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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, 04 Dec 2011 05:35:34 -0500
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2011/Dec/04/t132299495294txwa72efdpnbq.htm/, Retrieved Sun, 05 May 2024 14:23:15 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=150564, Retrieved Sun, 05 May 2024 14:23:15 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact116
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Central Tendency] [Paper - Central T...] [2011-11-29 18:42:39] [2ca9890f29577b21e1107ae30466e88a]
- R  D    [Central Tendency] [Central Tendency ...] [2011-12-04 10:35:34] [2489a3445a7d2af96337a363cd642931] [Current]
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Dataseries X:
6,8
7,5
7,5
7,6
7,6
7,4
7,3
7,1
6,9
6,8
7,5
7,6
7,8
8
8,1
8,2
8,3
8,2
8
7,9
7,6
7,6
8,3
8,4
8,4
8,4
8,4
8,6
8,9
8,8
8,3
7,5
7,2
7,4
8,8
9,3
9,3
8,7
8,2
8,3
8,5
8,6
8,5
8,2
8,1
7,9
8,6
8,7
8,7
8,5
8,4
8,5
8,7
8,7
8,6
8,5
8,3
8
8,2
8,1
8,1
8
7,9
7,9
8
8
7,9
8
7,7
7,2
7,5
7,3
7
7
7
7,2
7,3
7,1
6,8
6,4
6,1
6,5
7,7
7,9
7,5
6,9
6,6
6,9
7,7
8
8
7,7
7,3
7,4
8,1
8,3
8,1
7,9
7,9
8,3
8,6
8,7
8,5
8,3
8
8
8,8
8,7
8,5
8,1
7,8
7,6
7,4
7,1
6,9
6,7
6,6
6,5
7,1
7,2
6,9




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Herman Ole Andreas Wold' @ wold.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 & 1 seconds \tabularnewline
R Server & 'Herman Ole Andreas Wold' @ wold.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=150564&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]'Herman Ole Andreas Wold' @ wold.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=150564&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=150564&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'Herman Ole Andreas Wold' @ wold.wessa.net







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean7.842148760330580.0608112292320286128.958892286298
Geometric Mean7.81314084171827
Harmonic Mean7.78341139358375
Quadratic Mean7.87039121335399
Winsorized Mean ( 1 / 40 )7.844628099173550.0602674298739638130.16364088495
Winsorized Mean ( 2 / 40 )7.83966942148760.0587809977874282133.370812279139
Winsorized Mean ( 3 / 40 )7.837190082644630.0584243551733119134.142517438081
Winsorized Mean ( 4 / 40 )7.84049586776860.0578134469234841135.617166680019
Winsorized Mean ( 5 / 40 )7.84049586776860.0578134469234841135.617166680019
Winsorized Mean ( 6 / 40 )7.84049586776860.0562924588747573139.281460154593
Winsorized Mean ( 7 / 40 )7.846280991735540.0553481508212392141.762296938828
Winsorized Mean ( 8 / 40 )7.846280991735540.0553481508212392141.762296938828
Winsorized Mean ( 9 / 40 )7.846280991735540.0553481508212392141.762296938828
Winsorized Mean ( 10 / 40 )7.854545454545450.05408899920234145.215211417808
Winsorized Mean ( 11 / 40 )7.854545454545450.05408899920234145.215211417808
Winsorized Mean ( 12 / 40 )7.854545454545450.05408899920234145.215211417808
Winsorized Mean ( 13 / 40 )7.843801652892560.052746764448228148.706782964696
Winsorized Mean ( 14 / 40 )7.843801652892560.052746764448228148.706782964696
Winsorized Mean ( 15 / 40 )7.856198347107440.050953613674927154.18334011064
Winsorized Mean ( 16 / 40 )7.856198347107440.050953613674927154.18334011064
Winsorized Mean ( 17 / 40 )7.856198347107440.050953613674927154.18334011064
Winsorized Mean ( 18 / 40 )7.856198347107440.0471632263536691166.57465899799
Winsorized Mean ( 19 / 40 )7.856198347107440.0471632263536691166.57465899799
Winsorized Mean ( 20 / 40 )7.856198347107440.0471632263536691166.57465899799
Winsorized Mean ( 21 / 40 )7.856198347107440.0471632263536691166.57465899799
Winsorized Mean ( 22 / 40 )7.874380165289260.0448064236469205175.742215610427
Winsorized Mean ( 23 / 40 )7.874380165289260.0448064236469205175.742215610427
Winsorized Mean ( 24 / 40 )7.874380165289260.0448064236469205175.742215610427
Winsorized Mean ( 25 / 40 )7.853719008264460.0424952002202184.814260612219
Winsorized Mean ( 26 / 40 )7.875206611570250.0398219347846618197.760522037808
Winsorized Mean ( 27 / 40 )7.875206611570250.0398219347846618197.760522037808
Winsorized Mean ( 28 / 40 )7.875206611570250.0398219347846618197.760522037808
Winsorized Mean ( 29 / 40 )7.875206611570250.0398219347846618197.760522037808
Winsorized Mean ( 30 / 40 )7.875206611570250.0342427123560326229.981974841513
Winsorized Mean ( 31 / 40 )7.875206611570250.0342427123560326229.981974841513
Winsorized Mean ( 32 / 40 )7.875206611570250.0342427123560326229.981974841513
Winsorized Mean ( 33 / 40 )7.875206611570250.0342427123560326229.981974841513
Winsorized Mean ( 34 / 40 )7.903305785123970.0310942290513789254.172752508668
Winsorized Mean ( 35 / 40 )7.903305785123970.0310942290513789254.172752508668
Winsorized Mean ( 36 / 40 )7.903305785123970.0310942290513789254.172752508668
Winsorized Mean ( 37 / 40 )7.903305785123970.0310942290513789254.172752508668
Winsorized Mean ( 38 / 40 )7.871900826446280.0278777126067966282.372551058121
Winsorized Mean ( 39 / 40 )7.871900826446280.0278777126067966282.372551058121
Winsorized Mean ( 40 / 40 )7.904958677685950.024304406737719325.247958651791
Trimmed Mean ( 1 / 40 )7.844537815126050.0587906596263031133.431702671633
Trimmed Mean ( 2 / 40 )7.844444444444440.0571506925330416137.258956921811
Trimmed Mean ( 3 / 40 )7.846956521739130.0561995157180374139.626764065168
Trimmed Mean ( 4 / 40 )7.850442477876110.0552852031565544141.998980371756
Trimmed Mean ( 5 / 40 )7.853153153153150.0544621504440533144.19469464799
Trimmed Mean ( 6 / 40 )7.855963302752290.0535430254754544146.722439253151
Trimmed Mean ( 7 / 40 )7.85887850467290.0528662380987547148.655905683934
Trimmed Mean ( 8 / 40 )7.860952380952380.052300470972169150.303663329064
Trimmed Mean ( 9 / 40 )7.86310679611650.0516617130310555152.203756607717
Trimmed Mean ( 10 / 40 )7.865346534653470.0509403775649933154.402988564785
Trimmed Mean ( 11 / 40 )7.866666666666670.0503338678007558156.289731156892
Trimmed Mean ( 12 / 40 )7.86804123711340.0496453572281835158.484935478453
Trimmed Mean ( 13 / 40 )7.869473684210530.0488633096806419161.050770724362
Trimmed Mean ( 14 / 40 )7.872043010752690.0481632138105199163.445135570112
Trimmed Mean ( 15 / 40 )7.874725274725280.0473625098797397166.264948684526
Trimmed Mean ( 16 / 40 )7.876404494382020.0466996158037281168.661012704803
Trimmed Mean ( 17 / 40 )7.878160919540230.0459368977642128171.499628903494
Trimmed Mean ( 18 / 40 )7.880.0450583188860874174.884465173269
Trimmed Mean ( 19 / 40 )7.881927710843370.0445417645281986176.955892841952
Trimmed Mean ( 20 / 40 )7.883950617283950.0439365700952983179.439373628476
Trimmed Mean ( 21 / 40 )7.886075949367090.0432280013569344182.429807111636
Trimmed Mean ( 22 / 40 )7.888311688311690.0423979626687669186.054026933769
Trimmed Mean ( 23 / 40 )7.889333333333330.0417445398418357188.990784500798
Trimmed Mean ( 24 / 40 )7.890410958904110.0409720355853386192.580398952099
Trimmed Mean ( 25 / 40 )7.891549295774650.0400576284504638197.004905208842
Trimmed Mean ( 26 / 40 )7.894202898550720.0392754095059849200.9960684776
Trimmed Mean ( 27 / 40 )7.89552238805970.0387171512522491203.928288437829
Trimmed Mean ( 28 / 40 )7.896923076923080.0380390254294363207.600562521565
Trimmed Mean ( 29 / 40 )7.89841269841270.0372156956886704212.233374984771
Trimmed Mean ( 30 / 40 )7.90.0362142984170074218.145880089448
Trimmed Mean ( 31 / 40 )7.90.0358165601563881220.568361827761
Trimmed Mean ( 32 / 40 )7.903508771929820.0353078931692975223.845380239296
Trimmed Mean ( 33 / 40 )7.905454545454550.0346622162856456228.071237000745
Trimmed Mean ( 34 / 40 )7.907547169811320.0338451455834207233.639035480612
Trimmed Mean ( 35 / 40 )7.90784313725490.033354088117592237.087673012534
Trimmed Mean ( 36 / 40 )7.908163265306120.0327114698691814241.755057077294
Trimmed Mean ( 37 / 40 )7.908510638297870.0318747820705459248.111834013315
Trimmed Mean ( 38 / 40 )7.908888888888890.0307847237175499256.909529591787
Trimmed Mean ( 39 / 40 )7.911627906976740.0299887949405894263.81946732606
Trimmed Mean ( 40 / 40 )7.914634146341460.0289155573810287273.715427375237
Median8
Midrange7.7
Midmean - Weighted Average at Xnp7.9
Midmean - Weighted Average at X(n+1)p7.9
Midmean - Empirical Distribution Function7.9
Midmean - Empirical Distribution Function - Averaging7.9
Midmean - Empirical Distribution Function - Interpolation7.9
Midmean - Closest Observation7.86307692307693
Midmean - True Basic - Statistics Graphics Toolkit7.9
Midmean - MS Excel (old versions)7.9
Number of observations121

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 7.84214876033058 & 0.0608112292320286 & 128.958892286298 \tabularnewline
Geometric Mean & 7.81314084171827 &  &  \tabularnewline
Harmonic Mean & 7.78341139358375 &  &  \tabularnewline
Quadratic Mean & 7.87039121335399 &  &  \tabularnewline
Winsorized Mean ( 1 / 40 ) & 7.84462809917355 & 0.0602674298739638 & 130.16364088495 \tabularnewline
Winsorized Mean ( 2 / 40 ) & 7.8396694214876 & 0.0587809977874282 & 133.370812279139 \tabularnewline
Winsorized Mean ( 3 / 40 ) & 7.83719008264463 & 0.0584243551733119 & 134.142517438081 \tabularnewline
Winsorized Mean ( 4 / 40 ) & 7.8404958677686 & 0.0578134469234841 & 135.617166680019 \tabularnewline
Winsorized Mean ( 5 / 40 ) & 7.8404958677686 & 0.0578134469234841 & 135.617166680019 \tabularnewline
Winsorized Mean ( 6 / 40 ) & 7.8404958677686 & 0.0562924588747573 & 139.281460154593 \tabularnewline
Winsorized Mean ( 7 / 40 ) & 7.84628099173554 & 0.0553481508212392 & 141.762296938828 \tabularnewline
Winsorized Mean ( 8 / 40 ) & 7.84628099173554 & 0.0553481508212392 & 141.762296938828 \tabularnewline
Winsorized Mean ( 9 / 40 ) & 7.84628099173554 & 0.0553481508212392 & 141.762296938828 \tabularnewline
Winsorized Mean ( 10 / 40 ) & 7.85454545454545 & 0.05408899920234 & 145.215211417808 \tabularnewline
Winsorized Mean ( 11 / 40 ) & 7.85454545454545 & 0.05408899920234 & 145.215211417808 \tabularnewline
Winsorized Mean ( 12 / 40 ) & 7.85454545454545 & 0.05408899920234 & 145.215211417808 \tabularnewline
Winsorized Mean ( 13 / 40 ) & 7.84380165289256 & 0.052746764448228 & 148.706782964696 \tabularnewline
Winsorized Mean ( 14 / 40 ) & 7.84380165289256 & 0.052746764448228 & 148.706782964696 \tabularnewline
Winsorized Mean ( 15 / 40 ) & 7.85619834710744 & 0.050953613674927 & 154.18334011064 \tabularnewline
Winsorized Mean ( 16 / 40 ) & 7.85619834710744 & 0.050953613674927 & 154.18334011064 \tabularnewline
Winsorized Mean ( 17 / 40 ) & 7.85619834710744 & 0.050953613674927 & 154.18334011064 \tabularnewline
Winsorized Mean ( 18 / 40 ) & 7.85619834710744 & 0.0471632263536691 & 166.57465899799 \tabularnewline
Winsorized Mean ( 19 / 40 ) & 7.85619834710744 & 0.0471632263536691 & 166.57465899799 \tabularnewline
Winsorized Mean ( 20 / 40 ) & 7.85619834710744 & 0.0471632263536691 & 166.57465899799 \tabularnewline
Winsorized Mean ( 21 / 40 ) & 7.85619834710744 & 0.0471632263536691 & 166.57465899799 \tabularnewline
Winsorized Mean ( 22 / 40 ) & 7.87438016528926 & 0.0448064236469205 & 175.742215610427 \tabularnewline
Winsorized Mean ( 23 / 40 ) & 7.87438016528926 & 0.0448064236469205 & 175.742215610427 \tabularnewline
Winsorized Mean ( 24 / 40 ) & 7.87438016528926 & 0.0448064236469205 & 175.742215610427 \tabularnewline
Winsorized Mean ( 25 / 40 ) & 7.85371900826446 & 0.0424952002202 & 184.814260612219 \tabularnewline
Winsorized Mean ( 26 / 40 ) & 7.87520661157025 & 0.0398219347846618 & 197.760522037808 \tabularnewline
Winsorized Mean ( 27 / 40 ) & 7.87520661157025 & 0.0398219347846618 & 197.760522037808 \tabularnewline
Winsorized Mean ( 28 / 40 ) & 7.87520661157025 & 0.0398219347846618 & 197.760522037808 \tabularnewline
Winsorized Mean ( 29 / 40 ) & 7.87520661157025 & 0.0398219347846618 & 197.760522037808 \tabularnewline
Winsorized Mean ( 30 / 40 ) & 7.87520661157025 & 0.0342427123560326 & 229.981974841513 \tabularnewline
Winsorized Mean ( 31 / 40 ) & 7.87520661157025 & 0.0342427123560326 & 229.981974841513 \tabularnewline
Winsorized Mean ( 32 / 40 ) & 7.87520661157025 & 0.0342427123560326 & 229.981974841513 \tabularnewline
Winsorized Mean ( 33 / 40 ) & 7.87520661157025 & 0.0342427123560326 & 229.981974841513 \tabularnewline
Winsorized Mean ( 34 / 40 ) & 7.90330578512397 & 0.0310942290513789 & 254.172752508668 \tabularnewline
Winsorized Mean ( 35 / 40 ) & 7.90330578512397 & 0.0310942290513789 & 254.172752508668 \tabularnewline
Winsorized Mean ( 36 / 40 ) & 7.90330578512397 & 0.0310942290513789 & 254.172752508668 \tabularnewline
Winsorized Mean ( 37 / 40 ) & 7.90330578512397 & 0.0310942290513789 & 254.172752508668 \tabularnewline
Winsorized Mean ( 38 / 40 ) & 7.87190082644628 & 0.0278777126067966 & 282.372551058121 \tabularnewline
Winsorized Mean ( 39 / 40 ) & 7.87190082644628 & 0.0278777126067966 & 282.372551058121 \tabularnewline
Winsorized Mean ( 40 / 40 ) & 7.90495867768595 & 0.024304406737719 & 325.247958651791 \tabularnewline
Trimmed Mean ( 1 / 40 ) & 7.84453781512605 & 0.0587906596263031 & 133.431702671633 \tabularnewline
Trimmed Mean ( 2 / 40 ) & 7.84444444444444 & 0.0571506925330416 & 137.258956921811 \tabularnewline
Trimmed Mean ( 3 / 40 ) & 7.84695652173913 & 0.0561995157180374 & 139.626764065168 \tabularnewline
Trimmed Mean ( 4 / 40 ) & 7.85044247787611 & 0.0552852031565544 & 141.998980371756 \tabularnewline
Trimmed Mean ( 5 / 40 ) & 7.85315315315315 & 0.0544621504440533 & 144.19469464799 \tabularnewline
Trimmed Mean ( 6 / 40 ) & 7.85596330275229 & 0.0535430254754544 & 146.722439253151 \tabularnewline
Trimmed Mean ( 7 / 40 ) & 7.8588785046729 & 0.0528662380987547 & 148.655905683934 \tabularnewline
Trimmed Mean ( 8 / 40 ) & 7.86095238095238 & 0.052300470972169 & 150.303663329064 \tabularnewline
Trimmed Mean ( 9 / 40 ) & 7.8631067961165 & 0.0516617130310555 & 152.203756607717 \tabularnewline
Trimmed Mean ( 10 / 40 ) & 7.86534653465347 & 0.0509403775649933 & 154.402988564785 \tabularnewline
Trimmed Mean ( 11 / 40 ) & 7.86666666666667 & 0.0503338678007558 & 156.289731156892 \tabularnewline
Trimmed Mean ( 12 / 40 ) & 7.8680412371134 & 0.0496453572281835 & 158.484935478453 \tabularnewline
Trimmed Mean ( 13 / 40 ) & 7.86947368421053 & 0.0488633096806419 & 161.050770724362 \tabularnewline
Trimmed Mean ( 14 / 40 ) & 7.87204301075269 & 0.0481632138105199 & 163.445135570112 \tabularnewline
Trimmed Mean ( 15 / 40 ) & 7.87472527472528 & 0.0473625098797397 & 166.264948684526 \tabularnewline
Trimmed Mean ( 16 / 40 ) & 7.87640449438202 & 0.0466996158037281 & 168.661012704803 \tabularnewline
Trimmed Mean ( 17 / 40 ) & 7.87816091954023 & 0.0459368977642128 & 171.499628903494 \tabularnewline
Trimmed Mean ( 18 / 40 ) & 7.88 & 0.0450583188860874 & 174.884465173269 \tabularnewline
Trimmed Mean ( 19 / 40 ) & 7.88192771084337 & 0.0445417645281986 & 176.955892841952 \tabularnewline
Trimmed Mean ( 20 / 40 ) & 7.88395061728395 & 0.0439365700952983 & 179.439373628476 \tabularnewline
Trimmed Mean ( 21 / 40 ) & 7.88607594936709 & 0.0432280013569344 & 182.429807111636 \tabularnewline
Trimmed Mean ( 22 / 40 ) & 7.88831168831169 & 0.0423979626687669 & 186.054026933769 \tabularnewline
Trimmed Mean ( 23 / 40 ) & 7.88933333333333 & 0.0417445398418357 & 188.990784500798 \tabularnewline
Trimmed Mean ( 24 / 40 ) & 7.89041095890411 & 0.0409720355853386 & 192.580398952099 \tabularnewline
Trimmed Mean ( 25 / 40 ) & 7.89154929577465 & 0.0400576284504638 & 197.004905208842 \tabularnewline
Trimmed Mean ( 26 / 40 ) & 7.89420289855072 & 0.0392754095059849 & 200.9960684776 \tabularnewline
Trimmed Mean ( 27 / 40 ) & 7.8955223880597 & 0.0387171512522491 & 203.928288437829 \tabularnewline
Trimmed Mean ( 28 / 40 ) & 7.89692307692308 & 0.0380390254294363 & 207.600562521565 \tabularnewline
Trimmed Mean ( 29 / 40 ) & 7.8984126984127 & 0.0372156956886704 & 212.233374984771 \tabularnewline
Trimmed Mean ( 30 / 40 ) & 7.9 & 0.0362142984170074 & 218.145880089448 \tabularnewline
Trimmed Mean ( 31 / 40 ) & 7.9 & 0.0358165601563881 & 220.568361827761 \tabularnewline
Trimmed Mean ( 32 / 40 ) & 7.90350877192982 & 0.0353078931692975 & 223.845380239296 \tabularnewline
Trimmed Mean ( 33 / 40 ) & 7.90545454545455 & 0.0346622162856456 & 228.071237000745 \tabularnewline
Trimmed Mean ( 34 / 40 ) & 7.90754716981132 & 0.0338451455834207 & 233.639035480612 \tabularnewline
Trimmed Mean ( 35 / 40 ) & 7.9078431372549 & 0.033354088117592 & 237.087673012534 \tabularnewline
Trimmed Mean ( 36 / 40 ) & 7.90816326530612 & 0.0327114698691814 & 241.755057077294 \tabularnewline
Trimmed Mean ( 37 / 40 ) & 7.90851063829787 & 0.0318747820705459 & 248.111834013315 \tabularnewline
Trimmed Mean ( 38 / 40 ) & 7.90888888888889 & 0.0307847237175499 & 256.909529591787 \tabularnewline
Trimmed Mean ( 39 / 40 ) & 7.91162790697674 & 0.0299887949405894 & 263.81946732606 \tabularnewline
Trimmed Mean ( 40 / 40 ) & 7.91463414634146 & 0.0289155573810287 & 273.715427375237 \tabularnewline
Median & 8 &  &  \tabularnewline
Midrange & 7.7 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 7.9 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 7.9 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 7.9 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 7.9 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 7.9 &  &  \tabularnewline
Midmean - Closest Observation & 7.86307692307693 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 7.9 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 7.9 &  &  \tabularnewline
Number of observations & 121 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=150564&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]7.84214876033058[/C][C]0.0608112292320286[/C][C]128.958892286298[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]7.81314084171827[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]7.78341139358375[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]7.87039121335399[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 40 )[/C][C]7.84462809917355[/C][C]0.0602674298739638[/C][C]130.16364088495[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 40 )[/C][C]7.8396694214876[/C][C]0.0587809977874282[/C][C]133.370812279139[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 40 )[/C][C]7.83719008264463[/C][C]0.0584243551733119[/C][C]134.142517438081[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 40 )[/C][C]7.8404958677686[/C][C]0.0578134469234841[/C][C]135.617166680019[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 40 )[/C][C]7.8404958677686[/C][C]0.0578134469234841[/C][C]135.617166680019[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 40 )[/C][C]7.8404958677686[/C][C]0.0562924588747573[/C][C]139.281460154593[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 40 )[/C][C]7.84628099173554[/C][C]0.0553481508212392[/C][C]141.762296938828[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 40 )[/C][C]7.84628099173554[/C][C]0.0553481508212392[/C][C]141.762296938828[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 40 )[/C][C]7.84628099173554[/C][C]0.0553481508212392[/C][C]141.762296938828[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 40 )[/C][C]7.85454545454545[/C][C]0.05408899920234[/C][C]145.215211417808[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 40 )[/C][C]7.85454545454545[/C][C]0.05408899920234[/C][C]145.215211417808[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 40 )[/C][C]7.85454545454545[/C][C]0.05408899920234[/C][C]145.215211417808[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 40 )[/C][C]7.84380165289256[/C][C]0.052746764448228[/C][C]148.706782964696[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 40 )[/C][C]7.84380165289256[/C][C]0.052746764448228[/C][C]148.706782964696[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 40 )[/C][C]7.85619834710744[/C][C]0.050953613674927[/C][C]154.18334011064[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 40 )[/C][C]7.85619834710744[/C][C]0.050953613674927[/C][C]154.18334011064[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 40 )[/C][C]7.85619834710744[/C][C]0.050953613674927[/C][C]154.18334011064[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 40 )[/C][C]7.85619834710744[/C][C]0.0471632263536691[/C][C]166.57465899799[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 40 )[/C][C]7.85619834710744[/C][C]0.0471632263536691[/C][C]166.57465899799[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 40 )[/C][C]7.85619834710744[/C][C]0.0471632263536691[/C][C]166.57465899799[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 40 )[/C][C]7.85619834710744[/C][C]0.0471632263536691[/C][C]166.57465899799[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 40 )[/C][C]7.87438016528926[/C][C]0.0448064236469205[/C][C]175.742215610427[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 40 )[/C][C]7.87438016528926[/C][C]0.0448064236469205[/C][C]175.742215610427[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 40 )[/C][C]7.87438016528926[/C][C]0.0448064236469205[/C][C]175.742215610427[/C][/ROW]
[ROW][C]Winsorized Mean ( 25 / 40 )[/C][C]7.85371900826446[/C][C]0.0424952002202[/C][C]184.814260612219[/C][/ROW]
[ROW][C]Winsorized Mean ( 26 / 40 )[/C][C]7.87520661157025[/C][C]0.0398219347846618[/C][C]197.760522037808[/C][/ROW]
[ROW][C]Winsorized Mean ( 27 / 40 )[/C][C]7.87520661157025[/C][C]0.0398219347846618[/C][C]197.760522037808[/C][/ROW]
[ROW][C]Winsorized Mean ( 28 / 40 )[/C][C]7.87520661157025[/C][C]0.0398219347846618[/C][C]197.760522037808[/C][/ROW]
[ROW][C]Winsorized Mean ( 29 / 40 )[/C][C]7.87520661157025[/C][C]0.0398219347846618[/C][C]197.760522037808[/C][/ROW]
[ROW][C]Winsorized Mean ( 30 / 40 )[/C][C]7.87520661157025[/C][C]0.0342427123560326[/C][C]229.981974841513[/C][/ROW]
[ROW][C]Winsorized Mean ( 31 / 40 )[/C][C]7.87520661157025[/C][C]0.0342427123560326[/C][C]229.981974841513[/C][/ROW]
[ROW][C]Winsorized Mean ( 32 / 40 )[/C][C]7.87520661157025[/C][C]0.0342427123560326[/C][C]229.981974841513[/C][/ROW]
[ROW][C]Winsorized Mean ( 33 / 40 )[/C][C]7.87520661157025[/C][C]0.0342427123560326[/C][C]229.981974841513[/C][/ROW]
[ROW][C]Winsorized Mean ( 34 / 40 )[/C][C]7.90330578512397[/C][C]0.0310942290513789[/C][C]254.172752508668[/C][/ROW]
[ROW][C]Winsorized Mean ( 35 / 40 )[/C][C]7.90330578512397[/C][C]0.0310942290513789[/C][C]254.172752508668[/C][/ROW]
[ROW][C]Winsorized Mean ( 36 / 40 )[/C][C]7.90330578512397[/C][C]0.0310942290513789[/C][C]254.172752508668[/C][/ROW]
[ROW][C]Winsorized Mean ( 37 / 40 )[/C][C]7.90330578512397[/C][C]0.0310942290513789[/C][C]254.172752508668[/C][/ROW]
[ROW][C]Winsorized Mean ( 38 / 40 )[/C][C]7.87190082644628[/C][C]0.0278777126067966[/C][C]282.372551058121[/C][/ROW]
[ROW][C]Winsorized Mean ( 39 / 40 )[/C][C]7.87190082644628[/C][C]0.0278777126067966[/C][C]282.372551058121[/C][/ROW]
[ROW][C]Winsorized Mean ( 40 / 40 )[/C][C]7.90495867768595[/C][C]0.024304406737719[/C][C]325.247958651791[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 40 )[/C][C]7.84453781512605[/C][C]0.0587906596263031[/C][C]133.431702671633[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 40 )[/C][C]7.84444444444444[/C][C]0.0571506925330416[/C][C]137.258956921811[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 40 )[/C][C]7.84695652173913[/C][C]0.0561995157180374[/C][C]139.626764065168[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 40 )[/C][C]7.85044247787611[/C][C]0.0552852031565544[/C][C]141.998980371756[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 40 )[/C][C]7.85315315315315[/C][C]0.0544621504440533[/C][C]144.19469464799[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 40 )[/C][C]7.85596330275229[/C][C]0.0535430254754544[/C][C]146.722439253151[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 40 )[/C][C]7.8588785046729[/C][C]0.0528662380987547[/C][C]148.655905683934[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 40 )[/C][C]7.86095238095238[/C][C]0.052300470972169[/C][C]150.303663329064[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 40 )[/C][C]7.8631067961165[/C][C]0.0516617130310555[/C][C]152.203756607717[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 40 )[/C][C]7.86534653465347[/C][C]0.0509403775649933[/C][C]154.402988564785[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 40 )[/C][C]7.86666666666667[/C][C]0.0503338678007558[/C][C]156.289731156892[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 40 )[/C][C]7.8680412371134[/C][C]0.0496453572281835[/C][C]158.484935478453[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 40 )[/C][C]7.86947368421053[/C][C]0.0488633096806419[/C][C]161.050770724362[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 40 )[/C][C]7.87204301075269[/C][C]0.0481632138105199[/C][C]163.445135570112[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 40 )[/C][C]7.87472527472528[/C][C]0.0473625098797397[/C][C]166.264948684526[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 40 )[/C][C]7.87640449438202[/C][C]0.0466996158037281[/C][C]168.661012704803[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 40 )[/C][C]7.87816091954023[/C][C]0.0459368977642128[/C][C]171.499628903494[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 40 )[/C][C]7.88[/C][C]0.0450583188860874[/C][C]174.884465173269[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 40 )[/C][C]7.88192771084337[/C][C]0.0445417645281986[/C][C]176.955892841952[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 40 )[/C][C]7.88395061728395[/C][C]0.0439365700952983[/C][C]179.439373628476[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 40 )[/C][C]7.88607594936709[/C][C]0.0432280013569344[/C][C]182.429807111636[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 40 )[/C][C]7.88831168831169[/C][C]0.0423979626687669[/C][C]186.054026933769[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 40 )[/C][C]7.88933333333333[/C][C]0.0417445398418357[/C][C]188.990784500798[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 40 )[/C][C]7.89041095890411[/C][C]0.0409720355853386[/C][C]192.580398952099[/C][/ROW]
[ROW][C]Trimmed Mean ( 25 / 40 )[/C][C]7.89154929577465[/C][C]0.0400576284504638[/C][C]197.004905208842[/C][/ROW]
[ROW][C]Trimmed Mean ( 26 / 40 )[/C][C]7.89420289855072[/C][C]0.0392754095059849[/C][C]200.9960684776[/C][/ROW]
[ROW][C]Trimmed Mean ( 27 / 40 )[/C][C]7.8955223880597[/C][C]0.0387171512522491[/C][C]203.928288437829[/C][/ROW]
[ROW][C]Trimmed Mean ( 28 / 40 )[/C][C]7.89692307692308[/C][C]0.0380390254294363[/C][C]207.600562521565[/C][/ROW]
[ROW][C]Trimmed Mean ( 29 / 40 )[/C][C]7.8984126984127[/C][C]0.0372156956886704[/C][C]212.233374984771[/C][/ROW]
[ROW][C]Trimmed Mean ( 30 / 40 )[/C][C]7.9[/C][C]0.0362142984170074[/C][C]218.145880089448[/C][/ROW]
[ROW][C]Trimmed Mean ( 31 / 40 )[/C][C]7.9[/C][C]0.0358165601563881[/C][C]220.568361827761[/C][/ROW]
[ROW][C]Trimmed Mean ( 32 / 40 )[/C][C]7.90350877192982[/C][C]0.0353078931692975[/C][C]223.845380239296[/C][/ROW]
[ROW][C]Trimmed Mean ( 33 / 40 )[/C][C]7.90545454545455[/C][C]0.0346622162856456[/C][C]228.071237000745[/C][/ROW]
[ROW][C]Trimmed Mean ( 34 / 40 )[/C][C]7.90754716981132[/C][C]0.0338451455834207[/C][C]233.639035480612[/C][/ROW]
[ROW][C]Trimmed Mean ( 35 / 40 )[/C][C]7.9078431372549[/C][C]0.033354088117592[/C][C]237.087673012534[/C][/ROW]
[ROW][C]Trimmed Mean ( 36 / 40 )[/C][C]7.90816326530612[/C][C]0.0327114698691814[/C][C]241.755057077294[/C][/ROW]
[ROW][C]Trimmed Mean ( 37 / 40 )[/C][C]7.90851063829787[/C][C]0.0318747820705459[/C][C]248.111834013315[/C][/ROW]
[ROW][C]Trimmed Mean ( 38 / 40 )[/C][C]7.90888888888889[/C][C]0.0307847237175499[/C][C]256.909529591787[/C][/ROW]
[ROW][C]Trimmed Mean ( 39 / 40 )[/C][C]7.91162790697674[/C][C]0.0299887949405894[/C][C]263.81946732606[/C][/ROW]
[ROW][C]Trimmed Mean ( 40 / 40 )[/C][C]7.91463414634146[/C][C]0.0289155573810287[/C][C]273.715427375237[/C][/ROW]
[ROW][C]Median[/C][C]8[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]7.7[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]7.9[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]7.9[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]7.9[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]7.9[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]7.9[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]7.86307692307693[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]7.9[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]7.9[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]121[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=150564&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=150564&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 Mean7.842148760330580.0608112292320286128.958892286298
Geometric Mean7.81314084171827
Harmonic Mean7.78341139358375
Quadratic Mean7.87039121335399
Winsorized Mean ( 1 / 40 )7.844628099173550.0602674298739638130.16364088495
Winsorized Mean ( 2 / 40 )7.83966942148760.0587809977874282133.370812279139
Winsorized Mean ( 3 / 40 )7.837190082644630.0584243551733119134.142517438081
Winsorized Mean ( 4 / 40 )7.84049586776860.0578134469234841135.617166680019
Winsorized Mean ( 5 / 40 )7.84049586776860.0578134469234841135.617166680019
Winsorized Mean ( 6 / 40 )7.84049586776860.0562924588747573139.281460154593
Winsorized Mean ( 7 / 40 )7.846280991735540.0553481508212392141.762296938828
Winsorized Mean ( 8 / 40 )7.846280991735540.0553481508212392141.762296938828
Winsorized Mean ( 9 / 40 )7.846280991735540.0553481508212392141.762296938828
Winsorized Mean ( 10 / 40 )7.854545454545450.05408899920234145.215211417808
Winsorized Mean ( 11 / 40 )7.854545454545450.05408899920234145.215211417808
Winsorized Mean ( 12 / 40 )7.854545454545450.05408899920234145.215211417808
Winsorized Mean ( 13 / 40 )7.843801652892560.052746764448228148.706782964696
Winsorized Mean ( 14 / 40 )7.843801652892560.052746764448228148.706782964696
Winsorized Mean ( 15 / 40 )7.856198347107440.050953613674927154.18334011064
Winsorized Mean ( 16 / 40 )7.856198347107440.050953613674927154.18334011064
Winsorized Mean ( 17 / 40 )7.856198347107440.050953613674927154.18334011064
Winsorized Mean ( 18 / 40 )7.856198347107440.0471632263536691166.57465899799
Winsorized Mean ( 19 / 40 )7.856198347107440.0471632263536691166.57465899799
Winsorized Mean ( 20 / 40 )7.856198347107440.0471632263536691166.57465899799
Winsorized Mean ( 21 / 40 )7.856198347107440.0471632263536691166.57465899799
Winsorized Mean ( 22 / 40 )7.874380165289260.0448064236469205175.742215610427
Winsorized Mean ( 23 / 40 )7.874380165289260.0448064236469205175.742215610427
Winsorized Mean ( 24 / 40 )7.874380165289260.0448064236469205175.742215610427
Winsorized Mean ( 25 / 40 )7.853719008264460.0424952002202184.814260612219
Winsorized Mean ( 26 / 40 )7.875206611570250.0398219347846618197.760522037808
Winsorized Mean ( 27 / 40 )7.875206611570250.0398219347846618197.760522037808
Winsorized Mean ( 28 / 40 )7.875206611570250.0398219347846618197.760522037808
Winsorized Mean ( 29 / 40 )7.875206611570250.0398219347846618197.760522037808
Winsorized Mean ( 30 / 40 )7.875206611570250.0342427123560326229.981974841513
Winsorized Mean ( 31 / 40 )7.875206611570250.0342427123560326229.981974841513
Winsorized Mean ( 32 / 40 )7.875206611570250.0342427123560326229.981974841513
Winsorized Mean ( 33 / 40 )7.875206611570250.0342427123560326229.981974841513
Winsorized Mean ( 34 / 40 )7.903305785123970.0310942290513789254.172752508668
Winsorized Mean ( 35 / 40 )7.903305785123970.0310942290513789254.172752508668
Winsorized Mean ( 36 / 40 )7.903305785123970.0310942290513789254.172752508668
Winsorized Mean ( 37 / 40 )7.903305785123970.0310942290513789254.172752508668
Winsorized Mean ( 38 / 40 )7.871900826446280.0278777126067966282.372551058121
Winsorized Mean ( 39 / 40 )7.871900826446280.0278777126067966282.372551058121
Winsorized Mean ( 40 / 40 )7.904958677685950.024304406737719325.247958651791
Trimmed Mean ( 1 / 40 )7.844537815126050.0587906596263031133.431702671633
Trimmed Mean ( 2 / 40 )7.844444444444440.0571506925330416137.258956921811
Trimmed Mean ( 3 / 40 )7.846956521739130.0561995157180374139.626764065168
Trimmed Mean ( 4 / 40 )7.850442477876110.0552852031565544141.998980371756
Trimmed Mean ( 5 / 40 )7.853153153153150.0544621504440533144.19469464799
Trimmed Mean ( 6 / 40 )7.855963302752290.0535430254754544146.722439253151
Trimmed Mean ( 7 / 40 )7.85887850467290.0528662380987547148.655905683934
Trimmed Mean ( 8 / 40 )7.860952380952380.052300470972169150.303663329064
Trimmed Mean ( 9 / 40 )7.86310679611650.0516617130310555152.203756607717
Trimmed Mean ( 10 / 40 )7.865346534653470.0509403775649933154.402988564785
Trimmed Mean ( 11 / 40 )7.866666666666670.0503338678007558156.289731156892
Trimmed Mean ( 12 / 40 )7.86804123711340.0496453572281835158.484935478453
Trimmed Mean ( 13 / 40 )7.869473684210530.0488633096806419161.050770724362
Trimmed Mean ( 14 / 40 )7.872043010752690.0481632138105199163.445135570112
Trimmed Mean ( 15 / 40 )7.874725274725280.0473625098797397166.264948684526
Trimmed Mean ( 16 / 40 )7.876404494382020.0466996158037281168.661012704803
Trimmed Mean ( 17 / 40 )7.878160919540230.0459368977642128171.499628903494
Trimmed Mean ( 18 / 40 )7.880.0450583188860874174.884465173269
Trimmed Mean ( 19 / 40 )7.881927710843370.0445417645281986176.955892841952
Trimmed Mean ( 20 / 40 )7.883950617283950.0439365700952983179.439373628476
Trimmed Mean ( 21 / 40 )7.886075949367090.0432280013569344182.429807111636
Trimmed Mean ( 22 / 40 )7.888311688311690.0423979626687669186.054026933769
Trimmed Mean ( 23 / 40 )7.889333333333330.0417445398418357188.990784500798
Trimmed Mean ( 24 / 40 )7.890410958904110.0409720355853386192.580398952099
Trimmed Mean ( 25 / 40 )7.891549295774650.0400576284504638197.004905208842
Trimmed Mean ( 26 / 40 )7.894202898550720.0392754095059849200.9960684776
Trimmed Mean ( 27 / 40 )7.89552238805970.0387171512522491203.928288437829
Trimmed Mean ( 28 / 40 )7.896923076923080.0380390254294363207.600562521565
Trimmed Mean ( 29 / 40 )7.89841269841270.0372156956886704212.233374984771
Trimmed Mean ( 30 / 40 )7.90.0362142984170074218.145880089448
Trimmed Mean ( 31 / 40 )7.90.0358165601563881220.568361827761
Trimmed Mean ( 32 / 40 )7.903508771929820.0353078931692975223.845380239296
Trimmed Mean ( 33 / 40 )7.905454545454550.0346622162856456228.071237000745
Trimmed Mean ( 34 / 40 )7.907547169811320.0338451455834207233.639035480612
Trimmed Mean ( 35 / 40 )7.90784313725490.033354088117592237.087673012534
Trimmed Mean ( 36 / 40 )7.908163265306120.0327114698691814241.755057077294
Trimmed Mean ( 37 / 40 )7.908510638297870.0318747820705459248.111834013315
Trimmed Mean ( 38 / 40 )7.908888888888890.0307847237175499256.909529591787
Trimmed Mean ( 39 / 40 )7.911627906976740.0299887949405894263.81946732606
Trimmed Mean ( 40 / 40 )7.914634146341460.0289155573810287273.715427375237
Median8
Midrange7.7
Midmean - Weighted Average at Xnp7.9
Midmean - Weighted Average at X(n+1)p7.9
Midmean - Empirical Distribution Function7.9
Midmean - Empirical Distribution Function - Averaging7.9
Midmean - Empirical Distribution Function - Interpolation7.9
Midmean - Closest Observation7.86307692307693
Midmean - True Basic - Statistics Graphics Toolkit7.9
Midmean - MS Excel (old versions)7.9
Number of observations121



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')