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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 computationMon, 13 Oct 2014 15:23:57 +0100
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2014/Oct/13/t1413210404u08auyezx9o9v3n.htm/, Retrieved Fri, 10 May 2024 17:16:13 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=240757, Retrieved Fri, 10 May 2024 17:16:13 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact77
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [] [2014-10-13 14:23:57] [77e76d07a5b02a0482982fb19d5d5436] [Current]
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Dataseries X:
21,94
21,95
21,96
22,1
22,13
22,18
22,18
22,27
22,3
22,04
22,05
22,06
22,06
22,06
21,97
22,03
22,08
22,13
22,13
22,4
22,4
22,12
22,22
22,14
22,14
22,19
22,29
22,24
22,26
22,29
22,29
22,29
22,29
22,35
22,39
22,43
22,43
22,11
22,12
22,05
22,05
22,08
22,08
22,09
22,09
22,24
22,25
22,24
22,24
22,25
22,28
22,23
22,29
22,31
22,31
22,31
22,39
22,42
22,42
22,42
22,15
21,95
21,96
21,97
21,66
21,66
21,68
21,75
21,55
21,59
21,54
21,54




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Sir Maurice George Kendall' @ kendall.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 Maurice George Kendall' @ kendall.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=240757&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 Maurice George Kendall' @ kendall.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=240757&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=240757&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 Maurice George Kendall' @ kendall.wessa.net







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean22.12569444444440.0265024479845553834.85474463863
Geometric Mean22.1245594301099
Harmonic Mean22.1234162762823
Quadratic Mean22.1268213625706
Winsorized Mean ( 1 / 24 )22.12569444444440.0265024479845553834.85474463863
Winsorized Mean ( 2 / 24 )22.12569444444440.0263722200463977838.977318008033
Winsorized Mean ( 3 / 24 )22.12736111111110.025872107094151855.259335105083
Winsorized Mean ( 4 / 24 )22.131250.0247814685893716893.056435303103
Winsorized Mean ( 5 / 24 )22.12986111111110.0245598921864075901.056932300325
Winsorized Mean ( 6 / 24 )22.13152777777780.0241155438887649917.728742916246
Winsorized Mean ( 7 / 24 )22.13736111111110.0222264215026883995.993039564809
Winsorized Mean ( 8 / 24 )22.15847222222220.01771653397216241250.72275745579
Winsorized Mean ( 9 / 24 )22.15472222222220.01662432676248981332.66883758631
Winsorized Mean ( 10 / 24 )22.14916666666670.01576399445339791405.04785967445
Winsorized Mean ( 11 / 24 )22.15069444444440.01549562812402561429.48025515018
Winsorized Mean ( 12 / 24 )22.15069444444440.01549562812402561429.48025515018
Winsorized Mean ( 13 / 24 )22.15069444444440.01492721830083091483.91307730868
Winsorized Mean ( 14 / 24 )22.148750.01465825823311881511.00830997486
Winsorized Mean ( 15 / 24 )22.161250.01266045297926031750.43104984501
Winsorized Mean ( 16 / 24 )22.16347222222220.01234157782145121795.83782097127
Winsorized Mean ( 17 / 24 )22.16583333333330.01201484150022081844.87105659495
Winsorized Mean ( 18 / 24 )22.16583333333330.01201484150022081844.87105659495
Winsorized Mean ( 19 / 24 )22.16583333333330.01201484150022081844.87105659495
Winsorized Mean ( 20 / 24 )22.16583333333330.01124097621053821971.87796844132
Winsorized Mean ( 21 / 24 )22.16291666666670.01082915683306792046.59670261585
Winsorized Mean ( 22 / 24 )22.15986111111110.010409256623642128.86106206517
Winsorized Mean ( 23 / 24 )22.16305555555560.009136503700994342425.76988757127
Winsorized Mean ( 24 / 24 )22.16305555555560.009136503700994342425.76988757127
Trimmed Mean ( 1 / 24 )22.12971428571430.0255530718201149866.029510717931
Trimmed Mean ( 2 / 24 )22.13397058823530.0244097482163233906.767672983773
Trimmed Mean ( 3 / 24 )22.13848484848480.0231063643986296958.111993152754
Trimmed Mean ( 4 / 24 )22.142656250.02176060472575971017.55702697858
Trimmed Mean ( 5 / 24 )22.14596774193550.02055992991238251077.14218075217
Trimmed Mean ( 6 / 24 )22.14983333333330.01914189015141241157.13929805929
Trimmed Mean ( 7 / 24 )22.15362068965520.0175041232302051265.62298484206
Trimmed Mean ( 8 / 24 )22.15660714285710.01605242382821571380.26552126738
Trimmed Mean ( 9 / 24 )22.15629629629630.01555247715038891424.61526109635
Trimmed Mean ( 10 / 24 )22.15653846153850.01519328614372131458.31114164165
Trimmed Mean ( 11 / 24 )22.15760.01492719747607691484.3777631743
Trimmed Mean ( 12 / 24 )22.15854166666670.01464106480636921513.4515118755
Trimmed Mean ( 13 / 24 )22.15956521739130.01426443339468531553.48373147773
Trimmed Mean ( 14 / 24 )22.16068181818180.01389859730732861594.45455740319
Trimmed Mean ( 15 / 24 )22.16214285714290.0134671093044531645.64958641976
Trimmed Mean ( 16 / 24 )22.162250.01336128880241491658.6910385467
Trimmed Mean ( 17 / 24 )22.16210526315790.01326048201686531671.28956812966
Trimmed Mean ( 18 / 24 )22.16166666666670.01316259732172831683.68492364976
Trimmed Mean ( 19 / 24 )22.16117647058820.01299091075288291705.89860034796
Trimmed Mean ( 20 / 24 )22.1606250.01271538232145011742.82018737386
Trimmed Mean ( 21 / 24 )22.160.01250287323299971772.3926002474
Trimmed Mean ( 22 / 24 )22.15964285714290.01227422712636151805.37989308918
Trimmed Mean ( 23 / 24 )22.15961538461540.01201896922792361843.72011978632
Trimmed Mean ( 24 / 24 )22.15916666666670.01199209683389141847.81418742731
Median22.14
Midrange21.985
Midmean - Weighted Average at Xnp22.1714634146341
Midmean - Weighted Average at X(n+1)p22.1714634146341
Midmean - Empirical Distribution Function22.1714634146341
Midmean - Empirical Distribution Function - Averaging22.1714634146341
Midmean - Empirical Distribution Function - Interpolation22.1714634146341
Midmean - Closest Observation22.1714634146341
Midmean - True Basic - Statistics Graphics Toolkit22.1714634146341
Midmean - MS Excel (old versions)22.1714634146341
Number of observations72

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 22.1256944444444 & 0.0265024479845553 & 834.85474463863 \tabularnewline
Geometric Mean & 22.1245594301099 &  &  \tabularnewline
Harmonic Mean & 22.1234162762823 &  &  \tabularnewline
Quadratic Mean & 22.1268213625706 &  &  \tabularnewline
Winsorized Mean ( 1 / 24 ) & 22.1256944444444 & 0.0265024479845553 & 834.85474463863 \tabularnewline
Winsorized Mean ( 2 / 24 ) & 22.1256944444444 & 0.0263722200463977 & 838.977318008033 \tabularnewline
Winsorized Mean ( 3 / 24 ) & 22.1273611111111 & 0.025872107094151 & 855.259335105083 \tabularnewline
Winsorized Mean ( 4 / 24 ) & 22.13125 & 0.0247814685893716 & 893.056435303103 \tabularnewline
Winsorized Mean ( 5 / 24 ) & 22.1298611111111 & 0.0245598921864075 & 901.056932300325 \tabularnewline
Winsorized Mean ( 6 / 24 ) & 22.1315277777778 & 0.0241155438887649 & 917.728742916246 \tabularnewline
Winsorized Mean ( 7 / 24 ) & 22.1373611111111 & 0.0222264215026883 & 995.993039564809 \tabularnewline
Winsorized Mean ( 8 / 24 ) & 22.1584722222222 & 0.0177165339721624 & 1250.72275745579 \tabularnewline
Winsorized Mean ( 9 / 24 ) & 22.1547222222222 & 0.0166243267624898 & 1332.66883758631 \tabularnewline
Winsorized Mean ( 10 / 24 ) & 22.1491666666667 & 0.0157639944533979 & 1405.04785967445 \tabularnewline
Winsorized Mean ( 11 / 24 ) & 22.1506944444444 & 0.0154956281240256 & 1429.48025515018 \tabularnewline
Winsorized Mean ( 12 / 24 ) & 22.1506944444444 & 0.0154956281240256 & 1429.48025515018 \tabularnewline
Winsorized Mean ( 13 / 24 ) & 22.1506944444444 & 0.0149272183008309 & 1483.91307730868 \tabularnewline
Winsorized Mean ( 14 / 24 ) & 22.14875 & 0.0146582582331188 & 1511.00830997486 \tabularnewline
Winsorized Mean ( 15 / 24 ) & 22.16125 & 0.0126604529792603 & 1750.43104984501 \tabularnewline
Winsorized Mean ( 16 / 24 ) & 22.1634722222222 & 0.0123415778214512 & 1795.83782097127 \tabularnewline
Winsorized Mean ( 17 / 24 ) & 22.1658333333333 & 0.0120148415002208 & 1844.87105659495 \tabularnewline
Winsorized Mean ( 18 / 24 ) & 22.1658333333333 & 0.0120148415002208 & 1844.87105659495 \tabularnewline
Winsorized Mean ( 19 / 24 ) & 22.1658333333333 & 0.0120148415002208 & 1844.87105659495 \tabularnewline
Winsorized Mean ( 20 / 24 ) & 22.1658333333333 & 0.0112409762105382 & 1971.87796844132 \tabularnewline
Winsorized Mean ( 21 / 24 ) & 22.1629166666667 & 0.0108291568330679 & 2046.59670261585 \tabularnewline
Winsorized Mean ( 22 / 24 ) & 22.1598611111111 & 0.01040925662364 & 2128.86106206517 \tabularnewline
Winsorized Mean ( 23 / 24 ) & 22.1630555555556 & 0.00913650370099434 & 2425.76988757127 \tabularnewline
Winsorized Mean ( 24 / 24 ) & 22.1630555555556 & 0.00913650370099434 & 2425.76988757127 \tabularnewline
Trimmed Mean ( 1 / 24 ) & 22.1297142857143 & 0.0255530718201149 & 866.029510717931 \tabularnewline
Trimmed Mean ( 2 / 24 ) & 22.1339705882353 & 0.0244097482163233 & 906.767672983773 \tabularnewline
Trimmed Mean ( 3 / 24 ) & 22.1384848484848 & 0.0231063643986296 & 958.111993152754 \tabularnewline
Trimmed Mean ( 4 / 24 ) & 22.14265625 & 0.0217606047257597 & 1017.55702697858 \tabularnewline
Trimmed Mean ( 5 / 24 ) & 22.1459677419355 & 0.0205599299123825 & 1077.14218075217 \tabularnewline
Trimmed Mean ( 6 / 24 ) & 22.1498333333333 & 0.0191418901514124 & 1157.13929805929 \tabularnewline
Trimmed Mean ( 7 / 24 ) & 22.1536206896552 & 0.017504123230205 & 1265.62298484206 \tabularnewline
Trimmed Mean ( 8 / 24 ) & 22.1566071428571 & 0.0160524238282157 & 1380.26552126738 \tabularnewline
Trimmed Mean ( 9 / 24 ) & 22.1562962962963 & 0.0155524771503889 & 1424.61526109635 \tabularnewline
Trimmed Mean ( 10 / 24 ) & 22.1565384615385 & 0.0151932861437213 & 1458.31114164165 \tabularnewline
Trimmed Mean ( 11 / 24 ) & 22.1576 & 0.0149271974760769 & 1484.3777631743 \tabularnewline
Trimmed Mean ( 12 / 24 ) & 22.1585416666667 & 0.0146410648063692 & 1513.4515118755 \tabularnewline
Trimmed Mean ( 13 / 24 ) & 22.1595652173913 & 0.0142644333946853 & 1553.48373147773 \tabularnewline
Trimmed Mean ( 14 / 24 ) & 22.1606818181818 & 0.0138985973073286 & 1594.45455740319 \tabularnewline
Trimmed Mean ( 15 / 24 ) & 22.1621428571429 & 0.013467109304453 & 1645.64958641976 \tabularnewline
Trimmed Mean ( 16 / 24 ) & 22.16225 & 0.0133612888024149 & 1658.6910385467 \tabularnewline
Trimmed Mean ( 17 / 24 ) & 22.1621052631579 & 0.0132604820168653 & 1671.28956812966 \tabularnewline
Trimmed Mean ( 18 / 24 ) & 22.1616666666667 & 0.0131625973217283 & 1683.68492364976 \tabularnewline
Trimmed Mean ( 19 / 24 ) & 22.1611764705882 & 0.0129909107528829 & 1705.89860034796 \tabularnewline
Trimmed Mean ( 20 / 24 ) & 22.160625 & 0.0127153823214501 & 1742.82018737386 \tabularnewline
Trimmed Mean ( 21 / 24 ) & 22.16 & 0.0125028732329997 & 1772.3926002474 \tabularnewline
Trimmed Mean ( 22 / 24 ) & 22.1596428571429 & 0.0122742271263615 & 1805.37989308918 \tabularnewline
Trimmed Mean ( 23 / 24 ) & 22.1596153846154 & 0.0120189692279236 & 1843.72011978632 \tabularnewline
Trimmed Mean ( 24 / 24 ) & 22.1591666666667 & 0.0119920968338914 & 1847.81418742731 \tabularnewline
Median & 22.14 &  &  \tabularnewline
Midrange & 21.985 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 22.1714634146341 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 22.1714634146341 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 22.1714634146341 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 22.1714634146341 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 22.1714634146341 &  &  \tabularnewline
Midmean - Closest Observation & 22.1714634146341 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 22.1714634146341 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 22.1714634146341 &  &  \tabularnewline
Number of observations & 72 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=240757&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]22.1256944444444[/C][C]0.0265024479845553[/C][C]834.85474463863[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]22.1245594301099[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]22.1234162762823[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]22.1268213625706[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 24 )[/C][C]22.1256944444444[/C][C]0.0265024479845553[/C][C]834.85474463863[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 24 )[/C][C]22.1256944444444[/C][C]0.0263722200463977[/C][C]838.977318008033[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 24 )[/C][C]22.1273611111111[/C][C]0.025872107094151[/C][C]855.259335105083[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 24 )[/C][C]22.13125[/C][C]0.0247814685893716[/C][C]893.056435303103[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 24 )[/C][C]22.1298611111111[/C][C]0.0245598921864075[/C][C]901.056932300325[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 24 )[/C][C]22.1315277777778[/C][C]0.0241155438887649[/C][C]917.728742916246[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 24 )[/C][C]22.1373611111111[/C][C]0.0222264215026883[/C][C]995.993039564809[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 24 )[/C][C]22.1584722222222[/C][C]0.0177165339721624[/C][C]1250.72275745579[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 24 )[/C][C]22.1547222222222[/C][C]0.0166243267624898[/C][C]1332.66883758631[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 24 )[/C][C]22.1491666666667[/C][C]0.0157639944533979[/C][C]1405.04785967445[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 24 )[/C][C]22.1506944444444[/C][C]0.0154956281240256[/C][C]1429.48025515018[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 24 )[/C][C]22.1506944444444[/C][C]0.0154956281240256[/C][C]1429.48025515018[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 24 )[/C][C]22.1506944444444[/C][C]0.0149272183008309[/C][C]1483.91307730868[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 24 )[/C][C]22.14875[/C][C]0.0146582582331188[/C][C]1511.00830997486[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 24 )[/C][C]22.16125[/C][C]0.0126604529792603[/C][C]1750.43104984501[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 24 )[/C][C]22.1634722222222[/C][C]0.0123415778214512[/C][C]1795.83782097127[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 24 )[/C][C]22.1658333333333[/C][C]0.0120148415002208[/C][C]1844.87105659495[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 24 )[/C][C]22.1658333333333[/C][C]0.0120148415002208[/C][C]1844.87105659495[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 24 )[/C][C]22.1658333333333[/C][C]0.0120148415002208[/C][C]1844.87105659495[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 24 )[/C][C]22.1658333333333[/C][C]0.0112409762105382[/C][C]1971.87796844132[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 24 )[/C][C]22.1629166666667[/C][C]0.0108291568330679[/C][C]2046.59670261585[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 24 )[/C][C]22.1598611111111[/C][C]0.01040925662364[/C][C]2128.86106206517[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 24 )[/C][C]22.1630555555556[/C][C]0.00913650370099434[/C][C]2425.76988757127[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 24 )[/C][C]22.1630555555556[/C][C]0.00913650370099434[/C][C]2425.76988757127[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 24 )[/C][C]22.1297142857143[/C][C]0.0255530718201149[/C][C]866.029510717931[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 24 )[/C][C]22.1339705882353[/C][C]0.0244097482163233[/C][C]906.767672983773[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 24 )[/C][C]22.1384848484848[/C][C]0.0231063643986296[/C][C]958.111993152754[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 24 )[/C][C]22.14265625[/C][C]0.0217606047257597[/C][C]1017.55702697858[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 24 )[/C][C]22.1459677419355[/C][C]0.0205599299123825[/C][C]1077.14218075217[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 24 )[/C][C]22.1498333333333[/C][C]0.0191418901514124[/C][C]1157.13929805929[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 24 )[/C][C]22.1536206896552[/C][C]0.017504123230205[/C][C]1265.62298484206[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 24 )[/C][C]22.1566071428571[/C][C]0.0160524238282157[/C][C]1380.26552126738[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 24 )[/C][C]22.1562962962963[/C][C]0.0155524771503889[/C][C]1424.61526109635[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 24 )[/C][C]22.1565384615385[/C][C]0.0151932861437213[/C][C]1458.31114164165[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 24 )[/C][C]22.1576[/C][C]0.0149271974760769[/C][C]1484.3777631743[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 24 )[/C][C]22.1585416666667[/C][C]0.0146410648063692[/C][C]1513.4515118755[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 24 )[/C][C]22.1595652173913[/C][C]0.0142644333946853[/C][C]1553.48373147773[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 24 )[/C][C]22.1606818181818[/C][C]0.0138985973073286[/C][C]1594.45455740319[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 24 )[/C][C]22.1621428571429[/C][C]0.013467109304453[/C][C]1645.64958641976[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 24 )[/C][C]22.16225[/C][C]0.0133612888024149[/C][C]1658.6910385467[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 24 )[/C][C]22.1621052631579[/C][C]0.0132604820168653[/C][C]1671.28956812966[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 24 )[/C][C]22.1616666666667[/C][C]0.0131625973217283[/C][C]1683.68492364976[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 24 )[/C][C]22.1611764705882[/C][C]0.0129909107528829[/C][C]1705.89860034796[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 24 )[/C][C]22.160625[/C][C]0.0127153823214501[/C][C]1742.82018737386[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 24 )[/C][C]22.16[/C][C]0.0125028732329997[/C][C]1772.3926002474[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 24 )[/C][C]22.1596428571429[/C][C]0.0122742271263615[/C][C]1805.37989308918[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 24 )[/C][C]22.1596153846154[/C][C]0.0120189692279236[/C][C]1843.72011978632[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 24 )[/C][C]22.1591666666667[/C][C]0.0119920968338914[/C][C]1847.81418742731[/C][/ROW]
[ROW][C]Median[/C][C]22.14[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]21.985[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]22.1714634146341[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]22.1714634146341[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]22.1714634146341[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]22.1714634146341[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]22.1714634146341[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]22.1714634146341[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]22.1714634146341[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]22.1714634146341[/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=240757&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=240757&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 Mean22.12569444444440.0265024479845553834.85474463863
Geometric Mean22.1245594301099
Harmonic Mean22.1234162762823
Quadratic Mean22.1268213625706
Winsorized Mean ( 1 / 24 )22.12569444444440.0265024479845553834.85474463863
Winsorized Mean ( 2 / 24 )22.12569444444440.0263722200463977838.977318008033
Winsorized Mean ( 3 / 24 )22.12736111111110.025872107094151855.259335105083
Winsorized Mean ( 4 / 24 )22.131250.0247814685893716893.056435303103
Winsorized Mean ( 5 / 24 )22.12986111111110.0245598921864075901.056932300325
Winsorized Mean ( 6 / 24 )22.13152777777780.0241155438887649917.728742916246
Winsorized Mean ( 7 / 24 )22.13736111111110.0222264215026883995.993039564809
Winsorized Mean ( 8 / 24 )22.15847222222220.01771653397216241250.72275745579
Winsorized Mean ( 9 / 24 )22.15472222222220.01662432676248981332.66883758631
Winsorized Mean ( 10 / 24 )22.14916666666670.01576399445339791405.04785967445
Winsorized Mean ( 11 / 24 )22.15069444444440.01549562812402561429.48025515018
Winsorized Mean ( 12 / 24 )22.15069444444440.01549562812402561429.48025515018
Winsorized Mean ( 13 / 24 )22.15069444444440.01492721830083091483.91307730868
Winsorized Mean ( 14 / 24 )22.148750.01465825823311881511.00830997486
Winsorized Mean ( 15 / 24 )22.161250.01266045297926031750.43104984501
Winsorized Mean ( 16 / 24 )22.16347222222220.01234157782145121795.83782097127
Winsorized Mean ( 17 / 24 )22.16583333333330.01201484150022081844.87105659495
Winsorized Mean ( 18 / 24 )22.16583333333330.01201484150022081844.87105659495
Winsorized Mean ( 19 / 24 )22.16583333333330.01201484150022081844.87105659495
Winsorized Mean ( 20 / 24 )22.16583333333330.01124097621053821971.87796844132
Winsorized Mean ( 21 / 24 )22.16291666666670.01082915683306792046.59670261585
Winsorized Mean ( 22 / 24 )22.15986111111110.010409256623642128.86106206517
Winsorized Mean ( 23 / 24 )22.16305555555560.009136503700994342425.76988757127
Winsorized Mean ( 24 / 24 )22.16305555555560.009136503700994342425.76988757127
Trimmed Mean ( 1 / 24 )22.12971428571430.0255530718201149866.029510717931
Trimmed Mean ( 2 / 24 )22.13397058823530.0244097482163233906.767672983773
Trimmed Mean ( 3 / 24 )22.13848484848480.0231063643986296958.111993152754
Trimmed Mean ( 4 / 24 )22.142656250.02176060472575971017.55702697858
Trimmed Mean ( 5 / 24 )22.14596774193550.02055992991238251077.14218075217
Trimmed Mean ( 6 / 24 )22.14983333333330.01914189015141241157.13929805929
Trimmed Mean ( 7 / 24 )22.15362068965520.0175041232302051265.62298484206
Trimmed Mean ( 8 / 24 )22.15660714285710.01605242382821571380.26552126738
Trimmed Mean ( 9 / 24 )22.15629629629630.01555247715038891424.61526109635
Trimmed Mean ( 10 / 24 )22.15653846153850.01519328614372131458.31114164165
Trimmed Mean ( 11 / 24 )22.15760.01492719747607691484.3777631743
Trimmed Mean ( 12 / 24 )22.15854166666670.01464106480636921513.4515118755
Trimmed Mean ( 13 / 24 )22.15956521739130.01426443339468531553.48373147773
Trimmed Mean ( 14 / 24 )22.16068181818180.01389859730732861594.45455740319
Trimmed Mean ( 15 / 24 )22.16214285714290.0134671093044531645.64958641976
Trimmed Mean ( 16 / 24 )22.162250.01336128880241491658.6910385467
Trimmed Mean ( 17 / 24 )22.16210526315790.01326048201686531671.28956812966
Trimmed Mean ( 18 / 24 )22.16166666666670.01316259732172831683.68492364976
Trimmed Mean ( 19 / 24 )22.16117647058820.01299091075288291705.89860034796
Trimmed Mean ( 20 / 24 )22.1606250.01271538232145011742.82018737386
Trimmed Mean ( 21 / 24 )22.160.01250287323299971772.3926002474
Trimmed Mean ( 22 / 24 )22.15964285714290.01227422712636151805.37989308918
Trimmed Mean ( 23 / 24 )22.15961538461540.01201896922792361843.72011978632
Trimmed Mean ( 24 / 24 )22.15916666666670.01199209683389141847.81418742731
Median22.14
Midrange21.985
Midmean - Weighted Average at Xnp22.1714634146341
Midmean - Weighted Average at X(n+1)p22.1714634146341
Midmean - Empirical Distribution Function22.1714634146341
Midmean - Empirical Distribution Function - Averaging22.1714634146341
Midmean - Empirical Distribution Function - Interpolation22.1714634146341
Midmean - Closest Observation22.1714634146341
Midmean - True Basic - Statistics Graphics Toolkit22.1714634146341
Midmean - MS Excel (old versions)22.1714634146341
Number of observations72



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')