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Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationFri, 09 Oct 2015 22:23:29 +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/2015/Oct/09/t1444425840xze3s1plf3xa7b3.htm/, Retrieved Tue, 14 May 2024 08:03:22 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=282080, Retrieved Tue, 14 May 2024 08:03:22 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact65
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [] [2015-10-09 21:23:29] [3e69b53d94b342798d3f1a806941de01] [Current]
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Dataseries X:
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
1855,87
1868,53
1865,71
1872,59
1875,95
1875,95
1875,95
1878,08
1878,26
1876,39
1876,77
1876,88




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Sir Maurice George Kendall' @ kendall.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 & 'Sir Maurice George Kendall' @ kendall.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=282080&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]'Sir Maurice George Kendall' @ kendall.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=282080&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=282080&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'Sir Maurice George Kendall' @ kendall.wessa.net







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean1895.241527777782.41157046976904785.895146559532
Geometric Mean1895.13223658938
Harmonic Mean1895.02258885955
Quadratic Mean1895.35045871066
Winsorized Mean ( 1 / 24 )1895.254027777782.40687904382439787.432186357952
Winsorized Mean ( 2 / 24 )1895.533472222222.327479470801814.414690227054
Winsorized Mean ( 3 / 24 )1895.772222222222.26978294156256835.221812406934
Winsorized Mean ( 4 / 24 )1895.828333333332.25810437486006839.566299255243
Winsorized Mean ( 5 / 24 )1896.026944444442.21855290249685854.623273716206
Winsorized Mean ( 6 / 24 )1896.255277777782.17371857969287872.355462888719
Winsorized Mean ( 7 / 24 )1896.321388888892.15364907881425880.515496950397
Winsorized Mean ( 8 / 24 )1896.465833333332.12718479925647891.537883307654
Winsorized Mean ( 9 / 24 )1896.434583333332.12203372955155893.687294845264
Winsorized Mean ( 10 / 24 )1896.460972222222.09309320599997906.056627954222
Winsorized Mean ( 11 / 24 )1896.624444444442.06598085971551918.026145075522
Winsorized Mean ( 12 / 24 )1897.109444444441.98802556646788954.268132383747
Winsorized Mean ( 13 / 24 )1896.54251.872466903936631012.85768843912
Winsorized Mean ( 14 / 24 )1896.466666666671.86081112313791019.16129105497
Winsorized Mean ( 15 / 24 )1896.41.850647615361741024.72236435423
Winsorized Mean ( 16 / 24 )1896.471111111111.831435899840661035.51050368517
Winsorized Mean ( 17 / 24 )1896.286944444441.776333720959951067.5285404252
Winsorized Mean ( 18 / 24 )1895.704444444441.683314238827331126.17383060044
Winsorized Mean ( 19 / 24 )1894.960277777781.489015360507461272.62641342529
Winsorized Mean ( 20 / 24 )1894.115833333331.371085261608831381.47195245231
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 )1895.577571428572.33701421086152811.110845034092
Trimmed Mean ( 2 / 24 )1895.920147058822.25316691078576841.44682667901
Trimmed Mean ( 3 / 24 )1896.131060606062.20404397479586860.29638350645
Trimmed Mean ( 4 / 24 )1896.2656252.17098702585222873.457833888079
Trimmed Mean ( 5 / 24 )1896.392580645162.13464299988014888.388634891945
Trimmed Mean ( 6 / 24 )1896.480333333332.10229321879175902.100770901642
Trimmed Mean ( 7 / 24 )1896.526896551722.07443325603658914.238571442511
Trimmed Mean ( 8 / 24 )1896.564642857142.04425609567243927.752959559255
Trimmed Mean ( 9 / 24 )1896.581111111112.01224871979562942.518234676149
Trimmed Mean ( 10 / 24 )1896.603653846151.97250742014762961.51914789969
Trimmed Mean ( 11 / 24 )1896.62421.92835391556464983.545699101949
Trimmed Mean ( 12 / 24 )1896.624166666671.877814927958631010.01655617281
Trimmed Mean ( 13 / 24 )1896.560869565221.830069791601951036.33253675264
Trimmed Mean ( 14 / 24 )1896.563181818181.793710994087241057.34044562919
Trimmed Mean ( 15 / 24 )1896.5751.747359655752221085.39475187983
Trimmed Mean ( 16 / 24 )1896.5961.687219902680141124.09532212562
Trimmed Mean ( 17 / 24 )1896.610789473681.610485661425911177.66387798476
Trimmed Mean ( 18 / 24 )1896.648888888891.520200163187461247.63102571448
Trimmed Mean ( 19 / 24 )1896.761.420792377651341335.00153142394
Trimmed Mean ( 20 / 24 )1896.9731251.337227092861591418.58711592553
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
Midrange1883.48
Midmean - Weighted Average at Xnp1896.11162162162
Midmean - Weighted Average at X(n+1)p1896.64888888889
Midmean - Empirical Distribution Function1896.11162162162
Midmean - Empirical Distribution Function - Averaging1896.64888888889
Midmean - Empirical Distribution Function - Interpolation1896.64888888889
Midmean - Closest Observation1896.11162162162
Midmean - True Basic - Statistics Graphics Toolkit1896.64888888889
Midmean - MS Excel (old versions)1896.61078947368
Number of observations72

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 1895.24152777778 & 2.41157046976904 & 785.895146559532 \tabularnewline
Geometric Mean & 1895.13223658938 &  &  \tabularnewline
Harmonic Mean & 1895.02258885955 &  &  \tabularnewline
Quadratic Mean & 1895.35045871066 &  &  \tabularnewline
Winsorized Mean ( 1 / 24 ) & 1895.25402777778 & 2.40687904382439 & 787.432186357952 \tabularnewline
Winsorized Mean ( 2 / 24 ) & 1895.53347222222 & 2.327479470801 & 814.414690227054 \tabularnewline
Winsorized Mean ( 3 / 24 ) & 1895.77222222222 & 2.26978294156256 & 835.221812406934 \tabularnewline
Winsorized Mean ( 4 / 24 ) & 1895.82833333333 & 2.25810437486006 & 839.566299255243 \tabularnewline
Winsorized Mean ( 5 / 24 ) & 1896.02694444444 & 2.21855290249685 & 854.623273716206 \tabularnewline
Winsorized Mean ( 6 / 24 ) & 1896.25527777778 & 2.17371857969287 & 872.355462888719 \tabularnewline
Winsorized Mean ( 7 / 24 ) & 1896.32138888889 & 2.15364907881425 & 880.515496950397 \tabularnewline
Winsorized Mean ( 8 / 24 ) & 1896.46583333333 & 2.12718479925647 & 891.537883307654 \tabularnewline
Winsorized Mean ( 9 / 24 ) & 1896.43458333333 & 2.12203372955155 & 893.687294845264 \tabularnewline
Winsorized Mean ( 10 / 24 ) & 1896.46097222222 & 2.09309320599997 & 906.056627954222 \tabularnewline
Winsorized Mean ( 11 / 24 ) & 1896.62444444444 & 2.06598085971551 & 918.026145075522 \tabularnewline
Winsorized Mean ( 12 / 24 ) & 1897.10944444444 & 1.98802556646788 & 954.268132383747 \tabularnewline
Winsorized Mean ( 13 / 24 ) & 1896.5425 & 1.87246690393663 & 1012.85768843912 \tabularnewline
Winsorized Mean ( 14 / 24 ) & 1896.46666666667 & 1.8608111231379 & 1019.16129105497 \tabularnewline
Winsorized Mean ( 15 / 24 ) & 1896.4 & 1.85064761536174 & 1024.72236435423 \tabularnewline
Winsorized Mean ( 16 / 24 ) & 1896.47111111111 & 1.83143589984066 & 1035.51050368517 \tabularnewline
Winsorized Mean ( 17 / 24 ) & 1896.28694444444 & 1.77633372095995 & 1067.5285404252 \tabularnewline
Winsorized Mean ( 18 / 24 ) & 1895.70444444444 & 1.68331423882733 & 1126.17383060044 \tabularnewline
Winsorized Mean ( 19 / 24 ) & 1894.96027777778 & 1.48901536050746 & 1272.62641342529 \tabularnewline
Winsorized Mean ( 20 / 24 ) & 1894.11583333333 & 1.37108526160883 & 1381.47195245231 \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 ) & 1895.57757142857 & 2.33701421086152 & 811.110845034092 \tabularnewline
Trimmed Mean ( 2 / 24 ) & 1895.92014705882 & 2.25316691078576 & 841.44682667901 \tabularnewline
Trimmed Mean ( 3 / 24 ) & 1896.13106060606 & 2.20404397479586 & 860.29638350645 \tabularnewline
Trimmed Mean ( 4 / 24 ) & 1896.265625 & 2.17098702585222 & 873.457833888079 \tabularnewline
Trimmed Mean ( 5 / 24 ) & 1896.39258064516 & 2.13464299988014 & 888.388634891945 \tabularnewline
Trimmed Mean ( 6 / 24 ) & 1896.48033333333 & 2.10229321879175 & 902.100770901642 \tabularnewline
Trimmed Mean ( 7 / 24 ) & 1896.52689655172 & 2.07443325603658 & 914.238571442511 \tabularnewline
Trimmed Mean ( 8 / 24 ) & 1896.56464285714 & 2.04425609567243 & 927.752959559255 \tabularnewline
Trimmed Mean ( 9 / 24 ) & 1896.58111111111 & 2.01224871979562 & 942.518234676149 \tabularnewline
Trimmed Mean ( 10 / 24 ) & 1896.60365384615 & 1.97250742014762 & 961.51914789969 \tabularnewline
Trimmed Mean ( 11 / 24 ) & 1896.6242 & 1.92835391556464 & 983.545699101949 \tabularnewline
Trimmed Mean ( 12 / 24 ) & 1896.62416666667 & 1.87781492795863 & 1010.01655617281 \tabularnewline
Trimmed Mean ( 13 / 24 ) & 1896.56086956522 & 1.83006979160195 & 1036.33253675264 \tabularnewline
Trimmed Mean ( 14 / 24 ) & 1896.56318181818 & 1.79371099408724 & 1057.34044562919 \tabularnewline
Trimmed Mean ( 15 / 24 ) & 1896.575 & 1.74735965575222 & 1085.39475187983 \tabularnewline
Trimmed Mean ( 16 / 24 ) & 1896.596 & 1.68721990268014 & 1124.09532212562 \tabularnewline
Trimmed Mean ( 17 / 24 ) & 1896.61078947368 & 1.61048566142591 & 1177.66387798476 \tabularnewline
Trimmed Mean ( 18 / 24 ) & 1896.64888888889 & 1.52020016318746 & 1247.63102571448 \tabularnewline
Trimmed Mean ( 19 / 24 ) & 1896.76 & 1.42079237765134 & 1335.00153142394 \tabularnewline
Trimmed Mean ( 20 / 24 ) & 1896.973125 & 1.33722709286159 & 1418.58711592553 \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 & 1883.48 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 1896.11162162162 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 1896.64888888889 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 1896.11162162162 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 1896.64888888889 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 1896.64888888889 &  &  \tabularnewline
Midmean - Closest Observation & 1896.11162162162 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 1896.64888888889 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 1896.61078947368 &  &  \tabularnewline
Number of observations & 72 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=282080&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]1895.24152777778[/C][C]2.41157046976904[/C][C]785.895146559532[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]1895.13223658938[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]1895.02258885955[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]1895.35045871066[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 24 )[/C][C]1895.25402777778[/C][C]2.40687904382439[/C][C]787.432186357952[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 24 )[/C][C]1895.53347222222[/C][C]2.327479470801[/C][C]814.414690227054[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 24 )[/C][C]1895.77222222222[/C][C]2.26978294156256[/C][C]835.221812406934[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 24 )[/C][C]1895.82833333333[/C][C]2.25810437486006[/C][C]839.566299255243[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 24 )[/C][C]1896.02694444444[/C][C]2.21855290249685[/C][C]854.623273716206[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 24 )[/C][C]1896.25527777778[/C][C]2.17371857969287[/C][C]872.355462888719[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 24 )[/C][C]1896.32138888889[/C][C]2.15364907881425[/C][C]880.515496950397[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 24 )[/C][C]1896.46583333333[/C][C]2.12718479925647[/C][C]891.537883307654[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 24 )[/C][C]1896.43458333333[/C][C]2.12203372955155[/C][C]893.687294845264[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 24 )[/C][C]1896.46097222222[/C][C]2.09309320599997[/C][C]906.056627954222[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 24 )[/C][C]1896.62444444444[/C][C]2.06598085971551[/C][C]918.026145075522[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 24 )[/C][C]1897.10944444444[/C][C]1.98802556646788[/C][C]954.268132383747[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 24 )[/C][C]1896.5425[/C][C]1.87246690393663[/C][C]1012.85768843912[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 24 )[/C][C]1896.46666666667[/C][C]1.8608111231379[/C][C]1019.16129105497[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 24 )[/C][C]1896.4[/C][C]1.85064761536174[/C][C]1024.72236435423[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 24 )[/C][C]1896.47111111111[/C][C]1.83143589984066[/C][C]1035.51050368517[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 24 )[/C][C]1896.28694444444[/C][C]1.77633372095995[/C][C]1067.5285404252[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 24 )[/C][C]1895.70444444444[/C][C]1.68331423882733[/C][C]1126.17383060044[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 24 )[/C][C]1894.96027777778[/C][C]1.48901536050746[/C][C]1272.62641342529[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 24 )[/C][C]1894.11583333333[/C][C]1.37108526160883[/C][C]1381.47195245231[/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]1895.57757142857[/C][C]2.33701421086152[/C][C]811.110845034092[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 24 )[/C][C]1895.92014705882[/C][C]2.25316691078576[/C][C]841.44682667901[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 24 )[/C][C]1896.13106060606[/C][C]2.20404397479586[/C][C]860.29638350645[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 24 )[/C][C]1896.265625[/C][C]2.17098702585222[/C][C]873.457833888079[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 24 )[/C][C]1896.39258064516[/C][C]2.13464299988014[/C][C]888.388634891945[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 24 )[/C][C]1896.48033333333[/C][C]2.10229321879175[/C][C]902.100770901642[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 24 )[/C][C]1896.52689655172[/C][C]2.07443325603658[/C][C]914.238571442511[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 24 )[/C][C]1896.56464285714[/C][C]2.04425609567243[/C][C]927.752959559255[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 24 )[/C][C]1896.58111111111[/C][C]2.01224871979562[/C][C]942.518234676149[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 24 )[/C][C]1896.60365384615[/C][C]1.97250742014762[/C][C]961.51914789969[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 24 )[/C][C]1896.6242[/C][C]1.92835391556464[/C][C]983.545699101949[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 24 )[/C][C]1896.62416666667[/C][C]1.87781492795863[/C][C]1010.01655617281[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 24 )[/C][C]1896.56086956522[/C][C]1.83006979160195[/C][C]1036.33253675264[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 24 )[/C][C]1896.56318181818[/C][C]1.79371099408724[/C][C]1057.34044562919[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 24 )[/C][C]1896.575[/C][C]1.74735965575222[/C][C]1085.39475187983[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 24 )[/C][C]1896.596[/C][C]1.68721990268014[/C][C]1124.09532212562[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 24 )[/C][C]1896.61078947368[/C][C]1.61048566142591[/C][C]1177.66387798476[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 24 )[/C][C]1896.64888888889[/C][C]1.52020016318746[/C][C]1247.63102571448[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 24 )[/C][C]1896.76[/C][C]1.42079237765134[/C][C]1335.00153142394[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 24 )[/C][C]1896.973125[/C][C]1.33722709286159[/C][C]1418.58711592553[/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]1883.48[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]1896.11162162162[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]1896.64888888889[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]1896.11162162162[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]1896.64888888889[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]1896.64888888889[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]1896.11162162162[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]1896.64888888889[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]1896.61078947368[/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=282080&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=282080&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 Mean1895.241527777782.41157046976904785.895146559532
Geometric Mean1895.13223658938
Harmonic Mean1895.02258885955
Quadratic Mean1895.35045871066
Winsorized Mean ( 1 / 24 )1895.254027777782.40687904382439787.432186357952
Winsorized Mean ( 2 / 24 )1895.533472222222.327479470801814.414690227054
Winsorized Mean ( 3 / 24 )1895.772222222222.26978294156256835.221812406934
Winsorized Mean ( 4 / 24 )1895.828333333332.25810437486006839.566299255243
Winsorized Mean ( 5 / 24 )1896.026944444442.21855290249685854.623273716206
Winsorized Mean ( 6 / 24 )1896.255277777782.17371857969287872.355462888719
Winsorized Mean ( 7 / 24 )1896.321388888892.15364907881425880.515496950397
Winsorized Mean ( 8 / 24 )1896.465833333332.12718479925647891.537883307654
Winsorized Mean ( 9 / 24 )1896.434583333332.12203372955155893.687294845264
Winsorized Mean ( 10 / 24 )1896.460972222222.09309320599997906.056627954222
Winsorized Mean ( 11 / 24 )1896.624444444442.06598085971551918.026145075522
Winsorized Mean ( 12 / 24 )1897.109444444441.98802556646788954.268132383747
Winsorized Mean ( 13 / 24 )1896.54251.872466903936631012.85768843912
Winsorized Mean ( 14 / 24 )1896.466666666671.86081112313791019.16129105497
Winsorized Mean ( 15 / 24 )1896.41.850647615361741024.72236435423
Winsorized Mean ( 16 / 24 )1896.471111111111.831435899840661035.51050368517
Winsorized Mean ( 17 / 24 )1896.286944444441.776333720959951067.5285404252
Winsorized Mean ( 18 / 24 )1895.704444444441.683314238827331126.17383060044
Winsorized Mean ( 19 / 24 )1894.960277777781.489015360507461272.62641342529
Winsorized Mean ( 20 / 24 )1894.115833333331.371085261608831381.47195245231
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 )1895.577571428572.33701421086152811.110845034092
Trimmed Mean ( 2 / 24 )1895.920147058822.25316691078576841.44682667901
Trimmed Mean ( 3 / 24 )1896.131060606062.20404397479586860.29638350645
Trimmed Mean ( 4 / 24 )1896.2656252.17098702585222873.457833888079
Trimmed Mean ( 5 / 24 )1896.392580645162.13464299988014888.388634891945
Trimmed Mean ( 6 / 24 )1896.480333333332.10229321879175902.100770901642
Trimmed Mean ( 7 / 24 )1896.526896551722.07443325603658914.238571442511
Trimmed Mean ( 8 / 24 )1896.564642857142.04425609567243927.752959559255
Trimmed Mean ( 9 / 24 )1896.581111111112.01224871979562942.518234676149
Trimmed Mean ( 10 / 24 )1896.603653846151.97250742014762961.51914789969
Trimmed Mean ( 11 / 24 )1896.62421.92835391556464983.545699101949
Trimmed Mean ( 12 / 24 )1896.624166666671.877814927958631010.01655617281
Trimmed Mean ( 13 / 24 )1896.560869565221.830069791601951036.33253675264
Trimmed Mean ( 14 / 24 )1896.563181818181.793710994087241057.34044562919
Trimmed Mean ( 15 / 24 )1896.5751.747359655752221085.39475187983
Trimmed Mean ( 16 / 24 )1896.5961.687219902680141124.09532212562
Trimmed Mean ( 17 / 24 )1896.610789473681.610485661425911177.66387798476
Trimmed Mean ( 18 / 24 )1896.648888888891.520200163187461247.63102571448
Trimmed Mean ( 19 / 24 )1896.761.420792377651341335.00153142394
Trimmed Mean ( 20 / 24 )1896.9731251.337227092861591418.58711592553
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
Midrange1883.48
Midmean - Weighted Average at Xnp1896.11162162162
Midmean - Weighted Average at X(n+1)p1896.64888888889
Midmean - Empirical Distribution Function1896.11162162162
Midmean - Empirical Distribution Function - Averaging1896.64888888889
Midmean - Empirical Distribution Function - Interpolation1896.64888888889
Midmean - Closest Observation1896.11162162162
Midmean - True Basic - Statistics Graphics Toolkit1896.64888888889
Midmean - MS Excel (old versions)1896.61078947368
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')