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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 computationTue, 20 Oct 2009 16:16:53 -0600
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2009/Oct/21/t1256077084lnv3nyr035habv7.htm/, Retrieved Thu, 02 May 2024 12:39:17 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=49219, Retrieved Thu, 02 May 2024 12:39:17 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsY[t]/X[t] central tendency
Estimated Impact178
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Univariate Data Series] [tijdreeks 2: werk...] [2009-10-12 19:58:30] [616e2df490b611f6cb7080068870ecbd]
-   PD  [Univariate Data Series] [Y[t]-X[t]] [2009-10-20 21:41:47] [616e2df490b611f6cb7080068870ecbd]
-    D    [Univariate Data Series] [Y[t]/X[t]] [2009-10-20 22:13:56] [616e2df490b611f6cb7080068870ecbd]
- RM          [Central Tendency] [Y[t]/X[t] central...] [2009-10-20 22:16:53] [88e98f4c87ea17c4967db8279bda8533] [Current]
- RM            [Univariate Explorative Data Analysis] [part 2 model 3] [2009-10-21 16:06:07] [616e2df490b611f6cb7080068870ecbd]
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Dataseries X:
1.207317
1.225
1.24
1.220588
1.230769
1.287879
1.368421
1.3875
1.345679
1.298701
1.226667
1.210526
1.217949
1.230769
1.217949
1.213333
1.186667
1.267606
1.346667
1.373333
1.342105
1.246753
1.194805
1.177215
1.160494
1.146341
1.121951
1.097561
1.139241
1.232877
1.42029
1.515152
1.462687
1.347826
1.285714
1.267606
1.263889
1.28169
1.318841
1.314286
1.294118
1.296875
1.253731
1.227273
1.203125
1.253968
1.274194
1.230769
1.161765
1.117647
1.109375
1.114754
1.12069
1.131148
1.138889
1.191781
1.202899
1.295082
1.293103
1.258065
1.169014
1.090909
1.037975
1
0.972973
0.973333
1.0125
1.049383




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=49219&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=49219&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=49219&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 Mean1.222293852941180.013242923106324792.297889455948
Geometric Mean1.21741560444057
Harmonic Mean1.21245041440982
Quadratic Mean1.22709102709155
Winsorized Mean ( 1 / 22 )1.221527602941180.013007158666502393.9119475867554
Winsorized Mean ( 2 / 22 )1.221064955882350.012469829901958397.9215406691792
Winsorized Mean ( 3 / 22 )1.220169808823530.0120022237906056101.661977822692
Winsorized Mean ( 4 / 22 )1.220834985294120.0114603964584116106.526418150051
Winsorized Mean ( 5 / 22 )1.221312632352940.0111930211285299109.113761005949
Winsorized Mean ( 6 / 22 )1.223159485294120.0100636812750696121.541953869724
Winsorized Mean ( 7 / 22 )1.223724941176470.00990937265336102123.491666322733
Winsorized Mean ( 8 / 22 )1.224998588235290.00963105665058947127.192543111074
Winsorized Mean ( 9 / 22 )1.225237485294120.00941687682413528130.110811490478
Winsorized Mean ( 10 / 22 )1.222241750.00874138084739068139.822503027636
Winsorized Mean ( 11 / 22 )1.221997161764710.00853356090859948143.198973424244
Winsorized Mean ( 12 / 22 )1.219469397058820.00806972890132542151.116525966384
Winsorized Mean ( 13 / 22 )1.220878558823530.00770700048470188158.411636439745
Winsorized Mean ( 14 / 22 )1.222103147058820.00737991881018891165.598454195940
Winsorized Mean ( 15 / 22 )1.221968147058820.00733554875841165166.581695153699
Winsorized Mean ( 16 / 22 )1.223399911764710.0070228560059998174.202619378715
Winsorized Mean ( 17 / 22 )1.225632161764710.00626411067986305195.659403928588
Winsorized Mean ( 18 / 22 )1.225395514705880.00612732405480959199.988690616749
Winsorized Mean ( 19 / 22 )1.226296617647060.0056521684003964216.960382419083
Winsorized Mean ( 20 / 22 )1.226503970588240.00497174699308888246.694767914211
Winsorized Mean ( 21 / 22 )1.227388441176470.00425762354220302288.280170618698
Winsorized Mean ( 22 / 22 )1.229042970588240.00402512102872208305.343109391779
Trimmed Mean ( 1 / 22 )1.221634196969700.012319115992870299.165735404775
Trimmed Mean ( 2 / 22 )1.2217474531250.0114790645321904106.432667026036
Trimmed Mean ( 3 / 22 )1.222121725806450.0108190801208382112.959855381104
Trimmed Mean ( 4 / 22 )1.222859116666670.0102423827088925119.392054702758
Trimmed Mean ( 5 / 22 )1.223452396551720.00975383225484942125.432995420179
Trimmed Mean ( 6 / 22 )1.223972053571430.0092440320216427132.406730169886
Trimmed Mean ( 7 / 22 )1.224142592592590.00896739585987481136.510377340438
Trimmed Mean ( 8 / 22 )1.224220615384620.00866482376048508141.286268391001
Trimmed Mean ( 9 / 22 )1.224088360.00835848418592359146.448606322839
Trimmed Mean ( 10 / 22 )1.223907479166670.0080248928918964152.513870982948
Trimmed Mean ( 11 / 22 )1.224153717391300.00777017336489009157.545225814742
Trimmed Mean ( 12 / 22 )1.224456704545450.00749012286158146163.476184192648
Trimmed Mean ( 13 / 22 )1.225129595238100.00723370529292406169.364045897267
Trimmed Mean ( 14 / 22 )1.22568550.00698505341682492175.472602263526
Trimmed Mean ( 15 / 22 )1.226143394736840.00673394202549732182.0840438029
Trimmed Mean ( 16 / 22 )1.226669166666670.00639778708412601191.733352569710
Trimmed Mean ( 17 / 22 )1.227077823529410.00602299290737887203.732237842435
Trimmed Mean ( 18 / 22 )1.227258531250.00573006151201016214.178945318070
Trimmed Mean ( 19 / 22 )1.227493133333330.00534583740582352229.616623205965
Trimmed Mean ( 20 / 22 )1.227646071428570.00494748562240842248.135348967615
Trimmed Mean ( 21 / 22 )1.227795423076920.00460676652801176266.520001743355
Trimmed Mean ( 22 / 22 )1.227850333333330.00436512695818932281.286282184712
Median1.22697
Midrange1.2440625
Midmean - Weighted Average at Xnp1.22477105714286
Midmean - Weighted Average at X(n+1)p1.22707782352941
Midmean - Empirical Distribution Function1.22477105714286
Midmean - Empirical Distribution Function - Averaging1.22707782352941
Midmean - Empirical Distribution Function - Interpolation1.22707782352941
Midmean - Closest Observation1.22477105714286
Midmean - True Basic - Statistics Graphics Toolkit1.22707782352941
Midmean - MS Excel (old versions)1.22666916666667
Number of observations68

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 1.22229385294118 & 0.0132429231063247 & 92.297889455948 \tabularnewline
Geometric Mean & 1.21741560444057 &  &  \tabularnewline
Harmonic Mean & 1.21245041440982 &  &  \tabularnewline
Quadratic Mean & 1.22709102709155 &  &  \tabularnewline
Winsorized Mean ( 1 / 22 ) & 1.22152760294118 & 0.0130071586665023 & 93.9119475867554 \tabularnewline
Winsorized Mean ( 2 / 22 ) & 1.22106495588235 & 0.0124698299019583 & 97.9215406691792 \tabularnewline
Winsorized Mean ( 3 / 22 ) & 1.22016980882353 & 0.0120022237906056 & 101.661977822692 \tabularnewline
Winsorized Mean ( 4 / 22 ) & 1.22083498529412 & 0.0114603964584116 & 106.526418150051 \tabularnewline
Winsorized Mean ( 5 / 22 ) & 1.22131263235294 & 0.0111930211285299 & 109.113761005949 \tabularnewline
Winsorized Mean ( 6 / 22 ) & 1.22315948529412 & 0.0100636812750696 & 121.541953869724 \tabularnewline
Winsorized Mean ( 7 / 22 ) & 1.22372494117647 & 0.00990937265336102 & 123.491666322733 \tabularnewline
Winsorized Mean ( 8 / 22 ) & 1.22499858823529 & 0.00963105665058947 & 127.192543111074 \tabularnewline
Winsorized Mean ( 9 / 22 ) & 1.22523748529412 & 0.00941687682413528 & 130.110811490478 \tabularnewline
Winsorized Mean ( 10 / 22 ) & 1.22224175 & 0.00874138084739068 & 139.822503027636 \tabularnewline
Winsorized Mean ( 11 / 22 ) & 1.22199716176471 & 0.00853356090859948 & 143.198973424244 \tabularnewline
Winsorized Mean ( 12 / 22 ) & 1.21946939705882 & 0.00806972890132542 & 151.116525966384 \tabularnewline
Winsorized Mean ( 13 / 22 ) & 1.22087855882353 & 0.00770700048470188 & 158.411636439745 \tabularnewline
Winsorized Mean ( 14 / 22 ) & 1.22210314705882 & 0.00737991881018891 & 165.598454195940 \tabularnewline
Winsorized Mean ( 15 / 22 ) & 1.22196814705882 & 0.00733554875841165 & 166.581695153699 \tabularnewline
Winsorized Mean ( 16 / 22 ) & 1.22339991176471 & 0.0070228560059998 & 174.202619378715 \tabularnewline
Winsorized Mean ( 17 / 22 ) & 1.22563216176471 & 0.00626411067986305 & 195.659403928588 \tabularnewline
Winsorized Mean ( 18 / 22 ) & 1.22539551470588 & 0.00612732405480959 & 199.988690616749 \tabularnewline
Winsorized Mean ( 19 / 22 ) & 1.22629661764706 & 0.0056521684003964 & 216.960382419083 \tabularnewline
Winsorized Mean ( 20 / 22 ) & 1.22650397058824 & 0.00497174699308888 & 246.694767914211 \tabularnewline
Winsorized Mean ( 21 / 22 ) & 1.22738844117647 & 0.00425762354220302 & 288.280170618698 \tabularnewline
Winsorized Mean ( 22 / 22 ) & 1.22904297058824 & 0.00402512102872208 & 305.343109391779 \tabularnewline
Trimmed Mean ( 1 / 22 ) & 1.22163419696970 & 0.0123191159928702 & 99.165735404775 \tabularnewline
Trimmed Mean ( 2 / 22 ) & 1.221747453125 & 0.0114790645321904 & 106.432667026036 \tabularnewline
Trimmed Mean ( 3 / 22 ) & 1.22212172580645 & 0.0108190801208382 & 112.959855381104 \tabularnewline
Trimmed Mean ( 4 / 22 ) & 1.22285911666667 & 0.0102423827088925 & 119.392054702758 \tabularnewline
Trimmed Mean ( 5 / 22 ) & 1.22345239655172 & 0.00975383225484942 & 125.432995420179 \tabularnewline
Trimmed Mean ( 6 / 22 ) & 1.22397205357143 & 0.0092440320216427 & 132.406730169886 \tabularnewline
Trimmed Mean ( 7 / 22 ) & 1.22414259259259 & 0.00896739585987481 & 136.510377340438 \tabularnewline
Trimmed Mean ( 8 / 22 ) & 1.22422061538462 & 0.00866482376048508 & 141.286268391001 \tabularnewline
Trimmed Mean ( 9 / 22 ) & 1.22408836 & 0.00835848418592359 & 146.448606322839 \tabularnewline
Trimmed Mean ( 10 / 22 ) & 1.22390747916667 & 0.0080248928918964 & 152.513870982948 \tabularnewline
Trimmed Mean ( 11 / 22 ) & 1.22415371739130 & 0.00777017336489009 & 157.545225814742 \tabularnewline
Trimmed Mean ( 12 / 22 ) & 1.22445670454545 & 0.00749012286158146 & 163.476184192648 \tabularnewline
Trimmed Mean ( 13 / 22 ) & 1.22512959523810 & 0.00723370529292406 & 169.364045897267 \tabularnewline
Trimmed Mean ( 14 / 22 ) & 1.2256855 & 0.00698505341682492 & 175.472602263526 \tabularnewline
Trimmed Mean ( 15 / 22 ) & 1.22614339473684 & 0.00673394202549732 & 182.0840438029 \tabularnewline
Trimmed Mean ( 16 / 22 ) & 1.22666916666667 & 0.00639778708412601 & 191.733352569710 \tabularnewline
Trimmed Mean ( 17 / 22 ) & 1.22707782352941 & 0.00602299290737887 & 203.732237842435 \tabularnewline
Trimmed Mean ( 18 / 22 ) & 1.22725853125 & 0.00573006151201016 & 214.178945318070 \tabularnewline
Trimmed Mean ( 19 / 22 ) & 1.22749313333333 & 0.00534583740582352 & 229.616623205965 \tabularnewline
Trimmed Mean ( 20 / 22 ) & 1.22764607142857 & 0.00494748562240842 & 248.135348967615 \tabularnewline
Trimmed Mean ( 21 / 22 ) & 1.22779542307692 & 0.00460676652801176 & 266.520001743355 \tabularnewline
Trimmed Mean ( 22 / 22 ) & 1.22785033333333 & 0.00436512695818932 & 281.286282184712 \tabularnewline
Median & 1.22697 &  &  \tabularnewline
Midrange & 1.2440625 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 1.22477105714286 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 1.22707782352941 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 1.22477105714286 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 1.22707782352941 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 1.22707782352941 &  &  \tabularnewline
Midmean - Closest Observation & 1.22477105714286 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 1.22707782352941 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 1.22666916666667 &  &  \tabularnewline
Number of observations & 68 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=49219&T=1

[TABLE]
[ROW][C]Central Tendency - Ungrouped Data[/C][/ROW]
[ROW][C]Measure[/C][C]Value[/C][C]S.E.[/C][C]Value/S.E.[/C][/ROW]
[ROW][C]Arithmetic Mean[/C][C]1.22229385294118[/C][C]0.0132429231063247[/C][C]92.297889455948[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]1.21741560444057[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]1.21245041440982[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]1.22709102709155[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 22 )[/C][C]1.22152760294118[/C][C]0.0130071586665023[/C][C]93.9119475867554[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 22 )[/C][C]1.22106495588235[/C][C]0.0124698299019583[/C][C]97.9215406691792[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 22 )[/C][C]1.22016980882353[/C][C]0.0120022237906056[/C][C]101.661977822692[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 22 )[/C][C]1.22083498529412[/C][C]0.0114603964584116[/C][C]106.526418150051[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 22 )[/C][C]1.22131263235294[/C][C]0.0111930211285299[/C][C]109.113761005949[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 22 )[/C][C]1.22315948529412[/C][C]0.0100636812750696[/C][C]121.541953869724[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 22 )[/C][C]1.22372494117647[/C][C]0.00990937265336102[/C][C]123.491666322733[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 22 )[/C][C]1.22499858823529[/C][C]0.00963105665058947[/C][C]127.192543111074[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 22 )[/C][C]1.22523748529412[/C][C]0.00941687682413528[/C][C]130.110811490478[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 22 )[/C][C]1.22224175[/C][C]0.00874138084739068[/C][C]139.822503027636[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 22 )[/C][C]1.22199716176471[/C][C]0.00853356090859948[/C][C]143.198973424244[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 22 )[/C][C]1.21946939705882[/C][C]0.00806972890132542[/C][C]151.116525966384[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 22 )[/C][C]1.22087855882353[/C][C]0.00770700048470188[/C][C]158.411636439745[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 22 )[/C][C]1.22210314705882[/C][C]0.00737991881018891[/C][C]165.598454195940[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 22 )[/C][C]1.22196814705882[/C][C]0.00733554875841165[/C][C]166.581695153699[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 22 )[/C][C]1.22339991176471[/C][C]0.0070228560059998[/C][C]174.202619378715[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 22 )[/C][C]1.22563216176471[/C][C]0.00626411067986305[/C][C]195.659403928588[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 22 )[/C][C]1.22539551470588[/C][C]0.00612732405480959[/C][C]199.988690616749[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 22 )[/C][C]1.22629661764706[/C][C]0.0056521684003964[/C][C]216.960382419083[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 22 )[/C][C]1.22650397058824[/C][C]0.00497174699308888[/C][C]246.694767914211[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 22 )[/C][C]1.22738844117647[/C][C]0.00425762354220302[/C][C]288.280170618698[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 22 )[/C][C]1.22904297058824[/C][C]0.00402512102872208[/C][C]305.343109391779[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 22 )[/C][C]1.22163419696970[/C][C]0.0123191159928702[/C][C]99.165735404775[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 22 )[/C][C]1.221747453125[/C][C]0.0114790645321904[/C][C]106.432667026036[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 22 )[/C][C]1.22212172580645[/C][C]0.0108190801208382[/C][C]112.959855381104[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 22 )[/C][C]1.22285911666667[/C][C]0.0102423827088925[/C][C]119.392054702758[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 22 )[/C][C]1.22345239655172[/C][C]0.00975383225484942[/C][C]125.432995420179[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 22 )[/C][C]1.22397205357143[/C][C]0.0092440320216427[/C][C]132.406730169886[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 22 )[/C][C]1.22414259259259[/C][C]0.00896739585987481[/C][C]136.510377340438[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 22 )[/C][C]1.22422061538462[/C][C]0.00866482376048508[/C][C]141.286268391001[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 22 )[/C][C]1.22408836[/C][C]0.00835848418592359[/C][C]146.448606322839[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 22 )[/C][C]1.22390747916667[/C][C]0.0080248928918964[/C][C]152.513870982948[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 22 )[/C][C]1.22415371739130[/C][C]0.00777017336489009[/C][C]157.545225814742[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 22 )[/C][C]1.22445670454545[/C][C]0.00749012286158146[/C][C]163.476184192648[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 22 )[/C][C]1.22512959523810[/C][C]0.00723370529292406[/C][C]169.364045897267[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 22 )[/C][C]1.2256855[/C][C]0.00698505341682492[/C][C]175.472602263526[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 22 )[/C][C]1.22614339473684[/C][C]0.00673394202549732[/C][C]182.0840438029[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 22 )[/C][C]1.22666916666667[/C][C]0.00639778708412601[/C][C]191.733352569710[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 22 )[/C][C]1.22707782352941[/C][C]0.00602299290737887[/C][C]203.732237842435[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 22 )[/C][C]1.22725853125[/C][C]0.00573006151201016[/C][C]214.178945318070[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 22 )[/C][C]1.22749313333333[/C][C]0.00534583740582352[/C][C]229.616623205965[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 22 )[/C][C]1.22764607142857[/C][C]0.00494748562240842[/C][C]248.135348967615[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 22 )[/C][C]1.22779542307692[/C][C]0.00460676652801176[/C][C]266.520001743355[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 22 )[/C][C]1.22785033333333[/C][C]0.00436512695818932[/C][C]281.286282184712[/C][/ROW]
[ROW][C]Median[/C][C]1.22697[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]1.2440625[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]1.22477105714286[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]1.22707782352941[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]1.22477105714286[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]1.22707782352941[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]1.22707782352941[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]1.22477105714286[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]1.22707782352941[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]1.22666916666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]68[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=49219&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=49219&T=1

As an alternative you can also use a QR Code:  

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

Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean1.222293852941180.013242923106324792.297889455948
Geometric Mean1.21741560444057
Harmonic Mean1.21245041440982
Quadratic Mean1.22709102709155
Winsorized Mean ( 1 / 22 )1.221527602941180.013007158666502393.9119475867554
Winsorized Mean ( 2 / 22 )1.221064955882350.012469829901958397.9215406691792
Winsorized Mean ( 3 / 22 )1.220169808823530.0120022237906056101.661977822692
Winsorized Mean ( 4 / 22 )1.220834985294120.0114603964584116106.526418150051
Winsorized Mean ( 5 / 22 )1.221312632352940.0111930211285299109.113761005949
Winsorized Mean ( 6 / 22 )1.223159485294120.0100636812750696121.541953869724
Winsorized Mean ( 7 / 22 )1.223724941176470.00990937265336102123.491666322733
Winsorized Mean ( 8 / 22 )1.224998588235290.00963105665058947127.192543111074
Winsorized Mean ( 9 / 22 )1.225237485294120.00941687682413528130.110811490478
Winsorized Mean ( 10 / 22 )1.222241750.00874138084739068139.822503027636
Winsorized Mean ( 11 / 22 )1.221997161764710.00853356090859948143.198973424244
Winsorized Mean ( 12 / 22 )1.219469397058820.00806972890132542151.116525966384
Winsorized Mean ( 13 / 22 )1.220878558823530.00770700048470188158.411636439745
Winsorized Mean ( 14 / 22 )1.222103147058820.00737991881018891165.598454195940
Winsorized Mean ( 15 / 22 )1.221968147058820.00733554875841165166.581695153699
Winsorized Mean ( 16 / 22 )1.223399911764710.0070228560059998174.202619378715
Winsorized Mean ( 17 / 22 )1.225632161764710.00626411067986305195.659403928588
Winsorized Mean ( 18 / 22 )1.225395514705880.00612732405480959199.988690616749
Winsorized Mean ( 19 / 22 )1.226296617647060.0056521684003964216.960382419083
Winsorized Mean ( 20 / 22 )1.226503970588240.00497174699308888246.694767914211
Winsorized Mean ( 21 / 22 )1.227388441176470.00425762354220302288.280170618698
Winsorized Mean ( 22 / 22 )1.229042970588240.00402512102872208305.343109391779
Trimmed Mean ( 1 / 22 )1.221634196969700.012319115992870299.165735404775
Trimmed Mean ( 2 / 22 )1.2217474531250.0114790645321904106.432667026036
Trimmed Mean ( 3 / 22 )1.222121725806450.0108190801208382112.959855381104
Trimmed Mean ( 4 / 22 )1.222859116666670.0102423827088925119.392054702758
Trimmed Mean ( 5 / 22 )1.223452396551720.00975383225484942125.432995420179
Trimmed Mean ( 6 / 22 )1.223972053571430.0092440320216427132.406730169886
Trimmed Mean ( 7 / 22 )1.224142592592590.00896739585987481136.510377340438
Trimmed Mean ( 8 / 22 )1.224220615384620.00866482376048508141.286268391001
Trimmed Mean ( 9 / 22 )1.224088360.00835848418592359146.448606322839
Trimmed Mean ( 10 / 22 )1.223907479166670.0080248928918964152.513870982948
Trimmed Mean ( 11 / 22 )1.224153717391300.00777017336489009157.545225814742
Trimmed Mean ( 12 / 22 )1.224456704545450.00749012286158146163.476184192648
Trimmed Mean ( 13 / 22 )1.225129595238100.00723370529292406169.364045897267
Trimmed Mean ( 14 / 22 )1.22568550.00698505341682492175.472602263526
Trimmed Mean ( 15 / 22 )1.226143394736840.00673394202549732182.0840438029
Trimmed Mean ( 16 / 22 )1.226669166666670.00639778708412601191.733352569710
Trimmed Mean ( 17 / 22 )1.227077823529410.00602299290737887203.732237842435
Trimmed Mean ( 18 / 22 )1.227258531250.00573006151201016214.178945318070
Trimmed Mean ( 19 / 22 )1.227493133333330.00534583740582352229.616623205965
Trimmed Mean ( 20 / 22 )1.227646071428570.00494748562240842248.135348967615
Trimmed Mean ( 21 / 22 )1.227795423076920.00460676652801176266.520001743355
Trimmed Mean ( 22 / 22 )1.227850333333330.00436512695818932281.286282184712
Median1.22697
Midrange1.2440625
Midmean - Weighted Average at Xnp1.22477105714286
Midmean - Weighted Average at X(n+1)p1.22707782352941
Midmean - Empirical Distribution Function1.22477105714286
Midmean - Empirical Distribution Function - Averaging1.22707782352941
Midmean - Empirical Distribution Function - Interpolation1.22707782352941
Midmean - Closest Observation1.22477105714286
Midmean - True Basic - Statistics Graphics Toolkit1.22707782352941
Midmean - MS Excel (old versions)1.22666916666667
Number of observations68



Parameters (Session):
par1 = 0 ; par2 = 36 ;
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')