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Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationSun, 15 Jan 2012 10:41:57 -0500
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/Jan/15/t132664274891ueelnq7mhb5q8.htm/, Retrieved Fri, 03 May 2024 06:34:04 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=161092, Retrieved Fri, 03 May 2024 06:34:04 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsKDG2011W52a
Estimated Impact110
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [] [2012-01-15 15:41:57] [618e20b48371a4632e04cdc6ff96552f] [Current]
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Dataseries X:
100.7
100.6
100.3
99.9
99.7
99.5
99.3
99
98.8
98.9
99.2
99.6
99.8
99.9
100
100.2
100.2
100.2
100.2
100.1
100.2
100.1
99.9
99.8
99.9
99.8
99.8
99.9
99.9
99.9
99.9
100
100.1
100.2
100.4
100.6
101
101.3
101.5
101.6
101.7
102.1
102.6
102.8
102.8
102.5
102.1
101.8
101.5
101.3
101.5
101.7
101.9
102
101.9
102
102.3
102.8
103.6
104.2
104.4
104.6
104.8
105.2
105.8
106.1
106.2
106.4
106.9
107.4
108
108.5
108.9




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'AstonUniversity' @ aston.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 & 'AstonUniversity' @ aston.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=161092&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]'AstonUniversity' @ aston.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=161092&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=161092&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'AstonUniversity' @ aston.wessa.net







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean101.7835616438360.293537792604852346.747724511413
Geometric Mean101.753673419507
Harmonic Mean101.724363394465
Quadratic Mean101.814032727684
Winsorized Mean ( 1 / 24 )101.7794520547950.291547326557703349.100961605458
Winsorized Mean ( 2 / 24 )101.7684931506850.286915819783508354.698089591136
Winsorized Mean ( 3 / 24 )101.7520547945210.278648548635965365.162694342444
Winsorized Mean ( 4 / 24 )101.7301369863010.270461616575701376.135210142943
Winsorized Mean ( 5 / 24 )101.7095890410960.259955244242132391.258077280256
Winsorized Mean ( 6 / 24 )101.7013698630140.254924804255145398.946544884759
Winsorized Mean ( 7 / 24 )101.7013698630140.251506065895458404.369451293025
Winsorized Mean ( 8 / 24 )101.6794520547950.242434686587318419.409670646171
Winsorized Mean ( 9 / 24 )101.6054794520550.225495314869294450.587984548368
Winsorized Mean ( 10 / 24 )101.5506849315070.213634591154058475.347575422725
Winsorized Mean ( 11 / 24 )101.5205479452050.207342015044834489.6284427604
Winsorized Mean ( 12 / 24 )101.5041095890410.198754094528766510.701979899841
Winsorized Mean ( 13 / 24 )101.4684931506850.191623250118638529.52078147022
Winsorized Mean ( 14 / 24 )101.3534246575340.169598440048091597.608236424786
Winsorized Mean ( 15 / 24 )101.189041095890.141267388496591716.294412834934
Winsorized Mean ( 16 / 24 )101.189041095890.141267388496591716.294412834934
Winsorized Mean ( 17 / 24 )101.189041095890.141267388496591716.294412834934
Winsorized Mean ( 18 / 24 )101.1397260273970.133614710606711756.950530133599
Winsorized Mean ( 19 / 24 )101.1136986301370.12970689162104779.555329454332
Winsorized Mean ( 20 / 24 )101.0863013698630.118194739542221855.252118337752
Winsorized Mean ( 21 / 24 )101.0287671232880.110200444397534916.77277415361
Winsorized Mean ( 22 / 24 )101.0589041095890.106358638012634950.171100325533
Winsorized Mean ( 23 / 24 )101.0273972602740.102132145612062989.183147527473
Winsorized Mean ( 24 / 24 )101.0273972602740.102132145612062989.183147527473
Trimmed Mean ( 1 / 24 )101.7253521126760.281235548682046361.70872633062
Trimmed Mean ( 2 / 24 )101.6681159420290.268790768462516378.242588179538
Trimmed Mean ( 3 / 24 )101.6134328358210.256783988667064395.715610475889
Trimmed Mean ( 4 / 24 )101.5615384615380.24616962088877412.567310681395
Trimmed Mean ( 5 / 24 )101.5126984126980.236423384440179429.368265127697
Trimmed Mean ( 6 / 24 )101.4655737704920.227997762019282445.028814633324
Trimmed Mean ( 7 / 24 )101.4169491525420.219067047671815462.949358337433
Trimmed Mean ( 8 / 24 )101.3649122807020.208820101432655485.417407544896
Trimmed Mean ( 9 / 24 )101.3127272727270.198412123310199510.617625488208
Trimmed Mean ( 10 / 24 )101.2679245283020.189927294639166533.193108029555
Trimmed Mean ( 11 / 24 )101.2274509803920.182253398932721555.421471276704
Trimmed Mean ( 12 / 24 )101.1877551020410.174004277379721581.524527016216
Trimmed Mean ( 13 / 24 )101.1468085106380.165415158022212611.472429250145
Trimmed Mean ( 14 / 24 )101.1066666666670.156036773702466647.966913616521
Trimmed Mean ( 15 / 24 )101.0767441860470.149744603886617674.994233932995
Trimmed Mean ( 16 / 24 )101.0634146341460.1484372289753680.849510138482
Trimmed Mean ( 17 / 24 )101.0487179487180.146385686327464690.29097368627
Trimmed Mean ( 18 / 24 )101.0324324324320.14332254589901704.930489468304
Trimmed Mean ( 19 / 24 )101.020.14087362475375717.096618877982
Trimmed Mean ( 20 / 24 )101.0090909090910.138194776106952730.918300637627
Trimmed Mean ( 21 / 24 )1010.137097406703158736.702483502726
Trimmed Mean ( 22 / 24 )100.9965517241380.137131302242401736.495242680701
Trimmed Mean ( 23 / 24 )100.9888888888890.137367738339692735.171810422885
Trimmed Mean ( 24 / 24 )100.9840.138043471413899731.537674079618
Median101
Midrange103.85
Midmean - Weighted Average at Xnp100.833333333333
Midmean - Weighted Average at X(n+1)p100.874418604651
Midmean - Empirical Distribution Function100.874418604651
Midmean - Empirical Distribution Function - Averaging100.874418604651
Midmean - Empirical Distribution Function - Interpolation100.874418604651
Midmean - Closest Observation100.874418604651
Midmean - True Basic - Statistics Graphics Toolkit100.874418604651
Midmean - MS Excel (old versions)100.874418604651
Number of observations73

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 101.783561643836 & 0.293537792604852 & 346.747724511413 \tabularnewline
Geometric Mean & 101.753673419507 &  &  \tabularnewline
Harmonic Mean & 101.724363394465 &  &  \tabularnewline
Quadratic Mean & 101.814032727684 &  &  \tabularnewline
Winsorized Mean ( 1 / 24 ) & 101.779452054795 & 0.291547326557703 & 349.100961605458 \tabularnewline
Winsorized Mean ( 2 / 24 ) & 101.768493150685 & 0.286915819783508 & 354.698089591136 \tabularnewline
Winsorized Mean ( 3 / 24 ) & 101.752054794521 & 0.278648548635965 & 365.162694342444 \tabularnewline
Winsorized Mean ( 4 / 24 ) & 101.730136986301 & 0.270461616575701 & 376.135210142943 \tabularnewline
Winsorized Mean ( 5 / 24 ) & 101.709589041096 & 0.259955244242132 & 391.258077280256 \tabularnewline
Winsorized Mean ( 6 / 24 ) & 101.701369863014 & 0.254924804255145 & 398.946544884759 \tabularnewline
Winsorized Mean ( 7 / 24 ) & 101.701369863014 & 0.251506065895458 & 404.369451293025 \tabularnewline
Winsorized Mean ( 8 / 24 ) & 101.679452054795 & 0.242434686587318 & 419.409670646171 \tabularnewline
Winsorized Mean ( 9 / 24 ) & 101.605479452055 & 0.225495314869294 & 450.587984548368 \tabularnewline
Winsorized Mean ( 10 / 24 ) & 101.550684931507 & 0.213634591154058 & 475.347575422725 \tabularnewline
Winsorized Mean ( 11 / 24 ) & 101.520547945205 & 0.207342015044834 & 489.6284427604 \tabularnewline
Winsorized Mean ( 12 / 24 ) & 101.504109589041 & 0.198754094528766 & 510.701979899841 \tabularnewline
Winsorized Mean ( 13 / 24 ) & 101.468493150685 & 0.191623250118638 & 529.52078147022 \tabularnewline
Winsorized Mean ( 14 / 24 ) & 101.353424657534 & 0.169598440048091 & 597.608236424786 \tabularnewline
Winsorized Mean ( 15 / 24 ) & 101.18904109589 & 0.141267388496591 & 716.294412834934 \tabularnewline
Winsorized Mean ( 16 / 24 ) & 101.18904109589 & 0.141267388496591 & 716.294412834934 \tabularnewline
Winsorized Mean ( 17 / 24 ) & 101.18904109589 & 0.141267388496591 & 716.294412834934 \tabularnewline
Winsorized Mean ( 18 / 24 ) & 101.139726027397 & 0.133614710606711 & 756.950530133599 \tabularnewline
Winsorized Mean ( 19 / 24 ) & 101.113698630137 & 0.12970689162104 & 779.555329454332 \tabularnewline
Winsorized Mean ( 20 / 24 ) & 101.086301369863 & 0.118194739542221 & 855.252118337752 \tabularnewline
Winsorized Mean ( 21 / 24 ) & 101.028767123288 & 0.110200444397534 & 916.77277415361 \tabularnewline
Winsorized Mean ( 22 / 24 ) & 101.058904109589 & 0.106358638012634 & 950.171100325533 \tabularnewline
Winsorized Mean ( 23 / 24 ) & 101.027397260274 & 0.102132145612062 & 989.183147527473 \tabularnewline
Winsorized Mean ( 24 / 24 ) & 101.027397260274 & 0.102132145612062 & 989.183147527473 \tabularnewline
Trimmed Mean ( 1 / 24 ) & 101.725352112676 & 0.281235548682046 & 361.70872633062 \tabularnewline
Trimmed Mean ( 2 / 24 ) & 101.668115942029 & 0.268790768462516 & 378.242588179538 \tabularnewline
Trimmed Mean ( 3 / 24 ) & 101.613432835821 & 0.256783988667064 & 395.715610475889 \tabularnewline
Trimmed Mean ( 4 / 24 ) & 101.561538461538 & 0.24616962088877 & 412.567310681395 \tabularnewline
Trimmed Mean ( 5 / 24 ) & 101.512698412698 & 0.236423384440179 & 429.368265127697 \tabularnewline
Trimmed Mean ( 6 / 24 ) & 101.465573770492 & 0.227997762019282 & 445.028814633324 \tabularnewline
Trimmed Mean ( 7 / 24 ) & 101.416949152542 & 0.219067047671815 & 462.949358337433 \tabularnewline
Trimmed Mean ( 8 / 24 ) & 101.364912280702 & 0.208820101432655 & 485.417407544896 \tabularnewline
Trimmed Mean ( 9 / 24 ) & 101.312727272727 & 0.198412123310199 & 510.617625488208 \tabularnewline
Trimmed Mean ( 10 / 24 ) & 101.267924528302 & 0.189927294639166 & 533.193108029555 \tabularnewline
Trimmed Mean ( 11 / 24 ) & 101.227450980392 & 0.182253398932721 & 555.421471276704 \tabularnewline
Trimmed Mean ( 12 / 24 ) & 101.187755102041 & 0.174004277379721 & 581.524527016216 \tabularnewline
Trimmed Mean ( 13 / 24 ) & 101.146808510638 & 0.165415158022212 & 611.472429250145 \tabularnewline
Trimmed Mean ( 14 / 24 ) & 101.106666666667 & 0.156036773702466 & 647.966913616521 \tabularnewline
Trimmed Mean ( 15 / 24 ) & 101.076744186047 & 0.149744603886617 & 674.994233932995 \tabularnewline
Trimmed Mean ( 16 / 24 ) & 101.063414634146 & 0.1484372289753 & 680.849510138482 \tabularnewline
Trimmed Mean ( 17 / 24 ) & 101.048717948718 & 0.146385686327464 & 690.29097368627 \tabularnewline
Trimmed Mean ( 18 / 24 ) & 101.032432432432 & 0.14332254589901 & 704.930489468304 \tabularnewline
Trimmed Mean ( 19 / 24 ) & 101.02 & 0.14087362475375 & 717.096618877982 \tabularnewline
Trimmed Mean ( 20 / 24 ) & 101.009090909091 & 0.138194776106952 & 730.918300637627 \tabularnewline
Trimmed Mean ( 21 / 24 ) & 101 & 0.137097406703158 & 736.702483502726 \tabularnewline
Trimmed Mean ( 22 / 24 ) & 100.996551724138 & 0.137131302242401 & 736.495242680701 \tabularnewline
Trimmed Mean ( 23 / 24 ) & 100.988888888889 & 0.137367738339692 & 735.171810422885 \tabularnewline
Trimmed Mean ( 24 / 24 ) & 100.984 & 0.138043471413899 & 731.537674079618 \tabularnewline
Median & 101 &  &  \tabularnewline
Midrange & 103.85 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 100.833333333333 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 100.874418604651 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 100.874418604651 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 100.874418604651 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 100.874418604651 &  &  \tabularnewline
Midmean - Closest Observation & 100.874418604651 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 100.874418604651 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 100.874418604651 &  &  \tabularnewline
Number of observations & 73 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=161092&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]101.783561643836[/C][C]0.293537792604852[/C][C]346.747724511413[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]101.753673419507[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]101.724363394465[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]101.814032727684[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 24 )[/C][C]101.779452054795[/C][C]0.291547326557703[/C][C]349.100961605458[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 24 )[/C][C]101.768493150685[/C][C]0.286915819783508[/C][C]354.698089591136[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 24 )[/C][C]101.752054794521[/C][C]0.278648548635965[/C][C]365.162694342444[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 24 )[/C][C]101.730136986301[/C][C]0.270461616575701[/C][C]376.135210142943[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 24 )[/C][C]101.709589041096[/C][C]0.259955244242132[/C][C]391.258077280256[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 24 )[/C][C]101.701369863014[/C][C]0.254924804255145[/C][C]398.946544884759[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 24 )[/C][C]101.701369863014[/C][C]0.251506065895458[/C][C]404.369451293025[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 24 )[/C][C]101.679452054795[/C][C]0.242434686587318[/C][C]419.409670646171[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 24 )[/C][C]101.605479452055[/C][C]0.225495314869294[/C][C]450.587984548368[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 24 )[/C][C]101.550684931507[/C][C]0.213634591154058[/C][C]475.347575422725[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 24 )[/C][C]101.520547945205[/C][C]0.207342015044834[/C][C]489.6284427604[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 24 )[/C][C]101.504109589041[/C][C]0.198754094528766[/C][C]510.701979899841[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 24 )[/C][C]101.468493150685[/C][C]0.191623250118638[/C][C]529.52078147022[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 24 )[/C][C]101.353424657534[/C][C]0.169598440048091[/C][C]597.608236424786[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 24 )[/C][C]101.18904109589[/C][C]0.141267388496591[/C][C]716.294412834934[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 24 )[/C][C]101.18904109589[/C][C]0.141267388496591[/C][C]716.294412834934[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 24 )[/C][C]101.18904109589[/C][C]0.141267388496591[/C][C]716.294412834934[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 24 )[/C][C]101.139726027397[/C][C]0.133614710606711[/C][C]756.950530133599[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 24 )[/C][C]101.113698630137[/C][C]0.12970689162104[/C][C]779.555329454332[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 24 )[/C][C]101.086301369863[/C][C]0.118194739542221[/C][C]855.252118337752[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 24 )[/C][C]101.028767123288[/C][C]0.110200444397534[/C][C]916.77277415361[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 24 )[/C][C]101.058904109589[/C][C]0.106358638012634[/C][C]950.171100325533[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 24 )[/C][C]101.027397260274[/C][C]0.102132145612062[/C][C]989.183147527473[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 24 )[/C][C]101.027397260274[/C][C]0.102132145612062[/C][C]989.183147527473[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 24 )[/C][C]101.725352112676[/C][C]0.281235548682046[/C][C]361.70872633062[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 24 )[/C][C]101.668115942029[/C][C]0.268790768462516[/C][C]378.242588179538[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 24 )[/C][C]101.613432835821[/C][C]0.256783988667064[/C][C]395.715610475889[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 24 )[/C][C]101.561538461538[/C][C]0.24616962088877[/C][C]412.567310681395[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 24 )[/C][C]101.512698412698[/C][C]0.236423384440179[/C][C]429.368265127697[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 24 )[/C][C]101.465573770492[/C][C]0.227997762019282[/C][C]445.028814633324[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 24 )[/C][C]101.416949152542[/C][C]0.219067047671815[/C][C]462.949358337433[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 24 )[/C][C]101.364912280702[/C][C]0.208820101432655[/C][C]485.417407544896[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 24 )[/C][C]101.312727272727[/C][C]0.198412123310199[/C][C]510.617625488208[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 24 )[/C][C]101.267924528302[/C][C]0.189927294639166[/C][C]533.193108029555[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 24 )[/C][C]101.227450980392[/C][C]0.182253398932721[/C][C]555.421471276704[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 24 )[/C][C]101.187755102041[/C][C]0.174004277379721[/C][C]581.524527016216[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 24 )[/C][C]101.146808510638[/C][C]0.165415158022212[/C][C]611.472429250145[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 24 )[/C][C]101.106666666667[/C][C]0.156036773702466[/C][C]647.966913616521[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 24 )[/C][C]101.076744186047[/C][C]0.149744603886617[/C][C]674.994233932995[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 24 )[/C][C]101.063414634146[/C][C]0.1484372289753[/C][C]680.849510138482[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 24 )[/C][C]101.048717948718[/C][C]0.146385686327464[/C][C]690.29097368627[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 24 )[/C][C]101.032432432432[/C][C]0.14332254589901[/C][C]704.930489468304[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 24 )[/C][C]101.02[/C][C]0.14087362475375[/C][C]717.096618877982[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 24 )[/C][C]101.009090909091[/C][C]0.138194776106952[/C][C]730.918300637627[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 24 )[/C][C]101[/C][C]0.137097406703158[/C][C]736.702483502726[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 24 )[/C][C]100.996551724138[/C][C]0.137131302242401[/C][C]736.495242680701[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 24 )[/C][C]100.988888888889[/C][C]0.137367738339692[/C][C]735.171810422885[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 24 )[/C][C]100.984[/C][C]0.138043471413899[/C][C]731.537674079618[/C][/ROW]
[ROW][C]Median[/C][C]101[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]103.85[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]100.833333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]100.874418604651[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]100.874418604651[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]100.874418604651[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]100.874418604651[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]100.874418604651[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]100.874418604651[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]100.874418604651[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]73[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=161092&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=161092&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 Mean101.7835616438360.293537792604852346.747724511413
Geometric Mean101.753673419507
Harmonic Mean101.724363394465
Quadratic Mean101.814032727684
Winsorized Mean ( 1 / 24 )101.7794520547950.291547326557703349.100961605458
Winsorized Mean ( 2 / 24 )101.7684931506850.286915819783508354.698089591136
Winsorized Mean ( 3 / 24 )101.7520547945210.278648548635965365.162694342444
Winsorized Mean ( 4 / 24 )101.7301369863010.270461616575701376.135210142943
Winsorized Mean ( 5 / 24 )101.7095890410960.259955244242132391.258077280256
Winsorized Mean ( 6 / 24 )101.7013698630140.254924804255145398.946544884759
Winsorized Mean ( 7 / 24 )101.7013698630140.251506065895458404.369451293025
Winsorized Mean ( 8 / 24 )101.6794520547950.242434686587318419.409670646171
Winsorized Mean ( 9 / 24 )101.6054794520550.225495314869294450.587984548368
Winsorized Mean ( 10 / 24 )101.5506849315070.213634591154058475.347575422725
Winsorized Mean ( 11 / 24 )101.5205479452050.207342015044834489.6284427604
Winsorized Mean ( 12 / 24 )101.5041095890410.198754094528766510.701979899841
Winsorized Mean ( 13 / 24 )101.4684931506850.191623250118638529.52078147022
Winsorized Mean ( 14 / 24 )101.3534246575340.169598440048091597.608236424786
Winsorized Mean ( 15 / 24 )101.189041095890.141267388496591716.294412834934
Winsorized Mean ( 16 / 24 )101.189041095890.141267388496591716.294412834934
Winsorized Mean ( 17 / 24 )101.189041095890.141267388496591716.294412834934
Winsorized Mean ( 18 / 24 )101.1397260273970.133614710606711756.950530133599
Winsorized Mean ( 19 / 24 )101.1136986301370.12970689162104779.555329454332
Winsorized Mean ( 20 / 24 )101.0863013698630.118194739542221855.252118337752
Winsorized Mean ( 21 / 24 )101.0287671232880.110200444397534916.77277415361
Winsorized Mean ( 22 / 24 )101.0589041095890.106358638012634950.171100325533
Winsorized Mean ( 23 / 24 )101.0273972602740.102132145612062989.183147527473
Winsorized Mean ( 24 / 24 )101.0273972602740.102132145612062989.183147527473
Trimmed Mean ( 1 / 24 )101.7253521126760.281235548682046361.70872633062
Trimmed Mean ( 2 / 24 )101.6681159420290.268790768462516378.242588179538
Trimmed Mean ( 3 / 24 )101.6134328358210.256783988667064395.715610475889
Trimmed Mean ( 4 / 24 )101.5615384615380.24616962088877412.567310681395
Trimmed Mean ( 5 / 24 )101.5126984126980.236423384440179429.368265127697
Trimmed Mean ( 6 / 24 )101.4655737704920.227997762019282445.028814633324
Trimmed Mean ( 7 / 24 )101.4169491525420.219067047671815462.949358337433
Trimmed Mean ( 8 / 24 )101.3649122807020.208820101432655485.417407544896
Trimmed Mean ( 9 / 24 )101.3127272727270.198412123310199510.617625488208
Trimmed Mean ( 10 / 24 )101.2679245283020.189927294639166533.193108029555
Trimmed Mean ( 11 / 24 )101.2274509803920.182253398932721555.421471276704
Trimmed Mean ( 12 / 24 )101.1877551020410.174004277379721581.524527016216
Trimmed Mean ( 13 / 24 )101.1468085106380.165415158022212611.472429250145
Trimmed Mean ( 14 / 24 )101.1066666666670.156036773702466647.966913616521
Trimmed Mean ( 15 / 24 )101.0767441860470.149744603886617674.994233932995
Trimmed Mean ( 16 / 24 )101.0634146341460.1484372289753680.849510138482
Trimmed Mean ( 17 / 24 )101.0487179487180.146385686327464690.29097368627
Trimmed Mean ( 18 / 24 )101.0324324324320.14332254589901704.930489468304
Trimmed Mean ( 19 / 24 )101.020.14087362475375717.096618877982
Trimmed Mean ( 20 / 24 )101.0090909090910.138194776106952730.918300637627
Trimmed Mean ( 21 / 24 )1010.137097406703158736.702483502726
Trimmed Mean ( 22 / 24 )100.9965517241380.137131302242401736.495242680701
Trimmed Mean ( 23 / 24 )100.9888888888890.137367738339692735.171810422885
Trimmed Mean ( 24 / 24 )100.9840.138043471413899731.537674079618
Median101
Midrange103.85
Midmean - Weighted Average at Xnp100.833333333333
Midmean - Weighted Average at X(n+1)p100.874418604651
Midmean - Empirical Distribution Function100.874418604651
Midmean - Empirical Distribution Function - Averaging100.874418604651
Midmean - Empirical Distribution Function - Interpolation100.874418604651
Midmean - Closest Observation100.874418604651
Midmean - True Basic - Statistics Graphics Toolkit100.874418604651
Midmean - MS Excel (old versions)100.874418604651
Number of observations73



Parameters (Session):
par2 = grey ; par3 = FALSE ; par4 = Unknown ;
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')