Free Statistics

of Irreproducible Research!

Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationThu, 25 Nov 2010 10:34:48 +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/t12906813813my4w99xh87byva.htm/, Retrieved Thu, 28 Mar 2024 15:26:30 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=100728, Retrieved Thu, 28 Mar 2024 15:26:30 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact140
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [Maatstaven centra...] [2010-11-25 10:34:48] [4b5105369ca2b03f8f7589f5d63124c0] [Current]
-         [Central Tendency] [uitvoer] [2010-11-26 18:05:43] [c1605865773cc027e55b238d879a644c]
Feedback Forum

Post a new message
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
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
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 time2 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 & 2 seconds \tabularnewline
R Server & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=100728&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'George Udny Yule' @ 72.249.76.132[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=100728&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=100728&T=0

As an alternative you can also use a QR Code:  

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

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'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=100728&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=100728&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=100728&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')