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Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationThu, 29 Nov 2007 02:47:47 -0700
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2007/Nov/29/t1196329066anh67r34twifzrg.htm/, Retrieved Fri, 03 May 2024 04:18:37 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=7318, Retrieved Fri, 03 May 2024 04:18:37 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact265
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [Central Tendency ...] [2007-11-29 09:47:47] [7c5c775a3769ba2649d285a4261e023c] [Current]
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Dataseries X:
102,3
98,7
104,4
97,6
102,7
103,0
92,9
96,1
94,9
99,9
96,3
89,5
104,6
101,5
109,8
112,1
110,1
107,1
108,1
99,0
104,0
106,7
101,1
97,8
113,8
107,1
117,5
113,7
106,6
109,8
108,8
102,0
114,5
116,5
108,6
113,9
109,3
112,5
123,4
115,2
110,8
120,4
117,6
111,2
131,1
118,9
115,7
119,6
113,1
106,4
115,5
111,8
109,6
121,5
109,5
109,0
113,4
112,7
114,4
109,2
116,2
113,8
123,6
112,6
117,7
113,3
110,7
114,7
116,9
120,6
111,6
111,9
116,1
111,9
125,1
115,1
116,7
115,8
116,8
113,0
106,5




Summary of compuational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135

\begin{tabular}{lllllllll}
\hline
Summary of compuational 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 & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=7318&T=0

[TABLE]
[ROW][C]Summary of compuational 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]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=7318&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=7318&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 compuational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean110.4370370370370.865059843153027127.664043026791
Geometric Mean110.160001355186
Harmonic Mean109.876459911879
Quadratic Mean110.707747841327
Winsorized Mean ( 1 / 27 )110.4049382716050.833918130426986132.393018263166
Winsorized Mean ( 2 / 27 )110.4172839506170.813713083256329135.695598636251
Winsorized Mean ( 3 / 27 )110.4543209876540.801944106497862137.733191244481
Winsorized Mean ( 4 / 27 )110.3703703703700.781900668686714141.156511038351
Winsorized Mean ( 5 / 27 )110.3950617283950.754721560206163146.272569314489
Winsorized Mean ( 6 / 27 )110.3950617283950.749106260149774147.369028402357
Winsorized Mean ( 7 / 27 )110.4037037037040.721763624579962152.963795824366
Winsorized Mean ( 8 / 27 )110.3641975308640.705035479017023156.537083331943
Winsorized Mean ( 9 / 27 )110.3308641975310.665825028862384165.705492306350
Winsorized Mean ( 10 / 27 )110.4666666666670.635942481287555173.705437075081
Winsorized Mean ( 11 / 27 )110.5074074074070.624138363542086177.05594442274
Winsorized Mean ( 12 / 27 )110.4925925925930.598712037838225184.55047770803
Winsorized Mean ( 13 / 27 )110.5246913580250.588090472548097187.938245078414
Winsorized Mean ( 14 / 27 )110.5765432098770.573809211433864192.706113820589
Winsorized Mean ( 15 / 27 )110.5950617283950.559414103873744197.698021845648
Winsorized Mean ( 16 / 27 )110.7333333333330.5187889506424213.445820687229
Winsorized Mean ( 17 / 27 )110.7962962962960.50253199776646220.476102593941
Winsorized Mean ( 18 / 27 )110.7740740740740.486771861340753227.568770653588
Winsorized Mean ( 19 / 27 )111.1728395061730.419964770515716264.719441513279
Winsorized Mean ( 20 / 27 )111.1481481481480.409855858097709271.188384775143
Winsorized Mean ( 21 / 27 )111.0962962962960.39597685290735280.562602284963
Winsorized Mean ( 22 / 27 )111.0962962962960.388620718825099285.873323049191
Winsorized Mean ( 23 / 27 )111.0962962962960.358203871723103310.148228610369
Winsorized Mean ( 24 / 27 )111.0370370370370.350821102296009316.506151740406
Winsorized Mean ( 25 / 27 )111.3148148148150.30488872242014365.099810616877
Winsorized Mean ( 26 / 27 )111.3148148148150.26398016615025421.678705783743
Winsorized Mean ( 27 / 27 )111.3481481481480.251398011566279442.915787020027
Trimmed Mean ( 1 / 27 )110.4405063291140.804064082625867137.352866165149
Trimmed Mean ( 2 / 27 )110.4779220779220.769058650372203143.653441807662
Trimmed Mean ( 3 / 27 )110.5106666666670.740857971904558149.1657927127
Trimmed Mean ( 4 / 27 )110.5315068493150.713054710000085155.011256919265
Trimmed Mean ( 5 / 27 )110.5774647887320.687544246779853160.829597959153
Trimmed Mean ( 6 / 27 )110.6202898550720.665879478911462166.126594013541
Trimmed Mean ( 7 / 27 )110.6656716417910.641591588077948172.486163625241
Trimmed Mean ( 8 / 27 )110.7123076923080.619617234872852178.678547757030
Trimmed Mean ( 9 / 27 )110.7682539682540.597124983365689185.502628518254
Trimmed Mean ( 10 / 27 )110.8327868852460.578837733670353191.474709470763
Trimmed Mean ( 11 / 27 )110.8830508474580.563247827678897196.863699065469
Trimmed Mean ( 12 / 27 )110.9315789473680.546595511759651202.950036289627
Trimmed Mean ( 13 / 27 )110.9854545454550.531216874946318208.926824014524
Trimmed Mean ( 14 / 27 )111.0396226415090.514205600215983215.944016546823
Trimmed Mean ( 15 / 27 )111.0921568627450.495856107664191224.041118271311
Trimmed Mean ( 16 / 27 )111.1469387755100.475640474404035233.678470939157
Trimmed Mean ( 17 / 27 )111.1914893617020.458951765751219242.272712862761
Trimmed Mean ( 18 / 27 )111.2333333333330.441015815470318252.220735473419
Trimmed Mean ( 19 / 27 )111.2813953488370.421031478924477264.306592070277
Trimmed Mean ( 20 / 27 )111.2926829268290.410819974873311270.903777162125
Trimmed Mean ( 21 / 27 )111.3076923076920.399145250982282278.865130009108
Trimmed Mean ( 22 / 27 )111.3297297297300.386305844090083288.190643328111
Trimmed Mean ( 23 / 27 )111.3542857142860.370222346481589300.776781230366
Trimmed Mean ( 24 / 27 )111.3818181818180.355941308190035312.921865540687
Trimmed Mean ( 25 / 27 )111.4193548387100.337110407709075330.512948549675
Trimmed Mean ( 26 / 27 )111.4310344827590.325027602021367342.835604698684
Trimmed Mean ( 27 / 27 )111.4444444444440.319514113547329348.793495245513
Median111.8
Midrange110.3
Midmean - Weighted Average at Xnp111.1875
Midmean - Weighted Average at X(n+1)p111.292682926829
Midmean - Empirical Distribution Function111.292682926829
Midmean - Empirical Distribution Function - Averaging111.292682926829
Midmean - Empirical Distribution Function - Interpolation111.292682926829
Midmean - Closest Observation111.176190476190
Midmean - True Basic - Statistics Graphics Toolkit111.292682926829
Midmean - MS Excel (old versions)111.292682926829
Number of observations81

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 110.437037037037 & 0.865059843153027 & 127.664043026791 \tabularnewline
Geometric Mean & 110.160001355186 &  &  \tabularnewline
Harmonic Mean & 109.876459911879 &  &  \tabularnewline
Quadratic Mean & 110.707747841327 &  &  \tabularnewline
Winsorized Mean ( 1 / 27 ) & 110.404938271605 & 0.833918130426986 & 132.393018263166 \tabularnewline
Winsorized Mean ( 2 / 27 ) & 110.417283950617 & 0.813713083256329 & 135.695598636251 \tabularnewline
Winsorized Mean ( 3 / 27 ) & 110.454320987654 & 0.801944106497862 & 137.733191244481 \tabularnewline
Winsorized Mean ( 4 / 27 ) & 110.370370370370 & 0.781900668686714 & 141.156511038351 \tabularnewline
Winsorized Mean ( 5 / 27 ) & 110.395061728395 & 0.754721560206163 & 146.272569314489 \tabularnewline
Winsorized Mean ( 6 / 27 ) & 110.395061728395 & 0.749106260149774 & 147.369028402357 \tabularnewline
Winsorized Mean ( 7 / 27 ) & 110.403703703704 & 0.721763624579962 & 152.963795824366 \tabularnewline
Winsorized Mean ( 8 / 27 ) & 110.364197530864 & 0.705035479017023 & 156.537083331943 \tabularnewline
Winsorized Mean ( 9 / 27 ) & 110.330864197531 & 0.665825028862384 & 165.705492306350 \tabularnewline
Winsorized Mean ( 10 / 27 ) & 110.466666666667 & 0.635942481287555 & 173.705437075081 \tabularnewline
Winsorized Mean ( 11 / 27 ) & 110.507407407407 & 0.624138363542086 & 177.05594442274 \tabularnewline
Winsorized Mean ( 12 / 27 ) & 110.492592592593 & 0.598712037838225 & 184.55047770803 \tabularnewline
Winsorized Mean ( 13 / 27 ) & 110.524691358025 & 0.588090472548097 & 187.938245078414 \tabularnewline
Winsorized Mean ( 14 / 27 ) & 110.576543209877 & 0.573809211433864 & 192.706113820589 \tabularnewline
Winsorized Mean ( 15 / 27 ) & 110.595061728395 & 0.559414103873744 & 197.698021845648 \tabularnewline
Winsorized Mean ( 16 / 27 ) & 110.733333333333 & 0.5187889506424 & 213.445820687229 \tabularnewline
Winsorized Mean ( 17 / 27 ) & 110.796296296296 & 0.50253199776646 & 220.476102593941 \tabularnewline
Winsorized Mean ( 18 / 27 ) & 110.774074074074 & 0.486771861340753 & 227.568770653588 \tabularnewline
Winsorized Mean ( 19 / 27 ) & 111.172839506173 & 0.419964770515716 & 264.719441513279 \tabularnewline
Winsorized Mean ( 20 / 27 ) & 111.148148148148 & 0.409855858097709 & 271.188384775143 \tabularnewline
Winsorized Mean ( 21 / 27 ) & 111.096296296296 & 0.39597685290735 & 280.562602284963 \tabularnewline
Winsorized Mean ( 22 / 27 ) & 111.096296296296 & 0.388620718825099 & 285.873323049191 \tabularnewline
Winsorized Mean ( 23 / 27 ) & 111.096296296296 & 0.358203871723103 & 310.148228610369 \tabularnewline
Winsorized Mean ( 24 / 27 ) & 111.037037037037 & 0.350821102296009 & 316.506151740406 \tabularnewline
Winsorized Mean ( 25 / 27 ) & 111.314814814815 & 0.30488872242014 & 365.099810616877 \tabularnewline
Winsorized Mean ( 26 / 27 ) & 111.314814814815 & 0.26398016615025 & 421.678705783743 \tabularnewline
Winsorized Mean ( 27 / 27 ) & 111.348148148148 & 0.251398011566279 & 442.915787020027 \tabularnewline
Trimmed Mean ( 1 / 27 ) & 110.440506329114 & 0.804064082625867 & 137.352866165149 \tabularnewline
Trimmed Mean ( 2 / 27 ) & 110.477922077922 & 0.769058650372203 & 143.653441807662 \tabularnewline
Trimmed Mean ( 3 / 27 ) & 110.510666666667 & 0.740857971904558 & 149.1657927127 \tabularnewline
Trimmed Mean ( 4 / 27 ) & 110.531506849315 & 0.713054710000085 & 155.011256919265 \tabularnewline
Trimmed Mean ( 5 / 27 ) & 110.577464788732 & 0.687544246779853 & 160.829597959153 \tabularnewline
Trimmed Mean ( 6 / 27 ) & 110.620289855072 & 0.665879478911462 & 166.126594013541 \tabularnewline
Trimmed Mean ( 7 / 27 ) & 110.665671641791 & 0.641591588077948 & 172.486163625241 \tabularnewline
Trimmed Mean ( 8 / 27 ) & 110.712307692308 & 0.619617234872852 & 178.678547757030 \tabularnewline
Trimmed Mean ( 9 / 27 ) & 110.768253968254 & 0.597124983365689 & 185.502628518254 \tabularnewline
Trimmed Mean ( 10 / 27 ) & 110.832786885246 & 0.578837733670353 & 191.474709470763 \tabularnewline
Trimmed Mean ( 11 / 27 ) & 110.883050847458 & 0.563247827678897 & 196.863699065469 \tabularnewline
Trimmed Mean ( 12 / 27 ) & 110.931578947368 & 0.546595511759651 & 202.950036289627 \tabularnewline
Trimmed Mean ( 13 / 27 ) & 110.985454545455 & 0.531216874946318 & 208.926824014524 \tabularnewline
Trimmed Mean ( 14 / 27 ) & 111.039622641509 & 0.514205600215983 & 215.944016546823 \tabularnewline
Trimmed Mean ( 15 / 27 ) & 111.092156862745 & 0.495856107664191 & 224.041118271311 \tabularnewline
Trimmed Mean ( 16 / 27 ) & 111.146938775510 & 0.475640474404035 & 233.678470939157 \tabularnewline
Trimmed Mean ( 17 / 27 ) & 111.191489361702 & 0.458951765751219 & 242.272712862761 \tabularnewline
Trimmed Mean ( 18 / 27 ) & 111.233333333333 & 0.441015815470318 & 252.220735473419 \tabularnewline
Trimmed Mean ( 19 / 27 ) & 111.281395348837 & 0.421031478924477 & 264.306592070277 \tabularnewline
Trimmed Mean ( 20 / 27 ) & 111.292682926829 & 0.410819974873311 & 270.903777162125 \tabularnewline
Trimmed Mean ( 21 / 27 ) & 111.307692307692 & 0.399145250982282 & 278.865130009108 \tabularnewline
Trimmed Mean ( 22 / 27 ) & 111.329729729730 & 0.386305844090083 & 288.190643328111 \tabularnewline
Trimmed Mean ( 23 / 27 ) & 111.354285714286 & 0.370222346481589 & 300.776781230366 \tabularnewline
Trimmed Mean ( 24 / 27 ) & 111.381818181818 & 0.355941308190035 & 312.921865540687 \tabularnewline
Trimmed Mean ( 25 / 27 ) & 111.419354838710 & 0.337110407709075 & 330.512948549675 \tabularnewline
Trimmed Mean ( 26 / 27 ) & 111.431034482759 & 0.325027602021367 & 342.835604698684 \tabularnewline
Trimmed Mean ( 27 / 27 ) & 111.444444444444 & 0.319514113547329 & 348.793495245513 \tabularnewline
Median & 111.8 &  &  \tabularnewline
Midrange & 110.3 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 111.1875 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 111.292682926829 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 111.292682926829 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 111.292682926829 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 111.292682926829 &  &  \tabularnewline
Midmean - Closest Observation & 111.176190476190 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 111.292682926829 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 111.292682926829 &  &  \tabularnewline
Number of observations & 81 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=7318&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]110.437037037037[/C][C]0.865059843153027[/C][C]127.664043026791[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]110.160001355186[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]109.876459911879[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]110.707747841327[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 27 )[/C][C]110.404938271605[/C][C]0.833918130426986[/C][C]132.393018263166[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 27 )[/C][C]110.417283950617[/C][C]0.813713083256329[/C][C]135.695598636251[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 27 )[/C][C]110.454320987654[/C][C]0.801944106497862[/C][C]137.733191244481[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 27 )[/C][C]110.370370370370[/C][C]0.781900668686714[/C][C]141.156511038351[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 27 )[/C][C]110.395061728395[/C][C]0.754721560206163[/C][C]146.272569314489[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 27 )[/C][C]110.395061728395[/C][C]0.749106260149774[/C][C]147.369028402357[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 27 )[/C][C]110.403703703704[/C][C]0.721763624579962[/C][C]152.963795824366[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 27 )[/C][C]110.364197530864[/C][C]0.705035479017023[/C][C]156.537083331943[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 27 )[/C][C]110.330864197531[/C][C]0.665825028862384[/C][C]165.705492306350[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 27 )[/C][C]110.466666666667[/C][C]0.635942481287555[/C][C]173.705437075081[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 27 )[/C][C]110.507407407407[/C][C]0.624138363542086[/C][C]177.05594442274[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 27 )[/C][C]110.492592592593[/C][C]0.598712037838225[/C][C]184.55047770803[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 27 )[/C][C]110.524691358025[/C][C]0.588090472548097[/C][C]187.938245078414[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 27 )[/C][C]110.576543209877[/C][C]0.573809211433864[/C][C]192.706113820589[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 27 )[/C][C]110.595061728395[/C][C]0.559414103873744[/C][C]197.698021845648[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 27 )[/C][C]110.733333333333[/C][C]0.5187889506424[/C][C]213.445820687229[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 27 )[/C][C]110.796296296296[/C][C]0.50253199776646[/C][C]220.476102593941[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 27 )[/C][C]110.774074074074[/C][C]0.486771861340753[/C][C]227.568770653588[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 27 )[/C][C]111.172839506173[/C][C]0.419964770515716[/C][C]264.719441513279[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 27 )[/C][C]111.148148148148[/C][C]0.409855858097709[/C][C]271.188384775143[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 27 )[/C][C]111.096296296296[/C][C]0.39597685290735[/C][C]280.562602284963[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 27 )[/C][C]111.096296296296[/C][C]0.388620718825099[/C][C]285.873323049191[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 27 )[/C][C]111.096296296296[/C][C]0.358203871723103[/C][C]310.148228610369[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 27 )[/C][C]111.037037037037[/C][C]0.350821102296009[/C][C]316.506151740406[/C][/ROW]
[ROW][C]Winsorized Mean ( 25 / 27 )[/C][C]111.314814814815[/C][C]0.30488872242014[/C][C]365.099810616877[/C][/ROW]
[ROW][C]Winsorized Mean ( 26 / 27 )[/C][C]111.314814814815[/C][C]0.26398016615025[/C][C]421.678705783743[/C][/ROW]
[ROW][C]Winsorized Mean ( 27 / 27 )[/C][C]111.348148148148[/C][C]0.251398011566279[/C][C]442.915787020027[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 27 )[/C][C]110.440506329114[/C][C]0.804064082625867[/C][C]137.352866165149[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 27 )[/C][C]110.477922077922[/C][C]0.769058650372203[/C][C]143.653441807662[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 27 )[/C][C]110.510666666667[/C][C]0.740857971904558[/C][C]149.1657927127[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 27 )[/C][C]110.531506849315[/C][C]0.713054710000085[/C][C]155.011256919265[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 27 )[/C][C]110.577464788732[/C][C]0.687544246779853[/C][C]160.829597959153[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 27 )[/C][C]110.620289855072[/C][C]0.665879478911462[/C][C]166.126594013541[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 27 )[/C][C]110.665671641791[/C][C]0.641591588077948[/C][C]172.486163625241[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 27 )[/C][C]110.712307692308[/C][C]0.619617234872852[/C][C]178.678547757030[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 27 )[/C][C]110.768253968254[/C][C]0.597124983365689[/C][C]185.502628518254[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 27 )[/C][C]110.832786885246[/C][C]0.578837733670353[/C][C]191.474709470763[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 27 )[/C][C]110.883050847458[/C][C]0.563247827678897[/C][C]196.863699065469[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 27 )[/C][C]110.931578947368[/C][C]0.546595511759651[/C][C]202.950036289627[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 27 )[/C][C]110.985454545455[/C][C]0.531216874946318[/C][C]208.926824014524[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 27 )[/C][C]111.039622641509[/C][C]0.514205600215983[/C][C]215.944016546823[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 27 )[/C][C]111.092156862745[/C][C]0.495856107664191[/C][C]224.041118271311[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 27 )[/C][C]111.146938775510[/C][C]0.475640474404035[/C][C]233.678470939157[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 27 )[/C][C]111.191489361702[/C][C]0.458951765751219[/C][C]242.272712862761[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 27 )[/C][C]111.233333333333[/C][C]0.441015815470318[/C][C]252.220735473419[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 27 )[/C][C]111.281395348837[/C][C]0.421031478924477[/C][C]264.306592070277[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 27 )[/C][C]111.292682926829[/C][C]0.410819974873311[/C][C]270.903777162125[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 27 )[/C][C]111.307692307692[/C][C]0.399145250982282[/C][C]278.865130009108[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 27 )[/C][C]111.329729729730[/C][C]0.386305844090083[/C][C]288.190643328111[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 27 )[/C][C]111.354285714286[/C][C]0.370222346481589[/C][C]300.776781230366[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 27 )[/C][C]111.381818181818[/C][C]0.355941308190035[/C][C]312.921865540687[/C][/ROW]
[ROW][C]Trimmed Mean ( 25 / 27 )[/C][C]111.419354838710[/C][C]0.337110407709075[/C][C]330.512948549675[/C][/ROW]
[ROW][C]Trimmed Mean ( 26 / 27 )[/C][C]111.431034482759[/C][C]0.325027602021367[/C][C]342.835604698684[/C][/ROW]
[ROW][C]Trimmed Mean ( 27 / 27 )[/C][C]111.444444444444[/C][C]0.319514113547329[/C][C]348.793495245513[/C][/ROW]
[ROW][C]Median[/C][C]111.8[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]110.3[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]111.1875[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]111.292682926829[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]111.292682926829[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]111.292682926829[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]111.292682926829[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]111.176190476190[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]111.292682926829[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]111.292682926829[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]81[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=7318&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=7318&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 Mean110.4370370370370.865059843153027127.664043026791
Geometric Mean110.160001355186
Harmonic Mean109.876459911879
Quadratic Mean110.707747841327
Winsorized Mean ( 1 / 27 )110.4049382716050.833918130426986132.393018263166
Winsorized Mean ( 2 / 27 )110.4172839506170.813713083256329135.695598636251
Winsorized Mean ( 3 / 27 )110.4543209876540.801944106497862137.733191244481
Winsorized Mean ( 4 / 27 )110.3703703703700.781900668686714141.156511038351
Winsorized Mean ( 5 / 27 )110.3950617283950.754721560206163146.272569314489
Winsorized Mean ( 6 / 27 )110.3950617283950.749106260149774147.369028402357
Winsorized Mean ( 7 / 27 )110.4037037037040.721763624579962152.963795824366
Winsorized Mean ( 8 / 27 )110.3641975308640.705035479017023156.537083331943
Winsorized Mean ( 9 / 27 )110.3308641975310.665825028862384165.705492306350
Winsorized Mean ( 10 / 27 )110.4666666666670.635942481287555173.705437075081
Winsorized Mean ( 11 / 27 )110.5074074074070.624138363542086177.05594442274
Winsorized Mean ( 12 / 27 )110.4925925925930.598712037838225184.55047770803
Winsorized Mean ( 13 / 27 )110.5246913580250.588090472548097187.938245078414
Winsorized Mean ( 14 / 27 )110.5765432098770.573809211433864192.706113820589
Winsorized Mean ( 15 / 27 )110.5950617283950.559414103873744197.698021845648
Winsorized Mean ( 16 / 27 )110.7333333333330.5187889506424213.445820687229
Winsorized Mean ( 17 / 27 )110.7962962962960.50253199776646220.476102593941
Winsorized Mean ( 18 / 27 )110.7740740740740.486771861340753227.568770653588
Winsorized Mean ( 19 / 27 )111.1728395061730.419964770515716264.719441513279
Winsorized Mean ( 20 / 27 )111.1481481481480.409855858097709271.188384775143
Winsorized Mean ( 21 / 27 )111.0962962962960.39597685290735280.562602284963
Winsorized Mean ( 22 / 27 )111.0962962962960.388620718825099285.873323049191
Winsorized Mean ( 23 / 27 )111.0962962962960.358203871723103310.148228610369
Winsorized Mean ( 24 / 27 )111.0370370370370.350821102296009316.506151740406
Winsorized Mean ( 25 / 27 )111.3148148148150.30488872242014365.099810616877
Winsorized Mean ( 26 / 27 )111.3148148148150.26398016615025421.678705783743
Winsorized Mean ( 27 / 27 )111.3481481481480.251398011566279442.915787020027
Trimmed Mean ( 1 / 27 )110.4405063291140.804064082625867137.352866165149
Trimmed Mean ( 2 / 27 )110.4779220779220.769058650372203143.653441807662
Trimmed Mean ( 3 / 27 )110.5106666666670.740857971904558149.1657927127
Trimmed Mean ( 4 / 27 )110.5315068493150.713054710000085155.011256919265
Trimmed Mean ( 5 / 27 )110.5774647887320.687544246779853160.829597959153
Trimmed Mean ( 6 / 27 )110.6202898550720.665879478911462166.126594013541
Trimmed Mean ( 7 / 27 )110.6656716417910.641591588077948172.486163625241
Trimmed Mean ( 8 / 27 )110.7123076923080.619617234872852178.678547757030
Trimmed Mean ( 9 / 27 )110.7682539682540.597124983365689185.502628518254
Trimmed Mean ( 10 / 27 )110.8327868852460.578837733670353191.474709470763
Trimmed Mean ( 11 / 27 )110.8830508474580.563247827678897196.863699065469
Trimmed Mean ( 12 / 27 )110.9315789473680.546595511759651202.950036289627
Trimmed Mean ( 13 / 27 )110.9854545454550.531216874946318208.926824014524
Trimmed Mean ( 14 / 27 )111.0396226415090.514205600215983215.944016546823
Trimmed Mean ( 15 / 27 )111.0921568627450.495856107664191224.041118271311
Trimmed Mean ( 16 / 27 )111.1469387755100.475640474404035233.678470939157
Trimmed Mean ( 17 / 27 )111.1914893617020.458951765751219242.272712862761
Trimmed Mean ( 18 / 27 )111.2333333333330.441015815470318252.220735473419
Trimmed Mean ( 19 / 27 )111.2813953488370.421031478924477264.306592070277
Trimmed Mean ( 20 / 27 )111.2926829268290.410819974873311270.903777162125
Trimmed Mean ( 21 / 27 )111.3076923076920.399145250982282278.865130009108
Trimmed Mean ( 22 / 27 )111.3297297297300.386305844090083288.190643328111
Trimmed Mean ( 23 / 27 )111.3542857142860.370222346481589300.776781230366
Trimmed Mean ( 24 / 27 )111.3818181818180.355941308190035312.921865540687
Trimmed Mean ( 25 / 27 )111.4193548387100.337110407709075330.512948549675
Trimmed Mean ( 26 / 27 )111.4310344827590.325027602021367342.835604698684
Trimmed Mean ( 27 / 27 )111.4444444444440.319514113547329348.793495245513
Median111.8
Midrange110.3
Midmean - Weighted Average at Xnp111.1875
Midmean - Weighted Average at X(n+1)p111.292682926829
Midmean - Empirical Distribution Function111.292682926829
Midmean - Empirical Distribution Function - Averaging111.292682926829
Midmean - Empirical Distribution Function - Interpolation111.292682926829
Midmean - Closest Observation111.176190476190
Midmean - True Basic - Statistics Graphics Toolkit111.292682926829
Midmean - MS Excel (old versions)111.292682926829
Number of observations81



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')