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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 computationTue, 20 Oct 2009 11:09:41 -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/20/t1256058770i1m507osoqszhzr.htm/, Retrieved Fri, 03 May 2024 02:00:39 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=48835, Retrieved Fri, 03 May 2024 02:00:39 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsSDHW, DSHW
Estimated Impact101
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Univariate Data Series] [DSHW-WS2.2] [2009-10-07 15:28:18] [f15cfb7053d35072d573abca87df96a0]
- RMP     [Central Tendency] [DSHW-WS3-2.1] [2009-10-20 17:09:41] [36295456a56d4c7dcc9b9537ce63463b] [Current]
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Dataseries X:
8
8.1
7.7
7.5
7.6
7.8
7.8
7.8
7.5
7.5
7.1
7.5
7.5
7.6
7.7
7.7
7.9
8.1
8.2
8.2
8.2
7.9
7.3
6.9
6.6
6.7
6.9
7
7.1
7.2
7.1
6.9
7
6.8
6.4
6.7
6.6
6.4
6.3
6.2
6.5
6.8
6.8
6.4
6.1
5.8
6.1
7.2
7.3
6.9
6.1
5.8
6.2
7.1
7.7
7.9
7.7
7.4
7.5
8
8.1
7.4
8.1
8.3




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'RServer@AstonUniversity' @ vre.aston.ac.uk

\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 & 'RServer@AstonUniversity' @ vre.aston.ac.uk \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=48835&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]'RServer@AstonUniversity' @ vre.aston.ac.uk[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=48835&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=48835&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'RServer@AstonUniversity' @ vre.aston.ac.uk







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean7.2218750.083940311784388386.035837209544
Geometric Mean7.1903081193854
Harmonic Mean7.15794720365018
Quadratic Mean7.25254265757879
Winsorized Mean ( 1 / 21 )7.22031250.083635751482791686.3304552418066
Winsorized Mean ( 2 / 21 )7.22968750.081335568113691788.887158074488
Winsorized Mean ( 3 / 21 )7.22968750.081335568113691788.887158074488
Winsorized Mean ( 4 / 21 )7.22343750.08020132738419390.0663085711431
Winsorized Mean ( 5 / 21 )7.231250.078517861429690492.096879211048
Winsorized Mean ( 6 / 21 )7.231250.078517861429690492.096879211048
Winsorized Mean ( 7 / 21 )7.24218750.076304940117981494.9111222524027
Winsorized Mean ( 8 / 21 )7.24218750.0717484544210226100.938585485097
Winsorized Mean ( 9 / 21 )7.24218750.0717484544210226100.938585485097
Winsorized Mean ( 10 / 21 )7.22656250.0692305423462188104.384022645096
Winsorized Mean ( 11 / 21 )7.243750.066064054715078109.647372254715
Winsorized Mean ( 12 / 21 )7.26250.0628166581384472115.614236975064
Winsorized Mean ( 13 / 21 )7.24218750.0596702532632799121.370148506756
Winsorized Mean ( 14 / 21 )7.26406250.0560508904384971129.597628925639
Winsorized Mean ( 15 / 21 )7.26406250.0560508904384971129.597628925639
Winsorized Mean ( 16 / 21 )7.26406250.0484566974245833149.908328179104
Winsorized Mean ( 17 / 21 )7.26406250.0484566974245833149.908328179104
Winsorized Mean ( 18 / 21 )7.26406250.0484566974245833149.908328179104
Winsorized Mean ( 19 / 21 )7.293750.0440888240346905165.433081051584
Winsorized Mean ( 20 / 21 )7.293750.0440888240346905165.433081051584
Winsorized Mean ( 21 / 21 )7.26093750.0394416126826972184.093321903780
Trimmed Mean ( 1 / 21 )7.227419354838710.081665935284710688.4998050857053
Trimmed Mean ( 2 / 21 )7.2350.079255896784663591.2865829990837
Trimmed Mean ( 3 / 21 )7.237931034482760.077811395994958193.018907345548
Trimmed Mean ( 4 / 21 )7.241071428571430.076011652631731795.2626495789223
Trimmed Mean ( 5 / 21 )7.24629629629630.074193213064743797.6679132358496
Trimmed Mean ( 6 / 21 )7.250.0724750958422643100.03436236606
Trimmed Mean ( 7 / 21 )7.2540.0702886178262054103.203053699763
Trimmed Mean ( 8 / 21 )7.256250.0681510011217789106.473124100317
Trimmed Mean ( 9 / 21 )7.258695652173910.0666359412497984108.930638871945
Trimmed Mean ( 10 / 21 )7.261363636363640.0646355786252185112.343136563653
Trimmed Mean ( 11 / 21 )7.266666666666670.06262424738726116.035991965389
Trimmed Mean ( 12 / 21 )7.270.0607854571001304119.600976069396
Trimmed Mean ( 13 / 21 )7.271052631578950.0591437113141058122.938727888806
Trimmed Mean ( 14 / 21 )7.2750.0576490476800155126.194625805101
Trimmed Mean ( 15 / 21 )7.27647058823530.0564958351168563128.796584264745
Trimmed Mean ( 16 / 21 )7.2781250.0547601763631435132.909086189477
Trimmed Mean ( 17 / 21 )7.280.0543297721137410133.996512717909
Trimmed Mean ( 18 / 21 )7.282142857142860.0534655037449658136.202641835738
Trimmed Mean ( 19 / 21 )7.284615384615380.0519444400496435140.238596809465
Trimmed Mean ( 20 / 21 )7.283333333333330.0509570246137657142.930898900361
Trimmed Mean ( 21 / 21 )7.281818181818180.049076476955042148.376954370398
Median7.3
Midrange7.05
Midmean - Weighted Average at Xnp7.24411764705882
Midmean - Weighted Average at X(n+1)p7.278125
Midmean - Empirical Distribution Function7.24411764705882
Midmean - Empirical Distribution Function - Averaging7.278125
Midmean - Empirical Distribution Function - Interpolation7.278125
Midmean - Closest Observation7.24411764705882
Midmean - True Basic - Statistics Graphics Toolkit7.278125
Midmean - MS Excel (old versions)7.28918918918919
Number of observations64

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 7.221875 & 0.0839403117843883 & 86.035837209544 \tabularnewline
Geometric Mean & 7.1903081193854 &  &  \tabularnewline
Harmonic Mean & 7.15794720365018 &  &  \tabularnewline
Quadratic Mean & 7.25254265757879 &  &  \tabularnewline
Winsorized Mean ( 1 / 21 ) & 7.2203125 & 0.0836357514827916 & 86.3304552418066 \tabularnewline
Winsorized Mean ( 2 / 21 ) & 7.2296875 & 0.0813355681136917 & 88.887158074488 \tabularnewline
Winsorized Mean ( 3 / 21 ) & 7.2296875 & 0.0813355681136917 & 88.887158074488 \tabularnewline
Winsorized Mean ( 4 / 21 ) & 7.2234375 & 0.080201327384193 & 90.0663085711431 \tabularnewline
Winsorized Mean ( 5 / 21 ) & 7.23125 & 0.0785178614296904 & 92.096879211048 \tabularnewline
Winsorized Mean ( 6 / 21 ) & 7.23125 & 0.0785178614296904 & 92.096879211048 \tabularnewline
Winsorized Mean ( 7 / 21 ) & 7.2421875 & 0.0763049401179814 & 94.9111222524027 \tabularnewline
Winsorized Mean ( 8 / 21 ) & 7.2421875 & 0.0717484544210226 & 100.938585485097 \tabularnewline
Winsorized Mean ( 9 / 21 ) & 7.2421875 & 0.0717484544210226 & 100.938585485097 \tabularnewline
Winsorized Mean ( 10 / 21 ) & 7.2265625 & 0.0692305423462188 & 104.384022645096 \tabularnewline
Winsorized Mean ( 11 / 21 ) & 7.24375 & 0.066064054715078 & 109.647372254715 \tabularnewline
Winsorized Mean ( 12 / 21 ) & 7.2625 & 0.0628166581384472 & 115.614236975064 \tabularnewline
Winsorized Mean ( 13 / 21 ) & 7.2421875 & 0.0596702532632799 & 121.370148506756 \tabularnewline
Winsorized Mean ( 14 / 21 ) & 7.2640625 & 0.0560508904384971 & 129.597628925639 \tabularnewline
Winsorized Mean ( 15 / 21 ) & 7.2640625 & 0.0560508904384971 & 129.597628925639 \tabularnewline
Winsorized Mean ( 16 / 21 ) & 7.2640625 & 0.0484566974245833 & 149.908328179104 \tabularnewline
Winsorized Mean ( 17 / 21 ) & 7.2640625 & 0.0484566974245833 & 149.908328179104 \tabularnewline
Winsorized Mean ( 18 / 21 ) & 7.2640625 & 0.0484566974245833 & 149.908328179104 \tabularnewline
Winsorized Mean ( 19 / 21 ) & 7.29375 & 0.0440888240346905 & 165.433081051584 \tabularnewline
Winsorized Mean ( 20 / 21 ) & 7.29375 & 0.0440888240346905 & 165.433081051584 \tabularnewline
Winsorized Mean ( 21 / 21 ) & 7.2609375 & 0.0394416126826972 & 184.093321903780 \tabularnewline
Trimmed Mean ( 1 / 21 ) & 7.22741935483871 & 0.0816659352847106 & 88.4998050857053 \tabularnewline
Trimmed Mean ( 2 / 21 ) & 7.235 & 0.0792558967846635 & 91.2865829990837 \tabularnewline
Trimmed Mean ( 3 / 21 ) & 7.23793103448276 & 0.0778113959949581 & 93.018907345548 \tabularnewline
Trimmed Mean ( 4 / 21 ) & 7.24107142857143 & 0.0760116526317317 & 95.2626495789223 \tabularnewline
Trimmed Mean ( 5 / 21 ) & 7.2462962962963 & 0.0741932130647437 & 97.6679132358496 \tabularnewline
Trimmed Mean ( 6 / 21 ) & 7.25 & 0.0724750958422643 & 100.03436236606 \tabularnewline
Trimmed Mean ( 7 / 21 ) & 7.254 & 0.0702886178262054 & 103.203053699763 \tabularnewline
Trimmed Mean ( 8 / 21 ) & 7.25625 & 0.0681510011217789 & 106.473124100317 \tabularnewline
Trimmed Mean ( 9 / 21 ) & 7.25869565217391 & 0.0666359412497984 & 108.930638871945 \tabularnewline
Trimmed Mean ( 10 / 21 ) & 7.26136363636364 & 0.0646355786252185 & 112.343136563653 \tabularnewline
Trimmed Mean ( 11 / 21 ) & 7.26666666666667 & 0.06262424738726 & 116.035991965389 \tabularnewline
Trimmed Mean ( 12 / 21 ) & 7.27 & 0.0607854571001304 & 119.600976069396 \tabularnewline
Trimmed Mean ( 13 / 21 ) & 7.27105263157895 & 0.0591437113141058 & 122.938727888806 \tabularnewline
Trimmed Mean ( 14 / 21 ) & 7.275 & 0.0576490476800155 & 126.194625805101 \tabularnewline
Trimmed Mean ( 15 / 21 ) & 7.2764705882353 & 0.0564958351168563 & 128.796584264745 \tabularnewline
Trimmed Mean ( 16 / 21 ) & 7.278125 & 0.0547601763631435 & 132.909086189477 \tabularnewline
Trimmed Mean ( 17 / 21 ) & 7.28 & 0.0543297721137410 & 133.996512717909 \tabularnewline
Trimmed Mean ( 18 / 21 ) & 7.28214285714286 & 0.0534655037449658 & 136.202641835738 \tabularnewline
Trimmed Mean ( 19 / 21 ) & 7.28461538461538 & 0.0519444400496435 & 140.238596809465 \tabularnewline
Trimmed Mean ( 20 / 21 ) & 7.28333333333333 & 0.0509570246137657 & 142.930898900361 \tabularnewline
Trimmed Mean ( 21 / 21 ) & 7.28181818181818 & 0.049076476955042 & 148.376954370398 \tabularnewline
Median & 7.3 &  &  \tabularnewline
Midrange & 7.05 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 7.24411764705882 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 7.278125 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 7.24411764705882 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 7.278125 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 7.278125 &  &  \tabularnewline
Midmean - Closest Observation & 7.24411764705882 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 7.278125 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 7.28918918918919 &  &  \tabularnewline
Number of observations & 64 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=48835&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]7.221875[/C][C]0.0839403117843883[/C][C]86.035837209544[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]7.1903081193854[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]7.15794720365018[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]7.25254265757879[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 21 )[/C][C]7.2203125[/C][C]0.0836357514827916[/C][C]86.3304552418066[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 21 )[/C][C]7.2296875[/C][C]0.0813355681136917[/C][C]88.887158074488[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 21 )[/C][C]7.2296875[/C][C]0.0813355681136917[/C][C]88.887158074488[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 21 )[/C][C]7.2234375[/C][C]0.080201327384193[/C][C]90.0663085711431[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 21 )[/C][C]7.23125[/C][C]0.0785178614296904[/C][C]92.096879211048[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 21 )[/C][C]7.23125[/C][C]0.0785178614296904[/C][C]92.096879211048[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 21 )[/C][C]7.2421875[/C][C]0.0763049401179814[/C][C]94.9111222524027[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 21 )[/C][C]7.2421875[/C][C]0.0717484544210226[/C][C]100.938585485097[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 21 )[/C][C]7.2421875[/C][C]0.0717484544210226[/C][C]100.938585485097[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 21 )[/C][C]7.2265625[/C][C]0.0692305423462188[/C][C]104.384022645096[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 21 )[/C][C]7.24375[/C][C]0.066064054715078[/C][C]109.647372254715[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 21 )[/C][C]7.2625[/C][C]0.0628166581384472[/C][C]115.614236975064[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 21 )[/C][C]7.2421875[/C][C]0.0596702532632799[/C][C]121.370148506756[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 21 )[/C][C]7.2640625[/C][C]0.0560508904384971[/C][C]129.597628925639[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 21 )[/C][C]7.2640625[/C][C]0.0560508904384971[/C][C]129.597628925639[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 21 )[/C][C]7.2640625[/C][C]0.0484566974245833[/C][C]149.908328179104[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 21 )[/C][C]7.2640625[/C][C]0.0484566974245833[/C][C]149.908328179104[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 21 )[/C][C]7.2640625[/C][C]0.0484566974245833[/C][C]149.908328179104[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 21 )[/C][C]7.29375[/C][C]0.0440888240346905[/C][C]165.433081051584[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 21 )[/C][C]7.29375[/C][C]0.0440888240346905[/C][C]165.433081051584[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 21 )[/C][C]7.2609375[/C][C]0.0394416126826972[/C][C]184.093321903780[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 21 )[/C][C]7.22741935483871[/C][C]0.0816659352847106[/C][C]88.4998050857053[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 21 )[/C][C]7.235[/C][C]0.0792558967846635[/C][C]91.2865829990837[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 21 )[/C][C]7.23793103448276[/C][C]0.0778113959949581[/C][C]93.018907345548[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 21 )[/C][C]7.24107142857143[/C][C]0.0760116526317317[/C][C]95.2626495789223[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 21 )[/C][C]7.2462962962963[/C][C]0.0741932130647437[/C][C]97.6679132358496[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 21 )[/C][C]7.25[/C][C]0.0724750958422643[/C][C]100.03436236606[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 21 )[/C][C]7.254[/C][C]0.0702886178262054[/C][C]103.203053699763[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 21 )[/C][C]7.25625[/C][C]0.0681510011217789[/C][C]106.473124100317[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 21 )[/C][C]7.25869565217391[/C][C]0.0666359412497984[/C][C]108.930638871945[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 21 )[/C][C]7.26136363636364[/C][C]0.0646355786252185[/C][C]112.343136563653[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 21 )[/C][C]7.26666666666667[/C][C]0.06262424738726[/C][C]116.035991965389[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 21 )[/C][C]7.27[/C][C]0.0607854571001304[/C][C]119.600976069396[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 21 )[/C][C]7.27105263157895[/C][C]0.0591437113141058[/C][C]122.938727888806[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 21 )[/C][C]7.275[/C][C]0.0576490476800155[/C][C]126.194625805101[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 21 )[/C][C]7.2764705882353[/C][C]0.0564958351168563[/C][C]128.796584264745[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 21 )[/C][C]7.278125[/C][C]0.0547601763631435[/C][C]132.909086189477[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 21 )[/C][C]7.28[/C][C]0.0543297721137410[/C][C]133.996512717909[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 21 )[/C][C]7.28214285714286[/C][C]0.0534655037449658[/C][C]136.202641835738[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 21 )[/C][C]7.28461538461538[/C][C]0.0519444400496435[/C][C]140.238596809465[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 21 )[/C][C]7.28333333333333[/C][C]0.0509570246137657[/C][C]142.930898900361[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 21 )[/C][C]7.28181818181818[/C][C]0.049076476955042[/C][C]148.376954370398[/C][/ROW]
[ROW][C]Median[/C][C]7.3[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]7.05[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]7.24411764705882[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]7.278125[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]7.24411764705882[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]7.278125[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]7.278125[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]7.24411764705882[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]7.278125[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]7.28918918918919[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]64[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=48835&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=48835&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 Mean7.2218750.083940311784388386.035837209544
Geometric Mean7.1903081193854
Harmonic Mean7.15794720365018
Quadratic Mean7.25254265757879
Winsorized Mean ( 1 / 21 )7.22031250.083635751482791686.3304552418066
Winsorized Mean ( 2 / 21 )7.22968750.081335568113691788.887158074488
Winsorized Mean ( 3 / 21 )7.22968750.081335568113691788.887158074488
Winsorized Mean ( 4 / 21 )7.22343750.08020132738419390.0663085711431
Winsorized Mean ( 5 / 21 )7.231250.078517861429690492.096879211048
Winsorized Mean ( 6 / 21 )7.231250.078517861429690492.096879211048
Winsorized Mean ( 7 / 21 )7.24218750.076304940117981494.9111222524027
Winsorized Mean ( 8 / 21 )7.24218750.0717484544210226100.938585485097
Winsorized Mean ( 9 / 21 )7.24218750.0717484544210226100.938585485097
Winsorized Mean ( 10 / 21 )7.22656250.0692305423462188104.384022645096
Winsorized Mean ( 11 / 21 )7.243750.066064054715078109.647372254715
Winsorized Mean ( 12 / 21 )7.26250.0628166581384472115.614236975064
Winsorized Mean ( 13 / 21 )7.24218750.0596702532632799121.370148506756
Winsorized Mean ( 14 / 21 )7.26406250.0560508904384971129.597628925639
Winsorized Mean ( 15 / 21 )7.26406250.0560508904384971129.597628925639
Winsorized Mean ( 16 / 21 )7.26406250.0484566974245833149.908328179104
Winsorized Mean ( 17 / 21 )7.26406250.0484566974245833149.908328179104
Winsorized Mean ( 18 / 21 )7.26406250.0484566974245833149.908328179104
Winsorized Mean ( 19 / 21 )7.293750.0440888240346905165.433081051584
Winsorized Mean ( 20 / 21 )7.293750.0440888240346905165.433081051584
Winsorized Mean ( 21 / 21 )7.26093750.0394416126826972184.093321903780
Trimmed Mean ( 1 / 21 )7.227419354838710.081665935284710688.4998050857053
Trimmed Mean ( 2 / 21 )7.2350.079255896784663591.2865829990837
Trimmed Mean ( 3 / 21 )7.237931034482760.077811395994958193.018907345548
Trimmed Mean ( 4 / 21 )7.241071428571430.076011652631731795.2626495789223
Trimmed Mean ( 5 / 21 )7.24629629629630.074193213064743797.6679132358496
Trimmed Mean ( 6 / 21 )7.250.0724750958422643100.03436236606
Trimmed Mean ( 7 / 21 )7.2540.0702886178262054103.203053699763
Trimmed Mean ( 8 / 21 )7.256250.0681510011217789106.473124100317
Trimmed Mean ( 9 / 21 )7.258695652173910.0666359412497984108.930638871945
Trimmed Mean ( 10 / 21 )7.261363636363640.0646355786252185112.343136563653
Trimmed Mean ( 11 / 21 )7.266666666666670.06262424738726116.035991965389
Trimmed Mean ( 12 / 21 )7.270.0607854571001304119.600976069396
Trimmed Mean ( 13 / 21 )7.271052631578950.0591437113141058122.938727888806
Trimmed Mean ( 14 / 21 )7.2750.0576490476800155126.194625805101
Trimmed Mean ( 15 / 21 )7.27647058823530.0564958351168563128.796584264745
Trimmed Mean ( 16 / 21 )7.2781250.0547601763631435132.909086189477
Trimmed Mean ( 17 / 21 )7.280.0543297721137410133.996512717909
Trimmed Mean ( 18 / 21 )7.282142857142860.0534655037449658136.202641835738
Trimmed Mean ( 19 / 21 )7.284615384615380.0519444400496435140.238596809465
Trimmed Mean ( 20 / 21 )7.283333333333330.0509570246137657142.930898900361
Trimmed Mean ( 21 / 21 )7.281818181818180.049076476955042148.376954370398
Median7.3
Midrange7.05
Midmean - Weighted Average at Xnp7.24411764705882
Midmean - Weighted Average at X(n+1)p7.278125
Midmean - Empirical Distribution Function7.24411764705882
Midmean - Empirical Distribution Function - Averaging7.278125
Midmean - Empirical Distribution Function - Interpolation7.278125
Midmean - Closest Observation7.24411764705882
Midmean - True Basic - Statistics Graphics Toolkit7.278125
Midmean - MS Excel (old versions)7.28918918918919
Number of observations64



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')