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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, 22 Oct 2007 10:37:07 -0700
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2007/Oct/22/4hpa1apjpeb3a3n1193074368.htm/, Retrieved Mon, 06 May 2024 09:42:45 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=1349, Retrieved Mon, 06 May 2024 09:42:45 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsWerkloosheid, mannen, central tendency
Estimated Impact196
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [Central Tendency ...] [2007-10-22 17:37:07] [9fe578921d87f9af8e79a90d6142ba02] [Current]
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Dataseries X:
8,1
8,2
8
8,1
8,3
8,2
8,1
7,7
7,6
7,7
8,2
8,4
8,4
8,6
8,4
8,5
8,7
8,7
8,6
7,4
7,3
7,4
9
9,2
9,2
8,5
8,3
8,3
8,6
8,6
8,5
8,1
8,1
8
8,6
8,7
8,7
8,6
8,4
8,4
8,7
8,7
8,5
8,3
8,3
8,3
8,1
8,2
8,1
8,1
7,9
7,7
8,1
8
7,7
7,8
7,6
7,4
7,7
7,9
7,6




Summary of compuational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135

\begin{tabular}{lllllllll}
\hline
Summary of compuational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 1 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=1349&T=0

[TABLE]
[ROW][C]Summary of compuational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=1349&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=1349&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 compuational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean8.214754098360660.0556057583198594147.732075716101
Geometric Mean8.20339678918807
Harmonic Mean8.19197171169507
Quadratic Mean8.22603822736272
Winsorized Mean ( 1 / 20 )8.216393442622950.0551788115600996148.904864209948
Winsorized Mean ( 2 / 20 )8.209836065573770.0533933193070748153.761484996980
Winsorized Mean ( 3 / 20 )8.195081967213110.0503227957073566162.850291841299
Winsorized Mean ( 4 / 20 )8.208196721311480.0471768607011232173.987768565449
Winsorized Mean ( 5 / 20 )8.208196721311480.0471768607011232173.987768565449
Winsorized Mean ( 6 / 20 )8.208196721311480.0471768607011232173.987768565449
Winsorized Mean ( 7 / 20 )8.219672131147540.0448323941314557183.342252636479
Winsorized Mean ( 8 / 20 )8.219672131147540.0448323941314557183.342252636479
Winsorized Mean ( 9 / 20 )8.204918032786890.0423636500997207193.678259863660
Winsorized Mean ( 10 / 20 )8.204918032786890.0423636500997207193.678259863660
Winsorized Mean ( 11 / 20 )8.204918032786890.0423636500997207193.678259863660
Winsorized Mean ( 12 / 20 )8.224590163934430.0385995085974071213.074996620214
Winsorized Mean ( 13 / 20 )8.245901639344260.0348747775903599236.443131944836
Winsorized Mean ( 14 / 20 )8.245901639344260.0348747775903599236.443131944836
Winsorized Mean ( 15 / 20 )8.245901639344260.0269155500276057306.361996351066
Winsorized Mean ( 16 / 20 )8.245901639344260.0269155500276057306.361996351066
Winsorized Mean ( 17 / 20 )8.245901639344260.0269155500276057306.361996351066
Winsorized Mean ( 18 / 20 )8.275409836065570.0227430092189421363.866089856446
Winsorized Mean ( 19 / 20 )8.244262295081970.0178831346141570461.007674155486
Winsorized Mean ( 20 / 20 )8.244262295081970.0178831346141570461.007674155486
Trimmed Mean ( 1 / 20 )8.21355932203390.0527145986763614155.811853419593
Trimmed Mean ( 2 / 20 )8.210526315789470.0496658136791345165.315449553158
Trimmed Mean ( 3 / 20 )8.21090909090910.0471170708498832174.266119323703
Trimmed Mean ( 4 / 20 )8.216981132075470.045456549458297180.765615296294
Trimmed Mean ( 5 / 20 )8.219607843137250.044635307210213184.150358917134
Trimmed Mean ( 6 / 20 )8.222448979591840.0435719463398636188.709701316904
Trimmed Mean ( 7 / 20 )8.225531914893620.0421955367542965194.938435379805
Trimmed Mean ( 8 / 20 )8.226666666666670.0411206650105405200.061615359526
Trimmed Mean ( 9 / 20 )8.227906976744190.0397006491595738207.248676052442
Trimmed Mean ( 10 / 20 )8.231707317073170.0384832913363208213.903411876417
Trimmed Mean ( 11 / 20 )8.235897435897440.0368252941234198223.647838583308
Trimmed Mean ( 12 / 20 )8.240540540540540.0345410621850105238.572296833322
Trimmed Mean ( 13 / 20 )8.242857142857140.0326132710745192252.745488915317
Trimmed Mean ( 14 / 20 )8.242424242424240.0310883098919443265.129377282747
Trimmed Mean ( 15 / 20 )8.241935483870970.0288765237640631285.419933202905
Trimmed Mean ( 16 / 20 )8.241379310344830.028300481892584291.209857896605
Trimmed Mean ( 17 / 20 )8.240740740740740.0273519111658280301.285737979300
Trimmed Mean ( 18 / 20 )8.240.0258198889747162319.13382772749
Trimmed Mean ( 19 / 20 )8.234782608695650.0248383673412886331.534778254409
Trimmed Mean ( 20 / 20 )8.233333333333330.0251976315339486326.750286916476
Median8.2
Midrange8.25
Midmean - Weighted Average at Xnp8.24193548387097
Midmean - Weighted Average at X(n+1)p8.24193548387097
Midmean - Empirical Distribution Function8.24193548387097
Midmean - Empirical Distribution Function - Averaging8.24193548387097
Midmean - Empirical Distribution Function - Interpolation8.24193548387097
Midmean - Closest Observation8.22121212121212
Midmean - True Basic - Statistics Graphics Toolkit8.24193548387097
Midmean - MS Excel (old versions)8.24193548387097
Number of observations61

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 8.21475409836066 & 0.0556057583198594 & 147.732075716101 \tabularnewline
Geometric Mean & 8.20339678918807 &  &  \tabularnewline
Harmonic Mean & 8.19197171169507 &  &  \tabularnewline
Quadratic Mean & 8.22603822736272 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 8.21639344262295 & 0.0551788115600996 & 148.904864209948 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 8.20983606557377 & 0.0533933193070748 & 153.761484996980 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 8.19508196721311 & 0.0503227957073566 & 162.850291841299 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 8.20819672131148 & 0.0471768607011232 & 173.987768565449 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 8.20819672131148 & 0.0471768607011232 & 173.987768565449 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 8.20819672131148 & 0.0471768607011232 & 173.987768565449 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 8.21967213114754 & 0.0448323941314557 & 183.342252636479 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 8.21967213114754 & 0.0448323941314557 & 183.342252636479 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 8.20491803278689 & 0.0423636500997207 & 193.678259863660 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 8.20491803278689 & 0.0423636500997207 & 193.678259863660 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 8.20491803278689 & 0.0423636500997207 & 193.678259863660 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 8.22459016393443 & 0.0385995085974071 & 213.074996620214 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 8.24590163934426 & 0.0348747775903599 & 236.443131944836 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 8.24590163934426 & 0.0348747775903599 & 236.443131944836 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 8.24590163934426 & 0.0269155500276057 & 306.361996351066 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 8.24590163934426 & 0.0269155500276057 & 306.361996351066 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 8.24590163934426 & 0.0269155500276057 & 306.361996351066 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 8.27540983606557 & 0.0227430092189421 & 363.866089856446 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 8.24426229508197 & 0.0178831346141570 & 461.007674155486 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 8.24426229508197 & 0.0178831346141570 & 461.007674155486 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 8.2135593220339 & 0.0527145986763614 & 155.811853419593 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 8.21052631578947 & 0.0496658136791345 & 165.315449553158 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 8.2109090909091 & 0.0471170708498832 & 174.266119323703 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 8.21698113207547 & 0.045456549458297 & 180.765615296294 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 8.21960784313725 & 0.044635307210213 & 184.150358917134 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 8.22244897959184 & 0.0435719463398636 & 188.709701316904 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 8.22553191489362 & 0.0421955367542965 & 194.938435379805 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 8.22666666666667 & 0.0411206650105405 & 200.061615359526 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 8.22790697674419 & 0.0397006491595738 & 207.248676052442 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 8.23170731707317 & 0.0384832913363208 & 213.903411876417 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 8.23589743589744 & 0.0368252941234198 & 223.647838583308 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 8.24054054054054 & 0.0345410621850105 & 238.572296833322 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 8.24285714285714 & 0.0326132710745192 & 252.745488915317 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 8.24242424242424 & 0.0310883098919443 & 265.129377282747 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 8.24193548387097 & 0.0288765237640631 & 285.419933202905 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 8.24137931034483 & 0.028300481892584 & 291.209857896605 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 8.24074074074074 & 0.0273519111658280 & 301.285737979300 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 8.24 & 0.0258198889747162 & 319.13382772749 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 8.23478260869565 & 0.0248383673412886 & 331.534778254409 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 8.23333333333333 & 0.0251976315339486 & 326.750286916476 \tabularnewline
Median & 8.2 &  &  \tabularnewline
Midrange & 8.25 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 8.24193548387097 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 8.24193548387097 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 8.24193548387097 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 8.24193548387097 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 8.24193548387097 &  &  \tabularnewline
Midmean - Closest Observation & 8.22121212121212 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 8.24193548387097 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 8.24193548387097 &  &  \tabularnewline
Number of observations & 61 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=1349&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]8.21475409836066[/C][C]0.0556057583198594[/C][C]147.732075716101[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]8.20339678918807[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]8.19197171169507[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]8.22603822736272[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]8.21639344262295[/C][C]0.0551788115600996[/C][C]148.904864209948[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]8.20983606557377[/C][C]0.0533933193070748[/C][C]153.761484996980[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]8.19508196721311[/C][C]0.0503227957073566[/C][C]162.850291841299[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]8.20819672131148[/C][C]0.0471768607011232[/C][C]173.987768565449[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]8.20819672131148[/C][C]0.0471768607011232[/C][C]173.987768565449[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]8.20819672131148[/C][C]0.0471768607011232[/C][C]173.987768565449[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]8.21967213114754[/C][C]0.0448323941314557[/C][C]183.342252636479[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]8.21967213114754[/C][C]0.0448323941314557[/C][C]183.342252636479[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]8.20491803278689[/C][C]0.0423636500997207[/C][C]193.678259863660[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]8.20491803278689[/C][C]0.0423636500997207[/C][C]193.678259863660[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]8.20491803278689[/C][C]0.0423636500997207[/C][C]193.678259863660[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]8.22459016393443[/C][C]0.0385995085974071[/C][C]213.074996620214[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]8.24590163934426[/C][C]0.0348747775903599[/C][C]236.443131944836[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]8.24590163934426[/C][C]0.0348747775903599[/C][C]236.443131944836[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]8.24590163934426[/C][C]0.0269155500276057[/C][C]306.361996351066[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]8.24590163934426[/C][C]0.0269155500276057[/C][C]306.361996351066[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]8.24590163934426[/C][C]0.0269155500276057[/C][C]306.361996351066[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]8.27540983606557[/C][C]0.0227430092189421[/C][C]363.866089856446[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]8.24426229508197[/C][C]0.0178831346141570[/C][C]461.007674155486[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]8.24426229508197[/C][C]0.0178831346141570[/C][C]461.007674155486[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]8.2135593220339[/C][C]0.0527145986763614[/C][C]155.811853419593[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]8.21052631578947[/C][C]0.0496658136791345[/C][C]165.315449553158[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]8.2109090909091[/C][C]0.0471170708498832[/C][C]174.266119323703[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]8.21698113207547[/C][C]0.045456549458297[/C][C]180.765615296294[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]8.21960784313725[/C][C]0.044635307210213[/C][C]184.150358917134[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]8.22244897959184[/C][C]0.0435719463398636[/C][C]188.709701316904[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]8.22553191489362[/C][C]0.0421955367542965[/C][C]194.938435379805[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]8.22666666666667[/C][C]0.0411206650105405[/C][C]200.061615359526[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]8.22790697674419[/C][C]0.0397006491595738[/C][C]207.248676052442[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]8.23170731707317[/C][C]0.0384832913363208[/C][C]213.903411876417[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]8.23589743589744[/C][C]0.0368252941234198[/C][C]223.647838583308[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]8.24054054054054[/C][C]0.0345410621850105[/C][C]238.572296833322[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]8.24285714285714[/C][C]0.0326132710745192[/C][C]252.745488915317[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]8.24242424242424[/C][C]0.0310883098919443[/C][C]265.129377282747[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]8.24193548387097[/C][C]0.0288765237640631[/C][C]285.419933202905[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]8.24137931034483[/C][C]0.028300481892584[/C][C]291.209857896605[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]8.24074074074074[/C][C]0.0273519111658280[/C][C]301.285737979300[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]8.24[/C][C]0.0258198889747162[/C][C]319.13382772749[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]8.23478260869565[/C][C]0.0248383673412886[/C][C]331.534778254409[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]8.23333333333333[/C][C]0.0251976315339486[/C][C]326.750286916476[/C][/ROW]
[ROW][C]Median[/C][C]8.2[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]8.25[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]8.24193548387097[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]8.24193548387097[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]8.24193548387097[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]8.24193548387097[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]8.24193548387097[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]8.22121212121212[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]8.24193548387097[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]8.24193548387097[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]61[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=1349&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=1349&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 Mean8.214754098360660.0556057583198594147.732075716101
Geometric Mean8.20339678918807
Harmonic Mean8.19197171169507
Quadratic Mean8.22603822736272
Winsorized Mean ( 1 / 20 )8.216393442622950.0551788115600996148.904864209948
Winsorized Mean ( 2 / 20 )8.209836065573770.0533933193070748153.761484996980
Winsorized Mean ( 3 / 20 )8.195081967213110.0503227957073566162.850291841299
Winsorized Mean ( 4 / 20 )8.208196721311480.0471768607011232173.987768565449
Winsorized Mean ( 5 / 20 )8.208196721311480.0471768607011232173.987768565449
Winsorized Mean ( 6 / 20 )8.208196721311480.0471768607011232173.987768565449
Winsorized Mean ( 7 / 20 )8.219672131147540.0448323941314557183.342252636479
Winsorized Mean ( 8 / 20 )8.219672131147540.0448323941314557183.342252636479
Winsorized Mean ( 9 / 20 )8.204918032786890.0423636500997207193.678259863660
Winsorized Mean ( 10 / 20 )8.204918032786890.0423636500997207193.678259863660
Winsorized Mean ( 11 / 20 )8.204918032786890.0423636500997207193.678259863660
Winsorized Mean ( 12 / 20 )8.224590163934430.0385995085974071213.074996620214
Winsorized Mean ( 13 / 20 )8.245901639344260.0348747775903599236.443131944836
Winsorized Mean ( 14 / 20 )8.245901639344260.0348747775903599236.443131944836
Winsorized Mean ( 15 / 20 )8.245901639344260.0269155500276057306.361996351066
Winsorized Mean ( 16 / 20 )8.245901639344260.0269155500276057306.361996351066
Winsorized Mean ( 17 / 20 )8.245901639344260.0269155500276057306.361996351066
Winsorized Mean ( 18 / 20 )8.275409836065570.0227430092189421363.866089856446
Winsorized Mean ( 19 / 20 )8.244262295081970.0178831346141570461.007674155486
Winsorized Mean ( 20 / 20 )8.244262295081970.0178831346141570461.007674155486
Trimmed Mean ( 1 / 20 )8.21355932203390.0527145986763614155.811853419593
Trimmed Mean ( 2 / 20 )8.210526315789470.0496658136791345165.315449553158
Trimmed Mean ( 3 / 20 )8.21090909090910.0471170708498832174.266119323703
Trimmed Mean ( 4 / 20 )8.216981132075470.045456549458297180.765615296294
Trimmed Mean ( 5 / 20 )8.219607843137250.044635307210213184.150358917134
Trimmed Mean ( 6 / 20 )8.222448979591840.0435719463398636188.709701316904
Trimmed Mean ( 7 / 20 )8.225531914893620.0421955367542965194.938435379805
Trimmed Mean ( 8 / 20 )8.226666666666670.0411206650105405200.061615359526
Trimmed Mean ( 9 / 20 )8.227906976744190.0397006491595738207.248676052442
Trimmed Mean ( 10 / 20 )8.231707317073170.0384832913363208213.903411876417
Trimmed Mean ( 11 / 20 )8.235897435897440.0368252941234198223.647838583308
Trimmed Mean ( 12 / 20 )8.240540540540540.0345410621850105238.572296833322
Trimmed Mean ( 13 / 20 )8.242857142857140.0326132710745192252.745488915317
Trimmed Mean ( 14 / 20 )8.242424242424240.0310883098919443265.129377282747
Trimmed Mean ( 15 / 20 )8.241935483870970.0288765237640631285.419933202905
Trimmed Mean ( 16 / 20 )8.241379310344830.028300481892584291.209857896605
Trimmed Mean ( 17 / 20 )8.240740740740740.0273519111658280301.285737979300
Trimmed Mean ( 18 / 20 )8.240.0258198889747162319.13382772749
Trimmed Mean ( 19 / 20 )8.234782608695650.0248383673412886331.534778254409
Trimmed Mean ( 20 / 20 )8.233333333333330.0251976315339486326.750286916476
Median8.2
Midrange8.25
Midmean - Weighted Average at Xnp8.24193548387097
Midmean - Weighted Average at X(n+1)p8.24193548387097
Midmean - Empirical Distribution Function8.24193548387097
Midmean - Empirical Distribution Function - Averaging8.24193548387097
Midmean - Empirical Distribution Function - Interpolation8.24193548387097
Midmean - Closest Observation8.22121212121212
Midmean - True Basic - Statistics Graphics Toolkit8.24193548387097
Midmean - MS Excel (old versions)8.24193548387097
Number of observations61



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')