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Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationSat, 11 Oct 2014 15:16:46 +0100
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2014/Oct/11/t14130370310o79eenrb7jjh4b.htm/, Retrieved Tue, 14 May 2024 17:31:29 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=240475, Retrieved Tue, 14 May 2024 17:31:29 +0000
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Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact78
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [] [2014-10-11 14:16:46] [072d4f39c76834f6beee313555a90f83] [Current]
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Dataseries X:
164,88
164,88
164,57
164,53
165,03
165,92
165,92
165,92
165,92
166,12
166,34
165,48
165,61
165,61
165,94
165,88
166,23
166,32
166,43
166,43
166,2
166,21
168,02
168,68
168,65
168,65
168,75
168,8
168,58
168,98
169
169
168,94
169,96
171,59
172,41
172,65
172,65
172,65
172,38
171,95
171,95
171,87
171,87
171,91
171,99
172,15
172,73
173,2
164,97
164,97
164,43
163,16
162,98
161,69
162,19
162
162,22
164,08
164,58
164,68




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' @ yule.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 & 'George Udny Yule' @ yule.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=240475&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' @ yule.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=240475&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=240475&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' @ yule.wessa.net







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean167.5127868852460.421995722348217396.953755723191
Geometric Mean167.480988810618
Harmonic Mean167.449288678658
Quadratic Mean167.544676410331
Winsorized Mean ( 1 / 20 )167.5101639344260.419189531047795399.604836303336
Winsorized Mean ( 2 / 20 )167.5137704918030.417303611343267401.419412481454
Winsorized Mean ( 3 / 20 )167.5152459016390.416990624218574401.724250312719
Winsorized Mean ( 4 / 20 )167.5650819672130.407031411023958411.676046194258
Winsorized Mean ( 5 / 20 )167.5601639344260.400259648774814418.628668783686
Winsorized Mean ( 6 / 20 )167.6477049180330.384342842273276436.193123635256
Winsorized Mean ( 7 / 20 )167.6614754098360.372977081883245449.522191989051
Winsorized Mean ( 8 / 20 )167.6536065573770.366928473307638456.910866158959
Winsorized Mean ( 9 / 20 )167.6536065573770.364934011011204459.408006649809
Winsorized Mean ( 10 / 20 )167.6552459016390.364703383224471459.703017886317
Winsorized Mean ( 11 / 20 )167.6660655737710.360777414894189464.735481357515
Winsorized Mean ( 12 / 20 )167.6975409836070.353908053242084473.844942061537
Winsorized Mean ( 13 / 20 )167.6975409836070.353908053242084473.844942061537
Winsorized Mean ( 14 / 20 )167.653934426230.338633163763483495.090122192895
Winsorized Mean ( 15 / 20 )167.2531147540980.265132665110118630.828022207798
Winsorized Mean ( 16 / 20 )167.0170491803280.222471014169219750.736224240383
Winsorized Mean ( 17 / 20 )167.1424590163930.204610072416538816.882849619106
Winsorized Mean ( 18 / 20 )167.1749180327870.198599140835205841.77060046552
Winsorized Mean ( 19 / 20 )167.1624590163930.196717274548742849.759937960985
Winsorized Mean ( 20 / 20 )167.2050819672130.178527618434126936.578236094652
Trimmed Mean ( 1 / 20 )167.5150847457630.413649589893728404.968574461296
Trimmed Mean ( 2 / 20 )167.5203508771930.40667657591816411.925251654782
Trimmed Mean ( 3 / 20 )167.5240.399151001358536419.700813551316
Trimmed Mean ( 4 / 20 )167.5273584905660.389808496667616429.768360419845
Trimmed Mean ( 5 / 20 )167.5160784313730.381868274016708438.675034899713
Trimmed Mean ( 6 / 20 )167.5051020408160.373959909366885447.922619096798
Trimmed Mean ( 7 / 20 )167.4742553191490.368370884661273454.634886449145
Trimmed Mean ( 8 / 20 )167.4380.363893035676889460.129718307313
Trimmed Mean ( 9 / 20 )167.399767441860.359145578957977466.10560521879
Trimmed Mean ( 10 / 20 )167.3578048780490.352831320196493474.328086250525
Trimmed Mean ( 11 / 20 )167.3112820512820.343902580807399486.507782693798
Trimmed Mean ( 12 / 20 )167.2581081081080.332316204443014503.310118110083
Trimmed Mean ( 13 / 20 )167.1942857142860.31759423552605526.439925577843
Trimmed Mean ( 14 / 20 )167.1227272727270.29619342341979564.235104693283
Trimmed Mean ( 15 / 20 )167.0480645161290.270164991147819618.318694092862
Trimmed Mean ( 16 / 20 )167.0193103448280.260395176679696641.407081630674
Trimmed Mean ( 17 / 20 )167.019629629630.259238684572287644.269700354297
Trimmed Mean ( 18 / 20 )167.0020.261015963751901639.815272596651
Trimmed Mean ( 19 / 20 )166.976521739130.263048868072701634.773770221971
Trimmed Mean ( 20 / 20 )166.9480952380950.264002722792255632.372626586385
Median166.32
Midrange167.445
Midmean - Weighted Average at Xnp166.887096774194
Midmean - Weighted Average at X(n+1)p166.983125
Midmean - Empirical Distribution Function166.983125
Midmean - Empirical Distribution Function - Averaging166.983125
Midmean - Empirical Distribution Function - Interpolation166.983125
Midmean - Closest Observation166.983125
Midmean - True Basic - Statistics Graphics Toolkit166.983125
Midmean - MS Excel (old versions)166.983125
Number of observations61

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 167.512786885246 & 0.421995722348217 & 396.953755723191 \tabularnewline
Geometric Mean & 167.480988810618 &  &  \tabularnewline
Harmonic Mean & 167.449288678658 &  &  \tabularnewline
Quadratic Mean & 167.544676410331 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 167.510163934426 & 0.419189531047795 & 399.604836303336 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 167.513770491803 & 0.417303611343267 & 401.419412481454 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 167.515245901639 & 0.416990624218574 & 401.724250312719 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 167.565081967213 & 0.407031411023958 & 411.676046194258 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 167.560163934426 & 0.400259648774814 & 418.628668783686 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 167.647704918033 & 0.384342842273276 & 436.193123635256 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 167.661475409836 & 0.372977081883245 & 449.522191989051 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 167.653606557377 & 0.366928473307638 & 456.910866158959 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 167.653606557377 & 0.364934011011204 & 459.408006649809 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 167.655245901639 & 0.364703383224471 & 459.703017886317 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 167.666065573771 & 0.360777414894189 & 464.735481357515 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 167.697540983607 & 0.353908053242084 & 473.844942061537 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 167.697540983607 & 0.353908053242084 & 473.844942061537 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 167.65393442623 & 0.338633163763483 & 495.090122192895 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 167.253114754098 & 0.265132665110118 & 630.828022207798 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 167.017049180328 & 0.222471014169219 & 750.736224240383 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 167.142459016393 & 0.204610072416538 & 816.882849619106 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 167.174918032787 & 0.198599140835205 & 841.77060046552 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 167.162459016393 & 0.196717274548742 & 849.759937960985 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 167.205081967213 & 0.178527618434126 & 936.578236094652 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 167.515084745763 & 0.413649589893728 & 404.968574461296 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 167.520350877193 & 0.40667657591816 & 411.925251654782 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 167.524 & 0.399151001358536 & 419.700813551316 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 167.527358490566 & 0.389808496667616 & 429.768360419845 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 167.516078431373 & 0.381868274016708 & 438.675034899713 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 167.505102040816 & 0.373959909366885 & 447.922619096798 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 167.474255319149 & 0.368370884661273 & 454.634886449145 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 167.438 & 0.363893035676889 & 460.129718307313 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 167.39976744186 & 0.359145578957977 & 466.10560521879 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 167.357804878049 & 0.352831320196493 & 474.328086250525 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 167.311282051282 & 0.343902580807399 & 486.507782693798 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 167.258108108108 & 0.332316204443014 & 503.310118110083 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 167.194285714286 & 0.31759423552605 & 526.439925577843 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 167.122727272727 & 0.29619342341979 & 564.235104693283 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 167.048064516129 & 0.270164991147819 & 618.318694092862 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 167.019310344828 & 0.260395176679696 & 641.407081630674 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 167.01962962963 & 0.259238684572287 & 644.269700354297 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 167.002 & 0.261015963751901 & 639.815272596651 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 166.97652173913 & 0.263048868072701 & 634.773770221971 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 166.948095238095 & 0.264002722792255 & 632.372626586385 \tabularnewline
Median & 166.32 &  &  \tabularnewline
Midrange & 167.445 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 166.887096774194 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 166.983125 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 166.983125 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 166.983125 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 166.983125 &  &  \tabularnewline
Midmean - Closest Observation & 166.983125 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 166.983125 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 166.983125 &  &  \tabularnewline
Number of observations & 61 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=240475&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]167.512786885246[/C][C]0.421995722348217[/C][C]396.953755723191[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]167.480988810618[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]167.449288678658[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]167.544676410331[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]167.510163934426[/C][C]0.419189531047795[/C][C]399.604836303336[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]167.513770491803[/C][C]0.417303611343267[/C][C]401.419412481454[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]167.515245901639[/C][C]0.416990624218574[/C][C]401.724250312719[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]167.565081967213[/C][C]0.407031411023958[/C][C]411.676046194258[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]167.560163934426[/C][C]0.400259648774814[/C][C]418.628668783686[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]167.647704918033[/C][C]0.384342842273276[/C][C]436.193123635256[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]167.661475409836[/C][C]0.372977081883245[/C][C]449.522191989051[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]167.653606557377[/C][C]0.366928473307638[/C][C]456.910866158959[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]167.653606557377[/C][C]0.364934011011204[/C][C]459.408006649809[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]167.655245901639[/C][C]0.364703383224471[/C][C]459.703017886317[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]167.666065573771[/C][C]0.360777414894189[/C][C]464.735481357515[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]167.697540983607[/C][C]0.353908053242084[/C][C]473.844942061537[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]167.697540983607[/C][C]0.353908053242084[/C][C]473.844942061537[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]167.65393442623[/C][C]0.338633163763483[/C][C]495.090122192895[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]167.253114754098[/C][C]0.265132665110118[/C][C]630.828022207798[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]167.017049180328[/C][C]0.222471014169219[/C][C]750.736224240383[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]167.142459016393[/C][C]0.204610072416538[/C][C]816.882849619106[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]167.174918032787[/C][C]0.198599140835205[/C][C]841.77060046552[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]167.162459016393[/C][C]0.196717274548742[/C][C]849.759937960985[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]167.205081967213[/C][C]0.178527618434126[/C][C]936.578236094652[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]167.515084745763[/C][C]0.413649589893728[/C][C]404.968574461296[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]167.520350877193[/C][C]0.40667657591816[/C][C]411.925251654782[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]167.524[/C][C]0.399151001358536[/C][C]419.700813551316[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]167.527358490566[/C][C]0.389808496667616[/C][C]429.768360419845[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]167.516078431373[/C][C]0.381868274016708[/C][C]438.675034899713[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]167.505102040816[/C][C]0.373959909366885[/C][C]447.922619096798[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]167.474255319149[/C][C]0.368370884661273[/C][C]454.634886449145[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]167.438[/C][C]0.363893035676889[/C][C]460.129718307313[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]167.39976744186[/C][C]0.359145578957977[/C][C]466.10560521879[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]167.357804878049[/C][C]0.352831320196493[/C][C]474.328086250525[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]167.311282051282[/C][C]0.343902580807399[/C][C]486.507782693798[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]167.258108108108[/C][C]0.332316204443014[/C][C]503.310118110083[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]167.194285714286[/C][C]0.31759423552605[/C][C]526.439925577843[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]167.122727272727[/C][C]0.29619342341979[/C][C]564.235104693283[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]167.048064516129[/C][C]0.270164991147819[/C][C]618.318694092862[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]167.019310344828[/C][C]0.260395176679696[/C][C]641.407081630674[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]167.01962962963[/C][C]0.259238684572287[/C][C]644.269700354297[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]167.002[/C][C]0.261015963751901[/C][C]639.815272596651[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]166.97652173913[/C][C]0.263048868072701[/C][C]634.773770221971[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]166.948095238095[/C][C]0.264002722792255[/C][C]632.372626586385[/C][/ROW]
[ROW][C]Median[/C][C]166.32[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]167.445[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]166.887096774194[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]166.983125[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]166.983125[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]166.983125[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]166.983125[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]166.983125[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]166.983125[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]166.983125[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]61[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=240475&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=240475&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 Mean167.5127868852460.421995722348217396.953755723191
Geometric Mean167.480988810618
Harmonic Mean167.449288678658
Quadratic Mean167.544676410331
Winsorized Mean ( 1 / 20 )167.5101639344260.419189531047795399.604836303336
Winsorized Mean ( 2 / 20 )167.5137704918030.417303611343267401.419412481454
Winsorized Mean ( 3 / 20 )167.5152459016390.416990624218574401.724250312719
Winsorized Mean ( 4 / 20 )167.5650819672130.407031411023958411.676046194258
Winsorized Mean ( 5 / 20 )167.5601639344260.400259648774814418.628668783686
Winsorized Mean ( 6 / 20 )167.6477049180330.384342842273276436.193123635256
Winsorized Mean ( 7 / 20 )167.6614754098360.372977081883245449.522191989051
Winsorized Mean ( 8 / 20 )167.6536065573770.366928473307638456.910866158959
Winsorized Mean ( 9 / 20 )167.6536065573770.364934011011204459.408006649809
Winsorized Mean ( 10 / 20 )167.6552459016390.364703383224471459.703017886317
Winsorized Mean ( 11 / 20 )167.6660655737710.360777414894189464.735481357515
Winsorized Mean ( 12 / 20 )167.6975409836070.353908053242084473.844942061537
Winsorized Mean ( 13 / 20 )167.6975409836070.353908053242084473.844942061537
Winsorized Mean ( 14 / 20 )167.653934426230.338633163763483495.090122192895
Winsorized Mean ( 15 / 20 )167.2531147540980.265132665110118630.828022207798
Winsorized Mean ( 16 / 20 )167.0170491803280.222471014169219750.736224240383
Winsorized Mean ( 17 / 20 )167.1424590163930.204610072416538816.882849619106
Winsorized Mean ( 18 / 20 )167.1749180327870.198599140835205841.77060046552
Winsorized Mean ( 19 / 20 )167.1624590163930.196717274548742849.759937960985
Winsorized Mean ( 20 / 20 )167.2050819672130.178527618434126936.578236094652
Trimmed Mean ( 1 / 20 )167.5150847457630.413649589893728404.968574461296
Trimmed Mean ( 2 / 20 )167.5203508771930.40667657591816411.925251654782
Trimmed Mean ( 3 / 20 )167.5240.399151001358536419.700813551316
Trimmed Mean ( 4 / 20 )167.5273584905660.389808496667616429.768360419845
Trimmed Mean ( 5 / 20 )167.5160784313730.381868274016708438.675034899713
Trimmed Mean ( 6 / 20 )167.5051020408160.373959909366885447.922619096798
Trimmed Mean ( 7 / 20 )167.4742553191490.368370884661273454.634886449145
Trimmed Mean ( 8 / 20 )167.4380.363893035676889460.129718307313
Trimmed Mean ( 9 / 20 )167.399767441860.359145578957977466.10560521879
Trimmed Mean ( 10 / 20 )167.3578048780490.352831320196493474.328086250525
Trimmed Mean ( 11 / 20 )167.3112820512820.343902580807399486.507782693798
Trimmed Mean ( 12 / 20 )167.2581081081080.332316204443014503.310118110083
Trimmed Mean ( 13 / 20 )167.1942857142860.31759423552605526.439925577843
Trimmed Mean ( 14 / 20 )167.1227272727270.29619342341979564.235104693283
Trimmed Mean ( 15 / 20 )167.0480645161290.270164991147819618.318694092862
Trimmed Mean ( 16 / 20 )167.0193103448280.260395176679696641.407081630674
Trimmed Mean ( 17 / 20 )167.019629629630.259238684572287644.269700354297
Trimmed Mean ( 18 / 20 )167.0020.261015963751901639.815272596651
Trimmed Mean ( 19 / 20 )166.976521739130.263048868072701634.773770221971
Trimmed Mean ( 20 / 20 )166.9480952380950.264002722792255632.372626586385
Median166.32
Midrange167.445
Midmean - Weighted Average at Xnp166.887096774194
Midmean - Weighted Average at X(n+1)p166.983125
Midmean - Empirical Distribution Function166.983125
Midmean - Empirical Distribution Function - Averaging166.983125
Midmean - Empirical Distribution Function - Interpolation166.983125
Midmean - Closest Observation166.983125
Midmean - True Basic - Statistics Graphics Toolkit166.983125
Midmean - MS Excel (old versions)166.983125
Number of observations61



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')