881682687
Winsorized Mean ( 6 / 24 )31228.7083333333650.89110082412647.9783919211572
Winsorized Mean ( 7 / 24 )31253.6944444444640.07564523820848.8281262956243
Winsorized Mean ( 8 / 24 )31270.25633.23897331104949.3814362633046
Winsorized Mean ( 9 / 24 )31309.375597.66218208594752.3864081390004
Winsorized Mean ( 10 / 24 )31100.9027777778545.67309734901856.9954848953921
Winsorized Mean ( 11 / 24 )31117.4027777778527.4836885906158.9921611811746
Winsorized Mean ( 12 / 24 )31080.7361111111512.28727253958560.6705217504881
Winsorized Mean ( 13 / 24 )31023.6805555556499.07093410823962.1628679117328
Winsorized Mean ( 14 / 24 )31068.4027777778479.27329071294564.8239811810958
Winsorized Mean ( 15 / 24 )31037.7777777778471.76676811590165.7905131845841
Winsorized Mean ( 16 / 24 )31050.4444444444467.20188326010466.4604436689692
Winsorized Mean ( 17 / 24 )30984.8055555556443.36159350734769.8860839759276
Winsorized Mean ( 18 / 24 )30746.0555555556390.68224047660878.6983701077564
Winsorized Mean ( 19 / 24 )30899.375365.05343169992584.6434311166792
Winsorized Mean ( 20 / 24 )30850.4861111111356.48569406854286.5406007153247
Winsorized Mean ( 21 / 24 )30812.5694444444347.29191247031488.7223927135886
Winsorized Mean ( 22 / 24 )30751.7638888889333.22247774792992.2859829166491
Winsorized Mean ( 23 / 24 )30785.9444444444309.87455996624899.3496995939186
Winsorized Mean ( 24 / 24 )30676.2777777778293.421453781435104.546812724294
Trimmed Mean ( 1 / 24 )31223.1428571429716.67643345043543.566582351284
Trimmed Mean ( 2 / 24 )31186.0882352941687.68084180258145.3496539958096
Trimmed Mean ( 3 / 24 )31166.0757575758665.86454774901546.8054289163375
Trimmed Mean ( 4 / 24 )31146.921875640.73175409580748.6114847217993
Trimmed Mean ( 5 / 24 )31116.6451612903613.97068079693550.6809952568107
Trimmed Mean ( 6 / 24 )31079.35594.31736173092152.2941983547021
Trimmed Mean ( 7 / 24 )31048.4482758621576.16749943061653.8878855654735
Trimmed Mean ( 8 / 24 )31010.75556.70793086878855.7038049585627
Trimmed Mean ( 9 / 24 )30967.5534.2709876971657.962159116065
Trimmed Mean ( 10 / 24 )30914.9038461538515.13595802329660.0130962800228
Trimmed Mean ( 11 / 24 )30888.12503.71011880619961.3212219623567
Trimmed Mean ( 12 / 24 )30856.8541666667493.05390242851362.5831253229774
Trimmed Mean ( 13 / 24 )30827.652173913482.54708485175763.8852728400247
Trimmed Mean ( 14 / 24 )30802.9772727273471.65862647105665.3077788552174
Trimmed Mean ( 15 / 24 )30770.4761904762461.45311467984466.6816957380918
Trimmed Mean ( 16 / 24 )30738.4449.28178126244968.4167515398184
Trimmed Mean ( 17 / 24 )30701.4473684211433.60233713304470.8055394060313
Trimmed Mean ( 18 / 24 )30668.1111111111418.23835912562173.3268731620567
Trimmed Mean ( 19 / 24 )30658.9411764706410.72215854181674.6464259082559
Trimmed Mean ( 20 / 24 )30630.46875405.52498576709375.5328767031685
Trimmed Mean ( 21 / 24 )30604.0666666667399.15759551039576.6716379968515
Trimmed Mean ( 22 / 24 )30578.5357142857391.18486908955378.1690145261867
Trimmed Mean ( 23 / 24 )30556.7307692308382.36971459446679.9140978035843
Trimmed Mean ( 24 / 24 )30526.8333333333375.03213710925481.3979131725457
Median30305
Midrange31864.5
Midmean - Weighted Average at Xnp30559.6486486487
Midmean - Weighted Average at X(n+1)p30668.1111111111
Midmean - Empirical Distribution Function30559.6486486487
Midmean - Empirical Distribution Function - Averaging30668.1111111111
Midmean - Empirical Distribution Function - Interpolation30668.1111111111
Midmean - Closest Observation30559.6486486487
Midmean - True Basic - Statistics Graphics Toolkit30668.1111111111
Midmean - MS Excel (old versions)30701.4473684211
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')