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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 computationSat, 25 Dec 2010 16:31:23 +0000
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2010/Dec/25/t1293294564j3r2kdg7nww7e18.htm/, Retrieved Mon, 29 Apr 2024 07:53:27 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=115420, Retrieved Mon, 29 Apr 2024 07:53:27 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact115
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [Deposito's met va...] [2010-12-25 16:31:23] [f593aab944ee27cf123b0a348e80fa81] [Current]
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Dataseries X:
61,2
62
65,1
63,2
66,3
61,9
62,1
66,3
72
65,3
67,6
70,5
74,2
77,8
78,5
77,8
81,4
84,5
88
93,9
98,9
96,7
98,9
102,2
105,4
105,1
116,6
112
108,8
106,9
109,5
106,7
118,9
117,5
113,7
119,6
120,6
117,5
120,3
119,8
108
98,8
94,6
84,6
84,4
79,1
73,3
74,3
67,8
64,8
66,5
57,7
53,8
51,8
50,9
49
48,1
42,6
40,9
43,3
43,7




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

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 2 seconds \tabularnewline
R Server & 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=115420&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Sir Ronald Aylmer Fisher' @ 193.190.124.24[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=115420&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=115420&T=0

As an alternative you can also use a QR Code:  

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

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







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean82.5114754098363.1031678669891526.5894334262661
Geometric Mean78.8421243719206
Harmonic Mean75.094405057376
Quadratic Mean85.9413906272805
Winsorized Mean ( 1 / 20 )82.53442622950823.0960550301920726.6579325705293
Winsorized Mean ( 2 / 20 )82.54098360655743.0878427019816526.7309547709752
Winsorized Mean ( 3 / 20 )82.55081967213123.081718191311526.7872707844839
Winsorized Mean ( 4 / 20 )82.79344262295083.0145257344340827.4648319227215
Winsorized Mean ( 5 / 20 )82.75245901639342.9778679123816527.7891637410504
Winsorized Mean ( 6 / 20 )82.9393442622952.9432587406973628.1794268086142
Winsorized Mean ( 7 / 20 )82.9393442622952.9045811551448428.5546658303507
Winsorized Mean ( 8 / 20 )82.82131147540982.786483883023629.7225158846212
Winsorized Mean ( 9 / 20 )83.14590163934432.6443222749558831.4431801398835
Winsorized Mean ( 10 / 20 )83.30983606557382.4822745440664733.5618943781679
Winsorized Mean ( 11 / 20 )83.30983606557382.4415984025049934.1210233345913
Winsorized Mean ( 12 / 20 )83.1721311475412.4115264321683634.4894130282269
Winsorized Mean ( 13 / 20 )82.95901639344262.3685408307511635.0253689175934
Winsorized Mean ( 14 / 20 )83.16557377049182.3241966533215235.7825030216955
Winsorized Mean ( 15 / 20 )83.23934426229512.2150840054732537.5784142075962
Winsorized Mean ( 16 / 20 )83.23934426229512.1910938440127637.9898581202943
Winsorized Mean ( 17 / 20 )82.48688524590162.0513603049196940.2108225688471
Winsorized Mean ( 18 / 20 )81.80819672131151.8574062282179344.0443213113382
Winsorized Mean ( 19 / 20 )81.80819672131151.8574062282179344.0443213113382
Winsorized Mean ( 20 / 20 )81.84098360655741.8432677342587744.3999436899317
Trimmed Mean ( 1 / 20 )82.5711864406783.0609463349595626.9757053554383
Trimmed Mean ( 2 / 20 )82.61052631578953.0162889905481627.3881337546428
Trimmed Mean ( 3 / 20 )82.64909090909092.9651373571868527.8736129065885
Trimmed Mean ( 4 / 20 )82.68679245283022.9032463159017628.4808050904724
Trimmed Mean ( 5 / 20 )82.65490196078432.8506749303684728.9948534925027
Trimmed Mean ( 6 / 20 )82.6306122448982.7951096203565629.5625658625715
Trimmed Mean ( 7 / 20 )82.5638297872342.7333220199722330.2064042158021
Trimmed Mean ( 8 / 20 )82.49111111111112.6635679386606330.9701546988104
Trimmed Mean ( 9 / 20 )82.43255813953492.6044061840971331.6511912169767
Trimmed Mean ( 10 / 20 )82.31463414634152.5618532758570832.1308932568759
Trimmed Mean ( 11 / 20 )82.15897435897442.542175203077232.3183761133081
Trimmed Mean ( 12 / 20 )81.98648648648652.5196499892844132.53883945594
Trimmed Mean ( 13 / 20 )81.81428571428572.4901795111194432.8547742638469
Trimmed Mean ( 14 / 20 )81.65151515151522.4541944661135333.2701895790754
Trimmed Mean ( 15 / 20 )81.43870967741942.4076655244937133.8247604781168
Trimmed Mean ( 16 / 20 )81.18620689655172.3640978665463834.3413054279151
Trimmed Mean ( 17 / 20 )80.89629629629632.2974436523350835.2114386849379
Trimmed Mean ( 18 / 20 )80.6682.2386507841406036.0342044286142
Trimmed Mean ( 19 / 20 )80.52.2082489978178736.4542223633058
Trimmed Mean ( 20 / 20 )80.32.1416504538945437.4944472633135
Median78.5
Midrange80.75
Midmean - Weighted Average at Xnp80.64
Midmean - Weighted Average at X(n+1)p81.4387096774194
Midmean - Empirical Distribution Function81.4387096774194
Midmean - Empirical Distribution Function - Averaging81.4387096774194
Midmean - Empirical Distribution Function - Interpolation81.4387096774194
Midmean - Closest Observation80.86875
Midmean - True Basic - Statistics Graphics Toolkit81.4387096774194
Midmean - MS Excel (old versions)81.4387096774194
Number of observations61

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 82.511475409836 & 3.10316786698915 & 26.5894334262661 \tabularnewline
Geometric Mean & 78.8421243719206 &  &  \tabularnewline
Harmonic Mean & 75.094405057376 &  &  \tabularnewline
Quadratic Mean & 85.9413906272805 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 82.5344262295082 & 3.09605503019207 & 26.6579325705293 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 82.5409836065574 & 3.08784270198165 & 26.7309547709752 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 82.5508196721312 & 3.0817181913115 & 26.7872707844839 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 82.7934426229508 & 3.01452573443408 & 27.4648319227215 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 82.7524590163934 & 2.97786791238165 & 27.7891637410504 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 82.939344262295 & 2.94325874069736 & 28.1794268086142 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 82.939344262295 & 2.90458115514484 & 28.5546658303507 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 82.8213114754098 & 2.7864838830236 & 29.7225158846212 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 83.1459016393443 & 2.64432227495588 & 31.4431801398835 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 83.3098360655738 & 2.48227454406647 & 33.5618943781679 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 83.3098360655738 & 2.44159840250499 & 34.1210233345913 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 83.172131147541 & 2.41152643216836 & 34.4894130282269 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 82.9590163934426 & 2.36854083075116 & 35.0253689175934 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 83.1655737704918 & 2.32419665332152 & 35.7825030216955 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 83.2393442622951 & 2.21508400547325 & 37.5784142075962 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 83.2393442622951 & 2.19109384401276 & 37.9898581202943 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 82.4868852459016 & 2.05136030491969 & 40.2108225688471 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 81.8081967213115 & 1.85740622821793 & 44.0443213113382 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 81.8081967213115 & 1.85740622821793 & 44.0443213113382 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 81.8409836065574 & 1.84326773425877 & 44.3999436899317 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 82.571186440678 & 3.06094633495956 & 26.9757053554383 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 82.6105263157895 & 3.01628899054816 & 27.3881337546428 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 82.6490909090909 & 2.96513735718685 & 27.8736129065885 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 82.6867924528302 & 2.90324631590176 & 28.4808050904724 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 82.6549019607843 & 2.85067493036847 & 28.9948534925027 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 82.630612244898 & 2.79510962035656 & 29.5625658625715 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 82.563829787234 & 2.73332201997223 & 30.2064042158021 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 82.4911111111111 & 2.66356793866063 & 30.9701546988104 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 82.4325581395349 & 2.60440618409713 & 31.6511912169767 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 82.3146341463415 & 2.56185327585708 & 32.1308932568759 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 82.1589743589744 & 2.5421752030772 & 32.3183761133081 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 81.9864864864865 & 2.51964998928441 & 32.53883945594 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 81.8142857142857 & 2.49017951111944 & 32.8547742638469 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 81.6515151515152 & 2.45419446611353 & 33.2701895790754 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 81.4387096774194 & 2.40766552449371 & 33.8247604781168 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 81.1862068965517 & 2.36409786654638 & 34.3413054279151 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 80.8962962962963 & 2.29744365233508 & 35.2114386849379 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 80.668 & 2.23865078414060 & 36.0342044286142 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 80.5 & 2.20824899781787 & 36.4542223633058 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 80.3 & 2.14165045389454 & 37.4944472633135 \tabularnewline
Median & 78.5 &  &  \tabularnewline
Midrange & 80.75 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 80.64 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 81.4387096774194 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 81.4387096774194 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 81.4387096774194 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 81.4387096774194 &  &  \tabularnewline
Midmean - Closest Observation & 80.86875 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 81.4387096774194 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 81.4387096774194 &  &  \tabularnewline
Number of observations & 61 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=115420&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]82.511475409836[/C][C]3.10316786698915[/C][C]26.5894334262661[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]78.8421243719206[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]75.094405057376[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]85.9413906272805[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]82.5344262295082[/C][C]3.09605503019207[/C][C]26.6579325705293[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]82.5409836065574[/C][C]3.08784270198165[/C][C]26.7309547709752[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]82.5508196721312[/C][C]3.0817181913115[/C][C]26.7872707844839[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]82.7934426229508[/C][C]3.01452573443408[/C][C]27.4648319227215[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]82.7524590163934[/C][C]2.97786791238165[/C][C]27.7891637410504[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]82.939344262295[/C][C]2.94325874069736[/C][C]28.1794268086142[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]82.939344262295[/C][C]2.90458115514484[/C][C]28.5546658303507[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]82.8213114754098[/C][C]2.7864838830236[/C][C]29.7225158846212[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]83.1459016393443[/C][C]2.64432227495588[/C][C]31.4431801398835[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]83.3098360655738[/C][C]2.48227454406647[/C][C]33.5618943781679[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]83.3098360655738[/C][C]2.44159840250499[/C][C]34.1210233345913[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]83.172131147541[/C][C]2.41152643216836[/C][C]34.4894130282269[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]82.9590163934426[/C][C]2.36854083075116[/C][C]35.0253689175934[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]83.1655737704918[/C][C]2.32419665332152[/C][C]35.7825030216955[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]83.2393442622951[/C][C]2.21508400547325[/C][C]37.5784142075962[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]83.2393442622951[/C][C]2.19109384401276[/C][C]37.9898581202943[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]82.4868852459016[/C][C]2.05136030491969[/C][C]40.2108225688471[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]81.8081967213115[/C][C]1.85740622821793[/C][C]44.0443213113382[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]81.8081967213115[/C][C]1.85740622821793[/C][C]44.0443213113382[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]81.8409836065574[/C][C]1.84326773425877[/C][C]44.3999436899317[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]82.571186440678[/C][C]3.06094633495956[/C][C]26.9757053554383[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]82.6105263157895[/C][C]3.01628899054816[/C][C]27.3881337546428[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]82.6490909090909[/C][C]2.96513735718685[/C][C]27.8736129065885[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]82.6867924528302[/C][C]2.90324631590176[/C][C]28.4808050904724[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]82.6549019607843[/C][C]2.85067493036847[/C][C]28.9948534925027[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]82.630612244898[/C][C]2.79510962035656[/C][C]29.5625658625715[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]82.563829787234[/C][C]2.73332201997223[/C][C]30.2064042158021[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]82.4911111111111[/C][C]2.66356793866063[/C][C]30.9701546988104[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]82.4325581395349[/C][C]2.60440618409713[/C][C]31.6511912169767[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]82.3146341463415[/C][C]2.56185327585708[/C][C]32.1308932568759[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]82.1589743589744[/C][C]2.5421752030772[/C][C]32.3183761133081[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]81.9864864864865[/C][C]2.51964998928441[/C][C]32.53883945594[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]81.8142857142857[/C][C]2.49017951111944[/C][C]32.8547742638469[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]81.6515151515152[/C][C]2.45419446611353[/C][C]33.2701895790754[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]81.4387096774194[/C][C]2.40766552449371[/C][C]33.8247604781168[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]81.1862068965517[/C][C]2.36409786654638[/C][C]34.3413054279151[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]80.8962962962963[/C][C]2.29744365233508[/C][C]35.2114386849379[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]80.668[/C][C]2.23865078414060[/C][C]36.0342044286142[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]80.5[/C][C]2.20824899781787[/C][C]36.4542223633058[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]80.3[/C][C]2.14165045389454[/C][C]37.4944472633135[/C][/ROW]
[ROW][C]Median[/C][C]78.5[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]80.75[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]80.64[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]81.4387096774194[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]81.4387096774194[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]81.4387096774194[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]81.4387096774194[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]80.86875[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]81.4387096774194[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]81.4387096774194[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]61[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=115420&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=115420&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 Mean82.5114754098363.1031678669891526.5894334262661
Geometric Mean78.8421243719206
Harmonic Mean75.094405057376
Quadratic Mean85.9413906272805
Winsorized Mean ( 1 / 20 )82.53442622950823.0960550301920726.6579325705293
Winsorized Mean ( 2 / 20 )82.54098360655743.0878427019816526.7309547709752
Winsorized Mean ( 3 / 20 )82.55081967213123.081718191311526.7872707844839
Winsorized Mean ( 4 / 20 )82.79344262295083.0145257344340827.4648319227215
Winsorized Mean ( 5 / 20 )82.75245901639342.9778679123816527.7891637410504
Winsorized Mean ( 6 / 20 )82.9393442622952.9432587406973628.1794268086142
Winsorized Mean ( 7 / 20 )82.9393442622952.9045811551448428.5546658303507
Winsorized Mean ( 8 / 20 )82.82131147540982.786483883023629.7225158846212
Winsorized Mean ( 9 / 20 )83.14590163934432.6443222749558831.4431801398835
Winsorized Mean ( 10 / 20 )83.30983606557382.4822745440664733.5618943781679
Winsorized Mean ( 11 / 20 )83.30983606557382.4415984025049934.1210233345913
Winsorized Mean ( 12 / 20 )83.1721311475412.4115264321683634.4894130282269
Winsorized Mean ( 13 / 20 )82.95901639344262.3685408307511635.0253689175934
Winsorized Mean ( 14 / 20 )83.16557377049182.3241966533215235.7825030216955
Winsorized Mean ( 15 / 20 )83.23934426229512.2150840054732537.5784142075962
Winsorized Mean ( 16 / 20 )83.23934426229512.1910938440127637.9898581202943
Winsorized Mean ( 17 / 20 )82.48688524590162.0513603049196940.2108225688471
Winsorized Mean ( 18 / 20 )81.80819672131151.8574062282179344.0443213113382
Winsorized Mean ( 19 / 20 )81.80819672131151.8574062282179344.0443213113382
Winsorized Mean ( 20 / 20 )81.84098360655741.8432677342587744.3999436899317
Trimmed Mean ( 1 / 20 )82.5711864406783.0609463349595626.9757053554383
Trimmed Mean ( 2 / 20 )82.61052631578953.0162889905481627.3881337546428
Trimmed Mean ( 3 / 20 )82.64909090909092.9651373571868527.8736129065885
Trimmed Mean ( 4 / 20 )82.68679245283022.9032463159017628.4808050904724
Trimmed Mean ( 5 / 20 )82.65490196078432.8506749303684728.9948534925027
Trimmed Mean ( 6 / 20 )82.6306122448982.7951096203565629.5625658625715
Trimmed Mean ( 7 / 20 )82.5638297872342.7333220199722330.2064042158021
Trimmed Mean ( 8 / 20 )82.49111111111112.6635679386606330.9701546988104
Trimmed Mean ( 9 / 20 )82.43255813953492.6044061840971331.6511912169767
Trimmed Mean ( 10 / 20 )82.31463414634152.5618532758570832.1308932568759
Trimmed Mean ( 11 / 20 )82.15897435897442.542175203077232.3183761133081
Trimmed Mean ( 12 / 20 )81.98648648648652.5196499892844132.53883945594
Trimmed Mean ( 13 / 20 )81.81428571428572.4901795111194432.8547742638469
Trimmed Mean ( 14 / 20 )81.65151515151522.4541944661135333.2701895790754
Trimmed Mean ( 15 / 20 )81.43870967741942.4076655244937133.8247604781168
Trimmed Mean ( 16 / 20 )81.18620689655172.3640978665463834.3413054279151
Trimmed Mean ( 17 / 20 )80.89629629629632.2974436523350835.2114386849379
Trimmed Mean ( 18 / 20 )80.6682.2386507841406036.0342044286142
Trimmed Mean ( 19 / 20 )80.52.2082489978178736.4542223633058
Trimmed Mean ( 20 / 20 )80.32.1416504538945437.4944472633135
Median78.5
Midrange80.75
Midmean - Weighted Average at Xnp80.64
Midmean - Weighted Average at X(n+1)p81.4387096774194
Midmean - Empirical Distribution Function81.4387096774194
Midmean - Empirical Distribution Function - Averaging81.4387096774194
Midmean - Empirical Distribution Function - Interpolation81.4387096774194
Midmean - Closest Observation80.86875
Midmean - True Basic - Statistics Graphics Toolkit81.4387096774194
Midmean - MS Excel (old versions)81.4387096774194
Number of observations61



Parameters (Session):
Parameters (R input):
R code (references can be found in the software module):
geomean <- function(x) {
return(exp(mean(log(x))))
}
harmean <- function(x) {
return(1/mean(1/x))
}
quamean <- function(x) {
return(sqrt(mean(x*x)))
}
winmean <- function(x) {
x <-sort(x[!is.na(x)])
n<-length(x)
denom <- 3
nodenom <- n/denom
if (nodenom>40) denom <- n/40
sqrtn = sqrt(n)
roundnodenom = floor(nodenom)
win <- array(NA,dim=c(roundnodenom,2))
for (j in 1:roundnodenom) {
win[j,1] <- (j*x[j+1]+sum(x[(j+1):(n-j)])+j*x[n-j])/n
win[j,2] <- sd(c(rep(x[j+1],j),x[(j+1):(n-j)],rep(x[n-j],j)))/sqrtn
}
return(win)
}
trimean <- function(x) {
x <-sort(x[!is.na(x)])
n<-length(x)
denom <- 3
nodenom <- n/denom
if (nodenom>40) denom <- n/40
sqrtn = sqrt(n)
roundnodenom = floor(nodenom)
tri <- array(NA,dim=c(roundnodenom,2))
for (j in 1:roundnodenom) {
tri[j,1] <- mean(x,trim=j/n)
tri[j,2] <- sd(x[(j+1):(n-j)]) / sqrt(n-j*2)
}
return(tri)
}
midrange <- function(x) {
return((max(x)+min(x))/2)
}
q1 <- function(data,n,p,i,f) {
np <- n*p;
i <<- floor(np)
f <<- np - i
qvalue <- (1-f)*data[i] + f*data[i+1]
}
q2 <- function(data,n,p,i,f) {
np <- (n+1)*p
i <<- floor(np)
f <<- np - i
qvalue <- (1-f)*data[i] + f*data[i+1]
}
q3 <- function(data,n,p,i,f) {
np <- n*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- data[i]
} else {
qvalue <- data[i+1]
}
}
q4 <- function(data,n,p,i,f) {
np <- n*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- (data[i]+data[i+1])/2
} else {
qvalue <- data[i+1]
}
}
q5 <- function(data,n,p,i,f) {
np <- (n-1)*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- data[i+1]
} else {
qvalue <- data[i+1] + f*(data[i+2]-data[i+1])
}
}
q6 <- function(data,n,p,i,f) {
np <- n*p+0.5
i <<- floor(np)
f <<- np - i
qvalue <- data[i]
}
q7 <- function(data,n,p,i,f) {
np <- (n+1)*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- data[i]
} else {
qvalue <- f*data[i] + (1-f)*data[i+1]
}
}
q8 <- function(data,n,p,i,f) {
np <- (n+1)*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- data[i]
} else {
if (f == 0.5) {
qvalue <- (data[i]+data[i+1])/2
} else {
if (f < 0.5) {
qvalue <- data[i]
} else {
qvalue <- data[i+1]
}
}
}
}
midmean <- function(x,def) {
x <-sort(x[!is.na(x)])
n<-length(x)
if (def==1) {
qvalue1 <- q1(x,n,0.25,i,f)
qvalue3 <- q1(x,n,0.75,i,f)
}
if (def==2) {
qvalue1 <- q2(x,n,0.25,i,f)
qvalue3 <- q2(x,n,0.75,i,f)
}
if (def==3) {
qvalue1 <- q3(x,n,0.25,i,f)
qvalue3 <- q3(x,n,0.75,i,f)
}
if (def==4) {
qvalue1 <- q4(x,n,0.25,i,f)
qvalue3 <- q4(x,n,0.75,i,f)
}
if (def==5) {
qvalue1 <- q5(x,n,0.25,i,f)
qvalue3 <- q5(x,n,0.75,i,f)
}
if (def==6) {
qvalue1 <- q6(x,n,0.25,i,f)
qvalue3 <- q6(x,n,0.75,i,f)
}
if (def==7) {
qvalue1 <- q7(x,n,0.25,i,f)
qvalue3 <- q7(x,n,0.75,i,f)
}
if (def==8) {
qvalue1 <- q8(x,n,0.25,i,f)
qvalue3 <- q8(x,n,0.75,i,f)
}
midm <- 0
myn <- 0
roundno4 <- round(n/4)
round3no4 <- round(3*n/4)
for (i in 1:n) {
if ((x[i]>=qvalue1) & (x[i]<=qvalue3)){
midm = midm + x[i]
myn = myn + 1
}
}
midm = midm / myn
return(midm)
}
(arm <- mean(x))
sqrtn <- sqrt(length(x))
(armse <- sd(x) / sqrtn)
(armose <- arm / armse)
(geo <- geomean(x))
(har <- harmean(x))
(qua <- quamean(x))
(win <- winmean(x))
(tri <- trimean(x))
(midr <- midrange(x))
midm <- array(NA,dim=8)
for (j in 1:8) midm[j] <- midmean(x,j)
midm
bitmap(file='test1.png')
lb <- win[,1] - 2*win[,2]
ub <- win[,1] + 2*win[,2]
if ((ylimmin == '') | (ylimmax == '')) plot(win[,1],type='b',main=main, xlab='j', pch=19, ylab='Winsorized Mean(j/n)', ylim=c(min(lb),max(ub))) else plot(win[,1],type='l',main=main, xlab='j', pch=19, ylab='Winsorized Mean(j/n)', ylim=c(ylimmin,ylimmax))
lines(ub,lty=3)
lines(lb,lty=3)
grid()
dev.off()
bitmap(file='test2.png')
lb <- tri[,1] - 2*tri[,2]
ub <- tri[,1] + 2*tri[,2]
if ((ylimmin == '') | (ylimmax == '')) plot(tri[,1],type='b',main=main, xlab='j', pch=19, ylab='Trimmed Mean(j/n)', ylim=c(min(lb),max(ub))) else plot(tri[,1],type='l',main=main, xlab='j', pch=19, ylab='Trimmed Mean(j/n)', ylim=c(ylimmin,ylimmax))
lines(ub,lty=3)
lines(lb,lty=3)
grid()
dev.off()
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Central Tendency - Ungrouped Data',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Measure',header=TRUE)
a<-table.element(a,'Value',header=TRUE)
a<-table.element(a,'S.E.',header=TRUE)
a<-table.element(a,'Value/S.E.',header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('arithmetic_mean.htm', 'Arithmetic Mean', 'click to view the definition of the Arithmetic Mean'),header=TRUE)
a<-table.element(a,arm)
a<-table.element(a,hyperlink('arithmetic_mean_standard_error.htm', armse, 'click to view the definition of the Standard Error of the Arithmetic Mean'))
a<-table.element(a,armose)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('geometric_mean.htm', 'Geometric Mean', 'click to view the definition of the Geometric Mean'),header=TRUE)
a<-table.element(a,geo)
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('harmonic_mean.htm', 'Harmonic Mean', 'click to view the definition of the Harmonic Mean'),header=TRUE)
a<-table.element(a,har)
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('quadratic_mean.htm', 'Quadratic Mean', 'click to view the definition of the Quadratic Mean'),header=TRUE)
a<-table.element(a,qua)
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
for (j in 1:length(win[,1])) {
a<-table.row.start(a)
mylabel <- paste('Winsorized Mean (',j)
mylabel <- paste(mylabel,'/')
mylabel <- paste(mylabel,length(win[,1]))
mylabel <- paste(mylabel,')')
a<-table.element(a,hyperlink('winsorized_mean.htm', mylabel, 'click to view the definition of the Winsorized Mean'),header=TRUE)
a<-table.element(a,win[j,1])
a<-table.element(a,win[j,2])
a<-table.element(a,win[j,1]/win[j,2])
a<-table.row.end(a)
}
for (j in 1:length(tri[,1])) {
a<-table.row.start(a)
mylabel <- paste('Trimmed Mean (',j)
mylabel <- paste(mylabel,'/')
mylabel <- paste(mylabel,length(tri[,1]))
mylabel <- paste(mylabel,')')
a<-table.element(a,hyperlink('arithmetic_mean.htm', mylabel, 'click to view the definition of the Trimmed Mean'),header=TRUE)
a<-table.element(a,tri[j,1])
a<-table.element(a,tri[j,2])
a<-table.element(a,tri[j,1]/tri[j,2])
a<-table.row.end(a)
}
a<-table.row.start(a)
a<-table.element(a,hyperlink('median_1.htm', 'Median', 'click to view the definition of the Median'),header=TRUE)
a<-table.element(a,median(x))
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('midrange.htm', 'Midrange', 'click to view the definition of the Midrange'),header=TRUE)
a<-table.element(a,midr)
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_1.htm','Weighted Average at Xnp',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[1])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_2.htm','Weighted Average at X(n+1)p',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[2])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_3.htm','Empirical Distribution Function',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[3])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_4.htm','Empirical Distribution Function - Averaging',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[4])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_5.htm','Empirical Distribution Function - Interpolation',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[5])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_6.htm','Closest Observation',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[6])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_7.htm','True Basic - Statistics Graphics Toolkit',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[7])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_8.htm','MS Excel (old versions)',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[8])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Number of observations',header=TRUE)
a<-table.element(a,length(x))
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable.tab')