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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 computationThu, 16 Dec 2010 18:37:14 +0000
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2010/Dec/16/t1292524542he676deaxizuopb.htm/, Retrieved Fri, 03 May 2024 13:13:08 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=111164, Retrieved Fri, 03 May 2024 13:13:08 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsKDGP1W52
Estimated Impact135
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [WERKLOOSHEID] [2010-12-16 18:37:14] [d08a5fa9e4c562ec79e796d78c067f4f] [Current]
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Dataseries X:
8,6
8,5
8,4
8,0
7,9
8,1
8,6
8,8
8,8
8,6
8,3
8,3
8,3
8,4
8,4
8,5
8,6
8,6
8,6
8,6
8,6
8,5
8,4
8,4
8,4
8,5
8,5
8,6
8,6
8,4
8,2
8,0
8,0
8,0
8,0
7,9
7,9
7,8
7,9
8,0
7,9
7,4
7,2
7,0
7,0
7,1
7,2
7,2
7,0
6,9
6,8
6,8
6,8
6,9
7,2
7,3
7,2
7,1
7,1
7,3
7,5
7,6
7,7
7,7
7,7
7,8
8,0
8,1
8,1
8,0
8,1
8,2
8,3
8,4
8,6
8,6
8,7
8,8
8,9




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'RServer@AstonUniversity' @ vre.aston.ac.uk

\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 & 'RServer@AstonUniversity' @ vre.aston.ac.uk \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=111164&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]'RServer@AstonUniversity' @ vre.aston.ac.uk[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=111164&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=111164&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'RServer@AstonUniversity' @ vre.aston.ac.uk







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean7.983544303797470.0674675292991142118.331653563343
Geometric Mean7.96061275560207
Harmonic Mean7.9370116755202
Quadratic Mean8.00574951621993
Winsorized Mean ( 1 / 26 )7.982278481012660.0672586382524538118.680346322971
Winsorized Mean ( 2 / 26 )7.982278481012660.0672586382524538118.680346322971
Winsorized Mean ( 3 / 26 )7.986075949367090.066432585895239120.213233336435
Winsorized Mean ( 4 / 26 )7.981012658227850.0656793809008427121.51473641746
Winsorized Mean ( 5 / 26 )7.981012658227850.0635444460391176125.597328416629
Winsorized Mean ( 6 / 26 )7.981012658227850.0635444460391176125.597328416629
Winsorized Mean ( 7 / 26 )7.981012658227850.0635444460391176125.597328416629
Winsorized Mean ( 8 / 26 )7.991139240506330.061602263976491129.721518734376
Winsorized Mean ( 9 / 26 )7.991139240506330.061602263976491129.721518734376
Winsorized Mean ( 10 / 26 )7.991139240506330.061602263976491129.721518734376
Winsorized Mean ( 11 / 26 )8.005063291139240.0590935184929068135.464319866148
Winsorized Mean ( 12 / 26 )8.005063291139240.0590935184929068135.464319866148
Winsorized Mean ( 13 / 26 )8.005063291139240.0590935184929068135.464319866148
Winsorized Mean ( 14 / 26 )8.005063291139240.0590935184929068135.464319866148
Winsorized Mean ( 15 / 26 )8.005063291139240.0590935184929068135.464319866148
Winsorized Mean ( 16 / 26 )8.02531645569620.055629773609826144.262971695407
Winsorized Mean ( 17 / 26 )8.003797468354430.0529077583392566151.278332698056
Winsorized Mean ( 18 / 26 )8.026582278481010.0490979606456667163.480970959421
Winsorized Mean ( 19 / 26 )8.05063291139240.0452506961692569177.911802313043
Winsorized Mean ( 20 / 26 )8.075949367088610.0414056487730773195.044628121846
Winsorized Mean ( 21 / 26 )8.102531645569620.0376170545075299215.395164550901
Winsorized Mean ( 22 / 26 )8.07468354430380.0340145430850766237.389152166694
Winsorized Mean ( 23 / 26 )8.07468354430380.0340145430850766237.389152166694
Winsorized Mean ( 24 / 26 )8.105063291139240.0298703644075263271.341292679276
Winsorized Mean ( 25 / 26 )8.105063291139240.0298703644075263271.341292679276
Winsorized Mean ( 26 / 26 )8.13797468354430.0257508975127966316.026836715117
Trimmed Mean ( 1 / 26 )7.987012987012990.0664074358568644120.272871312609
Trimmed Mean ( 2 / 26 )7.9920.065395814947232122.209655257737
Trimmed Mean ( 3 / 26 )7.99726027397260.0641942389536564124.57909626043
Trimmed Mean ( 4 / 26 )8.001408450704230.0631338827723226126.737151262491
Trimmed Mean ( 5 / 26 )8.00724637681160.0621207621514747128.898070459709
Trimmed Mean ( 6 / 26 )8.01343283582090.0615235307191372130.249885566601
Trimmed Mean ( 7 / 26 )8.020.0607722735362865131.968075790539
Trimmed Mean ( 8 / 26 )8.026984126984130.0598344853620166134.153140591391
Trimmed Mean ( 9 / 26 )8.03278688524590.059124824494034135.8614922579
Trimmed Mean ( 10 / 26 )8.038983050847460.0582231016727546138.072050782023
Trimmed Mean ( 11 / 26 )8.045614035087720.0570840175455361140.943374013045
Trimmed Mean ( 12 / 26 )8.050909090909090.0561906762981782143.278380352402
Trimmed Mean ( 13 / 26 )8.05660377358490.0550438164271605146.367099822125
Trimmed Mean ( 14 / 26 )8.062745098039220.0535750003386292150.494541242695
Trimmed Mean ( 15 / 26 )8.069387755102040.0516894903751589156.112735810219
Trimmed Mean ( 16 / 26 )8.076595744680850.0492508884067795163.988833622118
Trimmed Mean ( 17 / 26 )8.082222222222220.0469567702424788172.120488280745
Trimmed Mean ( 18 / 26 )8.09069767441860.0444996738062593181.814763623741
Trimmed Mean ( 19 / 26 )8.097560975609760.0422662589408414191.584521046531
Trimmed Mean ( 20 / 26 )8.10256410256410.0403237872767403200.937576794475
Trimmed Mean ( 21 / 26 )8.10256410256410.0387387387387388209.159212880143
Trimmed Mean ( 22 / 26 )8.105714285714280.0375606752033119215.803210188286
Trimmed Mean ( 23 / 26 )8.109090909090910.0367638956319725220.572133874699
Trimmed Mean ( 24 / 26 )8.112903225806450.035542473602166228.259386688045
Trimmed Mean ( 25 / 26 )8.113793103448280.0349961778106628231.847979152058
Trimmed Mean ( 26 / 26 )8.114814814814820.0340536294419288238.295152317109
Median8.1
Midrange7.85
Midmean - Weighted Average at Xnp8.11627906976744
Midmean - Weighted Average at X(n+1)p8.11627906976744
Midmean - Empirical Distribution Function8.11627906976744
Midmean - Empirical Distribution Function - Averaging8.11627906976744
Midmean - Empirical Distribution Function - Interpolation8.13095238095238
Midmean - Closest Observation8.11627906976744
Midmean - True Basic - Statistics Graphics Toolkit8.11627906976744
Midmean - MS Excel (old versions)8.11627906976744
Number of observations79

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 7.98354430379747 & 0.0674675292991142 & 118.331653563343 \tabularnewline
Geometric Mean & 7.96061275560207 &  &  \tabularnewline
Harmonic Mean & 7.9370116755202 &  &  \tabularnewline
Quadratic Mean & 8.00574951621993 &  &  \tabularnewline
Winsorized Mean ( 1 / 26 ) & 7.98227848101266 & 0.0672586382524538 & 118.680346322971 \tabularnewline
Winsorized Mean ( 2 / 26 ) & 7.98227848101266 & 0.0672586382524538 & 118.680346322971 \tabularnewline
Winsorized Mean ( 3 / 26 ) & 7.98607594936709 & 0.066432585895239 & 120.213233336435 \tabularnewline
Winsorized Mean ( 4 / 26 ) & 7.98101265822785 & 0.0656793809008427 & 121.51473641746 \tabularnewline
Winsorized Mean ( 5 / 26 ) & 7.98101265822785 & 0.0635444460391176 & 125.597328416629 \tabularnewline
Winsorized Mean ( 6 / 26 ) & 7.98101265822785 & 0.0635444460391176 & 125.597328416629 \tabularnewline
Winsorized Mean ( 7 / 26 ) & 7.98101265822785 & 0.0635444460391176 & 125.597328416629 \tabularnewline
Winsorized Mean ( 8 / 26 ) & 7.99113924050633 & 0.061602263976491 & 129.721518734376 \tabularnewline
Winsorized Mean ( 9 / 26 ) & 7.99113924050633 & 0.061602263976491 & 129.721518734376 \tabularnewline
Winsorized Mean ( 10 / 26 ) & 7.99113924050633 & 0.061602263976491 & 129.721518734376 \tabularnewline
Winsorized Mean ( 11 / 26 ) & 8.00506329113924 & 0.0590935184929068 & 135.464319866148 \tabularnewline
Winsorized Mean ( 12 / 26 ) & 8.00506329113924 & 0.0590935184929068 & 135.464319866148 \tabularnewline
Winsorized Mean ( 13 / 26 ) & 8.00506329113924 & 0.0590935184929068 & 135.464319866148 \tabularnewline
Winsorized Mean ( 14 / 26 ) & 8.00506329113924 & 0.0590935184929068 & 135.464319866148 \tabularnewline
Winsorized Mean ( 15 / 26 ) & 8.00506329113924 & 0.0590935184929068 & 135.464319866148 \tabularnewline
Winsorized Mean ( 16 / 26 ) & 8.0253164556962 & 0.055629773609826 & 144.262971695407 \tabularnewline
Winsorized Mean ( 17 / 26 ) & 8.00379746835443 & 0.0529077583392566 & 151.278332698056 \tabularnewline
Winsorized Mean ( 18 / 26 ) & 8.02658227848101 & 0.0490979606456667 & 163.480970959421 \tabularnewline
Winsorized Mean ( 19 / 26 ) & 8.0506329113924 & 0.0452506961692569 & 177.911802313043 \tabularnewline
Winsorized Mean ( 20 / 26 ) & 8.07594936708861 & 0.0414056487730773 & 195.044628121846 \tabularnewline
Winsorized Mean ( 21 / 26 ) & 8.10253164556962 & 0.0376170545075299 & 215.395164550901 \tabularnewline
Winsorized Mean ( 22 / 26 ) & 8.0746835443038 & 0.0340145430850766 & 237.389152166694 \tabularnewline
Winsorized Mean ( 23 / 26 ) & 8.0746835443038 & 0.0340145430850766 & 237.389152166694 \tabularnewline
Winsorized Mean ( 24 / 26 ) & 8.10506329113924 & 0.0298703644075263 & 271.341292679276 \tabularnewline
Winsorized Mean ( 25 / 26 ) & 8.10506329113924 & 0.0298703644075263 & 271.341292679276 \tabularnewline
Winsorized Mean ( 26 / 26 ) & 8.1379746835443 & 0.0257508975127966 & 316.026836715117 \tabularnewline
Trimmed Mean ( 1 / 26 ) & 7.98701298701299 & 0.0664074358568644 & 120.272871312609 \tabularnewline
Trimmed Mean ( 2 / 26 ) & 7.992 & 0.065395814947232 & 122.209655257737 \tabularnewline
Trimmed Mean ( 3 / 26 ) & 7.9972602739726 & 0.0641942389536564 & 124.57909626043 \tabularnewline
Trimmed Mean ( 4 / 26 ) & 8.00140845070423 & 0.0631338827723226 & 126.737151262491 \tabularnewline
Trimmed Mean ( 5 / 26 ) & 8.0072463768116 & 0.0621207621514747 & 128.898070459709 \tabularnewline
Trimmed Mean ( 6 / 26 ) & 8.0134328358209 & 0.0615235307191372 & 130.249885566601 \tabularnewline
Trimmed Mean ( 7 / 26 ) & 8.02 & 0.0607722735362865 & 131.968075790539 \tabularnewline
Trimmed Mean ( 8 / 26 ) & 8.02698412698413 & 0.0598344853620166 & 134.153140591391 \tabularnewline
Trimmed Mean ( 9 / 26 ) & 8.0327868852459 & 0.059124824494034 & 135.8614922579 \tabularnewline
Trimmed Mean ( 10 / 26 ) & 8.03898305084746 & 0.0582231016727546 & 138.072050782023 \tabularnewline
Trimmed Mean ( 11 / 26 ) & 8.04561403508772 & 0.0570840175455361 & 140.943374013045 \tabularnewline
Trimmed Mean ( 12 / 26 ) & 8.05090909090909 & 0.0561906762981782 & 143.278380352402 \tabularnewline
Trimmed Mean ( 13 / 26 ) & 8.0566037735849 & 0.0550438164271605 & 146.367099822125 \tabularnewline
Trimmed Mean ( 14 / 26 ) & 8.06274509803922 & 0.0535750003386292 & 150.494541242695 \tabularnewline
Trimmed Mean ( 15 / 26 ) & 8.06938775510204 & 0.0516894903751589 & 156.112735810219 \tabularnewline
Trimmed Mean ( 16 / 26 ) & 8.07659574468085 & 0.0492508884067795 & 163.988833622118 \tabularnewline
Trimmed Mean ( 17 / 26 ) & 8.08222222222222 & 0.0469567702424788 & 172.120488280745 \tabularnewline
Trimmed Mean ( 18 / 26 ) & 8.0906976744186 & 0.0444996738062593 & 181.814763623741 \tabularnewline
Trimmed Mean ( 19 / 26 ) & 8.09756097560976 & 0.0422662589408414 & 191.584521046531 \tabularnewline
Trimmed Mean ( 20 / 26 ) & 8.1025641025641 & 0.0403237872767403 & 200.937576794475 \tabularnewline
Trimmed Mean ( 21 / 26 ) & 8.1025641025641 & 0.0387387387387388 & 209.159212880143 \tabularnewline
Trimmed Mean ( 22 / 26 ) & 8.10571428571428 & 0.0375606752033119 & 215.803210188286 \tabularnewline
Trimmed Mean ( 23 / 26 ) & 8.10909090909091 & 0.0367638956319725 & 220.572133874699 \tabularnewline
Trimmed Mean ( 24 / 26 ) & 8.11290322580645 & 0.035542473602166 & 228.259386688045 \tabularnewline
Trimmed Mean ( 25 / 26 ) & 8.11379310344828 & 0.0349961778106628 & 231.847979152058 \tabularnewline
Trimmed Mean ( 26 / 26 ) & 8.11481481481482 & 0.0340536294419288 & 238.295152317109 \tabularnewline
Median & 8.1 &  &  \tabularnewline
Midrange & 7.85 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 8.11627906976744 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 8.11627906976744 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 8.11627906976744 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 8.11627906976744 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 8.13095238095238 &  &  \tabularnewline
Midmean - Closest Observation & 8.11627906976744 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 8.11627906976744 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 8.11627906976744 &  &  \tabularnewline
Number of observations & 79 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=111164&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]7.98354430379747[/C][C]0.0674675292991142[/C][C]118.331653563343[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]7.96061275560207[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]7.9370116755202[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]8.00574951621993[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 26 )[/C][C]7.98227848101266[/C][C]0.0672586382524538[/C][C]118.680346322971[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 26 )[/C][C]7.98227848101266[/C][C]0.0672586382524538[/C][C]118.680346322971[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 26 )[/C][C]7.98607594936709[/C][C]0.066432585895239[/C][C]120.213233336435[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 26 )[/C][C]7.98101265822785[/C][C]0.0656793809008427[/C][C]121.51473641746[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 26 )[/C][C]7.98101265822785[/C][C]0.0635444460391176[/C][C]125.597328416629[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 26 )[/C][C]7.98101265822785[/C][C]0.0635444460391176[/C][C]125.597328416629[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 26 )[/C][C]7.98101265822785[/C][C]0.0635444460391176[/C][C]125.597328416629[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 26 )[/C][C]7.99113924050633[/C][C]0.061602263976491[/C][C]129.721518734376[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 26 )[/C][C]7.99113924050633[/C][C]0.061602263976491[/C][C]129.721518734376[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 26 )[/C][C]7.99113924050633[/C][C]0.061602263976491[/C][C]129.721518734376[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 26 )[/C][C]8.00506329113924[/C][C]0.0590935184929068[/C][C]135.464319866148[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 26 )[/C][C]8.00506329113924[/C][C]0.0590935184929068[/C][C]135.464319866148[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 26 )[/C][C]8.00506329113924[/C][C]0.0590935184929068[/C][C]135.464319866148[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 26 )[/C][C]8.00506329113924[/C][C]0.0590935184929068[/C][C]135.464319866148[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 26 )[/C][C]8.00506329113924[/C][C]0.0590935184929068[/C][C]135.464319866148[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 26 )[/C][C]8.0253164556962[/C][C]0.055629773609826[/C][C]144.262971695407[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 26 )[/C][C]8.00379746835443[/C][C]0.0529077583392566[/C][C]151.278332698056[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 26 )[/C][C]8.02658227848101[/C][C]0.0490979606456667[/C][C]163.480970959421[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 26 )[/C][C]8.0506329113924[/C][C]0.0452506961692569[/C][C]177.911802313043[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 26 )[/C][C]8.07594936708861[/C][C]0.0414056487730773[/C][C]195.044628121846[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 26 )[/C][C]8.10253164556962[/C][C]0.0376170545075299[/C][C]215.395164550901[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 26 )[/C][C]8.0746835443038[/C][C]0.0340145430850766[/C][C]237.389152166694[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 26 )[/C][C]8.0746835443038[/C][C]0.0340145430850766[/C][C]237.389152166694[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 26 )[/C][C]8.10506329113924[/C][C]0.0298703644075263[/C][C]271.341292679276[/C][/ROW]
[ROW][C]Winsorized Mean ( 25 / 26 )[/C][C]8.10506329113924[/C][C]0.0298703644075263[/C][C]271.341292679276[/C][/ROW]
[ROW][C]Winsorized Mean ( 26 / 26 )[/C][C]8.1379746835443[/C][C]0.0257508975127966[/C][C]316.026836715117[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 26 )[/C][C]7.98701298701299[/C][C]0.0664074358568644[/C][C]120.272871312609[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 26 )[/C][C]7.992[/C][C]0.065395814947232[/C][C]122.209655257737[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 26 )[/C][C]7.9972602739726[/C][C]0.0641942389536564[/C][C]124.57909626043[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 26 )[/C][C]8.00140845070423[/C][C]0.0631338827723226[/C][C]126.737151262491[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 26 )[/C][C]8.0072463768116[/C][C]0.0621207621514747[/C][C]128.898070459709[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 26 )[/C][C]8.0134328358209[/C][C]0.0615235307191372[/C][C]130.249885566601[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 26 )[/C][C]8.02[/C][C]0.0607722735362865[/C][C]131.968075790539[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 26 )[/C][C]8.02698412698413[/C][C]0.0598344853620166[/C][C]134.153140591391[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 26 )[/C][C]8.0327868852459[/C][C]0.059124824494034[/C][C]135.8614922579[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 26 )[/C][C]8.03898305084746[/C][C]0.0582231016727546[/C][C]138.072050782023[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 26 )[/C][C]8.04561403508772[/C][C]0.0570840175455361[/C][C]140.943374013045[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 26 )[/C][C]8.05090909090909[/C][C]0.0561906762981782[/C][C]143.278380352402[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 26 )[/C][C]8.0566037735849[/C][C]0.0550438164271605[/C][C]146.367099822125[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 26 )[/C][C]8.06274509803922[/C][C]0.0535750003386292[/C][C]150.494541242695[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 26 )[/C][C]8.06938775510204[/C][C]0.0516894903751589[/C][C]156.112735810219[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 26 )[/C][C]8.07659574468085[/C][C]0.0492508884067795[/C][C]163.988833622118[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 26 )[/C][C]8.08222222222222[/C][C]0.0469567702424788[/C][C]172.120488280745[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 26 )[/C][C]8.0906976744186[/C][C]0.0444996738062593[/C][C]181.814763623741[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 26 )[/C][C]8.09756097560976[/C][C]0.0422662589408414[/C][C]191.584521046531[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 26 )[/C][C]8.1025641025641[/C][C]0.0403237872767403[/C][C]200.937576794475[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 26 )[/C][C]8.1025641025641[/C][C]0.0387387387387388[/C][C]209.159212880143[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 26 )[/C][C]8.10571428571428[/C][C]0.0375606752033119[/C][C]215.803210188286[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 26 )[/C][C]8.10909090909091[/C][C]0.0367638956319725[/C][C]220.572133874699[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 26 )[/C][C]8.11290322580645[/C][C]0.035542473602166[/C][C]228.259386688045[/C][/ROW]
[ROW][C]Trimmed Mean ( 25 / 26 )[/C][C]8.11379310344828[/C][C]0.0349961778106628[/C][C]231.847979152058[/C][/ROW]
[ROW][C]Trimmed Mean ( 26 / 26 )[/C][C]8.11481481481482[/C][C]0.0340536294419288[/C][C]238.295152317109[/C][/ROW]
[ROW][C]Median[/C][C]8.1[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]7.85[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]8.11627906976744[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]8.11627906976744[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]8.11627906976744[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]8.11627906976744[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]8.13095238095238[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]8.11627906976744[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]8.11627906976744[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]8.11627906976744[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]79[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=111164&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=111164&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 Mean7.983544303797470.0674675292991142118.331653563343
Geometric Mean7.96061275560207
Harmonic Mean7.9370116755202
Quadratic Mean8.00574951621993
Winsorized Mean ( 1 / 26 )7.982278481012660.0672586382524538118.680346322971
Winsorized Mean ( 2 / 26 )7.982278481012660.0672586382524538118.680346322971
Winsorized Mean ( 3 / 26 )7.986075949367090.066432585895239120.213233336435
Winsorized Mean ( 4 / 26 )7.981012658227850.0656793809008427121.51473641746
Winsorized Mean ( 5 / 26 )7.981012658227850.0635444460391176125.597328416629
Winsorized Mean ( 6 / 26 )7.981012658227850.0635444460391176125.597328416629
Winsorized Mean ( 7 / 26 )7.981012658227850.0635444460391176125.597328416629
Winsorized Mean ( 8 / 26 )7.991139240506330.061602263976491129.721518734376
Winsorized Mean ( 9 / 26 )7.991139240506330.061602263976491129.721518734376
Winsorized Mean ( 10 / 26 )7.991139240506330.061602263976491129.721518734376
Winsorized Mean ( 11 / 26 )8.005063291139240.0590935184929068135.464319866148
Winsorized Mean ( 12 / 26 )8.005063291139240.0590935184929068135.464319866148
Winsorized Mean ( 13 / 26 )8.005063291139240.0590935184929068135.464319866148
Winsorized Mean ( 14 / 26 )8.005063291139240.0590935184929068135.464319866148
Winsorized Mean ( 15 / 26 )8.005063291139240.0590935184929068135.464319866148
Winsorized Mean ( 16 / 26 )8.02531645569620.055629773609826144.262971695407
Winsorized Mean ( 17 / 26 )8.003797468354430.0529077583392566151.278332698056
Winsorized Mean ( 18 / 26 )8.026582278481010.0490979606456667163.480970959421
Winsorized Mean ( 19 / 26 )8.05063291139240.0452506961692569177.911802313043
Winsorized Mean ( 20 / 26 )8.075949367088610.0414056487730773195.044628121846
Winsorized Mean ( 21 / 26 )8.102531645569620.0376170545075299215.395164550901
Winsorized Mean ( 22 / 26 )8.07468354430380.0340145430850766237.389152166694
Winsorized Mean ( 23 / 26 )8.07468354430380.0340145430850766237.389152166694
Winsorized Mean ( 24 / 26 )8.105063291139240.0298703644075263271.341292679276
Winsorized Mean ( 25 / 26 )8.105063291139240.0298703644075263271.341292679276
Winsorized Mean ( 26 / 26 )8.13797468354430.0257508975127966316.026836715117
Trimmed Mean ( 1 / 26 )7.987012987012990.0664074358568644120.272871312609
Trimmed Mean ( 2 / 26 )7.9920.065395814947232122.209655257737
Trimmed Mean ( 3 / 26 )7.99726027397260.0641942389536564124.57909626043
Trimmed Mean ( 4 / 26 )8.001408450704230.0631338827723226126.737151262491
Trimmed Mean ( 5 / 26 )8.00724637681160.0621207621514747128.898070459709
Trimmed Mean ( 6 / 26 )8.01343283582090.0615235307191372130.249885566601
Trimmed Mean ( 7 / 26 )8.020.0607722735362865131.968075790539
Trimmed Mean ( 8 / 26 )8.026984126984130.0598344853620166134.153140591391
Trimmed Mean ( 9 / 26 )8.03278688524590.059124824494034135.8614922579
Trimmed Mean ( 10 / 26 )8.038983050847460.0582231016727546138.072050782023
Trimmed Mean ( 11 / 26 )8.045614035087720.0570840175455361140.943374013045
Trimmed Mean ( 12 / 26 )8.050909090909090.0561906762981782143.278380352402
Trimmed Mean ( 13 / 26 )8.05660377358490.0550438164271605146.367099822125
Trimmed Mean ( 14 / 26 )8.062745098039220.0535750003386292150.494541242695
Trimmed Mean ( 15 / 26 )8.069387755102040.0516894903751589156.112735810219
Trimmed Mean ( 16 / 26 )8.076595744680850.0492508884067795163.988833622118
Trimmed Mean ( 17 / 26 )8.082222222222220.0469567702424788172.120488280745
Trimmed Mean ( 18 / 26 )8.09069767441860.0444996738062593181.814763623741
Trimmed Mean ( 19 / 26 )8.097560975609760.0422662589408414191.584521046531
Trimmed Mean ( 20 / 26 )8.10256410256410.0403237872767403200.937576794475
Trimmed Mean ( 21 / 26 )8.10256410256410.0387387387387388209.159212880143
Trimmed Mean ( 22 / 26 )8.105714285714280.0375606752033119215.803210188286
Trimmed Mean ( 23 / 26 )8.109090909090910.0367638956319725220.572133874699
Trimmed Mean ( 24 / 26 )8.112903225806450.035542473602166228.259386688045
Trimmed Mean ( 25 / 26 )8.113793103448280.0349961778106628231.847979152058
Trimmed Mean ( 26 / 26 )8.114814814814820.0340536294419288238.295152317109
Median8.1
Midrange7.85
Midmean - Weighted Average at Xnp8.11627906976744
Midmean - Weighted Average at X(n+1)p8.11627906976744
Midmean - Empirical Distribution Function8.11627906976744
Midmean - Empirical Distribution Function - Averaging8.11627906976744
Midmean - Empirical Distribution Function - Interpolation8.13095238095238
Midmean - Closest Observation8.11627906976744
Midmean - True Basic - Statistics Graphics Toolkit8.11627906976744
Midmean - MS Excel (old versions)8.11627906976744
Number of observations79



Parameters (Session):
par1 = PRIJS 2005 ; par2 = studio 100 ; par3 = de maximumprijzen van 2005 van studio 100 ; par4 = 12 ;
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')