Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationTue, 14 Mar 2017 22:23:07 +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/2017/Mar/14/t1489530206cn83x4pjvzdbv0e.htm/, Retrieved Tue, 14 May 2024 09:51:05 +0200
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=, Retrieved Tue, 14 May 2024 09:51:05 +0200
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact0
Dataseries X:
90,33
90,62
91,22
91,39
91,72
91,32
91,1
91,05
91,45
91,53
91,63
91,78
92,32
92,8
92,65
93,35
93,63
93,76
93,83
93,37
93,41
93,84
94,66
94,65
94,91
95,81
95,87
95,84
96,31
96,17
96,16
96,48
96,61
97,68
97,83
97,88
98,63
99,25
99,64
100,47
101,12
101,33
100,5
99,93
99,81
99,74
99,72
99,87
100,39
100,09
100,03
101,2
99,96
99,94
100,01
98,69
98,19
98,08
98,46
98,75
99,25
99,68
99,64
101,46
100,99
101,12
100,6
100,24
100,16
101,25
100,74
100,61




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Herman Ole Andreas Wold' @ wold.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 & 'Herman Ole Andreas Wold' @ wold.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&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]'Herman Ole Andreas Wold' @ wold.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&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'Herman Ole Andreas Wold' @ wold.wessa.net







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean96.86805555555560.42172041441902229.697335589042
Geometric Mean96.8021765056167
Harmonic Mean96.7356324117293
Quadratic Mean96.933211041303
Winsorized Mean ( 1 / 24 )96.87027777777780.420585839101262230.322252372493
Winsorized Mean ( 2 / 24 )96.880.417832266366423231.863376283726
Winsorized Mean ( 3 / 24 )96.880.417118862603822232.25993520225
Winsorized Mean ( 4 / 24 )96.88222222222220.415184369090809233.34747026816
Winsorized Mean ( 5 / 24 )96.88916666666670.413859310104594234.111361762479
Winsorized Mean ( 6 / 24 )96.88416666666670.411215931895589235.604117330907
Winsorized Mean ( 7 / 24 )96.86569444444440.406780453679442238.127701486803
Winsorized Mean ( 8 / 24 )96.86013888888890.403204568213785240.225797336533
Winsorized Mean ( 9 / 24 )96.87138888888890.400725686869705241.73990353752
Winsorized Mean ( 10 / 24 )96.870.396625929971187244.235166387223
Winsorized Mean ( 11 / 24 )96.87458333333330.394364097469888245.647572775638
Winsorized Mean ( 12 / 24 )96.951250.376661054504495257.39653420644
Winsorized Mean ( 13 / 24 )96.983750.363037547986491267.145232050788
Winsorized Mean ( 14 / 24 )96.99736111111110.356209724025659272.304079784537
Winsorized Mean ( 15 / 24 )97.09736111111110.335856354891655289.103837688091
Winsorized Mean ( 16 / 24 )97.08847222222220.333493251529058291.125747753738
Winsorized Mean ( 17 / 24 )97.09319444444440.331426519470971292.955417687837
Winsorized Mean ( 18 / 24 )97.13569444444440.32134704171693302.276610126723
Winsorized Mean ( 19 / 24 )97.16472222222220.315450033258633308.019375425326
Winsorized Mean ( 20 / 24 )97.18138888888890.312157562334842311.321590808187
Winsorized Mean ( 21 / 24 )97.16680555555560.309554922200763313.891973885454
Winsorized Mean ( 22 / 24 )97.39597222222220.270801977940963359.657536339913
Winsorized Mean ( 23 / 24 )97.37680555555550.267550678684744363.956488670676
Winsorized Mean ( 24 / 24 )97.45347222222220.254901186761864382.318628878202
Trimmed Mean ( 1 / 24 )96.89585714285710.418335778676403231.622208957196
Trimmed Mean ( 2 / 24 )96.92294117647060.415401318528992233.323624295878
Trimmed Mean ( 3 / 24 )96.94636363636360.41333380158427234.547388248378
Trimmed Mean ( 4 / 24 )96.971250.410855699429822236.022647694981
Trimmed Mean ( 5 / 24 )96.99709677419360.40823130303703237.603280426036
Trimmed Mean ( 6 / 24 )97.0230.405127049891355239.487834806437
Trimmed Mean ( 7 / 24 )97.0517241379310.401711864571347241.595363984311
Trimmed Mean ( 8 / 24 )97.08589285714290.398230320421447243.793322302523
Trimmed Mean ( 9 / 24 )97.12351851851850.39435456714314246.284756436624
Trimmed Mean ( 10 / 24 )97.16230769230770.389696929016012249.327876248969
Trimmed Mean ( 11 / 24 )97.20440.384333524375878252.916786683782
Trimmed Mean ( 12 / 24 )97.2493750.377626547086823257.527908856579
Trimmed Mean ( 13 / 24 )97.28826086956520.372663646814114261.061849475468
Trimmed Mean ( 14 / 24 )97.32659090909090.3686921837259263.977906788084
Trimmed Mean ( 15 / 24 )97.36690476190480.364352716770162267.232547694505
Trimmed Mean ( 16 / 24 )97.399250.362512490943062268.678328149796
Trimmed Mean ( 17 / 24 )97.43605263157890.359587945680948270.965847998784
Trimmed Mean ( 18 / 24 )97.47638888888890.355130012583761274.480853306922
Trimmed Mean ( 19 / 24 )97.51647058823530.35056635673278278.168365889621
Trimmed Mean ( 20 / 24 )97.5581250.344674471685171283.044243233397
Trimmed Mean ( 21 / 24 )97.60333333333330.33607618639995290.420259700221
Trimmed Mean ( 22 / 24 )97.65678571428570.323022290896034302.322125954202
Trimmed Mean ( 23 / 24 )97.68961538461540.316661664031906308.498395861308
Trimmed Mean ( 24 / 24 )97.73041666666670.306203659118385319.168023491457
Median97.98
Midrange95.895
Midmean - Weighted Average at Xnp97.3664864864865
Midmean - Weighted Average at X(n+1)p97.4763888888889
Midmean - Empirical Distribution Function97.3664864864865
Midmean - Empirical Distribution Function - Averaging97.4763888888889
Midmean - Empirical Distribution Function - Interpolation97.4763888888889
Midmean - Closest Observation97.3664864864865
Midmean - True Basic - Statistics Graphics Toolkit97.4763888888889
Midmean - MS Excel (old versions)97.4360526315789
Number of observations72

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 96.8680555555556 & 0.42172041441902 & 229.697335589042 \tabularnewline
Geometric Mean & 96.8021765056167 &  &  \tabularnewline
Harmonic Mean & 96.7356324117293 &  &  \tabularnewline
Quadratic Mean & 96.933211041303 &  &  \tabularnewline
Winsorized Mean ( 1 / 24 ) & 96.8702777777778 & 0.420585839101262 & 230.322252372493 \tabularnewline
Winsorized Mean ( 2 / 24 ) & 96.88 & 0.417832266366423 & 231.863376283726 \tabularnewline
Winsorized Mean ( 3 / 24 ) & 96.88 & 0.417118862603822 & 232.25993520225 \tabularnewline
Winsorized Mean ( 4 / 24 ) & 96.8822222222222 & 0.415184369090809 & 233.34747026816 \tabularnewline
Winsorized Mean ( 5 / 24 ) & 96.8891666666667 & 0.413859310104594 & 234.111361762479 \tabularnewline
Winsorized Mean ( 6 / 24 ) & 96.8841666666667 & 0.411215931895589 & 235.604117330907 \tabularnewline
Winsorized Mean ( 7 / 24 ) & 96.8656944444444 & 0.406780453679442 & 238.127701486803 \tabularnewline
Winsorized Mean ( 8 / 24 ) & 96.8601388888889 & 0.403204568213785 & 240.225797336533 \tabularnewline
Winsorized Mean ( 9 / 24 ) & 96.8713888888889 & 0.400725686869705 & 241.73990353752 \tabularnewline
Winsorized Mean ( 10 / 24 ) & 96.87 & 0.396625929971187 & 244.235166387223 \tabularnewline
Winsorized Mean ( 11 / 24 ) & 96.8745833333333 & 0.394364097469888 & 245.647572775638 \tabularnewline
Winsorized Mean ( 12 / 24 ) & 96.95125 & 0.376661054504495 & 257.39653420644 \tabularnewline
Winsorized Mean ( 13 / 24 ) & 96.98375 & 0.363037547986491 & 267.145232050788 \tabularnewline
Winsorized Mean ( 14 / 24 ) & 96.9973611111111 & 0.356209724025659 & 272.304079784537 \tabularnewline
Winsorized Mean ( 15 / 24 ) & 97.0973611111111 & 0.335856354891655 & 289.103837688091 \tabularnewline
Winsorized Mean ( 16 / 24 ) & 97.0884722222222 & 0.333493251529058 & 291.125747753738 \tabularnewline
Winsorized Mean ( 17 / 24 ) & 97.0931944444444 & 0.331426519470971 & 292.955417687837 \tabularnewline
Winsorized Mean ( 18 / 24 ) & 97.1356944444444 & 0.32134704171693 & 302.276610126723 \tabularnewline
Winsorized Mean ( 19 / 24 ) & 97.1647222222222 & 0.315450033258633 & 308.019375425326 \tabularnewline
Winsorized Mean ( 20 / 24 ) & 97.1813888888889 & 0.312157562334842 & 311.321590808187 \tabularnewline
Winsorized Mean ( 21 / 24 ) & 97.1668055555556 & 0.309554922200763 & 313.891973885454 \tabularnewline
Winsorized Mean ( 22 / 24 ) & 97.3959722222222 & 0.270801977940963 & 359.657536339913 \tabularnewline
Winsorized Mean ( 23 / 24 ) & 97.3768055555555 & 0.267550678684744 & 363.956488670676 \tabularnewline
Winsorized Mean ( 24 / 24 ) & 97.4534722222222 & 0.254901186761864 & 382.318628878202 \tabularnewline
Trimmed Mean ( 1 / 24 ) & 96.8958571428571 & 0.418335778676403 & 231.622208957196 \tabularnewline
Trimmed Mean ( 2 / 24 ) & 96.9229411764706 & 0.415401318528992 & 233.323624295878 \tabularnewline
Trimmed Mean ( 3 / 24 ) & 96.9463636363636 & 0.41333380158427 & 234.547388248378 \tabularnewline
Trimmed Mean ( 4 / 24 ) & 96.97125 & 0.410855699429822 & 236.022647694981 \tabularnewline
Trimmed Mean ( 5 / 24 ) & 96.9970967741936 & 0.40823130303703 & 237.603280426036 \tabularnewline
Trimmed Mean ( 6 / 24 ) & 97.023 & 0.405127049891355 & 239.487834806437 \tabularnewline
Trimmed Mean ( 7 / 24 ) & 97.051724137931 & 0.401711864571347 & 241.595363984311 \tabularnewline
Trimmed Mean ( 8 / 24 ) & 97.0858928571429 & 0.398230320421447 & 243.793322302523 \tabularnewline
Trimmed Mean ( 9 / 24 ) & 97.1235185185185 & 0.39435456714314 & 246.284756436624 \tabularnewline
Trimmed Mean ( 10 / 24 ) & 97.1623076923077 & 0.389696929016012 & 249.327876248969 \tabularnewline
Trimmed Mean ( 11 / 24 ) & 97.2044 & 0.384333524375878 & 252.916786683782 \tabularnewline
Trimmed Mean ( 12 / 24 ) & 97.249375 & 0.377626547086823 & 257.527908856579 \tabularnewline
Trimmed Mean ( 13 / 24 ) & 97.2882608695652 & 0.372663646814114 & 261.061849475468 \tabularnewline
Trimmed Mean ( 14 / 24 ) & 97.3265909090909 & 0.3686921837259 & 263.977906788084 \tabularnewline
Trimmed Mean ( 15 / 24 ) & 97.3669047619048 & 0.364352716770162 & 267.232547694505 \tabularnewline
Trimmed Mean ( 16 / 24 ) & 97.39925 & 0.362512490943062 & 268.678328149796 \tabularnewline
Trimmed Mean ( 17 / 24 ) & 97.4360526315789 & 0.359587945680948 & 270.965847998784 \tabularnewline
Trimmed Mean ( 18 / 24 ) & 97.4763888888889 & 0.355130012583761 & 274.480853306922 \tabularnewline
Trimmed Mean ( 19 / 24 ) & 97.5164705882353 & 0.35056635673278 & 278.168365889621 \tabularnewline
Trimmed Mean ( 20 / 24 ) & 97.558125 & 0.344674471685171 & 283.044243233397 \tabularnewline
Trimmed Mean ( 21 / 24 ) & 97.6033333333333 & 0.33607618639995 & 290.420259700221 \tabularnewline
Trimmed Mean ( 22 / 24 ) & 97.6567857142857 & 0.323022290896034 & 302.322125954202 \tabularnewline
Trimmed Mean ( 23 / 24 ) & 97.6896153846154 & 0.316661664031906 & 308.498395861308 \tabularnewline
Trimmed Mean ( 24 / 24 ) & 97.7304166666667 & 0.306203659118385 & 319.168023491457 \tabularnewline
Median & 97.98 &  &  \tabularnewline
Midrange & 95.895 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 97.3664864864865 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 97.4763888888889 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 97.3664864864865 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 97.4763888888889 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 97.4763888888889 &  &  \tabularnewline
Midmean - Closest Observation & 97.3664864864865 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 97.4763888888889 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 97.4360526315789 &  &  \tabularnewline
Number of observations & 72 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&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]96.8680555555556[/C][C]0.42172041441902[/C][C]229.697335589042[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]96.8021765056167[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]96.7356324117293[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]96.933211041303[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 24 )[/C][C]96.8702777777778[/C][C]0.420585839101262[/C][C]230.322252372493[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 24 )[/C][C]96.88[/C][C]0.417832266366423[/C][C]231.863376283726[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 24 )[/C][C]96.88[/C][C]0.417118862603822[/C][C]232.25993520225[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 24 )[/C][C]96.8822222222222[/C][C]0.415184369090809[/C][C]233.34747026816[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 24 )[/C][C]96.8891666666667[/C][C]0.413859310104594[/C][C]234.111361762479[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 24 )[/C][C]96.8841666666667[/C][C]0.411215931895589[/C][C]235.604117330907[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 24 )[/C][C]96.8656944444444[/C][C]0.406780453679442[/C][C]238.127701486803[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 24 )[/C][C]96.8601388888889[/C][C]0.403204568213785[/C][C]240.225797336533[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 24 )[/C][C]96.8713888888889[/C][C]0.400725686869705[/C][C]241.73990353752[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 24 )[/C][C]96.87[/C][C]0.396625929971187[/C][C]244.235166387223[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 24 )[/C][C]96.8745833333333[/C][C]0.394364097469888[/C][C]245.647572775638[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 24 )[/C][C]96.95125[/C][C]0.376661054504495[/C][C]257.39653420644[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 24 )[/C][C]96.98375[/C][C]0.363037547986491[/C][C]267.145232050788[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 24 )[/C][C]96.9973611111111[/C][C]0.356209724025659[/C][C]272.304079784537[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 24 )[/C][C]97.0973611111111[/C][C]0.335856354891655[/C][C]289.103837688091[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 24 )[/C][C]97.0884722222222[/C][C]0.333493251529058[/C][C]291.125747753738[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 24 )[/C][C]97.0931944444444[/C][C]0.331426519470971[/C][C]292.955417687837[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 24 )[/C][C]97.1356944444444[/C][C]0.32134704171693[/C][C]302.276610126723[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 24 )[/C][C]97.1647222222222[/C][C]0.315450033258633[/C][C]308.019375425326[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 24 )[/C][C]97.1813888888889[/C][C]0.312157562334842[/C][C]311.321590808187[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 24 )[/C][C]97.1668055555556[/C][C]0.309554922200763[/C][C]313.891973885454[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 24 )[/C][C]97.3959722222222[/C][C]0.270801977940963[/C][C]359.657536339913[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 24 )[/C][C]97.3768055555555[/C][C]0.267550678684744[/C][C]363.956488670676[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 24 )[/C][C]97.4534722222222[/C][C]0.254901186761864[/C][C]382.318628878202[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 24 )[/C][C]96.8958571428571[/C][C]0.418335778676403[/C][C]231.622208957196[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 24 )[/C][C]96.9229411764706[/C][C]0.415401318528992[/C][C]233.323624295878[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 24 )[/C][C]96.9463636363636[/C][C]0.41333380158427[/C][C]234.547388248378[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 24 )[/C][C]96.97125[/C][C]0.410855699429822[/C][C]236.022647694981[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 24 )[/C][C]96.9970967741936[/C][C]0.40823130303703[/C][C]237.603280426036[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 24 )[/C][C]97.023[/C][C]0.405127049891355[/C][C]239.487834806437[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 24 )[/C][C]97.051724137931[/C][C]0.401711864571347[/C][C]241.595363984311[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 24 )[/C][C]97.0858928571429[/C][C]0.398230320421447[/C][C]243.793322302523[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 24 )[/C][C]97.1235185185185[/C][C]0.39435456714314[/C][C]246.284756436624[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 24 )[/C][C]97.1623076923077[/C][C]0.389696929016012[/C][C]249.327876248969[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 24 )[/C][C]97.2044[/C][C]0.384333524375878[/C][C]252.916786683782[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 24 )[/C][C]97.249375[/C][C]0.377626547086823[/C][C]257.527908856579[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 24 )[/C][C]97.2882608695652[/C][C]0.372663646814114[/C][C]261.061849475468[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 24 )[/C][C]97.3265909090909[/C][C]0.3686921837259[/C][C]263.977906788084[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 24 )[/C][C]97.3669047619048[/C][C]0.364352716770162[/C][C]267.232547694505[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 24 )[/C][C]97.39925[/C][C]0.362512490943062[/C][C]268.678328149796[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 24 )[/C][C]97.4360526315789[/C][C]0.359587945680948[/C][C]270.965847998784[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 24 )[/C][C]97.4763888888889[/C][C]0.355130012583761[/C][C]274.480853306922[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 24 )[/C][C]97.5164705882353[/C][C]0.35056635673278[/C][C]278.168365889621[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 24 )[/C][C]97.558125[/C][C]0.344674471685171[/C][C]283.044243233397[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 24 )[/C][C]97.6033333333333[/C][C]0.33607618639995[/C][C]290.420259700221[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 24 )[/C][C]97.6567857142857[/C][C]0.323022290896034[/C][C]302.322125954202[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 24 )[/C][C]97.6896153846154[/C][C]0.316661664031906[/C][C]308.498395861308[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 24 )[/C][C]97.7304166666667[/C][C]0.306203659118385[/C][C]319.168023491457[/C][/ROW]
[ROW][C]Median[/C][C]97.98[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]95.895[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]97.3664864864865[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]97.4763888888889[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]97.3664864864865[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]97.4763888888889[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]97.4763888888889[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]97.3664864864865[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]97.4763888888889[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]97.4360526315789[/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=&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&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 Mean96.86805555555560.42172041441902229.697335589042
Geometric Mean96.8021765056167
Harmonic Mean96.7356324117293
Quadratic Mean96.933211041303
Winsorized Mean ( 1 / 24 )96.87027777777780.420585839101262230.322252372493
Winsorized Mean ( 2 / 24 )96.880.417832266366423231.863376283726
Winsorized Mean ( 3 / 24 )96.880.417118862603822232.25993520225
Winsorized Mean ( 4 / 24 )96.88222222222220.415184369090809233.34747026816
Winsorized Mean ( 5 / 24 )96.88916666666670.413859310104594234.111361762479
Winsorized Mean ( 6 / 24 )96.88416666666670.411215931895589235.604117330907
Winsorized Mean ( 7 / 24 )96.86569444444440.406780453679442238.127701486803
Winsorized Mean ( 8 / 24 )96.86013888888890.403204568213785240.225797336533
Winsorized Mean ( 9 / 24 )96.87138888888890.400725686869705241.73990353752
Winsorized Mean ( 10 / 24 )96.870.396625929971187244.235166387223
Winsorized Mean ( 11 / 24 )96.87458333333330.394364097469888245.647572775638
Winsorized Mean ( 12 / 24 )96.951250.376661054504495257.39653420644
Winsorized Mean ( 13 / 24 )96.983750.363037547986491267.145232050788
Winsorized Mean ( 14 / 24 )96.99736111111110.356209724025659272.304079784537
Winsorized Mean ( 15 / 24 )97.09736111111110.335856354891655289.103837688091
Winsorized Mean ( 16 / 24 )97.08847222222220.333493251529058291.125747753738
Winsorized Mean ( 17 / 24 )97.09319444444440.331426519470971292.955417687837
Winsorized Mean ( 18 / 24 )97.13569444444440.32134704171693302.276610126723
Winsorized Mean ( 19 / 24 )97.16472222222220.315450033258633308.019375425326
Winsorized Mean ( 20 / 24 )97.18138888888890.312157562334842311.321590808187
Winsorized Mean ( 21 / 24 )97.16680555555560.309554922200763313.891973885454
Winsorized Mean ( 22 / 24 )97.39597222222220.270801977940963359.657536339913
Winsorized Mean ( 23 / 24 )97.37680555555550.267550678684744363.956488670676
Winsorized Mean ( 24 / 24 )97.45347222222220.254901186761864382.318628878202
Trimmed Mean ( 1 / 24 )96.89585714285710.418335778676403231.622208957196
Trimmed Mean ( 2 / 24 )96.92294117647060.415401318528992233.323624295878
Trimmed Mean ( 3 / 24 )96.94636363636360.41333380158427234.547388248378
Trimmed Mean ( 4 / 24 )96.971250.410855699429822236.022647694981
Trimmed Mean ( 5 / 24 )96.99709677419360.40823130303703237.603280426036
Trimmed Mean ( 6 / 24 )97.0230.405127049891355239.487834806437
Trimmed Mean ( 7 / 24 )97.0517241379310.401711864571347241.595363984311
Trimmed Mean ( 8 / 24 )97.08589285714290.398230320421447243.793322302523
Trimmed Mean ( 9 / 24 )97.12351851851850.39435456714314246.284756436624
Trimmed Mean ( 10 / 24 )97.16230769230770.389696929016012249.327876248969
Trimmed Mean ( 11 / 24 )97.20440.384333524375878252.916786683782
Trimmed Mean ( 12 / 24 )97.2493750.377626547086823257.527908856579
Trimmed Mean ( 13 / 24 )97.28826086956520.372663646814114261.061849475468
Trimmed Mean ( 14 / 24 )97.32659090909090.3686921837259263.977906788084
Trimmed Mean ( 15 / 24 )97.36690476190480.364352716770162267.232547694505
Trimmed Mean ( 16 / 24 )97.399250.362512490943062268.678328149796
Trimmed Mean ( 17 / 24 )97.43605263157890.359587945680948270.965847998784
Trimmed Mean ( 18 / 24 )97.47638888888890.355130012583761274.480853306922
Trimmed Mean ( 19 / 24 )97.51647058823530.35056635673278278.168365889621
Trimmed Mean ( 20 / 24 )97.5581250.344674471685171283.044243233397
Trimmed Mean ( 21 / 24 )97.60333333333330.33607618639995290.420259700221
Trimmed Mean ( 22 / 24 )97.65678571428570.323022290896034302.322125954202
Trimmed Mean ( 23 / 24 )97.68961538461540.316661664031906308.498395861308
Trimmed Mean ( 24 / 24 )97.73041666666670.306203659118385319.168023491457
Median97.98
Midrange95.895
Midmean - Weighted Average at Xnp97.3664864864865
Midmean - Weighted Average at X(n+1)p97.4763888888889
Midmean - Empirical Distribution Function97.3664864864865
Midmean - Empirical Distribution Function - Averaging97.4763888888889
Midmean - Empirical Distribution Function - Interpolation97.4763888888889
Midmean - Closest Observation97.3664864864865
Midmean - True Basic - Statistics Graphics Toolkit97.4763888888889
Midmean - MS Excel (old versions)97.4360526315789
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')