Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationWed, 07 Mar 2012 11:03:48 -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/2012/Mar/07/t1331136276z90zpn2vipwc56c.htm/, Retrieved Mon, 29 Apr 2024 02:28:40 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=163645, Retrieved Mon, 29 Apr 2024 02:28:40 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsKDG2011W51a
Estimated Impact73
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [centrummaten spor...] [2012-03-07 16:03:48] [f6a7b86b75cb82ac7a5a766dce297b13] [Current]
Feedback Forum

Post a new message
Dataseries X:
162,32
162,76
163,39
162,58
162,66
162,66
162,66
162,89
163,03
162,38
162,44
162,51
162,51
162,42
162,07
161,45
162,22
162,21
162,21
162,21
162,41
163,96
163,79
163,86
163,86
164,39
164,74
164,27
165,2
165,42
165,42
165,5
165,71
165,74
165,29
164,88
164,88
164,57
164,53
165,03
165,92
165,92
165,92
165,92
166,12
166,34
165,48
165,61
165,61
165,94
165,88
166,23
166,32
166,43
166,43
166,2
166,21
168,02
168,68
168,65




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=163645&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=163645&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=163645&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 Mean164.5143333333330.229431299696887717.052701835719
Geometric Mean164.504905813671
Harmonic Mean164.495489870874
Quadratic Mean164.523772010815
Winsorized Mean ( 1 / 20 )164.5241666666670.227160598216983724.263661735534
Winsorized Mean ( 2 / 20 )164.5078333333330.220244098231999746.934127424588
Winsorized Mean ( 3 / 20 )164.4283333333330.202676604536304811.284231396725
Winsorized Mean ( 4 / 20 )164.4283333333330.202676604536304811.284231396725
Winsorized Mean ( 5 / 20 )164.4216666666670.201288528145765816.845690021634
Winsorized Mean ( 6 / 20 )164.4296666666670.199141230676068825.693735588766
Winsorized Mean ( 7 / 20 )164.4261666666670.196231313359386837.920125242856
Winsorized Mean ( 8 / 20 )164.42750.195113124509686842.729059939979
Winsorized Mean ( 9 / 20 )164.42750.194618651448224844.870205278057
Winsorized Mean ( 10 / 20 )164.41750.192005123666334856.318294326999
Winsorized Mean ( 11 / 20 )164.3973333333330.184960045565911888.826193950897
Winsorized Mean ( 12 / 20 )164.3933333333330.184396659569157891.520126869101
Winsorized Mean ( 13 / 20 )164.40850.181790968462927904.382111994349
Winsorized Mean ( 14 / 20 )164.4271666666670.178634666741813920.466165194684
Winsorized Mean ( 15 / 20 )164.4271666666670.178634666741813920.466165194684
Winsorized Mean ( 16 / 20 )164.41650.17713233984569928.212770989377
Winsorized Mean ( 17 / 20 )164.4051666666670.166915942116325984.957845141548
Winsorized Mean ( 18 / 20 )164.4351666666670.1592293395704381032.69389366477
Winsorized Mean ( 19 / 20 )164.4478333333330.1477144312567551113.28210747054
Winsorized Mean ( 20 / 20 )164.5678333333330.1286088300530281279.59980092719
Trimmed Mean ( 1 / 20 )164.4953448275860.219702022191848748.720212888828
Trimmed Mean ( 2 / 20 )164.4644642857140.210426579669381781.576474531489
Trimmed Mean ( 3 / 20 )164.440370370370.203588176375632807.710807659912
Trimmed Mean ( 4 / 20 )164.4450.203374899937493808.58060680321
Trimmed Mean ( 5 / 20 )164.450.202790331049947810.936099115576
Trimmed Mean ( 6 / 20 )164.4570833333330.202167106274335813.471025846164
Trimmed Mean ( 7 / 20 )164.4630434782610.201644176387605815.610182374552
Trimmed Mean ( 8 / 20 )164.4702272727270.201347860042767816.846164830325
Trimmed Mean ( 9 / 20 )164.4778571428570.200796479010654819.127197614505
Trimmed Mean ( 10 / 20 )164.486250.199721500807037823.578079151928
Trimmed Mean ( 11 / 20 )164.4971052631580.198439111017996828.955060417701
Trimmed Mean ( 12 / 20 )164.5122222222220.197859221682838831.460979291278
Trimmed Mean ( 13 / 20 )164.5297058823530.196506242295209837.274704155106
Trimmed Mean ( 14 / 20 )164.54718750.194639987341705845.392510281688
Trimmed Mean ( 15 / 20 )164.5643333333330.192164730179355856.371162282168
Trimmed Mean ( 16 / 20 )164.5839285714290.187759231228626876.569037348805
Trimmed Mean ( 17 / 20 )164.6080769230770.180832280330331910.28038037447
Trimmed Mean ( 18 / 20 )164.6379166666670.173085782500657951.192606856901
Trimmed Mean ( 19 / 20 )164.6686363636360.1632453541492631008.71866903527
Trimmed Mean ( 20 / 20 )164.70350.1514513557479581087.50099453778
Median164.81
Midrange165.065
Midmean - Weighted Average at Xnp164.627941176471
Midmean - Weighted Average at X(n+1)p164.627941176471
Midmean - Empirical Distribution Function164.627941176471
Midmean - Empirical Distribution Function - Averaging164.627941176471
Midmean - Empirical Distribution Function - Interpolation164.627941176471
Midmean - Closest Observation164.627941176471
Midmean - True Basic - Statistics Graphics Toolkit164.627941176471
Midmean - MS Excel (old versions)164.627941176471
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 164.514333333333 & 0.229431299696887 & 717.052701835719 \tabularnewline
Geometric Mean & 164.504905813671 &  &  \tabularnewline
Harmonic Mean & 164.495489870874 &  &  \tabularnewline
Quadratic Mean & 164.523772010815 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 164.524166666667 & 0.227160598216983 & 724.263661735534 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 164.507833333333 & 0.220244098231999 & 746.934127424588 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 164.428333333333 & 0.202676604536304 & 811.284231396725 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 164.428333333333 & 0.202676604536304 & 811.284231396725 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 164.421666666667 & 0.201288528145765 & 816.845690021634 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 164.429666666667 & 0.199141230676068 & 825.693735588766 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 164.426166666667 & 0.196231313359386 & 837.920125242856 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 164.4275 & 0.195113124509686 & 842.729059939979 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 164.4275 & 0.194618651448224 & 844.870205278057 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 164.4175 & 0.192005123666334 & 856.318294326999 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 164.397333333333 & 0.184960045565911 & 888.826193950897 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 164.393333333333 & 0.184396659569157 & 891.520126869101 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 164.4085 & 0.181790968462927 & 904.382111994349 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 164.427166666667 & 0.178634666741813 & 920.466165194684 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 164.427166666667 & 0.178634666741813 & 920.466165194684 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 164.4165 & 0.17713233984569 & 928.212770989377 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 164.405166666667 & 0.166915942116325 & 984.957845141548 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 164.435166666667 & 0.159229339570438 & 1032.69389366477 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 164.447833333333 & 0.147714431256755 & 1113.28210747054 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 164.567833333333 & 0.128608830053028 & 1279.59980092719 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 164.495344827586 & 0.219702022191848 & 748.720212888828 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 164.464464285714 & 0.210426579669381 & 781.576474531489 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 164.44037037037 & 0.203588176375632 & 807.710807659912 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 164.445 & 0.203374899937493 & 808.58060680321 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 164.45 & 0.202790331049947 & 810.936099115576 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 164.457083333333 & 0.202167106274335 & 813.471025846164 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 164.463043478261 & 0.201644176387605 & 815.610182374552 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 164.470227272727 & 0.201347860042767 & 816.846164830325 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 164.477857142857 & 0.200796479010654 & 819.127197614505 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 164.48625 & 0.199721500807037 & 823.578079151928 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 164.497105263158 & 0.198439111017996 & 828.955060417701 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 164.512222222222 & 0.197859221682838 & 831.460979291278 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 164.529705882353 & 0.196506242295209 & 837.274704155106 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 164.5471875 & 0.194639987341705 & 845.392510281688 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 164.564333333333 & 0.192164730179355 & 856.371162282168 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 164.583928571429 & 0.187759231228626 & 876.569037348805 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 164.608076923077 & 0.180832280330331 & 910.28038037447 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 164.637916666667 & 0.173085782500657 & 951.192606856901 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 164.668636363636 & 0.163245354149263 & 1008.71866903527 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 164.7035 & 0.151451355747958 & 1087.50099453778 \tabularnewline
Median & 164.81 &  &  \tabularnewline
Midrange & 165.065 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 164.627941176471 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 164.627941176471 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 164.627941176471 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 164.627941176471 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 164.627941176471 &  &  \tabularnewline
Midmean - Closest Observation & 164.627941176471 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 164.627941176471 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 164.627941176471 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=163645&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]164.514333333333[/C][C]0.229431299696887[/C][C]717.052701835719[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]164.504905813671[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]164.495489870874[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]164.523772010815[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]164.524166666667[/C][C]0.227160598216983[/C][C]724.263661735534[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]164.507833333333[/C][C]0.220244098231999[/C][C]746.934127424588[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]164.428333333333[/C][C]0.202676604536304[/C][C]811.284231396725[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]164.428333333333[/C][C]0.202676604536304[/C][C]811.284231396725[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]164.421666666667[/C][C]0.201288528145765[/C][C]816.845690021634[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]164.429666666667[/C][C]0.199141230676068[/C][C]825.693735588766[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]164.426166666667[/C][C]0.196231313359386[/C][C]837.920125242856[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]164.4275[/C][C]0.195113124509686[/C][C]842.729059939979[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]164.4275[/C][C]0.194618651448224[/C][C]844.870205278057[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]164.4175[/C][C]0.192005123666334[/C][C]856.318294326999[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]164.397333333333[/C][C]0.184960045565911[/C][C]888.826193950897[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]164.393333333333[/C][C]0.184396659569157[/C][C]891.520126869101[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]164.4085[/C][C]0.181790968462927[/C][C]904.382111994349[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]164.427166666667[/C][C]0.178634666741813[/C][C]920.466165194684[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]164.427166666667[/C][C]0.178634666741813[/C][C]920.466165194684[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]164.4165[/C][C]0.17713233984569[/C][C]928.212770989377[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]164.405166666667[/C][C]0.166915942116325[/C][C]984.957845141548[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]164.435166666667[/C][C]0.159229339570438[/C][C]1032.69389366477[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]164.447833333333[/C][C]0.147714431256755[/C][C]1113.28210747054[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]164.567833333333[/C][C]0.128608830053028[/C][C]1279.59980092719[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]164.495344827586[/C][C]0.219702022191848[/C][C]748.720212888828[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]164.464464285714[/C][C]0.210426579669381[/C][C]781.576474531489[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]164.44037037037[/C][C]0.203588176375632[/C][C]807.710807659912[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]164.445[/C][C]0.203374899937493[/C][C]808.58060680321[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]164.45[/C][C]0.202790331049947[/C][C]810.936099115576[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]164.457083333333[/C][C]0.202167106274335[/C][C]813.471025846164[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]164.463043478261[/C][C]0.201644176387605[/C][C]815.610182374552[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]164.470227272727[/C][C]0.201347860042767[/C][C]816.846164830325[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]164.477857142857[/C][C]0.200796479010654[/C][C]819.127197614505[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]164.48625[/C][C]0.199721500807037[/C][C]823.578079151928[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]164.497105263158[/C][C]0.198439111017996[/C][C]828.955060417701[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]164.512222222222[/C][C]0.197859221682838[/C][C]831.460979291278[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]164.529705882353[/C][C]0.196506242295209[/C][C]837.274704155106[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]164.5471875[/C][C]0.194639987341705[/C][C]845.392510281688[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]164.564333333333[/C][C]0.192164730179355[/C][C]856.371162282168[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]164.583928571429[/C][C]0.187759231228626[/C][C]876.569037348805[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]164.608076923077[/C][C]0.180832280330331[/C][C]910.28038037447[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]164.637916666667[/C][C]0.173085782500657[/C][C]951.192606856901[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]164.668636363636[/C][C]0.163245354149263[/C][C]1008.71866903527[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]164.7035[/C][C]0.151451355747958[/C][C]1087.50099453778[/C][/ROW]
[ROW][C]Median[/C][C]164.81[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]165.065[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]164.627941176471[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]164.627941176471[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]164.627941176471[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]164.627941176471[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]164.627941176471[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]164.627941176471[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]164.627941176471[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]164.627941176471[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]60[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=163645&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=163645&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 Mean164.5143333333330.229431299696887717.052701835719
Geometric Mean164.504905813671
Harmonic Mean164.495489870874
Quadratic Mean164.523772010815
Winsorized Mean ( 1 / 20 )164.5241666666670.227160598216983724.263661735534
Winsorized Mean ( 2 / 20 )164.5078333333330.220244098231999746.934127424588
Winsorized Mean ( 3 / 20 )164.4283333333330.202676604536304811.284231396725
Winsorized Mean ( 4 / 20 )164.4283333333330.202676604536304811.284231396725
Winsorized Mean ( 5 / 20 )164.4216666666670.201288528145765816.845690021634
Winsorized Mean ( 6 / 20 )164.4296666666670.199141230676068825.693735588766
Winsorized Mean ( 7 / 20 )164.4261666666670.196231313359386837.920125242856
Winsorized Mean ( 8 / 20 )164.42750.195113124509686842.729059939979
Winsorized Mean ( 9 / 20 )164.42750.194618651448224844.870205278057
Winsorized Mean ( 10 / 20 )164.41750.192005123666334856.318294326999
Winsorized Mean ( 11 / 20 )164.3973333333330.184960045565911888.826193950897
Winsorized Mean ( 12 / 20 )164.3933333333330.184396659569157891.520126869101
Winsorized Mean ( 13 / 20 )164.40850.181790968462927904.382111994349
Winsorized Mean ( 14 / 20 )164.4271666666670.178634666741813920.466165194684
Winsorized Mean ( 15 / 20 )164.4271666666670.178634666741813920.466165194684
Winsorized Mean ( 16 / 20 )164.41650.17713233984569928.212770989377
Winsorized Mean ( 17 / 20 )164.4051666666670.166915942116325984.957845141548
Winsorized Mean ( 18 / 20 )164.4351666666670.1592293395704381032.69389366477
Winsorized Mean ( 19 / 20 )164.4478333333330.1477144312567551113.28210747054
Winsorized Mean ( 20 / 20 )164.5678333333330.1286088300530281279.59980092719
Trimmed Mean ( 1 / 20 )164.4953448275860.219702022191848748.720212888828
Trimmed Mean ( 2 / 20 )164.4644642857140.210426579669381781.576474531489
Trimmed Mean ( 3 / 20 )164.440370370370.203588176375632807.710807659912
Trimmed Mean ( 4 / 20 )164.4450.203374899937493808.58060680321
Trimmed Mean ( 5 / 20 )164.450.202790331049947810.936099115576
Trimmed Mean ( 6 / 20 )164.4570833333330.202167106274335813.471025846164
Trimmed Mean ( 7 / 20 )164.4630434782610.201644176387605815.610182374552
Trimmed Mean ( 8 / 20 )164.4702272727270.201347860042767816.846164830325
Trimmed Mean ( 9 / 20 )164.4778571428570.200796479010654819.127197614505
Trimmed Mean ( 10 / 20 )164.486250.199721500807037823.578079151928
Trimmed Mean ( 11 / 20 )164.4971052631580.198439111017996828.955060417701
Trimmed Mean ( 12 / 20 )164.5122222222220.197859221682838831.460979291278
Trimmed Mean ( 13 / 20 )164.5297058823530.196506242295209837.274704155106
Trimmed Mean ( 14 / 20 )164.54718750.194639987341705845.392510281688
Trimmed Mean ( 15 / 20 )164.5643333333330.192164730179355856.371162282168
Trimmed Mean ( 16 / 20 )164.5839285714290.187759231228626876.569037348805
Trimmed Mean ( 17 / 20 )164.6080769230770.180832280330331910.28038037447
Trimmed Mean ( 18 / 20 )164.6379166666670.173085782500657951.192606856901
Trimmed Mean ( 19 / 20 )164.6686363636360.1632453541492631008.71866903527
Trimmed Mean ( 20 / 20 )164.70350.1514513557479581087.50099453778
Median164.81
Midrange165.065
Midmean - Weighted Average at Xnp164.627941176471
Midmean - Weighted Average at X(n+1)p164.627941176471
Midmean - Empirical Distribution Function164.627941176471
Midmean - Empirical Distribution Function - Averaging164.627941176471
Midmean - Empirical Distribution Function - Interpolation164.627941176471
Midmean - Closest Observation164.627941176471
Midmean - True Basic - Statistics Graphics Toolkit164.627941176471
Midmean - MS Excel (old versions)164.627941176471
Number of observations60



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')