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Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationThu, 11 Dec 2008 10:41:16 -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/2008/Dec/11/t1229017323dqhq3kpu3d99xhk.htm/, Retrieved Mon, 27 May 2024 13:08:31 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=32391, Retrieved Mon, 27 May 2024 13:08:31 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact230
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
F     [Univariate Data Series] [Airline data] [2007-10-18 09:58:47] [42daae401fd3def69a25014f2252b4c2]
- R PD  [Univariate Data Series] [Tijdreeks 2 Buite...] [2008-12-11 16:25:30] [2d4aec5ed1856c4828162be37be304d9]
- RMP       [Central Tendency] [Central tendency ...] [2008-12-11 17:41:16] [d7f41258beeebb8716e3f5d39f3cdc01] [Current]
- RMP         [Blocked Bootstrap Plot - Central Tendency] [Blocked Bootstrap...] [2008-12-12 08:14:08] [2d4aec5ed1856c4828162be37be304d9]
- RMP           [Tukey lambda PPCC Plot] [Tukey Lambda PPCC...] [2008-12-12 08:45:26] [2d4aec5ed1856c4828162be37be304d9]
- RMP             [Univariate Explorative Data Analysis] [Lag plot + ACF Ti...] [2008-12-12 08:54:04] [2d4aec5ed1856c4828162be37be304d9]
- RMP               [Variance Reduction Matrix] [VRM tijdreeks 2] [2008-12-12 10:58:24] [2d4aec5ed1856c4828162be37be304d9]
- RMP                 [Spectral Analysis] [Spectrum tijdreeks 2] [2008-12-12 11:59:54] [2d4aec5ed1856c4828162be37be304d9]
- RMP                 [(Partial) Autocorrelation Function] [P(ACF) Tijdreeks ...] [2008-12-12 12:11:12] [2d4aec5ed1856c4828162be37be304d9]
- RMP                 [(Partial) Autocorrelation Function] [P(ACF) Tijdreeks ...] [2008-12-12 12:17:09] [2d4aec5ed1856c4828162be37be304d9]
- RMP                   [ARIMA Backward Selection] [ARIMA Backward Se...] [2008-12-12 12:29:19] [2d4aec5ed1856c4828162be37be304d9]
- RMPD                    [Bivariate Kernel Density Estimation] [Bivariate Kernel ...] [2008-12-22 09:26:11] [2d4aec5ed1856c4828162be37be304d9]
- RMPD                      [Kendall tau Correlation Matrix] [Kendall Tau Corre...] [2008-12-22 09:35:25] [2d4aec5ed1856c4828162be37be304d9]
- RM D                        [Pearson Correlation] [Pearson correlati...] [2008-12-22 09:46:51] [2d4aec5ed1856c4828162be37be304d9]
- RMP                           [Cross Correlation Function] [Cross Correlation...] [2008-12-22 10:31:31] [2d4aec5ed1856c4828162be37be304d9]
-   P                             [Cross Correlation Function] [Cross Correlation...] [2008-12-22 11:21:14] [2d4aec5ed1856c4828162be37be304d9]
- RMP                     [ARIMA Forecasting] [Arima forecast (p...] [2008-12-22 15:10:16] [2d4aec5ed1856c4828162be37be304d9]
-    D                [Variance Reduction Matrix] [VRM Xt] [2008-12-22 11:17:14] [2d4aec5ed1856c4828162be37be304d9]
- RMP             [Standard Deviation-Mean Plot] [SD Mean Plot Tijd...] [2008-12-12 09:35:09] [2d4aec5ed1856c4828162be37be304d9]
- RMP               [Box-Cox Normality Plot] [Box-Cox Normality...] [2008-12-12 09:46:16] [2d4aec5ed1856c4828162be37be304d9]
- RMP                 [Mean Plot] [Mean plot Yt] [2008-12-22 13:33:34] [2d4aec5ed1856c4828162be37be304d9]
- RMP               [Maximum-likelihood Fitting - Normal Distribution] [ML Fitting - Norm...] [2008-12-12 10:38:01] [2d4aec5ed1856c4828162be37be304d9]
-    D              [Standard Deviation-Mean Plot] [SD Mean Plot Xt] [2008-12-22 11:11:05] [2d4aec5ed1856c4828162be37be304d9]
- RM D        [Box-Cox Linearity Plot] [Box-Cox linearity...] [2008-12-22 14:11:54] [2d4aec5ed1856c4828162be37be304d9]
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Post a new message
Dataseries X:
2220.6
2161.5
1863.6
1955.1
1907.4
1889.4
2246.3
2213
1965
2285.6
1983.8
1872.4
2371.4
2287
2198.2
2330.4
2014.4
2066.1
2355.8
2232.5
2091.7
2376.5
1931.9
2025.7
2404.9
2316.1
2368.1
2282.5
2158.6
2174.8
2594.1
2281.4
2547.9
2606.3
2190.8
2262.3
2423.8
2520.4
2482.9
2215.9
2441.9
2333.8
2670.2
2431
2559.3
2661.4
2404.6
2378.3
2489.2
2941
2700.9
2335.6
2770
2764.2
2784.9
2898.8
2853.4
3022.6
2851.4
2630.8




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'Sir Ronald Aylmer Fisher' @ 193.190.124.24

\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 & 3 seconds \tabularnewline
R Server & 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=32391&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]3 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Sir Ronald Aylmer Fisher' @ 193.190.124.24[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=32391&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=32391&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 time3 seconds
R Server'Sir Ronald Aylmer Fisher' @ 193.190.124.24







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean2359.9937.396395918371863.1074182964408
Geometric Mean2342.66248915639
Harmonic Mean2325.50380643558
Quadratic Mean2377.40693515715
Winsorized Mean ( 1 / 20 )2358.7766666666736.977735580011363.789105245853
Winsorized Mean ( 2 / 20 )2357.9366666666736.488423206001464.6215007251627
Winsorized Mean ( 3 / 20 )2356.5666666666735.741869342627665.932943911697
Winsorized Mean ( 4 / 20 )2358.0666666666735.369636237997866.6692371614889
Winsorized Mean ( 5 / 20 )2354.4583333333333.722293276032269.8190456402543
Winsorized Mean ( 6 / 20 )2353.9583333333333.205241851153570.8911666382445
Winsorized Mean ( 7 / 20 )2355.47532.632073891631972.1828164468588
Winsorized Mean ( 8 / 20 )2351.11530.122413227899278.0520133699783
Winsorized Mean ( 9 / 20 )2348.20528.913460047055281.2149426660945
Winsorized Mean ( 10 / 20 )2353.4716666666727.399403586612585.8949961895006
Winsorized Mean ( 11 / 20 )2352.55525.522163451790092.1769427753978
Winsorized Mean ( 12 / 20 )2361.03522.4240524650386105.290290578882
Winsorized Mean ( 13 / 20 )2359.0221.8416615590714108.005519342929
Winsorized Mean ( 14 / 20 )2354.0033333333319.9157020024993118.198360923352
Winsorized Mean ( 15 / 20 )2355.1533333333318.8179619486827125.154537975787
Winsorized Mean ( 16 / 20 )2349.7933333333317.2738494538108136.031828899316
Winsorized Mean ( 17 / 20 )2345.1466666666715.2011127058282154.274671338206
Winsorized Mean ( 18 / 20 )2344.1266666666714.7707272477524158.700829508809
Winsorized Mean ( 19 / 20 )2332.6316666666712.5511134607835185.85057604292
Winsorized Mean ( 20 / 20 )2332.96511.4226885001133204.239571093692
Trimmed Mean ( 1 / 20 )2357.1241379310335.916505591834565.6278805270777
Trimmed Mean ( 2 / 20 )2355.3535714285734.60669854498868.0606261347543
Trimmed Mean ( 3 / 20 )2353.9185185185233.313005759296170.660646341156
Trimmed Mean ( 4 / 20 )2352.932.068037822320273.3721225176529
Trimmed Mean ( 5 / 20 )2351.3530.648399931600876.7201552200963
Trimmed Mean ( 6 / 20 )2350.5729166666729.447755266650379.8218028974418
Trimmed Mean ( 7 / 20 )2349.8369565217428.076205022933883.6949635679856
Trimmed Mean ( 8 / 20 )2348.7386363636426.473418439806888.7206403549287
Trimmed Mean ( 9 / 20 )2348.3142857142925.161329991914393.33029241574
Trimmed Mean ( 10 / 20 )2348.332523.784488154316598.7337833281822
Trimmed Mean ( 11 / 20 )2347.5210526315822.3893432401213104.849929158479
Trimmed Mean ( 12 / 20 )2346.7583333333321.0647367165248111.406962494450
Trimmed Mean ( 13 / 20 )2344.6588235294120.1636761166996116.281317452206
Trimmed Mean ( 14 / 20 )2342.587519.0571745601950122.924177065209
Trimmed Mean ( 15 / 20 )2340.9566666666718.1016844858718129.322586994252
Trimmed Mean ( 16 / 20 )2338.9285714285717.0428194449571137.238358886719
Trimmed Mean ( 17 / 20 )2337.3615384615416.0185354914218145.916057039873
Trimmed Mean ( 18 / 20 )2336.2166666666715.2416283349095153.278679635284
Trimmed Mean ( 19 / 20 )2335.0181818181814.1275798492415165.280834136892
Trimmed Mean ( 20 / 20 )2335.39513.3467726731773174.978255581844
Median2334.7
Midrange2443.1
Midmean - Weighted Average at Xnp2335.59677419355
Midmean - Weighted Average at X(n+1)p2340.95666666667
Midmean - Empirical Distribution Function2335.59677419355
Midmean - Empirical Distribution Function - Averaging2340.95666666667
Midmean - Empirical Distribution Function - Interpolation2340.95666666667
Midmean - Closest Observation2335.59677419355
Midmean - True Basic - Statistics Graphics Toolkit2340.95666666667
Midmean - MS Excel (old versions)2342.5875
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 2359.99 & 37.3963959183718 & 63.1074182964408 \tabularnewline
Geometric Mean & 2342.66248915639 &  &  \tabularnewline
Harmonic Mean & 2325.50380643558 &  &  \tabularnewline
Quadratic Mean & 2377.40693515715 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 2358.77666666667 & 36.9777355800113 & 63.789105245853 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 2357.93666666667 & 36.4884232060014 & 64.6215007251627 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 2356.56666666667 & 35.7418693426276 & 65.932943911697 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 2358.06666666667 & 35.3696362379978 & 66.6692371614889 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 2354.45833333333 & 33.7222932760322 & 69.8190456402543 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 2353.95833333333 & 33.2052418511535 & 70.8911666382445 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 2355.475 & 32.6320738916319 & 72.1828164468588 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 2351.115 & 30.1224132278992 & 78.0520133699783 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 2348.205 & 28.9134600470552 & 81.2149426660945 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 2353.47166666667 & 27.3994035866125 & 85.8949961895006 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 2352.555 & 25.5221634517900 & 92.1769427753978 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 2361.035 & 22.4240524650386 & 105.290290578882 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 2359.02 & 21.8416615590714 & 108.005519342929 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 2354.00333333333 & 19.9157020024993 & 118.198360923352 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 2355.15333333333 & 18.8179619486827 & 125.154537975787 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 2349.79333333333 & 17.2738494538108 & 136.031828899316 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 2345.14666666667 & 15.2011127058282 & 154.274671338206 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 2344.12666666667 & 14.7707272477524 & 158.700829508809 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 2332.63166666667 & 12.5511134607835 & 185.85057604292 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 2332.965 & 11.4226885001133 & 204.239571093692 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 2357.12413793103 & 35.9165055918345 & 65.6278805270777 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 2355.35357142857 & 34.606698544988 & 68.0606261347543 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 2353.91851851852 & 33.3130057592961 & 70.660646341156 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 2352.9 & 32.0680378223202 & 73.3721225176529 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 2351.35 & 30.6483999316008 & 76.7201552200963 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 2350.57291666667 & 29.4477552666503 & 79.8218028974418 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 2349.83695652174 & 28.0762050229338 & 83.6949635679856 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 2348.73863636364 & 26.4734184398068 & 88.7206403549287 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 2348.31428571429 & 25.1613299919143 & 93.33029241574 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 2348.3325 & 23.7844881543165 & 98.7337833281822 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 2347.52105263158 & 22.3893432401213 & 104.849929158479 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 2346.75833333333 & 21.0647367165248 & 111.406962494450 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 2344.65882352941 & 20.1636761166996 & 116.281317452206 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 2342.5875 & 19.0571745601950 & 122.924177065209 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 2340.95666666667 & 18.1016844858718 & 129.322586994252 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 2338.92857142857 & 17.0428194449571 & 137.238358886719 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 2337.36153846154 & 16.0185354914218 & 145.916057039873 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 2336.21666666667 & 15.2416283349095 & 153.278679635284 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 2335.01818181818 & 14.1275798492415 & 165.280834136892 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 2335.395 & 13.3467726731773 & 174.978255581844 \tabularnewline
Median & 2334.7 &  &  \tabularnewline
Midrange & 2443.1 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 2335.59677419355 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 2340.95666666667 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 2335.59677419355 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 2340.95666666667 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 2340.95666666667 &  &  \tabularnewline
Midmean - Closest Observation & 2335.59677419355 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 2340.95666666667 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 2342.5875 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=32391&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]2359.99[/C][C]37.3963959183718[/C][C]63.1074182964408[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]2342.66248915639[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]2325.50380643558[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]2377.40693515715[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]2358.77666666667[/C][C]36.9777355800113[/C][C]63.789105245853[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]2357.93666666667[/C][C]36.4884232060014[/C][C]64.6215007251627[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]2356.56666666667[/C][C]35.7418693426276[/C][C]65.932943911697[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]2358.06666666667[/C][C]35.3696362379978[/C][C]66.6692371614889[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]2354.45833333333[/C][C]33.7222932760322[/C][C]69.8190456402543[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]2353.95833333333[/C][C]33.2052418511535[/C][C]70.8911666382445[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]2355.475[/C][C]32.6320738916319[/C][C]72.1828164468588[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]2351.115[/C][C]30.1224132278992[/C][C]78.0520133699783[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]2348.205[/C][C]28.9134600470552[/C][C]81.2149426660945[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]2353.47166666667[/C][C]27.3994035866125[/C][C]85.8949961895006[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]2352.555[/C][C]25.5221634517900[/C][C]92.1769427753978[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]2361.035[/C][C]22.4240524650386[/C][C]105.290290578882[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]2359.02[/C][C]21.8416615590714[/C][C]108.005519342929[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]2354.00333333333[/C][C]19.9157020024993[/C][C]118.198360923352[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]2355.15333333333[/C][C]18.8179619486827[/C][C]125.154537975787[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]2349.79333333333[/C][C]17.2738494538108[/C][C]136.031828899316[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]2345.14666666667[/C][C]15.2011127058282[/C][C]154.274671338206[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]2344.12666666667[/C][C]14.7707272477524[/C][C]158.700829508809[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]2332.63166666667[/C][C]12.5511134607835[/C][C]185.85057604292[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]2332.965[/C][C]11.4226885001133[/C][C]204.239571093692[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]2357.12413793103[/C][C]35.9165055918345[/C][C]65.6278805270777[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]2355.35357142857[/C][C]34.606698544988[/C][C]68.0606261347543[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]2353.91851851852[/C][C]33.3130057592961[/C][C]70.660646341156[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]2352.9[/C][C]32.0680378223202[/C][C]73.3721225176529[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]2351.35[/C][C]30.6483999316008[/C][C]76.7201552200963[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]2350.57291666667[/C][C]29.4477552666503[/C][C]79.8218028974418[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]2349.83695652174[/C][C]28.0762050229338[/C][C]83.6949635679856[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]2348.73863636364[/C][C]26.4734184398068[/C][C]88.7206403549287[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]2348.31428571429[/C][C]25.1613299919143[/C][C]93.33029241574[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]2348.3325[/C][C]23.7844881543165[/C][C]98.7337833281822[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]2347.52105263158[/C][C]22.3893432401213[/C][C]104.849929158479[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]2346.75833333333[/C][C]21.0647367165248[/C][C]111.406962494450[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]2344.65882352941[/C][C]20.1636761166996[/C][C]116.281317452206[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]2342.5875[/C][C]19.0571745601950[/C][C]122.924177065209[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]2340.95666666667[/C][C]18.1016844858718[/C][C]129.322586994252[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]2338.92857142857[/C][C]17.0428194449571[/C][C]137.238358886719[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]2337.36153846154[/C][C]16.0185354914218[/C][C]145.916057039873[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]2336.21666666667[/C][C]15.2416283349095[/C][C]153.278679635284[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]2335.01818181818[/C][C]14.1275798492415[/C][C]165.280834136892[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]2335.395[/C][C]13.3467726731773[/C][C]174.978255581844[/C][/ROW]
[ROW][C]Median[/C][C]2334.7[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]2443.1[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]2335.59677419355[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]2340.95666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]2335.59677419355[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]2340.95666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]2340.95666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]2335.59677419355[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]2340.95666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]2342.5875[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]60[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=32391&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=32391&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 Mean2359.9937.396395918371863.1074182964408
Geometric Mean2342.66248915639
Harmonic Mean2325.50380643558
Quadratic Mean2377.40693515715
Winsorized Mean ( 1 / 20 )2358.7766666666736.977735580011363.789105245853
Winsorized Mean ( 2 / 20 )2357.9366666666736.488423206001464.6215007251627
Winsorized Mean ( 3 / 20 )2356.5666666666735.741869342627665.932943911697
Winsorized Mean ( 4 / 20 )2358.0666666666735.369636237997866.6692371614889
Winsorized Mean ( 5 / 20 )2354.4583333333333.722293276032269.8190456402543
Winsorized Mean ( 6 / 20 )2353.9583333333333.205241851153570.8911666382445
Winsorized Mean ( 7 / 20 )2355.47532.632073891631972.1828164468588
Winsorized Mean ( 8 / 20 )2351.11530.122413227899278.0520133699783
Winsorized Mean ( 9 / 20 )2348.20528.913460047055281.2149426660945
Winsorized Mean ( 10 / 20 )2353.4716666666727.399403586612585.8949961895006
Winsorized Mean ( 11 / 20 )2352.55525.522163451790092.1769427753978
Winsorized Mean ( 12 / 20 )2361.03522.4240524650386105.290290578882
Winsorized Mean ( 13 / 20 )2359.0221.8416615590714108.005519342929
Winsorized Mean ( 14 / 20 )2354.0033333333319.9157020024993118.198360923352
Winsorized Mean ( 15 / 20 )2355.1533333333318.8179619486827125.154537975787
Winsorized Mean ( 16 / 20 )2349.7933333333317.2738494538108136.031828899316
Winsorized Mean ( 17 / 20 )2345.1466666666715.2011127058282154.274671338206
Winsorized Mean ( 18 / 20 )2344.1266666666714.7707272477524158.700829508809
Winsorized Mean ( 19 / 20 )2332.6316666666712.5511134607835185.85057604292
Winsorized Mean ( 20 / 20 )2332.96511.4226885001133204.239571093692
Trimmed Mean ( 1 / 20 )2357.1241379310335.916505591834565.6278805270777
Trimmed Mean ( 2 / 20 )2355.3535714285734.60669854498868.0606261347543
Trimmed Mean ( 3 / 20 )2353.9185185185233.313005759296170.660646341156
Trimmed Mean ( 4 / 20 )2352.932.068037822320273.3721225176529
Trimmed Mean ( 5 / 20 )2351.3530.648399931600876.7201552200963
Trimmed Mean ( 6 / 20 )2350.5729166666729.447755266650379.8218028974418
Trimmed Mean ( 7 / 20 )2349.8369565217428.076205022933883.6949635679856
Trimmed Mean ( 8 / 20 )2348.7386363636426.473418439806888.7206403549287
Trimmed Mean ( 9 / 20 )2348.3142857142925.161329991914393.33029241574
Trimmed Mean ( 10 / 20 )2348.332523.784488154316598.7337833281822
Trimmed Mean ( 11 / 20 )2347.5210526315822.3893432401213104.849929158479
Trimmed Mean ( 12 / 20 )2346.7583333333321.0647367165248111.406962494450
Trimmed Mean ( 13 / 20 )2344.6588235294120.1636761166996116.281317452206
Trimmed Mean ( 14 / 20 )2342.587519.0571745601950122.924177065209
Trimmed Mean ( 15 / 20 )2340.9566666666718.1016844858718129.322586994252
Trimmed Mean ( 16 / 20 )2338.9285714285717.0428194449571137.238358886719
Trimmed Mean ( 17 / 20 )2337.3615384615416.0185354914218145.916057039873
Trimmed Mean ( 18 / 20 )2336.2166666666715.2416283349095153.278679635284
Trimmed Mean ( 19 / 20 )2335.0181818181814.1275798492415165.280834136892
Trimmed Mean ( 20 / 20 )2335.39513.3467726731773174.978255581844
Median2334.7
Midrange2443.1
Midmean - Weighted Average at Xnp2335.59677419355
Midmean - Weighted Average at X(n+1)p2340.95666666667
Midmean - Empirical Distribution Function2335.59677419355
Midmean - Empirical Distribution Function - Averaging2340.95666666667
Midmean - Empirical Distribution Function - Interpolation2340.95666666667
Midmean - Closest Observation2335.59677419355
Midmean - True Basic - Statistics Graphics Toolkit2340.95666666667
Midmean - MS Excel (old versions)2342.5875
Number of observations60



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')