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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 computationThu, 25 Nov 2010 10:36:37 +0000
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2010/Nov/25/t1290681356stxe0iz3n6c3v2l.htm/, Retrieved Fri, 19 Apr 2024 13:33:06 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=100726, Retrieved Fri, 19 Apr 2024 13:33:06 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact129
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
F     [Central Tendency] [Time needed to su...] [2010-09-25 09:42:08] [b98453cac15ba1066b407e146608df68]
F    D  [Central Tendency] [Measures of Centr...] [2010-10-04 17:31:06] [62f7c80c4d96454bbd2b2b026ea9aad9]
-    D      [Central Tendency] [Central tendency:...] [2010-11-25 10:36:37] [8eb352cba3cf694c3df89d0a436a2f1b] [Current]
-    D        [Central Tendency] [Central tendency:...] [2010-11-25 10:39:49] [62f7c80c4d96454bbd2b2b026ea9aad9]
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Dataseries X:
16198.9
16554.2
19554.2
15903.8
18003.8
18329.6
16260.7
14851.9
18174.1
18406.6
18466.5
16016.5
17428.5
17167.2
19630,00
17183.6
18344.7
19301.4
18147.5
16192.9
18374.4
20515.2
18957.2
16471.5
18746.8
19009.5
19211.2
20547.7
19325.8
20605.5
20056.9
16141.4
20359.8
19711.6
15638.6
14384.5
13855.6
14308.3
15290.6
14423.8
13779.7
15686.3
14733.8
12522.5
16189.4
16059.1
16007.1
15806.8
15160,00
15692.1
18908.9
16969.9
16997.5
19858.9
17681.2




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'George Udny Yule' @ 72.249.76.132

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 1 seconds \tabularnewline
R Server & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=100726&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]'George Udny Yule' @ 72.249.76.132[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=100726&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=100726&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'George Udny Yule' @ 72.249.76.132







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean17238.2854545455272.25060031122063.3177132937071
Geometric Mean17119.6956148983
Harmonic Mean16998.7609949124
Quadratic Mean17353.9905047330
Winsorized Mean ( 1 / 18 )17260.0927272727265.55872901854164.9953883687537
Winsorized Mean ( 2 / 18 )17261.6709090909264.62484306432765.2307270519375
Winsorized Mean ( 3 / 18 )17277.8872727273257.1311349865967.1948469936492
Winsorized Mean ( 4 / 18 )17261.4251.23445161197168.7063413845012
Winsorized Mean ( 5 / 18 )17246.9727272727246.85855848099969.8658083130638
Winsorized Mean ( 6 / 18 )17264.7218181818236.81364132679872.9042538320538
Winsorized Mean ( 7 / 18 )17269.3672727273231.90239270968174.4682582656525
Winsorized Mean ( 8 / 18 )17303.1563636364221.47747828078178.1260311339651
Winsorized Mean ( 9 / 18 )17287.1527272727210.81974784120381.999684110684
Winsorized Mean ( 10 / 18 )17345.9890909091199.44137602106786.9728711111421
Winsorized Mean ( 11 / 18 )17337.4890909091194.69027538921889.0516439829807
Winsorized Mean ( 12 / 18 )17294.7472727273186.82514601681992.5718386494414
Winsorized Mean ( 13 / 18 )17309.4963636364180.48502229404695.9054449151781
Winsorized Mean ( 14 / 18 )17321.8927272727174.65072544369999.1801934018112
Winsorized Mean ( 15 / 18 )17305.8563636364163.115006746828106.096040510221
Winsorized Mean ( 16 / 18 )17227.0490909091149.772991093507115.021065982142
Winsorized Mean ( 17 / 18 )17221.7018181818144.989884181933118.778643871265
Winsorized Mean ( 18 / 18 )17238.0981818182139.435179791813123.628041413623
Trimmed Mean ( 1 / 18 )17263.7301886792260.15407692662666.3596373065808
Trimmed Mean ( 2 / 18 )17267.6529411765253.29419250292668.1723207727196
Trimmed Mean ( 3 / 18 )17271.0102040816245.20360468125570.435384612443
Trimmed Mean ( 4 / 18 )17268.3276595745238.61198172625772.3699100717635
Trimmed Mean ( 5 / 18 )17270.4444444444232.46824063644074.291629674498
Trimmed Mean ( 6 / 18 )17276.4488372093225.94344974958076.4635967821034
Trimmed Mean ( 7 / 18 )17276.4488372093220.58927868060278.3195309425008
Trimmed Mean ( 8 / 18 )17281.0256410256214.80873354449580.4484312899042
Trimmed Mean ( 9 / 18 )17276.9135135135209.95659615668782.2880244287255
Trimmed Mean ( 10 / 18 )17275.1257142857206.15208465053783.7979676197307
Trimmed Mean ( 11 / 18 )17263.3151515152203.62441412760684.7801832873374
Trimmed Mean ( 12 / 18 )17251.3516129032200.80257103647785.9120056275046
Trimmed Mean ( 13 / 18 )17244.4931034483198.44047133416686.9000813569386
Trimmed Mean ( 14 / 18 )17244.4931034483196.01555406086387.9751261886792
Trimmed Mean ( 15 / 18 )17234.3074074074193.18844988594389.209822934976
Trimmed Mean ( 16 / 18 )17206.9434782609191.65860302032689.7791343936488
Trimmed Mean ( 17 / 18 )17203.6523809524192.62004551510389.3139254273693
Trimmed Mean ( 18 / 18 )17200.5789473684193.65505454497188.8207074573108
Median17167.2
Midrange16564
Midmean - Weighted Average at Xnp17183.325
Midmean - Weighted Average at X(n+1)p17244.4931034483
Midmean - Empirical Distribution Function17244.4931034483
Midmean - Empirical Distribution Function - Averaging17244.4931034483
Midmean - Empirical Distribution Function - Interpolation17234.3074074074
Midmean - Closest Observation17183.325
Midmean - True Basic - Statistics Graphics Toolkit17244.4931034483
Midmean - MS Excel (old versions)17244.4931034483
Number of observations55

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 17238.2854545455 & 272.250600311220 & 63.3177132937071 \tabularnewline
Geometric Mean & 17119.6956148983 &  &  \tabularnewline
Harmonic Mean & 16998.7609949124 &  &  \tabularnewline
Quadratic Mean & 17353.9905047330 &  &  \tabularnewline
Winsorized Mean ( 1 / 18 ) & 17260.0927272727 & 265.558729018541 & 64.9953883687537 \tabularnewline
Winsorized Mean ( 2 / 18 ) & 17261.6709090909 & 264.624843064327 & 65.2307270519375 \tabularnewline
Winsorized Mean ( 3 / 18 ) & 17277.8872727273 & 257.13113498659 & 67.1948469936492 \tabularnewline
Winsorized Mean ( 4 / 18 ) & 17261.4 & 251.234451611971 & 68.7063413845012 \tabularnewline
Winsorized Mean ( 5 / 18 ) & 17246.9727272727 & 246.858558480999 & 69.8658083130638 \tabularnewline
Winsorized Mean ( 6 / 18 ) & 17264.7218181818 & 236.813641326798 & 72.9042538320538 \tabularnewline
Winsorized Mean ( 7 / 18 ) & 17269.3672727273 & 231.902392709681 & 74.4682582656525 \tabularnewline
Winsorized Mean ( 8 / 18 ) & 17303.1563636364 & 221.477478280781 & 78.1260311339651 \tabularnewline
Winsorized Mean ( 9 / 18 ) & 17287.1527272727 & 210.819747841203 & 81.999684110684 \tabularnewline
Winsorized Mean ( 10 / 18 ) & 17345.9890909091 & 199.441376021067 & 86.9728711111421 \tabularnewline
Winsorized Mean ( 11 / 18 ) & 17337.4890909091 & 194.690275389218 & 89.0516439829807 \tabularnewline
Winsorized Mean ( 12 / 18 ) & 17294.7472727273 & 186.825146016819 & 92.5718386494414 \tabularnewline
Winsorized Mean ( 13 / 18 ) & 17309.4963636364 & 180.485022294046 & 95.9054449151781 \tabularnewline
Winsorized Mean ( 14 / 18 ) & 17321.8927272727 & 174.650725443699 & 99.1801934018112 \tabularnewline
Winsorized Mean ( 15 / 18 ) & 17305.8563636364 & 163.115006746828 & 106.096040510221 \tabularnewline
Winsorized Mean ( 16 / 18 ) & 17227.0490909091 & 149.772991093507 & 115.021065982142 \tabularnewline
Winsorized Mean ( 17 / 18 ) & 17221.7018181818 & 144.989884181933 & 118.778643871265 \tabularnewline
Winsorized Mean ( 18 / 18 ) & 17238.0981818182 & 139.435179791813 & 123.628041413623 \tabularnewline
Trimmed Mean ( 1 / 18 ) & 17263.7301886792 & 260.154076926626 & 66.3596373065808 \tabularnewline
Trimmed Mean ( 2 / 18 ) & 17267.6529411765 & 253.294192502926 & 68.1723207727196 \tabularnewline
Trimmed Mean ( 3 / 18 ) & 17271.0102040816 & 245.203604681255 & 70.435384612443 \tabularnewline
Trimmed Mean ( 4 / 18 ) & 17268.3276595745 & 238.611981726257 & 72.3699100717635 \tabularnewline
Trimmed Mean ( 5 / 18 ) & 17270.4444444444 & 232.468240636440 & 74.291629674498 \tabularnewline
Trimmed Mean ( 6 / 18 ) & 17276.4488372093 & 225.943449749580 & 76.4635967821034 \tabularnewline
Trimmed Mean ( 7 / 18 ) & 17276.4488372093 & 220.589278680602 & 78.3195309425008 \tabularnewline
Trimmed Mean ( 8 / 18 ) & 17281.0256410256 & 214.808733544495 & 80.4484312899042 \tabularnewline
Trimmed Mean ( 9 / 18 ) & 17276.9135135135 & 209.956596156687 & 82.2880244287255 \tabularnewline
Trimmed Mean ( 10 / 18 ) & 17275.1257142857 & 206.152084650537 & 83.7979676197307 \tabularnewline
Trimmed Mean ( 11 / 18 ) & 17263.3151515152 & 203.624414127606 & 84.7801832873374 \tabularnewline
Trimmed Mean ( 12 / 18 ) & 17251.3516129032 & 200.802571036477 & 85.9120056275046 \tabularnewline
Trimmed Mean ( 13 / 18 ) & 17244.4931034483 & 198.440471334166 & 86.9000813569386 \tabularnewline
Trimmed Mean ( 14 / 18 ) & 17244.4931034483 & 196.015554060863 & 87.9751261886792 \tabularnewline
Trimmed Mean ( 15 / 18 ) & 17234.3074074074 & 193.188449885943 & 89.209822934976 \tabularnewline
Trimmed Mean ( 16 / 18 ) & 17206.9434782609 & 191.658603020326 & 89.7791343936488 \tabularnewline
Trimmed Mean ( 17 / 18 ) & 17203.6523809524 & 192.620045515103 & 89.3139254273693 \tabularnewline
Trimmed Mean ( 18 / 18 ) & 17200.5789473684 & 193.655054544971 & 88.8207074573108 \tabularnewline
Median & 17167.2 &  &  \tabularnewline
Midrange & 16564 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 17183.325 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 17244.4931034483 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 17244.4931034483 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 17244.4931034483 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 17234.3074074074 &  &  \tabularnewline
Midmean - Closest Observation & 17183.325 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 17244.4931034483 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 17244.4931034483 &  &  \tabularnewline
Number of observations & 55 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=100726&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]17238.2854545455[/C][C]272.250600311220[/C][C]63.3177132937071[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]17119.6956148983[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]16998.7609949124[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]17353.9905047330[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 18 )[/C][C]17260.0927272727[/C][C]265.558729018541[/C][C]64.9953883687537[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 18 )[/C][C]17261.6709090909[/C][C]264.624843064327[/C][C]65.2307270519375[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 18 )[/C][C]17277.8872727273[/C][C]257.13113498659[/C][C]67.1948469936492[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 18 )[/C][C]17261.4[/C][C]251.234451611971[/C][C]68.7063413845012[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 18 )[/C][C]17246.9727272727[/C][C]246.858558480999[/C][C]69.8658083130638[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 18 )[/C][C]17264.7218181818[/C][C]236.813641326798[/C][C]72.9042538320538[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 18 )[/C][C]17269.3672727273[/C][C]231.902392709681[/C][C]74.4682582656525[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 18 )[/C][C]17303.1563636364[/C][C]221.477478280781[/C][C]78.1260311339651[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 18 )[/C][C]17287.1527272727[/C][C]210.819747841203[/C][C]81.999684110684[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 18 )[/C][C]17345.9890909091[/C][C]199.441376021067[/C][C]86.9728711111421[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 18 )[/C][C]17337.4890909091[/C][C]194.690275389218[/C][C]89.0516439829807[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 18 )[/C][C]17294.7472727273[/C][C]186.825146016819[/C][C]92.5718386494414[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 18 )[/C][C]17309.4963636364[/C][C]180.485022294046[/C][C]95.9054449151781[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 18 )[/C][C]17321.8927272727[/C][C]174.650725443699[/C][C]99.1801934018112[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 18 )[/C][C]17305.8563636364[/C][C]163.115006746828[/C][C]106.096040510221[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 18 )[/C][C]17227.0490909091[/C][C]149.772991093507[/C][C]115.021065982142[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 18 )[/C][C]17221.7018181818[/C][C]144.989884181933[/C][C]118.778643871265[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 18 )[/C][C]17238.0981818182[/C][C]139.435179791813[/C][C]123.628041413623[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 18 )[/C][C]17263.7301886792[/C][C]260.154076926626[/C][C]66.3596373065808[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 18 )[/C][C]17267.6529411765[/C][C]253.294192502926[/C][C]68.1723207727196[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 18 )[/C][C]17271.0102040816[/C][C]245.203604681255[/C][C]70.435384612443[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 18 )[/C][C]17268.3276595745[/C][C]238.611981726257[/C][C]72.3699100717635[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 18 )[/C][C]17270.4444444444[/C][C]232.468240636440[/C][C]74.291629674498[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 18 )[/C][C]17276.4488372093[/C][C]225.943449749580[/C][C]76.4635967821034[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 18 )[/C][C]17276.4488372093[/C][C]220.589278680602[/C][C]78.3195309425008[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 18 )[/C][C]17281.0256410256[/C][C]214.808733544495[/C][C]80.4484312899042[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 18 )[/C][C]17276.9135135135[/C][C]209.956596156687[/C][C]82.2880244287255[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 18 )[/C][C]17275.1257142857[/C][C]206.152084650537[/C][C]83.7979676197307[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 18 )[/C][C]17263.3151515152[/C][C]203.624414127606[/C][C]84.7801832873374[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 18 )[/C][C]17251.3516129032[/C][C]200.802571036477[/C][C]85.9120056275046[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 18 )[/C][C]17244.4931034483[/C][C]198.440471334166[/C][C]86.9000813569386[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 18 )[/C][C]17244.4931034483[/C][C]196.015554060863[/C][C]87.9751261886792[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 18 )[/C][C]17234.3074074074[/C][C]193.188449885943[/C][C]89.209822934976[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 18 )[/C][C]17206.9434782609[/C][C]191.658603020326[/C][C]89.7791343936488[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 18 )[/C][C]17203.6523809524[/C][C]192.620045515103[/C][C]89.3139254273693[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 18 )[/C][C]17200.5789473684[/C][C]193.655054544971[/C][C]88.8207074573108[/C][/ROW]
[ROW][C]Median[/C][C]17167.2[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]16564[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]17183.325[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]17244.4931034483[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]17244.4931034483[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]17244.4931034483[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]17234.3074074074[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]17183.325[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]17244.4931034483[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]17244.4931034483[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]55[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=100726&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=100726&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 Mean17238.2854545455272.25060031122063.3177132937071
Geometric Mean17119.6956148983
Harmonic Mean16998.7609949124
Quadratic Mean17353.9905047330
Winsorized Mean ( 1 / 18 )17260.0927272727265.55872901854164.9953883687537
Winsorized Mean ( 2 / 18 )17261.6709090909264.62484306432765.2307270519375
Winsorized Mean ( 3 / 18 )17277.8872727273257.1311349865967.1948469936492
Winsorized Mean ( 4 / 18 )17261.4251.23445161197168.7063413845012
Winsorized Mean ( 5 / 18 )17246.9727272727246.85855848099969.8658083130638
Winsorized Mean ( 6 / 18 )17264.7218181818236.81364132679872.9042538320538
Winsorized Mean ( 7 / 18 )17269.3672727273231.90239270968174.4682582656525
Winsorized Mean ( 8 / 18 )17303.1563636364221.47747828078178.1260311339651
Winsorized Mean ( 9 / 18 )17287.1527272727210.81974784120381.999684110684
Winsorized Mean ( 10 / 18 )17345.9890909091199.44137602106786.9728711111421
Winsorized Mean ( 11 / 18 )17337.4890909091194.69027538921889.0516439829807
Winsorized Mean ( 12 / 18 )17294.7472727273186.82514601681992.5718386494414
Winsorized Mean ( 13 / 18 )17309.4963636364180.48502229404695.9054449151781
Winsorized Mean ( 14 / 18 )17321.8927272727174.65072544369999.1801934018112
Winsorized Mean ( 15 / 18 )17305.8563636364163.115006746828106.096040510221
Winsorized Mean ( 16 / 18 )17227.0490909091149.772991093507115.021065982142
Winsorized Mean ( 17 / 18 )17221.7018181818144.989884181933118.778643871265
Winsorized Mean ( 18 / 18 )17238.0981818182139.435179791813123.628041413623
Trimmed Mean ( 1 / 18 )17263.7301886792260.15407692662666.3596373065808
Trimmed Mean ( 2 / 18 )17267.6529411765253.29419250292668.1723207727196
Trimmed Mean ( 3 / 18 )17271.0102040816245.20360468125570.435384612443
Trimmed Mean ( 4 / 18 )17268.3276595745238.61198172625772.3699100717635
Trimmed Mean ( 5 / 18 )17270.4444444444232.46824063644074.291629674498
Trimmed Mean ( 6 / 18 )17276.4488372093225.94344974958076.4635967821034
Trimmed Mean ( 7 / 18 )17276.4488372093220.58927868060278.3195309425008
Trimmed Mean ( 8 / 18 )17281.0256410256214.80873354449580.4484312899042
Trimmed Mean ( 9 / 18 )17276.9135135135209.95659615668782.2880244287255
Trimmed Mean ( 10 / 18 )17275.1257142857206.15208465053783.7979676197307
Trimmed Mean ( 11 / 18 )17263.3151515152203.62441412760684.7801832873374
Trimmed Mean ( 12 / 18 )17251.3516129032200.80257103647785.9120056275046
Trimmed Mean ( 13 / 18 )17244.4931034483198.44047133416686.9000813569386
Trimmed Mean ( 14 / 18 )17244.4931034483196.01555406086387.9751261886792
Trimmed Mean ( 15 / 18 )17234.3074074074193.18844988594389.209822934976
Trimmed Mean ( 16 / 18 )17206.9434782609191.65860302032689.7791343936488
Trimmed Mean ( 17 / 18 )17203.6523809524192.62004551510389.3139254273693
Trimmed Mean ( 18 / 18 )17200.5789473684193.65505454497188.8207074573108
Median17167.2
Midrange16564
Midmean - Weighted Average at Xnp17183.325
Midmean - Weighted Average at X(n+1)p17244.4931034483
Midmean - Empirical Distribution Function17244.4931034483
Midmean - Empirical Distribution Function - Averaging17244.4931034483
Midmean - Empirical Distribution Function - Interpolation17234.3074074074
Midmean - Closest Observation17183.325
Midmean - True Basic - Statistics Graphics Toolkit17244.4931034483
Midmean - MS Excel (old versions)17244.4931034483
Number of observations55



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')