Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationSun, 25 Oct 2009 13:45:54 -0600
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2009/Oct/25/t125650000521h85107zodhk8c.htm/, Retrieved Mon, 29 Apr 2024 11:12:50 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=50381, Retrieved Mon, 29 Apr 2024 11:12:50 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsKDGP1W52
Estimated Impact161
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [Opgave 5: oefenin...] [2009-10-25 19:45:54] [712c3abbba27b8add982e356cd7e4c7f] [Current]
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Dataseries X:
5.2100
5.2300
5.2300
5.2300
5.2200
5.2100
5.2300
5.2500
5.2300
5.2300
5.2500
5.2400
5.2600
5.2700
5.2600
5.2900
5.2900
5.2900
5.2900
5.3100
5.3300
5.3400
5.3400
5.3700
5.4100
5.4100
5.3800
5.4400
5.4400
5.4600
5.4600
5.4500
5.4600
5.4600
5.4800
5.4700
5.4800
5.5100
5.5500
5.5800
5.5900
5.6000
5.6000
5.6700
5.7100
5.7000
5.7300
5.7200
5.7500
5.7500
5.7700
5.8300
5.8500
5.8700
5.8600
5.8700
5.9300
5.9700
5.9800
5.9900
5.9900
6.0300
6.0600
6.0700
6.0800
6.0800
6.1000
6.1300
6.1400
6.1400
6.1600
6.2000
6.1900
6.3200
6.3200
6.3300
6.3200
6.3300
6.3800
6.4200
6.4600
6.4700
6.4200
6.4800
6.4700
6.4900
6.4800
6.5100
6.5100
6.5200
6.5700
6.5900
6.6200
6.6300
6.6100
6.6400
6.6900
6.6900
6.7500
6.7700
6.8100
6.8100
6.8100
6.8700
6.8600
6.8800
6.8800
6.9200
6.9200
6.9900
7.0200
7.0500
7.0600
7.0600
7.0900
7.1200
7.2300
7.3100
7.4500
7.4900
7.5400
7.5500
7.5800
7.6000
7.6300
7.6400
7.6300
7.6600
7.6400
7.6900
7.7000
7.6800




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'George Udny Yule' @ 72.249.76.132

\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 & 3 seconds \tabularnewline
R Server & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=50381&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]3 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'George Udny Yule' @ 72.249.76.132[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=50381&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=50381&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 time3 seconds
R Server'George Udny Yule' @ 72.249.76.132







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean6.188712121212120.066165104239344893.5343817917245
Geometric Mean6.14350917569362
Harmonic Mean6.09962007244515
Quadratic Mean6.23487387785248
Winsorized Mean ( 1 / 44 )6.188636363636360.066151937207389993.5518538819907
Winsorized Mean ( 2 / 44 )6.188636363636360.066108737482218393.6129867145165
Winsorized Mean ( 3 / 44 )6.188409090909090.066005613632933493.7557997009727
Winsorized Mean ( 4 / 44 )6.187803030303030.065903067983065993.8924881599293
Winsorized Mean ( 5 / 44 )6.187803030303030.065903067983065993.8924881599293
Winsorized Mean ( 6 / 44 )6.187348484848480.065826816630804893.994344577693
Winsorized Mean ( 7 / 44 )6.187348484848480.065826816630804893.994344577693
Winsorized Mean ( 8 / 44 )6.18553030303030.065524919585415994.3996626347183
Winsorized Mean ( 9 / 44 )6.184848484848480.065225589853154594.8224232049526
Winsorized Mean ( 10 / 44 )6.183333333333330.064773459446400495.4609092393775
Winsorized Mean ( 11 / 44 )6.18250.064639552474929495.6457735749006
Winsorized Mean ( 12 / 44 )6.178863636363640.063818706448070496.8190046501712
Winsorized Mean ( 13 / 44 )6.174924242424240.063206451199156297.6945252466045
Winsorized Mean ( 14 / 44 )6.161136363636360.060874349428246101.210713896805
Winsorized Mean ( 15 / 44 )6.154318181818180.059336799781047103.718404169548
Winsorized Mean ( 16 / 44 )6.140984848484850.0575476006944814106.711396728548
Winsorized Mean ( 17 / 44 )6.137121212121210.0570504006188242107.573674252100
Winsorized Mean ( 18 / 44 )6.13303030303030.056533562709504108.484765669991
Winsorized Mean ( 19 / 44 )6.135909090909090.0562082553400489109.163841748655
Winsorized Mean ( 20 / 44 )6.137424242424240.0556807201837984110.225302800772
Winsorized Mean ( 21 / 44 )6.134242424242420.0549124090884376111.709584883867
Winsorized Mean ( 22 / 44 )6.129242424242420.0543020422106784112.873147578179
Winsorized Mean ( 23 / 44 )6.122272727272730.0522760461185803117.114303430395
Winsorized Mean ( 24 / 44 )6.124090909090910.0520770255680288117.596787494918
Winsorized Mean ( 25 / 44 )6.122196969696970.0505865794163595121.024134075313
Winsorized Mean ( 26 / 44 )6.122196969696970.0505865794163595121.024134075313
Winsorized Mean ( 27 / 44 )6.126287878787880.0496995838887198123.266381716696
Winsorized Mean ( 28 / 44 )6.124166666666670.0494579736714768123.825668785913
Winsorized Mean ( 29 / 44 )6.115378787878790.0479948872121639127.417296780914
Winsorized Mean ( 30 / 44 )6.117651515151510.0477551658172277128.104497397527
Winsorized Mean ( 31 / 44 )6.117651515151520.0477551658172277128.104497397527
Winsorized Mean ( 32 / 44 )6.107954545454550.0466936827350361130.809012861851
Winsorized Mean ( 33 / 44 )6.102954545454550.0461555490216129132.225803285251
Winsorized Mean ( 34 / 44 )6.090075757575760.0442537130615395137.617283076493
Winsorized Mean ( 35 / 44 )6.092727272727270.043970882174123138.562770894619
Winsorized Mean ( 36 / 44 )6.079090909090910.0425779081467091142.775706315689
Winsorized Mean ( 37 / 44 )6.084696969696970.0413988067519473146.977593005401
Winsorized Mean ( 38 / 44 )6.093333333333330.039900214807009152.714298978234
Winsorized Mean ( 39 / 44 )6.099242424242420.0386876465431943157.653488108476
Winsorized Mean ( 40 / 44 )6.096212121212120.0377695463844282161.405489469301
Winsorized Mean ( 41 / 44 )6.093106060606060.0368349553029989165.416409779381
Winsorized Mean ( 42 / 44 )6.077196969696970.0352862971495618172.22540931225
Winsorized Mean ( 43 / 44 )6.096742424242420.0326571178949298186.689543267655
Winsorized Mean ( 44 / 44 )6.106742424242430.0316680051725568192.836346683892
Trimmed Mean ( 1 / 44 )6.184615384615380.065731619803058794.0888936427457
Trimmed Mean ( 2 / 44 )6.180468750.065263214354047494.7006489210213
Trimmed Mean ( 3 / 44 )6.176190476190480.064766036282779595.3615634161118
Trimmed Mean ( 4 / 44 )6.171854838709680.064252583847022696.0561345424504
Trimmed Mean ( 5 / 44 )6.167540983606560.063711613107041996.8040312092628
Trimmed Mean ( 6 / 44 )6.163083333333330.063108083426326397.6591745260058
Trimmed Mean ( 7 / 44 )6.15855932203390.062452099613275398.612526402952
Trimmed Mean ( 8 / 44 )6.153879310344830.061720190232489599.7060975859634
Trimmed Mean ( 9 / 44 )6.149298245614030.0609592775897995100.875510484117
Trimmed Mean ( 10 / 44 )6.144642857142860.060159714573659102.138829957702
Trimmed Mean ( 11 / 44 )6.140.059337459599816103.475949954875
Trimmed Mean ( 12 / 44 )6.135277777777780.0584363366423271104.990800763746
Trimmed Mean ( 13 / 44 )6.130754716981130.0575463714907878106.535904144062
Trimmed Mean ( 14 / 44 )6.126442307692310.0566336770895214108.176664884538
Trimmed Mean ( 15 / 44 )6.123235294117650.055926248993078109.487680728874
Trimmed Mean ( 16 / 44 )6.12050.0553246387838697110.628828936602
Trimmed Mean ( 17 / 44 )6.118775510204080.054863460245081111.527335003495
Trimmed Mean ( 18 / 44 )6.117291666666670.0543932801832503112.464106706887
Trimmed Mean ( 19 / 44 )6.116063829787230.0539128358614811113.443556289662
Trimmed Mean ( 20 / 44 )6.11456521739130.0533946563111579114.516426171162
Trimmed Mean ( 21 / 44 )6.112888888888890.0528555954336937115.652635047076
Trimmed Mean ( 22 / 44 )6.111363636363640.0523197961724848116.807864010327
Trimmed Mean ( 23 / 44 )6.110116279069770.0517677900020619118.029305072254
Trimmed Mean ( 24 / 44 )6.109285714285710.0513533945666072118.965567239411
Trimmed Mean ( 25 / 44 )6.108292682926830.0508837303683742120.044120953902
Trimmed Mean ( 26 / 44 )6.1073750.0504943109184251120.951744640433
Trimmed Mean ( 27 / 44 )6.106410256410260.0500259587489375122.064832121582
Trimmed Mean ( 28 / 44 )6.105131578947370.0495653010422146123.173499415401
Trimmed Mean ( 29 / 44 )6.103918918918920.0490392016786551124.470193436606
Trimmed Mean ( 30 / 44 )6.103194444444440.0485807277057129125.629951066516
Trimmed Mean ( 31 / 44 )6.102285714285710.0480498237915653126.999127837737
Trimmed Mean ( 32 / 44 )6.101323529411760.0474040338335745128.708952297862
Trimmed Mean ( 33 / 44 )6.100909090909090.0467586808178843130.476501564938
Trimmed Mean ( 34 / 44 )6.100781250.0460424368000124132.503439739713
Trimmed Mean ( 35 / 44 )6.101451612903230.0454205606316194134.332371244571
Trimmed Mean ( 36 / 44 )6.1020.0446890069774745136.543647145163
Trimmed Mean ( 37 / 44 )6.103448275862070.0439755691153191138.791797324026
Trimmed Mean ( 38 / 44 )6.104642857142860.0432592338958305141.117683032552
Trimmed Mean ( 39 / 44 )6.105370370370370.0425864623547014143.364112273964
Trimmed Mean ( 40 / 44 )6.105769230769230.0419179567078184145.659991810393
Trimmed Mean ( 41 / 44 )6.10640.0412030908291787148.202474064777
Trimmed Mean ( 42 / 44 )6.107291666666670.0404317781759067151.051770221326
Trimmed Mean ( 43 / 44 )6.109347826086960.0396852376134507153.945098819725
Trimmed Mean ( 44 / 44 )6.110227272727270.0391944367578578155.895269282120
Median6.09
Midrange6.455
Midmean - Weighted Average at Xnp6.07304347826087
Midmean - Weighted Average at X(n+1)p6.07304347826087
Midmean - Empirical Distribution Function6.07304347826087
Midmean - Empirical Distribution Function - Averaging6.07304347826087
Midmean - Empirical Distribution Function - Interpolation6.07304347826087
Midmean - Closest Observation6.07304347826087
Midmean - True Basic - Statistics Graphics Toolkit6.07304347826087
Midmean - MS Excel (old versions)6.083
Number of observations132

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 6.18871212121212 & 0.0661651042393448 & 93.5343817917245 \tabularnewline
Geometric Mean & 6.14350917569362 &  &  \tabularnewline
Harmonic Mean & 6.09962007244515 &  &  \tabularnewline
Quadratic Mean & 6.23487387785248 &  &  \tabularnewline
Winsorized Mean ( 1 / 44 ) & 6.18863636363636 & 0.0661519372073899 & 93.5518538819907 \tabularnewline
Winsorized Mean ( 2 / 44 ) & 6.18863636363636 & 0.0661087374822183 & 93.6129867145165 \tabularnewline
Winsorized Mean ( 3 / 44 ) & 6.18840909090909 & 0.0660056136329334 & 93.7557997009727 \tabularnewline
Winsorized Mean ( 4 / 44 ) & 6.18780303030303 & 0.0659030679830659 & 93.8924881599293 \tabularnewline
Winsorized Mean ( 5 / 44 ) & 6.18780303030303 & 0.0659030679830659 & 93.8924881599293 \tabularnewline
Winsorized Mean ( 6 / 44 ) & 6.18734848484848 & 0.0658268166308048 & 93.994344577693 \tabularnewline
Winsorized Mean ( 7 / 44 ) & 6.18734848484848 & 0.0658268166308048 & 93.994344577693 \tabularnewline
Winsorized Mean ( 8 / 44 ) & 6.1855303030303 & 0.0655249195854159 & 94.3996626347183 \tabularnewline
Winsorized Mean ( 9 / 44 ) & 6.18484848484848 & 0.0652255898531545 & 94.8224232049526 \tabularnewline
Winsorized Mean ( 10 / 44 ) & 6.18333333333333 & 0.0647734594464004 & 95.4609092393775 \tabularnewline
Winsorized Mean ( 11 / 44 ) & 6.1825 & 0.0646395524749294 & 95.6457735749006 \tabularnewline
Winsorized Mean ( 12 / 44 ) & 6.17886363636364 & 0.0638187064480704 & 96.8190046501712 \tabularnewline
Winsorized Mean ( 13 / 44 ) & 6.17492424242424 & 0.0632064511991562 & 97.6945252466045 \tabularnewline
Winsorized Mean ( 14 / 44 ) & 6.16113636363636 & 0.060874349428246 & 101.210713896805 \tabularnewline
Winsorized Mean ( 15 / 44 ) & 6.15431818181818 & 0.059336799781047 & 103.718404169548 \tabularnewline
Winsorized Mean ( 16 / 44 ) & 6.14098484848485 & 0.0575476006944814 & 106.711396728548 \tabularnewline
Winsorized Mean ( 17 / 44 ) & 6.13712121212121 & 0.0570504006188242 & 107.573674252100 \tabularnewline
Winsorized Mean ( 18 / 44 ) & 6.1330303030303 & 0.056533562709504 & 108.484765669991 \tabularnewline
Winsorized Mean ( 19 / 44 ) & 6.13590909090909 & 0.0562082553400489 & 109.163841748655 \tabularnewline
Winsorized Mean ( 20 / 44 ) & 6.13742424242424 & 0.0556807201837984 & 110.225302800772 \tabularnewline
Winsorized Mean ( 21 / 44 ) & 6.13424242424242 & 0.0549124090884376 & 111.709584883867 \tabularnewline
Winsorized Mean ( 22 / 44 ) & 6.12924242424242 & 0.0543020422106784 & 112.873147578179 \tabularnewline
Winsorized Mean ( 23 / 44 ) & 6.12227272727273 & 0.0522760461185803 & 117.114303430395 \tabularnewline
Winsorized Mean ( 24 / 44 ) & 6.12409090909091 & 0.0520770255680288 & 117.596787494918 \tabularnewline
Winsorized Mean ( 25 / 44 ) & 6.12219696969697 & 0.0505865794163595 & 121.024134075313 \tabularnewline
Winsorized Mean ( 26 / 44 ) & 6.12219696969697 & 0.0505865794163595 & 121.024134075313 \tabularnewline
Winsorized Mean ( 27 / 44 ) & 6.12628787878788 & 0.0496995838887198 & 123.266381716696 \tabularnewline
Winsorized Mean ( 28 / 44 ) & 6.12416666666667 & 0.0494579736714768 & 123.825668785913 \tabularnewline
Winsorized Mean ( 29 / 44 ) & 6.11537878787879 & 0.0479948872121639 & 127.417296780914 \tabularnewline
Winsorized Mean ( 30 / 44 ) & 6.11765151515151 & 0.0477551658172277 & 128.104497397527 \tabularnewline
Winsorized Mean ( 31 / 44 ) & 6.11765151515152 & 0.0477551658172277 & 128.104497397527 \tabularnewline
Winsorized Mean ( 32 / 44 ) & 6.10795454545455 & 0.0466936827350361 & 130.809012861851 \tabularnewline
Winsorized Mean ( 33 / 44 ) & 6.10295454545455 & 0.0461555490216129 & 132.225803285251 \tabularnewline
Winsorized Mean ( 34 / 44 ) & 6.09007575757576 & 0.0442537130615395 & 137.617283076493 \tabularnewline
Winsorized Mean ( 35 / 44 ) & 6.09272727272727 & 0.043970882174123 & 138.562770894619 \tabularnewline
Winsorized Mean ( 36 / 44 ) & 6.07909090909091 & 0.0425779081467091 & 142.775706315689 \tabularnewline
Winsorized Mean ( 37 / 44 ) & 6.08469696969697 & 0.0413988067519473 & 146.977593005401 \tabularnewline
Winsorized Mean ( 38 / 44 ) & 6.09333333333333 & 0.039900214807009 & 152.714298978234 \tabularnewline
Winsorized Mean ( 39 / 44 ) & 6.09924242424242 & 0.0386876465431943 & 157.653488108476 \tabularnewline
Winsorized Mean ( 40 / 44 ) & 6.09621212121212 & 0.0377695463844282 & 161.405489469301 \tabularnewline
Winsorized Mean ( 41 / 44 ) & 6.09310606060606 & 0.0368349553029989 & 165.416409779381 \tabularnewline
Winsorized Mean ( 42 / 44 ) & 6.07719696969697 & 0.0352862971495618 & 172.22540931225 \tabularnewline
Winsorized Mean ( 43 / 44 ) & 6.09674242424242 & 0.0326571178949298 & 186.689543267655 \tabularnewline
Winsorized Mean ( 44 / 44 ) & 6.10674242424243 & 0.0316680051725568 & 192.836346683892 \tabularnewline
Trimmed Mean ( 1 / 44 ) & 6.18461538461538 & 0.0657316198030587 & 94.0888936427457 \tabularnewline
Trimmed Mean ( 2 / 44 ) & 6.18046875 & 0.0652632143540474 & 94.7006489210213 \tabularnewline
Trimmed Mean ( 3 / 44 ) & 6.17619047619048 & 0.0647660362827795 & 95.3615634161118 \tabularnewline
Trimmed Mean ( 4 / 44 ) & 6.17185483870968 & 0.0642525838470226 & 96.0561345424504 \tabularnewline
Trimmed Mean ( 5 / 44 ) & 6.16754098360656 & 0.0637116131070419 & 96.8040312092628 \tabularnewline
Trimmed Mean ( 6 / 44 ) & 6.16308333333333 & 0.0631080834263263 & 97.6591745260058 \tabularnewline
Trimmed Mean ( 7 / 44 ) & 6.1585593220339 & 0.0624520996132753 & 98.612526402952 \tabularnewline
Trimmed Mean ( 8 / 44 ) & 6.15387931034483 & 0.0617201902324895 & 99.7060975859634 \tabularnewline
Trimmed Mean ( 9 / 44 ) & 6.14929824561403 & 0.0609592775897995 & 100.875510484117 \tabularnewline
Trimmed Mean ( 10 / 44 ) & 6.14464285714286 & 0.060159714573659 & 102.138829957702 \tabularnewline
Trimmed Mean ( 11 / 44 ) & 6.14 & 0.059337459599816 & 103.475949954875 \tabularnewline
Trimmed Mean ( 12 / 44 ) & 6.13527777777778 & 0.0584363366423271 & 104.990800763746 \tabularnewline
Trimmed Mean ( 13 / 44 ) & 6.13075471698113 & 0.0575463714907878 & 106.535904144062 \tabularnewline
Trimmed Mean ( 14 / 44 ) & 6.12644230769231 & 0.0566336770895214 & 108.176664884538 \tabularnewline
Trimmed Mean ( 15 / 44 ) & 6.12323529411765 & 0.055926248993078 & 109.487680728874 \tabularnewline
Trimmed Mean ( 16 / 44 ) & 6.1205 & 0.0553246387838697 & 110.628828936602 \tabularnewline
Trimmed Mean ( 17 / 44 ) & 6.11877551020408 & 0.054863460245081 & 111.527335003495 \tabularnewline
Trimmed Mean ( 18 / 44 ) & 6.11729166666667 & 0.0543932801832503 & 112.464106706887 \tabularnewline
Trimmed Mean ( 19 / 44 ) & 6.11606382978723 & 0.0539128358614811 & 113.443556289662 \tabularnewline
Trimmed Mean ( 20 / 44 ) & 6.1145652173913 & 0.0533946563111579 & 114.516426171162 \tabularnewline
Trimmed Mean ( 21 / 44 ) & 6.11288888888889 & 0.0528555954336937 & 115.652635047076 \tabularnewline
Trimmed Mean ( 22 / 44 ) & 6.11136363636364 & 0.0523197961724848 & 116.807864010327 \tabularnewline
Trimmed Mean ( 23 / 44 ) & 6.11011627906977 & 0.0517677900020619 & 118.029305072254 \tabularnewline
Trimmed Mean ( 24 / 44 ) & 6.10928571428571 & 0.0513533945666072 & 118.965567239411 \tabularnewline
Trimmed Mean ( 25 / 44 ) & 6.10829268292683 & 0.0508837303683742 & 120.044120953902 \tabularnewline
Trimmed Mean ( 26 / 44 ) & 6.107375 & 0.0504943109184251 & 120.951744640433 \tabularnewline
Trimmed Mean ( 27 / 44 ) & 6.10641025641026 & 0.0500259587489375 & 122.064832121582 \tabularnewline
Trimmed Mean ( 28 / 44 ) & 6.10513157894737 & 0.0495653010422146 & 123.173499415401 \tabularnewline
Trimmed Mean ( 29 / 44 ) & 6.10391891891892 & 0.0490392016786551 & 124.470193436606 \tabularnewline
Trimmed Mean ( 30 / 44 ) & 6.10319444444444 & 0.0485807277057129 & 125.629951066516 \tabularnewline
Trimmed Mean ( 31 / 44 ) & 6.10228571428571 & 0.0480498237915653 & 126.999127837737 \tabularnewline
Trimmed Mean ( 32 / 44 ) & 6.10132352941176 & 0.0474040338335745 & 128.708952297862 \tabularnewline
Trimmed Mean ( 33 / 44 ) & 6.10090909090909 & 0.0467586808178843 & 130.476501564938 \tabularnewline
Trimmed Mean ( 34 / 44 ) & 6.10078125 & 0.0460424368000124 & 132.503439739713 \tabularnewline
Trimmed Mean ( 35 / 44 ) & 6.10145161290323 & 0.0454205606316194 & 134.332371244571 \tabularnewline
Trimmed Mean ( 36 / 44 ) & 6.102 & 0.0446890069774745 & 136.543647145163 \tabularnewline
Trimmed Mean ( 37 / 44 ) & 6.10344827586207 & 0.0439755691153191 & 138.791797324026 \tabularnewline
Trimmed Mean ( 38 / 44 ) & 6.10464285714286 & 0.0432592338958305 & 141.117683032552 \tabularnewline
Trimmed Mean ( 39 / 44 ) & 6.10537037037037 & 0.0425864623547014 & 143.364112273964 \tabularnewline
Trimmed Mean ( 40 / 44 ) & 6.10576923076923 & 0.0419179567078184 & 145.659991810393 \tabularnewline
Trimmed Mean ( 41 / 44 ) & 6.1064 & 0.0412030908291787 & 148.202474064777 \tabularnewline
Trimmed Mean ( 42 / 44 ) & 6.10729166666667 & 0.0404317781759067 & 151.051770221326 \tabularnewline
Trimmed Mean ( 43 / 44 ) & 6.10934782608696 & 0.0396852376134507 & 153.945098819725 \tabularnewline
Trimmed Mean ( 44 / 44 ) & 6.11022727272727 & 0.0391944367578578 & 155.895269282120 \tabularnewline
Median & 6.09 &  &  \tabularnewline
Midrange & 6.455 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 6.07304347826087 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 6.07304347826087 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 6.07304347826087 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 6.07304347826087 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 6.07304347826087 &  &  \tabularnewline
Midmean - Closest Observation & 6.07304347826087 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 6.07304347826087 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 6.083 &  &  \tabularnewline
Number of observations & 132 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=50381&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]6.18871212121212[/C][C]0.0661651042393448[/C][C]93.5343817917245[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]6.14350917569362[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]6.09962007244515[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]6.23487387785248[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 44 )[/C][C]6.18863636363636[/C][C]0.0661519372073899[/C][C]93.5518538819907[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 44 )[/C][C]6.18863636363636[/C][C]0.0661087374822183[/C][C]93.6129867145165[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 44 )[/C][C]6.18840909090909[/C][C]0.0660056136329334[/C][C]93.7557997009727[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 44 )[/C][C]6.18780303030303[/C][C]0.0659030679830659[/C][C]93.8924881599293[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 44 )[/C][C]6.18780303030303[/C][C]0.0659030679830659[/C][C]93.8924881599293[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 44 )[/C][C]6.18734848484848[/C][C]0.0658268166308048[/C][C]93.994344577693[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 44 )[/C][C]6.18734848484848[/C][C]0.0658268166308048[/C][C]93.994344577693[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 44 )[/C][C]6.1855303030303[/C][C]0.0655249195854159[/C][C]94.3996626347183[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 44 )[/C][C]6.18484848484848[/C][C]0.0652255898531545[/C][C]94.8224232049526[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 44 )[/C][C]6.18333333333333[/C][C]0.0647734594464004[/C][C]95.4609092393775[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 44 )[/C][C]6.1825[/C][C]0.0646395524749294[/C][C]95.6457735749006[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 44 )[/C][C]6.17886363636364[/C][C]0.0638187064480704[/C][C]96.8190046501712[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 44 )[/C][C]6.17492424242424[/C][C]0.0632064511991562[/C][C]97.6945252466045[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 44 )[/C][C]6.16113636363636[/C][C]0.060874349428246[/C][C]101.210713896805[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 44 )[/C][C]6.15431818181818[/C][C]0.059336799781047[/C][C]103.718404169548[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 44 )[/C][C]6.14098484848485[/C][C]0.0575476006944814[/C][C]106.711396728548[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 44 )[/C][C]6.13712121212121[/C][C]0.0570504006188242[/C][C]107.573674252100[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 44 )[/C][C]6.1330303030303[/C][C]0.056533562709504[/C][C]108.484765669991[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 44 )[/C][C]6.13590909090909[/C][C]0.0562082553400489[/C][C]109.163841748655[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 44 )[/C][C]6.13742424242424[/C][C]0.0556807201837984[/C][C]110.225302800772[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 44 )[/C][C]6.13424242424242[/C][C]0.0549124090884376[/C][C]111.709584883867[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 44 )[/C][C]6.12924242424242[/C][C]0.0543020422106784[/C][C]112.873147578179[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 44 )[/C][C]6.12227272727273[/C][C]0.0522760461185803[/C][C]117.114303430395[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 44 )[/C][C]6.12409090909091[/C][C]0.0520770255680288[/C][C]117.596787494918[/C][/ROW]
[ROW][C]Winsorized Mean ( 25 / 44 )[/C][C]6.12219696969697[/C][C]0.0505865794163595[/C][C]121.024134075313[/C][/ROW]
[ROW][C]Winsorized Mean ( 26 / 44 )[/C][C]6.12219696969697[/C][C]0.0505865794163595[/C][C]121.024134075313[/C][/ROW]
[ROW][C]Winsorized Mean ( 27 / 44 )[/C][C]6.12628787878788[/C][C]0.0496995838887198[/C][C]123.266381716696[/C][/ROW]
[ROW][C]Winsorized Mean ( 28 / 44 )[/C][C]6.12416666666667[/C][C]0.0494579736714768[/C][C]123.825668785913[/C][/ROW]
[ROW][C]Winsorized Mean ( 29 / 44 )[/C][C]6.11537878787879[/C][C]0.0479948872121639[/C][C]127.417296780914[/C][/ROW]
[ROW][C]Winsorized Mean ( 30 / 44 )[/C][C]6.11765151515151[/C][C]0.0477551658172277[/C][C]128.104497397527[/C][/ROW]
[ROW][C]Winsorized Mean ( 31 / 44 )[/C][C]6.11765151515152[/C][C]0.0477551658172277[/C][C]128.104497397527[/C][/ROW]
[ROW][C]Winsorized Mean ( 32 / 44 )[/C][C]6.10795454545455[/C][C]0.0466936827350361[/C][C]130.809012861851[/C][/ROW]
[ROW][C]Winsorized Mean ( 33 / 44 )[/C][C]6.10295454545455[/C][C]0.0461555490216129[/C][C]132.225803285251[/C][/ROW]
[ROW][C]Winsorized Mean ( 34 / 44 )[/C][C]6.09007575757576[/C][C]0.0442537130615395[/C][C]137.617283076493[/C][/ROW]
[ROW][C]Winsorized Mean ( 35 / 44 )[/C][C]6.09272727272727[/C][C]0.043970882174123[/C][C]138.562770894619[/C][/ROW]
[ROW][C]Winsorized Mean ( 36 / 44 )[/C][C]6.07909090909091[/C][C]0.0425779081467091[/C][C]142.775706315689[/C][/ROW]
[ROW][C]Winsorized Mean ( 37 / 44 )[/C][C]6.08469696969697[/C][C]0.0413988067519473[/C][C]146.977593005401[/C][/ROW]
[ROW][C]Winsorized Mean ( 38 / 44 )[/C][C]6.09333333333333[/C][C]0.039900214807009[/C][C]152.714298978234[/C][/ROW]
[ROW][C]Winsorized Mean ( 39 / 44 )[/C][C]6.09924242424242[/C][C]0.0386876465431943[/C][C]157.653488108476[/C][/ROW]
[ROW][C]Winsorized Mean ( 40 / 44 )[/C][C]6.09621212121212[/C][C]0.0377695463844282[/C][C]161.405489469301[/C][/ROW]
[ROW][C]Winsorized Mean ( 41 / 44 )[/C][C]6.09310606060606[/C][C]0.0368349553029989[/C][C]165.416409779381[/C][/ROW]
[ROW][C]Winsorized Mean ( 42 / 44 )[/C][C]6.07719696969697[/C][C]0.0352862971495618[/C][C]172.22540931225[/C][/ROW]
[ROW][C]Winsorized Mean ( 43 / 44 )[/C][C]6.09674242424242[/C][C]0.0326571178949298[/C][C]186.689543267655[/C][/ROW]
[ROW][C]Winsorized Mean ( 44 / 44 )[/C][C]6.10674242424243[/C][C]0.0316680051725568[/C][C]192.836346683892[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 44 )[/C][C]6.18461538461538[/C][C]0.0657316198030587[/C][C]94.0888936427457[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 44 )[/C][C]6.18046875[/C][C]0.0652632143540474[/C][C]94.7006489210213[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 44 )[/C][C]6.17619047619048[/C][C]0.0647660362827795[/C][C]95.3615634161118[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 44 )[/C][C]6.17185483870968[/C][C]0.0642525838470226[/C][C]96.0561345424504[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 44 )[/C][C]6.16754098360656[/C][C]0.0637116131070419[/C][C]96.8040312092628[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 44 )[/C][C]6.16308333333333[/C][C]0.0631080834263263[/C][C]97.6591745260058[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 44 )[/C][C]6.1585593220339[/C][C]0.0624520996132753[/C][C]98.612526402952[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 44 )[/C][C]6.15387931034483[/C][C]0.0617201902324895[/C][C]99.7060975859634[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 44 )[/C][C]6.14929824561403[/C][C]0.0609592775897995[/C][C]100.875510484117[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 44 )[/C][C]6.14464285714286[/C][C]0.060159714573659[/C][C]102.138829957702[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 44 )[/C][C]6.14[/C][C]0.059337459599816[/C][C]103.475949954875[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 44 )[/C][C]6.13527777777778[/C][C]0.0584363366423271[/C][C]104.990800763746[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 44 )[/C][C]6.13075471698113[/C][C]0.0575463714907878[/C][C]106.535904144062[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 44 )[/C][C]6.12644230769231[/C][C]0.0566336770895214[/C][C]108.176664884538[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 44 )[/C][C]6.12323529411765[/C][C]0.055926248993078[/C][C]109.487680728874[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 44 )[/C][C]6.1205[/C][C]0.0553246387838697[/C][C]110.628828936602[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 44 )[/C][C]6.11877551020408[/C][C]0.054863460245081[/C][C]111.527335003495[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 44 )[/C][C]6.11729166666667[/C][C]0.0543932801832503[/C][C]112.464106706887[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 44 )[/C][C]6.11606382978723[/C][C]0.0539128358614811[/C][C]113.443556289662[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 44 )[/C][C]6.1145652173913[/C][C]0.0533946563111579[/C][C]114.516426171162[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 44 )[/C][C]6.11288888888889[/C][C]0.0528555954336937[/C][C]115.652635047076[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 44 )[/C][C]6.11136363636364[/C][C]0.0523197961724848[/C][C]116.807864010327[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 44 )[/C][C]6.11011627906977[/C][C]0.0517677900020619[/C][C]118.029305072254[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 44 )[/C][C]6.10928571428571[/C][C]0.0513533945666072[/C][C]118.965567239411[/C][/ROW]
[ROW][C]Trimmed Mean ( 25 / 44 )[/C][C]6.10829268292683[/C][C]0.0508837303683742[/C][C]120.044120953902[/C][/ROW]
[ROW][C]Trimmed Mean ( 26 / 44 )[/C][C]6.107375[/C][C]0.0504943109184251[/C][C]120.951744640433[/C][/ROW]
[ROW][C]Trimmed Mean ( 27 / 44 )[/C][C]6.10641025641026[/C][C]0.0500259587489375[/C][C]122.064832121582[/C][/ROW]
[ROW][C]Trimmed Mean ( 28 / 44 )[/C][C]6.10513157894737[/C][C]0.0495653010422146[/C][C]123.173499415401[/C][/ROW]
[ROW][C]Trimmed Mean ( 29 / 44 )[/C][C]6.10391891891892[/C][C]0.0490392016786551[/C][C]124.470193436606[/C][/ROW]
[ROW][C]Trimmed Mean ( 30 / 44 )[/C][C]6.10319444444444[/C][C]0.0485807277057129[/C][C]125.629951066516[/C][/ROW]
[ROW][C]Trimmed Mean ( 31 / 44 )[/C][C]6.10228571428571[/C][C]0.0480498237915653[/C][C]126.999127837737[/C][/ROW]
[ROW][C]Trimmed Mean ( 32 / 44 )[/C][C]6.10132352941176[/C][C]0.0474040338335745[/C][C]128.708952297862[/C][/ROW]
[ROW][C]Trimmed Mean ( 33 / 44 )[/C][C]6.10090909090909[/C][C]0.0467586808178843[/C][C]130.476501564938[/C][/ROW]
[ROW][C]Trimmed Mean ( 34 / 44 )[/C][C]6.10078125[/C][C]0.0460424368000124[/C][C]132.503439739713[/C][/ROW]
[ROW][C]Trimmed Mean ( 35 / 44 )[/C][C]6.10145161290323[/C][C]0.0454205606316194[/C][C]134.332371244571[/C][/ROW]
[ROW][C]Trimmed Mean ( 36 / 44 )[/C][C]6.102[/C][C]0.0446890069774745[/C][C]136.543647145163[/C][/ROW]
[ROW][C]Trimmed Mean ( 37 / 44 )[/C][C]6.10344827586207[/C][C]0.0439755691153191[/C][C]138.791797324026[/C][/ROW]
[ROW][C]Trimmed Mean ( 38 / 44 )[/C][C]6.10464285714286[/C][C]0.0432592338958305[/C][C]141.117683032552[/C][/ROW]
[ROW][C]Trimmed Mean ( 39 / 44 )[/C][C]6.10537037037037[/C][C]0.0425864623547014[/C][C]143.364112273964[/C][/ROW]
[ROW][C]Trimmed Mean ( 40 / 44 )[/C][C]6.10576923076923[/C][C]0.0419179567078184[/C][C]145.659991810393[/C][/ROW]
[ROW][C]Trimmed Mean ( 41 / 44 )[/C][C]6.1064[/C][C]0.0412030908291787[/C][C]148.202474064777[/C][/ROW]
[ROW][C]Trimmed Mean ( 42 / 44 )[/C][C]6.10729166666667[/C][C]0.0404317781759067[/C][C]151.051770221326[/C][/ROW]
[ROW][C]Trimmed Mean ( 43 / 44 )[/C][C]6.10934782608696[/C][C]0.0396852376134507[/C][C]153.945098819725[/C][/ROW]
[ROW][C]Trimmed Mean ( 44 / 44 )[/C][C]6.11022727272727[/C][C]0.0391944367578578[/C][C]155.895269282120[/C][/ROW]
[ROW][C]Median[/C][C]6.09[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]6.455[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]6.07304347826087[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]6.07304347826087[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]6.07304347826087[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]6.07304347826087[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]6.07304347826087[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]6.07304347826087[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]6.07304347826087[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]6.083[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]132[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=50381&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=50381&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 Mean6.188712121212120.066165104239344893.5343817917245
Geometric Mean6.14350917569362
Harmonic Mean6.09962007244515
Quadratic Mean6.23487387785248
Winsorized Mean ( 1 / 44 )6.188636363636360.066151937207389993.5518538819907
Winsorized Mean ( 2 / 44 )6.188636363636360.066108737482218393.6129867145165
Winsorized Mean ( 3 / 44 )6.188409090909090.066005613632933493.7557997009727
Winsorized Mean ( 4 / 44 )6.187803030303030.065903067983065993.8924881599293
Winsorized Mean ( 5 / 44 )6.187803030303030.065903067983065993.8924881599293
Winsorized Mean ( 6 / 44 )6.187348484848480.065826816630804893.994344577693
Winsorized Mean ( 7 / 44 )6.187348484848480.065826816630804893.994344577693
Winsorized Mean ( 8 / 44 )6.18553030303030.065524919585415994.3996626347183
Winsorized Mean ( 9 / 44 )6.184848484848480.065225589853154594.8224232049526
Winsorized Mean ( 10 / 44 )6.183333333333330.064773459446400495.4609092393775
Winsorized Mean ( 11 / 44 )6.18250.064639552474929495.6457735749006
Winsorized Mean ( 12 / 44 )6.178863636363640.063818706448070496.8190046501712
Winsorized Mean ( 13 / 44 )6.174924242424240.063206451199156297.6945252466045
Winsorized Mean ( 14 / 44 )6.161136363636360.060874349428246101.210713896805
Winsorized Mean ( 15 / 44 )6.154318181818180.059336799781047103.718404169548
Winsorized Mean ( 16 / 44 )6.140984848484850.0575476006944814106.711396728548
Winsorized Mean ( 17 / 44 )6.137121212121210.0570504006188242107.573674252100
Winsorized Mean ( 18 / 44 )6.13303030303030.056533562709504108.484765669991
Winsorized Mean ( 19 / 44 )6.135909090909090.0562082553400489109.163841748655
Winsorized Mean ( 20 / 44 )6.137424242424240.0556807201837984110.225302800772
Winsorized Mean ( 21 / 44 )6.134242424242420.0549124090884376111.709584883867
Winsorized Mean ( 22 / 44 )6.129242424242420.0543020422106784112.873147578179
Winsorized Mean ( 23 / 44 )6.122272727272730.0522760461185803117.114303430395
Winsorized Mean ( 24 / 44 )6.124090909090910.0520770255680288117.596787494918
Winsorized Mean ( 25 / 44 )6.122196969696970.0505865794163595121.024134075313
Winsorized Mean ( 26 / 44 )6.122196969696970.0505865794163595121.024134075313
Winsorized Mean ( 27 / 44 )6.126287878787880.0496995838887198123.266381716696
Winsorized Mean ( 28 / 44 )6.124166666666670.0494579736714768123.825668785913
Winsorized Mean ( 29 / 44 )6.115378787878790.0479948872121639127.417296780914
Winsorized Mean ( 30 / 44 )6.117651515151510.0477551658172277128.104497397527
Winsorized Mean ( 31 / 44 )6.117651515151520.0477551658172277128.104497397527
Winsorized Mean ( 32 / 44 )6.107954545454550.0466936827350361130.809012861851
Winsorized Mean ( 33 / 44 )6.102954545454550.0461555490216129132.225803285251
Winsorized Mean ( 34 / 44 )6.090075757575760.0442537130615395137.617283076493
Winsorized Mean ( 35 / 44 )6.092727272727270.043970882174123138.562770894619
Winsorized Mean ( 36 / 44 )6.079090909090910.0425779081467091142.775706315689
Winsorized Mean ( 37 / 44 )6.084696969696970.0413988067519473146.977593005401
Winsorized Mean ( 38 / 44 )6.093333333333330.039900214807009152.714298978234
Winsorized Mean ( 39 / 44 )6.099242424242420.0386876465431943157.653488108476
Winsorized Mean ( 40 / 44 )6.096212121212120.0377695463844282161.405489469301
Winsorized Mean ( 41 / 44 )6.093106060606060.0368349553029989165.416409779381
Winsorized Mean ( 42 / 44 )6.077196969696970.0352862971495618172.22540931225
Winsorized Mean ( 43 / 44 )6.096742424242420.0326571178949298186.689543267655
Winsorized Mean ( 44 / 44 )6.106742424242430.0316680051725568192.836346683892
Trimmed Mean ( 1 / 44 )6.184615384615380.065731619803058794.0888936427457
Trimmed Mean ( 2 / 44 )6.180468750.065263214354047494.7006489210213
Trimmed Mean ( 3 / 44 )6.176190476190480.064766036282779595.3615634161118
Trimmed Mean ( 4 / 44 )6.171854838709680.064252583847022696.0561345424504
Trimmed Mean ( 5 / 44 )6.167540983606560.063711613107041996.8040312092628
Trimmed Mean ( 6 / 44 )6.163083333333330.063108083426326397.6591745260058
Trimmed Mean ( 7 / 44 )6.15855932203390.062452099613275398.612526402952
Trimmed Mean ( 8 / 44 )6.153879310344830.061720190232489599.7060975859634
Trimmed Mean ( 9 / 44 )6.149298245614030.0609592775897995100.875510484117
Trimmed Mean ( 10 / 44 )6.144642857142860.060159714573659102.138829957702
Trimmed Mean ( 11 / 44 )6.140.059337459599816103.475949954875
Trimmed Mean ( 12 / 44 )6.135277777777780.0584363366423271104.990800763746
Trimmed Mean ( 13 / 44 )6.130754716981130.0575463714907878106.535904144062
Trimmed Mean ( 14 / 44 )6.126442307692310.0566336770895214108.176664884538
Trimmed Mean ( 15 / 44 )6.123235294117650.055926248993078109.487680728874
Trimmed Mean ( 16 / 44 )6.12050.0553246387838697110.628828936602
Trimmed Mean ( 17 / 44 )6.118775510204080.054863460245081111.527335003495
Trimmed Mean ( 18 / 44 )6.117291666666670.0543932801832503112.464106706887
Trimmed Mean ( 19 / 44 )6.116063829787230.0539128358614811113.443556289662
Trimmed Mean ( 20 / 44 )6.11456521739130.0533946563111579114.516426171162
Trimmed Mean ( 21 / 44 )6.112888888888890.0528555954336937115.652635047076
Trimmed Mean ( 22 / 44 )6.111363636363640.0523197961724848116.807864010327
Trimmed Mean ( 23 / 44 )6.110116279069770.0517677900020619118.029305072254
Trimmed Mean ( 24 / 44 )6.109285714285710.0513533945666072118.965567239411
Trimmed Mean ( 25 / 44 )6.108292682926830.0508837303683742120.044120953902
Trimmed Mean ( 26 / 44 )6.1073750.0504943109184251120.951744640433
Trimmed Mean ( 27 / 44 )6.106410256410260.0500259587489375122.064832121582
Trimmed Mean ( 28 / 44 )6.105131578947370.0495653010422146123.173499415401
Trimmed Mean ( 29 / 44 )6.103918918918920.0490392016786551124.470193436606
Trimmed Mean ( 30 / 44 )6.103194444444440.0485807277057129125.629951066516
Trimmed Mean ( 31 / 44 )6.102285714285710.0480498237915653126.999127837737
Trimmed Mean ( 32 / 44 )6.101323529411760.0474040338335745128.708952297862
Trimmed Mean ( 33 / 44 )6.100909090909090.0467586808178843130.476501564938
Trimmed Mean ( 34 / 44 )6.100781250.0460424368000124132.503439739713
Trimmed Mean ( 35 / 44 )6.101451612903230.0454205606316194134.332371244571
Trimmed Mean ( 36 / 44 )6.1020.0446890069774745136.543647145163
Trimmed Mean ( 37 / 44 )6.103448275862070.0439755691153191138.791797324026
Trimmed Mean ( 38 / 44 )6.104642857142860.0432592338958305141.117683032552
Trimmed Mean ( 39 / 44 )6.105370370370370.0425864623547014143.364112273964
Trimmed Mean ( 40 / 44 )6.105769230769230.0419179567078184145.659991810393
Trimmed Mean ( 41 / 44 )6.10640.0412030908291787148.202474064777
Trimmed Mean ( 42 / 44 )6.107291666666670.0404317781759067151.051770221326
Trimmed Mean ( 43 / 44 )6.109347826086960.0396852376134507153.945098819725
Trimmed Mean ( 44 / 44 )6.110227272727270.0391944367578578155.895269282120
Median6.09
Midrange6.455
Midmean - Weighted Average at Xnp6.07304347826087
Midmean - Weighted Average at X(n+1)p6.07304347826087
Midmean - Empirical Distribution Function6.07304347826087
Midmean - Empirical Distribution Function - Averaging6.07304347826087
Midmean - Empirical Distribution Function - Interpolation6.07304347826087
Midmean - Closest Observation6.07304347826087
Midmean - True Basic - Statistics Graphics Toolkit6.07304347826087
Midmean - MS Excel (old versions)6.083
Number of observations132



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')