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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 computationFri, 26 Nov 2010 09:56:08 +0000
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2010/Nov/26/t1290765290f5lgly3drtoazsg.htm/, Retrieved Sat, 04 May 2024 03:13:19 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=101719, Retrieved Sat, 04 May 2024 03:13:19 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact101
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
F     [Univariate Data Series] [HPC Retail Sales] [2008-03-02 15:42:48] [74be16979710d4c4e7c6647856088456]
- RMPD    [Central Tendency] [] [2010-11-26 09:56:08] [df17410ebb98883e83037e1662207ccb] [Current]
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Dataseries X:
101,76
102,37
102,38
102,86
102,87
102,92
102,95
103,02
104,08
104,16
104,24
104,33
104,73
104,86
105,03
105,62
105,63
105,63
105,94
106,61
107,69
107,78
107,93
108,48
108,14
108,48
108,48
108,89
108,93
109,21
109,47
109,80
111,73
111,85
112,12
112,15
112,17
112,67
112,80
113,44
113,53
114,53
114,51
115,05
116,67
117,07
116,92
117,00
117,02
117,35
117,36
117,82
117,88
118,24
118,50
118,80
119,76
120,09




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

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 2 seconds \tabularnewline
R Server & 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=101719&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Sir Ronald Aylmer Fisher' @ 193.190.124.24[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=101719&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=101719&T=0

As an alternative you can also use a QR Code:  

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

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







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean110.2120689655170.732018803069449150.559068296311
Geometric Mean110.074139573097
Harmonic Mean109.936985882516
Quadratic Mean110.350549082271
Winsorized Mean ( 1 / 19 )110.2168965517240.728632677111493151.265376936779
Winsorized Mean ( 2 / 19 )110.1841379310340.721293874832377152.759009573789
Winsorized Mean ( 3 / 19 )110.1934482758620.713487576756154154.443401491099
Winsorized Mean ( 4 / 19 )110.1762068965520.709744755615557155.233562523469
Winsorized Mean ( 5 / 19 )110.1494827586210.70287906856159156.711855119027
Winsorized Mean ( 6 / 19 )110.1463793103450.701124914901888157.099508189291
Winsorized Mean ( 7 / 19 )110.0993103448280.689140370473178159.763257330624
Winsorized Mean ( 8 / 19 )110.2441379310350.663774748530415166.086670478371
Winsorized Mean ( 9 / 19 )110.2131034482760.653676567936037168.604947545038
Winsorized Mean ( 10 / 19 )110.2182758620690.649858383657628169.603529990215
Winsorized Mean ( 11 / 19 )110.2315517241380.646417359299048170.526905161812
Winsorized Mean ( 12 / 19 )110.2977586206900.630328995569763174.984427808196
Winsorized Mean ( 13 / 19 )110.2708620689660.61554987661758179.142042355526
Winsorized Mean ( 14 / 19 )109.9208620689660.540738850840583203.279017030296
Winsorized Mean ( 15 / 19 )109.9389655172410.494783782585575222.195976074109
Winsorized Mean ( 16 / 19 )109.9362068965520.493463739953498222.784772204157
Winsorized Mean ( 17 / 19 )109.6489655172410.448218540706677244.632819839101
Winsorized Mean ( 18 / 19 )109.7172413793100.428969825862509255.769135180329
Winsorized Mean ( 19 / 19 )109.7270689655170.363967600638602301.474825706999
Trimmed Mean ( 1 / 19 )110.1866071428570.721307852427172152.759472633056
Trimmed Mean ( 2 / 19 )110.1540740740740.711704949825253154.774916348580
Trimmed Mean ( 3 / 19 )110.1373076923080.704025438927072156.439386423530
Trimmed Mean ( 4 / 19 )110.11560.697386149584757157.897601014253
Trimmed Mean ( 5 / 19 )110.0972916666670.689662314556254159.639419673824
Trimmed Mean ( 6 / 19 )110.0841304347830.681338025458684161.570507327362
Trimmed Mean ( 7 / 19 )110.0704545454550.670343854409317164.199990529405
Trimmed Mean ( 8 / 19 )110.0647619047620.658784580916154167.072462065973
Trimmed Mean ( 9 / 19 )110.032250.649659031624894169.369230078728
Trimmed Mean ( 10 / 19 )110.0015789473680.639144890858145172.107421213483
Trimmed Mean ( 11 / 19 )109.9666666666670.624793172126991176.004911020884
Trimmed Mean ( 12 / 19 )109.9255882352940.604914983666806181.720723082374
Trimmed Mean ( 13 / 19 )109.8693750.580728466596328189.192335695112
Trimmed Mean ( 14 / 19 )109.8096666666670.549919844385563199.683040697248
Trimmed Mean ( 15 / 19 )109.7932142857140.530528850047933206.950506604484
Trimmed Mean ( 16 / 19 )109.7715384615380.515780720344693212.825982305385
Trimmed Mean ( 17 / 19 )109.7466666666670.491410151704325223.330076283609
Trimmed Mean ( 18 / 19 )109.7618181818180.4699487106415233.56127104166
Trimmed Mean ( 19 / 19 )109.7690.440983291245705248.918728167502
Median109.07
Midrange110.925
Midmean - Weighted Average at Xnp109.628965517241
Midmean - Weighted Average at X(n+1)p109.809666666667
Midmean - Empirical Distribution Function109.809666666667
Midmean - Empirical Distribution Function - Averaging109.809666666667
Midmean - Empirical Distribution Function - Interpolation109.793214285714
Midmean - Closest Observation109.809666666667
Midmean - True Basic - Statistics Graphics Toolkit109.809666666667
Midmean - MS Excel (old versions)109.809666666667
Number of observations58

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 110.212068965517 & 0.732018803069449 & 150.559068296311 \tabularnewline
Geometric Mean & 110.074139573097 &  &  \tabularnewline
Harmonic Mean & 109.936985882516 &  &  \tabularnewline
Quadratic Mean & 110.350549082271 &  &  \tabularnewline
Winsorized Mean ( 1 / 19 ) & 110.216896551724 & 0.728632677111493 & 151.265376936779 \tabularnewline
Winsorized Mean ( 2 / 19 ) & 110.184137931034 & 0.721293874832377 & 152.759009573789 \tabularnewline
Winsorized Mean ( 3 / 19 ) & 110.193448275862 & 0.713487576756154 & 154.443401491099 \tabularnewline
Winsorized Mean ( 4 / 19 ) & 110.176206896552 & 0.709744755615557 & 155.233562523469 \tabularnewline
Winsorized Mean ( 5 / 19 ) & 110.149482758621 & 0.70287906856159 & 156.711855119027 \tabularnewline
Winsorized Mean ( 6 / 19 ) & 110.146379310345 & 0.701124914901888 & 157.099508189291 \tabularnewline
Winsorized Mean ( 7 / 19 ) & 110.099310344828 & 0.689140370473178 & 159.763257330624 \tabularnewline
Winsorized Mean ( 8 / 19 ) & 110.244137931035 & 0.663774748530415 & 166.086670478371 \tabularnewline
Winsorized Mean ( 9 / 19 ) & 110.213103448276 & 0.653676567936037 & 168.604947545038 \tabularnewline
Winsorized Mean ( 10 / 19 ) & 110.218275862069 & 0.649858383657628 & 169.603529990215 \tabularnewline
Winsorized Mean ( 11 / 19 ) & 110.231551724138 & 0.646417359299048 & 170.526905161812 \tabularnewline
Winsorized Mean ( 12 / 19 ) & 110.297758620690 & 0.630328995569763 & 174.984427808196 \tabularnewline
Winsorized Mean ( 13 / 19 ) & 110.270862068966 & 0.61554987661758 & 179.142042355526 \tabularnewline
Winsorized Mean ( 14 / 19 ) & 109.920862068966 & 0.540738850840583 & 203.279017030296 \tabularnewline
Winsorized Mean ( 15 / 19 ) & 109.938965517241 & 0.494783782585575 & 222.195976074109 \tabularnewline
Winsorized Mean ( 16 / 19 ) & 109.936206896552 & 0.493463739953498 & 222.784772204157 \tabularnewline
Winsorized Mean ( 17 / 19 ) & 109.648965517241 & 0.448218540706677 & 244.632819839101 \tabularnewline
Winsorized Mean ( 18 / 19 ) & 109.717241379310 & 0.428969825862509 & 255.769135180329 \tabularnewline
Winsorized Mean ( 19 / 19 ) & 109.727068965517 & 0.363967600638602 & 301.474825706999 \tabularnewline
Trimmed Mean ( 1 / 19 ) & 110.186607142857 & 0.721307852427172 & 152.759472633056 \tabularnewline
Trimmed Mean ( 2 / 19 ) & 110.154074074074 & 0.711704949825253 & 154.774916348580 \tabularnewline
Trimmed Mean ( 3 / 19 ) & 110.137307692308 & 0.704025438927072 & 156.439386423530 \tabularnewline
Trimmed Mean ( 4 / 19 ) & 110.1156 & 0.697386149584757 & 157.897601014253 \tabularnewline
Trimmed Mean ( 5 / 19 ) & 110.097291666667 & 0.689662314556254 & 159.639419673824 \tabularnewline
Trimmed Mean ( 6 / 19 ) & 110.084130434783 & 0.681338025458684 & 161.570507327362 \tabularnewline
Trimmed Mean ( 7 / 19 ) & 110.070454545455 & 0.670343854409317 & 164.199990529405 \tabularnewline
Trimmed Mean ( 8 / 19 ) & 110.064761904762 & 0.658784580916154 & 167.072462065973 \tabularnewline
Trimmed Mean ( 9 / 19 ) & 110.03225 & 0.649659031624894 & 169.369230078728 \tabularnewline
Trimmed Mean ( 10 / 19 ) & 110.001578947368 & 0.639144890858145 & 172.107421213483 \tabularnewline
Trimmed Mean ( 11 / 19 ) & 109.966666666667 & 0.624793172126991 & 176.004911020884 \tabularnewline
Trimmed Mean ( 12 / 19 ) & 109.925588235294 & 0.604914983666806 & 181.720723082374 \tabularnewline
Trimmed Mean ( 13 / 19 ) & 109.869375 & 0.580728466596328 & 189.192335695112 \tabularnewline
Trimmed Mean ( 14 / 19 ) & 109.809666666667 & 0.549919844385563 & 199.683040697248 \tabularnewline
Trimmed Mean ( 15 / 19 ) & 109.793214285714 & 0.530528850047933 & 206.950506604484 \tabularnewline
Trimmed Mean ( 16 / 19 ) & 109.771538461538 & 0.515780720344693 & 212.825982305385 \tabularnewline
Trimmed Mean ( 17 / 19 ) & 109.746666666667 & 0.491410151704325 & 223.330076283609 \tabularnewline
Trimmed Mean ( 18 / 19 ) & 109.761818181818 & 0.4699487106415 & 233.56127104166 \tabularnewline
Trimmed Mean ( 19 / 19 ) & 109.769 & 0.440983291245705 & 248.918728167502 \tabularnewline
Median & 109.07 &  &  \tabularnewline
Midrange & 110.925 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 109.628965517241 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 109.809666666667 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 109.809666666667 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 109.809666666667 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 109.793214285714 &  &  \tabularnewline
Midmean - Closest Observation & 109.809666666667 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 109.809666666667 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 109.809666666667 &  &  \tabularnewline
Number of observations & 58 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=101719&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]110.212068965517[/C][C]0.732018803069449[/C][C]150.559068296311[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]110.074139573097[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]109.936985882516[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]110.350549082271[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 19 )[/C][C]110.216896551724[/C][C]0.728632677111493[/C][C]151.265376936779[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 19 )[/C][C]110.184137931034[/C][C]0.721293874832377[/C][C]152.759009573789[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 19 )[/C][C]110.193448275862[/C][C]0.713487576756154[/C][C]154.443401491099[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 19 )[/C][C]110.176206896552[/C][C]0.709744755615557[/C][C]155.233562523469[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 19 )[/C][C]110.149482758621[/C][C]0.70287906856159[/C][C]156.711855119027[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 19 )[/C][C]110.146379310345[/C][C]0.701124914901888[/C][C]157.099508189291[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 19 )[/C][C]110.099310344828[/C][C]0.689140370473178[/C][C]159.763257330624[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 19 )[/C][C]110.244137931035[/C][C]0.663774748530415[/C][C]166.086670478371[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 19 )[/C][C]110.213103448276[/C][C]0.653676567936037[/C][C]168.604947545038[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 19 )[/C][C]110.218275862069[/C][C]0.649858383657628[/C][C]169.603529990215[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 19 )[/C][C]110.231551724138[/C][C]0.646417359299048[/C][C]170.526905161812[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 19 )[/C][C]110.297758620690[/C][C]0.630328995569763[/C][C]174.984427808196[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 19 )[/C][C]110.270862068966[/C][C]0.61554987661758[/C][C]179.142042355526[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 19 )[/C][C]109.920862068966[/C][C]0.540738850840583[/C][C]203.279017030296[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 19 )[/C][C]109.938965517241[/C][C]0.494783782585575[/C][C]222.195976074109[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 19 )[/C][C]109.936206896552[/C][C]0.493463739953498[/C][C]222.784772204157[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 19 )[/C][C]109.648965517241[/C][C]0.448218540706677[/C][C]244.632819839101[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 19 )[/C][C]109.717241379310[/C][C]0.428969825862509[/C][C]255.769135180329[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 19 )[/C][C]109.727068965517[/C][C]0.363967600638602[/C][C]301.474825706999[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 19 )[/C][C]110.186607142857[/C][C]0.721307852427172[/C][C]152.759472633056[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 19 )[/C][C]110.154074074074[/C][C]0.711704949825253[/C][C]154.774916348580[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 19 )[/C][C]110.137307692308[/C][C]0.704025438927072[/C][C]156.439386423530[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 19 )[/C][C]110.1156[/C][C]0.697386149584757[/C][C]157.897601014253[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 19 )[/C][C]110.097291666667[/C][C]0.689662314556254[/C][C]159.639419673824[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 19 )[/C][C]110.084130434783[/C][C]0.681338025458684[/C][C]161.570507327362[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 19 )[/C][C]110.070454545455[/C][C]0.670343854409317[/C][C]164.199990529405[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 19 )[/C][C]110.064761904762[/C][C]0.658784580916154[/C][C]167.072462065973[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 19 )[/C][C]110.03225[/C][C]0.649659031624894[/C][C]169.369230078728[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 19 )[/C][C]110.001578947368[/C][C]0.639144890858145[/C][C]172.107421213483[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 19 )[/C][C]109.966666666667[/C][C]0.624793172126991[/C][C]176.004911020884[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 19 )[/C][C]109.925588235294[/C][C]0.604914983666806[/C][C]181.720723082374[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 19 )[/C][C]109.869375[/C][C]0.580728466596328[/C][C]189.192335695112[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 19 )[/C][C]109.809666666667[/C][C]0.549919844385563[/C][C]199.683040697248[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 19 )[/C][C]109.793214285714[/C][C]0.530528850047933[/C][C]206.950506604484[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 19 )[/C][C]109.771538461538[/C][C]0.515780720344693[/C][C]212.825982305385[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 19 )[/C][C]109.746666666667[/C][C]0.491410151704325[/C][C]223.330076283609[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 19 )[/C][C]109.761818181818[/C][C]0.4699487106415[/C][C]233.56127104166[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 19 )[/C][C]109.769[/C][C]0.440983291245705[/C][C]248.918728167502[/C][/ROW]
[ROW][C]Median[/C][C]109.07[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]110.925[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]109.628965517241[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]109.809666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]109.809666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]109.809666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]109.793214285714[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]109.809666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]109.809666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]109.809666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]58[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=101719&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=101719&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 Mean110.2120689655170.732018803069449150.559068296311
Geometric Mean110.074139573097
Harmonic Mean109.936985882516
Quadratic Mean110.350549082271
Winsorized Mean ( 1 / 19 )110.2168965517240.728632677111493151.265376936779
Winsorized Mean ( 2 / 19 )110.1841379310340.721293874832377152.759009573789
Winsorized Mean ( 3 / 19 )110.1934482758620.713487576756154154.443401491099
Winsorized Mean ( 4 / 19 )110.1762068965520.709744755615557155.233562523469
Winsorized Mean ( 5 / 19 )110.1494827586210.70287906856159156.711855119027
Winsorized Mean ( 6 / 19 )110.1463793103450.701124914901888157.099508189291
Winsorized Mean ( 7 / 19 )110.0993103448280.689140370473178159.763257330624
Winsorized Mean ( 8 / 19 )110.2441379310350.663774748530415166.086670478371
Winsorized Mean ( 9 / 19 )110.2131034482760.653676567936037168.604947545038
Winsorized Mean ( 10 / 19 )110.2182758620690.649858383657628169.603529990215
Winsorized Mean ( 11 / 19 )110.2315517241380.646417359299048170.526905161812
Winsorized Mean ( 12 / 19 )110.2977586206900.630328995569763174.984427808196
Winsorized Mean ( 13 / 19 )110.2708620689660.61554987661758179.142042355526
Winsorized Mean ( 14 / 19 )109.9208620689660.540738850840583203.279017030296
Winsorized Mean ( 15 / 19 )109.9389655172410.494783782585575222.195976074109
Winsorized Mean ( 16 / 19 )109.9362068965520.493463739953498222.784772204157
Winsorized Mean ( 17 / 19 )109.6489655172410.448218540706677244.632819839101
Winsorized Mean ( 18 / 19 )109.7172413793100.428969825862509255.769135180329
Winsorized Mean ( 19 / 19 )109.7270689655170.363967600638602301.474825706999
Trimmed Mean ( 1 / 19 )110.1866071428570.721307852427172152.759472633056
Trimmed Mean ( 2 / 19 )110.1540740740740.711704949825253154.774916348580
Trimmed Mean ( 3 / 19 )110.1373076923080.704025438927072156.439386423530
Trimmed Mean ( 4 / 19 )110.11560.697386149584757157.897601014253
Trimmed Mean ( 5 / 19 )110.0972916666670.689662314556254159.639419673824
Trimmed Mean ( 6 / 19 )110.0841304347830.681338025458684161.570507327362
Trimmed Mean ( 7 / 19 )110.0704545454550.670343854409317164.199990529405
Trimmed Mean ( 8 / 19 )110.0647619047620.658784580916154167.072462065973
Trimmed Mean ( 9 / 19 )110.032250.649659031624894169.369230078728
Trimmed Mean ( 10 / 19 )110.0015789473680.639144890858145172.107421213483
Trimmed Mean ( 11 / 19 )109.9666666666670.624793172126991176.004911020884
Trimmed Mean ( 12 / 19 )109.9255882352940.604914983666806181.720723082374
Trimmed Mean ( 13 / 19 )109.8693750.580728466596328189.192335695112
Trimmed Mean ( 14 / 19 )109.8096666666670.549919844385563199.683040697248
Trimmed Mean ( 15 / 19 )109.7932142857140.530528850047933206.950506604484
Trimmed Mean ( 16 / 19 )109.7715384615380.515780720344693212.825982305385
Trimmed Mean ( 17 / 19 )109.7466666666670.491410151704325223.330076283609
Trimmed Mean ( 18 / 19 )109.7618181818180.4699487106415233.56127104166
Trimmed Mean ( 19 / 19 )109.7690.440983291245705248.918728167502
Median109.07
Midrange110.925
Midmean - Weighted Average at Xnp109.628965517241
Midmean - Weighted Average at X(n+1)p109.809666666667
Midmean - Empirical Distribution Function109.809666666667
Midmean - Empirical Distribution Function - Averaging109.809666666667
Midmean - Empirical Distribution Function - Interpolation109.793214285714
Midmean - Closest Observation109.809666666667
Midmean - True Basic - Statistics Graphics Toolkit109.809666666667
Midmean - MS Excel (old versions)109.809666666667
Number of observations58



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')