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Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationFri, 04 Mar 2016 17:25:21 +0000
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2016/Mar/04/t1457112370v553wa5244107d2.htm/, Retrieved Sat, 18 May 2024 15:28:35 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=293407, Retrieved Sat, 18 May 2024 15:28:35 +0000
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Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact53
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [] [2016-03-04 17:25:21] [bfab382a4ab6d7836f6b75894769f754] [Current]
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Dataseries X:
100
99
99,3
99,5
100,7
102,9
101,2
99,5
99,5
99,5
99,4
99,5
99,7
99,8
99,8
100,1
100
100
100,1
100,1
100
99,9
99,9
99,8
100,4
102,2
103,1
103
102,9
102,8
103
103,5
103,6
103,2
103
103
106,1
104,8
105,3
106,3
107,9
106,1
106,8
108,7
110,8
111,8
111,3
111,7
110,8
110,3
110,5
110,5
112,5
113
113,5
112,8
109,5
111,5
111,5
111,2




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Sir Maurice George Kendall' @ kendall.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 & 'Sir Maurice George Kendall' @ kendall.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=293407&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]'Sir Maurice George Kendall' @ kendall.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=293407&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=293407&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'Sir Maurice George Kendall' @ kendall.wessa.net







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean104.4683333333330.625008436854543167.147077020412
Geometric Mean104.359671774674
Harmonic Mean104.252744893253
Quadratic Mean104.578583690288
Winsorized Mean ( 1 / 20 )104.4650.622296752833863167.870070869371
Winsorized Mean ( 2 / 20 )104.4616666666670.620297412111878168.40577540218
Winsorized Mean ( 3 / 20 )104.4516666666670.616241989974033169.497808273448
Winsorized Mean ( 4 / 20 )104.4050.606250050963944172.214418512617
Winsorized Mean ( 5 / 20 )104.3966666666670.604535431974207172.689078497422
Winsorized Mean ( 6 / 20 )104.3766666666670.600477054542482173.822906099541
Winsorized Mean ( 7 / 20 )104.3766666666670.600477054542482173.822906099541
Winsorized Mean ( 8 / 20 )104.3766666666670.591528550760949176.452457843997
Winsorized Mean ( 9 / 20 )104.3766666666670.586565059254496177.945591916651
Winsorized Mean ( 10 / 20 )104.310.57359851310589181.851935834331
Winsorized Mean ( 11 / 20 )104.310.57359851310589181.851935834331
Winsorized Mean ( 12 / 20 )104.270.559526131226615186.354120354335
Winsorized Mean ( 13 / 20 )104.270.559526131226615186.354120354335
Winsorized Mean ( 14 / 20 )104.2466666666670.547673387485368190.344590496378
Winsorized Mean ( 15 / 20 )104.0466666666670.510823344848475203.684243713509
Winsorized Mean ( 16 / 20 )103.8333333333330.472890299546202219.571713424815
Winsorized Mean ( 17 / 20 )103.6066666666670.434090169150281238.675450470288
Winsorized Mean ( 18 / 20 )103.3066666666670.376054950506408274.711625329092
Winsorized Mean ( 19 / 20 )103.1483333333330.351546154411811293.413345698279
Winsorized Mean ( 20 / 20 )103.0816666666670.341486379332036301.861722474259
Trimmed Mean ( 1 / 20 )104.4068965517240.620080698790484168.376304496137
Trimmed Mean ( 2 / 20 )104.3446428571430.616604230363099169.224662626297
Trimmed Mean ( 3 / 20 )104.279629629630.612828041503518170.161321883687
Trimmed Mean ( 4 / 20 )104.2134615384620.609193201132314171.067998370236
Trimmed Mean ( 5 / 20 )104.1560.607525324910956171.443058798028
Trimmed Mean ( 6 / 20 )104.0958333333330.604907225268498172.085617405427
Trimmed Mean ( 7 / 20 )104.0347826086960.601682162001312172.906542987174
Trimmed Mean ( 8 / 20 )103.9681818181820.59636648854575174.336056460366
Trimmed Mean ( 9 / 20 )103.8952380952380.590625098304681175.907252152773
Trimmed Mean ( 10 / 20 )103.8150.583046266361383178.056195519231
Trimmed Mean ( 11 / 20 )103.7368421052630.575191489577006180.351837579431
Trimmed Mean ( 12 / 20 )103.650.563090959411913184.073280288945
Trimmed Mean ( 13 / 20 )103.5588235294120.549057167037136188.612096784464
Trimmed Mean ( 14 / 20 )103.456250.527794740696089196.01606841242
Trimmed Mean ( 15 / 20 )103.3433333333330.499624763412063206.841895961233
Trimmed Mean ( 16 / 20 )103.2428571428570.471135871937335219.136056692769
Trimmed Mean ( 17 / 20 )103.1576923076920.442585865703719233.079500050617
Trimmed Mean ( 18 / 20 )103.0916666666670.414323119488878248.819488504151
Trimmed Mean ( 19 / 20 )103.0590909090910.394861973303878261.000293461479
Trimmed Mean ( 20 / 20 )103.0450.372648769303157276.520435563738
Median103
Midrange106.25
Midmean - Weighted Average at Xnp103.235483870968
Midmean - Weighted Average at X(n+1)p103.235483870968
Midmean - Empirical Distribution Function103.235483870968
Midmean - Empirical Distribution Function - Averaging103.235483870968
Midmean - Empirical Distribution Function - Interpolation103.235483870968
Midmean - Closest Observation103.235483870968
Midmean - True Basic - Statistics Graphics Toolkit103.235483870968
Midmean - MS Excel (old versions)103.45625
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 104.468333333333 & 0.625008436854543 & 167.147077020412 \tabularnewline
Geometric Mean & 104.359671774674 &  &  \tabularnewline
Harmonic Mean & 104.252744893253 &  &  \tabularnewline
Quadratic Mean & 104.578583690288 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 104.465 & 0.622296752833863 & 167.870070869371 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 104.461666666667 & 0.620297412111878 & 168.40577540218 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 104.451666666667 & 0.616241989974033 & 169.497808273448 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 104.405 & 0.606250050963944 & 172.214418512617 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 104.396666666667 & 0.604535431974207 & 172.689078497422 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 104.376666666667 & 0.600477054542482 & 173.822906099541 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 104.376666666667 & 0.600477054542482 & 173.822906099541 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 104.376666666667 & 0.591528550760949 & 176.452457843997 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 104.376666666667 & 0.586565059254496 & 177.945591916651 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 104.31 & 0.57359851310589 & 181.851935834331 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 104.31 & 0.57359851310589 & 181.851935834331 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 104.27 & 0.559526131226615 & 186.354120354335 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 104.27 & 0.559526131226615 & 186.354120354335 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 104.246666666667 & 0.547673387485368 & 190.344590496378 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 104.046666666667 & 0.510823344848475 & 203.684243713509 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 103.833333333333 & 0.472890299546202 & 219.571713424815 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 103.606666666667 & 0.434090169150281 & 238.675450470288 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 103.306666666667 & 0.376054950506408 & 274.711625329092 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 103.148333333333 & 0.351546154411811 & 293.413345698279 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 103.081666666667 & 0.341486379332036 & 301.861722474259 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 104.406896551724 & 0.620080698790484 & 168.376304496137 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 104.344642857143 & 0.616604230363099 & 169.224662626297 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 104.27962962963 & 0.612828041503518 & 170.161321883687 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 104.213461538462 & 0.609193201132314 & 171.067998370236 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 104.156 & 0.607525324910956 & 171.443058798028 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 104.095833333333 & 0.604907225268498 & 172.085617405427 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 104.034782608696 & 0.601682162001312 & 172.906542987174 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 103.968181818182 & 0.59636648854575 & 174.336056460366 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 103.895238095238 & 0.590625098304681 & 175.907252152773 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 103.815 & 0.583046266361383 & 178.056195519231 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 103.736842105263 & 0.575191489577006 & 180.351837579431 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 103.65 & 0.563090959411913 & 184.073280288945 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 103.558823529412 & 0.549057167037136 & 188.612096784464 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 103.45625 & 0.527794740696089 & 196.01606841242 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 103.343333333333 & 0.499624763412063 & 206.841895961233 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 103.242857142857 & 0.471135871937335 & 219.136056692769 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 103.157692307692 & 0.442585865703719 & 233.079500050617 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 103.091666666667 & 0.414323119488878 & 248.819488504151 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 103.059090909091 & 0.394861973303878 & 261.000293461479 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 103.045 & 0.372648769303157 & 276.520435563738 \tabularnewline
Median & 103 &  &  \tabularnewline
Midrange & 106.25 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 103.235483870968 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 103.235483870968 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 103.235483870968 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 103.235483870968 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 103.235483870968 &  &  \tabularnewline
Midmean - Closest Observation & 103.235483870968 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 103.235483870968 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 103.45625 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=293407&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]104.468333333333[/C][C]0.625008436854543[/C][C]167.147077020412[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]104.359671774674[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]104.252744893253[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]104.578583690288[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]104.465[/C][C]0.622296752833863[/C][C]167.870070869371[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]104.461666666667[/C][C]0.620297412111878[/C][C]168.40577540218[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]104.451666666667[/C][C]0.616241989974033[/C][C]169.497808273448[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]104.405[/C][C]0.606250050963944[/C][C]172.214418512617[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]104.396666666667[/C][C]0.604535431974207[/C][C]172.689078497422[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]104.376666666667[/C][C]0.600477054542482[/C][C]173.822906099541[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]104.376666666667[/C][C]0.600477054542482[/C][C]173.822906099541[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]104.376666666667[/C][C]0.591528550760949[/C][C]176.452457843997[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]104.376666666667[/C][C]0.586565059254496[/C][C]177.945591916651[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]104.31[/C][C]0.57359851310589[/C][C]181.851935834331[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]104.31[/C][C]0.57359851310589[/C][C]181.851935834331[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]104.27[/C][C]0.559526131226615[/C][C]186.354120354335[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]104.27[/C][C]0.559526131226615[/C][C]186.354120354335[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]104.246666666667[/C][C]0.547673387485368[/C][C]190.344590496378[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]104.046666666667[/C][C]0.510823344848475[/C][C]203.684243713509[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]103.833333333333[/C][C]0.472890299546202[/C][C]219.571713424815[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]103.606666666667[/C][C]0.434090169150281[/C][C]238.675450470288[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]103.306666666667[/C][C]0.376054950506408[/C][C]274.711625329092[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]103.148333333333[/C][C]0.351546154411811[/C][C]293.413345698279[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]103.081666666667[/C][C]0.341486379332036[/C][C]301.861722474259[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]104.406896551724[/C][C]0.620080698790484[/C][C]168.376304496137[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]104.344642857143[/C][C]0.616604230363099[/C][C]169.224662626297[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]104.27962962963[/C][C]0.612828041503518[/C][C]170.161321883687[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]104.213461538462[/C][C]0.609193201132314[/C][C]171.067998370236[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]104.156[/C][C]0.607525324910956[/C][C]171.443058798028[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]104.095833333333[/C][C]0.604907225268498[/C][C]172.085617405427[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]104.034782608696[/C][C]0.601682162001312[/C][C]172.906542987174[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]103.968181818182[/C][C]0.59636648854575[/C][C]174.336056460366[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]103.895238095238[/C][C]0.590625098304681[/C][C]175.907252152773[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]103.815[/C][C]0.583046266361383[/C][C]178.056195519231[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]103.736842105263[/C][C]0.575191489577006[/C][C]180.351837579431[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]103.65[/C][C]0.563090959411913[/C][C]184.073280288945[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]103.558823529412[/C][C]0.549057167037136[/C][C]188.612096784464[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]103.45625[/C][C]0.527794740696089[/C][C]196.01606841242[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]103.343333333333[/C][C]0.499624763412063[/C][C]206.841895961233[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]103.242857142857[/C][C]0.471135871937335[/C][C]219.136056692769[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]103.157692307692[/C][C]0.442585865703719[/C][C]233.079500050617[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]103.091666666667[/C][C]0.414323119488878[/C][C]248.819488504151[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]103.059090909091[/C][C]0.394861973303878[/C][C]261.000293461479[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]103.045[/C][C]0.372648769303157[/C][C]276.520435563738[/C][/ROW]
[ROW][C]Median[/C][C]103[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]106.25[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]103.235483870968[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]103.235483870968[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]103.235483870968[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]103.235483870968[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]103.235483870968[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]103.235483870968[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]103.235483870968[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]103.45625[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]60[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=293407&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=293407&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 Mean104.4683333333330.625008436854543167.147077020412
Geometric Mean104.359671774674
Harmonic Mean104.252744893253
Quadratic Mean104.578583690288
Winsorized Mean ( 1 / 20 )104.4650.622296752833863167.870070869371
Winsorized Mean ( 2 / 20 )104.4616666666670.620297412111878168.40577540218
Winsorized Mean ( 3 / 20 )104.4516666666670.616241989974033169.497808273448
Winsorized Mean ( 4 / 20 )104.4050.606250050963944172.214418512617
Winsorized Mean ( 5 / 20 )104.3966666666670.604535431974207172.689078497422
Winsorized Mean ( 6 / 20 )104.3766666666670.600477054542482173.822906099541
Winsorized Mean ( 7 / 20 )104.3766666666670.600477054542482173.822906099541
Winsorized Mean ( 8 / 20 )104.3766666666670.591528550760949176.452457843997
Winsorized Mean ( 9 / 20 )104.3766666666670.586565059254496177.945591916651
Winsorized Mean ( 10 / 20 )104.310.57359851310589181.851935834331
Winsorized Mean ( 11 / 20 )104.310.57359851310589181.851935834331
Winsorized Mean ( 12 / 20 )104.270.559526131226615186.354120354335
Winsorized Mean ( 13 / 20 )104.270.559526131226615186.354120354335
Winsorized Mean ( 14 / 20 )104.2466666666670.547673387485368190.344590496378
Winsorized Mean ( 15 / 20 )104.0466666666670.510823344848475203.684243713509
Winsorized Mean ( 16 / 20 )103.8333333333330.472890299546202219.571713424815
Winsorized Mean ( 17 / 20 )103.6066666666670.434090169150281238.675450470288
Winsorized Mean ( 18 / 20 )103.3066666666670.376054950506408274.711625329092
Winsorized Mean ( 19 / 20 )103.1483333333330.351546154411811293.413345698279
Winsorized Mean ( 20 / 20 )103.0816666666670.341486379332036301.861722474259
Trimmed Mean ( 1 / 20 )104.4068965517240.620080698790484168.376304496137
Trimmed Mean ( 2 / 20 )104.3446428571430.616604230363099169.224662626297
Trimmed Mean ( 3 / 20 )104.279629629630.612828041503518170.161321883687
Trimmed Mean ( 4 / 20 )104.2134615384620.609193201132314171.067998370236
Trimmed Mean ( 5 / 20 )104.1560.607525324910956171.443058798028
Trimmed Mean ( 6 / 20 )104.0958333333330.604907225268498172.085617405427
Trimmed Mean ( 7 / 20 )104.0347826086960.601682162001312172.906542987174
Trimmed Mean ( 8 / 20 )103.9681818181820.59636648854575174.336056460366
Trimmed Mean ( 9 / 20 )103.8952380952380.590625098304681175.907252152773
Trimmed Mean ( 10 / 20 )103.8150.583046266361383178.056195519231
Trimmed Mean ( 11 / 20 )103.7368421052630.575191489577006180.351837579431
Trimmed Mean ( 12 / 20 )103.650.563090959411913184.073280288945
Trimmed Mean ( 13 / 20 )103.5588235294120.549057167037136188.612096784464
Trimmed Mean ( 14 / 20 )103.456250.527794740696089196.01606841242
Trimmed Mean ( 15 / 20 )103.3433333333330.499624763412063206.841895961233
Trimmed Mean ( 16 / 20 )103.2428571428570.471135871937335219.136056692769
Trimmed Mean ( 17 / 20 )103.1576923076920.442585865703719233.079500050617
Trimmed Mean ( 18 / 20 )103.0916666666670.414323119488878248.819488504151
Trimmed Mean ( 19 / 20 )103.0590909090910.394861973303878261.000293461479
Trimmed Mean ( 20 / 20 )103.0450.372648769303157276.520435563738
Median103
Midrange106.25
Midmean - Weighted Average at Xnp103.235483870968
Midmean - Weighted Average at X(n+1)p103.235483870968
Midmean - Empirical Distribution Function103.235483870968
Midmean - Empirical Distribution Function - Averaging103.235483870968
Midmean - Empirical Distribution Function - Interpolation103.235483870968
Midmean - Closest Observation103.235483870968
Midmean - True Basic - Statistics Graphics Toolkit103.235483870968
Midmean - MS Excel (old versions)103.45625
Number of observations60



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')