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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 computationMon, 05 Dec 2011 16:55:18 -0500
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2011/Dec/05/t1323122129jihle0hop8z7e4b.htm/, Retrieved Thu, 25 Apr 2024 21:25:35 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=151288, Retrieved Thu, 25 Apr 2024 21:25:35 +0000
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Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact114
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Central Tendency] [Arabica Price in ...] [2008-01-19 12:03:37] [74be16979710d4c4e7c6647856088456]
- RMPD  [Maximum-likelihood Fitting - Normal Distribution] [] [2010-11-16 19:18:46] [b98453cac15ba1066b407e146608df68]
- RMPD    [Central Tendency] [] [2011-11-14 19:01:03] [b4c8fd31b0af00c33711722ddf8d2c4c]
- R  D        [Central Tendency] [] [2011-12-05 21:55:18] [c092f3a3bdd85c7279ddab6c8c6c9261] [Current]
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Dataseries X:
5
5
6
6
7
7
8
9
10
11
12
13
14
15
15
16
16
17
17
18
18
50
50
51
52
53
54
55
56
57
58
59
60
61
66
70
70
71
71
72
72
73
73
74
74
75
75
76
76
77
77
77
78
78
78
79
80
80
81




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gertrude Mary Cox' @ cox.wessa.net

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 1 seconds \tabularnewline
R Server & 'Gertrude Mary Cox' @ cox.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=151288&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gertrude Mary Cox' @ cox.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=151288&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=151288&T=0

As an alternative you can also use a QR Code:  

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

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gertrude Mary Cox' @ cox.wessa.net







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean48.03389830508473.7225493314723712.9034954349647
Geometric Mean34.9815176855759
Harmonic Mean21.5611296721576
Quadratic Mean55.776187130777
Winsorized Mean ( 1 / 19 )48.01694915254243.7199991457412312.90778499439
Winsorized Mean ( 2 / 19 )48.05084745762713.713310580841812.94016388113
Winsorized Mean ( 3 / 19 )483.705872257324812.9524162375339
Winsorized Mean ( 4 / 19 )483.6830919849031413.0325281575237
Winsorized Mean ( 5 / 19 )483.6830919849031413.0325281575237
Winsorized Mean ( 6 / 19 )48.10169491525423.6637366242901513.1291355924292
Winsorized Mean ( 7 / 19 )48.10169491525423.6250068957595213.2694078379611
Winsorized Mean ( 8 / 19 )48.23728813559323.5999820591028713.3993134809161
Winsorized Mean ( 9 / 19 )48.38983050847463.5722497686739513.5460378310661
Winsorized Mean ( 10 / 19 )48.38983050847463.5186749795096913.752287662334
Winsorized Mean ( 11 / 19 )48.57627118644073.4856475692627413.9360822404415
Winsorized Mean ( 12 / 19 )48.57627118644073.4227044199528814.1923652253645
Winsorized Mean ( 13 / 19 )48.79661016949153.384547314871314.4174702345229
Winsorized Mean ( 14 / 19 )48.55932203389833.3531888733506714.4815350008529
Winsorized Mean ( 15 / 19 )48.81355932203393.3095221152559714.74942835312
Winsorized Mean ( 16 / 19 )48.54237288135593.2742662420257414.8254201989767
Winsorized Mean ( 17 / 19 )48.83050847457633.2250619032177915.140952310359
Winsorized Mean ( 18 / 19 )48.52542372881363.1859712152768115.2309674036391
Winsorized Mean ( 19 / 19 )48.84745762711863.1311498047115715.6004856598096
Trimmed Mean ( 1 / 19 )48.21052631578953.7329173854818812.9149727511492
Trimmed Mean ( 2 / 19 )48.41818181818183.742529340527312.9372885053615
Trimmed Mean ( 3 / 19 )48.6226415094343.7521378922912812.9586499497603
Trimmed Mean ( 4 / 19 )48.86274509803923.7603733239617612.9941207663285
Trimmed Mean ( 5 / 19 )49.12244897959183.7713826491005113.0250503727877
Trimmed Mean ( 6 / 19 )49.40425531914893.7769273218957513.0805416966169
Trimmed Mean ( 7 / 19 )49.68888888888893.780976067425813.1418152357464
Trimmed Mean ( 8 / 19 )503.7869625389377513.203193716837
Trimmed Mean ( 9 / 19 )50.31707317073173.7907845613698213.2735248749007
Trimmed Mean ( 10 / 19 )50.64102564102563.7915466703120113.3562975862983
Trimmed Mean ( 11 / 19 )513.7930709705181413.445569670697
Trimmed Mean ( 12 / 19 )51.37142857142863.7896554718652413.5556989158552
Trimmed Mean ( 13 / 19 )51.78787878787883.785127788903413.6819366943705
Trimmed Mean ( 14 / 19 )52.22580645161293.7719136574968813.8459708238049
Trimmed Mean ( 15 / 19 )52.75862068965523.7408855318755114.1032438015296
Trimmed Mean ( 16 / 19 )53.33333333333333.6887447196624514.4583963886267
Trimmed Mean ( 17 / 19 )54.043.5960533922621315.0275855515053
Trimmed Mean ( 18 / 19 )54.82608695652173.4473178976420715.9039834980181
Trimmed Mean ( 19 / 19 )55.80952380952383.1874897180928817.5089266932335
Median57
Midrange43
Midmean - Weighted Average at Xnp51.0625
Midmean - Weighted Average at X(n+1)p51.0625
Midmean - Empirical Distribution Function51.0625
Midmean - Empirical Distribution Function - Averaging51.0625
Midmean - Empirical Distribution Function - Interpolation53.4666666666667
Midmean - Closest Observation51.0625
Midmean - True Basic - Statistics Graphics Toolkit51.0625
Midmean - MS Excel (old versions)51.0625
Number of observations59

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 48.0338983050847 & 3.72254933147237 & 12.9034954349647 \tabularnewline
Geometric Mean & 34.9815176855759 &  &  \tabularnewline
Harmonic Mean & 21.5611296721576 &  &  \tabularnewline
Quadratic Mean & 55.776187130777 &  &  \tabularnewline
Winsorized Mean ( 1 / 19 ) & 48.0169491525424 & 3.71999914574123 & 12.90778499439 \tabularnewline
Winsorized Mean ( 2 / 19 ) & 48.0508474576271 & 3.7133105808418 & 12.94016388113 \tabularnewline
Winsorized Mean ( 3 / 19 ) & 48 & 3.7058722573248 & 12.9524162375339 \tabularnewline
Winsorized Mean ( 4 / 19 ) & 48 & 3.68309198490314 & 13.0325281575237 \tabularnewline
Winsorized Mean ( 5 / 19 ) & 48 & 3.68309198490314 & 13.0325281575237 \tabularnewline
Winsorized Mean ( 6 / 19 ) & 48.1016949152542 & 3.66373662429015 & 13.1291355924292 \tabularnewline
Winsorized Mean ( 7 / 19 ) & 48.1016949152542 & 3.62500689575952 & 13.2694078379611 \tabularnewline
Winsorized Mean ( 8 / 19 ) & 48.2372881355932 & 3.59998205910287 & 13.3993134809161 \tabularnewline
Winsorized Mean ( 9 / 19 ) & 48.3898305084746 & 3.57224976867395 & 13.5460378310661 \tabularnewline
Winsorized Mean ( 10 / 19 ) & 48.3898305084746 & 3.51867497950969 & 13.752287662334 \tabularnewline
Winsorized Mean ( 11 / 19 ) & 48.5762711864407 & 3.48564756926274 & 13.9360822404415 \tabularnewline
Winsorized Mean ( 12 / 19 ) & 48.5762711864407 & 3.42270441995288 & 14.1923652253645 \tabularnewline
Winsorized Mean ( 13 / 19 ) & 48.7966101694915 & 3.3845473148713 & 14.4174702345229 \tabularnewline
Winsorized Mean ( 14 / 19 ) & 48.5593220338983 & 3.35318887335067 & 14.4815350008529 \tabularnewline
Winsorized Mean ( 15 / 19 ) & 48.8135593220339 & 3.30952211525597 & 14.74942835312 \tabularnewline
Winsorized Mean ( 16 / 19 ) & 48.5423728813559 & 3.27426624202574 & 14.8254201989767 \tabularnewline
Winsorized Mean ( 17 / 19 ) & 48.8305084745763 & 3.22506190321779 & 15.140952310359 \tabularnewline
Winsorized Mean ( 18 / 19 ) & 48.5254237288136 & 3.18597121527681 & 15.2309674036391 \tabularnewline
Winsorized Mean ( 19 / 19 ) & 48.8474576271186 & 3.13114980471157 & 15.6004856598096 \tabularnewline
Trimmed Mean ( 1 / 19 ) & 48.2105263157895 & 3.73291738548188 & 12.9149727511492 \tabularnewline
Trimmed Mean ( 2 / 19 ) & 48.4181818181818 & 3.7425293405273 & 12.9372885053615 \tabularnewline
Trimmed Mean ( 3 / 19 ) & 48.622641509434 & 3.75213789229128 & 12.9586499497603 \tabularnewline
Trimmed Mean ( 4 / 19 ) & 48.8627450980392 & 3.76037332396176 & 12.9941207663285 \tabularnewline
Trimmed Mean ( 5 / 19 ) & 49.1224489795918 & 3.77138264910051 & 13.0250503727877 \tabularnewline
Trimmed Mean ( 6 / 19 ) & 49.4042553191489 & 3.77692732189575 & 13.0805416966169 \tabularnewline
Trimmed Mean ( 7 / 19 ) & 49.6888888888889 & 3.7809760674258 & 13.1418152357464 \tabularnewline
Trimmed Mean ( 8 / 19 ) & 50 & 3.78696253893775 & 13.203193716837 \tabularnewline
Trimmed Mean ( 9 / 19 ) & 50.3170731707317 & 3.79078456136982 & 13.2735248749007 \tabularnewline
Trimmed Mean ( 10 / 19 ) & 50.6410256410256 & 3.79154667031201 & 13.3562975862983 \tabularnewline
Trimmed Mean ( 11 / 19 ) & 51 & 3.79307097051814 & 13.445569670697 \tabularnewline
Trimmed Mean ( 12 / 19 ) & 51.3714285714286 & 3.78965547186524 & 13.5556989158552 \tabularnewline
Trimmed Mean ( 13 / 19 ) & 51.7878787878788 & 3.7851277889034 & 13.6819366943705 \tabularnewline
Trimmed Mean ( 14 / 19 ) & 52.2258064516129 & 3.77191365749688 & 13.8459708238049 \tabularnewline
Trimmed Mean ( 15 / 19 ) & 52.7586206896552 & 3.74088553187551 & 14.1032438015296 \tabularnewline
Trimmed Mean ( 16 / 19 ) & 53.3333333333333 & 3.68874471966245 & 14.4583963886267 \tabularnewline
Trimmed Mean ( 17 / 19 ) & 54.04 & 3.59605339226213 & 15.0275855515053 \tabularnewline
Trimmed Mean ( 18 / 19 ) & 54.8260869565217 & 3.44731789764207 & 15.9039834980181 \tabularnewline
Trimmed Mean ( 19 / 19 ) & 55.8095238095238 & 3.18748971809288 & 17.5089266932335 \tabularnewline
Median & 57 &  &  \tabularnewline
Midrange & 43 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 51.0625 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 51.0625 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 51.0625 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 51.0625 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 53.4666666666667 &  &  \tabularnewline
Midmean - Closest Observation & 51.0625 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 51.0625 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 51.0625 &  &  \tabularnewline
Number of observations & 59 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=151288&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]48.0338983050847[/C][C]3.72254933147237[/C][C]12.9034954349647[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]34.9815176855759[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]21.5611296721576[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]55.776187130777[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 19 )[/C][C]48.0169491525424[/C][C]3.71999914574123[/C][C]12.90778499439[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 19 )[/C][C]48.0508474576271[/C][C]3.7133105808418[/C][C]12.94016388113[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 19 )[/C][C]48[/C][C]3.7058722573248[/C][C]12.9524162375339[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 19 )[/C][C]48[/C][C]3.68309198490314[/C][C]13.0325281575237[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 19 )[/C][C]48[/C][C]3.68309198490314[/C][C]13.0325281575237[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 19 )[/C][C]48.1016949152542[/C][C]3.66373662429015[/C][C]13.1291355924292[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 19 )[/C][C]48.1016949152542[/C][C]3.62500689575952[/C][C]13.2694078379611[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 19 )[/C][C]48.2372881355932[/C][C]3.59998205910287[/C][C]13.3993134809161[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 19 )[/C][C]48.3898305084746[/C][C]3.57224976867395[/C][C]13.5460378310661[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 19 )[/C][C]48.3898305084746[/C][C]3.51867497950969[/C][C]13.752287662334[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 19 )[/C][C]48.5762711864407[/C][C]3.48564756926274[/C][C]13.9360822404415[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 19 )[/C][C]48.5762711864407[/C][C]3.42270441995288[/C][C]14.1923652253645[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 19 )[/C][C]48.7966101694915[/C][C]3.3845473148713[/C][C]14.4174702345229[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 19 )[/C][C]48.5593220338983[/C][C]3.35318887335067[/C][C]14.4815350008529[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 19 )[/C][C]48.8135593220339[/C][C]3.30952211525597[/C][C]14.74942835312[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 19 )[/C][C]48.5423728813559[/C][C]3.27426624202574[/C][C]14.8254201989767[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 19 )[/C][C]48.8305084745763[/C][C]3.22506190321779[/C][C]15.140952310359[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 19 )[/C][C]48.5254237288136[/C][C]3.18597121527681[/C][C]15.2309674036391[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 19 )[/C][C]48.8474576271186[/C][C]3.13114980471157[/C][C]15.6004856598096[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 19 )[/C][C]48.2105263157895[/C][C]3.73291738548188[/C][C]12.9149727511492[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 19 )[/C][C]48.4181818181818[/C][C]3.7425293405273[/C][C]12.9372885053615[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 19 )[/C][C]48.622641509434[/C][C]3.75213789229128[/C][C]12.9586499497603[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 19 )[/C][C]48.8627450980392[/C][C]3.76037332396176[/C][C]12.9941207663285[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 19 )[/C][C]49.1224489795918[/C][C]3.77138264910051[/C][C]13.0250503727877[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 19 )[/C][C]49.4042553191489[/C][C]3.77692732189575[/C][C]13.0805416966169[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 19 )[/C][C]49.6888888888889[/C][C]3.7809760674258[/C][C]13.1418152357464[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 19 )[/C][C]50[/C][C]3.78696253893775[/C][C]13.203193716837[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 19 )[/C][C]50.3170731707317[/C][C]3.79078456136982[/C][C]13.2735248749007[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 19 )[/C][C]50.6410256410256[/C][C]3.79154667031201[/C][C]13.3562975862983[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 19 )[/C][C]51[/C][C]3.79307097051814[/C][C]13.445569670697[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 19 )[/C][C]51.3714285714286[/C][C]3.78965547186524[/C][C]13.5556989158552[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 19 )[/C][C]51.7878787878788[/C][C]3.7851277889034[/C][C]13.6819366943705[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 19 )[/C][C]52.2258064516129[/C][C]3.77191365749688[/C][C]13.8459708238049[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 19 )[/C][C]52.7586206896552[/C][C]3.74088553187551[/C][C]14.1032438015296[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 19 )[/C][C]53.3333333333333[/C][C]3.68874471966245[/C][C]14.4583963886267[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 19 )[/C][C]54.04[/C][C]3.59605339226213[/C][C]15.0275855515053[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 19 )[/C][C]54.8260869565217[/C][C]3.44731789764207[/C][C]15.9039834980181[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 19 )[/C][C]55.8095238095238[/C][C]3.18748971809288[/C][C]17.5089266932335[/C][/ROW]
[ROW][C]Median[/C][C]57[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]43[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]51.0625[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]51.0625[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]51.0625[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]51.0625[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]53.4666666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]51.0625[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]51.0625[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]51.0625[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]59[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=151288&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=151288&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 Mean48.03389830508473.7225493314723712.9034954349647
Geometric Mean34.9815176855759
Harmonic Mean21.5611296721576
Quadratic Mean55.776187130777
Winsorized Mean ( 1 / 19 )48.01694915254243.7199991457412312.90778499439
Winsorized Mean ( 2 / 19 )48.05084745762713.713310580841812.94016388113
Winsorized Mean ( 3 / 19 )483.705872257324812.9524162375339
Winsorized Mean ( 4 / 19 )483.6830919849031413.0325281575237
Winsorized Mean ( 5 / 19 )483.6830919849031413.0325281575237
Winsorized Mean ( 6 / 19 )48.10169491525423.6637366242901513.1291355924292
Winsorized Mean ( 7 / 19 )48.10169491525423.6250068957595213.2694078379611
Winsorized Mean ( 8 / 19 )48.23728813559323.5999820591028713.3993134809161
Winsorized Mean ( 9 / 19 )48.38983050847463.5722497686739513.5460378310661
Winsorized Mean ( 10 / 19 )48.38983050847463.5186749795096913.752287662334
Winsorized Mean ( 11 / 19 )48.57627118644073.4856475692627413.9360822404415
Winsorized Mean ( 12 / 19 )48.57627118644073.4227044199528814.1923652253645
Winsorized Mean ( 13 / 19 )48.79661016949153.384547314871314.4174702345229
Winsorized Mean ( 14 / 19 )48.55932203389833.3531888733506714.4815350008529
Winsorized Mean ( 15 / 19 )48.81355932203393.3095221152559714.74942835312
Winsorized Mean ( 16 / 19 )48.54237288135593.2742662420257414.8254201989767
Winsorized Mean ( 17 / 19 )48.83050847457633.2250619032177915.140952310359
Winsorized Mean ( 18 / 19 )48.52542372881363.1859712152768115.2309674036391
Winsorized Mean ( 19 / 19 )48.84745762711863.1311498047115715.6004856598096
Trimmed Mean ( 1 / 19 )48.21052631578953.7329173854818812.9149727511492
Trimmed Mean ( 2 / 19 )48.41818181818183.742529340527312.9372885053615
Trimmed Mean ( 3 / 19 )48.6226415094343.7521378922912812.9586499497603
Trimmed Mean ( 4 / 19 )48.86274509803923.7603733239617612.9941207663285
Trimmed Mean ( 5 / 19 )49.12244897959183.7713826491005113.0250503727877
Trimmed Mean ( 6 / 19 )49.40425531914893.7769273218957513.0805416966169
Trimmed Mean ( 7 / 19 )49.68888888888893.780976067425813.1418152357464
Trimmed Mean ( 8 / 19 )503.7869625389377513.203193716837
Trimmed Mean ( 9 / 19 )50.31707317073173.7907845613698213.2735248749007
Trimmed Mean ( 10 / 19 )50.64102564102563.7915466703120113.3562975862983
Trimmed Mean ( 11 / 19 )513.7930709705181413.445569670697
Trimmed Mean ( 12 / 19 )51.37142857142863.7896554718652413.5556989158552
Trimmed Mean ( 13 / 19 )51.78787878787883.785127788903413.6819366943705
Trimmed Mean ( 14 / 19 )52.22580645161293.7719136574968813.8459708238049
Trimmed Mean ( 15 / 19 )52.75862068965523.7408855318755114.1032438015296
Trimmed Mean ( 16 / 19 )53.33333333333333.6887447196624514.4583963886267
Trimmed Mean ( 17 / 19 )54.043.5960533922621315.0275855515053
Trimmed Mean ( 18 / 19 )54.82608695652173.4473178976420715.9039834980181
Trimmed Mean ( 19 / 19 )55.80952380952383.1874897180928817.5089266932335
Median57
Midrange43
Midmean - Weighted Average at Xnp51.0625
Midmean - Weighted Average at X(n+1)p51.0625
Midmean - Empirical Distribution Function51.0625
Midmean - Empirical Distribution Function - Averaging51.0625
Midmean - Empirical Distribution Function - Interpolation53.4666666666667
Midmean - Closest Observation51.0625
Midmean - True Basic - Statistics Graphics Toolkit51.0625
Midmean - MS Excel (old versions)51.0625
Number of observations59



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')