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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 computationSat, 11 Dec 2010 20:08:12 +0000
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2010/Dec/11/t1292098012woelw6qa5v71as7.htm/, Retrieved Mon, 06 May 2024 21:14:40 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=108294, Retrieved Mon, 06 May 2024 21:14:40 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact135
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Central Tendency] [] [2009-12-20 16:30:59] [ebd107afac1bd6180acb277edd05815b]
- R  D    [Central Tendency] [CLT van resiudu's...] [2010-12-11 20:08:12] [de8ccb310fbbdc3d90ae577a3e011cf9] [Current]
-    D      [Central Tendency] [CLT van resiudu's...] [2010-12-12 16:21:36] [04d4386fa51dbd2ef12d0f1f80644886]
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Dataseries X:
1.81599631530786
81.7153834956105
-20.9736908665659
-380.365901684407
-107.329398347448
79.1666741724123
-15.8540226802667
-9.58326516345511
-258.557233569299
222.122436883621
-85.9895951634096
-50.4050552899625
-5.39877697891487
110.751645636099
87.4210760309233
-14.4153329459499
-30.6612124590284
-10.1397493861907
54.6217835455867
101.806138595280
196.902558868216
-211.866403048994
228.712625579972
17.1652836048803
-385.911059008046
-124.308743325184
252.346757948190
-123.714461561155
235.539534700022
-146.829674336914
21.0503380760272
34.5688836459363
-318.745334756316
-62.0135124195656
-413.976462705086
-93.0765324730812
-19.3742226883348
-105.131291885215
-81.1867830172024
-132.134931970177
-116.850333046158
127.824269485207
149.959628704556
16.1732509312351
-479.17864279724
-117.712471515111
-178.116473768101
41.2779704984198
85.5463817358984




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time5 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 & 5 seconds \tabularnewline
R Server & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=108294&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]5 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=108294&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=108294&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 time5 seconds
R Server'George Udny Yule' @ 72.249.76.132







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean-39.863509191905724.1254165923033-1.65234490519112
Geometric MeanNaN
Harmonic Mean640.011522534532
Quadratic Mean171.83368180074
Winsorized Mean ( 1 / 16 )-38.875857011416223.5671257014111-1.64957990651734
Winsorized Mean ( 2 / 16 )-38.008979681743123.1303577233542-1.64325083668578
Winsorized Mean ( 3 / 16 )-38.072961194358122.9282048564795-1.66052952826783
Winsorized Mean ( 4 / 16 )-35.101476385159320.9522183064957-1.67531074140617
Winsorized Mean ( 5 / 16 )-33.749928321551418.2332963575925-1.85100530697499
Winsorized Mean ( 6 / 16 )-30.743135917352716.2719204258381-1.88933666787946
Winsorized Mean ( 7 / 16 )-28.36066371281214.7110273311999-1.92785065749034
Winsorized Mean ( 8 / 16 )-24.713105771527413.3940267522485-1.8450840982066
Winsorized Mean ( 9 / 16 )-24.656225807824912.3837118326418-1.99102063589969
Winsorized Mean ( 10 / 16 )-23.441635124158012.0275376055356-1.94899703438625
Winsorized Mean ( 11 / 16 )-24.168244945358911.8429203760299-2.04073355033912
Winsorized Mean ( 12 / 16 )-23.322543543845711.4719820470870-2.03300035234694
Winsorized Mean ( 13 / 16 )-29.605722687771110.2669352211032-2.8835988588803
Winsorized Mean ( 14 / 16 )-30.69797364447309.14963908230466-3.35510213772724
Winsorized Mean ( 15 / 16 )-32.07888600883548.69978039607556-3.68732135161781
Winsorized Mean ( 16 / 16 )-32.55685699912947.32622573552918-4.44387849547715
Trimmed Mean ( 1 / 16 )-39.863509191905722.4546307716986-1.77529123489970
Trimmed Mean ( 2 / 16 )-36.733618416049521.0028050785704-1.74898630343095
Trimmed Mean ( 3 / 16 )-32.34522567723719.4105190256891-1.66637613525065
Trimmed Mean ( 4 / 16 )-32.34522567723717.3619609387602-1.86299380532685
Trimmed Mean ( 5 / 16 )-28.480986241853915.5729389256227-1.82887677000987
Trimmed Mean ( 6 / 16 )-27.085428609934114.3571233364170-1.88654983141586
Trimmed Mean ( 7 / 16 )-26.231963571536413.4849631218601-1.94527514346794
Trimmed Mean ( 8 / 16 )-26.231963571536412.8568197677596-2.04031510477552
Trimmed Mean ( 9 / 16 )-25.991301971939912.4270716296315-2.09150657102237
Trimmed Mean ( 10 / 16 )-26.241948454858112.1308141856067-2.16324708740443
Trimmed Mean ( 11 / 16 )-26.750153466725911.7772839984127-2.27133467022882
Trimmed Mean ( 12 / 16 )-27.210202621442211.2693064574288-2.41454101228252
Trimmed Mean ( 13 / 16 )-27.900402964928510.5838178710110-2.63613785733668
Trimmed Mean ( 14 / 16 )-27.59431993775169.9948480558002-2.76085437054124
Trimmed Mean ( 15 / 16 )-27.02259425493459.49752955917744-2.84522349591665
Trimmed Mean ( 16 / 16 )-27.02259425493458.7739005967518-3.07988379363890
Median-15.8540226802667
Midrange-113.415942424525
Midmean - Weighted Average at Xnp-31.6425724878528
Midmean - Weighted Average at X(n+1)p-27.2102026214422
Midmean - Empirical Distribution Function-27.2102026214422
Midmean - Empirical Distribution Function - Averaging-27.2102026214422
Midmean - Empirical Distribution Function - Interpolation-27.2102026214422
Midmean - Closest Observation-30.9219048883542
Midmean - True Basic - Statistics Graphics Toolkit-27.2102026214422
Midmean - MS Excel (old versions)-27.2102026214422
Number of observations49

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & -39.8635091919057 & 24.1254165923033 & -1.65234490519112 \tabularnewline
Geometric Mean & NaN &  &  \tabularnewline
Harmonic Mean & 640.011522534532 &  &  \tabularnewline
Quadratic Mean & 171.83368180074 &  &  \tabularnewline
Winsorized Mean ( 1 / 16 ) & -38.8758570114162 & 23.5671257014111 & -1.64957990651734 \tabularnewline
Winsorized Mean ( 2 / 16 ) & -38.0089796817431 & 23.1303577233542 & -1.64325083668578 \tabularnewline
Winsorized Mean ( 3 / 16 ) & -38.0729611943581 & 22.9282048564795 & -1.66052952826783 \tabularnewline
Winsorized Mean ( 4 / 16 ) & -35.1014763851593 & 20.9522183064957 & -1.67531074140617 \tabularnewline
Winsorized Mean ( 5 / 16 ) & -33.7499283215514 & 18.2332963575925 & -1.85100530697499 \tabularnewline
Winsorized Mean ( 6 / 16 ) & -30.7431359173527 & 16.2719204258381 & -1.88933666787946 \tabularnewline
Winsorized Mean ( 7 / 16 ) & -28.360663712812 & 14.7110273311999 & -1.92785065749034 \tabularnewline
Winsorized Mean ( 8 / 16 ) & -24.7131057715274 & 13.3940267522485 & -1.8450840982066 \tabularnewline
Winsorized Mean ( 9 / 16 ) & -24.6562258078249 & 12.3837118326418 & -1.99102063589969 \tabularnewline
Winsorized Mean ( 10 / 16 ) & -23.4416351241580 & 12.0275376055356 & -1.94899703438625 \tabularnewline
Winsorized Mean ( 11 / 16 ) & -24.1682449453589 & 11.8429203760299 & -2.04073355033912 \tabularnewline
Winsorized Mean ( 12 / 16 ) & -23.3225435438457 & 11.4719820470870 & -2.03300035234694 \tabularnewline
Winsorized Mean ( 13 / 16 ) & -29.6057226877711 & 10.2669352211032 & -2.8835988588803 \tabularnewline
Winsorized Mean ( 14 / 16 ) & -30.6979736444730 & 9.14963908230466 & -3.35510213772724 \tabularnewline
Winsorized Mean ( 15 / 16 ) & -32.0788860088354 & 8.69978039607556 & -3.68732135161781 \tabularnewline
Winsorized Mean ( 16 / 16 ) & -32.5568569991294 & 7.32622573552918 & -4.44387849547715 \tabularnewline
Trimmed Mean ( 1 / 16 ) & -39.8635091919057 & 22.4546307716986 & -1.77529123489970 \tabularnewline
Trimmed Mean ( 2 / 16 ) & -36.7336184160495 & 21.0028050785704 & -1.74898630343095 \tabularnewline
Trimmed Mean ( 3 / 16 ) & -32.345225677237 & 19.4105190256891 & -1.66637613525065 \tabularnewline
Trimmed Mean ( 4 / 16 ) & -32.345225677237 & 17.3619609387602 & -1.86299380532685 \tabularnewline
Trimmed Mean ( 5 / 16 ) & -28.4809862418539 & 15.5729389256227 & -1.82887677000987 \tabularnewline
Trimmed Mean ( 6 / 16 ) & -27.0854286099341 & 14.3571233364170 & -1.88654983141586 \tabularnewline
Trimmed Mean ( 7 / 16 ) & -26.2319635715364 & 13.4849631218601 & -1.94527514346794 \tabularnewline
Trimmed Mean ( 8 / 16 ) & -26.2319635715364 & 12.8568197677596 & -2.04031510477552 \tabularnewline
Trimmed Mean ( 9 / 16 ) & -25.9913019719399 & 12.4270716296315 & -2.09150657102237 \tabularnewline
Trimmed Mean ( 10 / 16 ) & -26.2419484548581 & 12.1308141856067 & -2.16324708740443 \tabularnewline
Trimmed Mean ( 11 / 16 ) & -26.7501534667259 & 11.7772839984127 & -2.27133467022882 \tabularnewline
Trimmed Mean ( 12 / 16 ) & -27.2102026214422 & 11.2693064574288 & -2.41454101228252 \tabularnewline
Trimmed Mean ( 13 / 16 ) & -27.9004029649285 & 10.5838178710110 & -2.63613785733668 \tabularnewline
Trimmed Mean ( 14 / 16 ) & -27.5943199377516 & 9.9948480558002 & -2.76085437054124 \tabularnewline
Trimmed Mean ( 15 / 16 ) & -27.0225942549345 & 9.49752955917744 & -2.84522349591665 \tabularnewline
Trimmed Mean ( 16 / 16 ) & -27.0225942549345 & 8.7739005967518 & -3.07988379363890 \tabularnewline
Median & -15.8540226802667 &  &  \tabularnewline
Midrange & -113.415942424525 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & -31.6425724878528 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & -27.2102026214422 &  &  \tabularnewline
Midmean - Empirical Distribution Function & -27.2102026214422 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & -27.2102026214422 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & -27.2102026214422 &  &  \tabularnewline
Midmean - Closest Observation & -30.9219048883542 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & -27.2102026214422 &  &  \tabularnewline
Midmean - MS Excel (old versions) & -27.2102026214422 &  &  \tabularnewline
Number of observations & 49 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=108294&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]-39.8635091919057[/C][C]24.1254165923033[/C][C]-1.65234490519112[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]NaN[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]640.011522534532[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]171.83368180074[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 16 )[/C][C]-38.8758570114162[/C][C]23.5671257014111[/C][C]-1.64957990651734[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 16 )[/C][C]-38.0089796817431[/C][C]23.1303577233542[/C][C]-1.64325083668578[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 16 )[/C][C]-38.0729611943581[/C][C]22.9282048564795[/C][C]-1.66052952826783[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 16 )[/C][C]-35.1014763851593[/C][C]20.9522183064957[/C][C]-1.67531074140617[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 16 )[/C][C]-33.7499283215514[/C][C]18.2332963575925[/C][C]-1.85100530697499[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 16 )[/C][C]-30.7431359173527[/C][C]16.2719204258381[/C][C]-1.88933666787946[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 16 )[/C][C]-28.360663712812[/C][C]14.7110273311999[/C][C]-1.92785065749034[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 16 )[/C][C]-24.7131057715274[/C][C]13.3940267522485[/C][C]-1.8450840982066[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 16 )[/C][C]-24.6562258078249[/C][C]12.3837118326418[/C][C]-1.99102063589969[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 16 )[/C][C]-23.4416351241580[/C][C]12.0275376055356[/C][C]-1.94899703438625[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 16 )[/C][C]-24.1682449453589[/C][C]11.8429203760299[/C][C]-2.04073355033912[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 16 )[/C][C]-23.3225435438457[/C][C]11.4719820470870[/C][C]-2.03300035234694[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 16 )[/C][C]-29.6057226877711[/C][C]10.2669352211032[/C][C]-2.8835988588803[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 16 )[/C][C]-30.6979736444730[/C][C]9.14963908230466[/C][C]-3.35510213772724[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 16 )[/C][C]-32.0788860088354[/C][C]8.69978039607556[/C][C]-3.68732135161781[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 16 )[/C][C]-32.5568569991294[/C][C]7.32622573552918[/C][C]-4.44387849547715[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 16 )[/C][C]-39.8635091919057[/C][C]22.4546307716986[/C][C]-1.77529123489970[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 16 )[/C][C]-36.7336184160495[/C][C]21.0028050785704[/C][C]-1.74898630343095[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 16 )[/C][C]-32.345225677237[/C][C]19.4105190256891[/C][C]-1.66637613525065[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 16 )[/C][C]-32.345225677237[/C][C]17.3619609387602[/C][C]-1.86299380532685[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 16 )[/C][C]-28.4809862418539[/C][C]15.5729389256227[/C][C]-1.82887677000987[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 16 )[/C][C]-27.0854286099341[/C][C]14.3571233364170[/C][C]-1.88654983141586[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 16 )[/C][C]-26.2319635715364[/C][C]13.4849631218601[/C][C]-1.94527514346794[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 16 )[/C][C]-26.2319635715364[/C][C]12.8568197677596[/C][C]-2.04031510477552[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 16 )[/C][C]-25.9913019719399[/C][C]12.4270716296315[/C][C]-2.09150657102237[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 16 )[/C][C]-26.2419484548581[/C][C]12.1308141856067[/C][C]-2.16324708740443[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 16 )[/C][C]-26.7501534667259[/C][C]11.7772839984127[/C][C]-2.27133467022882[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 16 )[/C][C]-27.2102026214422[/C][C]11.2693064574288[/C][C]-2.41454101228252[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 16 )[/C][C]-27.9004029649285[/C][C]10.5838178710110[/C][C]-2.63613785733668[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 16 )[/C][C]-27.5943199377516[/C][C]9.9948480558002[/C][C]-2.76085437054124[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 16 )[/C][C]-27.0225942549345[/C][C]9.49752955917744[/C][C]-2.84522349591665[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 16 )[/C][C]-27.0225942549345[/C][C]8.7739005967518[/C][C]-3.07988379363890[/C][/ROW]
[ROW][C]Median[/C][C]-15.8540226802667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]-113.415942424525[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]-31.6425724878528[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]-27.2102026214422[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]-27.2102026214422[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]-27.2102026214422[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]-27.2102026214422[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]-30.9219048883542[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]-27.2102026214422[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]-27.2102026214422[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]49[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=108294&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=108294&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 Mean-39.863509191905724.1254165923033-1.65234490519112
Geometric MeanNaN
Harmonic Mean640.011522534532
Quadratic Mean171.83368180074
Winsorized Mean ( 1 / 16 )-38.875857011416223.5671257014111-1.64957990651734
Winsorized Mean ( 2 / 16 )-38.008979681743123.1303577233542-1.64325083668578
Winsorized Mean ( 3 / 16 )-38.072961194358122.9282048564795-1.66052952826783
Winsorized Mean ( 4 / 16 )-35.101476385159320.9522183064957-1.67531074140617
Winsorized Mean ( 5 / 16 )-33.749928321551418.2332963575925-1.85100530697499
Winsorized Mean ( 6 / 16 )-30.743135917352716.2719204258381-1.88933666787946
Winsorized Mean ( 7 / 16 )-28.36066371281214.7110273311999-1.92785065749034
Winsorized Mean ( 8 / 16 )-24.713105771527413.3940267522485-1.8450840982066
Winsorized Mean ( 9 / 16 )-24.656225807824912.3837118326418-1.99102063589969
Winsorized Mean ( 10 / 16 )-23.441635124158012.0275376055356-1.94899703438625
Winsorized Mean ( 11 / 16 )-24.168244945358911.8429203760299-2.04073355033912
Winsorized Mean ( 12 / 16 )-23.322543543845711.4719820470870-2.03300035234694
Winsorized Mean ( 13 / 16 )-29.605722687771110.2669352211032-2.8835988588803
Winsorized Mean ( 14 / 16 )-30.69797364447309.14963908230466-3.35510213772724
Winsorized Mean ( 15 / 16 )-32.07888600883548.69978039607556-3.68732135161781
Winsorized Mean ( 16 / 16 )-32.55685699912947.32622573552918-4.44387849547715
Trimmed Mean ( 1 / 16 )-39.863509191905722.4546307716986-1.77529123489970
Trimmed Mean ( 2 / 16 )-36.733618416049521.0028050785704-1.74898630343095
Trimmed Mean ( 3 / 16 )-32.34522567723719.4105190256891-1.66637613525065
Trimmed Mean ( 4 / 16 )-32.34522567723717.3619609387602-1.86299380532685
Trimmed Mean ( 5 / 16 )-28.480986241853915.5729389256227-1.82887677000987
Trimmed Mean ( 6 / 16 )-27.085428609934114.3571233364170-1.88654983141586
Trimmed Mean ( 7 / 16 )-26.231963571536413.4849631218601-1.94527514346794
Trimmed Mean ( 8 / 16 )-26.231963571536412.8568197677596-2.04031510477552
Trimmed Mean ( 9 / 16 )-25.991301971939912.4270716296315-2.09150657102237
Trimmed Mean ( 10 / 16 )-26.241948454858112.1308141856067-2.16324708740443
Trimmed Mean ( 11 / 16 )-26.750153466725911.7772839984127-2.27133467022882
Trimmed Mean ( 12 / 16 )-27.210202621442211.2693064574288-2.41454101228252
Trimmed Mean ( 13 / 16 )-27.900402964928510.5838178710110-2.63613785733668
Trimmed Mean ( 14 / 16 )-27.59431993775169.9948480558002-2.76085437054124
Trimmed Mean ( 15 / 16 )-27.02259425493459.49752955917744-2.84522349591665
Trimmed Mean ( 16 / 16 )-27.02259425493458.7739005967518-3.07988379363890
Median-15.8540226802667
Midrange-113.415942424525
Midmean - Weighted Average at Xnp-31.6425724878528
Midmean - Weighted Average at X(n+1)p-27.2102026214422
Midmean - Empirical Distribution Function-27.2102026214422
Midmean - Empirical Distribution Function - Averaging-27.2102026214422
Midmean - Empirical Distribution Function - Interpolation-27.2102026214422
Midmean - Closest Observation-30.9219048883542
Midmean - True Basic - Statistics Graphics Toolkit-27.2102026214422
Midmean - MS Excel (old versions)-27.2102026214422
Number of observations49



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')