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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 computationFri, 23 Oct 2009 07:19:29 -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/23/t1256304105iz18rnagz0oqvcr.htm/, Retrieved Thu, 02 May 2024 01:38:38 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=49974, Retrieved Thu, 02 May 2024 01:38:38 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact113
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [workshop 3 review] [2009-10-23 13:19:29] [6198946fb53eb5eb18db46bb758f7fde] [Current]
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Dataseries X:
18.1
17.8
16.8
15.1
14.5
15.1
18
19.1
19
17.7
16.7
16.8
17.3
17.4
17.3
16.6
16.4
16.1
17.6
17.8
17.8
17.3
16.9
17.2
17.5
17.6
17.4
17.2
16.9
16.3
16.7
16.6
16.5
16.2
16
16.1
16.3
16.2
16
16.2
15.6
14.7
15.1
14.7
14.1
14.2
14.1
14.5
14.7
14.4
13.5
12.9
12.3
13
15.4
16
15.2
14
13.3
14
15.4




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Sir Ronald Aylmer Fisher' @ 193.190.124.24

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 2 seconds \tabularnewline
R Server & 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=49974&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Sir Ronald Aylmer Fisher' @ 193.190.124.24[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=49974&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=49974&T=0

As an alternative you can also use a QR Code:  

The GUIDs for individual cells are displayed in the table below:

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Sir Ronald Aylmer Fisher' @ 193.190.124.24







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean16.01967213114750.19873671618846080.6075114774276
Geometric Mean15.9432729959569
Harmonic Mean15.8644033385152
Quadratic Mean16.0934667530382
Winsorized Mean ( 1 / 20 )16.0278688524590.19546960614492981.996731709662
Winsorized Mean ( 2 / 20 )16.00163934426230.18809502021568385.0721051833998
Winsorized Mean ( 3 / 20 )16.01147540983610.18341178193403387.2979654905424
Winsorized Mean ( 4 / 20 )16.01147540983610.17796816748357989.9681984493855
Winsorized Mean ( 5 / 20 )16.05245901639340.16898291951996894.9945654980624
Winsorized Mean ( 6 / 20 )16.05245901639340.16898291951996894.9945654980624
Winsorized Mean ( 7 / 20 )16.05245901639340.16474199993639797.4399911533845
Winsorized Mean ( 8 / 20 )16.03934426229510.1625997581734398.6431003494324
Winsorized Mean ( 9 / 20 )16.05409836065570.159705565332946100.523099036574
Winsorized Mean ( 10 / 20 )16.07049180327870.150887072133870106.506750883341
Winsorized Mean ( 11 / 20 )16.07049180327870.144788224136519110.993085930289
Winsorized Mean ( 12 / 20 )16.07049180327870.144788224136519110.993085930289
Winsorized Mean ( 13 / 20 )16.09180327868850.134007076763773120.081742451968
Winsorized Mean ( 14 / 20 )16.09180327868850.134007076763773120.081742451968
Winsorized Mean ( 15 / 20 )16.09180327868850.134007076763773120.081742451968
Winsorized Mean ( 16 / 20 )16.17049180327870.112578916153373143.636946915075
Winsorized Mean ( 17 / 20 )16.17049180327870.112578916153373143.636946915075
Winsorized Mean ( 18 / 20 )16.08196721311480.0997403239543607161.238369553257
Winsorized Mean ( 19 / 20 )16.11311475409840.0946802328991454170.184570323800
Winsorized Mean ( 20 / 20 )16.14590163934430.0797733733496561202.397127780655
Trimmed Mean ( 1 / 20 )16.03050847457630.18821587263666085.1708639128552
Trimmed Mean ( 2 / 20 )16.03333333333330.17929011600636989.4267553084955
Trimmed Mean ( 3 / 20 )16.05090909090910.17322204522326792.6608912290638
Trimmed Mean ( 4 / 20 )16.06603773584910.16794980322174795.6597592117257
Trimmed Mean ( 5 / 20 )16.08235294117650.16346027597669198.3869190546929
Trimmed Mean ( 6 / 20 )16.08979591836730.160839763132177100.036182626959
Trimmed Mean ( 7 / 20 )16.09787234042550.157380539595316102.286295254922
Trimmed Mean ( 8 / 20 )16.10666666666670.154049709935829104.554995094610
Trimmed Mean ( 9 / 20 )16.11860465116280.150166235458941107.338408010967
Trimmed Mean ( 10 / 20 )16.12926829268290.145763084692293110.653999445278
Trimmed Mean ( 11 / 20 )16.13846153846150.142211916561459113.481780772479
Trimmed Mean ( 12 / 20 )16.14864864864860.138883450912128116.274822828718
Trimmed Mean ( 13 / 20 )16.160.134113961323379120.494539424084
Trimmed Mean ( 14 / 20 )16.16969696969700.130448298164565123.954832659437
Trimmed Mean ( 15 / 20 )16.18064516129030.124987685831183129.457914623245
Trimmed Mean ( 16 / 20 )16.19310344827590.116805913972642138.632564889382
Trimmed Mean ( 17 / 20 )16.19629629629630.112404626427062144.089232010444
Trimmed Mean ( 18 / 20 )16.20.105356537528527153.763595311905
Trimmed Mean ( 19 / 20 )16.21739130434780.0989374725512222163.915560870546
Trimmed Mean ( 20 / 20 )16.23333333333330.0905889022251027179.197814904473
Median16.2
Midrange15.7
Midmean - Weighted Average at Xnp16.053125
Midmean - Weighted Average at X(n+1)p16.16
Midmean - Empirical Distribution Function16.16
Midmean - Empirical Distribution Function - Averaging16.16
Midmean - Empirical Distribution Function - Interpolation16.16
Midmean - Closest Observation16.16
Midmean - True Basic - Statistics Graphics Toolkit16.16
Midmean - MS Excel (old versions)16.16
Number of observations61

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 16.0196721311475 & 0.198736716188460 & 80.6075114774276 \tabularnewline
Geometric Mean & 15.9432729959569 &  &  \tabularnewline
Harmonic Mean & 15.8644033385152 &  &  \tabularnewline
Quadratic Mean & 16.0934667530382 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 16.027868852459 & 0.195469606144929 & 81.996731709662 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 16.0016393442623 & 0.188095020215683 & 85.0721051833998 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 16.0114754098361 & 0.183411781934033 & 87.2979654905424 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 16.0114754098361 & 0.177968167483579 & 89.9681984493855 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 16.0524590163934 & 0.168982919519968 & 94.9945654980624 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 16.0524590163934 & 0.168982919519968 & 94.9945654980624 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 16.0524590163934 & 0.164741999936397 & 97.4399911533845 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 16.0393442622951 & 0.16259975817343 & 98.6431003494324 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 16.0540983606557 & 0.159705565332946 & 100.523099036574 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 16.0704918032787 & 0.150887072133870 & 106.506750883341 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 16.0704918032787 & 0.144788224136519 & 110.993085930289 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 16.0704918032787 & 0.144788224136519 & 110.993085930289 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 16.0918032786885 & 0.134007076763773 & 120.081742451968 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 16.0918032786885 & 0.134007076763773 & 120.081742451968 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 16.0918032786885 & 0.134007076763773 & 120.081742451968 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 16.1704918032787 & 0.112578916153373 & 143.636946915075 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 16.1704918032787 & 0.112578916153373 & 143.636946915075 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 16.0819672131148 & 0.0997403239543607 & 161.238369553257 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 16.1131147540984 & 0.0946802328991454 & 170.184570323800 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 16.1459016393443 & 0.0797733733496561 & 202.397127780655 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 16.0305084745763 & 0.188215872636660 & 85.1708639128552 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 16.0333333333333 & 0.179290116006369 & 89.4267553084955 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 16.0509090909091 & 0.173222045223267 & 92.6608912290638 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 16.0660377358491 & 0.167949803221747 & 95.6597592117257 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 16.0823529411765 & 0.163460275976691 & 98.3869190546929 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 16.0897959183673 & 0.160839763132177 & 100.036182626959 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 16.0978723404255 & 0.157380539595316 & 102.286295254922 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 16.1066666666667 & 0.154049709935829 & 104.554995094610 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 16.1186046511628 & 0.150166235458941 & 107.338408010967 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 16.1292682926829 & 0.145763084692293 & 110.653999445278 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 16.1384615384615 & 0.142211916561459 & 113.481780772479 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 16.1486486486486 & 0.138883450912128 & 116.274822828718 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 16.16 & 0.134113961323379 & 120.494539424084 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 16.1696969696970 & 0.130448298164565 & 123.954832659437 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 16.1806451612903 & 0.124987685831183 & 129.457914623245 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 16.1931034482759 & 0.116805913972642 & 138.632564889382 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 16.1962962962963 & 0.112404626427062 & 144.089232010444 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 16.2 & 0.105356537528527 & 153.763595311905 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 16.2173913043478 & 0.0989374725512222 & 163.915560870546 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 16.2333333333333 & 0.0905889022251027 & 179.197814904473 \tabularnewline
Median & 16.2 &  &  \tabularnewline
Midrange & 15.7 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 16.053125 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 16.16 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 16.16 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 16.16 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 16.16 &  &  \tabularnewline
Midmean - Closest Observation & 16.16 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 16.16 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 16.16 &  &  \tabularnewline
Number of observations & 61 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=49974&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]16.0196721311475[/C][C]0.198736716188460[/C][C]80.6075114774276[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]15.9432729959569[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]15.8644033385152[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]16.0934667530382[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]16.027868852459[/C][C]0.195469606144929[/C][C]81.996731709662[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]16.0016393442623[/C][C]0.188095020215683[/C][C]85.0721051833998[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]16.0114754098361[/C][C]0.183411781934033[/C][C]87.2979654905424[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]16.0114754098361[/C][C]0.177968167483579[/C][C]89.9681984493855[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]16.0524590163934[/C][C]0.168982919519968[/C][C]94.9945654980624[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]16.0524590163934[/C][C]0.168982919519968[/C][C]94.9945654980624[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]16.0524590163934[/C][C]0.164741999936397[/C][C]97.4399911533845[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]16.0393442622951[/C][C]0.16259975817343[/C][C]98.6431003494324[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]16.0540983606557[/C][C]0.159705565332946[/C][C]100.523099036574[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]16.0704918032787[/C][C]0.150887072133870[/C][C]106.506750883341[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]16.0704918032787[/C][C]0.144788224136519[/C][C]110.993085930289[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]16.0704918032787[/C][C]0.144788224136519[/C][C]110.993085930289[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]16.0918032786885[/C][C]0.134007076763773[/C][C]120.081742451968[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]16.0918032786885[/C][C]0.134007076763773[/C][C]120.081742451968[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]16.0918032786885[/C][C]0.134007076763773[/C][C]120.081742451968[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]16.1704918032787[/C][C]0.112578916153373[/C][C]143.636946915075[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]16.1704918032787[/C][C]0.112578916153373[/C][C]143.636946915075[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]16.0819672131148[/C][C]0.0997403239543607[/C][C]161.238369553257[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]16.1131147540984[/C][C]0.0946802328991454[/C][C]170.184570323800[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]16.1459016393443[/C][C]0.0797733733496561[/C][C]202.397127780655[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]16.0305084745763[/C][C]0.188215872636660[/C][C]85.1708639128552[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]16.0333333333333[/C][C]0.179290116006369[/C][C]89.4267553084955[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]16.0509090909091[/C][C]0.173222045223267[/C][C]92.6608912290638[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]16.0660377358491[/C][C]0.167949803221747[/C][C]95.6597592117257[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]16.0823529411765[/C][C]0.163460275976691[/C][C]98.3869190546929[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]16.0897959183673[/C][C]0.160839763132177[/C][C]100.036182626959[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]16.0978723404255[/C][C]0.157380539595316[/C][C]102.286295254922[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]16.1066666666667[/C][C]0.154049709935829[/C][C]104.554995094610[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]16.1186046511628[/C][C]0.150166235458941[/C][C]107.338408010967[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]16.1292682926829[/C][C]0.145763084692293[/C][C]110.653999445278[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]16.1384615384615[/C][C]0.142211916561459[/C][C]113.481780772479[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]16.1486486486486[/C][C]0.138883450912128[/C][C]116.274822828718[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]16.16[/C][C]0.134113961323379[/C][C]120.494539424084[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]16.1696969696970[/C][C]0.130448298164565[/C][C]123.954832659437[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]16.1806451612903[/C][C]0.124987685831183[/C][C]129.457914623245[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]16.1931034482759[/C][C]0.116805913972642[/C][C]138.632564889382[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]16.1962962962963[/C][C]0.112404626427062[/C][C]144.089232010444[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]16.2[/C][C]0.105356537528527[/C][C]153.763595311905[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]16.2173913043478[/C][C]0.0989374725512222[/C][C]163.915560870546[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]16.2333333333333[/C][C]0.0905889022251027[/C][C]179.197814904473[/C][/ROW]
[ROW][C]Median[/C][C]16.2[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]15.7[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]16.053125[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]16.16[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]16.16[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]16.16[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]16.16[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]16.16[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]16.16[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]16.16[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]61[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=49974&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=49974&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 Mean16.01967213114750.19873671618846080.6075114774276
Geometric Mean15.9432729959569
Harmonic Mean15.8644033385152
Quadratic Mean16.0934667530382
Winsorized Mean ( 1 / 20 )16.0278688524590.19546960614492981.996731709662
Winsorized Mean ( 2 / 20 )16.00163934426230.18809502021568385.0721051833998
Winsorized Mean ( 3 / 20 )16.01147540983610.18341178193403387.2979654905424
Winsorized Mean ( 4 / 20 )16.01147540983610.17796816748357989.9681984493855
Winsorized Mean ( 5 / 20 )16.05245901639340.16898291951996894.9945654980624
Winsorized Mean ( 6 / 20 )16.05245901639340.16898291951996894.9945654980624
Winsorized Mean ( 7 / 20 )16.05245901639340.16474199993639797.4399911533845
Winsorized Mean ( 8 / 20 )16.03934426229510.1625997581734398.6431003494324
Winsorized Mean ( 9 / 20 )16.05409836065570.159705565332946100.523099036574
Winsorized Mean ( 10 / 20 )16.07049180327870.150887072133870106.506750883341
Winsorized Mean ( 11 / 20 )16.07049180327870.144788224136519110.993085930289
Winsorized Mean ( 12 / 20 )16.07049180327870.144788224136519110.993085930289
Winsorized Mean ( 13 / 20 )16.09180327868850.134007076763773120.081742451968
Winsorized Mean ( 14 / 20 )16.09180327868850.134007076763773120.081742451968
Winsorized Mean ( 15 / 20 )16.09180327868850.134007076763773120.081742451968
Winsorized Mean ( 16 / 20 )16.17049180327870.112578916153373143.636946915075
Winsorized Mean ( 17 / 20 )16.17049180327870.112578916153373143.636946915075
Winsorized Mean ( 18 / 20 )16.08196721311480.0997403239543607161.238369553257
Winsorized Mean ( 19 / 20 )16.11311475409840.0946802328991454170.184570323800
Winsorized Mean ( 20 / 20 )16.14590163934430.0797733733496561202.397127780655
Trimmed Mean ( 1 / 20 )16.03050847457630.18821587263666085.1708639128552
Trimmed Mean ( 2 / 20 )16.03333333333330.17929011600636989.4267553084955
Trimmed Mean ( 3 / 20 )16.05090909090910.17322204522326792.6608912290638
Trimmed Mean ( 4 / 20 )16.06603773584910.16794980322174795.6597592117257
Trimmed Mean ( 5 / 20 )16.08235294117650.16346027597669198.3869190546929
Trimmed Mean ( 6 / 20 )16.08979591836730.160839763132177100.036182626959
Trimmed Mean ( 7 / 20 )16.09787234042550.157380539595316102.286295254922
Trimmed Mean ( 8 / 20 )16.10666666666670.154049709935829104.554995094610
Trimmed Mean ( 9 / 20 )16.11860465116280.150166235458941107.338408010967
Trimmed Mean ( 10 / 20 )16.12926829268290.145763084692293110.653999445278
Trimmed Mean ( 11 / 20 )16.13846153846150.142211916561459113.481780772479
Trimmed Mean ( 12 / 20 )16.14864864864860.138883450912128116.274822828718
Trimmed Mean ( 13 / 20 )16.160.134113961323379120.494539424084
Trimmed Mean ( 14 / 20 )16.16969696969700.130448298164565123.954832659437
Trimmed Mean ( 15 / 20 )16.18064516129030.124987685831183129.457914623245
Trimmed Mean ( 16 / 20 )16.19310344827590.116805913972642138.632564889382
Trimmed Mean ( 17 / 20 )16.19629629629630.112404626427062144.089232010444
Trimmed Mean ( 18 / 20 )16.20.105356537528527153.763595311905
Trimmed Mean ( 19 / 20 )16.21739130434780.0989374725512222163.915560870546
Trimmed Mean ( 20 / 20 )16.23333333333330.0905889022251027179.197814904473
Median16.2
Midrange15.7
Midmean - Weighted Average at Xnp16.053125
Midmean - Weighted Average at X(n+1)p16.16
Midmean - Empirical Distribution Function16.16
Midmean - Empirical Distribution Function - Averaging16.16
Midmean - Empirical Distribution Function - Interpolation16.16
Midmean - Closest Observation16.16
Midmean - True Basic - Statistics Graphics Toolkit16.16
Midmean - MS Excel (old versions)16.16
Number of observations61



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')