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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 computationSat, 18 Oct 2008 04:50:13 -0600
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2008/Oct/18/t1224327047eqi9zq0v9g90zwy.htm/, Retrieved Sun, 19 May 2024 15:51:23 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=16572, Retrieved Sun, 19 May 2024 15:51:23 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact160

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
F     [Univariate Data Series] [uitvoer van belgi...] [2008-10-13 19:25:24] [1e1d8320a8a1170c475bf6e4ce119de6]
- RMP     [Central Tendency] [Central Tendency ...] [2008-10-18 10:50:13] [fdd69703d301fae09456f660b2f52997] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
64.5
57.9
72.5
82.9
62.7
66.6
70.9
56.3
81.2
67.8
57.2
62.8
51.2
66.5
71.5
67.8
56.9
90.6
64.1
65.7
77.9
84.2
81.7
65.9
76.1
80.1
74.3
86.5
70.9
91.5
93.7
77.5
100.3
85.7
95
73.7
87.6
87.6
92.9
80.7
74
87.7
68.2
117.4
100.1
97.7
101.1
87.6
83.2
85.9
118
87.3
79.5
93.2
99.2
66.6
83.9
100.4
73.5
60.8

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 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 & 2 seconds \tabularnewline
R Server & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=16572&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]'George Udny Yule' @ 72.249.76.132[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=16572&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=16572&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 time2 seconds
R Server'George Udny Yule' @ 72.249.76.132






Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean79.4451.9071267248488741.6569066779218
Geometric Mean78.1107660573266
Harmonic Mean76.7925332038766
Quadratic Mean80.784273428269
Winsorized Mean ( 1 / 20 )79.521.8841530639418842.204639061348
Winsorized Mean ( 2 / 20 )78.99666666666671.726928573378745.7440266403789
Winsorized Mean ( 3 / 20 )78.97666666666671.7161897203715146.0186107218788
Winsorized Mean ( 4 / 20 )79.01666666666671.7048620512921246.3478359476532
Winsorized Mean ( 5 / 20 )79.24166666666671.6530630559792147.9362637620179
Winsorized Mean ( 6 / 20 )79.34166666666671.5992270231468449.6125099928241
Winsorized Mean ( 7 / 20 )79.17833333333331.5611401954921250.7182721718173
Winsorized Mean ( 8 / 20 )78.99166666666671.4610272132615454.0658421346779
Winsorized Mean ( 9 / 20 )78.85666666666671.4152346368050855.7198535252692
Winsorized Mean ( 10 / 20 )78.97333333333331.3668096934942257.7793190297326
Winsorized Mean ( 11 / 20 )78.9551.3511272234735358.4363919461405
Winsorized Mean ( 12 / 20 )78.7951.2835540018660061.3881456373865
Winsorized Mean ( 13 / 20 )78.62166666666671.2477982681069863.0083152671328
Winsorized Mean ( 14 / 20 )77.9451.1435657017086168.1596167876862
Winsorized Mean ( 15 / 20 )78.221.0903967038428871.7353599147262
Winsorized Mean ( 16 / 20 )78.221.0903967038428871.7353599147263
Winsorized Mean ( 17 / 20 )78.33333333333331.0721399127292373.062603493539
Winsorized Mean ( 18 / 20 )79.05333333333330.93365652192956884.6706807873579
Winsorized Mean ( 19 / 20 )78.80.8962382149033387.9230529223746
Winsorized Mean ( 20 / 20 )78.80.83758463608095894.0800446969797
Trimmed Mean ( 1 / 20 )79.26724137931031.7897121269817244.2904979992462
Trimmed Mean ( 2 / 20 )78.99642857142861.6713435848079447.2652237932910
Trimmed Mean ( 3 / 20 )78.99629629629631.6324388149994248.3915817061261
Trimmed Mean ( 4 / 20 )79.00384615384621.5887067545251349.7284007440761
Trimmed Mean ( 5 / 20 )791.5379180201606051.3681476934319
Trimmed Mean ( 6 / 20 )78.93958333333331.4914197255382552.9291533306255
Trimmed Mean ( 7 / 20 )78.85217391304351.4485599683605054.4348702403322
Trimmed Mean ( 8 / 20 )78.78863636363641.4041700802470556.1104651580201
Trimmed Mean ( 9 / 20 )78.7523809523811.3741906628548157.3081909818665
Trimmed Mean ( 10 / 20 )78.7351.3457556737139758.5061624022064
Trimmed Mean ( 11 / 20 )78.69736842105261.3189853790646959.6650801973696
Trimmed Mean ( 12 / 20 )78.65833333333331.2849888826645361.2132403591143
Trimmed Mean ( 13 / 20 )78.63823529411761.2552067296470362.6496284928546
Trimmed Mean ( 14 / 20 )78.6406251.2213479083396564.3883896333086
Trimmed Mean ( 15 / 20 )78.741.1998141618552965.6268299736047
Trimmed Mean ( 16 / 20 )78.81428571428571.1807955605043366.7467666296302
Trimmed Mean ( 17 / 20 )78.91.1471570209736968.7787273733729
Trimmed Mean ( 18 / 20 )78.98333333333331.0976203949458071.9586969201986
Trimmed Mean ( 19 / 20 )78.97272727272731.0715967334910373.6963120589693
Trimmed Mean ( 20 / 20 )791.0370504733186976.1775844402153
Median79.8
Midrange84.6
Midmean - Weighted Average at Xnp77.98125
Midmean - Weighted Average at X(n+1)p78.74
Midmean - Empirical Distribution Function77.98125
Midmean - Empirical Distribution Function - Averaging78.74
Midmean - Empirical Distribution Function - Interpolation78.74
Midmean - Closest Observation77.98125
Midmean - True Basic - Statistics Graphics Toolkit78.74
Midmean - MS Excel (old versions)78.2757575757576
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 79.445 & 1.90712672484887 & 41.6569066779218 \tabularnewline
Geometric Mean & 78.1107660573266 &  &  \tabularnewline
Harmonic Mean & 76.7925332038766 &  &  \tabularnewline
Quadratic Mean & 80.784273428269 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 79.52 & 1.88415306394188 & 42.204639061348 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 78.9966666666667 & 1.7269285733787 & 45.7440266403789 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 78.9766666666667 & 1.71618972037151 & 46.0186107218788 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 79.0166666666667 & 1.70486205129212 & 46.3478359476532 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 79.2416666666667 & 1.65306305597921 & 47.9362637620179 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 79.3416666666667 & 1.59922702314684 & 49.6125099928241 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 79.1783333333333 & 1.56114019549212 & 50.7182721718173 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 78.9916666666667 & 1.46102721326154 & 54.0658421346779 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 78.8566666666667 & 1.41523463680508 & 55.7198535252692 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 78.9733333333333 & 1.36680969349422 & 57.7793190297326 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 78.955 & 1.35112722347353 & 58.4363919461405 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 78.795 & 1.28355400186600 & 61.3881456373865 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 78.6216666666667 & 1.24779826810698 & 63.0083152671328 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 77.945 & 1.14356570170861 & 68.1596167876862 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 78.22 & 1.09039670384288 & 71.7353599147262 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 78.22 & 1.09039670384288 & 71.7353599147263 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 78.3333333333333 & 1.07213991272923 & 73.062603493539 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 79.0533333333333 & 0.933656521929568 & 84.6706807873579 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 78.8 & 0.89623821490333 & 87.9230529223746 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 78.8 & 0.837584636080958 & 94.0800446969797 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 79.2672413793103 & 1.78971212698172 & 44.2904979992462 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 78.9964285714286 & 1.67134358480794 & 47.2652237932910 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 78.9962962962963 & 1.63243881499942 & 48.3915817061261 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 79.0038461538462 & 1.58870675452513 & 49.7284007440761 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 79 & 1.53791802016060 & 51.3681476934319 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 78.9395833333333 & 1.49141972553825 & 52.9291533306255 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 78.8521739130435 & 1.44855996836050 & 54.4348702403322 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 78.7886363636364 & 1.40417008024705 & 56.1104651580201 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 78.752380952381 & 1.37419066285481 & 57.3081909818665 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 78.735 & 1.34575567371397 & 58.5061624022064 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 78.6973684210526 & 1.31898537906469 & 59.6650801973696 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 78.6583333333333 & 1.28498888266453 & 61.2132403591143 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 78.6382352941176 & 1.25520672964703 & 62.6496284928546 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 78.640625 & 1.22134790833965 & 64.3883896333086 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 78.74 & 1.19981416185529 & 65.6268299736047 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 78.8142857142857 & 1.18079556050433 & 66.7467666296302 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 78.9 & 1.14715702097369 & 68.7787273733729 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 78.9833333333333 & 1.09762039494580 & 71.9586969201986 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 78.9727272727273 & 1.07159673349103 & 73.6963120589693 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 79 & 1.03705047331869 & 76.1775844402153 \tabularnewline
Median & 79.8 &  &  \tabularnewline
Midrange & 84.6 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 77.98125 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 78.74 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 77.98125 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 78.74 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 78.74 &  &  \tabularnewline
Midmean - Closest Observation & 77.98125 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 78.74 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 78.2757575757576 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=16572&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]79.445[/C][C]1.90712672484887[/C][C]41.6569066779218[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]78.1107660573266[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]76.7925332038766[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]80.784273428269[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]79.52[/C][C]1.88415306394188[/C][C]42.204639061348[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]78.9966666666667[/C][C]1.7269285733787[/C][C]45.7440266403789[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]78.9766666666667[/C][C]1.71618972037151[/C][C]46.0186107218788[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]79.0166666666667[/C][C]1.70486205129212[/C][C]46.3478359476532[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]79.2416666666667[/C][C]1.65306305597921[/C][C]47.9362637620179[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]79.3416666666667[/C][C]1.59922702314684[/C][C]49.6125099928241[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]79.1783333333333[/C][C]1.56114019549212[/C][C]50.7182721718173[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]78.9916666666667[/C][C]1.46102721326154[/C][C]54.0658421346779[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]78.8566666666667[/C][C]1.41523463680508[/C][C]55.7198535252692[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]78.9733333333333[/C][C]1.36680969349422[/C][C]57.7793190297326[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]78.955[/C][C]1.35112722347353[/C][C]58.4363919461405[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]78.795[/C][C]1.28355400186600[/C][C]61.3881456373865[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]78.6216666666667[/C][C]1.24779826810698[/C][C]63.0083152671328[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]77.945[/C][C]1.14356570170861[/C][C]68.1596167876862[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]78.22[/C][C]1.09039670384288[/C][C]71.7353599147262[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]78.22[/C][C]1.09039670384288[/C][C]71.7353599147263[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]78.3333333333333[/C][C]1.07213991272923[/C][C]73.062603493539[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]79.0533333333333[/C][C]0.933656521929568[/C][C]84.6706807873579[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]78.8[/C][C]0.89623821490333[/C][C]87.9230529223746[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]78.8[/C][C]0.837584636080958[/C][C]94.0800446969797[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]79.2672413793103[/C][C]1.78971212698172[/C][C]44.2904979992462[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]78.9964285714286[/C][C]1.67134358480794[/C][C]47.2652237932910[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]78.9962962962963[/C][C]1.63243881499942[/C][C]48.3915817061261[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]79.0038461538462[/C][C]1.58870675452513[/C][C]49.7284007440761[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]79[/C][C]1.53791802016060[/C][C]51.3681476934319[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]78.9395833333333[/C][C]1.49141972553825[/C][C]52.9291533306255[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]78.8521739130435[/C][C]1.44855996836050[/C][C]54.4348702403322[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]78.7886363636364[/C][C]1.40417008024705[/C][C]56.1104651580201[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]78.752380952381[/C][C]1.37419066285481[/C][C]57.3081909818665[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]78.735[/C][C]1.34575567371397[/C][C]58.5061624022064[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]78.6973684210526[/C][C]1.31898537906469[/C][C]59.6650801973696[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]78.6583333333333[/C][C]1.28498888266453[/C][C]61.2132403591143[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]78.6382352941176[/C][C]1.25520672964703[/C][C]62.6496284928546[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]78.640625[/C][C]1.22134790833965[/C][C]64.3883896333086[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]78.74[/C][C]1.19981416185529[/C][C]65.6268299736047[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]78.8142857142857[/C][C]1.18079556050433[/C][C]66.7467666296302[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]78.9[/C][C]1.14715702097369[/C][C]68.7787273733729[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]78.9833333333333[/C][C]1.09762039494580[/C][C]71.9586969201986[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]78.9727272727273[/C][C]1.07159673349103[/C][C]73.6963120589693[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]79[/C][C]1.03705047331869[/C][C]76.1775844402153[/C][/ROW]
[ROW][C]Median[/C][C]79.8[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]84.6[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]77.98125[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]78.74[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]77.98125[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]78.74[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]78.74[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]77.98125[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]78.74[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]78.2757575757576[/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=16572&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=16572&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 Mean79.4451.9071267248488741.6569066779218
Geometric Mean78.1107660573266
Harmonic Mean76.7925332038766
Quadratic Mean80.784273428269
Winsorized Mean ( 1 / 20 )79.521.8841530639418842.204639061348
Winsorized Mean ( 2 / 20 )78.99666666666671.726928573378745.7440266403789
Winsorized Mean ( 3 / 20 )78.97666666666671.7161897203715146.0186107218788
Winsorized Mean ( 4 / 20 )79.01666666666671.7048620512921246.3478359476532
Winsorized Mean ( 5 / 20 )79.24166666666671.6530630559792147.9362637620179
Winsorized Mean ( 6 / 20 )79.34166666666671.5992270231468449.6125099928241
Winsorized Mean ( 7 / 20 )79.17833333333331.5611401954921250.7182721718173
Winsorized Mean ( 8 / 20 )78.99166666666671.4610272132615454.0658421346779
Winsorized Mean ( 9 / 20 )78.85666666666671.4152346368050855.7198535252692
Winsorized Mean ( 10 / 20 )78.97333333333331.3668096934942257.7793190297326
Winsorized Mean ( 11 / 20 )78.9551.3511272234735358.4363919461405
Winsorized Mean ( 12 / 20 )78.7951.2835540018660061.3881456373865
Winsorized Mean ( 13 / 20 )78.62166666666671.2477982681069863.0083152671328
Winsorized Mean ( 14 / 20 )77.9451.1435657017086168.1596167876862
Winsorized Mean ( 15 / 20 )78.221.0903967038428871.7353599147262
Winsorized Mean ( 16 / 20 )78.221.0903967038428871.7353599147263
Winsorized Mean ( 17 / 20 )78.33333333333331.0721399127292373.062603493539
Winsorized Mean ( 18 / 20 )79.05333333333330.93365652192956884.6706807873579
Winsorized Mean ( 19 / 20 )78.80.8962382149033387.9230529223746
Winsorized Mean ( 20 / 20 )78.80.83758463608095894.0800446969797
Trimmed Mean ( 1 / 20 )79.26724137931031.7897121269817244.2904979992462
Trimmed Mean ( 2 / 20 )78.99642857142861.6713435848079447.2652237932910
Trimmed Mean ( 3 / 20 )78.99629629629631.6324388149994248.3915817061261
Trimmed Mean ( 4 / 20 )79.00384615384621.5887067545251349.7284007440761
Trimmed Mean ( 5 / 20 )791.5379180201606051.3681476934319
Trimmed Mean ( 6 / 20 )78.93958333333331.4914197255382552.9291533306255
Trimmed Mean ( 7 / 20 )78.85217391304351.4485599683605054.4348702403322
Trimmed Mean ( 8 / 20 )78.78863636363641.4041700802470556.1104651580201
Trimmed Mean ( 9 / 20 )78.7523809523811.3741906628548157.3081909818665
Trimmed Mean ( 10 / 20 )78.7351.3457556737139758.5061624022064
Trimmed Mean ( 11 / 20 )78.69736842105261.3189853790646959.6650801973696
Trimmed Mean ( 12 / 20 )78.65833333333331.2849888826645361.2132403591143
Trimmed Mean ( 13 / 20 )78.63823529411761.2552067296470362.6496284928546
Trimmed Mean ( 14 / 20 )78.6406251.2213479083396564.3883896333086
Trimmed Mean ( 15 / 20 )78.741.1998141618552965.6268299736047
Trimmed Mean ( 16 / 20 )78.81428571428571.1807955605043366.7467666296302
Trimmed Mean ( 17 / 20 )78.91.1471570209736968.7787273733729
Trimmed Mean ( 18 / 20 )78.98333333333331.0976203949458071.9586969201986
Trimmed Mean ( 19 / 20 )78.97272727272731.0715967334910373.6963120589693
Trimmed Mean ( 20 / 20 )791.0370504733186976.1775844402153
Median79.8
Midrange84.6
Midmean - Weighted Average at Xnp77.98125
Midmean - Weighted Average at X(n+1)p78.74
Midmean - Empirical Distribution Function77.98125
Midmean - Empirical Distribution Function - Averaging78.74
Midmean - Empirical Distribution Function - Interpolation78.74
Midmean - Closest Observation77.98125
Midmean - True Basic - Statistics Graphics Toolkit78.74
Midmean - MS Excel (old versions)78.2757575757576
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')