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Description of Statistical Computation

Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationSat, 05 Mar 2016 15:19:52 +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/05/t1457191215xxssokqend1akhd.htm/, Retrieved Sat, 27 Apr 2024 05:47:39 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=293481, Retrieved Sat, 27 Apr 2024 05:47:39 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact60

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [] [2016-03-05 15:19:52] [60c466f2753cef60360c0cd0685abd02] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
93,91
94,27
94,55
94,66
94,78
94,91
95,2
95,48
95,56
95,75
95,91
96,16
96,32
96,58
97,08
97,22
97,49
97,62
97,83
98,12
98,29
98,47
98,64
98,67
98,82
99,17
99,38
99,53
99,54
99,76
100,02
100,22
100,55
100,94
100,99
101,07
101,19
101,94
102,25
102,49
102,58
102,74
103,01
103,19
103,44
103,62
103,74
103,82
103,96
104,7
105,13
105,26
105,44
105,73
105,83
105,97
106,13
106,49
106,74
106,82

Tables (Output of Computation)





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=293481&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=293481&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=293481&T=0

As an alternative you can also use a QR Code:  
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 Mean100.2611666666670.494499066948367202.752994632314
Geometric Mean100.189313081937
Harmonic Mean100.117589357862
Quadratic Mean100.333089116536
Winsorized Mean ( 1 / 20 )100.2658333333330.492929172418021203.408195221005
Winsorized Mean ( 2 / 20 )100.2668333333330.489216628022505204.953853957558
Winsorized Mean ( 3 / 20 )100.2543333333330.48434214028022206.990730303439
Winsorized Mean ( 4 / 20 )100.2516666666670.480614964269188208.590397968792
Winsorized Mean ( 5 / 20 )100.2508333333330.476205238219532210.520223818112
Winsorized Mean ( 6 / 20 )100.2698333333330.468810460758675213.881390724659
Winsorized Mean ( 7 / 20 )100.2686666666670.456320364385504219.733052680416
Winsorized Mean ( 8 / 20 )100.2553333333330.449860271254846222.858829150838
Winsorized Mean ( 9 / 20 )100.2643333333330.441206638154719227.250282889383
Winsorized Mean ( 10 / 20 )100.2193333333330.423464648880192236.665170512705
Winsorized Mean ( 11 / 20 )100.12950.392147961885943255.336020410385
Winsorized Mean ( 12 / 20 )100.13350.382088139105623262.069113776703
Winsorized Mean ( 13 / 20 )100.17250.369849918026768270.846349066245
Winsorized Mean ( 14 / 20 )100.2611666666670.346565480533696289.299345428946
Winsorized Mean ( 15 / 20 )100.2511666666670.333808877594393300.325046443134
Winsorized Mean ( 16 / 20 )100.25650.312146371666615321.184255529575
Winsorized Mean ( 17 / 20 )100.2423333333330.29856827538423335.74341816568
Winsorized Mean ( 18 / 20 )100.2243333333330.276645704059159362.284076212877
Winsorized Mean ( 19 / 20 )100.26550.255575171092765392.313148305033
Winsorized Mean ( 20 / 20 )100.2921666666670.242982770269486412.754231731884
Trimmed Mean ( 1 / 20 )100.2575862068970.486439669172857206.104872938045
Trimmed Mean ( 2 / 20 )100.248750.478227318013939209.625728652076
Trimmed Mean ( 3 / 20 )100.2387037037040.470278702199641213.14744477021
Trimmed Mean ( 4 / 20 )100.2326923076920.462440988480578216.746990004114
Trimmed Mean ( 5 / 20 )100.2270.453775297265247220.873636365917
Trimmed Mean ( 6 / 20 )100.2210416666670.444039847860397225.702810568874
Trimmed Mean ( 7 / 20 )100.2104347826090.433642025670046231.090228461523
Trimmed Mean ( 8 / 20 )100.1990909090910.42361761475266236.531927426093
Trimmed Mean ( 9 / 20 )100.1890476190480.412060318521847243.141703084753
Trimmed Mean ( 10 / 20 )100.17650.398925086148984251.116070355595
Trimmed Mean ( 11 / 20 )100.1697368421050.386096835346885259.44200436688
Trimmed Mean ( 12 / 20 )100.1758333333330.377068974996302265.669784511748
Trimmed Mean ( 13 / 20 )100.1820588235290.366852192428287273.085621106416
Trimmed Mean ( 14 / 20 )100.18343750.355494773728371281.814093774973
Trimmed Mean ( 15 / 20 )100.1723333333330.345613791276197289.838935429752
Trimmed Mean ( 16 / 20 )100.1610714285710.334369555747881299.552006774487
Trimmed Mean ( 17 / 20 )100.1473076923080.323939955353698309.153922006813
Trimmed Mean ( 18 / 20 )100.1333333333330.311675385447295321.274434904858
Trimmed Mean ( 19 / 20 )100.1195454545450.299775873907388333.981331284439
Trimmed Mean ( 20 / 20 )100.09650.287709900493718347.907735633121
Median99.89
Midrange100.365
Midmean - Weighted Average at Xnp100.072580645161
Midmean - Weighted Average at X(n+1)p100.172333333333
Midmean - Empirical Distribution Function100.072580645161
Midmean - Empirical Distribution Function - Averaging100.172333333333
Midmean - Empirical Distribution Function - Interpolation100.172333333333
Midmean - Closest Observation100.072580645161
Midmean - True Basic - Statistics Graphics Toolkit100.172333333333
Midmean - MS Excel (old versions)100.1834375
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 100.261166666667 & 0.494499066948367 & 202.752994632314 \tabularnewline
Geometric Mean & 100.189313081937 &  &  \tabularnewline
Harmonic Mean & 100.117589357862 &  &  \tabularnewline
Quadratic Mean & 100.333089116536 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 100.265833333333 & 0.492929172418021 & 203.408195221005 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 100.266833333333 & 0.489216628022505 & 204.953853957558 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 100.254333333333 & 0.48434214028022 & 206.990730303439 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 100.251666666667 & 0.480614964269188 & 208.590397968792 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 100.250833333333 & 0.476205238219532 & 210.520223818112 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 100.269833333333 & 0.468810460758675 & 213.881390724659 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 100.268666666667 & 0.456320364385504 & 219.733052680416 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 100.255333333333 & 0.449860271254846 & 222.858829150838 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 100.264333333333 & 0.441206638154719 & 227.250282889383 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 100.219333333333 & 0.423464648880192 & 236.665170512705 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 100.1295 & 0.392147961885943 & 255.336020410385 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 100.1335 & 0.382088139105623 & 262.069113776703 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 100.1725 & 0.369849918026768 & 270.846349066245 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 100.261166666667 & 0.346565480533696 & 289.299345428946 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 100.251166666667 & 0.333808877594393 & 300.325046443134 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 100.2565 & 0.312146371666615 & 321.184255529575 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 100.242333333333 & 0.29856827538423 & 335.74341816568 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 100.224333333333 & 0.276645704059159 & 362.284076212877 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 100.2655 & 0.255575171092765 & 392.313148305033 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 100.292166666667 & 0.242982770269486 & 412.754231731884 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 100.257586206897 & 0.486439669172857 & 206.104872938045 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 100.24875 & 0.478227318013939 & 209.625728652076 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 100.238703703704 & 0.470278702199641 & 213.14744477021 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 100.232692307692 & 0.462440988480578 & 216.746990004114 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 100.227 & 0.453775297265247 & 220.873636365917 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 100.221041666667 & 0.444039847860397 & 225.702810568874 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 100.210434782609 & 0.433642025670046 & 231.090228461523 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 100.199090909091 & 0.42361761475266 & 236.531927426093 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 100.189047619048 & 0.412060318521847 & 243.141703084753 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 100.1765 & 0.398925086148984 & 251.116070355595 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 100.169736842105 & 0.386096835346885 & 259.44200436688 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 100.175833333333 & 0.377068974996302 & 265.669784511748 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 100.182058823529 & 0.366852192428287 & 273.085621106416 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 100.1834375 & 0.355494773728371 & 281.814093774973 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 100.172333333333 & 0.345613791276197 & 289.838935429752 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 100.161071428571 & 0.334369555747881 & 299.552006774487 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 100.147307692308 & 0.323939955353698 & 309.153922006813 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 100.133333333333 & 0.311675385447295 & 321.274434904858 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 100.119545454545 & 0.299775873907388 & 333.981331284439 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 100.0965 & 0.287709900493718 & 347.907735633121 \tabularnewline
Median & 99.89 &  &  \tabularnewline
Midrange & 100.365 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 100.072580645161 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 100.172333333333 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 100.072580645161 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 100.172333333333 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 100.172333333333 &  &  \tabularnewline
Midmean - Closest Observation & 100.072580645161 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 100.172333333333 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 100.1834375 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=293481&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]100.261166666667[/C][C]0.494499066948367[/C][C]202.752994632314[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]100.189313081937[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]100.117589357862[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]100.333089116536[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]100.265833333333[/C][C]0.492929172418021[/C][C]203.408195221005[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]100.266833333333[/C][C]0.489216628022505[/C][C]204.953853957558[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]100.254333333333[/C][C]0.48434214028022[/C][C]206.990730303439[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]100.251666666667[/C][C]0.480614964269188[/C][C]208.590397968792[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]100.250833333333[/C][C]0.476205238219532[/C][C]210.520223818112[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]100.269833333333[/C][C]0.468810460758675[/C][C]213.881390724659[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]100.268666666667[/C][C]0.456320364385504[/C][C]219.733052680416[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]100.255333333333[/C][C]0.449860271254846[/C][C]222.858829150838[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]100.264333333333[/C][C]0.441206638154719[/C][C]227.250282889383[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]100.219333333333[/C][C]0.423464648880192[/C][C]236.665170512705[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]100.1295[/C][C]0.392147961885943[/C][C]255.336020410385[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]100.1335[/C][C]0.382088139105623[/C][C]262.069113776703[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]100.1725[/C][C]0.369849918026768[/C][C]270.846349066245[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]100.261166666667[/C][C]0.346565480533696[/C][C]289.299345428946[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]100.251166666667[/C][C]0.333808877594393[/C][C]300.325046443134[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]100.2565[/C][C]0.312146371666615[/C][C]321.184255529575[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]100.242333333333[/C][C]0.29856827538423[/C][C]335.74341816568[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]100.224333333333[/C][C]0.276645704059159[/C][C]362.284076212877[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]100.2655[/C][C]0.255575171092765[/C][C]392.313148305033[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]100.292166666667[/C][C]0.242982770269486[/C][C]412.754231731884[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]100.257586206897[/C][C]0.486439669172857[/C][C]206.104872938045[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]100.24875[/C][C]0.478227318013939[/C][C]209.625728652076[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]100.238703703704[/C][C]0.470278702199641[/C][C]213.14744477021[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]100.232692307692[/C][C]0.462440988480578[/C][C]216.746990004114[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]100.227[/C][C]0.453775297265247[/C][C]220.873636365917[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]100.221041666667[/C][C]0.444039847860397[/C][C]225.702810568874[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]100.210434782609[/C][C]0.433642025670046[/C][C]231.090228461523[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]100.199090909091[/C][C]0.42361761475266[/C][C]236.531927426093[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]100.189047619048[/C][C]0.412060318521847[/C][C]243.141703084753[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]100.1765[/C][C]0.398925086148984[/C][C]251.116070355595[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]100.169736842105[/C][C]0.386096835346885[/C][C]259.44200436688[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]100.175833333333[/C][C]0.377068974996302[/C][C]265.669784511748[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]100.182058823529[/C][C]0.366852192428287[/C][C]273.085621106416[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]100.1834375[/C][C]0.355494773728371[/C][C]281.814093774973[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]100.172333333333[/C][C]0.345613791276197[/C][C]289.838935429752[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]100.161071428571[/C][C]0.334369555747881[/C][C]299.552006774487[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]100.147307692308[/C][C]0.323939955353698[/C][C]309.153922006813[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]100.133333333333[/C][C]0.311675385447295[/C][C]321.274434904858[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]100.119545454545[/C][C]0.299775873907388[/C][C]333.981331284439[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]100.0965[/C][C]0.287709900493718[/C][C]347.907735633121[/C][/ROW]
[ROW][C]Median[/C][C]99.89[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]100.365[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]100.072580645161[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]100.172333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]100.072580645161[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]100.172333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]100.172333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]100.072580645161[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]100.172333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]100.1834375[/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=293481&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=293481&T=1

As an alternative you can also use a QR Code:  
QR Code


The GUIDs for individual cells are displayed in the table below:

Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean100.2611666666670.494499066948367202.752994632314
Geometric Mean100.189313081937
Harmonic Mean100.117589357862
Quadratic Mean100.333089116536
Winsorized Mean ( 1 / 20 )100.2658333333330.492929172418021203.408195221005
Winsorized Mean ( 2 / 20 )100.2668333333330.489216628022505204.953853957558
Winsorized Mean ( 3 / 20 )100.2543333333330.48434214028022206.990730303439
Winsorized Mean ( 4 / 20 )100.2516666666670.480614964269188208.590397968792
Winsorized Mean ( 5 / 20 )100.2508333333330.476205238219532210.520223818112
Winsorized Mean ( 6 / 20 )100.2698333333330.468810460758675213.881390724659
Winsorized Mean ( 7 / 20 )100.2686666666670.456320364385504219.733052680416
Winsorized Mean ( 8 / 20 )100.2553333333330.449860271254846222.858829150838
Winsorized Mean ( 9 / 20 )100.2643333333330.441206638154719227.250282889383
Winsorized Mean ( 10 / 20 )100.2193333333330.423464648880192236.665170512705
Winsorized Mean ( 11 / 20 )100.12950.392147961885943255.336020410385
Winsorized Mean ( 12 / 20 )100.13350.382088139105623262.069113776703
Winsorized Mean ( 13 / 20 )100.17250.369849918026768270.846349066245
Winsorized Mean ( 14 / 20 )100.2611666666670.346565480533696289.299345428946
Winsorized Mean ( 15 / 20 )100.2511666666670.333808877594393300.325046443134
Winsorized Mean ( 16 / 20 )100.25650.312146371666615321.184255529575
Winsorized Mean ( 17 / 20 )100.2423333333330.29856827538423335.74341816568
Winsorized Mean ( 18 / 20 )100.2243333333330.276645704059159362.284076212877
Winsorized Mean ( 19 / 20 )100.26550.255575171092765392.313148305033
Winsorized Mean ( 20 / 20 )100.2921666666670.242982770269486412.754231731884
Trimmed Mean ( 1 / 20 )100.2575862068970.486439669172857206.104872938045
Trimmed Mean ( 2 / 20 )100.248750.478227318013939209.625728652076
Trimmed Mean ( 3 / 20 )100.2387037037040.470278702199641213.14744477021
Trimmed Mean ( 4 / 20 )100.2326923076920.462440988480578216.746990004114
Trimmed Mean ( 5 / 20 )100.2270.453775297265247220.873636365917
Trimmed Mean ( 6 / 20 )100.2210416666670.444039847860397225.702810568874
Trimmed Mean ( 7 / 20 )100.2104347826090.433642025670046231.090228461523
Trimmed Mean ( 8 / 20 )100.1990909090910.42361761475266236.531927426093
Trimmed Mean ( 9 / 20 )100.1890476190480.412060318521847243.141703084753
Trimmed Mean ( 10 / 20 )100.17650.398925086148984251.116070355595
Trimmed Mean ( 11 / 20 )100.1697368421050.386096835346885259.44200436688
Trimmed Mean ( 12 / 20 )100.1758333333330.377068974996302265.669784511748
Trimmed Mean ( 13 / 20 )100.1820588235290.366852192428287273.085621106416
Trimmed Mean ( 14 / 20 )100.18343750.355494773728371281.814093774973
Trimmed Mean ( 15 / 20 )100.1723333333330.345613791276197289.838935429752
Trimmed Mean ( 16 / 20 )100.1610714285710.334369555747881299.552006774487
Trimmed Mean ( 17 / 20 )100.1473076923080.323939955353698309.153922006813
Trimmed Mean ( 18 / 20 )100.1333333333330.311675385447295321.274434904858
Trimmed Mean ( 19 / 20 )100.1195454545450.299775873907388333.981331284439
Trimmed Mean ( 20 / 20 )100.09650.287709900493718347.907735633121
Median99.89
Midrange100.365
Midmean - Weighted Average at Xnp100.072580645161
Midmean - Weighted Average at X(n+1)p100.172333333333
Midmean - Empirical Distribution Function100.072580645161
Midmean - Empirical Distribution Function - Averaging100.172333333333
Midmean - Empirical Distribution Function - Interpolation100.172333333333
Midmean - Closest Observation100.072580645161
Midmean - True Basic - Statistics Graphics Toolkit100.172333333333
Midmean - MS Excel (old versions)100.1834375
Number of observations60


Figures (Output of Computation)

Input Parameters & R Code

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')