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Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationFri, 10 Oct 2014 13:38:35 +0100
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2014/Oct/10/t1412944941001wgexmpj67xpl.htm/, Retrieved Sun, 12 May 2024 23:16:34 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=240289, Retrieved Sun, 12 May 2024 23:16:34 +0000
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Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact79
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [] [2014-10-10 12:38:35] [f1a1c306ccf782003dcf1365fad9efec] [Current]
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Dataseries X:
1850,07
1841,55
1845
1844,01
1842,67
1842,67
1842,67
1842,9
1840,37
1841,59
1844,33
1844,33
1844,33
1845,39
1861,84
1862,85
1869,46
1870,8
1870,8
1871,52
1875,52
1880,38
1885,05
1886,42
1886,42
1891,65
1903,11
1905,29
1904,26
1905,37
1905,37
1905,12
1908,62
1915,08
1916,36
1916,68
1916,24
1922,05
1922,63
1922,47
1920,64
1920,66
1920,66
1921,19
1921,44
1921,73
1921,81
1921,81
1921,81
1921,48
1917,07
1912,64
1901,15
1898,12
1900,02
1900,02
1900,82
1901,9
1902,19
1901,84
1903,73
1889,7
1891,27
1894,48
1894,27
1893,98
1893,98
1895,62
1901,72
1905,4
1898,14
1898,09




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gwilym Jenkins' @ jenkins.wessa.net

\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 & 1 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=240289&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]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=240289&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=240289&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 time1 seconds
R Server'Gwilym Jenkins' @ jenkins.wessa.net







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean1890.314166666673.2433905873262582.82038988866
Geometric Mean1890.1153227764
Harmonic Mean1889.91520042507
Quadratic Mean1890.51171354698
Winsorized Mean ( 1 / 24 )1890.328333333333.23956432183483583.513134958433
Winsorized Mean ( 2 / 24 )1890.317777777783.23770835138552583.844365403959
Winsorized Mean ( 3 / 24 )1890.352777777783.22687932299748585.814524982549
Winsorized Mean ( 4 / 24 )1890.352777777783.22687932299748585.814524982549
Winsorized Mean ( 5 / 24 )1890.352777777783.22687932299748585.814524982549
Winsorized Mean ( 6 / 24 )1890.365277777783.22198167020039586.708886416541
Winsorized Mean ( 7 / 24 )1890.448888888893.1964160997053591.427658327457
Winsorized Mean ( 8 / 24 )1890.483.18854645285327592.897117214117
Winsorized Mean ( 9 / 24 )1890.448753.18428504403834593.680755288953
Winsorized Mean ( 10 / 24 )1890.375138888893.17433470530828595.518530458591
Winsorized Mean ( 11 / 24 )1890.47753.15348253568894599.488812322529
Winsorized Mean ( 12 / 24 )1890.539166666673.13984933147036602.111428633852
Winsorized Mean ( 13 / 24 )1890.739583333332.88530256803951655.30028090539
Winsorized Mean ( 14 / 24 )1892.952361111112.44083773919026775.533879502819
Winsorized Mean ( 15 / 24 )1893.096111111112.39410160158239790.733404906402
Winsorized Mean ( 16 / 24 )1894.538333333332.13781431352763886.203409409834
Winsorized Mean ( 17 / 24 )1894.580833333332.046883291953925.592993397121
Winsorized Mean ( 18 / 24 )1893.970833333331.96296065783543964.854199075912
Winsorized Mean ( 19 / 24 )1893.11.795167875027431054.55318487753
Winsorized Mean ( 20 / 24 )1893.316666666671.502884862788271259.78823364687
Winsorized Mean ( 21 / 24 )1894.725416666671.270492830355031491.33105783619
Winsorized Mean ( 22 / 24 )1896.152361111111.050098782391421805.6895150311
Winsorized Mean ( 23 / 24 )1896.564444444440.9824893109058011930.36649192236
Winsorized Mean ( 24 / 24 )1896.507777777780.9754217462354541944.2951575533
Trimmed Mean ( 1 / 24 )1890.5663.22493306396904586.234183004472
Trimmed Mean ( 2 / 24 )1890.817647058823.20530295567348589.902943093733
Trimmed Mean ( 3 / 24 )1891.09030303033.18081611970866594.529904232098
Trimmed Mean ( 4 / 24 )1891.3668753.15408469946808599.656336216643
Trimmed Mean ( 5 / 24 )1891.661290322583.1196737368553606.365104137274
Trimmed Mean ( 6 / 24 )1891.975333333333.07591302385489615.093898514143
Trimmed Mean ( 7 / 24 )1892.308448275863.02203184216096626.170916492638
Trimmed Mean ( 8 / 24 )1892.652.96091289888865639.211643378765
Trimmed Mean ( 9 / 24 )1893.011666666672.88563916658346656.011218792804
Trimmed Mean ( 10 / 24 )1893.405961538462.79109353329208678.374242551878
Trimmed Mean ( 11 / 24 )1893.84242.67252552818032708.633979369127
Trimmed Mean ( 12 / 24 )1894.301252.52505111290518750.203130668719
Trimmed Mean ( 13 / 24 )1894.791956521742.33507964919271811.446392064962
Trimmed Mean ( 14 / 24 )1895.302045454552.15408833915665879.862729397895
Trimmed Mean ( 15 / 24 )1895.589761904762.04463271446512927.105268586419
Trimmed Mean ( 16 / 24 )1895.8891.91015906841987992.52938215681
Trimmed Mean ( 17 / 24 )1896.048947368421.804521852615841050.7209677843
Trimmed Mean ( 18 / 24 )1896.221666666671.685039752722161125.32755598397
Trimmed Mean ( 19 / 24 )1896.486470588241.539551459226541231.84350820012
Trimmed Mean ( 20 / 24 )1896.88751.377999587410391376.55157325898
Trimmed Mean ( 21 / 24 )1897.3161.245290309133971523.59332284492
Trimmed Mean ( 22 / 24 )1897.633214285711.147021799653921654.40030421241
Trimmed Mean ( 23 / 24 )1897.819615384621.09230856175481737.43911000365
Trimmed Mean ( 24 / 24 )1897.983333333331.033092421659751837.18638675527
Median1899.08
Midrange1881.5
Midmean - Weighted Average at Xnp1895.53459459459
Midmean - Weighted Average at X(n+1)p1895.53459459459
Midmean - Empirical Distribution Function1895.53459459459
Midmean - Empirical Distribution Function - Averaging1895.53459459459
Midmean - Empirical Distribution Function - Interpolation1895.53459459459
Midmean - Closest Observation1895.53459459459
Midmean - True Basic - Statistics Graphics Toolkit1895.53459459459
Midmean - MS Excel (old versions)1896.04894736842
Number of observations72

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 1890.31416666667 & 3.2433905873262 & 582.82038988866 \tabularnewline
Geometric Mean & 1890.1153227764 &  &  \tabularnewline
Harmonic Mean & 1889.91520042507 &  &  \tabularnewline
Quadratic Mean & 1890.51171354698 &  &  \tabularnewline
Winsorized Mean ( 1 / 24 ) & 1890.32833333333 & 3.23956432183483 & 583.513134958433 \tabularnewline
Winsorized Mean ( 2 / 24 ) & 1890.31777777778 & 3.23770835138552 & 583.844365403959 \tabularnewline
Winsorized Mean ( 3 / 24 ) & 1890.35277777778 & 3.22687932299748 & 585.814524982549 \tabularnewline
Winsorized Mean ( 4 / 24 ) & 1890.35277777778 & 3.22687932299748 & 585.814524982549 \tabularnewline
Winsorized Mean ( 5 / 24 ) & 1890.35277777778 & 3.22687932299748 & 585.814524982549 \tabularnewline
Winsorized Mean ( 6 / 24 ) & 1890.36527777778 & 3.22198167020039 & 586.708886416541 \tabularnewline
Winsorized Mean ( 7 / 24 ) & 1890.44888888889 & 3.1964160997053 & 591.427658327457 \tabularnewline
Winsorized Mean ( 8 / 24 ) & 1890.48 & 3.18854645285327 & 592.897117214117 \tabularnewline
Winsorized Mean ( 9 / 24 ) & 1890.44875 & 3.18428504403834 & 593.680755288953 \tabularnewline
Winsorized Mean ( 10 / 24 ) & 1890.37513888889 & 3.17433470530828 & 595.518530458591 \tabularnewline
Winsorized Mean ( 11 / 24 ) & 1890.4775 & 3.15348253568894 & 599.488812322529 \tabularnewline
Winsorized Mean ( 12 / 24 ) & 1890.53916666667 & 3.13984933147036 & 602.111428633852 \tabularnewline
Winsorized Mean ( 13 / 24 ) & 1890.73958333333 & 2.88530256803951 & 655.30028090539 \tabularnewline
Winsorized Mean ( 14 / 24 ) & 1892.95236111111 & 2.44083773919026 & 775.533879502819 \tabularnewline
Winsorized Mean ( 15 / 24 ) & 1893.09611111111 & 2.39410160158239 & 790.733404906402 \tabularnewline
Winsorized Mean ( 16 / 24 ) & 1894.53833333333 & 2.13781431352763 & 886.203409409834 \tabularnewline
Winsorized Mean ( 17 / 24 ) & 1894.58083333333 & 2.046883291953 & 925.592993397121 \tabularnewline
Winsorized Mean ( 18 / 24 ) & 1893.97083333333 & 1.96296065783543 & 964.854199075912 \tabularnewline
Winsorized Mean ( 19 / 24 ) & 1893.1 & 1.79516787502743 & 1054.55318487753 \tabularnewline
Winsorized Mean ( 20 / 24 ) & 1893.31666666667 & 1.50288486278827 & 1259.78823364687 \tabularnewline
Winsorized Mean ( 21 / 24 ) & 1894.72541666667 & 1.27049283035503 & 1491.33105783619 \tabularnewline
Winsorized Mean ( 22 / 24 ) & 1896.15236111111 & 1.05009878239142 & 1805.6895150311 \tabularnewline
Winsorized Mean ( 23 / 24 ) & 1896.56444444444 & 0.982489310905801 & 1930.36649192236 \tabularnewline
Winsorized Mean ( 24 / 24 ) & 1896.50777777778 & 0.975421746235454 & 1944.2951575533 \tabularnewline
Trimmed Mean ( 1 / 24 ) & 1890.566 & 3.22493306396904 & 586.234183004472 \tabularnewline
Trimmed Mean ( 2 / 24 ) & 1890.81764705882 & 3.20530295567348 & 589.902943093733 \tabularnewline
Trimmed Mean ( 3 / 24 ) & 1891.0903030303 & 3.18081611970866 & 594.529904232098 \tabularnewline
Trimmed Mean ( 4 / 24 ) & 1891.366875 & 3.15408469946808 & 599.656336216643 \tabularnewline
Trimmed Mean ( 5 / 24 ) & 1891.66129032258 & 3.1196737368553 & 606.365104137274 \tabularnewline
Trimmed Mean ( 6 / 24 ) & 1891.97533333333 & 3.07591302385489 & 615.093898514143 \tabularnewline
Trimmed Mean ( 7 / 24 ) & 1892.30844827586 & 3.02203184216096 & 626.170916492638 \tabularnewline
Trimmed Mean ( 8 / 24 ) & 1892.65 & 2.96091289888865 & 639.211643378765 \tabularnewline
Trimmed Mean ( 9 / 24 ) & 1893.01166666667 & 2.88563916658346 & 656.011218792804 \tabularnewline
Trimmed Mean ( 10 / 24 ) & 1893.40596153846 & 2.79109353329208 & 678.374242551878 \tabularnewline
Trimmed Mean ( 11 / 24 ) & 1893.8424 & 2.67252552818032 & 708.633979369127 \tabularnewline
Trimmed Mean ( 12 / 24 ) & 1894.30125 & 2.52505111290518 & 750.203130668719 \tabularnewline
Trimmed Mean ( 13 / 24 ) & 1894.79195652174 & 2.33507964919271 & 811.446392064962 \tabularnewline
Trimmed Mean ( 14 / 24 ) & 1895.30204545455 & 2.15408833915665 & 879.862729397895 \tabularnewline
Trimmed Mean ( 15 / 24 ) & 1895.58976190476 & 2.04463271446512 & 927.105268586419 \tabularnewline
Trimmed Mean ( 16 / 24 ) & 1895.889 & 1.91015906841987 & 992.52938215681 \tabularnewline
Trimmed Mean ( 17 / 24 ) & 1896.04894736842 & 1.80452185261584 & 1050.7209677843 \tabularnewline
Trimmed Mean ( 18 / 24 ) & 1896.22166666667 & 1.68503975272216 & 1125.32755598397 \tabularnewline
Trimmed Mean ( 19 / 24 ) & 1896.48647058824 & 1.53955145922654 & 1231.84350820012 \tabularnewline
Trimmed Mean ( 20 / 24 ) & 1896.8875 & 1.37799958741039 & 1376.55157325898 \tabularnewline
Trimmed Mean ( 21 / 24 ) & 1897.316 & 1.24529030913397 & 1523.59332284492 \tabularnewline
Trimmed Mean ( 22 / 24 ) & 1897.63321428571 & 1.14702179965392 & 1654.40030421241 \tabularnewline
Trimmed Mean ( 23 / 24 ) & 1897.81961538462 & 1.0923085617548 & 1737.43911000365 \tabularnewline
Trimmed Mean ( 24 / 24 ) & 1897.98333333333 & 1.03309242165975 & 1837.18638675527 \tabularnewline
Median & 1899.08 &  &  \tabularnewline
Midrange & 1881.5 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 1895.53459459459 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 1895.53459459459 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 1895.53459459459 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 1895.53459459459 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 1895.53459459459 &  &  \tabularnewline
Midmean - Closest Observation & 1895.53459459459 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 1895.53459459459 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 1896.04894736842 &  &  \tabularnewline
Number of observations & 72 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=240289&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]1890.31416666667[/C][C]3.2433905873262[/C][C]582.82038988866[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]1890.1153227764[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]1889.91520042507[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]1890.51171354698[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 24 )[/C][C]1890.32833333333[/C][C]3.23956432183483[/C][C]583.513134958433[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 24 )[/C][C]1890.31777777778[/C][C]3.23770835138552[/C][C]583.844365403959[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 24 )[/C][C]1890.35277777778[/C][C]3.22687932299748[/C][C]585.814524982549[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 24 )[/C][C]1890.35277777778[/C][C]3.22687932299748[/C][C]585.814524982549[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 24 )[/C][C]1890.35277777778[/C][C]3.22687932299748[/C][C]585.814524982549[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 24 )[/C][C]1890.36527777778[/C][C]3.22198167020039[/C][C]586.708886416541[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 24 )[/C][C]1890.44888888889[/C][C]3.1964160997053[/C][C]591.427658327457[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 24 )[/C][C]1890.48[/C][C]3.18854645285327[/C][C]592.897117214117[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 24 )[/C][C]1890.44875[/C][C]3.18428504403834[/C][C]593.680755288953[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 24 )[/C][C]1890.37513888889[/C][C]3.17433470530828[/C][C]595.518530458591[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 24 )[/C][C]1890.4775[/C][C]3.15348253568894[/C][C]599.488812322529[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 24 )[/C][C]1890.53916666667[/C][C]3.13984933147036[/C][C]602.111428633852[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 24 )[/C][C]1890.73958333333[/C][C]2.88530256803951[/C][C]655.30028090539[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 24 )[/C][C]1892.95236111111[/C][C]2.44083773919026[/C][C]775.533879502819[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 24 )[/C][C]1893.09611111111[/C][C]2.39410160158239[/C][C]790.733404906402[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 24 )[/C][C]1894.53833333333[/C][C]2.13781431352763[/C][C]886.203409409834[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 24 )[/C][C]1894.58083333333[/C][C]2.046883291953[/C][C]925.592993397121[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 24 )[/C][C]1893.97083333333[/C][C]1.96296065783543[/C][C]964.854199075912[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 24 )[/C][C]1893.1[/C][C]1.79516787502743[/C][C]1054.55318487753[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 24 )[/C][C]1893.31666666667[/C][C]1.50288486278827[/C][C]1259.78823364687[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 24 )[/C][C]1894.72541666667[/C][C]1.27049283035503[/C][C]1491.33105783619[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 24 )[/C][C]1896.15236111111[/C][C]1.05009878239142[/C][C]1805.6895150311[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 24 )[/C][C]1896.56444444444[/C][C]0.982489310905801[/C][C]1930.36649192236[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 24 )[/C][C]1896.50777777778[/C][C]0.975421746235454[/C][C]1944.2951575533[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 24 )[/C][C]1890.566[/C][C]3.22493306396904[/C][C]586.234183004472[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 24 )[/C][C]1890.81764705882[/C][C]3.20530295567348[/C][C]589.902943093733[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 24 )[/C][C]1891.0903030303[/C][C]3.18081611970866[/C][C]594.529904232098[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 24 )[/C][C]1891.366875[/C][C]3.15408469946808[/C][C]599.656336216643[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 24 )[/C][C]1891.66129032258[/C][C]3.1196737368553[/C][C]606.365104137274[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 24 )[/C][C]1891.97533333333[/C][C]3.07591302385489[/C][C]615.093898514143[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 24 )[/C][C]1892.30844827586[/C][C]3.02203184216096[/C][C]626.170916492638[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 24 )[/C][C]1892.65[/C][C]2.96091289888865[/C][C]639.211643378765[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 24 )[/C][C]1893.01166666667[/C][C]2.88563916658346[/C][C]656.011218792804[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 24 )[/C][C]1893.40596153846[/C][C]2.79109353329208[/C][C]678.374242551878[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 24 )[/C][C]1893.8424[/C][C]2.67252552818032[/C][C]708.633979369127[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 24 )[/C][C]1894.30125[/C][C]2.52505111290518[/C][C]750.203130668719[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 24 )[/C][C]1894.79195652174[/C][C]2.33507964919271[/C][C]811.446392064962[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 24 )[/C][C]1895.30204545455[/C][C]2.15408833915665[/C][C]879.862729397895[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 24 )[/C][C]1895.58976190476[/C][C]2.04463271446512[/C][C]927.105268586419[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 24 )[/C][C]1895.889[/C][C]1.91015906841987[/C][C]992.52938215681[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 24 )[/C][C]1896.04894736842[/C][C]1.80452185261584[/C][C]1050.7209677843[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 24 )[/C][C]1896.22166666667[/C][C]1.68503975272216[/C][C]1125.32755598397[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 24 )[/C][C]1896.48647058824[/C][C]1.53955145922654[/C][C]1231.84350820012[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 24 )[/C][C]1896.8875[/C][C]1.37799958741039[/C][C]1376.55157325898[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 24 )[/C][C]1897.316[/C][C]1.24529030913397[/C][C]1523.59332284492[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 24 )[/C][C]1897.63321428571[/C][C]1.14702179965392[/C][C]1654.40030421241[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 24 )[/C][C]1897.81961538462[/C][C]1.0923085617548[/C][C]1737.43911000365[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 24 )[/C][C]1897.98333333333[/C][C]1.03309242165975[/C][C]1837.18638675527[/C][/ROW]
[ROW][C]Median[/C][C]1899.08[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]1881.5[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]1895.53459459459[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]1895.53459459459[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]1895.53459459459[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]1895.53459459459[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]1895.53459459459[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]1895.53459459459[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]1895.53459459459[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]1896.04894736842[/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=240289&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=240289&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 Mean1890.314166666673.2433905873262582.82038988866
Geometric Mean1890.1153227764
Harmonic Mean1889.91520042507
Quadratic Mean1890.51171354698
Winsorized Mean ( 1 / 24 )1890.328333333333.23956432183483583.513134958433
Winsorized Mean ( 2 / 24 )1890.317777777783.23770835138552583.844365403959
Winsorized Mean ( 3 / 24 )1890.352777777783.22687932299748585.814524982549
Winsorized Mean ( 4 / 24 )1890.352777777783.22687932299748585.814524982549
Winsorized Mean ( 5 / 24 )1890.352777777783.22687932299748585.814524982549
Winsorized Mean ( 6 / 24 )1890.365277777783.22198167020039586.708886416541
Winsorized Mean ( 7 / 24 )1890.448888888893.1964160997053591.427658327457
Winsorized Mean ( 8 / 24 )1890.483.18854645285327592.897117214117
Winsorized Mean ( 9 / 24 )1890.448753.18428504403834593.680755288953
Winsorized Mean ( 10 / 24 )1890.375138888893.17433470530828595.518530458591
Winsorized Mean ( 11 / 24 )1890.47753.15348253568894599.488812322529
Winsorized Mean ( 12 / 24 )1890.539166666673.13984933147036602.111428633852
Winsorized Mean ( 13 / 24 )1890.739583333332.88530256803951655.30028090539
Winsorized Mean ( 14 / 24 )1892.952361111112.44083773919026775.533879502819
Winsorized Mean ( 15 / 24 )1893.096111111112.39410160158239790.733404906402
Winsorized Mean ( 16 / 24 )1894.538333333332.13781431352763886.203409409834
Winsorized Mean ( 17 / 24 )1894.580833333332.046883291953925.592993397121
Winsorized Mean ( 18 / 24 )1893.970833333331.96296065783543964.854199075912
Winsorized Mean ( 19 / 24 )1893.11.795167875027431054.55318487753
Winsorized Mean ( 20 / 24 )1893.316666666671.502884862788271259.78823364687
Winsorized Mean ( 21 / 24 )1894.725416666671.270492830355031491.33105783619
Winsorized Mean ( 22 / 24 )1896.152361111111.050098782391421805.6895150311
Winsorized Mean ( 23 / 24 )1896.564444444440.9824893109058011930.36649192236
Winsorized Mean ( 24 / 24 )1896.507777777780.9754217462354541944.2951575533
Trimmed Mean ( 1 / 24 )1890.5663.22493306396904586.234183004472
Trimmed Mean ( 2 / 24 )1890.817647058823.20530295567348589.902943093733
Trimmed Mean ( 3 / 24 )1891.09030303033.18081611970866594.529904232098
Trimmed Mean ( 4 / 24 )1891.3668753.15408469946808599.656336216643
Trimmed Mean ( 5 / 24 )1891.661290322583.1196737368553606.365104137274
Trimmed Mean ( 6 / 24 )1891.975333333333.07591302385489615.093898514143
Trimmed Mean ( 7 / 24 )1892.308448275863.02203184216096626.170916492638
Trimmed Mean ( 8 / 24 )1892.652.96091289888865639.211643378765
Trimmed Mean ( 9 / 24 )1893.011666666672.88563916658346656.011218792804
Trimmed Mean ( 10 / 24 )1893.405961538462.79109353329208678.374242551878
Trimmed Mean ( 11 / 24 )1893.84242.67252552818032708.633979369127
Trimmed Mean ( 12 / 24 )1894.301252.52505111290518750.203130668719
Trimmed Mean ( 13 / 24 )1894.791956521742.33507964919271811.446392064962
Trimmed Mean ( 14 / 24 )1895.302045454552.15408833915665879.862729397895
Trimmed Mean ( 15 / 24 )1895.589761904762.04463271446512927.105268586419
Trimmed Mean ( 16 / 24 )1895.8891.91015906841987992.52938215681
Trimmed Mean ( 17 / 24 )1896.048947368421.804521852615841050.7209677843
Trimmed Mean ( 18 / 24 )1896.221666666671.685039752722161125.32755598397
Trimmed Mean ( 19 / 24 )1896.486470588241.539551459226541231.84350820012
Trimmed Mean ( 20 / 24 )1896.88751.377999587410391376.55157325898
Trimmed Mean ( 21 / 24 )1897.3161.245290309133971523.59332284492
Trimmed Mean ( 22 / 24 )1897.633214285711.147021799653921654.40030421241
Trimmed Mean ( 23 / 24 )1897.819615384621.09230856175481737.43911000365
Trimmed Mean ( 24 / 24 )1897.983333333331.033092421659751837.18638675527
Median1899.08
Midrange1881.5
Midmean - Weighted Average at Xnp1895.53459459459
Midmean - Weighted Average at X(n+1)p1895.53459459459
Midmean - Empirical Distribution Function1895.53459459459
Midmean - Empirical Distribution Function - Averaging1895.53459459459
Midmean - Empirical Distribution Function - Interpolation1895.53459459459
Midmean - Closest Observation1895.53459459459
Midmean - True Basic - Statistics Graphics Toolkit1895.53459459459
Midmean - MS Excel (old versions)1896.04894736842
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')