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of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationWed, 07 Mar 2012 16:12:56 -0500
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2012/Mar/07/t1331154865uhsmivcmp8d32tb.htm/, Retrieved Mon, 29 Apr 2024 05:43:41 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=163714, Retrieved Mon, 29 Apr 2024 05:43:41 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact128
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [Robuustheid gemid...] [2012-03-07 21:12:56] [f04aaaaa8bc197d3d2d83dbea45e225d] [Current]
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Dataseries X:
530.3
527.76
521.41
1601.93
1577.49
1551.43
1551.43
1516.88
1485.95
1438.22
1385.06
1329.49
1329.49
1276.16
1242.34
1181.59
1160.21
1135.18
1135.18
1084.96
1077.35
1061.13
1029.98
1013.08
1013.08
996.04
975.02
951.89
944.4
932.47
932.47
920.44
900.18
886.9
869.74
859.03
859.03
844.99
834.82
825.62
816.92
813.21
813.21
811.03
804.16
788.62
778.76
765.91
765.91
753.85
742.22
732.11
729.94
731.22
731.22
729.11
726.94
720.52
709.36
703.21




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Herman Ole Andreas Wold' @ wold.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 & 'Herman Ole Andreas Wold' @ wold.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=163714&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]'Herman Ole Andreas Wold' @ wold.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=163714&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=163714&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'Herman Ole Andreas Wold' @ wold.wessa.net







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean974.292536.142381804761926.9570640159535
Geometric Mean937.531647102299
Harmonic Mean903.480549405159
Quadratic Mean1013.07250951993
Winsorized Mean ( 1 / 20 )973.99136.002211531804427.053643611298
Winsorized Mean ( 2 / 20 )973.20735.741916714306627.2287300029002
Winsorized Mean ( 3 / 20 )981.852534.230880055256328.6832385967019
Winsorized Mean ( 4 / 20 )979.95916666666733.537131517348929.2201247491822
Winsorized Mean ( 5 / 20 )978.31166666666732.722732860889329.8970037382165
Winsorized Mean ( 6 / 20 )974.18066666666731.411379036693331.0136229781148
Winsorized Mean ( 7 / 20 )968.23183333333329.866238021059932.4189418382923
Winsorized Mean ( 8 / 20 )960.93316666666728.151025184783834.1349261832948
Winsorized Mean ( 9 / 20 )961.12516666666728.124372818108534.1741013349043
Winsorized Mean ( 10 / 20 )952.23683333333326.204720085769736.3383707292657
Winsorized Mean ( 11 / 20 )946.19966666666724.906250888711737.9904495017962
Winsorized Mean ( 12 / 20 )936.07166666666722.244004520950442.0819761021463
Winsorized Mean ( 13 / 20 )933.95916666666721.018650910992744.4347817860284
Winsorized Mean ( 14 / 20 )930.93283333333319.562929407704547.586576321576
Winsorized Mean ( 15 / 20 )930.93283333333319.562929407704547.586576321576
Winsorized Mean ( 16 / 20 )920.967516.771415682348154.9129255063015
Winsorized Mean ( 17 / 20 )921.60516.017648741768857.5368466906602
Winsorized Mean ( 18 / 20 )921.40114.574768716754763.2189105643085
Winsorized Mean ( 19 / 20 )913.71233333333312.708846583763771.8957717611175
Winsorized Mean ( 20 / 20 )908.80566666666711.747991890831577.3583838933295
Trimmed Mean ( 1 / 20 )971.27948275862134.890911619462927.8376069204457
Trimmed Mean ( 2 / 20 )968.37428571428633.516669321299228.8923185186215
Trimmed Mean ( 3 / 20 )965.68944444444431.983783665621830.1930958056857
Trimmed Mean ( 4 / 20 )959.47288461538530.787314787674131.1645523889442
Trimmed Mean ( 5 / 20 )953.32729.544664683927532.2673149348219
Trimmed Mean ( 6 / 20 )947.08083333333328.237331681962133.5400258069825
Trimmed Mean ( 7 / 20 )941.18956521739126.986652777099734.8761134991912
Trimmed Mean ( 8 / 20 )935.92159090909125.850426029226636.2052675592633
Trimmed Mean ( 9 / 20 )931.45523809523824.882491613136937.4341626464558
Trimmed Mean ( 10 / 20 )926.5102523.570031590243239.3088251262051
Trimmed Mean ( 11 / 20 )922.44815789473722.402501180769441.1761236145621
Trimmed Mean ( 12 / 20 )918.84944444444421.205840831903143.3300170329527
Trimmed Mean ( 13 / 20 )916.31676470588220.383091966047844.9547480937728
Trimmed Mean ( 14 / 20 )913.772187519.573869486647746.6832676146803
Trimmed Mean ( 15 / 20 )911.32066666666718.846211582680448.3556423352567
Trimmed Mean ( 16 / 20 )908.51892857142917.725466519030551.2550080188874
Trimmed Mean ( 17 / 20 )906.72346153846117.073444426876353.1072371144475
Trimmed Mean ( 18 / 20 )904.53516.279924509314755.5613755753267
Trimmed Mean ( 19 / 20 )901.97954545454515.539297878655658.0450643586338
Trimmed Mean ( 20 / 20 )900.12715.116604935946259.5455794349405
Median893.54
Midrange1061.67
Midmean - Weighted Average at Xnp913.7721875
Midmean - Weighted Average at X(n+1)p913.7721875
Midmean - Empirical Distribution Function913.7721875
Midmean - Empirical Distribution Function - Averaging913.7721875
Midmean - Empirical Distribution Function - Interpolation913.7721875
Midmean - Closest Observation913.7721875
Midmean - True Basic - Statistics Graphics Toolkit913.7721875
Midmean - MS Excel (old versions)913.7721875
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 974.2925 & 36.1423818047619 & 26.9570640159535 \tabularnewline
Geometric Mean & 937.531647102299 &  &  \tabularnewline
Harmonic Mean & 903.480549405159 &  &  \tabularnewline
Quadratic Mean & 1013.07250951993 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 973.991 & 36.0022115318044 & 27.053643611298 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 973.207 & 35.7419167143066 & 27.2287300029002 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 981.8525 & 34.2308800552563 & 28.6832385967019 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 979.959166666667 & 33.5371315173489 & 29.2201247491822 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 978.311666666667 & 32.7227328608893 & 29.8970037382165 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 974.180666666667 & 31.4113790366933 & 31.0136229781148 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 968.231833333333 & 29.8662380210599 & 32.4189418382923 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 960.933166666667 & 28.1510251847838 & 34.1349261832948 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 961.125166666667 & 28.1243728181085 & 34.1741013349043 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 952.236833333333 & 26.2047200857697 & 36.3383707292657 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 946.199666666667 & 24.9062508887117 & 37.9904495017962 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 936.071666666667 & 22.2440045209504 & 42.0819761021463 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 933.959166666667 & 21.0186509109927 & 44.4347817860284 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 930.932833333333 & 19.5629294077045 & 47.586576321576 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 930.932833333333 & 19.5629294077045 & 47.586576321576 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 920.9675 & 16.7714156823481 & 54.9129255063015 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 921.605 & 16.0176487417688 & 57.5368466906602 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 921.401 & 14.5747687167547 & 63.2189105643085 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 913.712333333333 & 12.7088465837637 & 71.8957717611175 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 908.805666666667 & 11.7479918908315 & 77.3583838933295 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 971.279482758621 & 34.8909116194629 & 27.8376069204457 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 968.374285714286 & 33.5166693212992 & 28.8923185186215 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 965.689444444444 & 31.9837836656218 & 30.1930958056857 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 959.472884615385 & 30.7873147876741 & 31.1645523889442 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 953.327 & 29.5446646839275 & 32.2673149348219 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 947.080833333333 & 28.2373316819621 & 33.5400258069825 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 941.189565217391 & 26.9866527770997 & 34.8761134991912 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 935.921590909091 & 25.8504260292266 & 36.2052675592633 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 931.455238095238 & 24.8824916131369 & 37.4341626464558 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 926.51025 & 23.5700315902432 & 39.3088251262051 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 922.448157894737 & 22.4025011807694 & 41.1761236145621 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 918.849444444444 & 21.2058408319031 & 43.3300170329527 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 916.316764705882 & 20.3830919660478 & 44.9547480937728 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 913.7721875 & 19.5738694866477 & 46.6832676146803 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 911.320666666667 & 18.8462115826804 & 48.3556423352567 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 908.518928571429 & 17.7254665190305 & 51.2550080188874 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 906.723461538461 & 17.0734444268763 & 53.1072371144475 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 904.535 & 16.2799245093147 & 55.5613755753267 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 901.979545454545 & 15.5392978786556 & 58.0450643586338 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 900.127 & 15.1166049359462 & 59.5455794349405 \tabularnewline
Median & 893.54 &  &  \tabularnewline
Midrange & 1061.67 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 913.7721875 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 913.7721875 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 913.7721875 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 913.7721875 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 913.7721875 &  &  \tabularnewline
Midmean - Closest Observation & 913.7721875 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 913.7721875 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 913.7721875 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=163714&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]974.2925[/C][C]36.1423818047619[/C][C]26.9570640159535[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]937.531647102299[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]903.480549405159[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]1013.07250951993[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]973.991[/C][C]36.0022115318044[/C][C]27.053643611298[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]973.207[/C][C]35.7419167143066[/C][C]27.2287300029002[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]981.8525[/C][C]34.2308800552563[/C][C]28.6832385967019[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]979.959166666667[/C][C]33.5371315173489[/C][C]29.2201247491822[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]978.311666666667[/C][C]32.7227328608893[/C][C]29.8970037382165[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]974.180666666667[/C][C]31.4113790366933[/C][C]31.0136229781148[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]968.231833333333[/C][C]29.8662380210599[/C][C]32.4189418382923[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]960.933166666667[/C][C]28.1510251847838[/C][C]34.1349261832948[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]961.125166666667[/C][C]28.1243728181085[/C][C]34.1741013349043[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]952.236833333333[/C][C]26.2047200857697[/C][C]36.3383707292657[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]946.199666666667[/C][C]24.9062508887117[/C][C]37.9904495017962[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]936.071666666667[/C][C]22.2440045209504[/C][C]42.0819761021463[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]933.959166666667[/C][C]21.0186509109927[/C][C]44.4347817860284[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]930.932833333333[/C][C]19.5629294077045[/C][C]47.586576321576[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]930.932833333333[/C][C]19.5629294077045[/C][C]47.586576321576[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]920.9675[/C][C]16.7714156823481[/C][C]54.9129255063015[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]921.605[/C][C]16.0176487417688[/C][C]57.5368466906602[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]921.401[/C][C]14.5747687167547[/C][C]63.2189105643085[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]913.712333333333[/C][C]12.7088465837637[/C][C]71.8957717611175[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]908.805666666667[/C][C]11.7479918908315[/C][C]77.3583838933295[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]971.279482758621[/C][C]34.8909116194629[/C][C]27.8376069204457[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]968.374285714286[/C][C]33.5166693212992[/C][C]28.8923185186215[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]965.689444444444[/C][C]31.9837836656218[/C][C]30.1930958056857[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]959.472884615385[/C][C]30.7873147876741[/C][C]31.1645523889442[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]953.327[/C][C]29.5446646839275[/C][C]32.2673149348219[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]947.080833333333[/C][C]28.2373316819621[/C][C]33.5400258069825[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]941.189565217391[/C][C]26.9866527770997[/C][C]34.8761134991912[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]935.921590909091[/C][C]25.8504260292266[/C][C]36.2052675592633[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]931.455238095238[/C][C]24.8824916131369[/C][C]37.4341626464558[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]926.51025[/C][C]23.5700315902432[/C][C]39.3088251262051[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]922.448157894737[/C][C]22.4025011807694[/C][C]41.1761236145621[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]918.849444444444[/C][C]21.2058408319031[/C][C]43.3300170329527[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]916.316764705882[/C][C]20.3830919660478[/C][C]44.9547480937728[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]913.7721875[/C][C]19.5738694866477[/C][C]46.6832676146803[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]911.320666666667[/C][C]18.8462115826804[/C][C]48.3556423352567[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]908.518928571429[/C][C]17.7254665190305[/C][C]51.2550080188874[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]906.723461538461[/C][C]17.0734444268763[/C][C]53.1072371144475[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]904.535[/C][C]16.2799245093147[/C][C]55.5613755753267[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]901.979545454545[/C][C]15.5392978786556[/C][C]58.0450643586338[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]900.127[/C][C]15.1166049359462[/C][C]59.5455794349405[/C][/ROW]
[ROW][C]Median[/C][C]893.54[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]1061.67[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]913.7721875[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]913.7721875[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]913.7721875[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]913.7721875[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]913.7721875[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]913.7721875[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]913.7721875[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]913.7721875[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]60[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=163714&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=163714&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 Mean974.292536.142381804761926.9570640159535
Geometric Mean937.531647102299
Harmonic Mean903.480549405159
Quadratic Mean1013.07250951993
Winsorized Mean ( 1 / 20 )973.99136.002211531804427.053643611298
Winsorized Mean ( 2 / 20 )973.20735.741916714306627.2287300029002
Winsorized Mean ( 3 / 20 )981.852534.230880055256328.6832385967019
Winsorized Mean ( 4 / 20 )979.95916666666733.537131517348929.2201247491822
Winsorized Mean ( 5 / 20 )978.31166666666732.722732860889329.8970037382165
Winsorized Mean ( 6 / 20 )974.18066666666731.411379036693331.0136229781148
Winsorized Mean ( 7 / 20 )968.23183333333329.866238021059932.4189418382923
Winsorized Mean ( 8 / 20 )960.93316666666728.151025184783834.1349261832948
Winsorized Mean ( 9 / 20 )961.12516666666728.124372818108534.1741013349043
Winsorized Mean ( 10 / 20 )952.23683333333326.204720085769736.3383707292657
Winsorized Mean ( 11 / 20 )946.19966666666724.906250888711737.9904495017962
Winsorized Mean ( 12 / 20 )936.07166666666722.244004520950442.0819761021463
Winsorized Mean ( 13 / 20 )933.95916666666721.018650910992744.4347817860284
Winsorized Mean ( 14 / 20 )930.93283333333319.562929407704547.586576321576
Winsorized Mean ( 15 / 20 )930.93283333333319.562929407704547.586576321576
Winsorized Mean ( 16 / 20 )920.967516.771415682348154.9129255063015
Winsorized Mean ( 17 / 20 )921.60516.017648741768857.5368466906602
Winsorized Mean ( 18 / 20 )921.40114.574768716754763.2189105643085
Winsorized Mean ( 19 / 20 )913.71233333333312.708846583763771.8957717611175
Winsorized Mean ( 20 / 20 )908.80566666666711.747991890831577.3583838933295
Trimmed Mean ( 1 / 20 )971.27948275862134.890911619462927.8376069204457
Trimmed Mean ( 2 / 20 )968.37428571428633.516669321299228.8923185186215
Trimmed Mean ( 3 / 20 )965.68944444444431.983783665621830.1930958056857
Trimmed Mean ( 4 / 20 )959.47288461538530.787314787674131.1645523889442
Trimmed Mean ( 5 / 20 )953.32729.544664683927532.2673149348219
Trimmed Mean ( 6 / 20 )947.08083333333328.237331681962133.5400258069825
Trimmed Mean ( 7 / 20 )941.18956521739126.986652777099734.8761134991912
Trimmed Mean ( 8 / 20 )935.92159090909125.850426029226636.2052675592633
Trimmed Mean ( 9 / 20 )931.45523809523824.882491613136937.4341626464558
Trimmed Mean ( 10 / 20 )926.5102523.570031590243239.3088251262051
Trimmed Mean ( 11 / 20 )922.44815789473722.402501180769441.1761236145621
Trimmed Mean ( 12 / 20 )918.84944444444421.205840831903143.3300170329527
Trimmed Mean ( 13 / 20 )916.31676470588220.383091966047844.9547480937728
Trimmed Mean ( 14 / 20 )913.772187519.573869486647746.6832676146803
Trimmed Mean ( 15 / 20 )911.32066666666718.846211582680448.3556423352567
Trimmed Mean ( 16 / 20 )908.51892857142917.725466519030551.2550080188874
Trimmed Mean ( 17 / 20 )906.72346153846117.073444426876353.1072371144475
Trimmed Mean ( 18 / 20 )904.53516.279924509314755.5613755753267
Trimmed Mean ( 19 / 20 )901.97954545454515.539297878655658.0450643586338
Trimmed Mean ( 20 / 20 )900.12715.116604935946259.5455794349405
Median893.54
Midrange1061.67
Midmean - Weighted Average at Xnp913.7721875
Midmean - Weighted Average at X(n+1)p913.7721875
Midmean - Empirical Distribution Function913.7721875
Midmean - Empirical Distribution Function - Averaging913.7721875
Midmean - Empirical Distribution Function - Interpolation913.7721875
Midmean - Closest Observation913.7721875
Midmean - True Basic - Statistics Graphics Toolkit913.7721875
Midmean - MS Excel (old versions)913.7721875
Number of observations60



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')