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Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationTue, 20 Oct 2009 23:08:56 -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/21/t1256101843dascxj57kolejbd.htm/, Retrieved Thu, 02 May 2024 05:24:56 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=49249, Retrieved Thu, 02 May 2024 05:24:56 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact165
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [WS3 Deel 3 Centra...] [2009-10-21 05:08:56] [762da55b2e2304daaed24a7cc507d14d] [Current]
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Dataseries X:
5.616
4.774
5.045
4.971
4.623
5.437
5.583
4.875
5.148
5.127
4.738
6.369
5.840
4.933
5.222
4.967
5.138
5.342
5.249
4.441
5.261
4.823
4.625
6.102
5.550
4.844
4.537
4.499
4.661
4.849
4.833
4.102
4.696
4.375
3.929
4.951
4.947
4.476
4.005
4.080
4.269
4.393
4.323
4.088
3.843
4.176
3.839
4.583
5.100
3.957
3.916
4.423
4.108
4.907
4.981
4.408
4.851
4.929
4.519
5.612




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'RServer@AstonUniversity' @ vre.aston.ac.uk

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 2 seconds \tabularnewline
R Server & 'RServer@AstonUniversity' @ vre.aston.ac.uk \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=49249&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]'RServer@AstonUniversity' @ vre.aston.ac.uk[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=49249&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=49249&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'RServer@AstonUniversity' @ vre.aston.ac.uk







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean4.780133333333330.07241739680283166.0080801626725
Geometric Mean4.74837893807066
Harmonic Mean4.71718147326928
Quadratic Mean4.8123889251251
Winsorized Mean ( 1 / 20 )4.775750.070868138175590467.3892403969622
Winsorized Mean ( 2 / 20 )4.769450.067777904274989270.368803093252
Winsorized Mean ( 3 / 20 )4.75890.064879674374126273.3496283066709
Winsorized Mean ( 4 / 20 )4.76050.064420272189168573.8975455741775
Winsorized Mean ( 5 / 20 )4.762083333333330.063052884680071175.5252254912053
Winsorized Mean ( 6 / 20 )4.766283333333330.060847652172889378.3314255049754
Winsorized Mean ( 7 / 20 )4.754033333333330.057907850851220182.0965251421201
Winsorized Mean ( 8 / 20 )4.743233333333330.055107031791950386.0731049939474
Winsorized Mean ( 9 / 20 )4.731983333333330.052775355336417489.6627469994133
Winsorized Mean ( 10 / 20 )4.741316666666670.050215960118861994.4185206345532
Winsorized Mean ( 11 / 20 )4.753416666666670.0462209951296175102.841071537656
Winsorized Mean ( 12 / 20 )4.749416666666670.0418583925102301113.463904890899
Winsorized Mean ( 13 / 20 )4.758516666666670.0396091746752661120.136728565519
Winsorized Mean ( 14 / 20 )4.760150.0385095030094378123.609748971141
Winsorized Mean ( 15 / 20 )4.757150.0368274325487888129.174087650497
Winsorized Mean ( 16 / 20 )4.746483333333330.033929658806188139.891867479306
Winsorized Mean ( 17 / 20 )4.733450.0304983506546726155.203474889381
Winsorized Mean ( 18 / 20 )4.740950.028401872153221166.923855386144
Winsorized Mean ( 19 / 20 )4.746966666666670.0270866361306424175.251243593757
Winsorized Mean ( 20 / 20 )4.74830.0253287235621564187.467007105500
Trimmed Mean ( 1 / 20 )4.768965517241380.067688670986999270.4544120560048
Trimmed Mean ( 2 / 20 )4.761696428571430.063731207668903674.715302011997
Trimmed Mean ( 3 / 20 )4.757388888888890.060946961262384278.0578521119
Trimmed Mean ( 4 / 20 )4.756807692307690.058923001360568180.7292157980771
Trimmed Mean ( 5 / 20 )4.75570.056555641736655284.0888698981503
Trimmed Mean ( 6 / 20 )4.754104166666670.054040331992874787.9732598107188
Trimmed Mean ( 7 / 20 )4.751456521739130.051546786650873492.1775503470422
Trimmed Mean ( 8 / 20 )4.750954545454550.049254387282134996.4574895275931
Trimmed Mean ( 9 / 20 )4.752333333333330.0470958282064989100.907734597977
Trimmed Mean ( 10 / 20 )4.7557250.0449005880193921105.916764340504
Trimmed Mean ( 11 / 20 )4.7580.0427159395729377111.386991543887
Trimmed Mean ( 12 / 20 )4.758694444444440.0409318601302377116.258934465796
Trimmed Mean ( 13 / 20 )4.760058823529410.0397134778501293119.860034457141
Trimmed Mean ( 14 / 20 )4.760281250.0386055119532872123.305740790589
Trimmed Mean ( 15 / 20 )4.76030.0372793786021913127.692579074271
Trimmed Mean ( 16 / 20 )4.760750.0358119583719442132.937438119264
Trimmed Mean ( 17 / 20 )4.762807692307690.0345205410079172137.970250559380
Trimmed Mean ( 18 / 20 )4.7671250.0335941415969761141.903462133085
Trimmed Mean ( 19 / 20 )4.771090909090910.0327757637394651145.567650139791
Trimmed Mean ( 20 / 20 )4.77490.0317722073185785150.285435069785
Median4.828
Midrange5.104
Midmean - Weighted Average at Xnp4.74845161290322
Midmean - Weighted Average at X(n+1)p4.7603
Midmean - Empirical Distribution Function4.74845161290322
Midmean - Empirical Distribution Function - Averaging4.7603
Midmean - Empirical Distribution Function - Interpolation4.7603
Midmean - Closest Observation4.74845161290322
Midmean - True Basic - Statistics Graphics Toolkit4.7603
Midmean - MS Excel (old versions)4.76028125
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 4.78013333333333 & 0.072417396802831 & 66.0080801626725 \tabularnewline
Geometric Mean & 4.74837893807066 &  &  \tabularnewline
Harmonic Mean & 4.71718147326928 &  &  \tabularnewline
Quadratic Mean & 4.8123889251251 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 4.77575 & 0.0708681381755904 & 67.3892403969622 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 4.76945 & 0.0677779042749892 & 70.368803093252 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 4.7589 & 0.0648796743741262 & 73.3496283066709 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 4.7605 & 0.0644202721891685 & 73.8975455741775 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 4.76208333333333 & 0.0630528846800711 & 75.5252254912053 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 4.76628333333333 & 0.0608476521728893 & 78.3314255049754 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 4.75403333333333 & 0.0579078508512201 & 82.0965251421201 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 4.74323333333333 & 0.0551070317919503 & 86.0731049939474 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 4.73198333333333 & 0.0527753553364174 & 89.6627469994133 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 4.74131666666667 & 0.0502159601188619 & 94.4185206345532 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 4.75341666666667 & 0.0462209951296175 & 102.841071537656 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 4.74941666666667 & 0.0418583925102301 & 113.463904890899 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 4.75851666666667 & 0.0396091746752661 & 120.136728565519 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 4.76015 & 0.0385095030094378 & 123.609748971141 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 4.75715 & 0.0368274325487888 & 129.174087650497 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 4.74648333333333 & 0.033929658806188 & 139.891867479306 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 4.73345 & 0.0304983506546726 & 155.203474889381 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 4.74095 & 0.028401872153221 & 166.923855386144 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 4.74696666666667 & 0.0270866361306424 & 175.251243593757 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 4.7483 & 0.0253287235621564 & 187.467007105500 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 4.76896551724138 & 0.0676886709869992 & 70.4544120560048 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 4.76169642857143 & 0.0637312076689036 & 74.715302011997 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 4.75738888888889 & 0.0609469612623842 & 78.0578521119 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 4.75680769230769 & 0.0589230013605681 & 80.7292157980771 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 4.7557 & 0.0565556417366552 & 84.0888698981503 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 4.75410416666667 & 0.0540403319928747 & 87.9732598107188 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 4.75145652173913 & 0.0515467866508734 & 92.1775503470422 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 4.75095454545455 & 0.0492543872821349 & 96.4574895275931 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 4.75233333333333 & 0.0470958282064989 & 100.907734597977 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 4.755725 & 0.0449005880193921 & 105.916764340504 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 4.758 & 0.0427159395729377 & 111.386991543887 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 4.75869444444444 & 0.0409318601302377 & 116.258934465796 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 4.76005882352941 & 0.0397134778501293 & 119.860034457141 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 4.76028125 & 0.0386055119532872 & 123.305740790589 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 4.7603 & 0.0372793786021913 & 127.692579074271 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 4.76075 & 0.0358119583719442 & 132.937438119264 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 4.76280769230769 & 0.0345205410079172 & 137.970250559380 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 4.767125 & 0.0335941415969761 & 141.903462133085 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 4.77109090909091 & 0.0327757637394651 & 145.567650139791 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 4.7749 & 0.0317722073185785 & 150.285435069785 \tabularnewline
Median & 4.828 &  &  \tabularnewline
Midrange & 5.104 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 4.74845161290322 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 4.7603 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 4.74845161290322 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 4.7603 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 4.7603 &  &  \tabularnewline
Midmean - Closest Observation & 4.74845161290322 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 4.7603 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 4.76028125 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=49249&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]4.78013333333333[/C][C]0.072417396802831[/C][C]66.0080801626725[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]4.74837893807066[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]4.71718147326928[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]4.8123889251251[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]4.77575[/C][C]0.0708681381755904[/C][C]67.3892403969622[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]4.76945[/C][C]0.0677779042749892[/C][C]70.368803093252[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]4.7589[/C][C]0.0648796743741262[/C][C]73.3496283066709[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]4.7605[/C][C]0.0644202721891685[/C][C]73.8975455741775[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]4.76208333333333[/C][C]0.0630528846800711[/C][C]75.5252254912053[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]4.76628333333333[/C][C]0.0608476521728893[/C][C]78.3314255049754[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]4.75403333333333[/C][C]0.0579078508512201[/C][C]82.0965251421201[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]4.74323333333333[/C][C]0.0551070317919503[/C][C]86.0731049939474[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]4.73198333333333[/C][C]0.0527753553364174[/C][C]89.6627469994133[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]4.74131666666667[/C][C]0.0502159601188619[/C][C]94.4185206345532[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]4.75341666666667[/C][C]0.0462209951296175[/C][C]102.841071537656[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]4.74941666666667[/C][C]0.0418583925102301[/C][C]113.463904890899[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]4.75851666666667[/C][C]0.0396091746752661[/C][C]120.136728565519[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]4.76015[/C][C]0.0385095030094378[/C][C]123.609748971141[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]4.75715[/C][C]0.0368274325487888[/C][C]129.174087650497[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]4.74648333333333[/C][C]0.033929658806188[/C][C]139.891867479306[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]4.73345[/C][C]0.0304983506546726[/C][C]155.203474889381[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]4.74095[/C][C]0.028401872153221[/C][C]166.923855386144[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]4.74696666666667[/C][C]0.0270866361306424[/C][C]175.251243593757[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]4.7483[/C][C]0.0253287235621564[/C][C]187.467007105500[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]4.76896551724138[/C][C]0.0676886709869992[/C][C]70.4544120560048[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]4.76169642857143[/C][C]0.0637312076689036[/C][C]74.715302011997[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]4.75738888888889[/C][C]0.0609469612623842[/C][C]78.0578521119[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]4.75680769230769[/C][C]0.0589230013605681[/C][C]80.7292157980771[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]4.7557[/C][C]0.0565556417366552[/C][C]84.0888698981503[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]4.75410416666667[/C][C]0.0540403319928747[/C][C]87.9732598107188[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]4.75145652173913[/C][C]0.0515467866508734[/C][C]92.1775503470422[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]4.75095454545455[/C][C]0.0492543872821349[/C][C]96.4574895275931[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]4.75233333333333[/C][C]0.0470958282064989[/C][C]100.907734597977[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]4.755725[/C][C]0.0449005880193921[/C][C]105.916764340504[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]4.758[/C][C]0.0427159395729377[/C][C]111.386991543887[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]4.75869444444444[/C][C]0.0409318601302377[/C][C]116.258934465796[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]4.76005882352941[/C][C]0.0397134778501293[/C][C]119.860034457141[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]4.76028125[/C][C]0.0386055119532872[/C][C]123.305740790589[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]4.7603[/C][C]0.0372793786021913[/C][C]127.692579074271[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]4.76075[/C][C]0.0358119583719442[/C][C]132.937438119264[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]4.76280769230769[/C][C]0.0345205410079172[/C][C]137.970250559380[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]4.767125[/C][C]0.0335941415969761[/C][C]141.903462133085[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]4.77109090909091[/C][C]0.0327757637394651[/C][C]145.567650139791[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]4.7749[/C][C]0.0317722073185785[/C][C]150.285435069785[/C][/ROW]
[ROW][C]Median[/C][C]4.828[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]5.104[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]4.74845161290322[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]4.7603[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]4.74845161290322[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]4.7603[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]4.7603[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]4.74845161290322[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]4.7603[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]4.76028125[/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=49249&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=49249&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 Mean4.780133333333330.07241739680283166.0080801626725
Geometric Mean4.74837893807066
Harmonic Mean4.71718147326928
Quadratic Mean4.8123889251251
Winsorized Mean ( 1 / 20 )4.775750.070868138175590467.3892403969622
Winsorized Mean ( 2 / 20 )4.769450.067777904274989270.368803093252
Winsorized Mean ( 3 / 20 )4.75890.064879674374126273.3496283066709
Winsorized Mean ( 4 / 20 )4.76050.064420272189168573.8975455741775
Winsorized Mean ( 5 / 20 )4.762083333333330.063052884680071175.5252254912053
Winsorized Mean ( 6 / 20 )4.766283333333330.060847652172889378.3314255049754
Winsorized Mean ( 7 / 20 )4.754033333333330.057907850851220182.0965251421201
Winsorized Mean ( 8 / 20 )4.743233333333330.055107031791950386.0731049939474
Winsorized Mean ( 9 / 20 )4.731983333333330.052775355336417489.6627469994133
Winsorized Mean ( 10 / 20 )4.741316666666670.050215960118861994.4185206345532
Winsorized Mean ( 11 / 20 )4.753416666666670.0462209951296175102.841071537656
Winsorized Mean ( 12 / 20 )4.749416666666670.0418583925102301113.463904890899
Winsorized Mean ( 13 / 20 )4.758516666666670.0396091746752661120.136728565519
Winsorized Mean ( 14 / 20 )4.760150.0385095030094378123.609748971141
Winsorized Mean ( 15 / 20 )4.757150.0368274325487888129.174087650497
Winsorized Mean ( 16 / 20 )4.746483333333330.033929658806188139.891867479306
Winsorized Mean ( 17 / 20 )4.733450.0304983506546726155.203474889381
Winsorized Mean ( 18 / 20 )4.740950.028401872153221166.923855386144
Winsorized Mean ( 19 / 20 )4.746966666666670.0270866361306424175.251243593757
Winsorized Mean ( 20 / 20 )4.74830.0253287235621564187.467007105500
Trimmed Mean ( 1 / 20 )4.768965517241380.067688670986999270.4544120560048
Trimmed Mean ( 2 / 20 )4.761696428571430.063731207668903674.715302011997
Trimmed Mean ( 3 / 20 )4.757388888888890.060946961262384278.0578521119
Trimmed Mean ( 4 / 20 )4.756807692307690.058923001360568180.7292157980771
Trimmed Mean ( 5 / 20 )4.75570.056555641736655284.0888698981503
Trimmed Mean ( 6 / 20 )4.754104166666670.054040331992874787.9732598107188
Trimmed Mean ( 7 / 20 )4.751456521739130.051546786650873492.1775503470422
Trimmed Mean ( 8 / 20 )4.750954545454550.049254387282134996.4574895275931
Trimmed Mean ( 9 / 20 )4.752333333333330.0470958282064989100.907734597977
Trimmed Mean ( 10 / 20 )4.7557250.0449005880193921105.916764340504
Trimmed Mean ( 11 / 20 )4.7580.0427159395729377111.386991543887
Trimmed Mean ( 12 / 20 )4.758694444444440.0409318601302377116.258934465796
Trimmed Mean ( 13 / 20 )4.760058823529410.0397134778501293119.860034457141
Trimmed Mean ( 14 / 20 )4.760281250.0386055119532872123.305740790589
Trimmed Mean ( 15 / 20 )4.76030.0372793786021913127.692579074271
Trimmed Mean ( 16 / 20 )4.760750.0358119583719442132.937438119264
Trimmed Mean ( 17 / 20 )4.762807692307690.0345205410079172137.970250559380
Trimmed Mean ( 18 / 20 )4.7671250.0335941415969761141.903462133085
Trimmed Mean ( 19 / 20 )4.771090909090910.0327757637394651145.567650139791
Trimmed Mean ( 20 / 20 )4.77490.0317722073185785150.285435069785
Median4.828
Midrange5.104
Midmean - Weighted Average at Xnp4.74845161290322
Midmean - Weighted Average at X(n+1)p4.7603
Midmean - Empirical Distribution Function4.74845161290322
Midmean - Empirical Distribution Function - Averaging4.7603
Midmean - Empirical Distribution Function - Interpolation4.7603
Midmean - Closest Observation4.74845161290322
Midmean - True Basic - Statistics Graphics Toolkit4.7603
Midmean - MS Excel (old versions)4.76028125
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')