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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, 06 Dec 2008 05:44:46 -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/06/t1228567542r0voxlrmn82qqvp.htm/, Retrieved Thu, 31 Oct 2024 23:40:48 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=29551, Retrieved Thu, 31 Oct 2024 23:40:48 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact180
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [Central Tendency ...] [2008-12-06 12:44:46] [6912578025c824de531bc660dd61b996] [Current]
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Dataseries X:
109
109
109,2
113,3
112,3
112,3
116,3
118,3
119,4
119,4
119,4
120,1
121,7
123,7
123,7
128,5
127,1
122,6
119,8
122,7
123,4
123,8
121,8
121,2
121,2
121,2
121,2
129,6
131
131
129,8
129,8
134,9
131,2
127,1
130,5
130,5
131,7
131,7
131,7
131,7
128,7
125
124,5
123
122,8
123,1
124,8
126,9
131,7
136,8
143,7
150,1
152,7
152,6
150,5
154,9
158
158,1
160,6
160,6




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'Herman Ole Andreas Wold' @ 193.190.124.10:1001

\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 & 3 seconds \tabularnewline
R Server & 'Herman Ole Andreas Wold' @ 193.190.124.10:1001 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=29551&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]3 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Herman Ole Andreas Wold' @ 193.190.124.10:1001[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=29551&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=29551&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 time3 seconds
R Server'Herman Ole Andreas Wold' @ 193.190.124.10:1001







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean128.91.6677313539213977.290625793485
Geometric Mean128.288098882989
Harmonic Mean127.709473048489
Quadratic Mean129.545704954395
Winsorized Mean ( 1 / 20 )128.91.6677313539213977.290625793485
Winsorized Mean ( 2 / 20 )128.8245901639341.6412521138749378.4916522421315
Winsorized Mean ( 3 / 20 )128.9721311475411.6114279910083380.0359258168516
Winsorized Mean ( 4 / 20 )128.7688524590161.5523603410051882.9503621405558
Winsorized Mean ( 5 / 20 )128.6704918032791.4884791524323386.44426869736
Winsorized Mean ( 6 / 20 )128.9557377049181.4387219673723689.6321461890505
Winsorized Mean ( 7 / 20 )128.9442622950821.3413628266554696.1292945746751
Winsorized Mean ( 8 / 20 )129.0360655737701.3089040023470198.5832920843655
Winsorized Mean ( 9 / 20 )128.0918032786891.06587734221374120.174994068879
Winsorized Mean ( 10 / 20 )126.9606557377050.810151705042454156.712199638032
Winsorized Mean ( 11 / 20 )126.6901639344260.732055661377856173.060834876918
Winsorized Mean ( 12 / 20 )126.1196721311480.615242720205403204.991734138750
Winsorized Mean ( 13 / 20 )126.3540983606560.578676527376064218.350135841163
Winsorized Mean ( 14 / 20 )126.3540983606560.578676527376064218.350135841163
Winsorized Mean ( 15 / 20 )126.3540983606560.578676527376064218.350135841163
Winsorized Mean ( 16 / 20 )126.3540983606560.578676527376064218.350135841163
Winsorized Mean ( 17 / 20 )126.3540983606560.537046027733495235.276106396150
Winsorized Mean ( 18 / 20 )126.3245901639340.523964791175734241.093661809742
Winsorized Mean ( 19 / 20 )126.5737704918030.48912714517743258.774782262164
Winsorized Mean ( 20 / 20 )126.4426229508200.460271118822181274.71335432556
Trimmed Mean ( 1 / 20 )128.71.6014677662784880.363777972925
Trimmed Mean ( 2 / 20 )128.4859649122811.5193085557077284.5687101738392
Trimmed Mean ( 3 / 20 )128.2981818181821.4351538612456989.3968133192498
Trimmed Mean ( 4 / 20 )128.0396226415091.3436307300094995.2937587551341
Trimmed Mean ( 5 / 20 )127.8215686274511.25305685433659102.007796521829
Trimmed Mean ( 6 / 20 )127.6102040816331.16128830091403109.886755925461
Trimmed Mean ( 7 / 20 )127.3191489361701.05700009363536120.453299581345
Trimmed Mean ( 8 / 20 )127.0044444444440.951431433834535133.487753218938
Trimmed Mean ( 9 / 20 )126.6441860465120.813618187542885155.655549477053
Trimmed Mean ( 10 / 20 )126.4048780487800.719840355095016175.601266522624
Trimmed Mean ( 11 / 20 )126.3179487179490.683513900584667184.806700507332
Trimmed Mean ( 12 / 20 )126.2621621621620.657668456038708191.984518951493
Trimmed Mean ( 13 / 20 )126.2828571428570.653735044037813193.17131350779
Trimmed Mean ( 14 / 20 )126.2727272727270.655242158672179192.711542750262
Trimmed Mean ( 15 / 20 )126.2612903225810.65434326296874192.958799254288
Trimmed Mean ( 16 / 20 )126.2482758620690.649926496216393194.25008304329
Trimmed Mean ( 17 / 20 )126.2333333333330.640267928248026197.157045924114
Trimmed Mean ( 18 / 20 )126.2160.635811292759102198.511730504638
Trimmed Mean ( 19 / 20 )126.20.628946041031856200.653143142383
Trimmed Mean ( 20 / 20 )126.1428571428570.625055099612043201.810779915484
Median125
Midrange134.8
Midmean - Weighted Average at Xnp126.433333333333
Midmean - Weighted Average at X(n+1)p126.433333333333
Midmean - Empirical Distribution Function126.433333333333
Midmean - Empirical Distribution Function - Averaging126.433333333333
Midmean - Empirical Distribution Function - Interpolation126.433333333333
Midmean - Closest Observation126.433333333333
Midmean - True Basic - Statistics Graphics Toolkit126.433333333333
Midmean - MS Excel (old versions)126.433333333333
Number of observations61

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 128.9 & 1.66773135392139 & 77.290625793485 \tabularnewline
Geometric Mean & 128.288098882989 &  &  \tabularnewline
Harmonic Mean & 127.709473048489 &  &  \tabularnewline
Quadratic Mean & 129.545704954395 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 128.9 & 1.66773135392139 & 77.290625793485 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 128.824590163934 & 1.64125211387493 & 78.4916522421315 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 128.972131147541 & 1.61142799100833 & 80.0359258168516 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 128.768852459016 & 1.55236034100518 & 82.9503621405558 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 128.670491803279 & 1.48847915243233 & 86.44426869736 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 128.955737704918 & 1.43872196737236 & 89.6321461890505 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 128.944262295082 & 1.34136282665546 & 96.1292945746751 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 129.036065573770 & 1.30890400234701 & 98.5832920843655 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 128.091803278689 & 1.06587734221374 & 120.174994068879 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 126.960655737705 & 0.810151705042454 & 156.712199638032 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 126.690163934426 & 0.732055661377856 & 173.060834876918 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 126.119672131148 & 0.615242720205403 & 204.991734138750 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 126.354098360656 & 0.578676527376064 & 218.350135841163 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 126.354098360656 & 0.578676527376064 & 218.350135841163 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 126.354098360656 & 0.578676527376064 & 218.350135841163 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 126.354098360656 & 0.578676527376064 & 218.350135841163 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 126.354098360656 & 0.537046027733495 & 235.276106396150 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 126.324590163934 & 0.523964791175734 & 241.093661809742 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 126.573770491803 & 0.48912714517743 & 258.774782262164 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 126.442622950820 & 0.460271118822181 & 274.71335432556 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 128.7 & 1.60146776627848 & 80.363777972925 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 128.485964912281 & 1.51930855570772 & 84.5687101738392 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 128.298181818182 & 1.43515386124569 & 89.3968133192498 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 128.039622641509 & 1.34363073000949 & 95.2937587551341 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 127.821568627451 & 1.25305685433659 & 102.007796521829 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 127.610204081633 & 1.16128830091403 & 109.886755925461 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 127.319148936170 & 1.05700009363536 & 120.453299581345 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 127.004444444444 & 0.951431433834535 & 133.487753218938 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 126.644186046512 & 0.813618187542885 & 155.655549477053 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 126.404878048780 & 0.719840355095016 & 175.601266522624 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 126.317948717949 & 0.683513900584667 & 184.806700507332 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 126.262162162162 & 0.657668456038708 & 191.984518951493 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 126.282857142857 & 0.653735044037813 & 193.17131350779 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 126.272727272727 & 0.655242158672179 & 192.711542750262 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 126.261290322581 & 0.65434326296874 & 192.958799254288 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 126.248275862069 & 0.649926496216393 & 194.25008304329 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 126.233333333333 & 0.640267928248026 & 197.157045924114 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 126.216 & 0.635811292759102 & 198.511730504638 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 126.2 & 0.628946041031856 & 200.653143142383 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 126.142857142857 & 0.625055099612043 & 201.810779915484 \tabularnewline
Median & 125 &  &  \tabularnewline
Midrange & 134.8 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 126.433333333333 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 126.433333333333 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 126.433333333333 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 126.433333333333 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 126.433333333333 &  &  \tabularnewline
Midmean - Closest Observation & 126.433333333333 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 126.433333333333 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 126.433333333333 &  &  \tabularnewline
Number of observations & 61 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=29551&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]128.9[/C][C]1.66773135392139[/C][C]77.290625793485[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]128.288098882989[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]127.709473048489[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]129.545704954395[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]128.9[/C][C]1.66773135392139[/C][C]77.290625793485[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]128.824590163934[/C][C]1.64125211387493[/C][C]78.4916522421315[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]128.972131147541[/C][C]1.61142799100833[/C][C]80.0359258168516[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]128.768852459016[/C][C]1.55236034100518[/C][C]82.9503621405558[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]128.670491803279[/C][C]1.48847915243233[/C][C]86.44426869736[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]128.955737704918[/C][C]1.43872196737236[/C][C]89.6321461890505[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]128.944262295082[/C][C]1.34136282665546[/C][C]96.1292945746751[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]129.036065573770[/C][C]1.30890400234701[/C][C]98.5832920843655[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]128.091803278689[/C][C]1.06587734221374[/C][C]120.174994068879[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]126.960655737705[/C][C]0.810151705042454[/C][C]156.712199638032[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]126.690163934426[/C][C]0.732055661377856[/C][C]173.060834876918[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]126.119672131148[/C][C]0.615242720205403[/C][C]204.991734138750[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]126.354098360656[/C][C]0.578676527376064[/C][C]218.350135841163[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]126.354098360656[/C][C]0.578676527376064[/C][C]218.350135841163[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]126.354098360656[/C][C]0.578676527376064[/C][C]218.350135841163[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]126.354098360656[/C][C]0.578676527376064[/C][C]218.350135841163[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]126.354098360656[/C][C]0.537046027733495[/C][C]235.276106396150[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]126.324590163934[/C][C]0.523964791175734[/C][C]241.093661809742[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]126.573770491803[/C][C]0.48912714517743[/C][C]258.774782262164[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]126.442622950820[/C][C]0.460271118822181[/C][C]274.71335432556[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]128.7[/C][C]1.60146776627848[/C][C]80.363777972925[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]128.485964912281[/C][C]1.51930855570772[/C][C]84.5687101738392[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]128.298181818182[/C][C]1.43515386124569[/C][C]89.3968133192498[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]128.039622641509[/C][C]1.34363073000949[/C][C]95.2937587551341[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]127.821568627451[/C][C]1.25305685433659[/C][C]102.007796521829[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]127.610204081633[/C][C]1.16128830091403[/C][C]109.886755925461[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]127.319148936170[/C][C]1.05700009363536[/C][C]120.453299581345[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]127.004444444444[/C][C]0.951431433834535[/C][C]133.487753218938[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]126.644186046512[/C][C]0.813618187542885[/C][C]155.655549477053[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]126.404878048780[/C][C]0.719840355095016[/C][C]175.601266522624[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]126.317948717949[/C][C]0.683513900584667[/C][C]184.806700507332[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]126.262162162162[/C][C]0.657668456038708[/C][C]191.984518951493[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]126.282857142857[/C][C]0.653735044037813[/C][C]193.17131350779[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]126.272727272727[/C][C]0.655242158672179[/C][C]192.711542750262[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]126.261290322581[/C][C]0.65434326296874[/C][C]192.958799254288[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]126.248275862069[/C][C]0.649926496216393[/C][C]194.25008304329[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]126.233333333333[/C][C]0.640267928248026[/C][C]197.157045924114[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]126.216[/C][C]0.635811292759102[/C][C]198.511730504638[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]126.2[/C][C]0.628946041031856[/C][C]200.653143142383[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]126.142857142857[/C][C]0.625055099612043[/C][C]201.810779915484[/C][/ROW]
[ROW][C]Median[/C][C]125[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]134.8[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]126.433333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]126.433333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]126.433333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]126.433333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]126.433333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]126.433333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]126.433333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]126.433333333333[/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=29551&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=29551&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 Mean128.91.6677313539213977.290625793485
Geometric Mean128.288098882989
Harmonic Mean127.709473048489
Quadratic Mean129.545704954395
Winsorized Mean ( 1 / 20 )128.91.6677313539213977.290625793485
Winsorized Mean ( 2 / 20 )128.8245901639341.6412521138749378.4916522421315
Winsorized Mean ( 3 / 20 )128.9721311475411.6114279910083380.0359258168516
Winsorized Mean ( 4 / 20 )128.7688524590161.5523603410051882.9503621405558
Winsorized Mean ( 5 / 20 )128.6704918032791.4884791524323386.44426869736
Winsorized Mean ( 6 / 20 )128.9557377049181.4387219673723689.6321461890505
Winsorized Mean ( 7 / 20 )128.9442622950821.3413628266554696.1292945746751
Winsorized Mean ( 8 / 20 )129.0360655737701.3089040023470198.5832920843655
Winsorized Mean ( 9 / 20 )128.0918032786891.06587734221374120.174994068879
Winsorized Mean ( 10 / 20 )126.9606557377050.810151705042454156.712199638032
Winsorized Mean ( 11 / 20 )126.6901639344260.732055661377856173.060834876918
Winsorized Mean ( 12 / 20 )126.1196721311480.615242720205403204.991734138750
Winsorized Mean ( 13 / 20 )126.3540983606560.578676527376064218.350135841163
Winsorized Mean ( 14 / 20 )126.3540983606560.578676527376064218.350135841163
Winsorized Mean ( 15 / 20 )126.3540983606560.578676527376064218.350135841163
Winsorized Mean ( 16 / 20 )126.3540983606560.578676527376064218.350135841163
Winsorized Mean ( 17 / 20 )126.3540983606560.537046027733495235.276106396150
Winsorized Mean ( 18 / 20 )126.3245901639340.523964791175734241.093661809742
Winsorized Mean ( 19 / 20 )126.5737704918030.48912714517743258.774782262164
Winsorized Mean ( 20 / 20 )126.4426229508200.460271118822181274.71335432556
Trimmed Mean ( 1 / 20 )128.71.6014677662784880.363777972925
Trimmed Mean ( 2 / 20 )128.4859649122811.5193085557077284.5687101738392
Trimmed Mean ( 3 / 20 )128.2981818181821.4351538612456989.3968133192498
Trimmed Mean ( 4 / 20 )128.0396226415091.3436307300094995.2937587551341
Trimmed Mean ( 5 / 20 )127.8215686274511.25305685433659102.007796521829
Trimmed Mean ( 6 / 20 )127.6102040816331.16128830091403109.886755925461
Trimmed Mean ( 7 / 20 )127.3191489361701.05700009363536120.453299581345
Trimmed Mean ( 8 / 20 )127.0044444444440.951431433834535133.487753218938
Trimmed Mean ( 9 / 20 )126.6441860465120.813618187542885155.655549477053
Trimmed Mean ( 10 / 20 )126.4048780487800.719840355095016175.601266522624
Trimmed Mean ( 11 / 20 )126.3179487179490.683513900584667184.806700507332
Trimmed Mean ( 12 / 20 )126.2621621621620.657668456038708191.984518951493
Trimmed Mean ( 13 / 20 )126.2828571428570.653735044037813193.17131350779
Trimmed Mean ( 14 / 20 )126.2727272727270.655242158672179192.711542750262
Trimmed Mean ( 15 / 20 )126.2612903225810.65434326296874192.958799254288
Trimmed Mean ( 16 / 20 )126.2482758620690.649926496216393194.25008304329
Trimmed Mean ( 17 / 20 )126.2333333333330.640267928248026197.157045924114
Trimmed Mean ( 18 / 20 )126.2160.635811292759102198.511730504638
Trimmed Mean ( 19 / 20 )126.20.628946041031856200.653143142383
Trimmed Mean ( 20 / 20 )126.1428571428570.625055099612043201.810779915484
Median125
Midrange134.8
Midmean - Weighted Average at Xnp126.433333333333
Midmean - Weighted Average at X(n+1)p126.433333333333
Midmean - Empirical Distribution Function126.433333333333
Midmean - Empirical Distribution Function - Averaging126.433333333333
Midmean - Empirical Distribution Function - Interpolation126.433333333333
Midmean - Closest Observation126.433333333333
Midmean - True Basic - Statistics Graphics Toolkit126.433333333333
Midmean - MS Excel (old versions)126.433333333333
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')