Free Statistics

of Irreproducible Research!

Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationWed, 30 Dec 2009 07:57:55 -0700
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2009/Dec/30/t1262185187fooln9fzi0fndlt.htm/, Retrieved Mon, 29 Apr 2024 03:34:23 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=71304, Retrieved Mon, 29 Apr 2024 03:34:23 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact141
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [ARIMA Backward Selection] [arima backward se...] [2008-12-17 10:56:10] [11edab5c4db3615abbf782b1c6e7cacf]
- RMPD  [Central Tendency] [central tendency ...] [2008-12-23 10:31:31] [74be16979710d4c4e7c6647856088456]
-  M D      [Central Tendency] [paper centraltend...] [2009-12-30 14:57:55] [1b03feaac1d41902024770a37504c07f] [Current]
Feedback Forum

Post a new message
Dataseries X:
1.72253096032993 
1.44114227554815 
1.21844280938542 
-4.8430869245474 
-18.1011453461693 
-6.73145604539303 
-0.303092086559358 
0.945728576856622 
-2.70053854018758 
-5.05586815617568 
0.741923468583488 
4.03502875153357 
7.92821581230946 
1.85123335163301 
5.65015347579261 
-12.4323085207163 
-3.59963162797111 
-9.2871671833107 
3.03663850466913 
3.24905094191389 
-6.12211412777286 
-3.68012610110207 
-2.60239587418152 
8.02361393692715 
3.15658032517451 
2.39331902216013 
11.0808402873687 
-8.78955697419477 
-7.68715255001899 
10.9621053016417 
-8.11995539823959 
-14.1286208176193 
16.5788082702985 
-3.76639375507993 
-0.386695023246311 
5.05233644968047 
-0.186770310317294 
-3.51607703193635 
-6.22928259464123 
3.49866200249415 
25.8585045131454 
12.3938966068163 
-3.35245798407308 
5.82024341201016 
-4.8044133425166 
7.22207736053638 
5.6463041373022 
2.11833244086977 




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135

\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 & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=71304&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]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=71304&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=71304&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'Gwilym Jenkins' @ 72.249.127.135







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean0.3166543058127181.145535289073170.276424749925352
Geometric MeanNaN
Harmonic Mean-7.66090518069192
Quadratic Mean7.85977554256175
Winsorized Mean ( 1 / 16 )0.2060882284315321.040273647425370.198109631001026
Winsorized Mean ( 2 / 16 )0.1023965881573990.9671697672096540.105872403820913
Winsorized Mean ( 3 / 16 )0.2169019017797740.8959976010376360.242078663523858
Winsorized Mean ( 4 / 16 )0.2484748370621850.8842565579202120.280998579921875
Winsorized Mean ( 5 / 16 )0.01213215073308370.7965418929815560.0152310265661880
Winsorized Mean ( 6 / 16 )0.05430774118344760.7824173977499230.0694101912094822
Winsorized Mean ( 7 / 16 )0.0907016238911590.732197650788060.123875873944061
Winsorized Mean ( 8 / 16 )-0.05924179240457760.669552022997695-0.0884797452173205
Winsorized Mean ( 9 / 16 )-0.07103956790754880.659699422799108-0.107684750740159
Winsorized Mean ( 10 / 16 )0.1502930639896950.6179055139727660.243229847591745
Winsorized Mean ( 11 / 16 )0.0629378344911960.5839082680347770.107787195243907
Winsorized Mean ( 12 / 16 )-0.1817206945378290.537747428368743-0.337929453403578
Winsorized Mean ( 13 / 16 )-0.04585638413857380.463981723224015-0.0988323070571336
Winsorized Mean ( 14 / 16 )-0.09349821106427380.447994481824038-0.208703934663637
Winsorized Mean ( 15 / 16 )-0.0972407559419050.439146148747591-0.221431421450986
Winsorized Mean ( 16 / 16 )-0.1093698307654450.428148436882723-0.255448394397393
Trimmed Mean ( 1 / 16 )0.1617836415659640.9749851270430040.165934471284328
Trimmed Mean ( 2 / 16 )0.1134513649853440.888586477005440.127676222766385
Trimmed Mean ( 3 / 16 )0.1197683803155990.8297913594101440.144335535622757
Trimmed Mean ( 4 / 16 )0.08091497172992870.791377229458780.102245766895853
Trimmed Mean ( 5 / 16 )0.02800133004605840.744730938527960.0375992571241985
Trimmed Mean ( 6 / 16 )0.03223311119618490.7179567124798390.0448956192426296
Trimmed Mean ( 7 / 16 )0.02703908061094670.685699055585520.0394328683854726
Trimmed Mean ( 8 / 16 )0.01339710705090120.6584544442200760.0203462930025018
Trimmed Mean ( 9 / 16 )0.02792488694199690.6409376316900120.0435688053896369
Trimmed Mean ( 10 / 16 )0.04677525929429130.617164672251370.0757905651398657
Trimmed Mean ( 11 / 16 )0.02766427996590910.5955648107256220.0464504945015197
Trimmed Mean ( 12 / 16 )0.02125090641585700.5735422662228340.0370520320251351
Trimmed Mean ( 13 / 16 )0.05815483386198170.5546993135811480.104840284525562
Trimmed Mean ( 14 / 16 )0.07735690487746890.5517478397257330.140203367023461
Trimmed Mean ( 15 / 16 )0.1099007364854200.5467801545925230.200996205810215
Trimmed Mean ( 16 / 16 )0.1513290349708850.5339086404365490.283436197711937
Median0.843826022720055
Midrange3.87867958348805
Midmean - Weighted Average at Xnp-0.173322606822673
Midmean - Weighted Average at X(n+1)p0.0212509064158569
Midmean - Empirical Distribution Function-0.173322606822673
Midmean - Empirical Distribution Function - Averaging0.0212509064158569
Midmean - Empirical Distribution Function - Interpolation0.0212509064158569
Midmean - Closest Observation-0.173322606822673
Midmean - True Basic - Statistics Graphics Toolkit0.0212509064158569
Midmean - MS Excel (old versions)0.0276642799659091
Number of observations48

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 0.316654305812718 & 1.14553528907317 & 0.276424749925352 \tabularnewline
Geometric Mean & NaN &  &  \tabularnewline
Harmonic Mean & -7.66090518069192 &  &  \tabularnewline
Quadratic Mean & 7.85977554256175 &  &  \tabularnewline
Winsorized Mean ( 1 / 16 ) & 0.206088228431532 & 1.04027364742537 & 0.198109631001026 \tabularnewline
Winsorized Mean ( 2 / 16 ) & 0.102396588157399 & 0.967169767209654 & 0.105872403820913 \tabularnewline
Winsorized Mean ( 3 / 16 ) & 0.216901901779774 & 0.895997601037636 & 0.242078663523858 \tabularnewline
Winsorized Mean ( 4 / 16 ) & 0.248474837062185 & 0.884256557920212 & 0.280998579921875 \tabularnewline
Winsorized Mean ( 5 / 16 ) & 0.0121321507330837 & 0.796541892981556 & 0.0152310265661880 \tabularnewline
Winsorized Mean ( 6 / 16 ) & 0.0543077411834476 & 0.782417397749923 & 0.0694101912094822 \tabularnewline
Winsorized Mean ( 7 / 16 ) & 0.090701623891159 & 0.73219765078806 & 0.123875873944061 \tabularnewline
Winsorized Mean ( 8 / 16 ) & -0.0592417924045776 & 0.669552022997695 & -0.0884797452173205 \tabularnewline
Winsorized Mean ( 9 / 16 ) & -0.0710395679075488 & 0.659699422799108 & -0.107684750740159 \tabularnewline
Winsorized Mean ( 10 / 16 ) & 0.150293063989695 & 0.617905513972766 & 0.243229847591745 \tabularnewline
Winsorized Mean ( 11 / 16 ) & 0.062937834491196 & 0.583908268034777 & 0.107787195243907 \tabularnewline
Winsorized Mean ( 12 / 16 ) & -0.181720694537829 & 0.537747428368743 & -0.337929453403578 \tabularnewline
Winsorized Mean ( 13 / 16 ) & -0.0458563841385738 & 0.463981723224015 & -0.0988323070571336 \tabularnewline
Winsorized Mean ( 14 / 16 ) & -0.0934982110642738 & 0.447994481824038 & -0.208703934663637 \tabularnewline
Winsorized Mean ( 15 / 16 ) & -0.097240755941905 & 0.439146148747591 & -0.221431421450986 \tabularnewline
Winsorized Mean ( 16 / 16 ) & -0.109369830765445 & 0.428148436882723 & -0.255448394397393 \tabularnewline
Trimmed Mean ( 1 / 16 ) & 0.161783641565964 & 0.974985127043004 & 0.165934471284328 \tabularnewline
Trimmed Mean ( 2 / 16 ) & 0.113451364985344 & 0.88858647700544 & 0.127676222766385 \tabularnewline
Trimmed Mean ( 3 / 16 ) & 0.119768380315599 & 0.829791359410144 & 0.144335535622757 \tabularnewline
Trimmed Mean ( 4 / 16 ) & 0.0809149717299287 & 0.79137722945878 & 0.102245766895853 \tabularnewline
Trimmed Mean ( 5 / 16 ) & 0.0280013300460584 & 0.74473093852796 & 0.0375992571241985 \tabularnewline
Trimmed Mean ( 6 / 16 ) & 0.0322331111961849 & 0.717956712479839 & 0.0448956192426296 \tabularnewline
Trimmed Mean ( 7 / 16 ) & 0.0270390806109467 & 0.68569905558552 & 0.0394328683854726 \tabularnewline
Trimmed Mean ( 8 / 16 ) & 0.0133971070509012 & 0.658454444220076 & 0.0203462930025018 \tabularnewline
Trimmed Mean ( 9 / 16 ) & 0.0279248869419969 & 0.640937631690012 & 0.0435688053896369 \tabularnewline
Trimmed Mean ( 10 / 16 ) & 0.0467752592942913 & 0.61716467225137 & 0.0757905651398657 \tabularnewline
Trimmed Mean ( 11 / 16 ) & 0.0276642799659091 & 0.595564810725622 & 0.0464504945015197 \tabularnewline
Trimmed Mean ( 12 / 16 ) & 0.0212509064158570 & 0.573542266222834 & 0.0370520320251351 \tabularnewline
Trimmed Mean ( 13 / 16 ) & 0.0581548338619817 & 0.554699313581148 & 0.104840284525562 \tabularnewline
Trimmed Mean ( 14 / 16 ) & 0.0773569048774689 & 0.551747839725733 & 0.140203367023461 \tabularnewline
Trimmed Mean ( 15 / 16 ) & 0.109900736485420 & 0.546780154592523 & 0.200996205810215 \tabularnewline
Trimmed Mean ( 16 / 16 ) & 0.151329034970885 & 0.533908640436549 & 0.283436197711937 \tabularnewline
Median & 0.843826022720055 &  &  \tabularnewline
Midrange & 3.87867958348805 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & -0.173322606822673 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 0.0212509064158569 &  &  \tabularnewline
Midmean - Empirical Distribution Function & -0.173322606822673 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 0.0212509064158569 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 0.0212509064158569 &  &  \tabularnewline
Midmean - Closest Observation & -0.173322606822673 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 0.0212509064158569 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 0.0276642799659091 &  &  \tabularnewline
Number of observations & 48 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=71304&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]0.316654305812718[/C][C]1.14553528907317[/C][C]0.276424749925352[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]NaN[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]-7.66090518069192[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]7.85977554256175[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 16 )[/C][C]0.206088228431532[/C][C]1.04027364742537[/C][C]0.198109631001026[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 16 )[/C][C]0.102396588157399[/C][C]0.967169767209654[/C][C]0.105872403820913[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 16 )[/C][C]0.216901901779774[/C][C]0.895997601037636[/C][C]0.242078663523858[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 16 )[/C][C]0.248474837062185[/C][C]0.884256557920212[/C][C]0.280998579921875[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 16 )[/C][C]0.0121321507330837[/C][C]0.796541892981556[/C][C]0.0152310265661880[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 16 )[/C][C]0.0543077411834476[/C][C]0.782417397749923[/C][C]0.0694101912094822[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 16 )[/C][C]0.090701623891159[/C][C]0.73219765078806[/C][C]0.123875873944061[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 16 )[/C][C]-0.0592417924045776[/C][C]0.669552022997695[/C][C]-0.0884797452173205[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 16 )[/C][C]-0.0710395679075488[/C][C]0.659699422799108[/C][C]-0.107684750740159[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 16 )[/C][C]0.150293063989695[/C][C]0.617905513972766[/C][C]0.243229847591745[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 16 )[/C][C]0.062937834491196[/C][C]0.583908268034777[/C][C]0.107787195243907[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 16 )[/C][C]-0.181720694537829[/C][C]0.537747428368743[/C][C]-0.337929453403578[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 16 )[/C][C]-0.0458563841385738[/C][C]0.463981723224015[/C][C]-0.0988323070571336[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 16 )[/C][C]-0.0934982110642738[/C][C]0.447994481824038[/C][C]-0.208703934663637[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 16 )[/C][C]-0.097240755941905[/C][C]0.439146148747591[/C][C]-0.221431421450986[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 16 )[/C][C]-0.109369830765445[/C][C]0.428148436882723[/C][C]-0.255448394397393[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 16 )[/C][C]0.161783641565964[/C][C]0.974985127043004[/C][C]0.165934471284328[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 16 )[/C][C]0.113451364985344[/C][C]0.88858647700544[/C][C]0.127676222766385[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 16 )[/C][C]0.119768380315599[/C][C]0.829791359410144[/C][C]0.144335535622757[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 16 )[/C][C]0.0809149717299287[/C][C]0.79137722945878[/C][C]0.102245766895853[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 16 )[/C][C]0.0280013300460584[/C][C]0.74473093852796[/C][C]0.0375992571241985[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 16 )[/C][C]0.0322331111961849[/C][C]0.717956712479839[/C][C]0.0448956192426296[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 16 )[/C][C]0.0270390806109467[/C][C]0.68569905558552[/C][C]0.0394328683854726[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 16 )[/C][C]0.0133971070509012[/C][C]0.658454444220076[/C][C]0.0203462930025018[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 16 )[/C][C]0.0279248869419969[/C][C]0.640937631690012[/C][C]0.0435688053896369[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 16 )[/C][C]0.0467752592942913[/C][C]0.61716467225137[/C][C]0.0757905651398657[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 16 )[/C][C]0.0276642799659091[/C][C]0.595564810725622[/C][C]0.0464504945015197[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 16 )[/C][C]0.0212509064158570[/C][C]0.573542266222834[/C][C]0.0370520320251351[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 16 )[/C][C]0.0581548338619817[/C][C]0.554699313581148[/C][C]0.104840284525562[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 16 )[/C][C]0.0773569048774689[/C][C]0.551747839725733[/C][C]0.140203367023461[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 16 )[/C][C]0.109900736485420[/C][C]0.546780154592523[/C][C]0.200996205810215[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 16 )[/C][C]0.151329034970885[/C][C]0.533908640436549[/C][C]0.283436197711937[/C][/ROW]
[ROW][C]Median[/C][C]0.843826022720055[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]3.87867958348805[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]-0.173322606822673[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]0.0212509064158569[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]-0.173322606822673[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]0.0212509064158569[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]0.0212509064158569[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]-0.173322606822673[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]0.0212509064158569[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]0.0276642799659091[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]48[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=71304&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=71304&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 Mean0.3166543058127181.145535289073170.276424749925352
Geometric MeanNaN
Harmonic Mean-7.66090518069192
Quadratic Mean7.85977554256175
Winsorized Mean ( 1 / 16 )0.2060882284315321.040273647425370.198109631001026
Winsorized Mean ( 2 / 16 )0.1023965881573990.9671697672096540.105872403820913
Winsorized Mean ( 3 / 16 )0.2169019017797740.8959976010376360.242078663523858
Winsorized Mean ( 4 / 16 )0.2484748370621850.8842565579202120.280998579921875
Winsorized Mean ( 5 / 16 )0.01213215073308370.7965418929815560.0152310265661880
Winsorized Mean ( 6 / 16 )0.05430774118344760.7824173977499230.0694101912094822
Winsorized Mean ( 7 / 16 )0.0907016238911590.732197650788060.123875873944061
Winsorized Mean ( 8 / 16 )-0.05924179240457760.669552022997695-0.0884797452173205
Winsorized Mean ( 9 / 16 )-0.07103956790754880.659699422799108-0.107684750740159
Winsorized Mean ( 10 / 16 )0.1502930639896950.6179055139727660.243229847591745
Winsorized Mean ( 11 / 16 )0.0629378344911960.5839082680347770.107787195243907
Winsorized Mean ( 12 / 16 )-0.1817206945378290.537747428368743-0.337929453403578
Winsorized Mean ( 13 / 16 )-0.04585638413857380.463981723224015-0.0988323070571336
Winsorized Mean ( 14 / 16 )-0.09349821106427380.447994481824038-0.208703934663637
Winsorized Mean ( 15 / 16 )-0.0972407559419050.439146148747591-0.221431421450986
Winsorized Mean ( 16 / 16 )-0.1093698307654450.428148436882723-0.255448394397393
Trimmed Mean ( 1 / 16 )0.1617836415659640.9749851270430040.165934471284328
Trimmed Mean ( 2 / 16 )0.1134513649853440.888586477005440.127676222766385
Trimmed Mean ( 3 / 16 )0.1197683803155990.8297913594101440.144335535622757
Trimmed Mean ( 4 / 16 )0.08091497172992870.791377229458780.102245766895853
Trimmed Mean ( 5 / 16 )0.02800133004605840.744730938527960.0375992571241985
Trimmed Mean ( 6 / 16 )0.03223311119618490.7179567124798390.0448956192426296
Trimmed Mean ( 7 / 16 )0.02703908061094670.685699055585520.0394328683854726
Trimmed Mean ( 8 / 16 )0.01339710705090120.6584544442200760.0203462930025018
Trimmed Mean ( 9 / 16 )0.02792488694199690.6409376316900120.0435688053896369
Trimmed Mean ( 10 / 16 )0.04677525929429130.617164672251370.0757905651398657
Trimmed Mean ( 11 / 16 )0.02766427996590910.5955648107256220.0464504945015197
Trimmed Mean ( 12 / 16 )0.02125090641585700.5735422662228340.0370520320251351
Trimmed Mean ( 13 / 16 )0.05815483386198170.5546993135811480.104840284525562
Trimmed Mean ( 14 / 16 )0.07735690487746890.5517478397257330.140203367023461
Trimmed Mean ( 15 / 16 )0.1099007364854200.5467801545925230.200996205810215
Trimmed Mean ( 16 / 16 )0.1513290349708850.5339086404365490.283436197711937
Median0.843826022720055
Midrange3.87867958348805
Midmean - Weighted Average at Xnp-0.173322606822673
Midmean - Weighted Average at X(n+1)p0.0212509064158569
Midmean - Empirical Distribution Function-0.173322606822673
Midmean - Empirical Distribution Function - Averaging0.0212509064158569
Midmean - Empirical Distribution Function - Interpolation0.0212509064158569
Midmean - Closest Observation-0.173322606822673
Midmean - True Basic - Statistics Graphics Toolkit0.0212509064158569
Midmean - MS Excel (old versions)0.0276642799659091
Number of observations48



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')