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 Mon, 09 Dec 2024 09:38:34 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=204936, Retrieved Mon, 09 Dec 2024 09:38:34 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact177
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]
Feedback Forum

Post a new message
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 Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 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 Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 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
MeasureValueS.E.Value/S.E.
Arithmetic Mean8.004722222222220.0311754413987889256.763717306443
Geometric Mean8.00037478959777
Harmonic Mean7.99599151610567
Quadratic Mean8.00903136049131
Winsorized Mean ( 1 / 24 )8.004861111111110.0311459491883508257.011307078902
Winsorized Mean ( 2 / 24 )8.004861111111110.0309190175102812258.897654443558
Winsorized Mean ( 3 / 24 )8.002777777777780.0305263055332268262.160049766489
Winsorized Mean ( 4 / 24 )8.002777777777780.0303153884792392263.98400875708
Winsorized Mean ( 5 / 24 )80.0298489939749157268.015733016764
Winsorized Mean ( 6 / 24 )7.999166666666670.0288388689087732277.374493846158
Winsorized Mean ( 7 / 24 )7.999166666666670.0285093606789485280.580359438691
Winsorized Mean ( 8 / 24 )7.998055555555560.0283517193099149282.101253477017
Winsorized Mean ( 9 / 24 )7.998055555555560.0283517193099149282.101253477017
Winsorized Mean ( 10 / 24 )7.993888888888890.0277892777447093287.660908726238
Winsorized Mean ( 11 / 24 )7.992361111111110.0271057549337838294.858458310257
Winsorized Mean ( 12 / 24 )7.997361111111110.0256374086758644311.941086254946
Winsorized Mean ( 13 / 24 )8.002777777777780.0241086986670195331.94565531343
Winsorized Mean ( 14 / 24 )8.006666666666670.0228615962294767350.223430870642
Winsorized Mean ( 15 / 24 )8.010833333333330.0221609827157908361.483668665344
Winsorized Mean ( 16 / 24 )8.010833333333330.0215305856617008372.067599980952
Winsorized Mean ( 17 / 24 )8.008472222222220.0212580277777801376.726961971188
Winsorized Mean ( 18 / 24 )8.010972222222220.020848735829528384.242588506316
Winsorized Mean ( 19 / 24 )8.016250.0199984716747824400.843130933266
Winsorized Mean ( 20 / 24 )8.016250.0199984716747824400.843130933266
Winsorized Mean ( 21 / 24 )8.013333333333330.0196666268798834407.458451430226
Winsorized Mean ( 22 / 24 )8.025555555555560.0177388560632379452.428021679918
Winsorized Mean ( 23 / 24 )8.022361111111110.0173774414588887461.65375553647
Winsorized Mean ( 24 / 24 )8.039027777777780.0148151887260457542.620679792277
Trimmed Mean ( 1 / 24 )8.0050.030644390595152261.222358954869
Trimmed Mean ( 2 / 24 )8.005147058823530.0300442259955923266.445441463459
Trimmed Mean ( 3 / 24 )8.005303030303030.0294678677652109271.662106470897
Trimmed Mean ( 4 / 24 )8.006250.0289485894878029276.567879183658
Trimmed Mean ( 5 / 24 )8.007258064516130.0283926623672438282.018570888019
Trimmed Mean ( 6 / 24 )8.0090.0278552554150431287.522044966595
Trimmed Mean ( 7 / 24 )8.011034482758620.0274690494643304291.638576469901
Trimmed Mean ( 8 / 24 )8.013214285714290.0270618665222125296.107228196436
Trimmed Mean ( 9 / 24 )8.015740740740740.0265768953474048301.605610285231
Trimmed Mean ( 10 / 24 )8.018461538461540.0259559096741458308.926238345196
Trimmed Mean ( 11 / 24 )8.0220.0252788529835368317.340347887796
Trimmed Mean ( 12 / 24 )8.026041666666670.0245522665521678326.896160467027
Trimmed Mean ( 13 / 24 )8.029782608695650.0239534353641078335.22467598646
Trimmed Mean ( 14 / 24 )8.033181818181820.0235123392715479341.658127904896
Trimmed Mean ( 15 / 24 )8.036428571428570.0231864167567476346.600712638784
Trimmed Mean ( 16 / 24 )8.03950.0228791417716034351.389928881785
Trimmed Mean ( 17 / 24 )8.042894736842110.0225567338929431356.562912654582
Trimmed Mean ( 18 / 24 )8.046944444444440.0221101838363433363.947423685252
Trimmed Mean ( 19 / 24 )8.051176470588230.0215477941841764373.642721931166
Trimmed Mean ( 20 / 24 )8.05531250.0209549457891018384.411039812348
Trimmed Mean ( 21 / 24 )8.060.0200287150183769402.422221925107
Trimmed Mean ( 22 / 24 )8.065714285714290.0186546770695289432.36954762884
Trimmed Mean ( 23 / 24 )8.070769230769230.0173641813195845464.794111638678
Trimmed Mean ( 24 / 24 )8.077083333333330.0152927846805291528.163019493575
Median8.09
Midrange7.995
Midmean - Weighted Average at Xnp8.03564102564103
Midmean - Weighted Average at X(n+1)p8.05054054054054
Midmean - Empirical Distribution Function8.03564102564103
Midmean - Empirical Distribution Function - Averaging8.05054054054054
Midmean - Empirical Distribution Function - Interpolation8.05054054054054
Midmean - Closest Observation8.03564102564103
Midmean - True Basic - Statistics Graphics Toolkit8.05054054054054
Midmean - MS Excel (old versions)8.03564102564103
Number of observations72

\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]Quadratic Mean[/C][C]8.00903136049131[/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
MeasureValueS.E.Value/S.E.
Arithmetic Mean8.004722222222220.0311754413987889256.763717306443
Geometric Mean8.00037478959777
Harmonic Mean7.99599151610567
Quadratic Mean8.00903136049131
Winsorized Mean ( 1 / 24 )8.004861111111110.0311459491883508257.011307078902
Winsorized Mean ( 2 / 24 )8.004861111111110.0309190175102812258.897654443558
Winsorized Mean ( 3 / 24 )8.002777777777780.0305263055332268262.160049766489
Winsorized Mean ( 4 / 24 )8.002777777777780.0303153884792392263.98400875708
Winsorized Mean ( 5 / 24 )80.0298489939749157268.015733016764
Winsorized Mean ( 6 / 24 )7.999166666666670.0288388689087732277.374493846158
Winsorized Mean ( 7 / 24 )7.999166666666670.0285093606789485280.580359438691
Winsorized Mean ( 8 / 24 )7.998055555555560.0283517193099149282.101253477017
Winsorized Mean ( 9 / 24 )7.998055555555560.0283517193099149282.101253477017
Winsorized Mean ( 10 / 24 )7.993888888888890.0277892777447093287.660908726238
Winsorized Mean ( 11 / 24 )7.992361111111110.0271057549337838294.858458310257
Winsorized Mean ( 12 / 24 )7.997361111111110.0256374086758644311.941086254946
Winsorized Mean ( 13 / 24 )8.002777777777780.0241086986670195331.94565531343
Winsorized Mean ( 14 / 24 )8.006666666666670.0228615962294767350.223430870642
Winsorized Mean ( 15 / 24 )8.010833333333330.0221609827157908361.483668665344
Winsorized Mean ( 16 / 24 )8.010833333333330.0215305856617008372.067599980952
Winsorized Mean ( 17 / 24 )8.008472222222220.0212580277777801376.726961971188
Winsorized Mean ( 18 / 24 )8.010972222222220.020848735829528384.242588506316
Winsorized Mean ( 19 / 24 )8.016250.0199984716747824400.843130933266
Winsorized Mean ( 20 / 24 )8.016250.0199984716747824400.843130933266
Winsorized Mean ( 21 / 24 )8.013333333333330.0196666268798834407.458451430226
Winsorized Mean ( 22 / 24 )8.025555555555560.0177388560632379452.428021679918
Winsorized Mean ( 23 / 24 )8.022361111111110.0173774414588887461.65375553647
Winsorized Mean ( 24 / 24 )8.039027777777780.0148151887260457542.620679792277
Trimmed Mean ( 1 / 24 )8.0050.030644390595152261.222358954869
Trimmed Mean ( 2 / 24 )8.005147058823530.0300442259955923266.445441463459
Trimmed Mean ( 3 / 24 )8.005303030303030.0294678677652109271.662106470897
Trimmed Mean ( 4 / 24 )8.006250.0289485894878029276.567879183658
Trimmed Mean ( 5 / 24 )8.007258064516130.0283926623672438282.018570888019
Trimmed Mean ( 6 / 24 )8.0090.0278552554150431287.522044966595
Trimmed Mean ( 7 / 24 )8.011034482758620.0274690494643304291.638576469901
Trimmed Mean ( 8 / 24 )8.013214285714290.0270618665222125296.107228196436
Trimmed Mean ( 9 / 24 )8.015740740740740.0265768953474048301.605610285231
Trimmed Mean ( 10 / 24 )8.018461538461540.0259559096741458308.926238345196
Trimmed Mean ( 11 / 24 )8.0220.0252788529835368317.340347887796
Trimmed Mean ( 12 / 24 )8.026041666666670.0245522665521678326.896160467027
Trimmed Mean ( 13 / 24 )8.029782608695650.0239534353641078335.22467598646
Trimmed Mean ( 14 / 24 )8.033181818181820.0235123392715479341.658127904896
Trimmed Mean ( 15 / 24 )8.036428571428570.0231864167567476346.600712638784
Trimmed Mean ( 16 / 24 )8.03950.0228791417716034351.389928881785
Trimmed Mean ( 17 / 24 )8.042894736842110.0225567338929431356.562912654582
Trimmed Mean ( 18 / 24 )8.046944444444440.0221101838363433363.947423685252
Trimmed Mean ( 19 / 24 )8.051176470588230.0215477941841764373.642721931166
Trimmed Mean ( 20 / 24 )8.05531250.0209549457891018384.411039812348
Trimmed Mean ( 21 / 24 )8.060.0200287150183769402.422221925107
Trimmed Mean ( 22 / 24 )8.065714285714290.0186546770695289432.36954762884
Trimmed Mean ( 23 / 24 )8.070769230769230.0173641813195845464.794111638678
Trimmed Mean ( 24 / 24 )8.077083333333330.0152927846805291528.163019493575
Median8.09
Midrange7.995
Midmean - Weighted Average at Xnp8.03564102564103
Midmean - Weighted Average at X(n+1)p8.05054054054054
Midmean - Empirical Distribution Function8.03564102564103
Midmean - Empirical Distribution Function - Averaging8.05054054054054
Midmean - Empirical Distribution Function - Interpolation8.05054054054054
Midmean - Closest Observation8.03564102564103
Midmean - True Basic - Statistics Graphics Toolkit8.05054054054054
Midmean - MS Excel (old versions)8.03564102564103
Number of observations72



Parameters (Session):
Parameters (R input):
R code (references can be found in the software module):
geomean <- function(x) {
return(exp(mean(log(x))))
}
harmean <- function(x) {
return(1/mean(1/x))
}
quamean <- function(x) {
return(sqrt(mean(x*x)))
}
winmean <- function(x) {
x <-sort(x[!is.na(x)])
n<-length(x)
denom <- 3
nodenom <- n/denom
if (nodenom>40) denom <- n/40
sqrtn = sqrt(n)
roundnodenom = floor(nodenom)
win <- array(NA,dim=c(roundnodenom,2))
for (j in 1:roundnodenom) {
win[j,1] <- (j*x[j+1]+sum(x[(j+1):(n-j)])+j*x[n-j])/n
win[j,2] <- sd(c(rep(x[j+1],j),x[(j+1):(n-j)],rep(x[n-j],j)))/sqrtn
}
return(win)
}
trimean <- function(x) {
x <-sort(x[!is.na(x)])
n<-length(x)
denom <- 3
nodenom <- n/denom
if (nodenom>40) denom <- n/40
sqrtn = sqrt(n)
roundnodenom = floor(nodenom)
tri <- array(NA,dim=c(roundnodenom,2))
for (j in 1:roundnodenom) {
tri[j,1] <- mean(x,trim=j/n)
tri[j,2] <- sd(x[(j+1):(n-j)]) / sqrt(n-j*2)
}
return(tri)
}
midrange <- function(x) {
return((max(x)+min(x))/2)
}
q1 <- function(data,n,p,i,f) {
np <- n*p;
i <<- floor(np)
f <<- np - i
qvalue <- (1-f)*data[i] + f*data[i+1]
}
q2 <- function(data,n,p,i,f) {
np <- (n+1)*p
i <<- floor(np)
f <<- np - i
qvalue <- (1-f)*data[i] + f*data[i+1]
}
q3 <- function(data,n,p,i,f) {
np <- n*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- data[i]
} else {
qvalue <- data[i+1]
}
}
q4 <- function(data,n,p,i,f) {
np <- n*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- (data[i]+data[i+1])/2
} else {
qvalue <- data[i+1]
}
}
q5 <- function(data,n,p,i,f) {
np <- (n-1)*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- data[i+1]
} else {
qvalue <- data[i+1] + f*(data[i+2]-data[i+1])
}
}
q6 <- function(data,n,p,i,f) {
np <- n*p+0.5
i <<- floor(np)
f <<- np - i
qvalue <- data[i]
}
q7 <- function(data,n,p,i,f) {
np <- (n+1)*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- data[i]
} else {
qvalue <- f*data[i] + (1-f)*data[i+1]
}
}
q8 <- function(data,n,p,i,f) {
np <- (n+1)*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- data[i]
} else {
if (f == 0.5) {
qvalue <- (data[i]+data[i+1])/2
} else {
if (f < 0.5) {
qvalue <- data[i]
} else {
qvalue <- data[i+1]
}
}
}
}
midmean <- function(x,def) {
x <-sort(x[!is.na(x)])
n<-length(x)
if (def==1) {
qvalue1 <- q1(x,n,0.25,i,f)
qvalue3 <- q1(x,n,0.75,i,f)
}
if (def==2) {
qvalue1 <- q2(x,n,0.25,i,f)
qvalue3 <- q2(x,n,0.75,i,f)
}
if (def==3) {
qvalue1 <- q3(x,n,0.25,i,f)
qvalue3 <- q3(x,n,0.75,i,f)
}
if (def==4) {
qvalue1 <- q4(x,n,0.25,i,f)
qvalue3 <- q4(x,n,0.75,i,f)
}
if (def==5) {
qvalue1 <- q5(x,n,0.25,i,f)
qvalue3 <- q5(x,n,0.75,i,f)
}
if (def==6) {
qvalue1 <- q6(x,n,0.25,i,f)
qvalue3 <- q6(x,n,0.75,i,f)
}
if (def==7) {
qvalue1 <- q7(x,n,0.25,i,f)
qvalue3 <- q7(x,n,0.75,i,f)
}
if (def==8) {
qvalue1 <- q8(x,n,0.25,i,f)
qvalue3 <- q8(x,n,0.75,i,f)
}
midm <- 0
myn <- 0
roundno4 <- round(n/4)
round3no4 <- round(3*n/4)
for (i in 1:n) {
if ((x[i]>=qvalue1) & (x[i]<=qvalue3)){
midm = midm + x[i]
myn = myn + 1
}
}
midm = midm / myn
return(midm)
}
(arm <- mean(x))
sqrtn <- sqrt(length(x))
(armse <- sd(x) / sqrtn)
(armose <- arm / armse)
(geo <- geomean(x))
(har <- harmean(x))
(qua <- quamean(x))
(win <- winmean(x))
(tri <- trimean(x))
(midr <- midrange(x))
midm <- array(NA,dim=8)
for (j in 1:8) midm[j] <- midmean(x,j)
midm
bitmap(file='test1.png')
lb <- win[,1] - 2*win[,2]
ub <- win[,1] + 2*win[,2]
if ((ylimmin == '') | (ylimmax == '')) plot(win[,1],type='b',main=main, xlab='j', pch=19, ylab='Winsorized Mean(j/n)', ylim=c(min(lb),max(ub))) else plot(win[,1],type='l',main=main, xlab='j', pch=19, ylab='Winsorized Mean(j/n)', ylim=c(ylimmin,ylimmax))
lines(ub,lty=3)
lines(lb,lty=3)
grid()
dev.off()
bitmap(file='test2.png')
lb <- tri[,1] - 2*tri[,2]
ub <- tri[,1] + 2*tri[,2]
if ((ylimmin == '') | (ylimmax == '')) plot(tri[,1],type='b',main=main, xlab='j', pch=19, ylab='Trimmed Mean(j/n)', ylim=c(min(lb),max(ub))) else plot(tri[,1],type='l',main=main, xlab='j', pch=19, ylab='Trimmed Mean(j/n)', ylim=c(ylimmin,ylimmax))
lines(ub,lty=3)
lines(lb,lty=3)
grid()
dev.off()
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Central Tendency - Ungrouped Data',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Measure',header=TRUE)
a<-table.element(a,'Value',header=TRUE)
a<-table.element(a,'S.E.',header=TRUE)
a<-table.element(a,'Value/S.E.',header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('arithmetic_mean.htm', 'Arithmetic Mean', 'click to view the definition of the Arithmetic Mean'),header=TRUE)
a<-table.element(a,arm)
a<-table.element(a,hyperlink('arithmetic_mean_standard_error.htm', armse, 'click to view the definition of the Standard Error of the Arithmetic Mean'))
a<-table.element(a,armose)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('geometric_mean.htm', 'Geometric Mean', 'click to view the definition of the Geometric Mean'),header=TRUE)
a<-table.element(a,geo)
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('harmonic_mean.htm', 'Harmonic Mean', 'click to view the definition of the Harmonic Mean'),header=TRUE)
a<-table.element(a,har)
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('quadratic_mean.htm', 'Quadratic Mean', 'click to view the definition of the Quadratic Mean'),header=TRUE)
a<-table.element(a,qua)
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
for (j in 1:length(win[,1])) {
a<-table.row.start(a)
mylabel <- paste('Winsorized Mean (',j)
mylabel <- paste(mylabel,'/')
mylabel <- paste(mylabel,length(win[,1]))
mylabel <- paste(mylabel,')')
a<-table.element(a,hyperlink('winsorized_mean.htm', mylabel, 'click to view the definition of the Winsorized Mean'),header=TRUE)
a<-table.element(a,win[j,1])
a<-table.element(a,win[j,2])
a<-table.element(a,win[j,1]/win[j,2])
a<-table.row.end(a)
}
for (j in 1:length(tri[,1])) {
a<-table.row.start(a)
mylabel <- paste('Trimmed Mean (',j)
mylabel <- paste(mylabel,'/')
mylabel <- paste(mylabel,length(tri[,1]))
mylabel <- paste(mylabel,')')
a<-table.element(a,hyperlink('arithmetic_mean.htm', mylabel, 'click to view the definition of the Trimmed Mean'),header=TRUE)
a<-table.element(a,tri[j,1])
a<-table.element(a,tri[j,2])
a<-table.element(a,tri[j,1]/tri[j,2])
a<-table.row.end(a)
}
a<-table.row.start(a)
a<-table.element(a,hyperlink('median_1.htm', 'Median', 'click to view the definition of the Median'),header=TRUE)
a<-table.element(a,median(x))
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('midrange.htm', 'Midrange', 'click to view the definition of the Midrange'),header=TRUE)
a<-table.element(a,midr)
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_1.htm','Weighted Average at Xnp',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[1])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_2.htm','Weighted Average at X(n+1)p',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[2])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_3.htm','Empirical Distribution Function',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[3])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_4.htm','Empirical Distribution Function - Averaging',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[4])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_5.htm','Empirical Distribution Function - Interpolation',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[5])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_6.htm','Closest Observation',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[6])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_7.htm','True Basic - Statistics Graphics Toolkit',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[7])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_8.htm','MS Excel (old versions)',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[8])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Number of observations',header=TRUE)
a<-table.element(a,length(x))
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable.tab')