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Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationFri, 12 Dec 2008 07:20:11 -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/2008/Dec/12/t12290916644n06etiqk0qjnbw.htm/, Retrieved Fri, 17 May 2024 00:15:09 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=32777, Retrieved Fri, 17 May 2024 00:15:09 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact158
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Central Tendency] [central tendency ...] [2008-12-12 13:49:21] [005293453b571dbccb80b45226e44173]
-    D  [Central Tendency] [Central tendency ...] [2008-12-12 14:08:41] [005293453b571dbccb80b45226e44173]
-    D      [Central Tendency] [Central tendency ...] [2008-12-12 14:20:11] [b0654df83a8a0e1de3ceb7bf60f0d58f] [Current]
-    D        [Central Tendency] [Central tendency ...] [2008-12-13 12:58:54] [005293453b571dbccb80b45226e44173]
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Dataseries X:
88827
85874
85211
87130
88620
89563
89056
88542
89504
89428
86040
96240
94423
93028
92285
91685
94260
93858
92437
92980
92099
92803
88551
98334
98329
96455
97109
97687
98512
98673
96028
98014
95580
97838
97760
99913
97588
93942
93656
93365
92881
93120
91063
90930
91946
94624
95484
95862
95530
94574
94677
93845
91533
91214
90922
89563
89945
91850
92505
92437




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'George Udny Yule' @ 72.249.76.132

\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 & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=32777&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]'George Udny Yule' @ 72.249.76.132[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=32777&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=32777&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'George Udny Yule' @ 72.249.76.132







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean93095.5333333333457.042575169853203.691162248366
Geometric Mean93028.9790021328
Harmonic Mean92962.0661258581
Quadratic Mean93161.701968316
Winsorized Mean ( 1 / 20 )93085.9166666667449.127412805258207.259485866717
Winsorized Mean ( 2 / 20 )93086.0833333333446.515951019743208.472022378474
Winsorized Mean ( 3 / 20 )93131.6833333333430.953192951469216.106261321566
Winsorized Mean ( 4 / 20 )93225.4833333333410.626907715416227.032085773451
Winsorized Mean ( 5 / 20 )93199.9833333333405.072045967962230.082485970174
Winsorized Mean ( 6 / 20 )93189.2833333333400.228075578373232.840445285266
Winsorized Mean ( 7 / 20 )93204.3333333333393.828396673431236.662297895750
Winsorized Mean ( 8 / 20 )93225.1333333333386.251537920743241.358607489772
Winsorized Mean ( 9 / 20 )93266.0833333333373.371785215878249.794138245899
Winsorized Mean ( 10 / 20 )93198.9166666667355.879833788017261.883107212479
Winsorized Mean ( 11 / 20 )93089.8333333333332.478090834753279.987872583160
Winsorized Mean ( 12 / 20 )93046.8333333333325.210514321471286.112623164934
Winsorized Mean ( 13 / 20 )93083.6666666667302.809241164863307.400349832745
Winsorized Mean ( 14 / 20 )93272.9258.553545689671360.748872157998
Winsorized Mean ( 15 / 20 )93204.4246.496958187074378.115822140346
Winsorized Mean ( 16 / 20 )93226.5333333333238.821187472317390.361233523889
Winsorized Mean ( 17 / 20 )93256.2833333333230.184256938185405.137538829933
Winsorized Mean ( 18 / 20 )93109.8833333333177.602648113030524.259544114884
Winsorized Mean ( 19 / 20 )93141.2333333333167.930479573746554.641620566748
Winsorized Mean ( 20 / 20 )93179.5666666667157.451406487514591.798884146873
Trimmed Mean ( 1 / 20 )93113.9310344828436.811811768207213.167154655363
Trimmed Mean ( 2 / 20 )93143.9464285714421.588512235709220.935684263842
Trimmed Mean ( 3 / 20 )93176.0925925926404.418172426811230.395414809049
Trimmed Mean ( 4 / 20 )93193.173076923390.747678053676238.499620883534
Trimmed Mean ( 5 / 20 )93183.48381.673261525176244.144637294309
Trimmed Mean ( 6 / 20 )93179.3541666667371.94849516854250.516819874334
Trimmed Mean ( 7 / 20 )93177.1956521739360.90128405216258.179174665135
Trimmed Mean ( 8 / 20 )93171.9090909091348.425503847943267.408407426944
Trimmed Mean ( 9 / 20 )93162.4047619048334.225472900855278.741186161896
Trimmed Mean ( 10 / 20 )93145.125319.068420014644291.928373844472
Trimmed Mean ( 11 / 20 )93136.6315789474303.889470017098306.481930991907
Trimmed Mean ( 12 / 20 )93143.7222222222290.126142820318321.045602153503
Trimmed Mean ( 13 / 20 )93157.9705882353273.034696708284341.194623655348
Trimmed Mean ( 14 / 20 )93168.6875256.132193366688363.752350984697
Trimmed Mean ( 15 / 20 )93153.8246.284306321434378.236849076457
Trimmed Mean ( 16 / 20 )93146.5714285714235.526790108163395.481853192985
Trimmed Mean ( 17 / 20 )93135.0384615385221.574883891649420.332109965505
Trimmed Mean ( 18 / 20 )93117.2083333333202.772405605994459.220316763757
Trimmed Mean ( 19 / 20 )93118.3181818182196.03039328758475.019799838957
Trimmed Mean ( 20 / 20 )93114.7188.008651816598495.268165056751
Median93004
Midrange92562
Midmean - Weighted Average at Xnp93081.806451613
Midmean - Weighted Average at X(n+1)p93153.8
Midmean - Empirical Distribution Function93081.806451613
Midmean - Empirical Distribution Function - Averaging93153.8
Midmean - Empirical Distribution Function - Interpolation93153.8
Midmean - Closest Observation93081.806451613
Midmean - True Basic - Statistics Graphics Toolkit93153.8
Midmean - MS Excel (old versions)93168.6875
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 93095.5333333333 & 457.042575169853 & 203.691162248366 \tabularnewline
Geometric Mean & 93028.9790021328 &  &  \tabularnewline
Harmonic Mean & 92962.0661258581 &  &  \tabularnewline
Quadratic Mean & 93161.701968316 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 93085.9166666667 & 449.127412805258 & 207.259485866717 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 93086.0833333333 & 446.515951019743 & 208.472022378474 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 93131.6833333333 & 430.953192951469 & 216.106261321566 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 93225.4833333333 & 410.626907715416 & 227.032085773451 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 93199.9833333333 & 405.072045967962 & 230.082485970174 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 93189.2833333333 & 400.228075578373 & 232.840445285266 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 93204.3333333333 & 393.828396673431 & 236.662297895750 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 93225.1333333333 & 386.251537920743 & 241.358607489772 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 93266.0833333333 & 373.371785215878 & 249.794138245899 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 93198.9166666667 & 355.879833788017 & 261.883107212479 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 93089.8333333333 & 332.478090834753 & 279.987872583160 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 93046.8333333333 & 325.210514321471 & 286.112623164934 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 93083.6666666667 & 302.809241164863 & 307.400349832745 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 93272.9 & 258.553545689671 & 360.748872157998 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 93204.4 & 246.496958187074 & 378.115822140346 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 93226.5333333333 & 238.821187472317 & 390.361233523889 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 93256.2833333333 & 230.184256938185 & 405.137538829933 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 93109.8833333333 & 177.602648113030 & 524.259544114884 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 93141.2333333333 & 167.930479573746 & 554.641620566748 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 93179.5666666667 & 157.451406487514 & 591.798884146873 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 93113.9310344828 & 436.811811768207 & 213.167154655363 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 93143.9464285714 & 421.588512235709 & 220.935684263842 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 93176.0925925926 & 404.418172426811 & 230.395414809049 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 93193.173076923 & 390.747678053676 & 238.499620883534 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 93183.48 & 381.673261525176 & 244.144637294309 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 93179.3541666667 & 371.94849516854 & 250.516819874334 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 93177.1956521739 & 360.90128405216 & 258.179174665135 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 93171.9090909091 & 348.425503847943 & 267.408407426944 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 93162.4047619048 & 334.225472900855 & 278.741186161896 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 93145.125 & 319.068420014644 & 291.928373844472 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 93136.6315789474 & 303.889470017098 & 306.481930991907 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 93143.7222222222 & 290.126142820318 & 321.045602153503 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 93157.9705882353 & 273.034696708284 & 341.194623655348 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 93168.6875 & 256.132193366688 & 363.752350984697 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 93153.8 & 246.284306321434 & 378.236849076457 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 93146.5714285714 & 235.526790108163 & 395.481853192985 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 93135.0384615385 & 221.574883891649 & 420.332109965505 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 93117.2083333333 & 202.772405605994 & 459.220316763757 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 93118.3181818182 & 196.03039328758 & 475.019799838957 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 93114.7 & 188.008651816598 & 495.268165056751 \tabularnewline
Median & 93004 &  &  \tabularnewline
Midrange & 92562 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 93081.806451613 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 93153.8 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 93081.806451613 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 93153.8 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 93153.8 &  &  \tabularnewline
Midmean - Closest Observation & 93081.806451613 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 93153.8 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 93168.6875 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=32777&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]93095.5333333333[/C][C]457.042575169853[/C][C]203.691162248366[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]93028.9790021328[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]92962.0661258581[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]93161.701968316[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]93085.9166666667[/C][C]449.127412805258[/C][C]207.259485866717[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]93086.0833333333[/C][C]446.515951019743[/C][C]208.472022378474[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]93131.6833333333[/C][C]430.953192951469[/C][C]216.106261321566[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]93225.4833333333[/C][C]410.626907715416[/C][C]227.032085773451[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]93199.9833333333[/C][C]405.072045967962[/C][C]230.082485970174[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]93189.2833333333[/C][C]400.228075578373[/C][C]232.840445285266[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]93204.3333333333[/C][C]393.828396673431[/C][C]236.662297895750[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]93225.1333333333[/C][C]386.251537920743[/C][C]241.358607489772[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]93266.0833333333[/C][C]373.371785215878[/C][C]249.794138245899[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]93198.9166666667[/C][C]355.879833788017[/C][C]261.883107212479[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]93089.8333333333[/C][C]332.478090834753[/C][C]279.987872583160[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]93046.8333333333[/C][C]325.210514321471[/C][C]286.112623164934[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]93083.6666666667[/C][C]302.809241164863[/C][C]307.400349832745[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]93272.9[/C][C]258.553545689671[/C][C]360.748872157998[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]93204.4[/C][C]246.496958187074[/C][C]378.115822140346[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]93226.5333333333[/C][C]238.821187472317[/C][C]390.361233523889[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]93256.2833333333[/C][C]230.184256938185[/C][C]405.137538829933[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]93109.8833333333[/C][C]177.602648113030[/C][C]524.259544114884[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]93141.2333333333[/C][C]167.930479573746[/C][C]554.641620566748[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]93179.5666666667[/C][C]157.451406487514[/C][C]591.798884146873[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]93113.9310344828[/C][C]436.811811768207[/C][C]213.167154655363[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]93143.9464285714[/C][C]421.588512235709[/C][C]220.935684263842[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]93176.0925925926[/C][C]404.418172426811[/C][C]230.395414809049[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]93193.173076923[/C][C]390.747678053676[/C][C]238.499620883534[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]93183.48[/C][C]381.673261525176[/C][C]244.144637294309[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]93179.3541666667[/C][C]371.94849516854[/C][C]250.516819874334[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]93177.1956521739[/C][C]360.90128405216[/C][C]258.179174665135[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]93171.9090909091[/C][C]348.425503847943[/C][C]267.408407426944[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]93162.4047619048[/C][C]334.225472900855[/C][C]278.741186161896[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]93145.125[/C][C]319.068420014644[/C][C]291.928373844472[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]93136.6315789474[/C][C]303.889470017098[/C][C]306.481930991907[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]93143.7222222222[/C][C]290.126142820318[/C][C]321.045602153503[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]93157.9705882353[/C][C]273.034696708284[/C][C]341.194623655348[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]93168.6875[/C][C]256.132193366688[/C][C]363.752350984697[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]93153.8[/C][C]246.284306321434[/C][C]378.236849076457[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]93146.5714285714[/C][C]235.526790108163[/C][C]395.481853192985[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]93135.0384615385[/C][C]221.574883891649[/C][C]420.332109965505[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]93117.2083333333[/C][C]202.772405605994[/C][C]459.220316763757[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]93118.3181818182[/C][C]196.03039328758[/C][C]475.019799838957[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]93114.7[/C][C]188.008651816598[/C][C]495.268165056751[/C][/ROW]
[ROW][C]Median[/C][C]93004[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]92562[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]93081.806451613[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]93153.8[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]93081.806451613[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]93153.8[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]93153.8[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]93081.806451613[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]93153.8[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]93168.6875[/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=32777&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=32777&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 Mean93095.5333333333457.042575169853203.691162248366
Geometric Mean93028.9790021328
Harmonic Mean92962.0661258581
Quadratic Mean93161.701968316
Winsorized Mean ( 1 / 20 )93085.9166666667449.127412805258207.259485866717
Winsorized Mean ( 2 / 20 )93086.0833333333446.515951019743208.472022378474
Winsorized Mean ( 3 / 20 )93131.6833333333430.953192951469216.106261321566
Winsorized Mean ( 4 / 20 )93225.4833333333410.626907715416227.032085773451
Winsorized Mean ( 5 / 20 )93199.9833333333405.072045967962230.082485970174
Winsorized Mean ( 6 / 20 )93189.2833333333400.228075578373232.840445285266
Winsorized Mean ( 7 / 20 )93204.3333333333393.828396673431236.662297895750
Winsorized Mean ( 8 / 20 )93225.1333333333386.251537920743241.358607489772
Winsorized Mean ( 9 / 20 )93266.0833333333373.371785215878249.794138245899
Winsorized Mean ( 10 / 20 )93198.9166666667355.879833788017261.883107212479
Winsorized Mean ( 11 / 20 )93089.8333333333332.478090834753279.987872583160
Winsorized Mean ( 12 / 20 )93046.8333333333325.210514321471286.112623164934
Winsorized Mean ( 13 / 20 )93083.6666666667302.809241164863307.400349832745
Winsorized Mean ( 14 / 20 )93272.9258.553545689671360.748872157998
Winsorized Mean ( 15 / 20 )93204.4246.496958187074378.115822140346
Winsorized Mean ( 16 / 20 )93226.5333333333238.821187472317390.361233523889
Winsorized Mean ( 17 / 20 )93256.2833333333230.184256938185405.137538829933
Winsorized Mean ( 18 / 20 )93109.8833333333177.602648113030524.259544114884
Winsorized Mean ( 19 / 20 )93141.2333333333167.930479573746554.641620566748
Winsorized Mean ( 20 / 20 )93179.5666666667157.451406487514591.798884146873
Trimmed Mean ( 1 / 20 )93113.9310344828436.811811768207213.167154655363
Trimmed Mean ( 2 / 20 )93143.9464285714421.588512235709220.935684263842
Trimmed Mean ( 3 / 20 )93176.0925925926404.418172426811230.395414809049
Trimmed Mean ( 4 / 20 )93193.173076923390.747678053676238.499620883534
Trimmed Mean ( 5 / 20 )93183.48381.673261525176244.144637294309
Trimmed Mean ( 6 / 20 )93179.3541666667371.94849516854250.516819874334
Trimmed Mean ( 7 / 20 )93177.1956521739360.90128405216258.179174665135
Trimmed Mean ( 8 / 20 )93171.9090909091348.425503847943267.408407426944
Trimmed Mean ( 9 / 20 )93162.4047619048334.225472900855278.741186161896
Trimmed Mean ( 10 / 20 )93145.125319.068420014644291.928373844472
Trimmed Mean ( 11 / 20 )93136.6315789474303.889470017098306.481930991907
Trimmed Mean ( 12 / 20 )93143.7222222222290.126142820318321.045602153503
Trimmed Mean ( 13 / 20 )93157.9705882353273.034696708284341.194623655348
Trimmed Mean ( 14 / 20 )93168.6875256.132193366688363.752350984697
Trimmed Mean ( 15 / 20 )93153.8246.284306321434378.236849076457
Trimmed Mean ( 16 / 20 )93146.5714285714235.526790108163395.481853192985
Trimmed Mean ( 17 / 20 )93135.0384615385221.574883891649420.332109965505
Trimmed Mean ( 18 / 20 )93117.2083333333202.772405605994459.220316763757
Trimmed Mean ( 19 / 20 )93118.3181818182196.03039328758475.019799838957
Trimmed Mean ( 20 / 20 )93114.7188.008651816598495.268165056751
Median93004
Midrange92562
Midmean - Weighted Average at Xnp93081.806451613
Midmean - Weighted Average at X(n+1)p93153.8
Midmean - Empirical Distribution Function93081.806451613
Midmean - Empirical Distribution Function - Averaging93153.8
Midmean - Empirical Distribution Function - Interpolation93153.8
Midmean - Closest Observation93081.806451613
Midmean - True Basic - Statistics Graphics Toolkit93153.8
Midmean - MS Excel (old versions)93168.6875
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')