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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, 27 Oct 2009 18:15:33 -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/28/t1256689125rjs11x0m3egl7ov.htm/, Retrieved Sun, 05 May 2024 21:34:39 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=51321, Retrieved Sun, 05 May 2024 21:34:39 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordscentral tendency
Estimated Impact117
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [WS 3 Yt=C+Et assu...] [2009-10-28 00:15:33] [a54ad7d84632b3d861404e40e79a6400] [Current]
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Dataseries X:
100.33
101.77
103.00
104.99
104.92
106.00
107.77
108.29
109.68
109.41
107.26
106.78
106.34
106.35
106.61
108.03
108.50
108.49
109.09
109.21
107.20
106.15
106.25
106.52
105.16
105.68
107.01
107.90
108.12
108.43
109.02
108.39
108.65
109.55
111.69
110.76
110.78
110.76
112.38
112.86
114.74
116.21
116.86
114.51
114.11
112.12
108.90
106.62
105.95
107.03
107.10
108.00
108.24
109.72
109.53
110.64
110.03




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 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 & 3 seconds \tabularnewline
R Server & 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=51321&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]'Sir Ronald Aylmer Fisher' @ 193.190.124.24[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=51321&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=51321&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'Sir Ronald Aylmer Fisher' @ 193.190.124.24







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean108.5331578947370.421467194879174257.512706121413
Geometric Mean108.487574231739
Harmonic Mean108.442209631954
Quadratic Mean108.578975405002
Winsorized Mean ( 1 / 19 )108.5470175438600.409414886368299265.12718798948
Winsorized Mean ( 2 / 19 )108.5385964912280.381260230447108284.683761440168
Winsorized Mean ( 3 / 19 )108.6275438596490.355052793623017305.947582474133
Winsorized Mean ( 4 / 19 )108.6043859649120.345994083563786313.890875954503
Winsorized Mean ( 5 / 19 )108.5096491228070.313941508858702345.63651527726
Winsorized Mean ( 6 / 19 )108.5138596491230.291722238284806371.976645617197
Winsorized Mean ( 7 / 19 )108.5150877192980.278649077598608389.432789996935
Winsorized Mean ( 8 / 19 )108.4617543859650.263915371822387410.971720354958
Winsorized Mean ( 9 / 19 )108.3417543859650.230530216299309469.967695017036
Winsorized Mean ( 10 / 19 )108.3557894736840.226923820391733477.498524776431
Winsorized Mean ( 11 / 19 )108.3731578947370.224077495922434483.64141811122
Winsorized Mean ( 12 / 19 )108.350.218973167580644494.809483724057
Winsorized Mean ( 13 / 19 )108.2496491228070.187762842489047576.523276319285
Winsorized Mean ( 14 / 19 )108.1956140350880.171618606104917630.442214225557
Winsorized Mean ( 15 / 19 )108.1877192982460.169522035138459638.19266451044
Winsorized Mean ( 16 / 19 )108.1961403508770.156492882281062691.380584048266
Winsorized Mean ( 17 / 19 )108.2587719298250.144727526851447748.01783934956
Winsorized Mean ( 18 / 19 )108.2271929824560.137875201094377784.964896684893
Winsorized Mean ( 19 / 19 )108.1838596491230.124215269722379870.93849162759
Trimmed Mean ( 1 / 19 )108.5309090909090.380669821912596285.105103802603
Trimmed Mean ( 2 / 19 )108.5135849056600.34376417710199315.662864643008
Trimmed Mean ( 3 / 19 )108.4996078431370.317162166819302342.095051661547
Trimmed Mean ( 4 / 19 )108.450.296987568167859365.166800310993
Trimmed Mean ( 5 / 19 )108.4031914893620.274864377689043394.387924694991
Trimmed Mean ( 6 / 19 )108.3762222222220.259102820526791418.274961275523
Trimmed Mean ( 7 / 19 )108.3458139534880.246331047128488439.838238892292
Trimmed Mean ( 8 / 19 )108.3121951219510.233681436323752463.503634802599
Trimmed Mean ( 9 / 19 )108.2848717948720.221591858287318488.668097428329
Trimmed Mean ( 10 / 19 )108.2751351351350.215718166992987501.92868150347
Trimmed Mean ( 11 / 19 )108.2620.208439500119541519.392917071435
Trimmed Mean ( 12 / 19 )108.2445454545450.198855194626019544.338535677267
Trimmed Mean ( 13 / 19 )108.2283870967740.186715295187127579.6439278759
Trimmed Mean ( 14 / 19 )108.2251724137930.179824504410869601.837734898003
Trimmed Mean ( 15 / 19 )108.2296296296300.174653488021038619.682039310848
Trimmed Mean ( 16 / 19 )108.2360.166924134464333648.414325150371
Trimmed Mean ( 17 / 19 )108.2421739130430.159487762700717678.686389978162
Trimmed Mean ( 18 / 19 )108.2395238095240.151923345631426712.461428226564
Trimmed Mean ( 19 / 19 )108.2415789473680.141636762907643764.219519885167
Median108.29
Midrange108.595
Midmean - Weighted Average at Xnp108.171785714286
Midmean - Weighted Average at X(n+1)p108.225172413793
Midmean - Empirical Distribution Function108.225172413793
Midmean - Empirical Distribution Function - Averaging108.225172413793
Midmean - Empirical Distribution Function - Interpolation108.225172413793
Midmean - Closest Observation108.168333333333
Midmean - True Basic - Statistics Graphics Toolkit108.225172413793
Midmean - MS Excel (old versions)108.225172413793
Number of observations57

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 108.533157894737 & 0.421467194879174 & 257.512706121413 \tabularnewline
Geometric Mean & 108.487574231739 &  &  \tabularnewline
Harmonic Mean & 108.442209631954 &  &  \tabularnewline
Quadratic Mean & 108.578975405002 &  &  \tabularnewline
Winsorized Mean ( 1 / 19 ) & 108.547017543860 & 0.409414886368299 & 265.12718798948 \tabularnewline
Winsorized Mean ( 2 / 19 ) & 108.538596491228 & 0.381260230447108 & 284.683761440168 \tabularnewline
Winsorized Mean ( 3 / 19 ) & 108.627543859649 & 0.355052793623017 & 305.947582474133 \tabularnewline
Winsorized Mean ( 4 / 19 ) & 108.604385964912 & 0.345994083563786 & 313.890875954503 \tabularnewline
Winsorized Mean ( 5 / 19 ) & 108.509649122807 & 0.313941508858702 & 345.63651527726 \tabularnewline
Winsorized Mean ( 6 / 19 ) & 108.513859649123 & 0.291722238284806 & 371.976645617197 \tabularnewline
Winsorized Mean ( 7 / 19 ) & 108.515087719298 & 0.278649077598608 & 389.432789996935 \tabularnewline
Winsorized Mean ( 8 / 19 ) & 108.461754385965 & 0.263915371822387 & 410.971720354958 \tabularnewline
Winsorized Mean ( 9 / 19 ) & 108.341754385965 & 0.230530216299309 & 469.967695017036 \tabularnewline
Winsorized Mean ( 10 / 19 ) & 108.355789473684 & 0.226923820391733 & 477.498524776431 \tabularnewline
Winsorized Mean ( 11 / 19 ) & 108.373157894737 & 0.224077495922434 & 483.64141811122 \tabularnewline
Winsorized Mean ( 12 / 19 ) & 108.35 & 0.218973167580644 & 494.809483724057 \tabularnewline
Winsorized Mean ( 13 / 19 ) & 108.249649122807 & 0.187762842489047 & 576.523276319285 \tabularnewline
Winsorized Mean ( 14 / 19 ) & 108.195614035088 & 0.171618606104917 & 630.442214225557 \tabularnewline
Winsorized Mean ( 15 / 19 ) & 108.187719298246 & 0.169522035138459 & 638.19266451044 \tabularnewline
Winsorized Mean ( 16 / 19 ) & 108.196140350877 & 0.156492882281062 & 691.380584048266 \tabularnewline
Winsorized Mean ( 17 / 19 ) & 108.258771929825 & 0.144727526851447 & 748.01783934956 \tabularnewline
Winsorized Mean ( 18 / 19 ) & 108.227192982456 & 0.137875201094377 & 784.964896684893 \tabularnewline
Winsorized Mean ( 19 / 19 ) & 108.183859649123 & 0.124215269722379 & 870.93849162759 \tabularnewline
Trimmed Mean ( 1 / 19 ) & 108.530909090909 & 0.380669821912596 & 285.105103802603 \tabularnewline
Trimmed Mean ( 2 / 19 ) & 108.513584905660 & 0.34376417710199 & 315.662864643008 \tabularnewline
Trimmed Mean ( 3 / 19 ) & 108.499607843137 & 0.317162166819302 & 342.095051661547 \tabularnewline
Trimmed Mean ( 4 / 19 ) & 108.45 & 0.296987568167859 & 365.166800310993 \tabularnewline
Trimmed Mean ( 5 / 19 ) & 108.403191489362 & 0.274864377689043 & 394.387924694991 \tabularnewline
Trimmed Mean ( 6 / 19 ) & 108.376222222222 & 0.259102820526791 & 418.274961275523 \tabularnewline
Trimmed Mean ( 7 / 19 ) & 108.345813953488 & 0.246331047128488 & 439.838238892292 \tabularnewline
Trimmed Mean ( 8 / 19 ) & 108.312195121951 & 0.233681436323752 & 463.503634802599 \tabularnewline
Trimmed Mean ( 9 / 19 ) & 108.284871794872 & 0.221591858287318 & 488.668097428329 \tabularnewline
Trimmed Mean ( 10 / 19 ) & 108.275135135135 & 0.215718166992987 & 501.92868150347 \tabularnewline
Trimmed Mean ( 11 / 19 ) & 108.262 & 0.208439500119541 & 519.392917071435 \tabularnewline
Trimmed Mean ( 12 / 19 ) & 108.244545454545 & 0.198855194626019 & 544.338535677267 \tabularnewline
Trimmed Mean ( 13 / 19 ) & 108.228387096774 & 0.186715295187127 & 579.6439278759 \tabularnewline
Trimmed Mean ( 14 / 19 ) & 108.225172413793 & 0.179824504410869 & 601.837734898003 \tabularnewline
Trimmed Mean ( 15 / 19 ) & 108.229629629630 & 0.174653488021038 & 619.682039310848 \tabularnewline
Trimmed Mean ( 16 / 19 ) & 108.236 & 0.166924134464333 & 648.414325150371 \tabularnewline
Trimmed Mean ( 17 / 19 ) & 108.242173913043 & 0.159487762700717 & 678.686389978162 \tabularnewline
Trimmed Mean ( 18 / 19 ) & 108.239523809524 & 0.151923345631426 & 712.461428226564 \tabularnewline
Trimmed Mean ( 19 / 19 ) & 108.241578947368 & 0.141636762907643 & 764.219519885167 \tabularnewline
Median & 108.29 &  &  \tabularnewline
Midrange & 108.595 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 108.171785714286 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 108.225172413793 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 108.225172413793 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 108.225172413793 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 108.225172413793 &  &  \tabularnewline
Midmean - Closest Observation & 108.168333333333 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 108.225172413793 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 108.225172413793 &  &  \tabularnewline
Number of observations & 57 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=51321&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]108.533157894737[/C][C]0.421467194879174[/C][C]257.512706121413[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]108.487574231739[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]108.442209631954[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]108.578975405002[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 19 )[/C][C]108.547017543860[/C][C]0.409414886368299[/C][C]265.12718798948[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 19 )[/C][C]108.538596491228[/C][C]0.381260230447108[/C][C]284.683761440168[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 19 )[/C][C]108.627543859649[/C][C]0.355052793623017[/C][C]305.947582474133[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 19 )[/C][C]108.604385964912[/C][C]0.345994083563786[/C][C]313.890875954503[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 19 )[/C][C]108.509649122807[/C][C]0.313941508858702[/C][C]345.63651527726[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 19 )[/C][C]108.513859649123[/C][C]0.291722238284806[/C][C]371.976645617197[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 19 )[/C][C]108.515087719298[/C][C]0.278649077598608[/C][C]389.432789996935[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 19 )[/C][C]108.461754385965[/C][C]0.263915371822387[/C][C]410.971720354958[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 19 )[/C][C]108.341754385965[/C][C]0.230530216299309[/C][C]469.967695017036[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 19 )[/C][C]108.355789473684[/C][C]0.226923820391733[/C][C]477.498524776431[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 19 )[/C][C]108.373157894737[/C][C]0.224077495922434[/C][C]483.64141811122[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 19 )[/C][C]108.35[/C][C]0.218973167580644[/C][C]494.809483724057[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 19 )[/C][C]108.249649122807[/C][C]0.187762842489047[/C][C]576.523276319285[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 19 )[/C][C]108.195614035088[/C][C]0.171618606104917[/C][C]630.442214225557[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 19 )[/C][C]108.187719298246[/C][C]0.169522035138459[/C][C]638.19266451044[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 19 )[/C][C]108.196140350877[/C][C]0.156492882281062[/C][C]691.380584048266[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 19 )[/C][C]108.258771929825[/C][C]0.144727526851447[/C][C]748.01783934956[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 19 )[/C][C]108.227192982456[/C][C]0.137875201094377[/C][C]784.964896684893[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 19 )[/C][C]108.183859649123[/C][C]0.124215269722379[/C][C]870.93849162759[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 19 )[/C][C]108.530909090909[/C][C]0.380669821912596[/C][C]285.105103802603[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 19 )[/C][C]108.513584905660[/C][C]0.34376417710199[/C][C]315.662864643008[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 19 )[/C][C]108.499607843137[/C][C]0.317162166819302[/C][C]342.095051661547[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 19 )[/C][C]108.45[/C][C]0.296987568167859[/C][C]365.166800310993[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 19 )[/C][C]108.403191489362[/C][C]0.274864377689043[/C][C]394.387924694991[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 19 )[/C][C]108.376222222222[/C][C]0.259102820526791[/C][C]418.274961275523[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 19 )[/C][C]108.345813953488[/C][C]0.246331047128488[/C][C]439.838238892292[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 19 )[/C][C]108.312195121951[/C][C]0.233681436323752[/C][C]463.503634802599[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 19 )[/C][C]108.284871794872[/C][C]0.221591858287318[/C][C]488.668097428329[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 19 )[/C][C]108.275135135135[/C][C]0.215718166992987[/C][C]501.92868150347[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 19 )[/C][C]108.262[/C][C]0.208439500119541[/C][C]519.392917071435[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 19 )[/C][C]108.244545454545[/C][C]0.198855194626019[/C][C]544.338535677267[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 19 )[/C][C]108.228387096774[/C][C]0.186715295187127[/C][C]579.6439278759[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 19 )[/C][C]108.225172413793[/C][C]0.179824504410869[/C][C]601.837734898003[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 19 )[/C][C]108.229629629630[/C][C]0.174653488021038[/C][C]619.682039310848[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 19 )[/C][C]108.236[/C][C]0.166924134464333[/C][C]648.414325150371[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 19 )[/C][C]108.242173913043[/C][C]0.159487762700717[/C][C]678.686389978162[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 19 )[/C][C]108.239523809524[/C][C]0.151923345631426[/C][C]712.461428226564[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 19 )[/C][C]108.241578947368[/C][C]0.141636762907643[/C][C]764.219519885167[/C][/ROW]
[ROW][C]Median[/C][C]108.29[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]108.595[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]108.171785714286[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]108.225172413793[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]108.225172413793[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]108.225172413793[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]108.225172413793[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]108.168333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]108.225172413793[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]108.225172413793[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]57[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=51321&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=51321&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 Mean108.5331578947370.421467194879174257.512706121413
Geometric Mean108.487574231739
Harmonic Mean108.442209631954
Quadratic Mean108.578975405002
Winsorized Mean ( 1 / 19 )108.5470175438600.409414886368299265.12718798948
Winsorized Mean ( 2 / 19 )108.5385964912280.381260230447108284.683761440168
Winsorized Mean ( 3 / 19 )108.6275438596490.355052793623017305.947582474133
Winsorized Mean ( 4 / 19 )108.6043859649120.345994083563786313.890875954503
Winsorized Mean ( 5 / 19 )108.5096491228070.313941508858702345.63651527726
Winsorized Mean ( 6 / 19 )108.5138596491230.291722238284806371.976645617197
Winsorized Mean ( 7 / 19 )108.5150877192980.278649077598608389.432789996935
Winsorized Mean ( 8 / 19 )108.4617543859650.263915371822387410.971720354958
Winsorized Mean ( 9 / 19 )108.3417543859650.230530216299309469.967695017036
Winsorized Mean ( 10 / 19 )108.3557894736840.226923820391733477.498524776431
Winsorized Mean ( 11 / 19 )108.3731578947370.224077495922434483.64141811122
Winsorized Mean ( 12 / 19 )108.350.218973167580644494.809483724057
Winsorized Mean ( 13 / 19 )108.2496491228070.187762842489047576.523276319285
Winsorized Mean ( 14 / 19 )108.1956140350880.171618606104917630.442214225557
Winsorized Mean ( 15 / 19 )108.1877192982460.169522035138459638.19266451044
Winsorized Mean ( 16 / 19 )108.1961403508770.156492882281062691.380584048266
Winsorized Mean ( 17 / 19 )108.2587719298250.144727526851447748.01783934956
Winsorized Mean ( 18 / 19 )108.2271929824560.137875201094377784.964896684893
Winsorized Mean ( 19 / 19 )108.1838596491230.124215269722379870.93849162759
Trimmed Mean ( 1 / 19 )108.5309090909090.380669821912596285.105103802603
Trimmed Mean ( 2 / 19 )108.5135849056600.34376417710199315.662864643008
Trimmed Mean ( 3 / 19 )108.4996078431370.317162166819302342.095051661547
Trimmed Mean ( 4 / 19 )108.450.296987568167859365.166800310993
Trimmed Mean ( 5 / 19 )108.4031914893620.274864377689043394.387924694991
Trimmed Mean ( 6 / 19 )108.3762222222220.259102820526791418.274961275523
Trimmed Mean ( 7 / 19 )108.3458139534880.246331047128488439.838238892292
Trimmed Mean ( 8 / 19 )108.3121951219510.233681436323752463.503634802599
Trimmed Mean ( 9 / 19 )108.2848717948720.221591858287318488.668097428329
Trimmed Mean ( 10 / 19 )108.2751351351350.215718166992987501.92868150347
Trimmed Mean ( 11 / 19 )108.2620.208439500119541519.392917071435
Trimmed Mean ( 12 / 19 )108.2445454545450.198855194626019544.338535677267
Trimmed Mean ( 13 / 19 )108.2283870967740.186715295187127579.6439278759
Trimmed Mean ( 14 / 19 )108.2251724137930.179824504410869601.837734898003
Trimmed Mean ( 15 / 19 )108.2296296296300.174653488021038619.682039310848
Trimmed Mean ( 16 / 19 )108.2360.166924134464333648.414325150371
Trimmed Mean ( 17 / 19 )108.2421739130430.159487762700717678.686389978162
Trimmed Mean ( 18 / 19 )108.2395238095240.151923345631426712.461428226564
Trimmed Mean ( 19 / 19 )108.2415789473680.141636762907643764.219519885167
Median108.29
Midrange108.595
Midmean - Weighted Average at Xnp108.171785714286
Midmean - Weighted Average at X(n+1)p108.225172413793
Midmean - Empirical Distribution Function108.225172413793
Midmean - Empirical Distribution Function - Averaging108.225172413793
Midmean - Empirical Distribution Function - Interpolation108.225172413793
Midmean - Closest Observation108.168333333333
Midmean - True Basic - Statistics Graphics Toolkit108.225172413793
Midmean - MS Excel (old versions)108.225172413793
Number of observations57



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')