Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationSun, 16 Oct 2016 17:29:35 +0100
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2016/Oct/16/t14766354148vjy8p7u27bk0tx.htm/, Retrieved Wed, 08 May 2024 08:22:50 +0200
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=, Retrieved Wed, 08 May 2024 08:22:50 +0200
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact0
Dataseries X:
84543
55735
65814
55382
57422
57729
48213
44789
50998
50328
47719
19946
80608
50747
61687
47539
54412
83362
36911
39254
37597
32557
35537
21500
56125
37432
43347
36870
36247
41293
36190
33381
36609
41861
45926
45079
51469
39013
37036
34865
37505
39379
35653
30515
35984
41068
37851
40333
56004
39797
37960
34357
35069
45299
40475
36277
41910
45234
46425
73241




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gertrude Mary Cox' @ cox.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 & 'Gertrude Mary Cox' @ cox.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&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]'Gertrude Mary Cox' @ cox.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&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'Gertrude Mary Cox' @ cox.wessa.net







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean45056.81688.2521285650826.6884307371173
Geometric Mean43390.3233696569
Harmonic Mean41830.1510897909
Quadratic Mean46885.7840498233
Winsorized Mean ( 1 / 20 )45063.01666666671674.1797697403126.9164742527361
Winsorized Mean ( 2 / 20 )45271.71666666671578.9666157009528.6717377153469
Winsorized Mean ( 3 / 20 )45005.46666666671431.4901027907831.4395933153333
Winsorized Mean ( 4 / 20 )44565.26666666671269.599805015935.1018222361088
Winsorized Mean ( 5 / 20 )44302.68333333331165.1436019959638.0233674694176
Winsorized Mean ( 6 / 20 )43957.68333333331064.0303016191141.3124356199668
Winsorized Mean ( 7 / 20 )43945.66666666671052.7919133456741.742025284951
Winsorized Mean ( 8 / 20 )43835.13333333331007.3150718300543.5168047805495
Winsorized Mean ( 9 / 20 )43834.38333333331001.1489363262443.7840782153609
Winsorized Mean ( 10 / 20 )43844.7166666667984.38639297445544.5401490508051
Winsorized Mean ( 11 / 20 )43817.7666666667966.11340129508545.3546825951576
Winsorized Mean ( 12 / 20 )43635.1666666667925.75010879608947.134930098375
Winsorized Mean ( 13 / 20 )43004.0166666667804.67373621033853.442798902816
Winsorized Mean ( 14 / 20 )42971.5833333333774.33489167063255.4948302027588
Winsorized Mean ( 15 / 20 )42974.0833333333754.32334451108456.9703743706713
Winsorized Mean ( 16 / 20 )42873.2833333333733.43698603299858.4553058405544
Winsorized Mean ( 17 / 20 )42309.45628.89444850368767.2759158562551
Winsorized Mean ( 18 / 20 )42280.05588.75900387755771.8121501693296
Winsorized Mean ( 19 / 20 )42246.1666666667576.63856933280573.2628181905127
Winsorized Mean ( 20 / 20 )41905.5515.80184053623281.2434092062073
Trimmed Mean ( 1 / 20 )44808.94827586211545.4806926449928.9935348200142
Trimmed Mean ( 2 / 20 )44536.73214285711379.6552118430332.2810596158748
Trimmed Mean ( 3 / 20 )44128.40740740741233.6807096264235.7697150187023
Trimmed Mean ( 4 / 20 )43791.07692307691127.0222296915138.8555573877753
Trimmed Mean ( 5 / 20 )43558.821063.7705336764940.9475715119281
Trimmed Mean ( 6 / 20 )43372.85416666671022.2425684665542.4291215261457
Trimmed Mean ( 7 / 20 )43245.71739130431001.9904213640743.1598111810601
Trimmed Mean ( 8 / 20 )43109.3636363636977.98299200662944.0798704974528
Trimmed Mean ( 9 / 20 )42979.7619047619958.5339680758944.8390597894378
Trimmed Mean ( 10 / 20 )42837.325933.02241803081945.91242843919
Trimmed Mean ( 11 / 20 )42678.2631578947901.92956950179547.3188424030373
Trimmed Mean ( 12 / 20 )42505.6111111111863.36044568365349.2327524658059
Trimmed Mean ( 13 / 20 )42339.5821.568929965451.5349332913346
Trimmed Mean ( 14 / 20 )42243.65625801.28858496166652.719653122253
Trimmed Mean ( 15 / 20 )42139.6666666667779.19394592359754.0811012291908
Trimmed Mean ( 16 / 20 )42020.4642857143750.62686057400955.9804964261217
Trimmed Mean ( 17 / 20 )41897.4615384615713.0066462755758.7616703958024
Trimmed Mean ( 18 / 20 )41836.875695.27139762084160.1734447054232
Trimmed Mean ( 19 / 20 )41769.7272727273678.57848356903461.5547475850344
Trimmed Mean ( 20 / 20 )41694.5651.21541629560164.0256648670522
Median41180.5
Midrange52244.5
Midmean - Weighted Average at Xnp41961.2580645161
Midmean - Weighted Average at X(n+1)p42139.6666666667
Midmean - Empirical Distribution Function41961.2580645161
Midmean - Empirical Distribution Function - Averaging42139.6666666667
Midmean - Empirical Distribution Function - Interpolation42139.6666666667
Midmean - Closest Observation41961.2580645161
Midmean - True Basic - Statistics Graphics Toolkit42139.6666666667
Midmean - MS Excel (old versions)42243.65625
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 45056.8 & 1688.25212856508 & 26.6884307371173 \tabularnewline
Geometric Mean & 43390.3233696569 &  &  \tabularnewline
Harmonic Mean & 41830.1510897909 &  &  \tabularnewline
Quadratic Mean & 46885.7840498233 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 45063.0166666667 & 1674.17976974031 & 26.9164742527361 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 45271.7166666667 & 1578.96661570095 & 28.6717377153469 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 45005.4666666667 & 1431.49010279078 & 31.4395933153333 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 44565.2666666667 & 1269.5998050159 & 35.1018222361088 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 44302.6833333333 & 1165.14360199596 & 38.0233674694176 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 43957.6833333333 & 1064.03030161911 & 41.3124356199668 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 43945.6666666667 & 1052.79191334567 & 41.742025284951 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 43835.1333333333 & 1007.31507183005 & 43.5168047805495 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 43834.3833333333 & 1001.14893632624 & 43.7840782153609 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 43844.7166666667 & 984.386392974455 & 44.5401490508051 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 43817.7666666667 & 966.113401295085 & 45.3546825951576 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 43635.1666666667 & 925.750108796089 & 47.134930098375 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 43004.0166666667 & 804.673736210338 & 53.442798902816 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 42971.5833333333 & 774.334891670632 & 55.4948302027588 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 42974.0833333333 & 754.323344511084 & 56.9703743706713 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 42873.2833333333 & 733.436986032998 & 58.4553058405544 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 42309.45 & 628.894448503687 & 67.2759158562551 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 42280.05 & 588.759003877557 & 71.8121501693296 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 42246.1666666667 & 576.638569332805 & 73.2628181905127 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 41905.5 & 515.801840536232 & 81.2434092062073 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 44808.9482758621 & 1545.48069264499 & 28.9935348200142 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 44536.7321428571 & 1379.65521184303 & 32.2810596158748 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 44128.4074074074 & 1233.68070962642 & 35.7697150187023 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 43791.0769230769 & 1127.02222969151 & 38.8555573877753 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 43558.82 & 1063.77053367649 & 40.9475715119281 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 43372.8541666667 & 1022.24256846655 & 42.4291215261457 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 43245.7173913043 & 1001.99042136407 & 43.1598111810601 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 43109.3636363636 & 977.982992006629 & 44.0798704974528 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 42979.7619047619 & 958.53396807589 & 44.8390597894378 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 42837.325 & 933.022418030819 & 45.91242843919 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 42678.2631578947 & 901.929569501795 & 47.3188424030373 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 42505.6111111111 & 863.360445683653 & 49.2327524658059 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 42339.5 & 821.5689299654 & 51.5349332913346 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 42243.65625 & 801.288584961666 & 52.719653122253 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 42139.6666666667 & 779.193945923597 & 54.0811012291908 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 42020.4642857143 & 750.626860574009 & 55.9804964261217 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 41897.4615384615 & 713.00664627557 & 58.7616703958024 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 41836.875 & 695.271397620841 & 60.1734447054232 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 41769.7272727273 & 678.578483569034 & 61.5547475850344 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 41694.5 & 651.215416295601 & 64.0256648670522 \tabularnewline
Median & 41180.5 &  &  \tabularnewline
Midrange & 52244.5 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 41961.2580645161 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 42139.6666666667 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 41961.2580645161 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 42139.6666666667 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 42139.6666666667 &  &  \tabularnewline
Midmean - Closest Observation & 41961.2580645161 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 42139.6666666667 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 42243.65625 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&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]45056.8[/C][C]1688.25212856508[/C][C]26.6884307371173[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]43390.3233696569[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]41830.1510897909[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]46885.7840498233[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]45063.0166666667[/C][C]1674.17976974031[/C][C]26.9164742527361[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]45271.7166666667[/C][C]1578.96661570095[/C][C]28.6717377153469[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]45005.4666666667[/C][C]1431.49010279078[/C][C]31.4395933153333[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]44565.2666666667[/C][C]1269.5998050159[/C][C]35.1018222361088[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]44302.6833333333[/C][C]1165.14360199596[/C][C]38.0233674694176[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]43957.6833333333[/C][C]1064.03030161911[/C][C]41.3124356199668[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]43945.6666666667[/C][C]1052.79191334567[/C][C]41.742025284951[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]43835.1333333333[/C][C]1007.31507183005[/C][C]43.5168047805495[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]43834.3833333333[/C][C]1001.14893632624[/C][C]43.7840782153609[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]43844.7166666667[/C][C]984.386392974455[/C][C]44.5401490508051[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]43817.7666666667[/C][C]966.113401295085[/C][C]45.3546825951576[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]43635.1666666667[/C][C]925.750108796089[/C][C]47.134930098375[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]43004.0166666667[/C][C]804.673736210338[/C][C]53.442798902816[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]42971.5833333333[/C][C]774.334891670632[/C][C]55.4948302027588[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]42974.0833333333[/C][C]754.323344511084[/C][C]56.9703743706713[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]42873.2833333333[/C][C]733.436986032998[/C][C]58.4553058405544[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]42309.45[/C][C]628.894448503687[/C][C]67.2759158562551[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]42280.05[/C][C]588.759003877557[/C][C]71.8121501693296[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]42246.1666666667[/C][C]576.638569332805[/C][C]73.2628181905127[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]41905.5[/C][C]515.801840536232[/C][C]81.2434092062073[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]44808.9482758621[/C][C]1545.48069264499[/C][C]28.9935348200142[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]44536.7321428571[/C][C]1379.65521184303[/C][C]32.2810596158748[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]44128.4074074074[/C][C]1233.68070962642[/C][C]35.7697150187023[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]43791.0769230769[/C][C]1127.02222969151[/C][C]38.8555573877753[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]43558.82[/C][C]1063.77053367649[/C][C]40.9475715119281[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]43372.8541666667[/C][C]1022.24256846655[/C][C]42.4291215261457[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]43245.7173913043[/C][C]1001.99042136407[/C][C]43.1598111810601[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]43109.3636363636[/C][C]977.982992006629[/C][C]44.0798704974528[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]42979.7619047619[/C][C]958.53396807589[/C][C]44.8390597894378[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]42837.325[/C][C]933.022418030819[/C][C]45.91242843919[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]42678.2631578947[/C][C]901.929569501795[/C][C]47.3188424030373[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]42505.6111111111[/C][C]863.360445683653[/C][C]49.2327524658059[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]42339.5[/C][C]821.5689299654[/C][C]51.5349332913346[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]42243.65625[/C][C]801.288584961666[/C][C]52.719653122253[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]42139.6666666667[/C][C]779.193945923597[/C][C]54.0811012291908[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]42020.4642857143[/C][C]750.626860574009[/C][C]55.9804964261217[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]41897.4615384615[/C][C]713.00664627557[/C][C]58.7616703958024[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]41836.875[/C][C]695.271397620841[/C][C]60.1734447054232[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]41769.7272727273[/C][C]678.578483569034[/C][C]61.5547475850344[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]41694.5[/C][C]651.215416295601[/C][C]64.0256648670522[/C][/ROW]
[ROW][C]Median[/C][C]41180.5[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]52244.5[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]41961.2580645161[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]42139.6666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]41961.2580645161[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]42139.6666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]42139.6666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]41961.2580645161[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]42139.6666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]42243.65625[/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=&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&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 Mean45056.81688.2521285650826.6884307371173
Geometric Mean43390.3233696569
Harmonic Mean41830.1510897909
Quadratic Mean46885.7840498233
Winsorized Mean ( 1 / 20 )45063.01666666671674.1797697403126.9164742527361
Winsorized Mean ( 2 / 20 )45271.71666666671578.9666157009528.6717377153469
Winsorized Mean ( 3 / 20 )45005.46666666671431.4901027907831.4395933153333
Winsorized Mean ( 4 / 20 )44565.26666666671269.599805015935.1018222361088
Winsorized Mean ( 5 / 20 )44302.68333333331165.1436019959638.0233674694176
Winsorized Mean ( 6 / 20 )43957.68333333331064.0303016191141.3124356199668
Winsorized Mean ( 7 / 20 )43945.66666666671052.7919133456741.742025284951
Winsorized Mean ( 8 / 20 )43835.13333333331007.3150718300543.5168047805495
Winsorized Mean ( 9 / 20 )43834.38333333331001.1489363262443.7840782153609
Winsorized Mean ( 10 / 20 )43844.7166666667984.38639297445544.5401490508051
Winsorized Mean ( 11 / 20 )43817.7666666667966.11340129508545.3546825951576
Winsorized Mean ( 12 / 20 )43635.1666666667925.75010879608947.134930098375
Winsorized Mean ( 13 / 20 )43004.0166666667804.67373621033853.442798902816
Winsorized Mean ( 14 / 20 )42971.5833333333774.33489167063255.4948302027588
Winsorized Mean ( 15 / 20 )42974.0833333333754.32334451108456.9703743706713
Winsorized Mean ( 16 / 20 )42873.2833333333733.43698603299858.4553058405544
Winsorized Mean ( 17 / 20 )42309.45628.89444850368767.2759158562551
Winsorized Mean ( 18 / 20 )42280.05588.75900387755771.8121501693296
Winsorized Mean ( 19 / 20 )42246.1666666667576.63856933280573.2628181905127
Winsorized Mean ( 20 / 20 )41905.5515.80184053623281.2434092062073
Trimmed Mean ( 1 / 20 )44808.94827586211545.4806926449928.9935348200142
Trimmed Mean ( 2 / 20 )44536.73214285711379.6552118430332.2810596158748
Trimmed Mean ( 3 / 20 )44128.40740740741233.6807096264235.7697150187023
Trimmed Mean ( 4 / 20 )43791.07692307691127.0222296915138.8555573877753
Trimmed Mean ( 5 / 20 )43558.821063.7705336764940.9475715119281
Trimmed Mean ( 6 / 20 )43372.85416666671022.2425684665542.4291215261457
Trimmed Mean ( 7 / 20 )43245.71739130431001.9904213640743.1598111810601
Trimmed Mean ( 8 / 20 )43109.3636363636977.98299200662944.0798704974528
Trimmed Mean ( 9 / 20 )42979.7619047619958.5339680758944.8390597894378
Trimmed Mean ( 10 / 20 )42837.325933.02241803081945.91242843919
Trimmed Mean ( 11 / 20 )42678.2631578947901.92956950179547.3188424030373
Trimmed Mean ( 12 / 20 )42505.6111111111863.36044568365349.2327524658059
Trimmed Mean ( 13 / 20 )42339.5821.568929965451.5349332913346
Trimmed Mean ( 14 / 20 )42243.65625801.28858496166652.719653122253
Trimmed Mean ( 15 / 20 )42139.6666666667779.19394592359754.0811012291908
Trimmed Mean ( 16 / 20 )42020.4642857143750.62686057400955.9804964261217
Trimmed Mean ( 17 / 20 )41897.4615384615713.0066462755758.7616703958024
Trimmed Mean ( 18 / 20 )41836.875695.27139762084160.1734447054232
Trimmed Mean ( 19 / 20 )41769.7272727273678.57848356903461.5547475850344
Trimmed Mean ( 20 / 20 )41694.5651.21541629560164.0256648670522
Median41180.5
Midrange52244.5
Midmean - Weighted Average at Xnp41961.2580645161
Midmean - Weighted Average at X(n+1)p42139.6666666667
Midmean - Empirical Distribution Function41961.2580645161
Midmean - Empirical Distribution Function - Averaging42139.6666666667
Midmean - Empirical Distribution Function - Interpolation42139.6666666667
Midmean - Closest Observation41961.2580645161
Midmean - True Basic - Statistics Graphics Toolkit42139.6666666667
Midmean - MS Excel (old versions)42243.65625
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')