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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, 18 Dec 2010 09:18:32 +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/Dec/18/t1292663851xnkqx7t8mhk1dad.htm/, Retrieved Fri, 29 Mar 2024 01:54:33 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=111800, Retrieved Fri, 29 Mar 2024 01:54:33 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact167
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Central Tendency] [Arabica Price in ...] [2008-01-06 21:28:17] [74be16979710d4c4e7c6647856088456]
- RM D  [Central Tendency] [US car sales] [2010-11-06 13:18:47] [97ad38b1c3b35a5feca8b85f7bc7b3ff]
-    D    [Central Tendency] [Winsorized en tri...] [2010-11-12 16:09:32] [39c51da0be01189e8a44eb69e891b7a1]
-    D        [Central Tendency] [univariate analys...] [2010-12-18 09:18:32] [ecfb965f5669057f3ac5b58964283289] [Current]
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Dataseries X:
62.027
56.493
65.566
62.653
53.470
59.600
42.542
42.018
44.038
44.988
43.309
26.843
69.770
64.886
79.354
63.025
54.003
55.926
45.629
40.361
43.039
44.570
43.269
25.563
68.707
60.223
74.283
61.232
61.531
65.305
51.699
44.599
35.221
55.066
45.335
28.702
69.517
69.240
71.525
77.740
62.107
65.450
51.493
43.067
49.172
54.483
38.158
27.898
58.648
56.000
62.381
59.849
48.345
55.376
45.400
38.389
44.098
48.290
41.267
31.238




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=111800&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=111800&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=111800&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 Mean52.56626666666671.6773120462482931.3395869207781
Geometric Mean50.855270338659
Harmonic Mean48.9967836801548
Quadratic Mean54.1220986067614
Winsorized Mean ( 1 / 20 )52.56071.6645177403918231.5771341599684
Winsorized Mean ( 2 / 20 )52.48063333333331.6275373414214732.245425034302
Winsorized Mean ( 3 / 20 )52.38293333333331.5875434457094632.9962203396102
Winsorized Mean ( 4 / 20 )52.4351.5229441710130434.4300211380178
Winsorized Mean ( 5 / 20 )52.74583333333331.4454527436040536.4908735804247
Winsorized Mean ( 6 / 20 )53.01183333333331.3829898125304838.3313259815969
Winsorized Mean ( 7 / 20 )52.97661.3658439474601638.786715055195
Winsorized Mean ( 8 / 20 )52.82073333333331.2421209098662442.5246309870281
Winsorized Mean ( 9 / 20 )52.93923333333331.2164828969719443.5182717859079
Winsorized Mean ( 10 / 20 )53.04023333333331.1922822075138344.4863078548609
Winsorized Mean ( 11 / 20 )53.05948333333331.1640869996055545.580341805477
Winsorized Mean ( 12 / 20 )52.78668333333331.0870885193328848.557851908626
Winsorized Mean ( 13 / 20 )52.712151.0734060693566249.1073709240292
Winsorized Mean ( 14 / 20 )52.69581666666671.0563393018423449.8853129621903
Winsorized Mean ( 15 / 20 )52.63731666666671.0442388422194550.4073536996481
Winsorized Mean ( 16 / 20 )52.81038333333331.0119475573412152.1868776205034
Winsorized Mean ( 17 / 20 )52.686850.98793529741503453.3302637711771
Winsorized Mean ( 18 / 20 )52.738750.953645210124755.3022753536441
Winsorized Mean ( 19 / 20 )52.42841666666670.90484347658251757.9419734169741
Winsorized Mean ( 20 / 20 )52.43341666666670.8677745138827560.4228585050969
Trimmed Mean ( 1 / 20 )52.56998275862071.6046467339100332.761094169633
Trimmed Mean ( 2 / 20 )52.57992857142861.5307642987145134.3488077266916
Trimmed Mean ( 3 / 20 )52.63509259259261.4643196306206235.9450843189778
Trimmed Mean ( 4 / 20 )52.73207692307691.4011793803766137.6340657460315
Trimmed Mean ( 5 / 20 )52.82121.3483168621716239.1756578011828
Trimmed Mean ( 6 / 20 )52.84004166666671.3089747771296640.3675017959743
Trimmed Mean ( 7 / 20 )52.80269565217391.2779964368602941.3167784582378
Trimmed Mean ( 8 / 20 )52.76881818181821.2423395312309442.4753594772384
Trimmed Mean ( 9 / 20 )52.75954761904761.2293359553269742.9171109739607
Trimmed Mean ( 10 / 20 )52.72961.2166682858085543.3393395842139
Trimmed Mean ( 11 / 20 )52.6805526315791.2034413094724543.7749246406312
Trimmed Mean ( 12 / 20 )52.62313888888891.1900337271149444.2198718320916
Trimmed Mean ( 13 / 20 )52.59908823529411.1882944542926944.2643555604262
Trimmed Mean ( 14 / 20 )52.582781251.1847326351557944.3836690993876
Trimmed Mean ( 15 / 20 )52.56663333333331.1791304271917944.580847140486
Trimmed Mean ( 16 / 20 )52.55653571428571.1688630260908644.963810592979
Trimmed Mean ( 17 / 20 )52.51992307692311.1573098965646145.3810368621443
Trimmed Mean ( 18 / 20 )52.4953751.1408467406065346.0143971416275
Trimmed Mean ( 19 / 20 )52.45851.1197510251056346.848360772924
Trimmed Mean ( 20 / 20 )52.463251.0969041575821747.8284721936336
Median53.7365
Midrange52.4585
Midmean - Weighted Average at Xnp52.2667096774193
Midmean - Weighted Average at X(n+1)p52.5666333333333
Midmean - Empirical Distribution Function52.2667096774193
Midmean - Empirical Distribution Function - Averaging52.5666333333333
Midmean - Empirical Distribution Function - Interpolation52.5666333333333
Midmean - Closest Observation52.2667096774193
Midmean - True Basic - Statistics Graphics Toolkit52.5666333333333
Midmean - MS Excel (old versions)52.58278125
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 52.5662666666667 & 1.67731204624829 & 31.3395869207781 \tabularnewline
Geometric Mean & 50.855270338659 &  &  \tabularnewline
Harmonic Mean & 48.9967836801548 &  &  \tabularnewline
Quadratic Mean & 54.1220986067614 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 52.5607 & 1.66451774039182 & 31.5771341599684 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 52.4806333333333 & 1.62753734142147 & 32.245425034302 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 52.3829333333333 & 1.58754344570946 & 32.9962203396102 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 52.435 & 1.52294417101304 & 34.4300211380178 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 52.7458333333333 & 1.44545274360405 & 36.4908735804247 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 53.0118333333333 & 1.38298981253048 & 38.3313259815969 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 52.9766 & 1.36584394746016 & 38.786715055195 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 52.8207333333333 & 1.24212090986624 & 42.5246309870281 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 52.9392333333333 & 1.21648289697194 & 43.5182717859079 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 53.0402333333333 & 1.19228220751383 & 44.4863078548609 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 53.0594833333333 & 1.16408699960555 & 45.580341805477 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 52.7866833333333 & 1.08708851933288 & 48.557851908626 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 52.71215 & 1.07340606935662 & 49.1073709240292 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 52.6958166666667 & 1.05633930184234 & 49.8853129621903 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 52.6373166666667 & 1.04423884221945 & 50.4073536996481 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 52.8103833333333 & 1.01194755734121 & 52.1868776205034 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 52.68685 & 0.987935297415034 & 53.3302637711771 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 52.73875 & 0.9536452101247 & 55.3022753536441 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 52.4284166666667 & 0.904843476582517 & 57.9419734169741 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 52.4334166666667 & 0.86777451388275 & 60.4228585050969 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 52.5699827586207 & 1.60464673391003 & 32.761094169633 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 52.5799285714286 & 1.53076429871451 & 34.3488077266916 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 52.6350925925926 & 1.46431963062062 & 35.9450843189778 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 52.7320769230769 & 1.40117938037661 & 37.6340657460315 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 52.8212 & 1.34831686217162 & 39.1756578011828 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 52.8400416666667 & 1.30897477712966 & 40.3675017959743 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 52.8026956521739 & 1.27799643686029 & 41.3167784582378 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 52.7688181818182 & 1.24233953123094 & 42.4753594772384 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 52.7595476190476 & 1.22933595532697 & 42.9171109739607 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 52.7296 & 1.21666828580855 & 43.3393395842139 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 52.680552631579 & 1.20344130947245 & 43.7749246406312 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 52.6231388888889 & 1.19003372711494 & 44.2198718320916 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 52.5990882352941 & 1.18829445429269 & 44.2643555604262 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 52.58278125 & 1.18473263515579 & 44.3836690993876 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 52.5666333333333 & 1.17913042719179 & 44.580847140486 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 52.5565357142857 & 1.16886302609086 & 44.963810592979 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 52.5199230769231 & 1.15730989656461 & 45.3810368621443 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 52.495375 & 1.14084674060653 & 46.0143971416275 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 52.4585 & 1.11975102510563 & 46.848360772924 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 52.46325 & 1.09690415758217 & 47.8284721936336 \tabularnewline
Median & 53.7365 &  &  \tabularnewline
Midrange & 52.4585 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 52.2667096774193 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 52.5666333333333 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 52.2667096774193 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 52.5666333333333 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 52.5666333333333 &  &  \tabularnewline
Midmean - Closest Observation & 52.2667096774193 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 52.5666333333333 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 52.58278125 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=111800&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]52.5662666666667[/C][C]1.67731204624829[/C][C]31.3395869207781[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]50.855270338659[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]48.9967836801548[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]54.1220986067614[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]52.5607[/C][C]1.66451774039182[/C][C]31.5771341599684[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]52.4806333333333[/C][C]1.62753734142147[/C][C]32.245425034302[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]52.3829333333333[/C][C]1.58754344570946[/C][C]32.9962203396102[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]52.435[/C][C]1.52294417101304[/C][C]34.4300211380178[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]52.7458333333333[/C][C]1.44545274360405[/C][C]36.4908735804247[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]53.0118333333333[/C][C]1.38298981253048[/C][C]38.3313259815969[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]52.9766[/C][C]1.36584394746016[/C][C]38.786715055195[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]52.8207333333333[/C][C]1.24212090986624[/C][C]42.5246309870281[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]52.9392333333333[/C][C]1.21648289697194[/C][C]43.5182717859079[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]53.0402333333333[/C][C]1.19228220751383[/C][C]44.4863078548609[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]53.0594833333333[/C][C]1.16408699960555[/C][C]45.580341805477[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]52.7866833333333[/C][C]1.08708851933288[/C][C]48.557851908626[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]52.71215[/C][C]1.07340606935662[/C][C]49.1073709240292[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]52.6958166666667[/C][C]1.05633930184234[/C][C]49.8853129621903[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]52.6373166666667[/C][C]1.04423884221945[/C][C]50.4073536996481[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]52.8103833333333[/C][C]1.01194755734121[/C][C]52.1868776205034[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]52.68685[/C][C]0.987935297415034[/C][C]53.3302637711771[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]52.73875[/C][C]0.9536452101247[/C][C]55.3022753536441[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]52.4284166666667[/C][C]0.904843476582517[/C][C]57.9419734169741[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]52.4334166666667[/C][C]0.86777451388275[/C][C]60.4228585050969[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]52.5699827586207[/C][C]1.60464673391003[/C][C]32.761094169633[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]52.5799285714286[/C][C]1.53076429871451[/C][C]34.3488077266916[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]52.6350925925926[/C][C]1.46431963062062[/C][C]35.9450843189778[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]52.7320769230769[/C][C]1.40117938037661[/C][C]37.6340657460315[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]52.8212[/C][C]1.34831686217162[/C][C]39.1756578011828[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]52.8400416666667[/C][C]1.30897477712966[/C][C]40.3675017959743[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]52.8026956521739[/C][C]1.27799643686029[/C][C]41.3167784582378[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]52.7688181818182[/C][C]1.24233953123094[/C][C]42.4753594772384[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]52.7595476190476[/C][C]1.22933595532697[/C][C]42.9171109739607[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]52.7296[/C][C]1.21666828580855[/C][C]43.3393395842139[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]52.680552631579[/C][C]1.20344130947245[/C][C]43.7749246406312[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]52.6231388888889[/C][C]1.19003372711494[/C][C]44.2198718320916[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]52.5990882352941[/C][C]1.18829445429269[/C][C]44.2643555604262[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]52.58278125[/C][C]1.18473263515579[/C][C]44.3836690993876[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]52.5666333333333[/C][C]1.17913042719179[/C][C]44.580847140486[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]52.5565357142857[/C][C]1.16886302609086[/C][C]44.963810592979[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]52.5199230769231[/C][C]1.15730989656461[/C][C]45.3810368621443[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]52.495375[/C][C]1.14084674060653[/C][C]46.0143971416275[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]52.4585[/C][C]1.11975102510563[/C][C]46.848360772924[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]52.46325[/C][C]1.09690415758217[/C][C]47.8284721936336[/C][/ROW]
[ROW][C]Median[/C][C]53.7365[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]52.4585[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]52.2667096774193[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]52.5666333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]52.2667096774193[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]52.5666333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]52.5666333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]52.2667096774193[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]52.5666333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]52.58278125[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]60[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=111800&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=111800&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 Mean52.56626666666671.6773120462482931.3395869207781
Geometric Mean50.855270338659
Harmonic Mean48.9967836801548
Quadratic Mean54.1220986067614
Winsorized Mean ( 1 / 20 )52.56071.6645177403918231.5771341599684
Winsorized Mean ( 2 / 20 )52.48063333333331.6275373414214732.245425034302
Winsorized Mean ( 3 / 20 )52.38293333333331.5875434457094632.9962203396102
Winsorized Mean ( 4 / 20 )52.4351.5229441710130434.4300211380178
Winsorized Mean ( 5 / 20 )52.74583333333331.4454527436040536.4908735804247
Winsorized Mean ( 6 / 20 )53.01183333333331.3829898125304838.3313259815969
Winsorized Mean ( 7 / 20 )52.97661.3658439474601638.786715055195
Winsorized Mean ( 8 / 20 )52.82073333333331.2421209098662442.5246309870281
Winsorized Mean ( 9 / 20 )52.93923333333331.2164828969719443.5182717859079
Winsorized Mean ( 10 / 20 )53.04023333333331.1922822075138344.4863078548609
Winsorized Mean ( 11 / 20 )53.05948333333331.1640869996055545.580341805477
Winsorized Mean ( 12 / 20 )52.78668333333331.0870885193328848.557851908626
Winsorized Mean ( 13 / 20 )52.712151.0734060693566249.1073709240292
Winsorized Mean ( 14 / 20 )52.69581666666671.0563393018423449.8853129621903
Winsorized Mean ( 15 / 20 )52.63731666666671.0442388422194550.4073536996481
Winsorized Mean ( 16 / 20 )52.81038333333331.0119475573412152.1868776205034
Winsorized Mean ( 17 / 20 )52.686850.98793529741503453.3302637711771
Winsorized Mean ( 18 / 20 )52.738750.953645210124755.3022753536441
Winsorized Mean ( 19 / 20 )52.42841666666670.90484347658251757.9419734169741
Winsorized Mean ( 20 / 20 )52.43341666666670.8677745138827560.4228585050969
Trimmed Mean ( 1 / 20 )52.56998275862071.6046467339100332.761094169633
Trimmed Mean ( 2 / 20 )52.57992857142861.5307642987145134.3488077266916
Trimmed Mean ( 3 / 20 )52.63509259259261.4643196306206235.9450843189778
Trimmed Mean ( 4 / 20 )52.73207692307691.4011793803766137.6340657460315
Trimmed Mean ( 5 / 20 )52.82121.3483168621716239.1756578011828
Trimmed Mean ( 6 / 20 )52.84004166666671.3089747771296640.3675017959743
Trimmed Mean ( 7 / 20 )52.80269565217391.2779964368602941.3167784582378
Trimmed Mean ( 8 / 20 )52.76881818181821.2423395312309442.4753594772384
Trimmed Mean ( 9 / 20 )52.75954761904761.2293359553269742.9171109739607
Trimmed Mean ( 10 / 20 )52.72961.2166682858085543.3393395842139
Trimmed Mean ( 11 / 20 )52.6805526315791.2034413094724543.7749246406312
Trimmed Mean ( 12 / 20 )52.62313888888891.1900337271149444.2198718320916
Trimmed Mean ( 13 / 20 )52.59908823529411.1882944542926944.2643555604262
Trimmed Mean ( 14 / 20 )52.582781251.1847326351557944.3836690993876
Trimmed Mean ( 15 / 20 )52.56663333333331.1791304271917944.580847140486
Trimmed Mean ( 16 / 20 )52.55653571428571.1688630260908644.963810592979
Trimmed Mean ( 17 / 20 )52.51992307692311.1573098965646145.3810368621443
Trimmed Mean ( 18 / 20 )52.4953751.1408467406065346.0143971416275
Trimmed Mean ( 19 / 20 )52.45851.1197510251056346.848360772924
Trimmed Mean ( 20 / 20 )52.463251.0969041575821747.8284721936336
Median53.7365
Midrange52.4585
Midmean - Weighted Average at Xnp52.2667096774193
Midmean - Weighted Average at X(n+1)p52.5666333333333
Midmean - Empirical Distribution Function52.2667096774193
Midmean - Empirical Distribution Function - Averaging52.5666333333333
Midmean - Empirical Distribution Function - Interpolation52.5666333333333
Midmean - Closest Observation52.2667096774193
Midmean - True Basic - Statistics Graphics Toolkit52.5666333333333
Midmean - MS Excel (old versions)52.58278125
Number of observations60



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')