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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, 16 Oct 2009 05:37:20 -0600
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2009/Oct/16/t1255693274h8ji086c61tu4ry.htm/, Retrieved Tue, 30 Apr 2024 03:41:47 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=46967, Retrieved Tue, 30 Apr 2024 03:41:47 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsW3
Estimated Impact150
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Univariate Data Series] [Workshop 2 ] [2009-10-08 16:59:47] [315ba876df544ad397193b5931d5f354]
- RMPD    [Central Tendency] [W3 ] [2009-10-16 11:37:20] [950726a732ba3ca782ecb1a5307d0f6f] [Current]
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Dataseries X:
1.094122842
1.137863515
1.187052127
1.154532788
1.086582638
1.160188095
1.125503018
1.12894466
1.156808051
1.121538712
1.13945463
1.193865568
1.103015148
1.114135812
1.160879048
1.082529707
1.012243888
1.096943013
1.087440068
1.080106082
1.111041009
1.129789982
1.180299033
1.127142801
1.076629451
1.122411245
1.142868527
1.096208612
1.099874575
1.158456249
1.128752818
1.118300303
1.144510743
1.149781596
1.167048105
1.145707758
1.120078224
1.141189871
1.117903382
1.099124532
1.016641417
1.127835646
1.11617671
1.10197648
1.106507575
1.133575559
1.103270758
1.133139011
1.095129476
1.134003988
1.123941246
1.072396531
1.07720065
1.152257786
1.13952907
1.109737036
1.125933986
1.139366384
1.114458511
1.144199774




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Sir Ronald Aylmer Fisher' @ 193.190.124.24

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 2 seconds \tabularnewline
R Server & 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=46967&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Sir Ronald Aylmer Fisher' @ 193.190.124.24[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=46967&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=46967&T=0

As an alternative you can also use a QR Code:  

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

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Sir Ronald Aylmer Fisher' @ 193.190.124.24







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean1.121135763666670.00439133454866258255.306388352515
Geometric Mean1.1206199973197
Harmonic Mean1.12009529907521
Quadratic Mean1.12164305636883
Winsorized Mean ( 1 / 20 )1.121095498466670.00433034206244486258.893057938640
Winsorized Mean ( 2 / 20 )1.122728899133330.00366125479613739306.651397307231
Winsorized Mean ( 3 / 20 )1.122277998733330.00345126672804155325.178575626978
Winsorized Mean ( 4 / 20 )1.12190480820.00335695856684455334.20275700768
Winsorized Mean ( 5 / 20 )1.122089348116670.00329214411446306340.838465481234
Winsorized Mean ( 6 / 20 )1.122158526016670.00320695887279162349.913600556979
Winsorized Mean ( 7 / 20 )1.12243907820.00307397343450716365.142738580614
Winsorized Mean ( 8 / 20 )1.12225003380.00299494080162914374.715264218089
Winsorized Mean ( 9 / 20 )1.12291119960.00274457103447293409.139055063899
Winsorized Mean ( 10 / 20 )1.12266627360.00264150702126759425.009763199971
Winsorized Mean ( 11 / 20 )1.12211724490.00248122300764555452.243607866906
Winsorized Mean ( 12 / 20 )1.12202472210.00241713956563693464.195257092795
Winsorized Mean ( 13 / 20 )1.122430007933330.00232473306827842482.821027174766
Winsorized Mean ( 14 / 20 )1.122294393666670.00224628966031244499.621403906816
Winsorized Mean ( 15 / 20 )1.122400205916670.00209385858554948536.043939959833
Winsorized Mean ( 16 / 20 )1.122234303783330.00198173476851017566.28885036266
Winsorized Mean ( 17 / 20 )1.122285635283330.00196672827001452570.635838409466
Winsorized Mean ( 18 / 20 )1.123230206583330.00180690173003956621.63325647972
Winsorized Mean ( 19 / 20 )1.123776960716670.00157730603362932712.466025461715
Winsorized Mean ( 20 / 20 )1.122925109383330.00132218445932508849.29534715341
Trimmed Mean ( 1 / 20 )1.121759247655170.00393131856158816285.339188387218
Trimmed Mean ( 2 / 20 )1.12247040750.00340711001525722329.449416800021
Trimmed Mean ( 3 / 20 )1.122326801037040.00323228446935967347.224018082597
Trimmed Mean ( 4 / 20 )1.122345571153850.00311983812260123359.744809521741
Trimmed Mean ( 5 / 20 )1.122477800040.00301622707130107372.146318398970
Trimmed Mean ( 6 / 20 )1.122574913020830.00290750599577687386.095476553226
Trimmed Mean ( 7 / 20 )1.122665431934780.00279577284870530401.558171099157
Trimmed Mean ( 8 / 20 )1.122709526818180.00269209788791021417.038894410228
Trimmed Mean ( 9 / 20 )1.122791579142860.00257919019581391435.327173996387
Trimmed Mean ( 10 / 20 )1.12277164240.00250191678609693448.764582674853
Trimmed Mean ( 11 / 20 )1.122788279578950.00242546342422773462.917011389873
Trimmed Mean ( 12 / 20 )1.12288995150.00236360731670342475.074663868498
Trimmed Mean ( 13 / 20 )1.123017191117650.00229272917453745489.81676666814
Trimmed Mean ( 14 / 20 )1.1231018810.00221753519372515506.4640616203
Trimmed Mean ( 15 / 20 )1.123217236333330.00213010587212774527.305825982896
Trimmed Mean ( 16 / 20 )1.123333954964290.00204865700487889548.327002660308
Trimmed Mean ( 17 / 20 )1.12349255850.00196003882076129573.1991359557
Trimmed Mean ( 18 / 20 )1.123670047208330.00182210357830932616.688348886814
Trimmed Mean ( 19 / 20 )1.123736689727270.00167205887841392672.067655173258
Trimmed Mean ( 20 / 20 )1.123730331150.00153562302384001731.774865122808
Median1.124722132
Midrange1.103054728
Midmean - Weighted Average at Xnp1.12246424725806
Midmean - Weighted Average at X(n+1)p1.12321723633333
Midmean - Empirical Distribution Function1.12246424725806
Midmean - Empirical Distribution Function - Averaging1.12321723633333
Midmean - Empirical Distribution Function - Interpolation1.12321723633333
Midmean - Closest Observation1.12246424725806
Midmean - True Basic - Statistics Graphics Toolkit1.12321723633333
Midmean - MS Excel (old versions)1.123101881
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 1.12113576366667 & 0.00439133454866258 & 255.306388352515 \tabularnewline
Geometric Mean & 1.1206199973197 &  &  \tabularnewline
Harmonic Mean & 1.12009529907521 &  &  \tabularnewline
Quadratic Mean & 1.12164305636883 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 1.12109549846667 & 0.00433034206244486 & 258.893057938640 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 1.12272889913333 & 0.00366125479613739 & 306.651397307231 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 1.12227799873333 & 0.00345126672804155 & 325.178575626978 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 1.1219048082 & 0.00335695856684455 & 334.20275700768 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 1.12208934811667 & 0.00329214411446306 & 340.838465481234 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 1.12215852601667 & 0.00320695887279162 & 349.913600556979 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 1.1224390782 & 0.00307397343450716 & 365.142738580614 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 1.1222500338 & 0.00299494080162914 & 374.715264218089 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 1.1229111996 & 0.00274457103447293 & 409.139055063899 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 1.1226662736 & 0.00264150702126759 & 425.009763199971 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 1.1221172449 & 0.00248122300764555 & 452.243607866906 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 1.1220247221 & 0.00241713956563693 & 464.195257092795 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 1.12243000793333 & 0.00232473306827842 & 482.821027174766 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 1.12229439366667 & 0.00224628966031244 & 499.621403906816 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 1.12240020591667 & 0.00209385858554948 & 536.043939959833 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 1.12223430378333 & 0.00198173476851017 & 566.28885036266 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 1.12228563528333 & 0.00196672827001452 & 570.635838409466 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 1.12323020658333 & 0.00180690173003956 & 621.63325647972 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 1.12377696071667 & 0.00157730603362932 & 712.466025461715 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 1.12292510938333 & 0.00132218445932508 & 849.29534715341 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 1.12175924765517 & 0.00393131856158816 & 285.339188387218 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 1.1224704075 & 0.00340711001525722 & 329.449416800021 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 1.12232680103704 & 0.00323228446935967 & 347.224018082597 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 1.12234557115385 & 0.00311983812260123 & 359.744809521741 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 1.12247780004 & 0.00301622707130107 & 372.146318398970 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 1.12257491302083 & 0.00290750599577687 & 386.095476553226 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 1.12266543193478 & 0.00279577284870530 & 401.558171099157 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 1.12270952681818 & 0.00269209788791021 & 417.038894410228 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 1.12279157914286 & 0.00257919019581391 & 435.327173996387 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 1.1227716424 & 0.00250191678609693 & 448.764582674853 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 1.12278827957895 & 0.00242546342422773 & 462.917011389873 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 1.1228899515 & 0.00236360731670342 & 475.074663868498 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 1.12301719111765 & 0.00229272917453745 & 489.81676666814 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 1.123101881 & 0.00221753519372515 & 506.4640616203 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 1.12321723633333 & 0.00213010587212774 & 527.305825982896 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 1.12333395496429 & 0.00204865700487889 & 548.327002660308 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 1.1234925585 & 0.00196003882076129 & 573.1991359557 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 1.12367004720833 & 0.00182210357830932 & 616.688348886814 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 1.12373668972727 & 0.00167205887841392 & 672.067655173258 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 1.12373033115 & 0.00153562302384001 & 731.774865122808 \tabularnewline
Median & 1.124722132 &  &  \tabularnewline
Midrange & 1.103054728 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 1.12246424725806 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 1.12321723633333 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 1.12246424725806 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 1.12321723633333 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 1.12321723633333 &  &  \tabularnewline
Midmean - Closest Observation & 1.12246424725806 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 1.12321723633333 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 1.123101881 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=46967&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]1.12113576366667[/C][C]0.00439133454866258[/C][C]255.306388352515[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]1.1206199973197[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]1.12009529907521[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]1.12164305636883[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]1.12109549846667[/C][C]0.00433034206244486[/C][C]258.893057938640[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]1.12272889913333[/C][C]0.00366125479613739[/C][C]306.651397307231[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]1.12227799873333[/C][C]0.00345126672804155[/C][C]325.178575626978[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]1.1219048082[/C][C]0.00335695856684455[/C][C]334.20275700768[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]1.12208934811667[/C][C]0.00329214411446306[/C][C]340.838465481234[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]1.12215852601667[/C][C]0.00320695887279162[/C][C]349.913600556979[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]1.1224390782[/C][C]0.00307397343450716[/C][C]365.142738580614[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]1.1222500338[/C][C]0.00299494080162914[/C][C]374.715264218089[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]1.1229111996[/C][C]0.00274457103447293[/C][C]409.139055063899[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]1.1226662736[/C][C]0.00264150702126759[/C][C]425.009763199971[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]1.1221172449[/C][C]0.00248122300764555[/C][C]452.243607866906[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]1.1220247221[/C][C]0.00241713956563693[/C][C]464.195257092795[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]1.12243000793333[/C][C]0.00232473306827842[/C][C]482.821027174766[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]1.12229439366667[/C][C]0.00224628966031244[/C][C]499.621403906816[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]1.12240020591667[/C][C]0.00209385858554948[/C][C]536.043939959833[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]1.12223430378333[/C][C]0.00198173476851017[/C][C]566.28885036266[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]1.12228563528333[/C][C]0.00196672827001452[/C][C]570.635838409466[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]1.12323020658333[/C][C]0.00180690173003956[/C][C]621.63325647972[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]1.12377696071667[/C][C]0.00157730603362932[/C][C]712.466025461715[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]1.12292510938333[/C][C]0.00132218445932508[/C][C]849.29534715341[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]1.12175924765517[/C][C]0.00393131856158816[/C][C]285.339188387218[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]1.1224704075[/C][C]0.00340711001525722[/C][C]329.449416800021[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]1.12232680103704[/C][C]0.00323228446935967[/C][C]347.224018082597[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]1.12234557115385[/C][C]0.00311983812260123[/C][C]359.744809521741[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]1.12247780004[/C][C]0.00301622707130107[/C][C]372.146318398970[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]1.12257491302083[/C][C]0.00290750599577687[/C][C]386.095476553226[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]1.12266543193478[/C][C]0.00279577284870530[/C][C]401.558171099157[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]1.12270952681818[/C][C]0.00269209788791021[/C][C]417.038894410228[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]1.12279157914286[/C][C]0.00257919019581391[/C][C]435.327173996387[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]1.1227716424[/C][C]0.00250191678609693[/C][C]448.764582674853[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]1.12278827957895[/C][C]0.00242546342422773[/C][C]462.917011389873[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]1.1228899515[/C][C]0.00236360731670342[/C][C]475.074663868498[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]1.12301719111765[/C][C]0.00229272917453745[/C][C]489.81676666814[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]1.123101881[/C][C]0.00221753519372515[/C][C]506.4640616203[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]1.12321723633333[/C][C]0.00213010587212774[/C][C]527.305825982896[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]1.12333395496429[/C][C]0.00204865700487889[/C][C]548.327002660308[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]1.1234925585[/C][C]0.00196003882076129[/C][C]573.1991359557[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]1.12367004720833[/C][C]0.00182210357830932[/C][C]616.688348886814[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]1.12373668972727[/C][C]0.00167205887841392[/C][C]672.067655173258[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]1.12373033115[/C][C]0.00153562302384001[/C][C]731.774865122808[/C][/ROW]
[ROW][C]Median[/C][C]1.124722132[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]1.103054728[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]1.12246424725806[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]1.12321723633333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]1.12246424725806[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]1.12321723633333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]1.12321723633333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]1.12246424725806[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]1.12321723633333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]1.123101881[/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=46967&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=46967&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 Mean1.121135763666670.00439133454866258255.306388352515
Geometric Mean1.1206199973197
Harmonic Mean1.12009529907521
Quadratic Mean1.12164305636883
Winsorized Mean ( 1 / 20 )1.121095498466670.00433034206244486258.893057938640
Winsorized Mean ( 2 / 20 )1.122728899133330.00366125479613739306.651397307231
Winsorized Mean ( 3 / 20 )1.122277998733330.00345126672804155325.178575626978
Winsorized Mean ( 4 / 20 )1.12190480820.00335695856684455334.20275700768
Winsorized Mean ( 5 / 20 )1.122089348116670.00329214411446306340.838465481234
Winsorized Mean ( 6 / 20 )1.122158526016670.00320695887279162349.913600556979
Winsorized Mean ( 7 / 20 )1.12243907820.00307397343450716365.142738580614
Winsorized Mean ( 8 / 20 )1.12225003380.00299494080162914374.715264218089
Winsorized Mean ( 9 / 20 )1.12291119960.00274457103447293409.139055063899
Winsorized Mean ( 10 / 20 )1.12266627360.00264150702126759425.009763199971
Winsorized Mean ( 11 / 20 )1.12211724490.00248122300764555452.243607866906
Winsorized Mean ( 12 / 20 )1.12202472210.00241713956563693464.195257092795
Winsorized Mean ( 13 / 20 )1.122430007933330.00232473306827842482.821027174766
Winsorized Mean ( 14 / 20 )1.122294393666670.00224628966031244499.621403906816
Winsorized Mean ( 15 / 20 )1.122400205916670.00209385858554948536.043939959833
Winsorized Mean ( 16 / 20 )1.122234303783330.00198173476851017566.28885036266
Winsorized Mean ( 17 / 20 )1.122285635283330.00196672827001452570.635838409466
Winsorized Mean ( 18 / 20 )1.123230206583330.00180690173003956621.63325647972
Winsorized Mean ( 19 / 20 )1.123776960716670.00157730603362932712.466025461715
Winsorized Mean ( 20 / 20 )1.122925109383330.00132218445932508849.29534715341
Trimmed Mean ( 1 / 20 )1.121759247655170.00393131856158816285.339188387218
Trimmed Mean ( 2 / 20 )1.12247040750.00340711001525722329.449416800021
Trimmed Mean ( 3 / 20 )1.122326801037040.00323228446935967347.224018082597
Trimmed Mean ( 4 / 20 )1.122345571153850.00311983812260123359.744809521741
Trimmed Mean ( 5 / 20 )1.122477800040.00301622707130107372.146318398970
Trimmed Mean ( 6 / 20 )1.122574913020830.00290750599577687386.095476553226
Trimmed Mean ( 7 / 20 )1.122665431934780.00279577284870530401.558171099157
Trimmed Mean ( 8 / 20 )1.122709526818180.00269209788791021417.038894410228
Trimmed Mean ( 9 / 20 )1.122791579142860.00257919019581391435.327173996387
Trimmed Mean ( 10 / 20 )1.12277164240.00250191678609693448.764582674853
Trimmed Mean ( 11 / 20 )1.122788279578950.00242546342422773462.917011389873
Trimmed Mean ( 12 / 20 )1.12288995150.00236360731670342475.074663868498
Trimmed Mean ( 13 / 20 )1.123017191117650.00229272917453745489.81676666814
Trimmed Mean ( 14 / 20 )1.1231018810.00221753519372515506.4640616203
Trimmed Mean ( 15 / 20 )1.123217236333330.00213010587212774527.305825982896
Trimmed Mean ( 16 / 20 )1.123333954964290.00204865700487889548.327002660308
Trimmed Mean ( 17 / 20 )1.12349255850.00196003882076129573.1991359557
Trimmed Mean ( 18 / 20 )1.123670047208330.00182210357830932616.688348886814
Trimmed Mean ( 19 / 20 )1.123736689727270.00167205887841392672.067655173258
Trimmed Mean ( 20 / 20 )1.123730331150.00153562302384001731.774865122808
Median1.124722132
Midrange1.103054728
Midmean - Weighted Average at Xnp1.12246424725806
Midmean - Weighted Average at X(n+1)p1.12321723633333
Midmean - Empirical Distribution Function1.12246424725806
Midmean - Empirical Distribution Function - Averaging1.12321723633333
Midmean - Empirical Distribution Function - Interpolation1.12321723633333
Midmean - Closest Observation1.12246424725806
Midmean - True Basic - Statistics Graphics Toolkit1.12321723633333
Midmean - MS Excel (old versions)1.123101881
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')