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of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationMon, 08 Oct 2012 11:37:45 -0400
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2012/Oct/08/t13497106982h7h43j3iclpzo5.htm/, Retrieved Thu, 02 May 2024 12:08:52 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=173802, Retrieved Thu, 02 May 2024 12:08:52 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact39
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [Maximumprijs tick...] [2012-10-08 15:37:45] [e37fb7c471ef9ca45817f7bbfd578e32] [Current]
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Dataseries X:
6.81
6.8
6.8
6.85
6.85
6.85
6.85
6.85
6.85
6.86
6.86
6.88
6.88
6.88
6.91
6.91
6.91
6.91
6.99
6.99
6.99
7.02
7.02
7.05
7.05
7.05
7.05
7.1
7.1
7.1
7.1
7.12
7.13
7.18
7.24
7.24
7.24
7.27
7.27
7.27
7.27
7.3
7.3
7.57
7.76
7.94
7.94
7.96
7.96
7.98
7.99
8
8
8.04
8.04
8.04
8.04
8.04
8.07
8.07
8.07
8.07
8.11
8.11
8.12
8.11
8.13
8.15
8.16
8.2
8.2
8.2




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' @ fisher.wessa.net

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 2 seconds \tabularnewline
R Server & 'Sir Ronald Aylmer Fisher' @ fisher.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=173802&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' @ fisher.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=173802&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=173802&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' @ fisher.wessa.net







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean7.430833333333330.0616310485894467120.569639871513
Geometric Mean7.41290089766909
Harmonic Mean7.39523204782667
Quadratic Mean7.44895760791028
Winsorized Mean ( 1 / 24 )7.430833333333330.0616310485894467120.569639871513
Winsorized Mean ( 2 / 24 )7.431111111111110.0615912988093935120.651963098037
Winsorized Mean ( 3 / 24 )7.431111111111110.0610746085320066121.672676906587
Winsorized Mean ( 4 / 24 )7.430555555555560.0609817595322809121.848821886193
Winsorized Mean ( 5 / 24 )7.429166666666670.0607535330992162122.283697551123
Winsorized Mean ( 6 / 24 )7.428333333333330.0606188740189385122.541592095765
Winsorized Mean ( 7 / 24 )7.427361111111110.0604634530049218122.840505164442
Winsorized Mean ( 8 / 24 )7.427361111111110.0604634530049218122.840505164442
Winsorized Mean ( 9 / 24 )7.428611111111110.0602963811682404123.201607910492
Winsorized Mean ( 10 / 24 )7.423055555555560.0594282351790628124.907891563483
Winsorized Mean ( 11 / 24 )7.426111111111110.0590252577018896125.812430139943
Winsorized Mean ( 12 / 24 )7.426111111111110.0590252577018896125.812430139943
Winsorized Mean ( 13 / 24 )7.426111111111110.0590252577018896125.812430139943
Winsorized Mean ( 14 / 24 )7.426111111111110.0573878969656144129.402043005003
Winsorized Mean ( 15 / 24 )7.426111111111110.0573878969656144129.402043005003
Winsorized Mean ( 16 / 24 )7.426111111111110.0573878969656144129.402043005003
Winsorized Mean ( 17 / 24 )7.426111111111110.0573878969656144129.402043005003
Winsorized Mean ( 18 / 24 )7.446111111111110.0549500255088702135.506963684833
Winsorized Mean ( 19 / 24 )7.435555555555560.053360061117033139.346833566164
Winsorized Mean ( 20 / 24 )7.435555555555560.053360061117033139.346833566164
Winsorized Mean ( 21 / 24 )7.441388888888890.0519107914050813143.349555795069
Winsorized Mean ( 22 / 24 )7.438333333333330.0514568661762677144.55472876745
Winsorized Mean ( 23 / 24 )7.441527777777780.0494277344018463150.553689499064
Winsorized Mean ( 24 / 24 )7.441527777777780.0494277344018463150.553689499064
Trimmed Mean ( 1 / 24 )7.428857142857140.061767460413451120.271370931083
Trimmed Mean ( 2 / 24 )7.426764705882350.0618650153308147120.047892434339
Trimmed Mean ( 3 / 24 )7.424393939393940.0619391869542521119.86586044272
Trimmed Mean ( 4 / 24 )7.4218750.0621756963153738119.369390932978
Trimmed Mean ( 5 / 24 )7.419354838709680.0624067240372625118.887106368212
Trimmed Mean ( 6 / 24 )7.4170.0626619032929401118.365380083111
Trimmed Mean ( 7 / 24 )7.414655172413790.0629095008281656117.862247749614
Trimmed Mean ( 8 / 24 )7.412321428571430.0631458788649365117.384088428411
Trimmed Mean ( 9 / 24 )7.409814814814810.0633280869176099117.006768646825
Trimmed Mean ( 10 / 24 )7.406923076923080.0634744033763001116.691495830407
Trimmed Mean ( 11 / 24 )7.40460.0637144202432917116.215449685107
Trimmed Mean ( 12 / 24 )7.401666666666670.0639545864289302115.73316442116
Trimmed Mean ( 13 / 24 )7.398478260869560.0641111409607964115.400820356538
Trimmed Mean ( 14 / 24 )7.3950.0641578227158997115.262639643277
Trimmed Mean ( 15 / 24 )7.391190476190480.0643742346624802114.815974355938
Trimmed Mean ( 16 / 24 )7.3870.0644644604931017114.590271034541
Trimmed Mean ( 17 / 24 )7.382368421052630.0643828721497295114.663545979808
Trimmed Mean ( 18 / 24 )7.377222222222220.0640654564960665115.151325311717
Trimmed Mean ( 19 / 24 )7.369117647058820.063891016341679115.33887029829
Trimmed Mean ( 20 / 24 )7.361250.063787939374755115.401909391563
Trimmed Mean ( 21 / 24 )7.352333333333330.0633194479636506116.114931032785
Trimmed Mean ( 22 / 24 )7.341428571428570.0626544953684211117.173213641886
Trimmed Mean ( 23 / 24 )7.329230769230770.0614289410042157119.31234120946
Trimmed Mean ( 24 / 24 )7.314583333333330.0597669967537787122.384990557032
Median7.24
Midrange7.5
Midmean - Weighted Average at Xnp7.395
Midmean - Weighted Average at X(n+1)p7.4435
Midmean - Empirical Distribution Function7.395
Midmean - Empirical Distribution Function - Averaging7.4435
Midmean - Empirical Distribution Function - Interpolation7.4435
Midmean - Closest Observation7.395
Midmean - True Basic - Statistics Graphics Toolkit7.4435
Midmean - MS Excel (old versions)7.395
Number of observations72

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 7.43083333333333 & 0.0616310485894467 & 120.569639871513 \tabularnewline
Geometric Mean & 7.41290089766909 &  &  \tabularnewline
Harmonic Mean & 7.39523204782667 &  &  \tabularnewline
Quadratic Mean & 7.44895760791028 &  &  \tabularnewline
Winsorized Mean ( 1 / 24 ) & 7.43083333333333 & 0.0616310485894467 & 120.569639871513 \tabularnewline
Winsorized Mean ( 2 / 24 ) & 7.43111111111111 & 0.0615912988093935 & 120.651963098037 \tabularnewline
Winsorized Mean ( 3 / 24 ) & 7.43111111111111 & 0.0610746085320066 & 121.672676906587 \tabularnewline
Winsorized Mean ( 4 / 24 ) & 7.43055555555556 & 0.0609817595322809 & 121.848821886193 \tabularnewline
Winsorized Mean ( 5 / 24 ) & 7.42916666666667 & 0.0607535330992162 & 122.283697551123 \tabularnewline
Winsorized Mean ( 6 / 24 ) & 7.42833333333333 & 0.0606188740189385 & 122.541592095765 \tabularnewline
Winsorized Mean ( 7 / 24 ) & 7.42736111111111 & 0.0604634530049218 & 122.840505164442 \tabularnewline
Winsorized Mean ( 8 / 24 ) & 7.42736111111111 & 0.0604634530049218 & 122.840505164442 \tabularnewline
Winsorized Mean ( 9 / 24 ) & 7.42861111111111 & 0.0602963811682404 & 123.201607910492 \tabularnewline
Winsorized Mean ( 10 / 24 ) & 7.42305555555556 & 0.0594282351790628 & 124.907891563483 \tabularnewline
Winsorized Mean ( 11 / 24 ) & 7.42611111111111 & 0.0590252577018896 & 125.812430139943 \tabularnewline
Winsorized Mean ( 12 / 24 ) & 7.42611111111111 & 0.0590252577018896 & 125.812430139943 \tabularnewline
Winsorized Mean ( 13 / 24 ) & 7.42611111111111 & 0.0590252577018896 & 125.812430139943 \tabularnewline
Winsorized Mean ( 14 / 24 ) & 7.42611111111111 & 0.0573878969656144 & 129.402043005003 \tabularnewline
Winsorized Mean ( 15 / 24 ) & 7.42611111111111 & 0.0573878969656144 & 129.402043005003 \tabularnewline
Winsorized Mean ( 16 / 24 ) & 7.42611111111111 & 0.0573878969656144 & 129.402043005003 \tabularnewline
Winsorized Mean ( 17 / 24 ) & 7.42611111111111 & 0.0573878969656144 & 129.402043005003 \tabularnewline
Winsorized Mean ( 18 / 24 ) & 7.44611111111111 & 0.0549500255088702 & 135.506963684833 \tabularnewline
Winsorized Mean ( 19 / 24 ) & 7.43555555555556 & 0.053360061117033 & 139.346833566164 \tabularnewline
Winsorized Mean ( 20 / 24 ) & 7.43555555555556 & 0.053360061117033 & 139.346833566164 \tabularnewline
Winsorized Mean ( 21 / 24 ) & 7.44138888888889 & 0.0519107914050813 & 143.349555795069 \tabularnewline
Winsorized Mean ( 22 / 24 ) & 7.43833333333333 & 0.0514568661762677 & 144.55472876745 \tabularnewline
Winsorized Mean ( 23 / 24 ) & 7.44152777777778 & 0.0494277344018463 & 150.553689499064 \tabularnewline
Winsorized Mean ( 24 / 24 ) & 7.44152777777778 & 0.0494277344018463 & 150.553689499064 \tabularnewline
Trimmed Mean ( 1 / 24 ) & 7.42885714285714 & 0.061767460413451 & 120.271370931083 \tabularnewline
Trimmed Mean ( 2 / 24 ) & 7.42676470588235 & 0.0618650153308147 & 120.047892434339 \tabularnewline
Trimmed Mean ( 3 / 24 ) & 7.42439393939394 & 0.0619391869542521 & 119.86586044272 \tabularnewline
Trimmed Mean ( 4 / 24 ) & 7.421875 & 0.0621756963153738 & 119.369390932978 \tabularnewline
Trimmed Mean ( 5 / 24 ) & 7.41935483870968 & 0.0624067240372625 & 118.887106368212 \tabularnewline
Trimmed Mean ( 6 / 24 ) & 7.417 & 0.0626619032929401 & 118.365380083111 \tabularnewline
Trimmed Mean ( 7 / 24 ) & 7.41465517241379 & 0.0629095008281656 & 117.862247749614 \tabularnewline
Trimmed Mean ( 8 / 24 ) & 7.41232142857143 & 0.0631458788649365 & 117.384088428411 \tabularnewline
Trimmed Mean ( 9 / 24 ) & 7.40981481481481 & 0.0633280869176099 & 117.006768646825 \tabularnewline
Trimmed Mean ( 10 / 24 ) & 7.40692307692308 & 0.0634744033763001 & 116.691495830407 \tabularnewline
Trimmed Mean ( 11 / 24 ) & 7.4046 & 0.0637144202432917 & 116.215449685107 \tabularnewline
Trimmed Mean ( 12 / 24 ) & 7.40166666666667 & 0.0639545864289302 & 115.73316442116 \tabularnewline
Trimmed Mean ( 13 / 24 ) & 7.39847826086956 & 0.0641111409607964 & 115.400820356538 \tabularnewline
Trimmed Mean ( 14 / 24 ) & 7.395 & 0.0641578227158997 & 115.262639643277 \tabularnewline
Trimmed Mean ( 15 / 24 ) & 7.39119047619048 & 0.0643742346624802 & 114.815974355938 \tabularnewline
Trimmed Mean ( 16 / 24 ) & 7.387 & 0.0644644604931017 & 114.590271034541 \tabularnewline
Trimmed Mean ( 17 / 24 ) & 7.38236842105263 & 0.0643828721497295 & 114.663545979808 \tabularnewline
Trimmed Mean ( 18 / 24 ) & 7.37722222222222 & 0.0640654564960665 & 115.151325311717 \tabularnewline
Trimmed Mean ( 19 / 24 ) & 7.36911764705882 & 0.063891016341679 & 115.33887029829 \tabularnewline
Trimmed Mean ( 20 / 24 ) & 7.36125 & 0.063787939374755 & 115.401909391563 \tabularnewline
Trimmed Mean ( 21 / 24 ) & 7.35233333333333 & 0.0633194479636506 & 116.114931032785 \tabularnewline
Trimmed Mean ( 22 / 24 ) & 7.34142857142857 & 0.0626544953684211 & 117.173213641886 \tabularnewline
Trimmed Mean ( 23 / 24 ) & 7.32923076923077 & 0.0614289410042157 & 119.31234120946 \tabularnewline
Trimmed Mean ( 24 / 24 ) & 7.31458333333333 & 0.0597669967537787 & 122.384990557032 \tabularnewline
Median & 7.24 &  &  \tabularnewline
Midrange & 7.5 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 7.395 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 7.4435 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 7.395 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 7.4435 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 7.4435 &  &  \tabularnewline
Midmean - Closest Observation & 7.395 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 7.4435 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 7.395 &  &  \tabularnewline
Number of observations & 72 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=173802&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]7.43083333333333[/C][C]0.0616310485894467[/C][C]120.569639871513[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]7.41290089766909[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]7.39523204782667[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]7.44895760791028[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 24 )[/C][C]7.43083333333333[/C][C]0.0616310485894467[/C][C]120.569639871513[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 24 )[/C][C]7.43111111111111[/C][C]0.0615912988093935[/C][C]120.651963098037[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 24 )[/C][C]7.43111111111111[/C][C]0.0610746085320066[/C][C]121.672676906587[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 24 )[/C][C]7.43055555555556[/C][C]0.0609817595322809[/C][C]121.848821886193[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 24 )[/C][C]7.42916666666667[/C][C]0.0607535330992162[/C][C]122.283697551123[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 24 )[/C][C]7.42833333333333[/C][C]0.0606188740189385[/C][C]122.541592095765[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 24 )[/C][C]7.42736111111111[/C][C]0.0604634530049218[/C][C]122.840505164442[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 24 )[/C][C]7.42736111111111[/C][C]0.0604634530049218[/C][C]122.840505164442[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 24 )[/C][C]7.42861111111111[/C][C]0.0602963811682404[/C][C]123.201607910492[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 24 )[/C][C]7.42305555555556[/C][C]0.0594282351790628[/C][C]124.907891563483[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 24 )[/C][C]7.42611111111111[/C][C]0.0590252577018896[/C][C]125.812430139943[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 24 )[/C][C]7.42611111111111[/C][C]0.0590252577018896[/C][C]125.812430139943[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 24 )[/C][C]7.42611111111111[/C][C]0.0590252577018896[/C][C]125.812430139943[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 24 )[/C][C]7.42611111111111[/C][C]0.0573878969656144[/C][C]129.402043005003[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 24 )[/C][C]7.42611111111111[/C][C]0.0573878969656144[/C][C]129.402043005003[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 24 )[/C][C]7.42611111111111[/C][C]0.0573878969656144[/C][C]129.402043005003[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 24 )[/C][C]7.42611111111111[/C][C]0.0573878969656144[/C][C]129.402043005003[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 24 )[/C][C]7.44611111111111[/C][C]0.0549500255088702[/C][C]135.506963684833[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 24 )[/C][C]7.43555555555556[/C][C]0.053360061117033[/C][C]139.346833566164[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 24 )[/C][C]7.43555555555556[/C][C]0.053360061117033[/C][C]139.346833566164[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 24 )[/C][C]7.44138888888889[/C][C]0.0519107914050813[/C][C]143.349555795069[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 24 )[/C][C]7.43833333333333[/C][C]0.0514568661762677[/C][C]144.55472876745[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 24 )[/C][C]7.44152777777778[/C][C]0.0494277344018463[/C][C]150.553689499064[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 24 )[/C][C]7.44152777777778[/C][C]0.0494277344018463[/C][C]150.553689499064[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 24 )[/C][C]7.42885714285714[/C][C]0.061767460413451[/C][C]120.271370931083[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 24 )[/C][C]7.42676470588235[/C][C]0.0618650153308147[/C][C]120.047892434339[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 24 )[/C][C]7.42439393939394[/C][C]0.0619391869542521[/C][C]119.86586044272[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 24 )[/C][C]7.421875[/C][C]0.0621756963153738[/C][C]119.369390932978[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 24 )[/C][C]7.41935483870968[/C][C]0.0624067240372625[/C][C]118.887106368212[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 24 )[/C][C]7.417[/C][C]0.0626619032929401[/C][C]118.365380083111[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 24 )[/C][C]7.41465517241379[/C][C]0.0629095008281656[/C][C]117.862247749614[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 24 )[/C][C]7.41232142857143[/C][C]0.0631458788649365[/C][C]117.384088428411[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 24 )[/C][C]7.40981481481481[/C][C]0.0633280869176099[/C][C]117.006768646825[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 24 )[/C][C]7.40692307692308[/C][C]0.0634744033763001[/C][C]116.691495830407[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 24 )[/C][C]7.4046[/C][C]0.0637144202432917[/C][C]116.215449685107[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 24 )[/C][C]7.40166666666667[/C][C]0.0639545864289302[/C][C]115.73316442116[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 24 )[/C][C]7.39847826086956[/C][C]0.0641111409607964[/C][C]115.400820356538[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 24 )[/C][C]7.395[/C][C]0.0641578227158997[/C][C]115.262639643277[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 24 )[/C][C]7.39119047619048[/C][C]0.0643742346624802[/C][C]114.815974355938[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 24 )[/C][C]7.387[/C][C]0.0644644604931017[/C][C]114.590271034541[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 24 )[/C][C]7.38236842105263[/C][C]0.0643828721497295[/C][C]114.663545979808[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 24 )[/C][C]7.37722222222222[/C][C]0.0640654564960665[/C][C]115.151325311717[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 24 )[/C][C]7.36911764705882[/C][C]0.063891016341679[/C][C]115.33887029829[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 24 )[/C][C]7.36125[/C][C]0.063787939374755[/C][C]115.401909391563[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 24 )[/C][C]7.35233333333333[/C][C]0.0633194479636506[/C][C]116.114931032785[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 24 )[/C][C]7.34142857142857[/C][C]0.0626544953684211[/C][C]117.173213641886[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 24 )[/C][C]7.32923076923077[/C][C]0.0614289410042157[/C][C]119.31234120946[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 24 )[/C][C]7.31458333333333[/C][C]0.0597669967537787[/C][C]122.384990557032[/C][/ROW]
[ROW][C]Median[/C][C]7.24[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]7.5[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]7.395[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]7.4435[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]7.395[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]7.4435[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]7.4435[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]7.395[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]7.4435[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]7.395[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]72[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=173802&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=173802&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 Mean7.430833333333330.0616310485894467120.569639871513
Geometric Mean7.41290089766909
Harmonic Mean7.39523204782667
Quadratic Mean7.44895760791028
Winsorized Mean ( 1 / 24 )7.430833333333330.0616310485894467120.569639871513
Winsorized Mean ( 2 / 24 )7.431111111111110.0615912988093935120.651963098037
Winsorized Mean ( 3 / 24 )7.431111111111110.0610746085320066121.672676906587
Winsorized Mean ( 4 / 24 )7.430555555555560.0609817595322809121.848821886193
Winsorized Mean ( 5 / 24 )7.429166666666670.0607535330992162122.283697551123
Winsorized Mean ( 6 / 24 )7.428333333333330.0606188740189385122.541592095765
Winsorized Mean ( 7 / 24 )7.427361111111110.0604634530049218122.840505164442
Winsorized Mean ( 8 / 24 )7.427361111111110.0604634530049218122.840505164442
Winsorized Mean ( 9 / 24 )7.428611111111110.0602963811682404123.201607910492
Winsorized Mean ( 10 / 24 )7.423055555555560.0594282351790628124.907891563483
Winsorized Mean ( 11 / 24 )7.426111111111110.0590252577018896125.812430139943
Winsorized Mean ( 12 / 24 )7.426111111111110.0590252577018896125.812430139943
Winsorized Mean ( 13 / 24 )7.426111111111110.0590252577018896125.812430139943
Winsorized Mean ( 14 / 24 )7.426111111111110.0573878969656144129.402043005003
Winsorized Mean ( 15 / 24 )7.426111111111110.0573878969656144129.402043005003
Winsorized Mean ( 16 / 24 )7.426111111111110.0573878969656144129.402043005003
Winsorized Mean ( 17 / 24 )7.426111111111110.0573878969656144129.402043005003
Winsorized Mean ( 18 / 24 )7.446111111111110.0549500255088702135.506963684833
Winsorized Mean ( 19 / 24 )7.435555555555560.053360061117033139.346833566164
Winsorized Mean ( 20 / 24 )7.435555555555560.053360061117033139.346833566164
Winsorized Mean ( 21 / 24 )7.441388888888890.0519107914050813143.349555795069
Winsorized Mean ( 22 / 24 )7.438333333333330.0514568661762677144.55472876745
Winsorized Mean ( 23 / 24 )7.441527777777780.0494277344018463150.553689499064
Winsorized Mean ( 24 / 24 )7.441527777777780.0494277344018463150.553689499064
Trimmed Mean ( 1 / 24 )7.428857142857140.061767460413451120.271370931083
Trimmed Mean ( 2 / 24 )7.426764705882350.0618650153308147120.047892434339
Trimmed Mean ( 3 / 24 )7.424393939393940.0619391869542521119.86586044272
Trimmed Mean ( 4 / 24 )7.4218750.0621756963153738119.369390932978
Trimmed Mean ( 5 / 24 )7.419354838709680.0624067240372625118.887106368212
Trimmed Mean ( 6 / 24 )7.4170.0626619032929401118.365380083111
Trimmed Mean ( 7 / 24 )7.414655172413790.0629095008281656117.862247749614
Trimmed Mean ( 8 / 24 )7.412321428571430.0631458788649365117.384088428411
Trimmed Mean ( 9 / 24 )7.409814814814810.0633280869176099117.006768646825
Trimmed Mean ( 10 / 24 )7.406923076923080.0634744033763001116.691495830407
Trimmed Mean ( 11 / 24 )7.40460.0637144202432917116.215449685107
Trimmed Mean ( 12 / 24 )7.401666666666670.0639545864289302115.73316442116
Trimmed Mean ( 13 / 24 )7.398478260869560.0641111409607964115.400820356538
Trimmed Mean ( 14 / 24 )7.3950.0641578227158997115.262639643277
Trimmed Mean ( 15 / 24 )7.391190476190480.0643742346624802114.815974355938
Trimmed Mean ( 16 / 24 )7.3870.0644644604931017114.590271034541
Trimmed Mean ( 17 / 24 )7.382368421052630.0643828721497295114.663545979808
Trimmed Mean ( 18 / 24 )7.377222222222220.0640654564960665115.151325311717
Trimmed Mean ( 19 / 24 )7.369117647058820.063891016341679115.33887029829
Trimmed Mean ( 20 / 24 )7.361250.063787939374755115.401909391563
Trimmed Mean ( 21 / 24 )7.352333333333330.0633194479636506116.114931032785
Trimmed Mean ( 22 / 24 )7.341428571428570.0626544953684211117.173213641886
Trimmed Mean ( 23 / 24 )7.329230769230770.0614289410042157119.31234120946
Trimmed Mean ( 24 / 24 )7.314583333333330.0597669967537787122.384990557032
Median7.24
Midrange7.5
Midmean - Weighted Average at Xnp7.395
Midmean - Weighted Average at X(n+1)p7.4435
Midmean - Empirical Distribution Function7.395
Midmean - Empirical Distribution Function - Averaging7.4435
Midmean - Empirical Distribution Function - Interpolation7.4435
Midmean - Closest Observation7.395
Midmean - True Basic - Statistics Graphics Toolkit7.4435
Midmean - MS Excel (old versions)7.395
Number of observations72



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')