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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 computationMon, 27 Oct 2008 12:44:02 -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/2008/Oct/27/t1225133072onavg0769gtbv3b.htm/, Retrieved Sun, 19 May 2024 13:35:12 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=19394, Retrieved Sun, 19 May 2024 13:35:12 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact158
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
F       [Central Tendency] [Q6 iA2] [2008-10-27 18:44:02] [b05bea52879de0a398b42c6968cc24b2] [Current]
- R       [Central Tendency] [Q6 Central tendency] [2008-11-01 10:49:05] [7d3039e6253bb5fb3b26df1537d500b4]
Feedback Forum
2008-11-01 10:55:50 [Stéphanie Claes] [reply
Je kan hier de R code aanpassen => http://www.freestatistics.org/blog/index.php?v=date/2008/Nov/01/t1225536614a5a0bqcl4pihxje.htm
We kijken naar de grafiek, stippellijn is 95% betrouwbaarheidsinterval, we willen weten of gemiddelde random component gelijk is aan nul als de extreme waarden worden weggenomen. Wat je ook doet met de outliers maakt niet uit want trimmed mean en winsorized mean is altijd nul of verschilt toch niet significant.
We kunnen besluiten dat het gemiddelde 0 is, het is heel robuust zelfs als we de outliers wegnemen.
De student heeft een fout besluit gemaakt, volgens hem is het gemiddelde niet gelijk aan nul.
2008-11-02 20:02:30 [Bernard Femont] [reply
de twee grafieken van central tendency blijven binnen de 2 lijnen van het betrouwbaarheidsinterval. We kunnen ook de R-code aanpassen en de volgende lijn invoegen: x

Post a new message
Dataseries X:
0.989130
0.919087
0.925417
0.925612
1.066667
0.851109
1.030693
0.989031
0.913001
0.792723
0.978170
0.987513
0.909434
0.883608
0.827451
0.825215
1.023256
0.815418
1.026193
0.914742
0.807276
0.739130
0.989733
0.972165
0.853890
0.856865
0.775739
0.789474
0.931350
0.739711
0.885246
0.842435
0.818458
0.727554
0.923239
0.922680
0.883762
0.818270
0.771047
0.825853
0.924485
0.755165
0.874671
0.815956
0.799808
0.712598
0.832981
0.910323
0.869150
0.779183
0.750255
0.758560
0.920890
0.743992
0.816254
0.769594
0.784007
0.683284
0.850505
0.900695
0.868398




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=19394&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=19394&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=19394&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 Mean0.8621000163934430.011429157591632375.4298826909705
Geometric Mean0.857584859570948
Harmonic Mean0.853105111120288
Quadratic Mean0.86663370397235
Winsorized Mean ( 1 / 20 )0.8619908360655740.011150250011855177.306861742929
Winsorized Mean ( 2 / 20 )0.8623336557377050.011008535368946178.3331866444522
Winsorized Mean ( 3 / 20 )0.8627585245901640.010860713118049579.4384784141238
Winsorized Mean ( 4 / 20 )0.8605983934426230.010353189461241983.1239877010219
Winsorized Mean ( 5 / 20 )0.8608998688524590.010275495612752383.7818341126095
Winsorized Mean ( 6 / 20 )0.8615061639344260.010158825960742084.8037132699835
Winsorized Mean ( 7 / 20 )0.8618954098360660.010020968020176986.0091967263708
Winsorized Mean ( 8 / 20 )0.8611153442622950.0096907647545949288.8593796329638
Winsorized Mean ( 9 / 20 )0.8618573278688520.0092340471316403893.3347334686766
Winsorized Mean ( 10 / 20 )0.8554045409836070.00798725070211619107.096242860759
Winsorized Mean ( 11 / 20 )0.8552159180327870.0076786800605147111.375381093227
Winsorized Mean ( 12 / 20 )0.855855065573770.0075570789668992113.252100358155
Winsorized Mean ( 13 / 20 )0.8566845081967210.00735497797984107116.476828420802
Winsorized Mean ( 14 / 20 )0.8576532622950820.00710734594734538120.671382629886
Winsorized Mean ( 15 / 20 )0.8583147377049180.00695955553076047123.328958855384
Winsorized Mean ( 16 / 20 )0.8597035901639340.00660047541098562130.248737648969
Winsorized Mean ( 17 / 20 )0.8612823606557380.00621440328930256138.594539259843
Winsorized Mean ( 18 / 20 )0.8624027868852460.00567637296759787151.928492332701
Winsorized Mean ( 19 / 20 )0.8620280819672130.00557024048952019154.755990084993
Winsorized Mean ( 20 / 20 )0.861247754098360.0054235775376513158.796983747250
Trimmed Mean ( 1 / 20 )0.8616635593220340.010868963376502979.2774369987137
Trimmed Mean ( 2 / 20 )0.8613133157894740.010522938775749381.8510241430288
Trimmed Mean ( 3 / 20 )0.8607474909090910.010189498094348484.473983206936
Trimmed Mean ( 4 / 20 )0.8599759622641510.0098451630297675287.3500986894737
Trimmed Mean ( 5 / 20 )0.8597898431372550.0096167570915124589.4053821839888
Trimmed Mean ( 6 / 20 )0.8595134693877550.0093515837687035691.9110057340492
Trimmed Mean ( 7 / 20 )0.8590824255319150.009047271462876794.954863359296
Trimmed Mean ( 8 / 20 )0.8585376888888890.0086940084569383498.750500777777
Trimmed Mean ( 9 / 20 )0.8580806046511630.0083309001480638102.999746654098
Trimmed Mean ( 10 / 20 )0.8574562682926830.00798177529254999107.426761198478
Trimmed Mean ( 11 / 20 )0.857777179487180.0078597467267377109.135473356813
Trimmed Mean ( 12 / 20 )0.8581610540540540.00776021020261744110.584769181202
Trimmed Mean ( 13 / 20 )0.8584959714285710.00763942491329408112.377041619274
Trimmed Mean ( 14 / 20 )0.8587535454545450.00750908662661986114.361917521400
Trimmed Mean ( 15 / 20 )0.8589081935483870.00737514342436363116.459863100560
Trimmed Mean ( 16 / 20 )0.8589914137931030.00720373164680675119.242561481850
Trimmed Mean ( 17 / 20 )0.8588908518518520.0070411226180775121.982089851229
Trimmed Mean ( 18 / 20 )0.85854760.00689356287802855124.543376943206
Trimmed Mean ( 19 / 20 )0.8579795652173910.00681305002764213125.931787046384
Trimmed Mean ( 20 / 20 )0.8573606190476190.00667010886306398128.537725043034
Median0.85389
Midrange0.8749755
Midmean - Weighted Average at Xnp0.856782466666667
Midmean - Weighted Average at X(n+1)p0.858908193548387
Midmean - Empirical Distribution Function0.858908193548387
Midmean - Empirical Distribution Function - Averaging0.858908193548387
Midmean - Empirical Distribution Function - Interpolation0.858908193548387
Midmean - Closest Observation0.856738375
Midmean - True Basic - Statistics Graphics Toolkit0.858908193548387
Midmean - MS Excel (old versions)0.858908193548387
Number of observations61

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 0.862100016393443 & 0.0114291575916323 & 75.4298826909705 \tabularnewline
Geometric Mean & 0.857584859570948 &  &  \tabularnewline
Harmonic Mean & 0.853105111120288 &  &  \tabularnewline
Quadratic Mean & 0.86663370397235 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 0.861990836065574 & 0.0111502500118551 & 77.306861742929 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 0.862333655737705 & 0.0110085353689461 & 78.3331866444522 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 0.862758524590164 & 0.0108607131180495 & 79.4384784141238 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 0.860598393442623 & 0.0103531894612419 & 83.1239877010219 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 0.860899868852459 & 0.0102754956127523 & 83.7818341126095 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 0.861506163934426 & 0.0101588259607420 & 84.8037132699835 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 0.861895409836066 & 0.0100209680201769 & 86.0091967263708 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 0.861115344262295 & 0.00969076475459492 & 88.8593796329638 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 0.861857327868852 & 0.00923404713164038 & 93.3347334686766 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 0.855404540983607 & 0.00798725070211619 & 107.096242860759 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 0.855215918032787 & 0.0076786800605147 & 111.375381093227 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 0.85585506557377 & 0.0075570789668992 & 113.252100358155 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 0.856684508196721 & 0.00735497797984107 & 116.476828420802 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 0.857653262295082 & 0.00710734594734538 & 120.671382629886 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 0.858314737704918 & 0.00695955553076047 & 123.328958855384 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 0.859703590163934 & 0.00660047541098562 & 130.248737648969 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 0.861282360655738 & 0.00621440328930256 & 138.594539259843 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 0.862402786885246 & 0.00567637296759787 & 151.928492332701 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 0.862028081967213 & 0.00557024048952019 & 154.755990084993 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 0.86124775409836 & 0.0054235775376513 & 158.796983747250 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 0.861663559322034 & 0.0108689633765029 & 79.2774369987137 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 0.861313315789474 & 0.0105229387757493 & 81.8510241430288 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 0.860747490909091 & 0.0101894980943484 & 84.473983206936 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 0.859975962264151 & 0.00984516302976752 & 87.3500986894737 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 0.859789843137255 & 0.00961675709151245 & 89.4053821839888 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 0.859513469387755 & 0.00935158376870356 & 91.9110057340492 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 0.859082425531915 & 0.0090472714628767 & 94.954863359296 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 0.858537688888889 & 0.00869400845693834 & 98.750500777777 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 0.858080604651163 & 0.0083309001480638 & 102.999746654098 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 0.857456268292683 & 0.00798177529254999 & 107.426761198478 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 0.85777717948718 & 0.0078597467267377 & 109.135473356813 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 0.858161054054054 & 0.00776021020261744 & 110.584769181202 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 0.858495971428571 & 0.00763942491329408 & 112.377041619274 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 0.858753545454545 & 0.00750908662661986 & 114.361917521400 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 0.858908193548387 & 0.00737514342436363 & 116.459863100560 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 0.858991413793103 & 0.00720373164680675 & 119.242561481850 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 0.858890851851852 & 0.0070411226180775 & 121.982089851229 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 0.8585476 & 0.00689356287802855 & 124.543376943206 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 0.857979565217391 & 0.00681305002764213 & 125.931787046384 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 0.857360619047619 & 0.00667010886306398 & 128.537725043034 \tabularnewline
Median & 0.85389 &  &  \tabularnewline
Midrange & 0.8749755 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 0.856782466666667 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 0.858908193548387 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 0.858908193548387 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 0.858908193548387 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 0.858908193548387 &  &  \tabularnewline
Midmean - Closest Observation & 0.856738375 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 0.858908193548387 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 0.858908193548387 &  &  \tabularnewline
Number of observations & 61 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=19394&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]0.862100016393443[/C][C]0.0114291575916323[/C][C]75.4298826909705[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]0.857584859570948[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]0.853105111120288[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]0.86663370397235[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]0.861990836065574[/C][C]0.0111502500118551[/C][C]77.306861742929[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]0.862333655737705[/C][C]0.0110085353689461[/C][C]78.3331866444522[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]0.862758524590164[/C][C]0.0108607131180495[/C][C]79.4384784141238[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]0.860598393442623[/C][C]0.0103531894612419[/C][C]83.1239877010219[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]0.860899868852459[/C][C]0.0102754956127523[/C][C]83.7818341126095[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]0.861506163934426[/C][C]0.0101588259607420[/C][C]84.8037132699835[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]0.861895409836066[/C][C]0.0100209680201769[/C][C]86.0091967263708[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]0.861115344262295[/C][C]0.00969076475459492[/C][C]88.8593796329638[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]0.861857327868852[/C][C]0.00923404713164038[/C][C]93.3347334686766[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]0.855404540983607[/C][C]0.00798725070211619[/C][C]107.096242860759[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]0.855215918032787[/C][C]0.0076786800605147[/C][C]111.375381093227[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]0.85585506557377[/C][C]0.0075570789668992[/C][C]113.252100358155[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]0.856684508196721[/C][C]0.00735497797984107[/C][C]116.476828420802[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]0.857653262295082[/C][C]0.00710734594734538[/C][C]120.671382629886[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]0.858314737704918[/C][C]0.00695955553076047[/C][C]123.328958855384[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]0.859703590163934[/C][C]0.00660047541098562[/C][C]130.248737648969[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]0.861282360655738[/C][C]0.00621440328930256[/C][C]138.594539259843[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]0.862402786885246[/C][C]0.00567637296759787[/C][C]151.928492332701[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]0.862028081967213[/C][C]0.00557024048952019[/C][C]154.755990084993[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]0.86124775409836[/C][C]0.0054235775376513[/C][C]158.796983747250[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]0.861663559322034[/C][C]0.0108689633765029[/C][C]79.2774369987137[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]0.861313315789474[/C][C]0.0105229387757493[/C][C]81.8510241430288[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]0.860747490909091[/C][C]0.0101894980943484[/C][C]84.473983206936[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]0.859975962264151[/C][C]0.00984516302976752[/C][C]87.3500986894737[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]0.859789843137255[/C][C]0.00961675709151245[/C][C]89.4053821839888[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]0.859513469387755[/C][C]0.00935158376870356[/C][C]91.9110057340492[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]0.859082425531915[/C][C]0.0090472714628767[/C][C]94.954863359296[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]0.858537688888889[/C][C]0.00869400845693834[/C][C]98.750500777777[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]0.858080604651163[/C][C]0.0083309001480638[/C][C]102.999746654098[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]0.857456268292683[/C][C]0.00798177529254999[/C][C]107.426761198478[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]0.85777717948718[/C][C]0.0078597467267377[/C][C]109.135473356813[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]0.858161054054054[/C][C]0.00776021020261744[/C][C]110.584769181202[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]0.858495971428571[/C][C]0.00763942491329408[/C][C]112.377041619274[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]0.858753545454545[/C][C]0.00750908662661986[/C][C]114.361917521400[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]0.858908193548387[/C][C]0.00737514342436363[/C][C]116.459863100560[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]0.858991413793103[/C][C]0.00720373164680675[/C][C]119.242561481850[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]0.858890851851852[/C][C]0.0070411226180775[/C][C]121.982089851229[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]0.8585476[/C][C]0.00689356287802855[/C][C]124.543376943206[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]0.857979565217391[/C][C]0.00681305002764213[/C][C]125.931787046384[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]0.857360619047619[/C][C]0.00667010886306398[/C][C]128.537725043034[/C][/ROW]
[ROW][C]Median[/C][C]0.85389[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]0.8749755[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]0.856782466666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]0.858908193548387[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]0.858908193548387[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]0.858908193548387[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]0.858908193548387[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]0.856738375[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]0.858908193548387[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]0.858908193548387[/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=19394&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=19394&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 Mean0.8621000163934430.011429157591632375.4298826909705
Geometric Mean0.857584859570948
Harmonic Mean0.853105111120288
Quadratic Mean0.86663370397235
Winsorized Mean ( 1 / 20 )0.8619908360655740.011150250011855177.306861742929
Winsorized Mean ( 2 / 20 )0.8623336557377050.011008535368946178.3331866444522
Winsorized Mean ( 3 / 20 )0.8627585245901640.010860713118049579.4384784141238
Winsorized Mean ( 4 / 20 )0.8605983934426230.010353189461241983.1239877010219
Winsorized Mean ( 5 / 20 )0.8608998688524590.010275495612752383.7818341126095
Winsorized Mean ( 6 / 20 )0.8615061639344260.010158825960742084.8037132699835
Winsorized Mean ( 7 / 20 )0.8618954098360660.010020968020176986.0091967263708
Winsorized Mean ( 8 / 20 )0.8611153442622950.0096907647545949288.8593796329638
Winsorized Mean ( 9 / 20 )0.8618573278688520.0092340471316403893.3347334686766
Winsorized Mean ( 10 / 20 )0.8554045409836070.00798725070211619107.096242860759
Winsorized Mean ( 11 / 20 )0.8552159180327870.0076786800605147111.375381093227
Winsorized Mean ( 12 / 20 )0.855855065573770.0075570789668992113.252100358155
Winsorized Mean ( 13 / 20 )0.8566845081967210.00735497797984107116.476828420802
Winsorized Mean ( 14 / 20 )0.8576532622950820.00710734594734538120.671382629886
Winsorized Mean ( 15 / 20 )0.8583147377049180.00695955553076047123.328958855384
Winsorized Mean ( 16 / 20 )0.8597035901639340.00660047541098562130.248737648969
Winsorized Mean ( 17 / 20 )0.8612823606557380.00621440328930256138.594539259843
Winsorized Mean ( 18 / 20 )0.8624027868852460.00567637296759787151.928492332701
Winsorized Mean ( 19 / 20 )0.8620280819672130.00557024048952019154.755990084993
Winsorized Mean ( 20 / 20 )0.861247754098360.0054235775376513158.796983747250
Trimmed Mean ( 1 / 20 )0.8616635593220340.010868963376502979.2774369987137
Trimmed Mean ( 2 / 20 )0.8613133157894740.010522938775749381.8510241430288
Trimmed Mean ( 3 / 20 )0.8607474909090910.010189498094348484.473983206936
Trimmed Mean ( 4 / 20 )0.8599759622641510.0098451630297675287.3500986894737
Trimmed Mean ( 5 / 20 )0.8597898431372550.0096167570915124589.4053821839888
Trimmed Mean ( 6 / 20 )0.8595134693877550.0093515837687035691.9110057340492
Trimmed Mean ( 7 / 20 )0.8590824255319150.009047271462876794.954863359296
Trimmed Mean ( 8 / 20 )0.8585376888888890.0086940084569383498.750500777777
Trimmed Mean ( 9 / 20 )0.8580806046511630.0083309001480638102.999746654098
Trimmed Mean ( 10 / 20 )0.8574562682926830.00798177529254999107.426761198478
Trimmed Mean ( 11 / 20 )0.857777179487180.0078597467267377109.135473356813
Trimmed Mean ( 12 / 20 )0.8581610540540540.00776021020261744110.584769181202
Trimmed Mean ( 13 / 20 )0.8584959714285710.00763942491329408112.377041619274
Trimmed Mean ( 14 / 20 )0.8587535454545450.00750908662661986114.361917521400
Trimmed Mean ( 15 / 20 )0.8589081935483870.00737514342436363116.459863100560
Trimmed Mean ( 16 / 20 )0.8589914137931030.00720373164680675119.242561481850
Trimmed Mean ( 17 / 20 )0.8588908518518520.0070411226180775121.982089851229
Trimmed Mean ( 18 / 20 )0.85854760.00689356287802855124.543376943206
Trimmed Mean ( 19 / 20 )0.8579795652173910.00681305002764213125.931787046384
Trimmed Mean ( 20 / 20 )0.8573606190476190.00667010886306398128.537725043034
Median0.85389
Midrange0.8749755
Midmean - Weighted Average at Xnp0.856782466666667
Midmean - Weighted Average at X(n+1)p0.858908193548387
Midmean - Empirical Distribution Function0.858908193548387
Midmean - Empirical Distribution Function - Averaging0.858908193548387
Midmean - Empirical Distribution Function - Interpolation0.858908193548387
Midmean - Closest Observation0.856738375
Midmean - True Basic - Statistics Graphics Toolkit0.858908193548387
Midmean - MS Excel (old versions)0.858908193548387
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')