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Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationSun, 15 Jan 2012 16:02:32 -0500
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2012/Jan/15/t1326661597pc85qs37q4w7eqq.htm/, Retrieved Fri, 03 May 2024 10:55:17 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=161135, Retrieved Fri, 03 May 2024 10:55:17 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsKDG2011W52a
Estimated Impact83
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [OPgave 5 oef 2 st...] [2012-01-15 21:02:32] [c8d6d2e44a5c33fd73238ca65c4ee2f1] [Current]
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Dataseries X:
11,8
11,87
11,86
12,11
11,92
12,61
13,34
13,31
13,47
13,24
13,18
13,3
13,15
13,47
13,65
13,52
14,13
14,84
15,29
15,51
15,43
15,42
15,56
15,43
15,36
15,18
15,41
15,15
15,21
15,09
15,09
15,5
15,41
15,42
15,47
15,23
15,59
15,22
15,45
15,02
15,5
15,59
15,98
15,76
15,43
15,45
15,32
15,4
15,42
15,54
15,6
15,67
15,61
16,01
16,06
16,15
15,87
15,89
15,73
15,78
16,07
16,2
16,42
16,61
16,89
17,62
17,83
17,94
18,07
17,85
17,86
17,85




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Herman Ole Andreas Wold' @ wold.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 & 'Herman Ole Andreas Wold' @ wold.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=161135&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]'Herman Ole Andreas Wold' @ wold.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=161135&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=161135&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'Herman Ole Andreas Wold' @ wold.wessa.net







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean15.18305555555560.17727601518263385.6464171981397
Geometric Mean15.1064765036994
Harmonic Mean15.0265137029248
Quadratic Mean15.256358601507
Winsorized Mean ( 1 / 24 )15.18208333333330.17664805658690785.9453742468096
Winsorized Mean ( 2 / 24 )15.18013888888890.17609199796438186.2057280533524
Winsorized Mean ( 3 / 24 )15.18180555555560.17545417549632786.528607897812
Winsorized Mean ( 4 / 24 )15.19236111111110.17274542463242887.9465325546987
Winsorized Mean ( 5 / 24 )15.22569444444440.16416893976035192.7440627116824
Winsorized Mean ( 6 / 24 )15.25319444444440.150782365833013101.160333704651
Winsorized Mean ( 7 / 24 )15.18513888888890.136001759553131111.653988439441
Winsorized Mean ( 8 / 24 )15.16069444444440.129405364238794117.156615057071
Winsorized Mean ( 9 / 24 )15.14444444444440.124243861514275121.892898851219
Winsorized Mean ( 10 / 24 )15.11527777777780.119788868160367126.182657954012
Winsorized Mean ( 11 / 24 )15.11222222222220.117856146602327128.225999728417
Winsorized Mean ( 12 / 24 )15.12055555555560.111679784964311135.392054707014
Winsorized Mean ( 13 / 24 )15.118750.111464314152203135.637581543413
Winsorized Mean ( 14 / 24 )15.118750.108299008195165139.601924818689
Winsorized Mean ( 15 / 24 )15.13958333333330.101971458290773148.4688322311
Winsorized Mean ( 16 / 24 )15.226250.0780362054078752195.117765150372
Winsorized Mean ( 17 / 24 )15.38916666666670.0461357924593573333.562421849013
Winsorized Mean ( 18 / 24 )15.41166666666670.0355402084444567433.640300415021
Winsorized Mean ( 19 / 24 )15.42486111111110.0319654749783722482.547533598282
Winsorized Mean ( 20 / 24 )15.41652777777780.0307516426538248501.323716307568
Winsorized Mean ( 21 / 24 )15.41652777777780.025685560787158600.202109875115
Winsorized Mean ( 22 / 24 )15.40736111111110.0218679643776758704.563115478635
Winsorized Mean ( 23 / 24 )15.413750.0200629267294551768.270263249804
Winsorized Mean ( 24 / 24 )15.413750.0191530748909353804.766341058634
Trimmed Mean ( 1 / 24 )15.19014285714290.17077990543897488.9457270637196
Trimmed Mean ( 2 / 24 )15.19867647058820.16378304569906592.7976177614518
Trimmed Mean ( 3 / 24 )15.20878787878790.15573324798901597.6592222610077
Trimmed Mean ( 4 / 24 )15.218906250.146254513766239104.057685866192
Trimmed Mean ( 5 / 24 )15.22661290322580.13571050930071112.199217154851
Trimmed Mean ( 6 / 24 )15.22683333333330.125808232614551121.032090006264
Trimmed Mean ( 7 / 24 )15.22137931034480.117942496338601129.057632175648
Trimmed Mean ( 8 / 24 )15.22803571428570.112575925214265135.269025640271
Trimmed Mean ( 9 / 24 )15.23925925925930.107647758739765141.565968838233
Trimmed Mean ( 10 / 24 )15.25384615384620.102750688124053148.454929425192
Trimmed Mean ( 11 / 24 )15.27380.0975315291773561156.603717062873
Trimmed Mean ( 12 / 24 )15.29583333333330.0912258096437278167.670020064163
Trimmed Mean ( 13 / 24 )15.31869565217390.0846068536274653181.057384779064
Trimmed Mean ( 14 / 24 )15.34386363636360.0756320903995954202.875043586601
Trimmed Mean ( 15 / 24 )15.37142857142860.0638510274648152240.738938459509
Trimmed Mean ( 16 / 24 )15.399250.0484098256343556318.101744805117
Trimmed Mean ( 17 / 24 )15.41973684210530.0356617722141584432.388405980097
Trimmed Mean ( 18 / 24 )15.42333333333330.0314819172083136489.910866332512
Trimmed Mean ( 19 / 24 )15.42470588235290.0292333268112938527.641139919589
Trimmed Mean ( 20 / 24 )15.42468750.0272088116323287566.900447856121
Trimmed Mean ( 21 / 24 )15.42566666666670.0246617733574473625.488947736536
Trimmed Mean ( 22 / 24 )15.42678571428570.0228119386003463676.259303716148
Trimmed Mean ( 23 / 24 )15.42923076923080.0214398843059671719.650840883342
Trimmed Mean ( 24 / 24 )15.431250.0200299820558936770.407579844013
Median15.43
Midrange14.935
Midmean - Weighted Average at Xnp15.4075675675676
Midmean - Weighted Average at X(n+1)p15.4233333333333
Midmean - Empirical Distribution Function15.4075675675676
Midmean - Empirical Distribution Function - Averaging15.4233333333333
Midmean - Empirical Distribution Function - Interpolation15.4233333333333
Midmean - Closest Observation15.4075675675676
Midmean - True Basic - Statistics Graphics Toolkit15.4233333333333
Midmean - MS Excel (old versions)15.4197368421053
Number of observations72

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 15.1830555555556 & 0.177276015182633 & 85.6464171981397 \tabularnewline
Geometric Mean & 15.1064765036994 &  &  \tabularnewline
Harmonic Mean & 15.0265137029248 &  &  \tabularnewline
Quadratic Mean & 15.256358601507 &  &  \tabularnewline
Winsorized Mean ( 1 / 24 ) & 15.1820833333333 & 0.176648056586907 & 85.9453742468096 \tabularnewline
Winsorized Mean ( 2 / 24 ) & 15.1801388888889 & 0.176091997964381 & 86.2057280533524 \tabularnewline
Winsorized Mean ( 3 / 24 ) & 15.1818055555556 & 0.175454175496327 & 86.528607897812 \tabularnewline
Winsorized Mean ( 4 / 24 ) & 15.1923611111111 & 0.172745424632428 & 87.9465325546987 \tabularnewline
Winsorized Mean ( 5 / 24 ) & 15.2256944444444 & 0.164168939760351 & 92.7440627116824 \tabularnewline
Winsorized Mean ( 6 / 24 ) & 15.2531944444444 & 0.150782365833013 & 101.160333704651 \tabularnewline
Winsorized Mean ( 7 / 24 ) & 15.1851388888889 & 0.136001759553131 & 111.653988439441 \tabularnewline
Winsorized Mean ( 8 / 24 ) & 15.1606944444444 & 0.129405364238794 & 117.156615057071 \tabularnewline
Winsorized Mean ( 9 / 24 ) & 15.1444444444444 & 0.124243861514275 & 121.892898851219 \tabularnewline
Winsorized Mean ( 10 / 24 ) & 15.1152777777778 & 0.119788868160367 & 126.182657954012 \tabularnewline
Winsorized Mean ( 11 / 24 ) & 15.1122222222222 & 0.117856146602327 & 128.225999728417 \tabularnewline
Winsorized Mean ( 12 / 24 ) & 15.1205555555556 & 0.111679784964311 & 135.392054707014 \tabularnewline
Winsorized Mean ( 13 / 24 ) & 15.11875 & 0.111464314152203 & 135.637581543413 \tabularnewline
Winsorized Mean ( 14 / 24 ) & 15.11875 & 0.108299008195165 & 139.601924818689 \tabularnewline
Winsorized Mean ( 15 / 24 ) & 15.1395833333333 & 0.101971458290773 & 148.4688322311 \tabularnewline
Winsorized Mean ( 16 / 24 ) & 15.22625 & 0.0780362054078752 & 195.117765150372 \tabularnewline
Winsorized Mean ( 17 / 24 ) & 15.3891666666667 & 0.0461357924593573 & 333.562421849013 \tabularnewline
Winsorized Mean ( 18 / 24 ) & 15.4116666666667 & 0.0355402084444567 & 433.640300415021 \tabularnewline
Winsorized Mean ( 19 / 24 ) & 15.4248611111111 & 0.0319654749783722 & 482.547533598282 \tabularnewline
Winsorized Mean ( 20 / 24 ) & 15.4165277777778 & 0.0307516426538248 & 501.323716307568 \tabularnewline
Winsorized Mean ( 21 / 24 ) & 15.4165277777778 & 0.025685560787158 & 600.202109875115 \tabularnewline
Winsorized Mean ( 22 / 24 ) & 15.4073611111111 & 0.0218679643776758 & 704.563115478635 \tabularnewline
Winsorized Mean ( 23 / 24 ) & 15.41375 & 0.0200629267294551 & 768.270263249804 \tabularnewline
Winsorized Mean ( 24 / 24 ) & 15.41375 & 0.0191530748909353 & 804.766341058634 \tabularnewline
Trimmed Mean ( 1 / 24 ) & 15.1901428571429 & 0.170779905438974 & 88.9457270637196 \tabularnewline
Trimmed Mean ( 2 / 24 ) & 15.1986764705882 & 0.163783045699065 & 92.7976177614518 \tabularnewline
Trimmed Mean ( 3 / 24 ) & 15.2087878787879 & 0.155733247989015 & 97.6592222610077 \tabularnewline
Trimmed Mean ( 4 / 24 ) & 15.21890625 & 0.146254513766239 & 104.057685866192 \tabularnewline
Trimmed Mean ( 5 / 24 ) & 15.2266129032258 & 0.13571050930071 & 112.199217154851 \tabularnewline
Trimmed Mean ( 6 / 24 ) & 15.2268333333333 & 0.125808232614551 & 121.032090006264 \tabularnewline
Trimmed Mean ( 7 / 24 ) & 15.2213793103448 & 0.117942496338601 & 129.057632175648 \tabularnewline
Trimmed Mean ( 8 / 24 ) & 15.2280357142857 & 0.112575925214265 & 135.269025640271 \tabularnewline
Trimmed Mean ( 9 / 24 ) & 15.2392592592593 & 0.107647758739765 & 141.565968838233 \tabularnewline
Trimmed Mean ( 10 / 24 ) & 15.2538461538462 & 0.102750688124053 & 148.454929425192 \tabularnewline
Trimmed Mean ( 11 / 24 ) & 15.2738 & 0.0975315291773561 & 156.603717062873 \tabularnewline
Trimmed Mean ( 12 / 24 ) & 15.2958333333333 & 0.0912258096437278 & 167.670020064163 \tabularnewline
Trimmed Mean ( 13 / 24 ) & 15.3186956521739 & 0.0846068536274653 & 181.057384779064 \tabularnewline
Trimmed Mean ( 14 / 24 ) & 15.3438636363636 & 0.0756320903995954 & 202.875043586601 \tabularnewline
Trimmed Mean ( 15 / 24 ) & 15.3714285714286 & 0.0638510274648152 & 240.738938459509 \tabularnewline
Trimmed Mean ( 16 / 24 ) & 15.39925 & 0.0484098256343556 & 318.101744805117 \tabularnewline
Trimmed Mean ( 17 / 24 ) & 15.4197368421053 & 0.0356617722141584 & 432.388405980097 \tabularnewline
Trimmed Mean ( 18 / 24 ) & 15.4233333333333 & 0.0314819172083136 & 489.910866332512 \tabularnewline
Trimmed Mean ( 19 / 24 ) & 15.4247058823529 & 0.0292333268112938 & 527.641139919589 \tabularnewline
Trimmed Mean ( 20 / 24 ) & 15.4246875 & 0.0272088116323287 & 566.900447856121 \tabularnewline
Trimmed Mean ( 21 / 24 ) & 15.4256666666667 & 0.0246617733574473 & 625.488947736536 \tabularnewline
Trimmed Mean ( 22 / 24 ) & 15.4267857142857 & 0.0228119386003463 & 676.259303716148 \tabularnewline
Trimmed Mean ( 23 / 24 ) & 15.4292307692308 & 0.0214398843059671 & 719.650840883342 \tabularnewline
Trimmed Mean ( 24 / 24 ) & 15.43125 & 0.0200299820558936 & 770.407579844013 \tabularnewline
Median & 15.43 &  &  \tabularnewline
Midrange & 14.935 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 15.4075675675676 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 15.4233333333333 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 15.4075675675676 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 15.4233333333333 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 15.4233333333333 &  &  \tabularnewline
Midmean - Closest Observation & 15.4075675675676 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 15.4233333333333 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 15.4197368421053 &  &  \tabularnewline
Number of observations & 72 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=161135&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]15.1830555555556[/C][C]0.177276015182633[/C][C]85.6464171981397[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]15.1064765036994[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]15.0265137029248[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]15.256358601507[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 24 )[/C][C]15.1820833333333[/C][C]0.176648056586907[/C][C]85.9453742468096[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 24 )[/C][C]15.1801388888889[/C][C]0.176091997964381[/C][C]86.2057280533524[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 24 )[/C][C]15.1818055555556[/C][C]0.175454175496327[/C][C]86.528607897812[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 24 )[/C][C]15.1923611111111[/C][C]0.172745424632428[/C][C]87.9465325546987[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 24 )[/C][C]15.2256944444444[/C][C]0.164168939760351[/C][C]92.7440627116824[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 24 )[/C][C]15.2531944444444[/C][C]0.150782365833013[/C][C]101.160333704651[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 24 )[/C][C]15.1851388888889[/C][C]0.136001759553131[/C][C]111.653988439441[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 24 )[/C][C]15.1606944444444[/C][C]0.129405364238794[/C][C]117.156615057071[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 24 )[/C][C]15.1444444444444[/C][C]0.124243861514275[/C][C]121.892898851219[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 24 )[/C][C]15.1152777777778[/C][C]0.119788868160367[/C][C]126.182657954012[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 24 )[/C][C]15.1122222222222[/C][C]0.117856146602327[/C][C]128.225999728417[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 24 )[/C][C]15.1205555555556[/C][C]0.111679784964311[/C][C]135.392054707014[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 24 )[/C][C]15.11875[/C][C]0.111464314152203[/C][C]135.637581543413[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 24 )[/C][C]15.11875[/C][C]0.108299008195165[/C][C]139.601924818689[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 24 )[/C][C]15.1395833333333[/C][C]0.101971458290773[/C][C]148.4688322311[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 24 )[/C][C]15.22625[/C][C]0.0780362054078752[/C][C]195.117765150372[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 24 )[/C][C]15.3891666666667[/C][C]0.0461357924593573[/C][C]333.562421849013[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 24 )[/C][C]15.4116666666667[/C][C]0.0355402084444567[/C][C]433.640300415021[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 24 )[/C][C]15.4248611111111[/C][C]0.0319654749783722[/C][C]482.547533598282[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 24 )[/C][C]15.4165277777778[/C][C]0.0307516426538248[/C][C]501.323716307568[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 24 )[/C][C]15.4165277777778[/C][C]0.025685560787158[/C][C]600.202109875115[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 24 )[/C][C]15.4073611111111[/C][C]0.0218679643776758[/C][C]704.563115478635[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 24 )[/C][C]15.41375[/C][C]0.0200629267294551[/C][C]768.270263249804[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 24 )[/C][C]15.41375[/C][C]0.0191530748909353[/C][C]804.766341058634[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 24 )[/C][C]15.1901428571429[/C][C]0.170779905438974[/C][C]88.9457270637196[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 24 )[/C][C]15.1986764705882[/C][C]0.163783045699065[/C][C]92.7976177614518[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 24 )[/C][C]15.2087878787879[/C][C]0.155733247989015[/C][C]97.6592222610077[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 24 )[/C][C]15.21890625[/C][C]0.146254513766239[/C][C]104.057685866192[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 24 )[/C][C]15.2266129032258[/C][C]0.13571050930071[/C][C]112.199217154851[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 24 )[/C][C]15.2268333333333[/C][C]0.125808232614551[/C][C]121.032090006264[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 24 )[/C][C]15.2213793103448[/C][C]0.117942496338601[/C][C]129.057632175648[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 24 )[/C][C]15.2280357142857[/C][C]0.112575925214265[/C][C]135.269025640271[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 24 )[/C][C]15.2392592592593[/C][C]0.107647758739765[/C][C]141.565968838233[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 24 )[/C][C]15.2538461538462[/C][C]0.102750688124053[/C][C]148.454929425192[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 24 )[/C][C]15.2738[/C][C]0.0975315291773561[/C][C]156.603717062873[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 24 )[/C][C]15.2958333333333[/C][C]0.0912258096437278[/C][C]167.670020064163[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 24 )[/C][C]15.3186956521739[/C][C]0.0846068536274653[/C][C]181.057384779064[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 24 )[/C][C]15.3438636363636[/C][C]0.0756320903995954[/C][C]202.875043586601[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 24 )[/C][C]15.3714285714286[/C][C]0.0638510274648152[/C][C]240.738938459509[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 24 )[/C][C]15.39925[/C][C]0.0484098256343556[/C][C]318.101744805117[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 24 )[/C][C]15.4197368421053[/C][C]0.0356617722141584[/C][C]432.388405980097[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 24 )[/C][C]15.4233333333333[/C][C]0.0314819172083136[/C][C]489.910866332512[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 24 )[/C][C]15.4247058823529[/C][C]0.0292333268112938[/C][C]527.641139919589[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 24 )[/C][C]15.4246875[/C][C]0.0272088116323287[/C][C]566.900447856121[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 24 )[/C][C]15.4256666666667[/C][C]0.0246617733574473[/C][C]625.488947736536[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 24 )[/C][C]15.4267857142857[/C][C]0.0228119386003463[/C][C]676.259303716148[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 24 )[/C][C]15.4292307692308[/C][C]0.0214398843059671[/C][C]719.650840883342[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 24 )[/C][C]15.43125[/C][C]0.0200299820558936[/C][C]770.407579844013[/C][/ROW]
[ROW][C]Median[/C][C]15.43[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]14.935[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]15.4075675675676[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]15.4233333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]15.4075675675676[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]15.4233333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]15.4233333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]15.4075675675676[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]15.4233333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]15.4197368421053[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]72[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=161135&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=161135&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 Mean15.18305555555560.17727601518263385.6464171981397
Geometric Mean15.1064765036994
Harmonic Mean15.0265137029248
Quadratic Mean15.256358601507
Winsorized Mean ( 1 / 24 )15.18208333333330.17664805658690785.9453742468096
Winsorized Mean ( 2 / 24 )15.18013888888890.17609199796438186.2057280533524
Winsorized Mean ( 3 / 24 )15.18180555555560.17545417549632786.528607897812
Winsorized Mean ( 4 / 24 )15.19236111111110.17274542463242887.9465325546987
Winsorized Mean ( 5 / 24 )15.22569444444440.16416893976035192.7440627116824
Winsorized Mean ( 6 / 24 )15.25319444444440.150782365833013101.160333704651
Winsorized Mean ( 7 / 24 )15.18513888888890.136001759553131111.653988439441
Winsorized Mean ( 8 / 24 )15.16069444444440.129405364238794117.156615057071
Winsorized Mean ( 9 / 24 )15.14444444444440.124243861514275121.892898851219
Winsorized Mean ( 10 / 24 )15.11527777777780.119788868160367126.182657954012
Winsorized Mean ( 11 / 24 )15.11222222222220.117856146602327128.225999728417
Winsorized Mean ( 12 / 24 )15.12055555555560.111679784964311135.392054707014
Winsorized Mean ( 13 / 24 )15.118750.111464314152203135.637581543413
Winsorized Mean ( 14 / 24 )15.118750.108299008195165139.601924818689
Winsorized Mean ( 15 / 24 )15.13958333333330.101971458290773148.4688322311
Winsorized Mean ( 16 / 24 )15.226250.0780362054078752195.117765150372
Winsorized Mean ( 17 / 24 )15.38916666666670.0461357924593573333.562421849013
Winsorized Mean ( 18 / 24 )15.41166666666670.0355402084444567433.640300415021
Winsorized Mean ( 19 / 24 )15.42486111111110.0319654749783722482.547533598282
Winsorized Mean ( 20 / 24 )15.41652777777780.0307516426538248501.323716307568
Winsorized Mean ( 21 / 24 )15.41652777777780.025685560787158600.202109875115
Winsorized Mean ( 22 / 24 )15.40736111111110.0218679643776758704.563115478635
Winsorized Mean ( 23 / 24 )15.413750.0200629267294551768.270263249804
Winsorized Mean ( 24 / 24 )15.413750.0191530748909353804.766341058634
Trimmed Mean ( 1 / 24 )15.19014285714290.17077990543897488.9457270637196
Trimmed Mean ( 2 / 24 )15.19867647058820.16378304569906592.7976177614518
Trimmed Mean ( 3 / 24 )15.20878787878790.15573324798901597.6592222610077
Trimmed Mean ( 4 / 24 )15.218906250.146254513766239104.057685866192
Trimmed Mean ( 5 / 24 )15.22661290322580.13571050930071112.199217154851
Trimmed Mean ( 6 / 24 )15.22683333333330.125808232614551121.032090006264
Trimmed Mean ( 7 / 24 )15.22137931034480.117942496338601129.057632175648
Trimmed Mean ( 8 / 24 )15.22803571428570.112575925214265135.269025640271
Trimmed Mean ( 9 / 24 )15.23925925925930.107647758739765141.565968838233
Trimmed Mean ( 10 / 24 )15.25384615384620.102750688124053148.454929425192
Trimmed Mean ( 11 / 24 )15.27380.0975315291773561156.603717062873
Trimmed Mean ( 12 / 24 )15.29583333333330.0912258096437278167.670020064163
Trimmed Mean ( 13 / 24 )15.31869565217390.0846068536274653181.057384779064
Trimmed Mean ( 14 / 24 )15.34386363636360.0756320903995954202.875043586601
Trimmed Mean ( 15 / 24 )15.37142857142860.0638510274648152240.738938459509
Trimmed Mean ( 16 / 24 )15.399250.0484098256343556318.101744805117
Trimmed Mean ( 17 / 24 )15.41973684210530.0356617722141584432.388405980097
Trimmed Mean ( 18 / 24 )15.42333333333330.0314819172083136489.910866332512
Trimmed Mean ( 19 / 24 )15.42470588235290.0292333268112938527.641139919589
Trimmed Mean ( 20 / 24 )15.42468750.0272088116323287566.900447856121
Trimmed Mean ( 21 / 24 )15.42566666666670.0246617733574473625.488947736536
Trimmed Mean ( 22 / 24 )15.42678571428570.0228119386003463676.259303716148
Trimmed Mean ( 23 / 24 )15.42923076923080.0214398843059671719.650840883342
Trimmed Mean ( 24 / 24 )15.431250.0200299820558936770.407579844013
Median15.43
Midrange14.935
Midmean - Weighted Average at Xnp15.4075675675676
Midmean - Weighted Average at X(n+1)p15.4233333333333
Midmean - Empirical Distribution Function15.4075675675676
Midmean - Empirical Distribution Function - Averaging15.4233333333333
Midmean - Empirical Distribution Function - Interpolation15.4233333333333
Midmean - Closest Observation15.4075675675676
Midmean - True Basic - Statistics Graphics Toolkit15.4233333333333
Midmean - MS Excel (old versions)15.4197368421053
Number of observations72



Parameters (Session):
par1 = grey ;
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')