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Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationMon, 17 Oct 2011 16:20:42 -0400
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2011/Oct/17/t1318882922gf44knzasce1e31.htm/, Retrieved Wed, 15 May 2024 10:13:57 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=131217, Retrieved Wed, 15 May 2024 10:13:57 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsKDG2011W52a
Estimated Impact55
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [Centrummaten gem....] [2011-10-17 20:20:42] [fbd10e07abbced8dffcb95f726fd6c98] [Current]
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Dataseries X:
1,26
1,27
1,24
1,25
1,27
1,25
1,26
1,27
1,26
1,26
1,28
1,27
1,28
1,27
1,26
1,27
1,27
1,28
1,27
1,26
1,3
1,31
1,28
1,29
1,31
1,29
1,29
1,32
1,3
1,29
1,31
1,29
1,33
1,35
1,32
1,33
1,34
1,34
1,33
1,33
1,35
1,32
1,35
1,32
1,36
1,37
1,34
1,32
1,34
1,32
1,33
1,35
1,33
1,33
1,35
1,33
1,36
1,39
1,37
1,37




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

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 1 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=131217&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' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=131217&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=131217&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' @ jenkins.wessa.net







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean1.30750.00483995260750949270.147273337208
Geometric Mean1.30697229231092
Harmonic Mean1.3064455224004
Quadratic Mean1.30802841457414
Winsorized Mean ( 1 / 20 )1.307333333333330.00471724008811977277.139452076186
Winsorized Mean ( 2 / 20 )1.307333333333330.00471724008811977277.139452076186
Winsorized Mean ( 3 / 20 )1.307833333333330.00462180820795402282.970057278141
Winsorized Mean ( 4 / 20 )1.307166666666670.00447902624270751291.841707512859
Winsorized Mean ( 5 / 20 )1.307166666666670.00447902624270751291.841707512859
Winsorized Mean ( 6 / 20 )1.306166666666670.00429223228679047304.309408110659
Winsorized Mean ( 7 / 20 )1.306166666666670.00429223228679047304.309408110659
Winsorized Mean ( 8 / 20 )1.306166666666670.00429223228679047304.309408110659
Winsorized Mean ( 9 / 20 )1.307666666666670.00403632284035397323.974745922948
Winsorized Mean ( 10 / 20 )1.307666666666670.00403632284035397323.974745922948
Winsorized Mean ( 11 / 20 )1.305833333333330.00373025246162982350.06567163092
Winsorized Mean ( 12 / 20 )1.305833333333330.00373025246162982350.06567163092
Winsorized Mean ( 13 / 20 )1.305833333333330.00373025246162982350.06567163092
Winsorized Mean ( 14 / 20 )1.305833333333330.00373025246162982350.06567163092
Winsorized Mean ( 15 / 20 )1.303333333333330.00336706100504225387.083373714217
Winsorized Mean ( 16 / 20 )1.303333333333330.00336706100504225387.083373714217
Winsorized Mean ( 17 / 20 )1.306166666666670.00291200191945468448.545949760661
Winsorized Mean ( 18 / 20 )1.306166666666670.00291200191945468448.545949760661
Winsorized Mean ( 19 / 20 )1.306166666666670.00291200191945468448.545949760661
Winsorized Mean ( 20 / 20 )1.306166666666670.00291200191945468448.545949760661
Trimmed Mean ( 1 / 20 )1.307241379310340.00465242687515794280.980532179986
Trimmed Mean ( 2 / 20 )1.307142857142860.00457061681104369285.988283678582
Trimmed Mean ( 3 / 20 )1.307037037037040.00446767745399756292.554028462269
Trimmed Mean ( 4 / 20 )1.306730769230770.00438289175192149298.143518752862
Trimmed Mean ( 5 / 20 )1.30660.00432939643245889301.797264441758
Trimmed Mean ( 6 / 20 )1.306458333333330.00425775870156548306.84179750557
Trimmed Mean ( 7 / 20 )1.306521739130430.00421886024520083309.685949094111
Trimmed Mean ( 8 / 20 )1.306590909090910.00416294920333833313.861842955742
Trimmed Mean ( 9 / 20 )1.306666666666670.00408485299651006319.880952333666
Trimmed Mean ( 10 / 20 )1.30650.00404383037509786323.084768353663
Trimmed Mean ( 11 / 20 )1.306315789473680.0039811263949934328.127183079765
Trimmed Mean ( 12 / 20 )1.306388888888890.00396718239500062329.29892271532
Trimmed Mean ( 13 / 20 )1.306470588235290.00393535899698456331.982568613528
Trimmed Mean ( 14 / 20 )1.30656250.00387842915387311336.879300398005
Trimmed Mean ( 15 / 20 )1.306666666666670.00378543285711276345.18289347319
Trimmed Mean ( 16 / 20 )1.307142857142860.00373943459980627349.55628244189
Trimmed Mean ( 17 / 20 )1.307692307692310.00365040323621683358.232289166926
Trimmed Mean ( 18 / 20 )1.307916666666670.0036603618389813357.318954847007
Trimmed Mean ( 19 / 20 )1.308181818181820.00364177087152348359.215849742507
Trimmed Mean ( 20 / 20 )1.30850.00357439726240295366.0757056199
Median1.31
Midrange1.315
Midmean - Weighted Average at Xnp1.30055555555556
Midmean - Weighted Average at X(n+1)p1.30055555555556
Midmean - Empirical Distribution Function1.30055555555556
Midmean - Empirical Distribution Function - Averaging1.30055555555556
Midmean - Empirical Distribution Function - Interpolation1.30055555555556
Midmean - Closest Observation1.30055555555556
Midmean - True Basic - Statistics Graphics Toolkit1.30055555555556
Midmean - MS Excel (old versions)1.3045
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 1.3075 & 0.00483995260750949 & 270.147273337208 \tabularnewline
Geometric Mean & 1.30697229231092 &  &  \tabularnewline
Harmonic Mean & 1.3064455224004 &  &  \tabularnewline
Quadratic Mean & 1.30802841457414 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 1.30733333333333 & 0.00471724008811977 & 277.139452076186 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 1.30733333333333 & 0.00471724008811977 & 277.139452076186 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 1.30783333333333 & 0.00462180820795402 & 282.970057278141 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 1.30716666666667 & 0.00447902624270751 & 291.841707512859 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 1.30716666666667 & 0.00447902624270751 & 291.841707512859 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 1.30616666666667 & 0.00429223228679047 & 304.309408110659 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 1.30616666666667 & 0.00429223228679047 & 304.309408110659 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 1.30616666666667 & 0.00429223228679047 & 304.309408110659 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 1.30766666666667 & 0.00403632284035397 & 323.974745922948 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 1.30766666666667 & 0.00403632284035397 & 323.974745922948 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 1.30583333333333 & 0.00373025246162982 & 350.06567163092 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 1.30583333333333 & 0.00373025246162982 & 350.06567163092 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 1.30583333333333 & 0.00373025246162982 & 350.06567163092 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 1.30583333333333 & 0.00373025246162982 & 350.06567163092 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 1.30333333333333 & 0.00336706100504225 & 387.083373714217 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 1.30333333333333 & 0.00336706100504225 & 387.083373714217 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 1.30616666666667 & 0.00291200191945468 & 448.545949760661 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 1.30616666666667 & 0.00291200191945468 & 448.545949760661 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 1.30616666666667 & 0.00291200191945468 & 448.545949760661 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 1.30616666666667 & 0.00291200191945468 & 448.545949760661 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 1.30724137931034 & 0.00465242687515794 & 280.980532179986 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 1.30714285714286 & 0.00457061681104369 & 285.988283678582 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 1.30703703703704 & 0.00446767745399756 & 292.554028462269 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 1.30673076923077 & 0.00438289175192149 & 298.143518752862 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 1.3066 & 0.00432939643245889 & 301.797264441758 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 1.30645833333333 & 0.00425775870156548 & 306.84179750557 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 1.30652173913043 & 0.00421886024520083 & 309.685949094111 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 1.30659090909091 & 0.00416294920333833 & 313.861842955742 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 1.30666666666667 & 0.00408485299651006 & 319.880952333666 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 1.3065 & 0.00404383037509786 & 323.084768353663 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 1.30631578947368 & 0.0039811263949934 & 328.127183079765 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 1.30638888888889 & 0.00396718239500062 & 329.29892271532 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 1.30647058823529 & 0.00393535899698456 & 331.982568613528 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 1.3065625 & 0.00387842915387311 & 336.879300398005 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 1.30666666666667 & 0.00378543285711276 & 345.18289347319 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 1.30714285714286 & 0.00373943459980627 & 349.55628244189 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 1.30769230769231 & 0.00365040323621683 & 358.232289166926 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 1.30791666666667 & 0.0036603618389813 & 357.318954847007 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 1.30818181818182 & 0.00364177087152348 & 359.215849742507 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 1.3085 & 0.00357439726240295 & 366.0757056199 \tabularnewline
Median & 1.31 &  &  \tabularnewline
Midrange & 1.315 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 1.30055555555556 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 1.30055555555556 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 1.30055555555556 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 1.30055555555556 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 1.30055555555556 &  &  \tabularnewline
Midmean - Closest Observation & 1.30055555555556 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 1.30055555555556 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 1.3045 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=131217&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]1.3075[/C][C]0.00483995260750949[/C][C]270.147273337208[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]1.30697229231092[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]1.3064455224004[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]1.30802841457414[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]1.30733333333333[/C][C]0.00471724008811977[/C][C]277.139452076186[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]1.30733333333333[/C][C]0.00471724008811977[/C][C]277.139452076186[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]1.30783333333333[/C][C]0.00462180820795402[/C][C]282.970057278141[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]1.30716666666667[/C][C]0.00447902624270751[/C][C]291.841707512859[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]1.30716666666667[/C][C]0.00447902624270751[/C][C]291.841707512859[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]1.30616666666667[/C][C]0.00429223228679047[/C][C]304.309408110659[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]1.30616666666667[/C][C]0.00429223228679047[/C][C]304.309408110659[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]1.30616666666667[/C][C]0.00429223228679047[/C][C]304.309408110659[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]1.30766666666667[/C][C]0.00403632284035397[/C][C]323.974745922948[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]1.30766666666667[/C][C]0.00403632284035397[/C][C]323.974745922948[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]1.30583333333333[/C][C]0.00373025246162982[/C][C]350.06567163092[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]1.30583333333333[/C][C]0.00373025246162982[/C][C]350.06567163092[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]1.30583333333333[/C][C]0.00373025246162982[/C][C]350.06567163092[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]1.30583333333333[/C][C]0.00373025246162982[/C][C]350.06567163092[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]1.30333333333333[/C][C]0.00336706100504225[/C][C]387.083373714217[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]1.30333333333333[/C][C]0.00336706100504225[/C][C]387.083373714217[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]1.30616666666667[/C][C]0.00291200191945468[/C][C]448.545949760661[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]1.30616666666667[/C][C]0.00291200191945468[/C][C]448.545949760661[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]1.30616666666667[/C][C]0.00291200191945468[/C][C]448.545949760661[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]1.30616666666667[/C][C]0.00291200191945468[/C][C]448.545949760661[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]1.30724137931034[/C][C]0.00465242687515794[/C][C]280.980532179986[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]1.30714285714286[/C][C]0.00457061681104369[/C][C]285.988283678582[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]1.30703703703704[/C][C]0.00446767745399756[/C][C]292.554028462269[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]1.30673076923077[/C][C]0.00438289175192149[/C][C]298.143518752862[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]1.3066[/C][C]0.00432939643245889[/C][C]301.797264441758[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]1.30645833333333[/C][C]0.00425775870156548[/C][C]306.84179750557[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]1.30652173913043[/C][C]0.00421886024520083[/C][C]309.685949094111[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]1.30659090909091[/C][C]0.00416294920333833[/C][C]313.861842955742[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]1.30666666666667[/C][C]0.00408485299651006[/C][C]319.880952333666[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]1.3065[/C][C]0.00404383037509786[/C][C]323.084768353663[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]1.30631578947368[/C][C]0.0039811263949934[/C][C]328.127183079765[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]1.30638888888889[/C][C]0.00396718239500062[/C][C]329.29892271532[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]1.30647058823529[/C][C]0.00393535899698456[/C][C]331.982568613528[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]1.3065625[/C][C]0.00387842915387311[/C][C]336.879300398005[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]1.30666666666667[/C][C]0.00378543285711276[/C][C]345.18289347319[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]1.30714285714286[/C][C]0.00373943459980627[/C][C]349.55628244189[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]1.30769230769231[/C][C]0.00365040323621683[/C][C]358.232289166926[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]1.30791666666667[/C][C]0.0036603618389813[/C][C]357.318954847007[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]1.30818181818182[/C][C]0.00364177087152348[/C][C]359.215849742507[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]1.3085[/C][C]0.00357439726240295[/C][C]366.0757056199[/C][/ROW]
[ROW][C]Median[/C][C]1.31[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]1.315[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]1.30055555555556[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]1.30055555555556[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]1.30055555555556[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]1.30055555555556[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]1.30055555555556[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]1.30055555555556[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]1.30055555555556[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]1.3045[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]60[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=131217&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=131217&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 Mean1.30750.00483995260750949270.147273337208
Geometric Mean1.30697229231092
Harmonic Mean1.3064455224004
Quadratic Mean1.30802841457414
Winsorized Mean ( 1 / 20 )1.307333333333330.00471724008811977277.139452076186
Winsorized Mean ( 2 / 20 )1.307333333333330.00471724008811977277.139452076186
Winsorized Mean ( 3 / 20 )1.307833333333330.00462180820795402282.970057278141
Winsorized Mean ( 4 / 20 )1.307166666666670.00447902624270751291.841707512859
Winsorized Mean ( 5 / 20 )1.307166666666670.00447902624270751291.841707512859
Winsorized Mean ( 6 / 20 )1.306166666666670.00429223228679047304.309408110659
Winsorized Mean ( 7 / 20 )1.306166666666670.00429223228679047304.309408110659
Winsorized Mean ( 8 / 20 )1.306166666666670.00429223228679047304.309408110659
Winsorized Mean ( 9 / 20 )1.307666666666670.00403632284035397323.974745922948
Winsorized Mean ( 10 / 20 )1.307666666666670.00403632284035397323.974745922948
Winsorized Mean ( 11 / 20 )1.305833333333330.00373025246162982350.06567163092
Winsorized Mean ( 12 / 20 )1.305833333333330.00373025246162982350.06567163092
Winsorized Mean ( 13 / 20 )1.305833333333330.00373025246162982350.06567163092
Winsorized Mean ( 14 / 20 )1.305833333333330.00373025246162982350.06567163092
Winsorized Mean ( 15 / 20 )1.303333333333330.00336706100504225387.083373714217
Winsorized Mean ( 16 / 20 )1.303333333333330.00336706100504225387.083373714217
Winsorized Mean ( 17 / 20 )1.306166666666670.00291200191945468448.545949760661
Winsorized Mean ( 18 / 20 )1.306166666666670.00291200191945468448.545949760661
Winsorized Mean ( 19 / 20 )1.306166666666670.00291200191945468448.545949760661
Winsorized Mean ( 20 / 20 )1.306166666666670.00291200191945468448.545949760661
Trimmed Mean ( 1 / 20 )1.307241379310340.00465242687515794280.980532179986
Trimmed Mean ( 2 / 20 )1.307142857142860.00457061681104369285.988283678582
Trimmed Mean ( 3 / 20 )1.307037037037040.00446767745399756292.554028462269
Trimmed Mean ( 4 / 20 )1.306730769230770.00438289175192149298.143518752862
Trimmed Mean ( 5 / 20 )1.30660.00432939643245889301.797264441758
Trimmed Mean ( 6 / 20 )1.306458333333330.00425775870156548306.84179750557
Trimmed Mean ( 7 / 20 )1.306521739130430.00421886024520083309.685949094111
Trimmed Mean ( 8 / 20 )1.306590909090910.00416294920333833313.861842955742
Trimmed Mean ( 9 / 20 )1.306666666666670.00408485299651006319.880952333666
Trimmed Mean ( 10 / 20 )1.30650.00404383037509786323.084768353663
Trimmed Mean ( 11 / 20 )1.306315789473680.0039811263949934328.127183079765
Trimmed Mean ( 12 / 20 )1.306388888888890.00396718239500062329.29892271532
Trimmed Mean ( 13 / 20 )1.306470588235290.00393535899698456331.982568613528
Trimmed Mean ( 14 / 20 )1.30656250.00387842915387311336.879300398005
Trimmed Mean ( 15 / 20 )1.306666666666670.00378543285711276345.18289347319
Trimmed Mean ( 16 / 20 )1.307142857142860.00373943459980627349.55628244189
Trimmed Mean ( 17 / 20 )1.307692307692310.00365040323621683358.232289166926
Trimmed Mean ( 18 / 20 )1.307916666666670.0036603618389813357.318954847007
Trimmed Mean ( 19 / 20 )1.308181818181820.00364177087152348359.215849742507
Trimmed Mean ( 20 / 20 )1.30850.00357439726240295366.0757056199
Median1.31
Midrange1.315
Midmean - Weighted Average at Xnp1.30055555555556
Midmean - Weighted Average at X(n+1)p1.30055555555556
Midmean - Empirical Distribution Function1.30055555555556
Midmean - Empirical Distribution Function - Averaging1.30055555555556
Midmean - Empirical Distribution Function - Interpolation1.30055555555556
Midmean - Closest Observation1.30055555555556
Midmean - True Basic - Statistics Graphics Toolkit1.30055555555556
Midmean - MS Excel (old versions)1.3045
Number of observations60



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')