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Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationThu, 10 Oct 2013 06:55:06 -0400
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2013/Oct/10/t1381402524ihgwbh6fpwfb6v8.htm/, Retrieved Thu, 02 May 2024 21:08:36 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=214544, Retrieved Thu, 02 May 2024 21:08:36 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact112
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [Motorfietsen en s...] [2013-10-10 10:55:06] [3d5e85e1419377f0daeb0f510d27f47a] [Current]
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Dataseries X:
1876,88
1876,68
1865,52
1858,99
1856,87
1858,22
1858,22
1859,32
1859,52
1852,48
1850,07
1850,07
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




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 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 & 3 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=214544&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]'Gwilym Jenkins' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=214544&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=214544&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'Gwilym Jenkins' @ jenkins.wessa.net







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean1884.237222222223.48507167477718540.659532444966
Geometric Mean1884.00806901249
Harmonic Mean1883.77862291714
Quadratic Mean1884.46604003701
Winsorized Mean ( 1 / 24 )1884.251388888893.4818592940281541.162416333324
Winsorized Mean ( 2 / 24 )1884.240833333333.4798729287932541.46828688563
Winsorized Mean ( 3 / 24 )1884.275833333333.47066301314064542.915237290131
Winsorized Mean ( 4 / 24 )1884.275833333333.47066301314064542.915237290131
Winsorized Mean ( 5 / 24 )1884.275833333333.47066301314064542.915237290132
Winsorized Mean ( 6 / 24 )1884.288333333333.46641850299003543.583624339646
Winsorized Mean ( 7 / 24 )1884.371944444443.44474671281496547.027721206411
Winsorized Mean ( 8 / 24 )1884.403055555563.43822020276638548.075150637348
Winsorized Mean ( 9 / 24 )1884.371805555563.43348969700908548.821162095531
Winsorized Mean ( 10 / 24 )1884.298194444443.42242314978911550.574289611311
Winsorized Mean ( 11 / 24 )1884.400555555563.40566496146769553.313545776229
Winsorized Mean ( 12 / 24 )1884.462222222223.39460038086714555.135217931261
Winsorized Mean ( 13 / 24 )1884.662638888893.16606008517717595.270648119561
Winsorized Mean ( 14 / 24 )1884.586805555563.15516164792022597.302774264455
Winsorized Mean ( 15 / 24 )1884.520138888893.14563411515489599.090698377709
Winsorized Mean ( 16 / 24 )1885.029027777783.06038490986775615.945079881875
Winsorized Mean ( 17 / 24 )1885.791666666672.86969766201276657.139492995928
Winsorized Mean ( 18 / 24 )1885.519166666672.73555764263837689.263182496179
Winsorized Mean ( 19 / 24 )1884.458333333332.59172677043359727.105324076298
Winsorized Mean ( 20 / 24 )1883.769444444442.44570658659271770.235258297626
Winsorized Mean ( 21 / 24 )1883.865694444442.43199791983805774.616490860278
Winsorized Mean ( 22 / 24 )1883.902361111112.42027547040073778.38344607905
Winsorized Mean ( 23 / 24 )1884.589166666672.30948126360965816.022713135639
Winsorized Mean ( 24 / 24 )1884.639166666672.22719506070291846.194031191804
Trimmed Mean ( 1 / 24 )1884.315428571433.48585361599145540.560687897816
Trimmed Mean ( 2 / 24 )1884.383235294123.48725295361189540.363220093451
Trimmed Mean ( 3 / 24 )1884.460909090913.48673032781341540.466492076744
Trimmed Mean ( 4 / 24 )1884.53031253.48654671337715540.514861100082
Trimmed Mean ( 5 / 24 )1884.604193548393.48262381975581541.144921497874
Trimmed Mean ( 6 / 24 )1884.6833.47417850550826542.483063841384
Trimmed Mean ( 7 / 24 )1884.764655172413.46134201998028544.518468354986
Trimmed Mean ( 8 / 24 )1884.836785714293.44716935548558546.778121798654
Trimmed Mean ( 9 / 24 )1884.909074074073.42732731956725549.96470961871
Trimmed Mean ( 10 / 24 )1884.991730769233.39990287680855554.42517009152
Trimmed Mean ( 11 / 24 )1885.09163.36423373159719560.333124983276
Trimmed Mean ( 12 / 24 )1885.185833333333.31932301898648567.942867431129
Trimmed Mean ( 13 / 24 )1885.28021739133.26119612165189578.094707299098
Trimmed Mean ( 14 / 24 )1885.357954545453.23209515138481583.323777995106
Trimmed Mean ( 15 / 24 )1885.452380952383.19134081407522590.802578225648
Trimmed Mean ( 16 / 24 )1885.564253.13482134377253601.490178617599
Trimmed Mean ( 17 / 24 )1885.627631578953.07499455721709613.213323305998
Trimmed Mean ( 18 / 24 )1885.608333333333.034210352022621.449443041009
Trimmed Mean ( 19 / 24 )1885.618823529413.0031577784975627.878707216241
Trimmed Mean ( 20 / 24 )1885.756252.98499529738377631.745132614712
Trimmed Mean ( 21 / 24 )1885.994666666672.98195314121441632.469585319705
Trimmed Mean ( 22 / 24 )1886.255357142862.96523830792554636.12268602535
Trimmed Mean ( 23 / 24 )1886.551538461542.92676159667763644.586679216747
Trimmed Mean ( 24 / 24 )1886.80752.89014957802072652.840778328212
Median1886.42
Midrange1881.5
Midmean - Weighted Average at Xnp1884.83162162162
Midmean - Weighted Average at X(n+1)p1885.60833333333
Midmean - Empirical Distribution Function1884.83162162162
Midmean - Empirical Distribution Function - Averaging1885.60833333333
Midmean - Empirical Distribution Function - Interpolation1885.60833333333
Midmean - Closest Observation1884.83162162162
Midmean - True Basic - Statistics Graphics Toolkit1885.60833333333
Midmean - MS Excel (old versions)1885.62763157895
Number of observations72

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 1884.23722222222 & 3.48507167477718 & 540.659532444966 \tabularnewline
Geometric Mean & 1884.00806901249 &  &  \tabularnewline
Harmonic Mean & 1883.77862291714 &  &  \tabularnewline
Quadratic Mean & 1884.46604003701 &  &  \tabularnewline
Winsorized Mean ( 1 / 24 ) & 1884.25138888889 & 3.4818592940281 & 541.162416333324 \tabularnewline
Winsorized Mean ( 2 / 24 ) & 1884.24083333333 & 3.4798729287932 & 541.46828688563 \tabularnewline
Winsorized Mean ( 3 / 24 ) & 1884.27583333333 & 3.47066301314064 & 542.915237290131 \tabularnewline
Winsorized Mean ( 4 / 24 ) & 1884.27583333333 & 3.47066301314064 & 542.915237290131 \tabularnewline
Winsorized Mean ( 5 / 24 ) & 1884.27583333333 & 3.47066301314064 & 542.915237290132 \tabularnewline
Winsorized Mean ( 6 / 24 ) & 1884.28833333333 & 3.46641850299003 & 543.583624339646 \tabularnewline
Winsorized Mean ( 7 / 24 ) & 1884.37194444444 & 3.44474671281496 & 547.027721206411 \tabularnewline
Winsorized Mean ( 8 / 24 ) & 1884.40305555556 & 3.43822020276638 & 548.075150637348 \tabularnewline
Winsorized Mean ( 9 / 24 ) & 1884.37180555556 & 3.43348969700908 & 548.821162095531 \tabularnewline
Winsorized Mean ( 10 / 24 ) & 1884.29819444444 & 3.42242314978911 & 550.574289611311 \tabularnewline
Winsorized Mean ( 11 / 24 ) & 1884.40055555556 & 3.40566496146769 & 553.313545776229 \tabularnewline
Winsorized Mean ( 12 / 24 ) & 1884.46222222222 & 3.39460038086714 & 555.135217931261 \tabularnewline
Winsorized Mean ( 13 / 24 ) & 1884.66263888889 & 3.16606008517717 & 595.270648119561 \tabularnewline
Winsorized Mean ( 14 / 24 ) & 1884.58680555556 & 3.15516164792022 & 597.302774264455 \tabularnewline
Winsorized Mean ( 15 / 24 ) & 1884.52013888889 & 3.14563411515489 & 599.090698377709 \tabularnewline
Winsorized Mean ( 16 / 24 ) & 1885.02902777778 & 3.06038490986775 & 615.945079881875 \tabularnewline
Winsorized Mean ( 17 / 24 ) & 1885.79166666667 & 2.86969766201276 & 657.139492995928 \tabularnewline
Winsorized Mean ( 18 / 24 ) & 1885.51916666667 & 2.73555764263837 & 689.263182496179 \tabularnewline
Winsorized Mean ( 19 / 24 ) & 1884.45833333333 & 2.59172677043359 & 727.105324076298 \tabularnewline
Winsorized Mean ( 20 / 24 ) & 1883.76944444444 & 2.44570658659271 & 770.235258297626 \tabularnewline
Winsorized Mean ( 21 / 24 ) & 1883.86569444444 & 2.43199791983805 & 774.616490860278 \tabularnewline
Winsorized Mean ( 22 / 24 ) & 1883.90236111111 & 2.42027547040073 & 778.38344607905 \tabularnewline
Winsorized Mean ( 23 / 24 ) & 1884.58916666667 & 2.30948126360965 & 816.022713135639 \tabularnewline
Winsorized Mean ( 24 / 24 ) & 1884.63916666667 & 2.22719506070291 & 846.194031191804 \tabularnewline
Trimmed Mean ( 1 / 24 ) & 1884.31542857143 & 3.48585361599145 & 540.560687897816 \tabularnewline
Trimmed Mean ( 2 / 24 ) & 1884.38323529412 & 3.48725295361189 & 540.363220093451 \tabularnewline
Trimmed Mean ( 3 / 24 ) & 1884.46090909091 & 3.48673032781341 & 540.466492076744 \tabularnewline
Trimmed Mean ( 4 / 24 ) & 1884.5303125 & 3.48654671337715 & 540.514861100082 \tabularnewline
Trimmed Mean ( 5 / 24 ) & 1884.60419354839 & 3.48262381975581 & 541.144921497874 \tabularnewline
Trimmed Mean ( 6 / 24 ) & 1884.683 & 3.47417850550826 & 542.483063841384 \tabularnewline
Trimmed Mean ( 7 / 24 ) & 1884.76465517241 & 3.46134201998028 & 544.518468354986 \tabularnewline
Trimmed Mean ( 8 / 24 ) & 1884.83678571429 & 3.44716935548558 & 546.778121798654 \tabularnewline
Trimmed Mean ( 9 / 24 ) & 1884.90907407407 & 3.42732731956725 & 549.96470961871 \tabularnewline
Trimmed Mean ( 10 / 24 ) & 1884.99173076923 & 3.39990287680855 & 554.42517009152 \tabularnewline
Trimmed Mean ( 11 / 24 ) & 1885.0916 & 3.36423373159719 & 560.333124983276 \tabularnewline
Trimmed Mean ( 12 / 24 ) & 1885.18583333333 & 3.31932301898648 & 567.942867431129 \tabularnewline
Trimmed Mean ( 13 / 24 ) & 1885.2802173913 & 3.26119612165189 & 578.094707299098 \tabularnewline
Trimmed Mean ( 14 / 24 ) & 1885.35795454545 & 3.23209515138481 & 583.323777995106 \tabularnewline
Trimmed Mean ( 15 / 24 ) & 1885.45238095238 & 3.19134081407522 & 590.802578225648 \tabularnewline
Trimmed Mean ( 16 / 24 ) & 1885.56425 & 3.13482134377253 & 601.490178617599 \tabularnewline
Trimmed Mean ( 17 / 24 ) & 1885.62763157895 & 3.07499455721709 & 613.213323305998 \tabularnewline
Trimmed Mean ( 18 / 24 ) & 1885.60833333333 & 3.034210352022 & 621.449443041009 \tabularnewline
Trimmed Mean ( 19 / 24 ) & 1885.61882352941 & 3.0031577784975 & 627.878707216241 \tabularnewline
Trimmed Mean ( 20 / 24 ) & 1885.75625 & 2.98499529738377 & 631.745132614712 \tabularnewline
Trimmed Mean ( 21 / 24 ) & 1885.99466666667 & 2.98195314121441 & 632.469585319705 \tabularnewline
Trimmed Mean ( 22 / 24 ) & 1886.25535714286 & 2.96523830792554 & 636.12268602535 \tabularnewline
Trimmed Mean ( 23 / 24 ) & 1886.55153846154 & 2.92676159667763 & 644.586679216747 \tabularnewline
Trimmed Mean ( 24 / 24 ) & 1886.8075 & 2.89014957802072 & 652.840778328212 \tabularnewline
Median & 1886.42 &  &  \tabularnewline
Midrange & 1881.5 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 1884.83162162162 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 1885.60833333333 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 1884.83162162162 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 1885.60833333333 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 1885.60833333333 &  &  \tabularnewline
Midmean - Closest Observation & 1884.83162162162 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 1885.60833333333 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 1885.62763157895 &  &  \tabularnewline
Number of observations & 72 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=214544&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]1884.23722222222[/C][C]3.48507167477718[/C][C]540.659532444966[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]1884.00806901249[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]1883.77862291714[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]1884.46604003701[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 24 )[/C][C]1884.25138888889[/C][C]3.4818592940281[/C][C]541.162416333324[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 24 )[/C][C]1884.24083333333[/C][C]3.4798729287932[/C][C]541.46828688563[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 24 )[/C][C]1884.27583333333[/C][C]3.47066301314064[/C][C]542.915237290131[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 24 )[/C][C]1884.27583333333[/C][C]3.47066301314064[/C][C]542.915237290131[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 24 )[/C][C]1884.27583333333[/C][C]3.47066301314064[/C][C]542.915237290132[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 24 )[/C][C]1884.28833333333[/C][C]3.46641850299003[/C][C]543.583624339646[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 24 )[/C][C]1884.37194444444[/C][C]3.44474671281496[/C][C]547.027721206411[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 24 )[/C][C]1884.40305555556[/C][C]3.43822020276638[/C][C]548.075150637348[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 24 )[/C][C]1884.37180555556[/C][C]3.43348969700908[/C][C]548.821162095531[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 24 )[/C][C]1884.29819444444[/C][C]3.42242314978911[/C][C]550.574289611311[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 24 )[/C][C]1884.40055555556[/C][C]3.40566496146769[/C][C]553.313545776229[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 24 )[/C][C]1884.46222222222[/C][C]3.39460038086714[/C][C]555.135217931261[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 24 )[/C][C]1884.66263888889[/C][C]3.16606008517717[/C][C]595.270648119561[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 24 )[/C][C]1884.58680555556[/C][C]3.15516164792022[/C][C]597.302774264455[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 24 )[/C][C]1884.52013888889[/C][C]3.14563411515489[/C][C]599.090698377709[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 24 )[/C][C]1885.02902777778[/C][C]3.06038490986775[/C][C]615.945079881875[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 24 )[/C][C]1885.79166666667[/C][C]2.86969766201276[/C][C]657.139492995928[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 24 )[/C][C]1885.51916666667[/C][C]2.73555764263837[/C][C]689.263182496179[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 24 )[/C][C]1884.45833333333[/C][C]2.59172677043359[/C][C]727.105324076298[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 24 )[/C][C]1883.76944444444[/C][C]2.44570658659271[/C][C]770.235258297626[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 24 )[/C][C]1883.86569444444[/C][C]2.43199791983805[/C][C]774.616490860278[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 24 )[/C][C]1883.90236111111[/C][C]2.42027547040073[/C][C]778.38344607905[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 24 )[/C][C]1884.58916666667[/C][C]2.30948126360965[/C][C]816.022713135639[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 24 )[/C][C]1884.63916666667[/C][C]2.22719506070291[/C][C]846.194031191804[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 24 )[/C][C]1884.31542857143[/C][C]3.48585361599145[/C][C]540.560687897816[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 24 )[/C][C]1884.38323529412[/C][C]3.48725295361189[/C][C]540.363220093451[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 24 )[/C][C]1884.46090909091[/C][C]3.48673032781341[/C][C]540.466492076744[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 24 )[/C][C]1884.5303125[/C][C]3.48654671337715[/C][C]540.514861100082[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 24 )[/C][C]1884.60419354839[/C][C]3.48262381975581[/C][C]541.144921497874[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 24 )[/C][C]1884.683[/C][C]3.47417850550826[/C][C]542.483063841384[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 24 )[/C][C]1884.76465517241[/C][C]3.46134201998028[/C][C]544.518468354986[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 24 )[/C][C]1884.83678571429[/C][C]3.44716935548558[/C][C]546.778121798654[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 24 )[/C][C]1884.90907407407[/C][C]3.42732731956725[/C][C]549.96470961871[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 24 )[/C][C]1884.99173076923[/C][C]3.39990287680855[/C][C]554.42517009152[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 24 )[/C][C]1885.0916[/C][C]3.36423373159719[/C][C]560.333124983276[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 24 )[/C][C]1885.18583333333[/C][C]3.31932301898648[/C][C]567.942867431129[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 24 )[/C][C]1885.2802173913[/C][C]3.26119612165189[/C][C]578.094707299098[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 24 )[/C][C]1885.35795454545[/C][C]3.23209515138481[/C][C]583.323777995106[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 24 )[/C][C]1885.45238095238[/C][C]3.19134081407522[/C][C]590.802578225648[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 24 )[/C][C]1885.56425[/C][C]3.13482134377253[/C][C]601.490178617599[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 24 )[/C][C]1885.62763157895[/C][C]3.07499455721709[/C][C]613.213323305998[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 24 )[/C][C]1885.60833333333[/C][C]3.034210352022[/C][C]621.449443041009[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 24 )[/C][C]1885.61882352941[/C][C]3.0031577784975[/C][C]627.878707216241[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 24 )[/C][C]1885.75625[/C][C]2.98499529738377[/C][C]631.745132614712[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 24 )[/C][C]1885.99466666667[/C][C]2.98195314121441[/C][C]632.469585319705[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 24 )[/C][C]1886.25535714286[/C][C]2.96523830792554[/C][C]636.12268602535[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 24 )[/C][C]1886.55153846154[/C][C]2.92676159667763[/C][C]644.586679216747[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 24 )[/C][C]1886.8075[/C][C]2.89014957802072[/C][C]652.840778328212[/C][/ROW]
[ROW][C]Median[/C][C]1886.42[/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]1884.83162162162[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]1885.60833333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]1884.83162162162[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]1885.60833333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]1885.60833333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]1884.83162162162[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]1885.60833333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]1885.62763157895[/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=214544&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=214544&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 Mean1884.237222222223.48507167477718540.659532444966
Geometric Mean1884.00806901249
Harmonic Mean1883.77862291714
Quadratic Mean1884.46604003701
Winsorized Mean ( 1 / 24 )1884.251388888893.4818592940281541.162416333324
Winsorized Mean ( 2 / 24 )1884.240833333333.4798729287932541.46828688563
Winsorized Mean ( 3 / 24 )1884.275833333333.47066301314064542.915237290131
Winsorized Mean ( 4 / 24 )1884.275833333333.47066301314064542.915237290131
Winsorized Mean ( 5 / 24 )1884.275833333333.47066301314064542.915237290132
Winsorized Mean ( 6 / 24 )1884.288333333333.46641850299003543.583624339646
Winsorized Mean ( 7 / 24 )1884.371944444443.44474671281496547.027721206411
Winsorized Mean ( 8 / 24 )1884.403055555563.43822020276638548.075150637348
Winsorized Mean ( 9 / 24 )1884.371805555563.43348969700908548.821162095531
Winsorized Mean ( 10 / 24 )1884.298194444443.42242314978911550.574289611311
Winsorized Mean ( 11 / 24 )1884.400555555563.40566496146769553.313545776229
Winsorized Mean ( 12 / 24 )1884.462222222223.39460038086714555.135217931261
Winsorized Mean ( 13 / 24 )1884.662638888893.16606008517717595.270648119561
Winsorized Mean ( 14 / 24 )1884.586805555563.15516164792022597.302774264455
Winsorized Mean ( 15 / 24 )1884.520138888893.14563411515489599.090698377709
Winsorized Mean ( 16 / 24 )1885.029027777783.06038490986775615.945079881875
Winsorized Mean ( 17 / 24 )1885.791666666672.86969766201276657.139492995928
Winsorized Mean ( 18 / 24 )1885.519166666672.73555764263837689.263182496179
Winsorized Mean ( 19 / 24 )1884.458333333332.59172677043359727.105324076298
Winsorized Mean ( 20 / 24 )1883.769444444442.44570658659271770.235258297626
Winsorized Mean ( 21 / 24 )1883.865694444442.43199791983805774.616490860278
Winsorized Mean ( 22 / 24 )1883.902361111112.42027547040073778.38344607905
Winsorized Mean ( 23 / 24 )1884.589166666672.30948126360965816.022713135639
Winsorized Mean ( 24 / 24 )1884.639166666672.22719506070291846.194031191804
Trimmed Mean ( 1 / 24 )1884.315428571433.48585361599145540.560687897816
Trimmed Mean ( 2 / 24 )1884.383235294123.48725295361189540.363220093451
Trimmed Mean ( 3 / 24 )1884.460909090913.48673032781341540.466492076744
Trimmed Mean ( 4 / 24 )1884.53031253.48654671337715540.514861100082
Trimmed Mean ( 5 / 24 )1884.604193548393.48262381975581541.144921497874
Trimmed Mean ( 6 / 24 )1884.6833.47417850550826542.483063841384
Trimmed Mean ( 7 / 24 )1884.764655172413.46134201998028544.518468354986
Trimmed Mean ( 8 / 24 )1884.836785714293.44716935548558546.778121798654
Trimmed Mean ( 9 / 24 )1884.909074074073.42732731956725549.96470961871
Trimmed Mean ( 10 / 24 )1884.991730769233.39990287680855554.42517009152
Trimmed Mean ( 11 / 24 )1885.09163.36423373159719560.333124983276
Trimmed Mean ( 12 / 24 )1885.185833333333.31932301898648567.942867431129
Trimmed Mean ( 13 / 24 )1885.28021739133.26119612165189578.094707299098
Trimmed Mean ( 14 / 24 )1885.357954545453.23209515138481583.323777995106
Trimmed Mean ( 15 / 24 )1885.452380952383.19134081407522590.802578225648
Trimmed Mean ( 16 / 24 )1885.564253.13482134377253601.490178617599
Trimmed Mean ( 17 / 24 )1885.627631578953.07499455721709613.213323305998
Trimmed Mean ( 18 / 24 )1885.608333333333.034210352022621.449443041009
Trimmed Mean ( 19 / 24 )1885.618823529413.0031577784975627.878707216241
Trimmed Mean ( 20 / 24 )1885.756252.98499529738377631.745132614712
Trimmed Mean ( 21 / 24 )1885.994666666672.98195314121441632.469585319705
Trimmed Mean ( 22 / 24 )1886.255357142862.96523830792554636.12268602535
Trimmed Mean ( 23 / 24 )1886.551538461542.92676159667763644.586679216747
Trimmed Mean ( 24 / 24 )1886.80752.89014957802072652.840778328212
Median1886.42
Midrange1881.5
Midmean - Weighted Average at Xnp1884.83162162162
Midmean - Weighted Average at X(n+1)p1885.60833333333
Midmean - Empirical Distribution Function1884.83162162162
Midmean - Empirical Distribution Function - Averaging1885.60833333333
Midmean - Empirical Distribution Function - Interpolation1885.60833333333
Midmean - Closest Observation1884.83162162162
Midmean - True Basic - Statistics Graphics Toolkit1885.60833333333
Midmean - MS Excel (old versions)1885.62763157895
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')