Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationTue, 16 Oct 2012 16:28:41 -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/16/t1350419379dyb4ikx8a6xg0kf.htm/, Retrieved Tue, 30 Apr 2024 12:26:01 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=179233, Retrieved Tue, 30 Apr 2024 12:26:01 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact57
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [Centrummaten Gemi...] [2012-10-16 20:28:41] [546261a30dc8ed318e881c0522cbd66e] [Current]
Feedback Forum

Post a new message
Dataseries X:
73,97
73,97
73,97
73,97
73,97
73,97
73,96
74,44
75,43
75,77
75,82
75,85
75,85
75,85
77,95
82,07
84,82
85,08
85,34
85,65
85,65
85,72
85,73
85,73
85,73
85,73
85,74
86,32
87,59
87,81
87,87
87,94
87,96
88,01
88,01
88,01
88,01
88,01
88,59
89,43
89,63
89,73
89,88
89,89
89,9
89,91
89,86
90,07
90,17
90,17
90,28
90,87
92,05
92,1
92,16
92,22
92,25
92,29
92,29
92,29
92,29
92,29
91,95
91,82
92,16
92,31
92,33
92,4
92,54
92,49
92,54
92,58




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 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 & 1 seconds \tabularnewline
R Server & 'Herman Ole Andreas Wold' @ wold.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=179233&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]1 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=179233&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=179233&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 time1 seconds
R Server'Herman Ole Andreas Wold' @ wold.wessa.net







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean86.34722222222220.751759938786479114.860100634795
Geometric Mean86.102355642114
Harmonic Mean85.8449282139611
Quadratic Mean86.5792581331631
Winsorized Mean ( 1 / 24 )86.34680555555560.751663044722047114.874352493257
Winsorized Mean ( 2 / 24 )86.34680555555550.751663044722047114.874352493257
Winsorized Mean ( 3 / 24 )86.34472222222220.75142217722669114.908402811451
Winsorized Mean ( 4 / 24 )86.33972222222220.750850013159896114.989306398049
Winsorized Mean ( 5 / 24 )86.33486111111110.75030017449084115.06709453946
Winsorized Mean ( 6 / 24 )86.33319444444440.750112871694158115.093604845705
Winsorized Mean ( 7 / 24 )86.37694444444440.739394701234179116.821156954826
Winsorized Mean ( 8 / 24 )86.48694444444440.714898726614408120.977896903001
Winsorized Mean ( 9 / 24 )86.52944444444440.705706088460248122.61399732747
Winsorized Mean ( 10 / 24 )86.53638888888890.704216267818734122.883257379058
Winsorized Mean ( 11 / 24 )86.54097222222220.703234399949539123.061346584342
Winsorized Mean ( 12 / 24 )86.53430555555560.702468591136438123.186013791111
Winsorized Mean ( 13 / 24 )86.52888888888890.701848903981598123.287061357522
Winsorized Mean ( 14 / 24 )86.92555555555550.614622226075457141.429242008706
Winsorized Mean ( 15 / 24 )87.78388888888890.447411244184097196.204029357761
Winsorized Mean ( 16 / 24 )88.38166666666670.344703042912921256.399438542217
Winsorized Mean ( 17 / 24 )88.431250.334100404813987264.68465385199
Winsorized Mean ( 18 / 24 )88.471250.321230879088497275.413279853543
Winsorized Mean ( 19 / 24 )88.518750.304959330358863290.264114548766
Winsorized Mean ( 20 / 24 )88.25486111111110.266477925654881331.19013852356
Winsorized Mean ( 21 / 24 )88.10319444444440.240752669077202365.948983170742
Winsorized Mean ( 22 / 24 )88.07263888888890.236082810947815373.058243992008
Winsorized Mean ( 23 / 24 )88.07263888888890.236082810947815373.058243992008
Winsorized Mean ( 24 / 24 )88.03930555555560.23194188792365379.574842404215
Trimmed Mean ( 1 / 24 )86.43514285714290.747137968939985115.68832859582
Trimmed Mean ( 2 / 24 )86.52867647058820.741195789662445116.741996753645
Trimmed Mean ( 3 / 24 )86.62787878787880.733549867856148118.094055474449
Trimmed Mean ( 4 / 24 )86.73406250.723938971777754119.80852790258
Trimmed Mean ( 5 / 24 )86.84854838709680.712004152076371121.977586975899
Trimmed Mean ( 6 / 24 )86.97183333333330.697142938259686124.754664445782
Trimmed Mean ( 7 / 24 )87.10396551724140.678490056065663128.379133545933
Trimmed Mean ( 8 / 24 )87.23750.658028206181065132.574104241354
Trimmed Mean ( 9 / 24 )87.36259259259260.638791890468332136.762213008907
Trimmed Mean ( 10 / 24 )87.49076923076920.616616249589203141.888523516947
Trimmed Mean ( 11 / 24 )87.62820.588373037992679148.933065150226
Trimmed Mean ( 12 / 24 )87.77645833333330.551687650089191159.105353036528
Trimmed Mean ( 13 / 24 )87.93847826086960.502733587152613174.920634921045
Trimmed Mean ( 14 / 24 )88.11590909090910.434582047297369202.760122372507
Trimmed Mean ( 15 / 24 )88.26166666666670.370777335290962238.044934967248
Trimmed Mean ( 16 / 24 )88.3190.342565883612751257.816099690298
Trimmed Mean ( 17 / 24 )88.31157894736840.333658441192789264.676591521752
Trimmed Mean ( 18 / 24 )88.29750.323793333803945272.697090340543
Trimmed Mean ( 19 / 24 )88.27705882352940.313111157647081281.935206291913
Trimmed Mean ( 20 / 24 )88.24843750.302074850988622292.140961788719
Trimmed Mean ( 21 / 24 )88.24766666666670.29729573624469296.834619229232
Trimmed Mean ( 22 / 24 )88.26535714285710.296287648978596297.904274603203
Trimmed Mean ( 23 / 24 )88.28961538461540.294293145725995300.005680277781
Trimmed Mean ( 24 / 24 )88.31791666666670.289266926506525305.316330951767
Median88.01
Midrange83.27
Midmean - Weighted Average at Xnp88.2105405405405
Midmean - Weighted Average at X(n+1)p88.2975
Midmean - Empirical Distribution Function88.2105405405405
Midmean - Empirical Distribution Function - Averaging88.2975
Midmean - Empirical Distribution Function - Interpolation88.2975
Midmean - Closest Observation88.2105405405405
Midmean - True Basic - Statistics Graphics Toolkit88.2975
Midmean - MS Excel (old versions)88.3115789473684
Number of observations72

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 86.3472222222222 & 0.751759938786479 & 114.860100634795 \tabularnewline
Geometric Mean & 86.102355642114 &  &  \tabularnewline
Harmonic Mean & 85.8449282139611 &  &  \tabularnewline
Quadratic Mean & 86.5792581331631 &  &  \tabularnewline
Winsorized Mean ( 1 / 24 ) & 86.3468055555556 & 0.751663044722047 & 114.874352493257 \tabularnewline
Winsorized Mean ( 2 / 24 ) & 86.3468055555555 & 0.751663044722047 & 114.874352493257 \tabularnewline
Winsorized Mean ( 3 / 24 ) & 86.3447222222222 & 0.75142217722669 & 114.908402811451 \tabularnewline
Winsorized Mean ( 4 / 24 ) & 86.3397222222222 & 0.750850013159896 & 114.989306398049 \tabularnewline
Winsorized Mean ( 5 / 24 ) & 86.3348611111111 & 0.75030017449084 & 115.06709453946 \tabularnewline
Winsorized Mean ( 6 / 24 ) & 86.3331944444444 & 0.750112871694158 & 115.093604845705 \tabularnewline
Winsorized Mean ( 7 / 24 ) & 86.3769444444444 & 0.739394701234179 & 116.821156954826 \tabularnewline
Winsorized Mean ( 8 / 24 ) & 86.4869444444444 & 0.714898726614408 & 120.977896903001 \tabularnewline
Winsorized Mean ( 9 / 24 ) & 86.5294444444444 & 0.705706088460248 & 122.61399732747 \tabularnewline
Winsorized Mean ( 10 / 24 ) & 86.5363888888889 & 0.704216267818734 & 122.883257379058 \tabularnewline
Winsorized Mean ( 11 / 24 ) & 86.5409722222222 & 0.703234399949539 & 123.061346584342 \tabularnewline
Winsorized Mean ( 12 / 24 ) & 86.5343055555556 & 0.702468591136438 & 123.186013791111 \tabularnewline
Winsorized Mean ( 13 / 24 ) & 86.5288888888889 & 0.701848903981598 & 123.287061357522 \tabularnewline
Winsorized Mean ( 14 / 24 ) & 86.9255555555555 & 0.614622226075457 & 141.429242008706 \tabularnewline
Winsorized Mean ( 15 / 24 ) & 87.7838888888889 & 0.447411244184097 & 196.204029357761 \tabularnewline
Winsorized Mean ( 16 / 24 ) & 88.3816666666667 & 0.344703042912921 & 256.399438542217 \tabularnewline
Winsorized Mean ( 17 / 24 ) & 88.43125 & 0.334100404813987 & 264.68465385199 \tabularnewline
Winsorized Mean ( 18 / 24 ) & 88.47125 & 0.321230879088497 & 275.413279853543 \tabularnewline
Winsorized Mean ( 19 / 24 ) & 88.51875 & 0.304959330358863 & 290.264114548766 \tabularnewline
Winsorized Mean ( 20 / 24 ) & 88.2548611111111 & 0.266477925654881 & 331.19013852356 \tabularnewline
Winsorized Mean ( 21 / 24 ) & 88.1031944444444 & 0.240752669077202 & 365.948983170742 \tabularnewline
Winsorized Mean ( 22 / 24 ) & 88.0726388888889 & 0.236082810947815 & 373.058243992008 \tabularnewline
Winsorized Mean ( 23 / 24 ) & 88.0726388888889 & 0.236082810947815 & 373.058243992008 \tabularnewline
Winsorized Mean ( 24 / 24 ) & 88.0393055555556 & 0.23194188792365 & 379.574842404215 \tabularnewline
Trimmed Mean ( 1 / 24 ) & 86.4351428571429 & 0.747137968939985 & 115.68832859582 \tabularnewline
Trimmed Mean ( 2 / 24 ) & 86.5286764705882 & 0.741195789662445 & 116.741996753645 \tabularnewline
Trimmed Mean ( 3 / 24 ) & 86.6278787878788 & 0.733549867856148 & 118.094055474449 \tabularnewline
Trimmed Mean ( 4 / 24 ) & 86.7340625 & 0.723938971777754 & 119.80852790258 \tabularnewline
Trimmed Mean ( 5 / 24 ) & 86.8485483870968 & 0.712004152076371 & 121.977586975899 \tabularnewline
Trimmed Mean ( 6 / 24 ) & 86.9718333333333 & 0.697142938259686 & 124.754664445782 \tabularnewline
Trimmed Mean ( 7 / 24 ) & 87.1039655172414 & 0.678490056065663 & 128.379133545933 \tabularnewline
Trimmed Mean ( 8 / 24 ) & 87.2375 & 0.658028206181065 & 132.574104241354 \tabularnewline
Trimmed Mean ( 9 / 24 ) & 87.3625925925926 & 0.638791890468332 & 136.762213008907 \tabularnewline
Trimmed Mean ( 10 / 24 ) & 87.4907692307692 & 0.616616249589203 & 141.888523516947 \tabularnewline
Trimmed Mean ( 11 / 24 ) & 87.6282 & 0.588373037992679 & 148.933065150226 \tabularnewline
Trimmed Mean ( 12 / 24 ) & 87.7764583333333 & 0.551687650089191 & 159.105353036528 \tabularnewline
Trimmed Mean ( 13 / 24 ) & 87.9384782608696 & 0.502733587152613 & 174.920634921045 \tabularnewline
Trimmed Mean ( 14 / 24 ) & 88.1159090909091 & 0.434582047297369 & 202.760122372507 \tabularnewline
Trimmed Mean ( 15 / 24 ) & 88.2616666666667 & 0.370777335290962 & 238.044934967248 \tabularnewline
Trimmed Mean ( 16 / 24 ) & 88.319 & 0.342565883612751 & 257.816099690298 \tabularnewline
Trimmed Mean ( 17 / 24 ) & 88.3115789473684 & 0.333658441192789 & 264.676591521752 \tabularnewline
Trimmed Mean ( 18 / 24 ) & 88.2975 & 0.323793333803945 & 272.697090340543 \tabularnewline
Trimmed Mean ( 19 / 24 ) & 88.2770588235294 & 0.313111157647081 & 281.935206291913 \tabularnewline
Trimmed Mean ( 20 / 24 ) & 88.2484375 & 0.302074850988622 & 292.140961788719 \tabularnewline
Trimmed Mean ( 21 / 24 ) & 88.2476666666667 & 0.29729573624469 & 296.834619229232 \tabularnewline
Trimmed Mean ( 22 / 24 ) & 88.2653571428571 & 0.296287648978596 & 297.904274603203 \tabularnewline
Trimmed Mean ( 23 / 24 ) & 88.2896153846154 & 0.294293145725995 & 300.005680277781 \tabularnewline
Trimmed Mean ( 24 / 24 ) & 88.3179166666667 & 0.289266926506525 & 305.316330951767 \tabularnewline
Median & 88.01 &  &  \tabularnewline
Midrange & 83.27 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 88.2105405405405 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 88.2975 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 88.2105405405405 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 88.2975 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 88.2975 &  &  \tabularnewline
Midmean - Closest Observation & 88.2105405405405 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 88.2975 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 88.3115789473684 &  &  \tabularnewline
Number of observations & 72 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=179233&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]86.3472222222222[/C][C]0.751759938786479[/C][C]114.860100634795[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]86.102355642114[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]85.8449282139611[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]86.5792581331631[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 24 )[/C][C]86.3468055555556[/C][C]0.751663044722047[/C][C]114.874352493257[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 24 )[/C][C]86.3468055555555[/C][C]0.751663044722047[/C][C]114.874352493257[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 24 )[/C][C]86.3447222222222[/C][C]0.75142217722669[/C][C]114.908402811451[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 24 )[/C][C]86.3397222222222[/C][C]0.750850013159896[/C][C]114.989306398049[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 24 )[/C][C]86.3348611111111[/C][C]0.75030017449084[/C][C]115.06709453946[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 24 )[/C][C]86.3331944444444[/C][C]0.750112871694158[/C][C]115.093604845705[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 24 )[/C][C]86.3769444444444[/C][C]0.739394701234179[/C][C]116.821156954826[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 24 )[/C][C]86.4869444444444[/C][C]0.714898726614408[/C][C]120.977896903001[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 24 )[/C][C]86.5294444444444[/C][C]0.705706088460248[/C][C]122.61399732747[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 24 )[/C][C]86.5363888888889[/C][C]0.704216267818734[/C][C]122.883257379058[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 24 )[/C][C]86.5409722222222[/C][C]0.703234399949539[/C][C]123.061346584342[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 24 )[/C][C]86.5343055555556[/C][C]0.702468591136438[/C][C]123.186013791111[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 24 )[/C][C]86.5288888888889[/C][C]0.701848903981598[/C][C]123.287061357522[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 24 )[/C][C]86.9255555555555[/C][C]0.614622226075457[/C][C]141.429242008706[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 24 )[/C][C]87.7838888888889[/C][C]0.447411244184097[/C][C]196.204029357761[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 24 )[/C][C]88.3816666666667[/C][C]0.344703042912921[/C][C]256.399438542217[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 24 )[/C][C]88.43125[/C][C]0.334100404813987[/C][C]264.68465385199[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 24 )[/C][C]88.47125[/C][C]0.321230879088497[/C][C]275.413279853543[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 24 )[/C][C]88.51875[/C][C]0.304959330358863[/C][C]290.264114548766[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 24 )[/C][C]88.2548611111111[/C][C]0.266477925654881[/C][C]331.19013852356[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 24 )[/C][C]88.1031944444444[/C][C]0.240752669077202[/C][C]365.948983170742[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 24 )[/C][C]88.0726388888889[/C][C]0.236082810947815[/C][C]373.058243992008[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 24 )[/C][C]88.0726388888889[/C][C]0.236082810947815[/C][C]373.058243992008[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 24 )[/C][C]88.0393055555556[/C][C]0.23194188792365[/C][C]379.574842404215[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 24 )[/C][C]86.4351428571429[/C][C]0.747137968939985[/C][C]115.68832859582[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 24 )[/C][C]86.5286764705882[/C][C]0.741195789662445[/C][C]116.741996753645[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 24 )[/C][C]86.6278787878788[/C][C]0.733549867856148[/C][C]118.094055474449[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 24 )[/C][C]86.7340625[/C][C]0.723938971777754[/C][C]119.80852790258[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 24 )[/C][C]86.8485483870968[/C][C]0.712004152076371[/C][C]121.977586975899[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 24 )[/C][C]86.9718333333333[/C][C]0.697142938259686[/C][C]124.754664445782[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 24 )[/C][C]87.1039655172414[/C][C]0.678490056065663[/C][C]128.379133545933[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 24 )[/C][C]87.2375[/C][C]0.658028206181065[/C][C]132.574104241354[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 24 )[/C][C]87.3625925925926[/C][C]0.638791890468332[/C][C]136.762213008907[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 24 )[/C][C]87.4907692307692[/C][C]0.616616249589203[/C][C]141.888523516947[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 24 )[/C][C]87.6282[/C][C]0.588373037992679[/C][C]148.933065150226[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 24 )[/C][C]87.7764583333333[/C][C]0.551687650089191[/C][C]159.105353036528[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 24 )[/C][C]87.9384782608696[/C][C]0.502733587152613[/C][C]174.920634921045[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 24 )[/C][C]88.1159090909091[/C][C]0.434582047297369[/C][C]202.760122372507[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 24 )[/C][C]88.2616666666667[/C][C]0.370777335290962[/C][C]238.044934967248[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 24 )[/C][C]88.319[/C][C]0.342565883612751[/C][C]257.816099690298[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 24 )[/C][C]88.3115789473684[/C][C]0.333658441192789[/C][C]264.676591521752[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 24 )[/C][C]88.2975[/C][C]0.323793333803945[/C][C]272.697090340543[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 24 )[/C][C]88.2770588235294[/C][C]0.313111157647081[/C][C]281.935206291913[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 24 )[/C][C]88.2484375[/C][C]0.302074850988622[/C][C]292.140961788719[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 24 )[/C][C]88.2476666666667[/C][C]0.29729573624469[/C][C]296.834619229232[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 24 )[/C][C]88.2653571428571[/C][C]0.296287648978596[/C][C]297.904274603203[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 24 )[/C][C]88.2896153846154[/C][C]0.294293145725995[/C][C]300.005680277781[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 24 )[/C][C]88.3179166666667[/C][C]0.289266926506525[/C][C]305.316330951767[/C][/ROW]
[ROW][C]Median[/C][C]88.01[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]83.27[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]88.2105405405405[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]88.2975[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]88.2105405405405[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]88.2975[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]88.2975[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]88.2105405405405[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]88.2975[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]88.3115789473684[/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=179233&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=179233&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 Mean86.34722222222220.751759938786479114.860100634795
Geometric Mean86.102355642114
Harmonic Mean85.8449282139611
Quadratic Mean86.5792581331631
Winsorized Mean ( 1 / 24 )86.34680555555560.751663044722047114.874352493257
Winsorized Mean ( 2 / 24 )86.34680555555550.751663044722047114.874352493257
Winsorized Mean ( 3 / 24 )86.34472222222220.75142217722669114.908402811451
Winsorized Mean ( 4 / 24 )86.33972222222220.750850013159896114.989306398049
Winsorized Mean ( 5 / 24 )86.33486111111110.75030017449084115.06709453946
Winsorized Mean ( 6 / 24 )86.33319444444440.750112871694158115.093604845705
Winsorized Mean ( 7 / 24 )86.37694444444440.739394701234179116.821156954826
Winsorized Mean ( 8 / 24 )86.48694444444440.714898726614408120.977896903001
Winsorized Mean ( 9 / 24 )86.52944444444440.705706088460248122.61399732747
Winsorized Mean ( 10 / 24 )86.53638888888890.704216267818734122.883257379058
Winsorized Mean ( 11 / 24 )86.54097222222220.703234399949539123.061346584342
Winsorized Mean ( 12 / 24 )86.53430555555560.702468591136438123.186013791111
Winsorized Mean ( 13 / 24 )86.52888888888890.701848903981598123.287061357522
Winsorized Mean ( 14 / 24 )86.92555555555550.614622226075457141.429242008706
Winsorized Mean ( 15 / 24 )87.78388888888890.447411244184097196.204029357761
Winsorized Mean ( 16 / 24 )88.38166666666670.344703042912921256.399438542217
Winsorized Mean ( 17 / 24 )88.431250.334100404813987264.68465385199
Winsorized Mean ( 18 / 24 )88.471250.321230879088497275.413279853543
Winsorized Mean ( 19 / 24 )88.518750.304959330358863290.264114548766
Winsorized Mean ( 20 / 24 )88.25486111111110.266477925654881331.19013852356
Winsorized Mean ( 21 / 24 )88.10319444444440.240752669077202365.948983170742
Winsorized Mean ( 22 / 24 )88.07263888888890.236082810947815373.058243992008
Winsorized Mean ( 23 / 24 )88.07263888888890.236082810947815373.058243992008
Winsorized Mean ( 24 / 24 )88.03930555555560.23194188792365379.574842404215
Trimmed Mean ( 1 / 24 )86.43514285714290.747137968939985115.68832859582
Trimmed Mean ( 2 / 24 )86.52867647058820.741195789662445116.741996753645
Trimmed Mean ( 3 / 24 )86.62787878787880.733549867856148118.094055474449
Trimmed Mean ( 4 / 24 )86.73406250.723938971777754119.80852790258
Trimmed Mean ( 5 / 24 )86.84854838709680.712004152076371121.977586975899
Trimmed Mean ( 6 / 24 )86.97183333333330.697142938259686124.754664445782
Trimmed Mean ( 7 / 24 )87.10396551724140.678490056065663128.379133545933
Trimmed Mean ( 8 / 24 )87.23750.658028206181065132.574104241354
Trimmed Mean ( 9 / 24 )87.36259259259260.638791890468332136.762213008907
Trimmed Mean ( 10 / 24 )87.49076923076920.616616249589203141.888523516947
Trimmed Mean ( 11 / 24 )87.62820.588373037992679148.933065150226
Trimmed Mean ( 12 / 24 )87.77645833333330.551687650089191159.105353036528
Trimmed Mean ( 13 / 24 )87.93847826086960.502733587152613174.920634921045
Trimmed Mean ( 14 / 24 )88.11590909090910.434582047297369202.760122372507
Trimmed Mean ( 15 / 24 )88.26166666666670.370777335290962238.044934967248
Trimmed Mean ( 16 / 24 )88.3190.342565883612751257.816099690298
Trimmed Mean ( 17 / 24 )88.31157894736840.333658441192789264.676591521752
Trimmed Mean ( 18 / 24 )88.29750.323793333803945272.697090340543
Trimmed Mean ( 19 / 24 )88.27705882352940.313111157647081281.935206291913
Trimmed Mean ( 20 / 24 )88.24843750.302074850988622292.140961788719
Trimmed Mean ( 21 / 24 )88.24766666666670.29729573624469296.834619229232
Trimmed Mean ( 22 / 24 )88.26535714285710.296287648978596297.904274603203
Trimmed Mean ( 23 / 24 )88.28961538461540.294293145725995300.005680277781
Trimmed Mean ( 24 / 24 )88.31791666666670.289266926506525305.316330951767
Median88.01
Midrange83.27
Midmean - Weighted Average at Xnp88.2105405405405
Midmean - Weighted Average at X(n+1)p88.2975
Midmean - Empirical Distribution Function88.2105405405405
Midmean - Empirical Distribution Function - Averaging88.2975
Midmean - Empirical Distribution Function - Interpolation88.2975
Midmean - Closest Observation88.2105405405405
Midmean - True Basic - Statistics Graphics Toolkit88.2975
Midmean - MS Excel (old versions)88.3115789473684
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')