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Description of Statistical Computation

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, 02 Dec 2008 11:17:20 -0700
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2008/Dec/02/t1228241920tskjz569wmhr6xg.htm/, Retrieved Fri, 24 May 2024 22:45:07 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=28200, Retrieved Fri, 24 May 2024 22:45:07 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact165

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [central tendency-...] [2008-12-02 18:17:20] [541f63fa3157af9df10fc4d202b2a90b] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
81,6
84,1
88,1
85,3
82,9
84,8
71,2
68,9
94,3
97,6
85,6
91,9
75,8
79,8
99
88,5
86,7
97,9
94,3
72,9
91,8
93,2
86,5
98,9
77,2
79,4
90,4
81,4
85,8
103,6
73,6
75,7
99,2
88,7
94,6
98,7
84,2
87,7
103,3
88,2
93,4
106,3
73,1
78,6
101,6
101,4
98,5
99
89,5
83,5
97,4
87,8
90,4
101,6
80
81,7
96,4
110,2
101,1
89,3

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'George Udny Yule' @ 72.249.76.132

\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 & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=28200&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]'George Udny Yule' @ 72.249.76.132[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=28200&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=28200&T=0

As an alternative you can also use a QR Code:  
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'George Udny Yule' @ 72.249.76.132






Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean89.2351.2427139632072571.8065481212572
Geometric Mean88.7161839082623
Harmonic Mean88.1895816727914
Quadratic Mean89.7440870847025
Winsorized Mean ( 1 / 20 )89.20833333333331.2155240939510573.390839208594
Winsorized Mean ( 2 / 20 )89.1751.1817339195001475.461149526553
Winsorized Mean ( 3 / 20 )89.171.1763303563815075.8035355597682
Winsorized Mean ( 4 / 20 )89.091.1466253605751677.6975663221954
Winsorized Mean ( 5 / 20 )89.2651.1084086037054980.53438028321
Winsorized Mean ( 6 / 20 )89.2551.1025840859846880.9507421107839
Winsorized Mean ( 7 / 20 )89.38333333333331.0632780744722884.0639297275977
Winsorized Mean ( 8 / 20 )89.31666666666670.98252863751673490.9048991105315
Winsorized Mean ( 9 / 20 )89.40666666666670.95567252820597993.5536640720477
Winsorized Mean ( 10 / 20 )89.47333333333330.94396646817141594.7844402848914
Winsorized Mean ( 11 / 20 )89.49166666666670.9344937046296695.7648684237334
Winsorized Mean ( 12 / 20 )89.73166666666670.881041665414217101.847245356415
Winsorized Mean ( 13 / 20 )89.73166666666670.866669355710735103.536217215249
Winsorized Mean ( 14 / 20 )89.6150.839228274097815106.782627284975
Winsorized Mean ( 15 / 20 )89.840.779983340398649115.181947288878
Winsorized Mean ( 16 / 20 )89.94666666666670.747207481704802120.377095878975
Winsorized Mean ( 17 / 20 )89.83333333333330.675201023285344133.046796783910
Winsorized Mean ( 18 / 20 )89.32333333333330.584790109948032152.744261255156
Winsorized Mean ( 19 / 20 )89.41833333333330.542449412709056164.841792134621
Winsorized Mean ( 20 / 20 )89.5850.518749174664104172.694250661714
Trimmed Mean ( 1 / 20 )89.22413793103451.1813618889027675.526507812018
Trimmed Mean ( 2 / 20 )89.24107142857141.1392403962407278.3338369347244
Trimmed Mean ( 3 / 20 )89.27777777777781.1096667761381180.4545830312088
Trimmed Mean ( 4 / 20 )89.31923076923081.0751759421825483.0740600351592
Trimmed Mean ( 5 / 20 )89.3881.0434583003119085.6651386771097
Trimmed Mean ( 6 / 20 )89.418751.0164936615239987.967838250893
Trimmed Mean ( 7 / 20 )89.4543478260870.98342645848271690.9619087980427
Trimmed Mean ( 8 / 20 )89.46818181818180.95239640293426393.9400669117785
Trimmed Mean ( 9 / 20 )89.49523809523810.93434252959644795.7841854141993
Trimmed Mean ( 10 / 20 )89.510.91673752639874797.6397250275391
Trimmed Mean ( 11 / 20 )89.51578947368420.89517853711501299.997694049029
Trimmed Mean ( 12 / 20 )89.51944444444440.867433904388827103.200306088471
Trimmed Mean ( 13 / 20 )89.48823529411760.843257463552784106.122079153725
Trimmed Mean ( 14 / 20 )89.4531250.812180264321925110.13949603255
Trimmed Mean ( 15 / 20 )89.430.775251535005727115.356108258901
Trimmed Mean ( 16 / 20 )89.37142857142860.739473878873286120.858127818661
Trimmed Mean ( 17 / 20 )89.28846153846150.695354407104241128.407126820836
Trimmed Mean ( 18 / 20 )89.20833333333330.654746235460916136.248715153794
Trimmed Mean ( 19 / 20 )89.1909090909090.628469903432037141.917550234057
Trimmed Mean ( 20 / 20 )89.1550.600590717982151148.445517605634
Median88.6
Midrange89.55
Midmean - Weighted Average at Xnp89.1806451612903
Midmean - Weighted Average at X(n+1)p89.43
Midmean - Empirical Distribution Function89.1806451612903
Midmean - Empirical Distribution Function - Averaging89.43
Midmean - Empirical Distribution Function - Interpolation89.43
Midmean - Closest Observation89.1806451612903
Midmean - True Basic - Statistics Graphics Toolkit89.43
Midmean - MS Excel (old versions)89.453125
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 89.235 & 1.24271396320725 & 71.8065481212572 \tabularnewline
Geometric Mean & 88.7161839082623 &  &  \tabularnewline
Harmonic Mean & 88.1895816727914 &  &  \tabularnewline
Quadratic Mean & 89.7440870847025 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 89.2083333333333 & 1.21552409395105 & 73.390839208594 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 89.175 & 1.18173391950014 & 75.461149526553 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 89.17 & 1.17633035638150 & 75.8035355597682 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 89.09 & 1.14662536057516 & 77.6975663221954 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 89.265 & 1.10840860370549 & 80.53438028321 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 89.255 & 1.10258408598468 & 80.9507421107839 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 89.3833333333333 & 1.06327807447228 & 84.0639297275977 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 89.3166666666667 & 0.982528637516734 & 90.9048991105315 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 89.4066666666667 & 0.955672528205979 & 93.5536640720477 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 89.4733333333333 & 0.943966468171415 & 94.7844402848914 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 89.4916666666667 & 0.93449370462966 & 95.7648684237334 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 89.7316666666667 & 0.881041665414217 & 101.847245356415 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 89.7316666666667 & 0.866669355710735 & 103.536217215249 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 89.615 & 0.839228274097815 & 106.782627284975 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 89.84 & 0.779983340398649 & 115.181947288878 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 89.9466666666667 & 0.747207481704802 & 120.377095878975 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 89.8333333333333 & 0.675201023285344 & 133.046796783910 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 89.3233333333333 & 0.584790109948032 & 152.744261255156 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 89.4183333333333 & 0.542449412709056 & 164.841792134621 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 89.585 & 0.518749174664104 & 172.694250661714 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 89.2241379310345 & 1.18136188890276 & 75.526507812018 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 89.2410714285714 & 1.13924039624072 & 78.3338369347244 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 89.2777777777778 & 1.10966677613811 & 80.4545830312088 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 89.3192307692308 & 1.07517594218254 & 83.0740600351592 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 89.388 & 1.04345830031190 & 85.6651386771097 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 89.41875 & 1.01649366152399 & 87.967838250893 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 89.454347826087 & 0.983426458482716 & 90.9619087980427 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 89.4681818181818 & 0.952396402934263 & 93.9400669117785 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 89.4952380952381 & 0.934342529596447 & 95.7841854141993 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 89.51 & 0.916737526398747 & 97.6397250275391 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 89.5157894736842 & 0.895178537115012 & 99.997694049029 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 89.5194444444444 & 0.867433904388827 & 103.200306088471 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 89.4882352941176 & 0.843257463552784 & 106.122079153725 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 89.453125 & 0.812180264321925 & 110.13949603255 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 89.43 & 0.775251535005727 & 115.356108258901 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 89.3714285714286 & 0.739473878873286 & 120.858127818661 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 89.2884615384615 & 0.695354407104241 & 128.407126820836 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 89.2083333333333 & 0.654746235460916 & 136.248715153794 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 89.190909090909 & 0.628469903432037 & 141.917550234057 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 89.155 & 0.600590717982151 & 148.445517605634 \tabularnewline
Median & 88.6 &  &  \tabularnewline
Midrange & 89.55 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 89.1806451612903 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 89.43 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 89.1806451612903 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 89.43 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 89.43 &  &  \tabularnewline
Midmean - Closest Observation & 89.1806451612903 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 89.43 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 89.453125 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=28200&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]89.235[/C][C]1.24271396320725[/C][C]71.8065481212572[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]88.7161839082623[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]88.1895816727914[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]89.7440870847025[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]89.2083333333333[/C][C]1.21552409395105[/C][C]73.390839208594[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]89.175[/C][C]1.18173391950014[/C][C]75.461149526553[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]89.17[/C][C]1.17633035638150[/C][C]75.8035355597682[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]89.09[/C][C]1.14662536057516[/C][C]77.6975663221954[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]89.265[/C][C]1.10840860370549[/C][C]80.53438028321[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]89.255[/C][C]1.10258408598468[/C][C]80.9507421107839[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]89.3833333333333[/C][C]1.06327807447228[/C][C]84.0639297275977[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]89.3166666666667[/C][C]0.982528637516734[/C][C]90.9048991105315[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]89.4066666666667[/C][C]0.955672528205979[/C][C]93.5536640720477[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]89.4733333333333[/C][C]0.943966468171415[/C][C]94.7844402848914[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]89.4916666666667[/C][C]0.93449370462966[/C][C]95.7648684237334[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]89.7316666666667[/C][C]0.881041665414217[/C][C]101.847245356415[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]89.7316666666667[/C][C]0.866669355710735[/C][C]103.536217215249[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]89.615[/C][C]0.839228274097815[/C][C]106.782627284975[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]89.84[/C][C]0.779983340398649[/C][C]115.181947288878[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]89.9466666666667[/C][C]0.747207481704802[/C][C]120.377095878975[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]89.8333333333333[/C][C]0.675201023285344[/C][C]133.046796783910[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]89.3233333333333[/C][C]0.584790109948032[/C][C]152.744261255156[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]89.4183333333333[/C][C]0.542449412709056[/C][C]164.841792134621[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]89.585[/C][C]0.518749174664104[/C][C]172.694250661714[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]89.2241379310345[/C][C]1.18136188890276[/C][C]75.526507812018[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]89.2410714285714[/C][C]1.13924039624072[/C][C]78.3338369347244[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]89.2777777777778[/C][C]1.10966677613811[/C][C]80.4545830312088[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]89.3192307692308[/C][C]1.07517594218254[/C][C]83.0740600351592[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]89.388[/C][C]1.04345830031190[/C][C]85.6651386771097[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]89.41875[/C][C]1.01649366152399[/C][C]87.967838250893[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]89.454347826087[/C][C]0.983426458482716[/C][C]90.9619087980427[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]89.4681818181818[/C][C]0.952396402934263[/C][C]93.9400669117785[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]89.4952380952381[/C][C]0.934342529596447[/C][C]95.7841854141993[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]89.51[/C][C]0.916737526398747[/C][C]97.6397250275391[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]89.5157894736842[/C][C]0.895178537115012[/C][C]99.997694049029[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]89.5194444444444[/C][C]0.867433904388827[/C][C]103.200306088471[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]89.4882352941176[/C][C]0.843257463552784[/C][C]106.122079153725[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]89.453125[/C][C]0.812180264321925[/C][C]110.13949603255[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]89.43[/C][C]0.775251535005727[/C][C]115.356108258901[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]89.3714285714286[/C][C]0.739473878873286[/C][C]120.858127818661[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]89.2884615384615[/C][C]0.695354407104241[/C][C]128.407126820836[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]89.2083333333333[/C][C]0.654746235460916[/C][C]136.248715153794[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]89.190909090909[/C][C]0.628469903432037[/C][C]141.917550234057[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]89.155[/C][C]0.600590717982151[/C][C]148.445517605634[/C][/ROW]
[ROW][C]Median[/C][C]88.6[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]89.55[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]89.1806451612903[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]89.43[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]89.1806451612903[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]89.43[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]89.43[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]89.1806451612903[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]89.43[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]89.453125[/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=28200&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=28200&T=1

As an alternative you can also use a QR Code:  
QR Code


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

Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean89.2351.2427139632072571.8065481212572
Geometric Mean88.7161839082623
Harmonic Mean88.1895816727914
Quadratic Mean89.7440870847025
Winsorized Mean ( 1 / 20 )89.20833333333331.2155240939510573.390839208594
Winsorized Mean ( 2 / 20 )89.1751.1817339195001475.461149526553
Winsorized Mean ( 3 / 20 )89.171.1763303563815075.8035355597682
Winsorized Mean ( 4 / 20 )89.091.1466253605751677.6975663221954
Winsorized Mean ( 5 / 20 )89.2651.1084086037054980.53438028321
Winsorized Mean ( 6 / 20 )89.2551.1025840859846880.9507421107839
Winsorized Mean ( 7 / 20 )89.38333333333331.0632780744722884.0639297275977
Winsorized Mean ( 8 / 20 )89.31666666666670.98252863751673490.9048991105315
Winsorized Mean ( 9 / 20 )89.40666666666670.95567252820597993.5536640720477
Winsorized Mean ( 10 / 20 )89.47333333333330.94396646817141594.7844402848914
Winsorized Mean ( 11 / 20 )89.49166666666670.9344937046296695.7648684237334
Winsorized Mean ( 12 / 20 )89.73166666666670.881041665414217101.847245356415
Winsorized Mean ( 13 / 20 )89.73166666666670.866669355710735103.536217215249
Winsorized Mean ( 14 / 20 )89.6150.839228274097815106.782627284975
Winsorized Mean ( 15 / 20 )89.840.779983340398649115.181947288878
Winsorized Mean ( 16 / 20 )89.94666666666670.747207481704802120.377095878975
Winsorized Mean ( 17 / 20 )89.83333333333330.675201023285344133.046796783910
Winsorized Mean ( 18 / 20 )89.32333333333330.584790109948032152.744261255156
Winsorized Mean ( 19 / 20 )89.41833333333330.542449412709056164.841792134621
Winsorized Mean ( 20 / 20 )89.5850.518749174664104172.694250661714
Trimmed Mean ( 1 / 20 )89.22413793103451.1813618889027675.526507812018
Trimmed Mean ( 2 / 20 )89.24107142857141.1392403962407278.3338369347244
Trimmed Mean ( 3 / 20 )89.27777777777781.1096667761381180.4545830312088
Trimmed Mean ( 4 / 20 )89.31923076923081.0751759421825483.0740600351592
Trimmed Mean ( 5 / 20 )89.3881.0434583003119085.6651386771097
Trimmed Mean ( 6 / 20 )89.418751.0164936615239987.967838250893
Trimmed Mean ( 7 / 20 )89.4543478260870.98342645848271690.9619087980427
Trimmed Mean ( 8 / 20 )89.46818181818180.95239640293426393.9400669117785
Trimmed Mean ( 9 / 20 )89.49523809523810.93434252959644795.7841854141993
Trimmed Mean ( 10 / 20 )89.510.91673752639874797.6397250275391
Trimmed Mean ( 11 / 20 )89.51578947368420.89517853711501299.997694049029
Trimmed Mean ( 12 / 20 )89.51944444444440.867433904388827103.200306088471
Trimmed Mean ( 13 / 20 )89.48823529411760.843257463552784106.122079153725
Trimmed Mean ( 14 / 20 )89.4531250.812180264321925110.13949603255
Trimmed Mean ( 15 / 20 )89.430.775251535005727115.356108258901
Trimmed Mean ( 16 / 20 )89.37142857142860.739473878873286120.858127818661
Trimmed Mean ( 17 / 20 )89.28846153846150.695354407104241128.407126820836
Trimmed Mean ( 18 / 20 )89.20833333333330.654746235460916136.248715153794
Trimmed Mean ( 19 / 20 )89.1909090909090.628469903432037141.917550234057
Trimmed Mean ( 20 / 20 )89.1550.600590717982151148.445517605634
Median88.6
Midrange89.55
Midmean - Weighted Average at Xnp89.1806451612903
Midmean - Weighted Average at X(n+1)p89.43
Midmean - Empirical Distribution Function89.1806451612903
Midmean - Empirical Distribution Function - Averaging89.43
Midmean - Empirical Distribution Function - Interpolation89.43
Midmean - Closest Observation89.1806451612903
Midmean - True Basic - Statistics Graphics Toolkit89.43
Midmean - MS Excel (old versions)89.453125
Number of observations60


Figures (Output of Computation)

Input Parameters & R Code

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')