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of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationTue, 08 Mar 2016 19:12:55 +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/2016/Mar/08/t1457464481h462t9mfq43mgnd.htm/, Retrieved Sun, 28 Apr 2024 23:27:18 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=293718, Retrieved Sun, 28 Apr 2024 23:27:18 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact67
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [Verhuur en handel...] [2016-03-08 19:12:55] [38f93cf143127a30e50d4675c70fea9c] [Current]
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Dataseries X:
16,8
17,2
17,4
17,6
17,7
17,7
17,6
17,6
17,5
17,5
17,6
17,6
17,9
18,2
18,4
18,5
19
19,5
19,7
19,9
19,7
19,5
19,7
19,7
19,7
19,9
20,1
20,1
20,1
20,1
20,2
20,3
20,8
21,1
21,2
21,3
21,6
21,7
21,8
22
21,9
21,9
22
22,1
21
19,7
19,8
19,9
19,8
20
20,2
20,3
20,7
20,9
21
21,2
23,7
23,7
23,7
23,8
24
24
24,1
24,3
24,4
24,4
24,5
24,6
24,7
24,6
24,6
24,6
24,7
24,7
24,8
24,9
25
25,1
25,2
25,3




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Sir Ronald Aylmer Fisher' @ fisher.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 & 2 seconds \tabularnewline
R Server & 'Sir Ronald Aylmer Fisher' @ fisher.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=293718&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]'Sir Ronald Aylmer Fisher' @ fisher.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=293718&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=293718&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'Sir Ronald Aylmer Fisher' @ fisher.wessa.net







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean21.141250.28444757559081774.3238888786033
Geometric Mean20.9904769627653
Harmonic Mean20.8408112505663
Quadratic Mean21.2918851913117
Winsorized Mean ( 1 / 26 )21.1450.28329492169509174.6395306822981
Winsorized Mean ( 2 / 26 )21.14750.28198536073861474.9950279142423
Winsorized Mean ( 3 / 26 )21.14750.28070308990736975.3376103090943
Winsorized Mean ( 4 / 26 )21.14250.27984384773284675.5510623917085
Winsorized Mean ( 5 / 26 )21.14250.27777241731817976.1144688307261
Winsorized Mean ( 6 / 26 )21.1350.27653541444639276.427824053968
Winsorized Mean ( 7 / 26 )21.1350.27653541444639276.427824053968
Winsorized Mean ( 8 / 26 )21.1350.27653541444639276.427824053968
Winsorized Mean ( 9 / 26 )21.123750.27471644616065376.8929210290049
Winsorized Mean ( 10 / 26 )21.136250.27270471203914877.5059948247826
Winsorized Mean ( 11 / 26 )21.136250.27270471203914877.5059948247826
Winsorized Mean ( 12 / 26 )21.166250.26799740074074978.9793107750156
Winsorized Mean ( 13 / 26 )21.198750.25801391968877382.1612648866806
Winsorized Mean ( 14 / 26 )21.216250.25011670535465784.8254016856494
Winsorized Mean ( 15 / 26 )21.2350.24746883194618785.8087858297147
Winsorized Mean ( 16 / 26 )21.3150.23084942212663892.3329146923625
Winsorized Mean ( 17 / 26 )21.378750.211142864751436101.252533563792
Winsorized Mean ( 18 / 26 )21.356250.207492898688917102.92520917556
Winsorized Mean ( 19 / 26 )21.403750.202269119435507105.818179560645
Winsorized Mean ( 20 / 26 )21.353750.19421982643647109.946293289397
Winsorized Mean ( 21 / 26 )21.32750.190053082191878112.218648358818
Winsorized Mean ( 22 / 26 )21.32750.190053082191878112.218648358818
Winsorized Mean ( 23 / 26 )21.32750.190053082191878112.218648358818
Winsorized Mean ( 24 / 26 )20.84750.118721765464201175.599646101003
Winsorized Mean ( 25 / 26 )20.84750.110793670134048188.165081766647
Winsorized Mean ( 26 / 26 )20.84750.110793670134048188.165081766647
Trimmed Mean ( 1 / 26 )21.14358974358970.2812878294007775.1670976616091
Trimmed Mean ( 2 / 26 )21.14210526315790.27884639019708875.8198994371587
Trimmed Mean ( 3 / 26 )21.13918918918920.27668113966336576.402711131337
Trimmed Mean ( 4 / 26 )21.13611111111110.27456969859751976.9790374505007
Trimmed Mean ( 5 / 26 )21.13428571428570.27224916819517377.6284675335894
Trimmed Mean ( 6 / 26 )21.13235294117650.26997415719063378.2754659226682
Trimmed Mean ( 7 / 26 )21.13181818181820.26745070426472579.0120117272218
Trimmed Mean ( 8 / 26 )21.131250.26430196888023479.9511637750055
Trimmed Mean ( 9 / 26 )21.13064516129030.26040066664710481.1466630764301
Trimmed Mean ( 10 / 26 )21.13166666666670.25597373261543382.5540435370149
Trimmed Mean ( 11 / 26 )21.13103448275860.25091733570247884.2151237721355
Trimmed Mean ( 12 / 26 )21.13035714285710.24464285714285786.3722627737226
Trimmed Mean ( 13 / 26 )21.12592592592590.23781537132798788.833307148972
Trimmed Mean ( 14 / 26 )21.11730769230770.23132709719415991.2876526288808
Trimmed Mean ( 15 / 26 )21.1060.22474311866607993.9116629032772
Trimmed Mean ( 16 / 26 )21.09166666666670.21686093309446197.258950082445
Trimmed Mean ( 17 / 26 )21.06739130434780.210131183958378100.258281077028
Trimmed Mean ( 18 / 26 )21.03409090909090.205241650535063102.484514494281
Trimmed Mean ( 19 / 26 )210.199447552917283105.290838081676
Trimmed Mean ( 20 / 26 )20.95750.192383414579137108.936105775267
Trimmed Mean ( 21 / 26 )20.91578947368420.184788769332833113.187557605363
Trimmed Mean ( 22 / 26 )20.87222222222220.175282588669418119.07755573822
Trimmed Mean ( 23 / 26 )20.82352941176470.16149142367417128.945110136492
Trimmed Mean ( 24 / 26 )20.768750.140666436547485147.645383715887
Trimmed Mean ( 25 / 26 )20.760.138597241683588149.786530726162
Trimmed Mean ( 26 / 26 )20.750.137292411841319151.137267688054
Median20.75
Midrange21.05
Midmean - Weighted Average at Xnp20.9268292682927
Midmean - Weighted Average at X(n+1)p20.9268292682927
Midmean - Empirical Distribution Function20.9268292682927
Midmean - Empirical Distribution Function - Averaging20.9268292682927
Midmean - Empirical Distribution Function - Interpolation20.9268292682927
Midmean - Closest Observation20.9268292682927
Midmean - True Basic - Statistics Graphics Toolkit20.9268292682927
Midmean - MS Excel (old versions)21.0697674418605
Number of observations80

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 21.14125 & 0.284447575590817 & 74.3238888786033 \tabularnewline
Geometric Mean & 20.9904769627653 &  &  \tabularnewline
Harmonic Mean & 20.8408112505663 &  &  \tabularnewline
Quadratic Mean & 21.2918851913117 &  &  \tabularnewline
Winsorized Mean ( 1 / 26 ) & 21.145 & 0.283294921695091 & 74.6395306822981 \tabularnewline
Winsorized Mean ( 2 / 26 ) & 21.1475 & 0.281985360738614 & 74.9950279142423 \tabularnewline
Winsorized Mean ( 3 / 26 ) & 21.1475 & 0.280703089907369 & 75.3376103090943 \tabularnewline
Winsorized Mean ( 4 / 26 ) & 21.1425 & 0.279843847732846 & 75.5510623917085 \tabularnewline
Winsorized Mean ( 5 / 26 ) & 21.1425 & 0.277772417318179 & 76.1144688307261 \tabularnewline
Winsorized Mean ( 6 / 26 ) & 21.135 & 0.276535414446392 & 76.427824053968 \tabularnewline
Winsorized Mean ( 7 / 26 ) & 21.135 & 0.276535414446392 & 76.427824053968 \tabularnewline
Winsorized Mean ( 8 / 26 ) & 21.135 & 0.276535414446392 & 76.427824053968 \tabularnewline
Winsorized Mean ( 9 / 26 ) & 21.12375 & 0.274716446160653 & 76.8929210290049 \tabularnewline
Winsorized Mean ( 10 / 26 ) & 21.13625 & 0.272704712039148 & 77.5059948247826 \tabularnewline
Winsorized Mean ( 11 / 26 ) & 21.13625 & 0.272704712039148 & 77.5059948247826 \tabularnewline
Winsorized Mean ( 12 / 26 ) & 21.16625 & 0.267997400740749 & 78.9793107750156 \tabularnewline
Winsorized Mean ( 13 / 26 ) & 21.19875 & 0.258013919688773 & 82.1612648866806 \tabularnewline
Winsorized Mean ( 14 / 26 ) & 21.21625 & 0.250116705354657 & 84.8254016856494 \tabularnewline
Winsorized Mean ( 15 / 26 ) & 21.235 & 0.247468831946187 & 85.8087858297147 \tabularnewline
Winsorized Mean ( 16 / 26 ) & 21.315 & 0.230849422126638 & 92.3329146923625 \tabularnewline
Winsorized Mean ( 17 / 26 ) & 21.37875 & 0.211142864751436 & 101.252533563792 \tabularnewline
Winsorized Mean ( 18 / 26 ) & 21.35625 & 0.207492898688917 & 102.92520917556 \tabularnewline
Winsorized Mean ( 19 / 26 ) & 21.40375 & 0.202269119435507 & 105.818179560645 \tabularnewline
Winsorized Mean ( 20 / 26 ) & 21.35375 & 0.19421982643647 & 109.946293289397 \tabularnewline
Winsorized Mean ( 21 / 26 ) & 21.3275 & 0.190053082191878 & 112.218648358818 \tabularnewline
Winsorized Mean ( 22 / 26 ) & 21.3275 & 0.190053082191878 & 112.218648358818 \tabularnewline
Winsorized Mean ( 23 / 26 ) & 21.3275 & 0.190053082191878 & 112.218648358818 \tabularnewline
Winsorized Mean ( 24 / 26 ) & 20.8475 & 0.118721765464201 & 175.599646101003 \tabularnewline
Winsorized Mean ( 25 / 26 ) & 20.8475 & 0.110793670134048 & 188.165081766647 \tabularnewline
Winsorized Mean ( 26 / 26 ) & 20.8475 & 0.110793670134048 & 188.165081766647 \tabularnewline
Trimmed Mean ( 1 / 26 ) & 21.1435897435897 & 0.28128782940077 & 75.1670976616091 \tabularnewline
Trimmed Mean ( 2 / 26 ) & 21.1421052631579 & 0.278846390197088 & 75.8198994371587 \tabularnewline
Trimmed Mean ( 3 / 26 ) & 21.1391891891892 & 0.276681139663365 & 76.402711131337 \tabularnewline
Trimmed Mean ( 4 / 26 ) & 21.1361111111111 & 0.274569698597519 & 76.9790374505007 \tabularnewline
Trimmed Mean ( 5 / 26 ) & 21.1342857142857 & 0.272249168195173 & 77.6284675335894 \tabularnewline
Trimmed Mean ( 6 / 26 ) & 21.1323529411765 & 0.269974157190633 & 78.2754659226682 \tabularnewline
Trimmed Mean ( 7 / 26 ) & 21.1318181818182 & 0.267450704264725 & 79.0120117272218 \tabularnewline
Trimmed Mean ( 8 / 26 ) & 21.13125 & 0.264301968880234 & 79.9511637750055 \tabularnewline
Trimmed Mean ( 9 / 26 ) & 21.1306451612903 & 0.260400666647104 & 81.1466630764301 \tabularnewline
Trimmed Mean ( 10 / 26 ) & 21.1316666666667 & 0.255973732615433 & 82.5540435370149 \tabularnewline
Trimmed Mean ( 11 / 26 ) & 21.1310344827586 & 0.250917335702478 & 84.2151237721355 \tabularnewline
Trimmed Mean ( 12 / 26 ) & 21.1303571428571 & 0.244642857142857 & 86.3722627737226 \tabularnewline
Trimmed Mean ( 13 / 26 ) & 21.1259259259259 & 0.237815371327987 & 88.833307148972 \tabularnewline
Trimmed Mean ( 14 / 26 ) & 21.1173076923077 & 0.231327097194159 & 91.2876526288808 \tabularnewline
Trimmed Mean ( 15 / 26 ) & 21.106 & 0.224743118666079 & 93.9116629032772 \tabularnewline
Trimmed Mean ( 16 / 26 ) & 21.0916666666667 & 0.216860933094461 & 97.258950082445 \tabularnewline
Trimmed Mean ( 17 / 26 ) & 21.0673913043478 & 0.210131183958378 & 100.258281077028 \tabularnewline
Trimmed Mean ( 18 / 26 ) & 21.0340909090909 & 0.205241650535063 & 102.484514494281 \tabularnewline
Trimmed Mean ( 19 / 26 ) & 21 & 0.199447552917283 & 105.290838081676 \tabularnewline
Trimmed Mean ( 20 / 26 ) & 20.9575 & 0.192383414579137 & 108.936105775267 \tabularnewline
Trimmed Mean ( 21 / 26 ) & 20.9157894736842 & 0.184788769332833 & 113.187557605363 \tabularnewline
Trimmed Mean ( 22 / 26 ) & 20.8722222222222 & 0.175282588669418 & 119.07755573822 \tabularnewline
Trimmed Mean ( 23 / 26 ) & 20.8235294117647 & 0.16149142367417 & 128.945110136492 \tabularnewline
Trimmed Mean ( 24 / 26 ) & 20.76875 & 0.140666436547485 & 147.645383715887 \tabularnewline
Trimmed Mean ( 25 / 26 ) & 20.76 & 0.138597241683588 & 149.786530726162 \tabularnewline
Trimmed Mean ( 26 / 26 ) & 20.75 & 0.137292411841319 & 151.137267688054 \tabularnewline
Median & 20.75 &  &  \tabularnewline
Midrange & 21.05 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 20.9268292682927 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 20.9268292682927 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 20.9268292682927 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 20.9268292682927 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 20.9268292682927 &  &  \tabularnewline
Midmean - Closest Observation & 20.9268292682927 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 20.9268292682927 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 21.0697674418605 &  &  \tabularnewline
Number of observations & 80 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=293718&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]21.14125[/C][C]0.284447575590817[/C][C]74.3238888786033[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]20.9904769627653[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]20.8408112505663[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]21.2918851913117[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 26 )[/C][C]21.145[/C][C]0.283294921695091[/C][C]74.6395306822981[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 26 )[/C][C]21.1475[/C][C]0.281985360738614[/C][C]74.9950279142423[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 26 )[/C][C]21.1475[/C][C]0.280703089907369[/C][C]75.3376103090943[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 26 )[/C][C]21.1425[/C][C]0.279843847732846[/C][C]75.5510623917085[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 26 )[/C][C]21.1425[/C][C]0.277772417318179[/C][C]76.1144688307261[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 26 )[/C][C]21.135[/C][C]0.276535414446392[/C][C]76.427824053968[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 26 )[/C][C]21.135[/C][C]0.276535414446392[/C][C]76.427824053968[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 26 )[/C][C]21.135[/C][C]0.276535414446392[/C][C]76.427824053968[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 26 )[/C][C]21.12375[/C][C]0.274716446160653[/C][C]76.8929210290049[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 26 )[/C][C]21.13625[/C][C]0.272704712039148[/C][C]77.5059948247826[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 26 )[/C][C]21.13625[/C][C]0.272704712039148[/C][C]77.5059948247826[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 26 )[/C][C]21.16625[/C][C]0.267997400740749[/C][C]78.9793107750156[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 26 )[/C][C]21.19875[/C][C]0.258013919688773[/C][C]82.1612648866806[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 26 )[/C][C]21.21625[/C][C]0.250116705354657[/C][C]84.8254016856494[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 26 )[/C][C]21.235[/C][C]0.247468831946187[/C][C]85.8087858297147[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 26 )[/C][C]21.315[/C][C]0.230849422126638[/C][C]92.3329146923625[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 26 )[/C][C]21.37875[/C][C]0.211142864751436[/C][C]101.252533563792[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 26 )[/C][C]21.35625[/C][C]0.207492898688917[/C][C]102.92520917556[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 26 )[/C][C]21.40375[/C][C]0.202269119435507[/C][C]105.818179560645[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 26 )[/C][C]21.35375[/C][C]0.19421982643647[/C][C]109.946293289397[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 26 )[/C][C]21.3275[/C][C]0.190053082191878[/C][C]112.218648358818[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 26 )[/C][C]21.3275[/C][C]0.190053082191878[/C][C]112.218648358818[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 26 )[/C][C]21.3275[/C][C]0.190053082191878[/C][C]112.218648358818[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 26 )[/C][C]20.8475[/C][C]0.118721765464201[/C][C]175.599646101003[/C][/ROW]
[ROW][C]Winsorized Mean ( 25 / 26 )[/C][C]20.8475[/C][C]0.110793670134048[/C][C]188.165081766647[/C][/ROW]
[ROW][C]Winsorized Mean ( 26 / 26 )[/C][C]20.8475[/C][C]0.110793670134048[/C][C]188.165081766647[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 26 )[/C][C]21.1435897435897[/C][C]0.28128782940077[/C][C]75.1670976616091[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 26 )[/C][C]21.1421052631579[/C][C]0.278846390197088[/C][C]75.8198994371587[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 26 )[/C][C]21.1391891891892[/C][C]0.276681139663365[/C][C]76.402711131337[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 26 )[/C][C]21.1361111111111[/C][C]0.274569698597519[/C][C]76.9790374505007[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 26 )[/C][C]21.1342857142857[/C][C]0.272249168195173[/C][C]77.6284675335894[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 26 )[/C][C]21.1323529411765[/C][C]0.269974157190633[/C][C]78.2754659226682[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 26 )[/C][C]21.1318181818182[/C][C]0.267450704264725[/C][C]79.0120117272218[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 26 )[/C][C]21.13125[/C][C]0.264301968880234[/C][C]79.9511637750055[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 26 )[/C][C]21.1306451612903[/C][C]0.260400666647104[/C][C]81.1466630764301[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 26 )[/C][C]21.1316666666667[/C][C]0.255973732615433[/C][C]82.5540435370149[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 26 )[/C][C]21.1310344827586[/C][C]0.250917335702478[/C][C]84.2151237721355[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 26 )[/C][C]21.1303571428571[/C][C]0.244642857142857[/C][C]86.3722627737226[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 26 )[/C][C]21.1259259259259[/C][C]0.237815371327987[/C][C]88.833307148972[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 26 )[/C][C]21.1173076923077[/C][C]0.231327097194159[/C][C]91.2876526288808[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 26 )[/C][C]21.106[/C][C]0.224743118666079[/C][C]93.9116629032772[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 26 )[/C][C]21.0916666666667[/C][C]0.216860933094461[/C][C]97.258950082445[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 26 )[/C][C]21.0673913043478[/C][C]0.210131183958378[/C][C]100.258281077028[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 26 )[/C][C]21.0340909090909[/C][C]0.205241650535063[/C][C]102.484514494281[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 26 )[/C][C]21[/C][C]0.199447552917283[/C][C]105.290838081676[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 26 )[/C][C]20.9575[/C][C]0.192383414579137[/C][C]108.936105775267[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 26 )[/C][C]20.9157894736842[/C][C]0.184788769332833[/C][C]113.187557605363[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 26 )[/C][C]20.8722222222222[/C][C]0.175282588669418[/C][C]119.07755573822[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 26 )[/C][C]20.8235294117647[/C][C]0.16149142367417[/C][C]128.945110136492[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 26 )[/C][C]20.76875[/C][C]0.140666436547485[/C][C]147.645383715887[/C][/ROW]
[ROW][C]Trimmed Mean ( 25 / 26 )[/C][C]20.76[/C][C]0.138597241683588[/C][C]149.786530726162[/C][/ROW]
[ROW][C]Trimmed Mean ( 26 / 26 )[/C][C]20.75[/C][C]0.137292411841319[/C][C]151.137267688054[/C][/ROW]
[ROW][C]Median[/C][C]20.75[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]21.05[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]20.9268292682927[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]20.9268292682927[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]20.9268292682927[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]20.9268292682927[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]20.9268292682927[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]20.9268292682927[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]20.9268292682927[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]21.0697674418605[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]80[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=293718&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=293718&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 Mean21.141250.28444757559081774.3238888786033
Geometric Mean20.9904769627653
Harmonic Mean20.8408112505663
Quadratic Mean21.2918851913117
Winsorized Mean ( 1 / 26 )21.1450.28329492169509174.6395306822981
Winsorized Mean ( 2 / 26 )21.14750.28198536073861474.9950279142423
Winsorized Mean ( 3 / 26 )21.14750.28070308990736975.3376103090943
Winsorized Mean ( 4 / 26 )21.14250.27984384773284675.5510623917085
Winsorized Mean ( 5 / 26 )21.14250.27777241731817976.1144688307261
Winsorized Mean ( 6 / 26 )21.1350.27653541444639276.427824053968
Winsorized Mean ( 7 / 26 )21.1350.27653541444639276.427824053968
Winsorized Mean ( 8 / 26 )21.1350.27653541444639276.427824053968
Winsorized Mean ( 9 / 26 )21.123750.27471644616065376.8929210290049
Winsorized Mean ( 10 / 26 )21.136250.27270471203914877.5059948247826
Winsorized Mean ( 11 / 26 )21.136250.27270471203914877.5059948247826
Winsorized Mean ( 12 / 26 )21.166250.26799740074074978.9793107750156
Winsorized Mean ( 13 / 26 )21.198750.25801391968877382.1612648866806
Winsorized Mean ( 14 / 26 )21.216250.25011670535465784.8254016856494
Winsorized Mean ( 15 / 26 )21.2350.24746883194618785.8087858297147
Winsorized Mean ( 16 / 26 )21.3150.23084942212663892.3329146923625
Winsorized Mean ( 17 / 26 )21.378750.211142864751436101.252533563792
Winsorized Mean ( 18 / 26 )21.356250.207492898688917102.92520917556
Winsorized Mean ( 19 / 26 )21.403750.202269119435507105.818179560645
Winsorized Mean ( 20 / 26 )21.353750.19421982643647109.946293289397
Winsorized Mean ( 21 / 26 )21.32750.190053082191878112.218648358818
Winsorized Mean ( 22 / 26 )21.32750.190053082191878112.218648358818
Winsorized Mean ( 23 / 26 )21.32750.190053082191878112.218648358818
Winsorized Mean ( 24 / 26 )20.84750.118721765464201175.599646101003
Winsorized Mean ( 25 / 26 )20.84750.110793670134048188.165081766647
Winsorized Mean ( 26 / 26 )20.84750.110793670134048188.165081766647
Trimmed Mean ( 1 / 26 )21.14358974358970.2812878294007775.1670976616091
Trimmed Mean ( 2 / 26 )21.14210526315790.27884639019708875.8198994371587
Trimmed Mean ( 3 / 26 )21.13918918918920.27668113966336576.402711131337
Trimmed Mean ( 4 / 26 )21.13611111111110.27456969859751976.9790374505007
Trimmed Mean ( 5 / 26 )21.13428571428570.27224916819517377.6284675335894
Trimmed Mean ( 6 / 26 )21.13235294117650.26997415719063378.2754659226682
Trimmed Mean ( 7 / 26 )21.13181818181820.26745070426472579.0120117272218
Trimmed Mean ( 8 / 26 )21.131250.26430196888023479.9511637750055
Trimmed Mean ( 9 / 26 )21.13064516129030.26040066664710481.1466630764301
Trimmed Mean ( 10 / 26 )21.13166666666670.25597373261543382.5540435370149
Trimmed Mean ( 11 / 26 )21.13103448275860.25091733570247884.2151237721355
Trimmed Mean ( 12 / 26 )21.13035714285710.24464285714285786.3722627737226
Trimmed Mean ( 13 / 26 )21.12592592592590.23781537132798788.833307148972
Trimmed Mean ( 14 / 26 )21.11730769230770.23132709719415991.2876526288808
Trimmed Mean ( 15 / 26 )21.1060.22474311866607993.9116629032772
Trimmed Mean ( 16 / 26 )21.09166666666670.21686093309446197.258950082445
Trimmed Mean ( 17 / 26 )21.06739130434780.210131183958378100.258281077028
Trimmed Mean ( 18 / 26 )21.03409090909090.205241650535063102.484514494281
Trimmed Mean ( 19 / 26 )210.199447552917283105.290838081676
Trimmed Mean ( 20 / 26 )20.95750.192383414579137108.936105775267
Trimmed Mean ( 21 / 26 )20.91578947368420.184788769332833113.187557605363
Trimmed Mean ( 22 / 26 )20.87222222222220.175282588669418119.07755573822
Trimmed Mean ( 23 / 26 )20.82352941176470.16149142367417128.945110136492
Trimmed Mean ( 24 / 26 )20.768750.140666436547485147.645383715887
Trimmed Mean ( 25 / 26 )20.760.138597241683588149.786530726162
Trimmed Mean ( 26 / 26 )20.750.137292411841319151.137267688054
Median20.75
Midrange21.05
Midmean - Weighted Average at Xnp20.9268292682927
Midmean - Weighted Average at X(n+1)p20.9268292682927
Midmean - Empirical Distribution Function20.9268292682927
Midmean - Empirical Distribution Function - Averaging20.9268292682927
Midmean - Empirical Distribution Function - Interpolation20.9268292682927
Midmean - Closest Observation20.9268292682927
Midmean - True Basic - Statistics Graphics Toolkit20.9268292682927
Midmean - MS Excel (old versions)21.0697674418605
Number of observations80



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')