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Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationSun, 07 Dec 2008 11:03:14 -0700
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2008/Dec/07/t1228673040ji041qnjsqx2bnk.htm/, Retrieved Sat, 18 May 2024 13:07:52 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=30202, Retrieved Sat, 18 May 2024 13:07:52 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact146
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Univariate Data Series] [Uitvoer per gewes...] [2008-12-07 13:15:03] [299afd6311e4c20059ea2f05c8dd029d]
- RMPD    [Central Tendency] [Uitvoer per gewes...] [2008-12-07 18:03:14] [5e2b1e7aa808f9f0d23fd35605d4968f] [Current]
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Dataseries X:
11316.9
11309.2
12710.3
12120.8
12469.5
12054.6
12112.9
9617.2
12645.8
13581.3
12162.3
10969.7
11880
11887.6
12926.9
12300
12092.8
12380.8
12196.9
9455
13168
13427.9
11980.5
11884.8
11691.7
12233.8
14341.4
13130.7
12421.1
14285.8
12864.6
11160.2
14316.2
14388.7
14013.9
13419
12769.6
13315.5
15332.9
14243
13824.4
14962.9
13202.9
12199
15508.9
14199.8
15169.6
14058
13786.2
14147.9
16541.7
13587.5
15582.4
15802.8
14130.5
12923.2
15612.2
16033.7
16036.6
14037.8
15330.6
15038.3
17401.8
14992.5
16043.7
16929.6
15921.3
14417.2
15961
17785.1
16469.7
14272




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=30202&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=30202&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=30202&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 Mean13673.4805555556208.96898430897765.4330622353901
Geometric Mean13559.0369216852
Harmonic Mean13443.2130938245
Quadratic Mean13786.3882539183
Winsorized Mean ( 1 / 24 )13670.4097222222206.92392188672166.0649073223443
Winsorized Mean ( 2 / 24 )13694.8625194.79173118612670.3051531839121
Winsorized Mean ( 3 / 24 )13686.6375189.65870565317472.1645624062655
Winsorized Mean ( 4 / 24 )13690.9152777778187.29866793965973.0967039348538
Winsorized Mean ( 5 / 24 )13661.8666666667181.36961000749975.3261070920414
Winsorized Mean ( 6 / 24 )13692.5083333333175.90855516412477.838785729086
Winsorized Mean ( 7 / 24 )13710.5333333333173.02426508073779.240523442973
Winsorized Mean ( 8 / 24 )13702.9888888889171.43156218938579.9327073374669
Winsorized Mean ( 9 / 24 )13698.3763888889170.46319003485480.3597327146586
Winsorized Mean ( 10 / 24 )13694.8208333333165.56916994104582.713592380814
Winsorized Mean ( 11 / 24 )13677.0222222222158.81712649559786.1180561820666
Winsorized Mean ( 12 / 24 )13678.4222222222157.05619793049087.092533771103
Winsorized Mean ( 13 / 24 )13668.7805555556154.29274231517888.5899125937753
Winsorized Mean ( 14 / 24 )13636.0944444444148.44189236992291.8614969584387
Winsorized Mean ( 15 / 24 )13644.2611111111147.12980816984592.7362121981452
Winsorized Mean ( 16 / 24 )13616.1722222222140.35823881878997.0101387479042
Winsorized Mean ( 17 / 24 )13585.6666666667135.529610711089100.241316974100
Winsorized Mean ( 18 / 24 )13582.9166666667132.557394218989102.468193092475
Winsorized Mean ( 19 / 24 )13592.575128.901687476282105.449162583702
Winsorized Mean ( 20 / 24 )13463.4361111111104.417051307243128.939056816453
Winsorized Mean ( 21 / 24 )13466.8777777778101.641376024325132.494052171774
Winsorized Mean ( 22 / 24 )13467.213888888997.671520579634137.882709401547
Winsorized Mean ( 23 / 24 )13515.481944444488.7050390273929152.364308641708
Winsorized Mean ( 24 / 24 )13526.848611111184.4710845645767160.135846258373
Trimmed Mean ( 1 / 24 )13675.0071428571197.56794900332669.2167287854315
Trimmed Mean ( 2 / 24 )13679.875186.32663360738873.418784717729
Trimmed Mean ( 3 / 24 )13671.7180.81870225794475.609988509357
Trimmed Mean ( 4 / 24 )13666.0984375176.57787724851777.3941710617931
Trimmed Mean ( 5 / 24 )13658.8935483871172.31614134893679.2664775421601
Trimmed Mean ( 6 / 24 )13658.18169.01684992388280.8095761230378
Trimmed Mean ( 7 / 24 )13651.0775862069166.45411542252682.0110548276628
Trimmed Mean ( 8 / 24 )13640.1571428571163.93989187633183.2021845735186
Trimmed Mean ( 9 / 24 )13629.6851851852161.12967668077084.5882984807838
Trimmed Mean ( 10 / 24 )13619.1173076923157.77163469979686.3217100691544
Trimmed Mean ( 11 / 24 )13608.216154.59467763787788.0251261422848
Trimmed Mean ( 12 / 24 )13598.8333333333151.99604261637989.4683381175603
Trimmed Mean ( 13 / 24 )13588.4521739130148.92899370694091.2411467753029
Trimmed Mean ( 14 / 24 )13578.3409090909145.47873686084893.33557055887
Trimmed Mean ( 15 / 24 )13571.2690476190142.23494694844695.414448690574
Trimmed Mean ( 16 / 24 )13562.51138.10506817785698.2042887994073
Trimmed Mean ( 17 / 24 )13556.1552631579134.15541584389101.048140158072
Trimmed Mean ( 18 / 24 )13552.6833333333129.913507582472104.320817638842
Trimmed Mean ( 19 / 24 )13549.1264705882124.719718161149108.636602698873
Trimmed Mean ( 20 / 24 )13543.98125118.342038657695114.447760099656
Trimmed Mean ( 21 / 24 )13553.6466666667116.335302133984116.505019697777
Trimmed Mean ( 22 / 24 )13564.2714285714113.804798865856119.188923171508
Trimmed Mean ( 23 / 24 )13576.4884615385110.836153685994122.491515719695
Trimmed Mean ( 24 / 24 )13584.4458333333109.098335010869124.515610911752
Median13584.4
Midrange13620.05
Midmean - Weighted Average at Xnp13516.0972972973
Midmean - Weighted Average at X(n+1)p13552.6833333333
Midmean - Empirical Distribution Function13516.0972972973
Midmean - Empirical Distribution Function - Averaging13552.6833333333
Midmean - Empirical Distribution Function - Interpolation13552.6833333333
Midmean - Closest Observation13516.0972972973
Midmean - True Basic - Statistics Graphics Toolkit13552.6833333333
Midmean - MS Excel (old versions)13556.1552631579
Number of observations72

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 13673.4805555556 & 208.968984308977 & 65.4330622353901 \tabularnewline
Geometric Mean & 13559.0369216852 &  &  \tabularnewline
Harmonic Mean & 13443.2130938245 &  &  \tabularnewline
Quadratic Mean & 13786.3882539183 &  &  \tabularnewline
Winsorized Mean ( 1 / 24 ) & 13670.4097222222 & 206.923921886721 & 66.0649073223443 \tabularnewline
Winsorized Mean ( 2 / 24 ) & 13694.8625 & 194.791731186126 & 70.3051531839121 \tabularnewline
Winsorized Mean ( 3 / 24 ) & 13686.6375 & 189.658705653174 & 72.1645624062655 \tabularnewline
Winsorized Mean ( 4 / 24 ) & 13690.9152777778 & 187.298667939659 & 73.0967039348538 \tabularnewline
Winsorized Mean ( 5 / 24 ) & 13661.8666666667 & 181.369610007499 & 75.3261070920414 \tabularnewline
Winsorized Mean ( 6 / 24 ) & 13692.5083333333 & 175.908555164124 & 77.838785729086 \tabularnewline
Winsorized Mean ( 7 / 24 ) & 13710.5333333333 & 173.024265080737 & 79.240523442973 \tabularnewline
Winsorized Mean ( 8 / 24 ) & 13702.9888888889 & 171.431562189385 & 79.9327073374669 \tabularnewline
Winsorized Mean ( 9 / 24 ) & 13698.3763888889 & 170.463190034854 & 80.3597327146586 \tabularnewline
Winsorized Mean ( 10 / 24 ) & 13694.8208333333 & 165.569169941045 & 82.713592380814 \tabularnewline
Winsorized Mean ( 11 / 24 ) & 13677.0222222222 & 158.817126495597 & 86.1180561820666 \tabularnewline
Winsorized Mean ( 12 / 24 ) & 13678.4222222222 & 157.056197930490 & 87.092533771103 \tabularnewline
Winsorized Mean ( 13 / 24 ) & 13668.7805555556 & 154.292742315178 & 88.5899125937753 \tabularnewline
Winsorized Mean ( 14 / 24 ) & 13636.0944444444 & 148.441892369922 & 91.8614969584387 \tabularnewline
Winsorized Mean ( 15 / 24 ) & 13644.2611111111 & 147.129808169845 & 92.7362121981452 \tabularnewline
Winsorized Mean ( 16 / 24 ) & 13616.1722222222 & 140.358238818789 & 97.0101387479042 \tabularnewline
Winsorized Mean ( 17 / 24 ) & 13585.6666666667 & 135.529610711089 & 100.241316974100 \tabularnewline
Winsorized Mean ( 18 / 24 ) & 13582.9166666667 & 132.557394218989 & 102.468193092475 \tabularnewline
Winsorized Mean ( 19 / 24 ) & 13592.575 & 128.901687476282 & 105.449162583702 \tabularnewline
Winsorized Mean ( 20 / 24 ) & 13463.4361111111 & 104.417051307243 & 128.939056816453 \tabularnewline
Winsorized Mean ( 21 / 24 ) & 13466.8777777778 & 101.641376024325 & 132.494052171774 \tabularnewline
Winsorized Mean ( 22 / 24 ) & 13467.2138888889 & 97.671520579634 & 137.882709401547 \tabularnewline
Winsorized Mean ( 23 / 24 ) & 13515.4819444444 & 88.7050390273929 & 152.364308641708 \tabularnewline
Winsorized Mean ( 24 / 24 ) & 13526.8486111111 & 84.4710845645767 & 160.135846258373 \tabularnewline
Trimmed Mean ( 1 / 24 ) & 13675.0071428571 & 197.567949003326 & 69.2167287854315 \tabularnewline
Trimmed Mean ( 2 / 24 ) & 13679.875 & 186.326633607388 & 73.418784717729 \tabularnewline
Trimmed Mean ( 3 / 24 ) & 13671.7 & 180.818702257944 & 75.609988509357 \tabularnewline
Trimmed Mean ( 4 / 24 ) & 13666.0984375 & 176.577877248517 & 77.3941710617931 \tabularnewline
Trimmed Mean ( 5 / 24 ) & 13658.8935483871 & 172.316141348936 & 79.2664775421601 \tabularnewline
Trimmed Mean ( 6 / 24 ) & 13658.18 & 169.016849923882 & 80.8095761230378 \tabularnewline
Trimmed Mean ( 7 / 24 ) & 13651.0775862069 & 166.454115422526 & 82.0110548276628 \tabularnewline
Trimmed Mean ( 8 / 24 ) & 13640.1571428571 & 163.939891876331 & 83.2021845735186 \tabularnewline
Trimmed Mean ( 9 / 24 ) & 13629.6851851852 & 161.129676680770 & 84.5882984807838 \tabularnewline
Trimmed Mean ( 10 / 24 ) & 13619.1173076923 & 157.771634699796 & 86.3217100691544 \tabularnewline
Trimmed Mean ( 11 / 24 ) & 13608.216 & 154.594677637877 & 88.0251261422848 \tabularnewline
Trimmed Mean ( 12 / 24 ) & 13598.8333333333 & 151.996042616379 & 89.4683381175603 \tabularnewline
Trimmed Mean ( 13 / 24 ) & 13588.4521739130 & 148.928993706940 & 91.2411467753029 \tabularnewline
Trimmed Mean ( 14 / 24 ) & 13578.3409090909 & 145.478736860848 & 93.33557055887 \tabularnewline
Trimmed Mean ( 15 / 24 ) & 13571.2690476190 & 142.234946948446 & 95.414448690574 \tabularnewline
Trimmed Mean ( 16 / 24 ) & 13562.51 & 138.105068177856 & 98.2042887994073 \tabularnewline
Trimmed Mean ( 17 / 24 ) & 13556.1552631579 & 134.15541584389 & 101.048140158072 \tabularnewline
Trimmed Mean ( 18 / 24 ) & 13552.6833333333 & 129.913507582472 & 104.320817638842 \tabularnewline
Trimmed Mean ( 19 / 24 ) & 13549.1264705882 & 124.719718161149 & 108.636602698873 \tabularnewline
Trimmed Mean ( 20 / 24 ) & 13543.98125 & 118.342038657695 & 114.447760099656 \tabularnewline
Trimmed Mean ( 21 / 24 ) & 13553.6466666667 & 116.335302133984 & 116.505019697777 \tabularnewline
Trimmed Mean ( 22 / 24 ) & 13564.2714285714 & 113.804798865856 & 119.188923171508 \tabularnewline
Trimmed Mean ( 23 / 24 ) & 13576.4884615385 & 110.836153685994 & 122.491515719695 \tabularnewline
Trimmed Mean ( 24 / 24 ) & 13584.4458333333 & 109.098335010869 & 124.515610911752 \tabularnewline
Median & 13584.4 &  &  \tabularnewline
Midrange & 13620.05 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 13516.0972972973 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 13552.6833333333 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 13516.0972972973 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 13552.6833333333 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 13552.6833333333 &  &  \tabularnewline
Midmean - Closest Observation & 13516.0972972973 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 13552.6833333333 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 13556.1552631579 &  &  \tabularnewline
Number of observations & 72 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=30202&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]13673.4805555556[/C][C]208.968984308977[/C][C]65.4330622353901[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]13559.0369216852[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]13443.2130938245[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]13786.3882539183[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 24 )[/C][C]13670.4097222222[/C][C]206.923921886721[/C][C]66.0649073223443[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 24 )[/C][C]13694.8625[/C][C]194.791731186126[/C][C]70.3051531839121[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 24 )[/C][C]13686.6375[/C][C]189.658705653174[/C][C]72.1645624062655[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 24 )[/C][C]13690.9152777778[/C][C]187.298667939659[/C][C]73.0967039348538[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 24 )[/C][C]13661.8666666667[/C][C]181.369610007499[/C][C]75.3261070920414[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 24 )[/C][C]13692.5083333333[/C][C]175.908555164124[/C][C]77.838785729086[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 24 )[/C][C]13710.5333333333[/C][C]173.024265080737[/C][C]79.240523442973[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 24 )[/C][C]13702.9888888889[/C][C]171.431562189385[/C][C]79.9327073374669[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 24 )[/C][C]13698.3763888889[/C][C]170.463190034854[/C][C]80.3597327146586[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 24 )[/C][C]13694.8208333333[/C][C]165.569169941045[/C][C]82.713592380814[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 24 )[/C][C]13677.0222222222[/C][C]158.817126495597[/C][C]86.1180561820666[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 24 )[/C][C]13678.4222222222[/C][C]157.056197930490[/C][C]87.092533771103[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 24 )[/C][C]13668.7805555556[/C][C]154.292742315178[/C][C]88.5899125937753[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 24 )[/C][C]13636.0944444444[/C][C]148.441892369922[/C][C]91.8614969584387[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 24 )[/C][C]13644.2611111111[/C][C]147.129808169845[/C][C]92.7362121981452[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 24 )[/C][C]13616.1722222222[/C][C]140.358238818789[/C][C]97.0101387479042[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 24 )[/C][C]13585.6666666667[/C][C]135.529610711089[/C][C]100.241316974100[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 24 )[/C][C]13582.9166666667[/C][C]132.557394218989[/C][C]102.468193092475[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 24 )[/C][C]13592.575[/C][C]128.901687476282[/C][C]105.449162583702[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 24 )[/C][C]13463.4361111111[/C][C]104.417051307243[/C][C]128.939056816453[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 24 )[/C][C]13466.8777777778[/C][C]101.641376024325[/C][C]132.494052171774[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 24 )[/C][C]13467.2138888889[/C][C]97.671520579634[/C][C]137.882709401547[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 24 )[/C][C]13515.4819444444[/C][C]88.7050390273929[/C][C]152.364308641708[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 24 )[/C][C]13526.8486111111[/C][C]84.4710845645767[/C][C]160.135846258373[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 24 )[/C][C]13675.0071428571[/C][C]197.567949003326[/C][C]69.2167287854315[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 24 )[/C][C]13679.875[/C][C]186.326633607388[/C][C]73.418784717729[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 24 )[/C][C]13671.7[/C][C]180.818702257944[/C][C]75.609988509357[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 24 )[/C][C]13666.0984375[/C][C]176.577877248517[/C][C]77.3941710617931[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 24 )[/C][C]13658.8935483871[/C][C]172.316141348936[/C][C]79.2664775421601[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 24 )[/C][C]13658.18[/C][C]169.016849923882[/C][C]80.8095761230378[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 24 )[/C][C]13651.0775862069[/C][C]166.454115422526[/C][C]82.0110548276628[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 24 )[/C][C]13640.1571428571[/C][C]163.939891876331[/C][C]83.2021845735186[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 24 )[/C][C]13629.6851851852[/C][C]161.129676680770[/C][C]84.5882984807838[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 24 )[/C][C]13619.1173076923[/C][C]157.771634699796[/C][C]86.3217100691544[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 24 )[/C][C]13608.216[/C][C]154.594677637877[/C][C]88.0251261422848[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 24 )[/C][C]13598.8333333333[/C][C]151.996042616379[/C][C]89.4683381175603[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 24 )[/C][C]13588.4521739130[/C][C]148.928993706940[/C][C]91.2411467753029[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 24 )[/C][C]13578.3409090909[/C][C]145.478736860848[/C][C]93.33557055887[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 24 )[/C][C]13571.2690476190[/C][C]142.234946948446[/C][C]95.414448690574[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 24 )[/C][C]13562.51[/C][C]138.105068177856[/C][C]98.2042887994073[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 24 )[/C][C]13556.1552631579[/C][C]134.15541584389[/C][C]101.048140158072[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 24 )[/C][C]13552.6833333333[/C][C]129.913507582472[/C][C]104.320817638842[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 24 )[/C][C]13549.1264705882[/C][C]124.719718161149[/C][C]108.636602698873[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 24 )[/C][C]13543.98125[/C][C]118.342038657695[/C][C]114.447760099656[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 24 )[/C][C]13553.6466666667[/C][C]116.335302133984[/C][C]116.505019697777[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 24 )[/C][C]13564.2714285714[/C][C]113.804798865856[/C][C]119.188923171508[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 24 )[/C][C]13576.4884615385[/C][C]110.836153685994[/C][C]122.491515719695[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 24 )[/C][C]13584.4458333333[/C][C]109.098335010869[/C][C]124.515610911752[/C][/ROW]
[ROW][C]Median[/C][C]13584.4[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]13620.05[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]13516.0972972973[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]13552.6833333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]13516.0972972973[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]13552.6833333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]13552.6833333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]13516.0972972973[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]13552.6833333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]13556.1552631579[/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=30202&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=30202&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 Mean13673.4805555556208.96898430897765.4330622353901
Geometric Mean13559.0369216852
Harmonic Mean13443.2130938245
Quadratic Mean13786.3882539183
Winsorized Mean ( 1 / 24 )13670.4097222222206.92392188672166.0649073223443
Winsorized Mean ( 2 / 24 )13694.8625194.79173118612670.3051531839121
Winsorized Mean ( 3 / 24 )13686.6375189.65870565317472.1645624062655
Winsorized Mean ( 4 / 24 )13690.9152777778187.29866793965973.0967039348538
Winsorized Mean ( 5 / 24 )13661.8666666667181.36961000749975.3261070920414
Winsorized Mean ( 6 / 24 )13692.5083333333175.90855516412477.838785729086
Winsorized Mean ( 7 / 24 )13710.5333333333173.02426508073779.240523442973
Winsorized Mean ( 8 / 24 )13702.9888888889171.43156218938579.9327073374669
Winsorized Mean ( 9 / 24 )13698.3763888889170.46319003485480.3597327146586
Winsorized Mean ( 10 / 24 )13694.8208333333165.56916994104582.713592380814
Winsorized Mean ( 11 / 24 )13677.0222222222158.81712649559786.1180561820666
Winsorized Mean ( 12 / 24 )13678.4222222222157.05619793049087.092533771103
Winsorized Mean ( 13 / 24 )13668.7805555556154.29274231517888.5899125937753
Winsorized Mean ( 14 / 24 )13636.0944444444148.44189236992291.8614969584387
Winsorized Mean ( 15 / 24 )13644.2611111111147.12980816984592.7362121981452
Winsorized Mean ( 16 / 24 )13616.1722222222140.35823881878997.0101387479042
Winsorized Mean ( 17 / 24 )13585.6666666667135.529610711089100.241316974100
Winsorized Mean ( 18 / 24 )13582.9166666667132.557394218989102.468193092475
Winsorized Mean ( 19 / 24 )13592.575128.901687476282105.449162583702
Winsorized Mean ( 20 / 24 )13463.4361111111104.417051307243128.939056816453
Winsorized Mean ( 21 / 24 )13466.8777777778101.641376024325132.494052171774
Winsorized Mean ( 22 / 24 )13467.213888888997.671520579634137.882709401547
Winsorized Mean ( 23 / 24 )13515.481944444488.7050390273929152.364308641708
Winsorized Mean ( 24 / 24 )13526.848611111184.4710845645767160.135846258373
Trimmed Mean ( 1 / 24 )13675.0071428571197.56794900332669.2167287854315
Trimmed Mean ( 2 / 24 )13679.875186.32663360738873.418784717729
Trimmed Mean ( 3 / 24 )13671.7180.81870225794475.609988509357
Trimmed Mean ( 4 / 24 )13666.0984375176.57787724851777.3941710617931
Trimmed Mean ( 5 / 24 )13658.8935483871172.31614134893679.2664775421601
Trimmed Mean ( 6 / 24 )13658.18169.01684992388280.8095761230378
Trimmed Mean ( 7 / 24 )13651.0775862069166.45411542252682.0110548276628
Trimmed Mean ( 8 / 24 )13640.1571428571163.93989187633183.2021845735186
Trimmed Mean ( 9 / 24 )13629.6851851852161.12967668077084.5882984807838
Trimmed Mean ( 10 / 24 )13619.1173076923157.77163469979686.3217100691544
Trimmed Mean ( 11 / 24 )13608.216154.59467763787788.0251261422848
Trimmed Mean ( 12 / 24 )13598.8333333333151.99604261637989.4683381175603
Trimmed Mean ( 13 / 24 )13588.4521739130148.92899370694091.2411467753029
Trimmed Mean ( 14 / 24 )13578.3409090909145.47873686084893.33557055887
Trimmed Mean ( 15 / 24 )13571.2690476190142.23494694844695.414448690574
Trimmed Mean ( 16 / 24 )13562.51138.10506817785698.2042887994073
Trimmed Mean ( 17 / 24 )13556.1552631579134.15541584389101.048140158072
Trimmed Mean ( 18 / 24 )13552.6833333333129.913507582472104.320817638842
Trimmed Mean ( 19 / 24 )13549.1264705882124.719718161149108.636602698873
Trimmed Mean ( 20 / 24 )13543.98125118.342038657695114.447760099656
Trimmed Mean ( 21 / 24 )13553.6466666667116.335302133984116.505019697777
Trimmed Mean ( 22 / 24 )13564.2714285714113.804798865856119.188923171508
Trimmed Mean ( 23 / 24 )13576.4884615385110.836153685994122.491515719695
Trimmed Mean ( 24 / 24 )13584.4458333333109.098335010869124.515610911752
Median13584.4
Midrange13620.05
Midmean - Weighted Average at Xnp13516.0972972973
Midmean - Weighted Average at X(n+1)p13552.6833333333
Midmean - Empirical Distribution Function13516.0972972973
Midmean - Empirical Distribution Function - Averaging13552.6833333333
Midmean - Empirical Distribution Function - Interpolation13552.6833333333
Midmean - Closest Observation13516.0972972973
Midmean - True Basic - Statistics Graphics Toolkit13552.6833333333
Midmean - MS Excel (old versions)13556.1552631579
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')