## Free Statistics

of Irreproducible Research!

Author's title
Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationSun, 30 Dec 2012 06:31:05 -0500
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2012/Dec/30/t1356867081otq0amzopna8ea2.htm/, Retrieved Tue, 28 Nov 2023 22:26:14 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=204936, Retrieved Tue, 28 Nov 2023 22:26:14 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact122
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [] [2012-12-30 11:31:05] [fd7ec8291d4731160120df3dd57458b8] [Current]
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Dataseries X:
7,66
7,53
7,54
7,56
7,57
7,56
7,57
7,61
7,61
7,6
7,61
7,61
7,62
7,7
7,73
7,75
7,76
7,76
7,77
7,79
7,79
7,79
7,83
7,83
7,88
7,95
8,01
8,05
8,1
8,1
8,16
8,18
8,2
7,99
8,01
8,02
8,03
8,04
8,07
8,08
8,08
8,1
8,11
8,15
8,16
8,17
8,18
8,15
8,15
8,17
8,16
8,15
8,16
8,15
8,18
8,19
8,18
8,2
8,21
8,22
8,23
8,25
8,28
8,28
8,29
8,3
8,34
8,38
8,39
8,44
8,46
8,46



 Summary of computational transaction Raw Input view raw input (R code) Raw Output view raw output of R engine Computing time 3 seconds R Server 'Sir Maurice George Kendall' @ kendall.wessa.net R Framework error message Warning: there are blank lines in the 'Data' field. Please, use NA for missing data - blank lines are simply deleted and are NOT treated as missing values.

\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 Maurice George Kendall' @ kendall.wessa.net \tabularnewline
R Framework error message & Warning: there are blank lines in the 'Data' field.
Please, use NA for missing data - blank lines are simply
deleted and are NOT treated as missing values. \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=204936&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 Maurice George Kendall' @ kendall.wessa.net[/C][/ROW]
[ROW][C]R Framework error message[/C][C]Warning: there are blank lines in the 'Data' field.
Please, use NA for missing data - blank lines are simply
deleted and are NOT treated as missing values.[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=204936&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=204936&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 Input view raw input (R code) Raw Output view raw output of R engine Computing time 3 seconds R Server 'Sir Maurice George Kendall' @ kendall.wessa.net R Framework error message Warning: there are blank lines in the 'Data' field. Please, use NA for missing data - blank lines are simply deleted and are NOT treated as missing values.

 Central Tendency - Ungrouped Data Measure Value S.E. Value/S.E. Arithmetic Mean 8.00472222222222 0.0311754413987889 256.763717306443 Geometric Mean 8.00037478959777 Harmonic Mean 7.99599151610567 Quadratic Mean 8.00903136049131 Winsorized Mean ( 1 / 24 ) 8.00486111111111 0.0311459491883508 257.011307078902 Winsorized Mean ( 2 / 24 ) 8.00486111111111 0.0309190175102812 258.897654443558 Winsorized Mean ( 3 / 24 ) 8.00277777777778 0.0305263055332268 262.160049766489 Winsorized Mean ( 4 / 24 ) 8.00277777777778 0.0303153884792392 263.98400875708 Winsorized Mean ( 5 / 24 ) 8 0.0298489939749157 268.015733016764 Winsorized Mean ( 6 / 24 ) 7.99916666666667 0.0288388689087732 277.374493846158 Winsorized Mean ( 7 / 24 ) 7.99916666666667 0.0285093606789485 280.580359438691 Winsorized Mean ( 8 / 24 ) 7.99805555555556 0.0283517193099149 282.101253477017 Winsorized Mean ( 9 / 24 ) 7.99805555555556 0.0283517193099149 282.101253477017 Winsorized Mean ( 10 / 24 ) 7.99388888888889 0.0277892777447093 287.660908726238 Winsorized Mean ( 11 / 24 ) 7.99236111111111 0.0271057549337838 294.858458310257 Winsorized Mean ( 12 / 24 ) 7.99736111111111 0.0256374086758644 311.941086254946 Winsorized Mean ( 13 / 24 ) 8.00277777777778 0.0241086986670195 331.94565531343 Winsorized Mean ( 14 / 24 ) 8.00666666666667 0.0228615962294767 350.223430870642 Winsorized Mean ( 15 / 24 ) 8.01083333333333 0.0221609827157908 361.483668665344 Winsorized Mean ( 16 / 24 ) 8.01083333333333 0.0215305856617008 372.067599980952 Winsorized Mean ( 17 / 24 ) 8.00847222222222 0.0212580277777801 376.726961971188 Winsorized Mean ( 18 / 24 ) 8.01097222222222 0.020848735829528 384.242588506316 Winsorized Mean ( 19 / 24 ) 8.01625 0.0199984716747824 400.843130933266 Winsorized Mean ( 20 / 24 ) 8.01625 0.0199984716747824 400.843130933266 Winsorized Mean ( 21 / 24 ) 8.01333333333333 0.0196666268798834 407.458451430226 Winsorized Mean ( 22 / 24 ) 8.02555555555556 0.0177388560632379 452.428021679918 Winsorized Mean ( 23 / 24 ) 8.02236111111111 0.0173774414588887 461.65375553647 Winsorized Mean ( 24 / 24 ) 8.03902777777778 0.0148151887260457 542.620679792277 Trimmed Mean ( 1 / 24 ) 8.005 0.030644390595152 261.222358954869 Trimmed Mean ( 2 / 24 ) 8.00514705882353 0.0300442259955923 266.445441463459 Trimmed Mean ( 3 / 24 ) 8.00530303030303 0.0294678677652109 271.662106470897 Trimmed Mean ( 4 / 24 ) 8.00625 0.0289485894878029 276.567879183658 Trimmed Mean ( 5 / 24 ) 8.00725806451613 0.0283926623672438 282.018570888019 Trimmed Mean ( 6 / 24 ) 8.009 0.0278552554150431 287.522044966595 Trimmed Mean ( 7 / 24 ) 8.01103448275862 0.0274690494643304 291.638576469901 Trimmed Mean ( 8 / 24 ) 8.01321428571429 0.0270618665222125 296.107228196436 Trimmed Mean ( 9 / 24 ) 8.01574074074074 0.0265768953474048 301.605610285231 Trimmed Mean ( 10 / 24 ) 8.01846153846154 0.0259559096741458 308.926238345196 Trimmed Mean ( 11 / 24 ) 8.022 0.0252788529835368 317.340347887796 Trimmed Mean ( 12 / 24 ) 8.02604166666667 0.0245522665521678 326.896160467027 Trimmed Mean ( 13 / 24 ) 8.02978260869565 0.0239534353641078 335.22467598646 Trimmed Mean ( 14 / 24 ) 8.03318181818182 0.0235123392715479 341.658127904896 Trimmed Mean ( 15 / 24 ) 8.03642857142857 0.0231864167567476 346.600712638784 Trimmed Mean ( 16 / 24 ) 8.0395 0.0228791417716034 351.389928881785 Trimmed Mean ( 17 / 24 ) 8.04289473684211 0.0225567338929431 356.562912654582 Trimmed Mean ( 18 / 24 ) 8.04694444444444 0.0221101838363433 363.947423685252 Trimmed Mean ( 19 / 24 ) 8.05117647058823 0.0215477941841764 373.642721931166 Trimmed Mean ( 20 / 24 ) 8.0553125 0.0209549457891018 384.411039812348 Trimmed Mean ( 21 / 24 ) 8.06 0.0200287150183769 402.422221925107 Trimmed Mean ( 22 / 24 ) 8.06571428571429 0.0186546770695289 432.36954762884 Trimmed Mean ( 23 / 24 ) 8.07076923076923 0.0173641813195845 464.794111638678 Trimmed Mean ( 24 / 24 ) 8.07708333333333 0.0152927846805291 528.163019493575 Median 8.09 Midrange 7.995 Midmean - Weighted Average at Xnp 8.03564102564103 Midmean - Weighted Average at X(n+1)p 8.05054054054054 Midmean - Empirical Distribution Function 8.03564102564103 Midmean - Empirical Distribution Function - Averaging 8.05054054054054 Midmean - Empirical Distribution Function - Interpolation 8.05054054054054 Midmean - Closest Observation 8.03564102564103 Midmean - True Basic - Statistics Graphics Toolkit 8.05054054054054 Midmean - MS Excel (old versions) 8.03564102564103 Number of observations 72

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 8.00472222222222 & 0.0311754413987889 & 256.763717306443 \tabularnewline
Geometric Mean & 8.00037478959777 &  &  \tabularnewline
Harmonic Mean & 7.99599151610567 &  &  \tabularnewline
Quadratic Mean & 8.00903136049131 &  &  \tabularnewline
Winsorized Mean ( 1 / 24 ) & 8.00486111111111 & 0.0311459491883508 & 257.011307078902 \tabularnewline
Winsorized Mean ( 2 / 24 ) & 8.00486111111111 & 0.0309190175102812 & 258.897654443558 \tabularnewline
Winsorized Mean ( 3 / 24 ) & 8.00277777777778 & 0.0305263055332268 & 262.160049766489 \tabularnewline
Winsorized Mean ( 4 / 24 ) & 8.00277777777778 & 0.0303153884792392 & 263.98400875708 \tabularnewline
Winsorized Mean ( 5 / 24 ) & 8 & 0.0298489939749157 & 268.015733016764 \tabularnewline
Winsorized Mean ( 6 / 24 ) & 7.99916666666667 & 0.0288388689087732 & 277.374493846158 \tabularnewline
Winsorized Mean ( 7 / 24 ) & 7.99916666666667 & 0.0285093606789485 & 280.580359438691 \tabularnewline
Winsorized Mean ( 8 / 24 ) & 7.99805555555556 & 0.0283517193099149 & 282.101253477017 \tabularnewline
Winsorized Mean ( 9 / 24 ) & 7.99805555555556 & 0.0283517193099149 & 282.101253477017 \tabularnewline
Winsorized Mean ( 10 / 24 ) & 7.99388888888889 & 0.0277892777447093 & 287.660908726238 \tabularnewline
Winsorized Mean ( 11 / 24 ) & 7.99236111111111 & 0.0271057549337838 & 294.858458310257 \tabularnewline
Winsorized Mean ( 12 / 24 ) & 7.99736111111111 & 0.0256374086758644 & 311.941086254946 \tabularnewline
Winsorized Mean ( 13 / 24 ) & 8.00277777777778 & 0.0241086986670195 & 331.94565531343 \tabularnewline
Winsorized Mean ( 14 / 24 ) & 8.00666666666667 & 0.0228615962294767 & 350.223430870642 \tabularnewline
Winsorized Mean ( 15 / 24 ) & 8.01083333333333 & 0.0221609827157908 & 361.483668665344 \tabularnewline
Winsorized Mean ( 16 / 24 ) & 8.01083333333333 & 0.0215305856617008 & 372.067599980952 \tabularnewline
Winsorized Mean ( 17 / 24 ) & 8.00847222222222 & 0.0212580277777801 & 376.726961971188 \tabularnewline
Winsorized Mean ( 18 / 24 ) & 8.01097222222222 & 0.020848735829528 & 384.242588506316 \tabularnewline
Winsorized Mean ( 19 / 24 ) & 8.01625 & 0.0199984716747824 & 400.843130933266 \tabularnewline
Winsorized Mean ( 20 / 24 ) & 8.01625 & 0.0199984716747824 & 400.843130933266 \tabularnewline
Winsorized Mean ( 21 / 24 ) & 8.01333333333333 & 0.0196666268798834 & 407.458451430226 \tabularnewline
Winsorized Mean ( 22 / 24 ) & 8.02555555555556 & 0.0177388560632379 & 452.428021679918 \tabularnewline
Winsorized Mean ( 23 / 24 ) & 8.02236111111111 & 0.0173774414588887 & 461.65375553647 \tabularnewline
Winsorized Mean ( 24 / 24 ) & 8.03902777777778 & 0.0148151887260457 & 542.620679792277 \tabularnewline
Trimmed Mean ( 1 / 24 ) & 8.005 & 0.030644390595152 & 261.222358954869 \tabularnewline
Trimmed Mean ( 2 / 24 ) & 8.00514705882353 & 0.0300442259955923 & 266.445441463459 \tabularnewline
Trimmed Mean ( 3 / 24 ) & 8.00530303030303 & 0.0294678677652109 & 271.662106470897 \tabularnewline
Trimmed Mean ( 4 / 24 ) & 8.00625 & 0.0289485894878029 & 276.567879183658 \tabularnewline
Trimmed Mean ( 5 / 24 ) & 8.00725806451613 & 0.0283926623672438 & 282.018570888019 \tabularnewline
Trimmed Mean ( 6 / 24 ) & 8.009 & 0.0278552554150431 & 287.522044966595 \tabularnewline
Trimmed Mean ( 7 / 24 ) & 8.01103448275862 & 0.0274690494643304 & 291.638576469901 \tabularnewline
Trimmed Mean ( 8 / 24 ) & 8.01321428571429 & 0.0270618665222125 & 296.107228196436 \tabularnewline
Trimmed Mean ( 9 / 24 ) & 8.01574074074074 & 0.0265768953474048 & 301.605610285231 \tabularnewline
Trimmed Mean ( 10 / 24 ) & 8.01846153846154 & 0.0259559096741458 & 308.926238345196 \tabularnewline
Trimmed Mean ( 11 / 24 ) & 8.022 & 0.0252788529835368 & 317.340347887796 \tabularnewline
Trimmed Mean ( 12 / 24 ) & 8.02604166666667 & 0.0245522665521678 & 326.896160467027 \tabularnewline
Trimmed Mean ( 13 / 24 ) & 8.02978260869565 & 0.0239534353641078 & 335.22467598646 \tabularnewline
Trimmed Mean ( 14 / 24 ) & 8.03318181818182 & 0.0235123392715479 & 341.658127904896 \tabularnewline
Trimmed Mean ( 15 / 24 ) & 8.03642857142857 & 0.0231864167567476 & 346.600712638784 \tabularnewline
Trimmed Mean ( 16 / 24 ) & 8.0395 & 0.0228791417716034 & 351.389928881785 \tabularnewline
Trimmed Mean ( 17 / 24 ) & 8.04289473684211 & 0.0225567338929431 & 356.562912654582 \tabularnewline
Trimmed Mean ( 18 / 24 ) & 8.04694444444444 & 0.0221101838363433 & 363.947423685252 \tabularnewline
Trimmed Mean ( 19 / 24 ) & 8.05117647058823 & 0.0215477941841764 & 373.642721931166 \tabularnewline
Trimmed Mean ( 20 / 24 ) & 8.0553125 & 0.0209549457891018 & 384.411039812348 \tabularnewline
Trimmed Mean ( 21 / 24 ) & 8.06 & 0.0200287150183769 & 402.422221925107 \tabularnewline
Trimmed Mean ( 22 / 24 ) & 8.06571428571429 & 0.0186546770695289 & 432.36954762884 \tabularnewline
Trimmed Mean ( 23 / 24 ) & 8.07076923076923 & 0.0173641813195845 & 464.794111638678 \tabularnewline
Trimmed Mean ( 24 / 24 ) & 8.07708333333333 & 0.0152927846805291 & 528.163019493575 \tabularnewline
Median & 8.09 &  &  \tabularnewline
Midrange & 7.995 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 8.03564102564103 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 8.05054054054054 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 8.03564102564103 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 8.05054054054054 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 8.05054054054054 &  &  \tabularnewline
Midmean - Closest Observation & 8.03564102564103 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 8.05054054054054 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 8.03564102564103 &  &  \tabularnewline
Number of observations & 72 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=204936&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]8.00472222222222[/C][C]0.0311754413987889[/C][C]256.763717306443[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]8.00037478959777[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]7.99599151610567[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 24 )[/C][C]8.00486111111111[/C][C]0.0311459491883508[/C][C]257.011307078902[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 24 )[/C][C]8.00486111111111[/C][C]0.0309190175102812[/C][C]258.897654443558[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 24 )[/C][C]8.00277777777778[/C][C]0.0305263055332268[/C][C]262.160049766489[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 24 )[/C][C]8.00277777777778[/C][C]0.0303153884792392[/C][C]263.98400875708[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 24 )[/C][C]8[/C][C]0.0298489939749157[/C][C]268.015733016764[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 24 )[/C][C]7.99916666666667[/C][C]0.0288388689087732[/C][C]277.374493846158[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 24 )[/C][C]7.99916666666667[/C][C]0.0285093606789485[/C][C]280.580359438691[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 24 )[/C][C]7.99805555555556[/C][C]0.0283517193099149[/C][C]282.101253477017[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 24 )[/C][C]7.99805555555556[/C][C]0.0283517193099149[/C][C]282.101253477017[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 24 )[/C][C]7.99388888888889[/C][C]0.0277892777447093[/C][C]287.660908726238[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 24 )[/C][C]7.99236111111111[/C][C]0.0271057549337838[/C][C]294.858458310257[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 24 )[/C][C]7.99736111111111[/C][C]0.0256374086758644[/C][C]311.941086254946[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 24 )[/C][C]8.00277777777778[/C][C]0.0241086986670195[/C][C]331.94565531343[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 24 )[/C][C]8.00666666666667[/C][C]0.0228615962294767[/C][C]350.223430870642[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 24 )[/C][C]8.01083333333333[/C][C]0.0221609827157908[/C][C]361.483668665344[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 24 )[/C][C]8.01083333333333[/C][C]0.0215305856617008[/C][C]372.067599980952[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 24 )[/C][C]8.00847222222222[/C][C]0.0212580277777801[/C][C]376.726961971188[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 24 )[/C][C]8.01097222222222[/C][C]0.020848735829528[/C][C]384.242588506316[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 24 )[/C][C]8.01625[/C][C]0.0199984716747824[/C][C]400.843130933266[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 24 )[/C][C]8.01625[/C][C]0.0199984716747824[/C][C]400.843130933266[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 24 )[/C][C]8.01333333333333[/C][C]0.0196666268798834[/C][C]407.458451430226[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 24 )[/C][C]8.02555555555556[/C][C]0.0177388560632379[/C][C]452.428021679918[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 24 )[/C][C]8.02236111111111[/C][C]0.0173774414588887[/C][C]461.65375553647[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 24 )[/C][C]8.03902777777778[/C][C]0.0148151887260457[/C][C]542.620679792277[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 24 )[/C][C]8.005[/C][C]0.030644390595152[/C][C]261.222358954869[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 24 )[/C][C]8.00514705882353[/C][C]0.0300442259955923[/C][C]266.445441463459[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 24 )[/C][C]8.00530303030303[/C][C]0.0294678677652109[/C][C]271.662106470897[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 24 )[/C][C]8.00625[/C][C]0.0289485894878029[/C][C]276.567879183658[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 24 )[/C][C]8.00725806451613[/C][C]0.0283926623672438[/C][C]282.018570888019[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 24 )[/C][C]8.009[/C][C]0.0278552554150431[/C][C]287.522044966595[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 24 )[/C][C]8.01103448275862[/C][C]0.0274690494643304[/C][C]291.638576469901[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 24 )[/C][C]8.01321428571429[/C][C]0.0270618665222125[/C][C]296.107228196436[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 24 )[/C][C]8.01574074074074[/C][C]0.0265768953474048[/C][C]301.605610285231[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 24 )[/C][C]8.01846153846154[/C][C]0.0259559096741458[/C][C]308.926238345196[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 24 )[/C][C]8.022[/C][C]0.0252788529835368[/C][C]317.340347887796[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 24 )[/C][C]8.02604166666667[/C][C]0.0245522665521678[/C][C]326.896160467027[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 24 )[/C][C]8.02978260869565[/C][C]0.0239534353641078[/C][C]335.22467598646[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 24 )[/C][C]8.03318181818182[/C][C]0.0235123392715479[/C][C]341.658127904896[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 24 )[/C][C]8.03642857142857[/C][C]0.0231864167567476[/C][C]346.600712638784[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 24 )[/C][C]8.0395[/C][C]0.0228791417716034[/C][C]351.389928881785[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 24 )[/C][C]8.04289473684211[/C][C]0.0225567338929431[/C][C]356.562912654582[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 24 )[/C][C]8.04694444444444[/C][C]0.0221101838363433[/C][C]363.947423685252[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 24 )[/C][C]8.05117647058823[/C][C]0.0215477941841764[/C][C]373.642721931166[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 24 )[/C][C]8.0553125[/C][C]0.0209549457891018[/C][C]384.411039812348[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 24 )[/C][C]8.06[/C][C]0.0200287150183769[/C][C]402.422221925107[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 24 )[/C][C]8.06571428571429[/C][C]0.0186546770695289[/C][C]432.36954762884[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 24 )[/C][C]8.07076923076923[/C][C]0.0173641813195845[/C][C]464.794111638678[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 24 )[/C][C]8.07708333333333[/C][C]0.0152927846805291[/C][C]528.163019493575[/C][/ROW]
[ROW][C]Median[/C][C]8.09[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]7.995[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]8.03564102564103[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]8.05054054054054[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]8.03564102564103[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]8.05054054054054[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]8.05054054054054[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]8.03564102564103[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]8.05054054054054[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]8.03564102564103[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]72[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=204936&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=204936&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 Measure Value S.E. Value/S.E. Arithmetic Mean 8.00472222222222 0.0311754413987889 256.763717306443 Geometric Mean 8.00037478959777 Harmonic Mean 7.99599151610567 Quadratic Mean 8.00903136049131 Winsorized Mean ( 1 / 24 ) 8.00486111111111 0.0311459491883508 257.011307078902 Winsorized Mean ( 2 / 24 ) 8.00486111111111 0.0309190175102812 258.897654443558 Winsorized Mean ( 3 / 24 ) 8.00277777777778 0.0305263055332268 262.160049766489 Winsorized Mean ( 4 / 24 ) 8.00277777777778 0.0303153884792392 263.98400875708 Winsorized Mean ( 5 / 24 ) 8 0.0298489939749157 268.015733016764 Winsorized Mean ( 6 / 24 ) 7.99916666666667 0.0288388689087732 277.374493846158 Winsorized Mean ( 7 / 24 ) 7.99916666666667 0.0285093606789485 280.580359438691 Winsorized Mean ( 8 / 24 ) 7.99805555555556 0.0283517193099149 282.101253477017 Winsorized Mean ( 9 / 24 ) 7.99805555555556 0.0283517193099149 282.101253477017 Winsorized Mean ( 10 / 24 ) 7.99388888888889 0.0277892777447093 287.660908726238 Winsorized Mean ( 11 / 24 ) 7.99236111111111 0.0271057549337838 294.858458310257 Winsorized Mean ( 12 / 24 ) 7.99736111111111 0.0256374086758644 311.941086254946 Winsorized Mean ( 13 / 24 ) 8.00277777777778 0.0241086986670195 331.94565531343 Winsorized Mean ( 14 / 24 ) 8.00666666666667 0.0228615962294767 350.223430870642 Winsorized Mean ( 15 / 24 ) 8.01083333333333 0.0221609827157908 361.483668665344 Winsorized Mean ( 16 / 24 ) 8.01083333333333 0.0215305856617008 372.067599980952 Winsorized Mean ( 17 / 24 ) 8.00847222222222 0.0212580277777801 376.726961971188 Winsorized Mean ( 18 / 24 ) 8.01097222222222 0.020848735829528 384.242588506316 Winsorized Mean ( 19 / 24 ) 8.01625 0.0199984716747824 400.843130933266 Winsorized Mean ( 20 / 24 ) 8.01625 0.0199984716747824 400.843130933266 Winsorized Mean ( 21 / 24 ) 8.01333333333333 0.0196666268798834 407.458451430226 Winsorized Mean ( 22 / 24 ) 8.02555555555556 0.0177388560632379 452.428021679918 Winsorized Mean ( 23 / 24 ) 8.02236111111111 0.0173774414588887 461.65375553647 Winsorized Mean ( 24 / 24 ) 8.03902777777778 0.0148151887260457 542.620679792277 Trimmed Mean ( 1 / 24 ) 8.005 0.030644390595152 261.222358954869 Trimmed Mean ( 2 / 24 ) 8.00514705882353 0.0300442259955923 266.445441463459 Trimmed Mean ( 3 / 24 ) 8.00530303030303 0.0294678677652109 271.662106470897 Trimmed Mean ( 4 / 24 ) 8.00625 0.0289485894878029 276.567879183658 Trimmed Mean ( 5 / 24 ) 8.00725806451613 0.0283926623672438 282.018570888019 Trimmed Mean ( 6 / 24 ) 8.009 0.0278552554150431 287.522044966595 Trimmed Mean ( 7 / 24 ) 8.01103448275862 0.0274690494643304 291.638576469901 Trimmed Mean ( 8 / 24 ) 8.01321428571429 0.0270618665222125 296.107228196436 Trimmed Mean ( 9 / 24 ) 8.01574074074074 0.0265768953474048 301.605610285231 Trimmed Mean ( 10 / 24 ) 8.01846153846154 0.0259559096741458 308.926238345196 Trimmed Mean ( 11 / 24 ) 8.022 0.0252788529835368 317.340347887796 Trimmed Mean ( 12 / 24 ) 8.02604166666667 0.0245522665521678 326.896160467027 Trimmed Mean ( 13 / 24 ) 8.02978260869565 0.0239534353641078 335.22467598646 Trimmed Mean ( 14 / 24 ) 8.03318181818182 0.0235123392715479 341.658127904896 Trimmed Mean ( 15 / 24 ) 8.03642857142857 0.0231864167567476 346.600712638784 Trimmed Mean ( 16 / 24 ) 8.0395 0.0228791417716034 351.389928881785 Trimmed Mean ( 17 / 24 ) 8.04289473684211 0.0225567338929431 356.562912654582 Trimmed Mean ( 18 / 24 ) 8.04694444444444 0.0221101838363433 363.947423685252 Trimmed Mean ( 19 / 24 ) 8.05117647058823 0.0215477941841764 373.642721931166 Trimmed Mean ( 20 / 24 ) 8.0553125 0.0209549457891018 384.411039812348 Trimmed Mean ( 21 / 24 ) 8.06 0.0200287150183769 402.422221925107 Trimmed Mean ( 22 / 24 ) 8.06571428571429 0.0186546770695289 432.36954762884 Trimmed Mean ( 23 / 24 ) 8.07076923076923 0.0173641813195845 464.794111638678 Trimmed Mean ( 24 / 24 ) 8.07708333333333 0.0152927846805291 528.163019493575 Median 8.09 Midrange 7.995 Midmean - Weighted Average at Xnp 8.03564102564103 Midmean - Weighted Average at X(n+1)p 8.05054054054054 Midmean - Empirical Distribution Function 8.03564102564103 Midmean - Empirical Distribution Function - Averaging 8.05054054054054 Midmean - Empirical Distribution Function - Interpolation 8.05054054054054 Midmean - Closest Observation 8.03564102564103 Midmean - True Basic - Statistics Graphics Toolkit 8.05054054054054 Midmean - MS Excel (old versions) 8.03564102564103 Number of observations 72

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 <- 3nodenom <- n/denomif (nodenom>40) denom <- n/40sqrtn = 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])/nwin[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 <- 3nodenom <- n/denomif (nodenom>40) denom <- n/40sqrtn = 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 - iqvalue <- (1-f)*data[i] + f*data[i+1]}q2 <- function(data,n,p,i,f) {np <- (n+1)*pi <<- floor(np)f <<- np - iqvalue <- (1-f)*data[i] + f*data[i+1]}q3 <- function(data,n,p,i,f) {np <- n*pi <<- floor(np)f <<- np - iif (f==0) {qvalue <- data[i]} else {qvalue <- data[i+1]}}q4 <- function(data,n,p,i,f) {np <- n*pi <<- floor(np)f <<- np - iif (f==0) {qvalue <- (data[i]+data[i+1])/2} else {qvalue <- data[i+1]}}q5 <- function(data,n,p,i,f) {np <- (n-1)*pi <<- floor(np)f <<- np - iif (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+0.5i <<- floor(np)f <<- np - iqvalue <- data[i]}q7 <- function(data,n,p,i,f) {np <- (n+1)*pi <<- floor(np)f <<- np - iif (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)*pi <<- floor(np)f <<- np - iif (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 <- 0myn <- 0roundno4 <- 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 / mynreturn(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)midmbitmap(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')