Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationThu, 13 Oct 2016 17:57:33 +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/2016/Oct/13/t1476377954t00f23mfz4vu1oa.htm/, Retrieved Tue, 30 Apr 2024 19:44:18 +0200
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=, Retrieved Tue, 30 Apr 2024 19:44:18 +0200
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact0
Dataseries X:
102,54
101,29
101,49
101,71
101,98
102,11
102,11
103,13
103,43
103,8
103,99
104,03
104,03
102,58
102,65
102,81
102,98
103,12
103,12
104,33
104,41
104,66
104,81
104,9
100,15
98,74
98,74
98,96
99,34
99,4
99,5
100,5
100,77
101,08
101,39
101,43
101,43
101,29
101,33
101,15
101,25
101,13
101,07
101,33
101,61
101,29
101,39
101,46
101,81
101,78
101,93
102,01
102,03
102,14
101,81
101,52
101,38
101,5
101,65
101,64




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

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&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'Gertrude Mary Cox' @ cox.wessa.net







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean101.8823333333330.188007748167458541.904971079103
Geometric Mean101.872100531527
Harmonic Mean101.861869096943
Quadratic Mean101.892567507809
Winsorized Mean ( 1 / 20 )101.8808333333330.187605230985258543.059662026903
Winsorized Mean ( 2 / 20 )101.8831666666670.184278175204971552.877010819882
Winsorized Mean ( 3 / 20 )101.8896666666670.176277414691503578.007493727885
Winsorized Mean ( 4 / 20 )101.8883333333330.174021910216515585.491408562092
Winsorized Mean ( 5 / 20 )101.8716666666670.166276973796933612.662501249741
Winsorized Mean ( 6 / 20 )101.9366666666670.151877639321265671.17626480249
Winsorized Mean ( 7 / 20 )101.9728333333330.143128698687395712.455533156563
Winsorized Mean ( 8 / 20 )101.98350.131151102099528777.603072848038
Winsorized Mean ( 9 / 20 )101.9730.111834800482096911.818142120488
Winsorized Mean ( 10 / 20 )101.9246666666670.1010021722277641009.1334118718
Winsorized Mean ( 11 / 20 )101.9320.09935407207768661025.9468773489
Winsorized Mean ( 12 / 20 )101.9360.09881078190900491031.6283105003
Winsorized Mean ( 13 / 20 )101.9273333333330.08986803465907121134.18896629943
Winsorized Mean ( 14 / 20 )101.8970.08094159853178921258.8953251273
Winsorized Mean ( 15 / 20 )101.8570.07345020220115011386.74907553086
Winsorized Mean ( 16 / 20 )101.8383333333330.07006702467829831453.44166961432
Winsorized Mean ( 17 / 20 )101.8383333333330.06655194932208071530.20812118489
Winsorized Mean ( 18 / 20 )101.7183333333330.0463078416238212196.56822184969
Winsorized Mean ( 19 / 20 )101.7246666666670.04263527270163482385.92743099228
Winsorized Mean ( 20 / 20 )101.7280.04218053745642642411.72839737018
Trimmed Mean ( 1 / 20 )101.8844827586210.179185522424917568.597738142113
Trimmed Mean ( 2 / 20 )101.8883928571430.168742441251725603.810114997381
Trimmed Mean ( 3 / 20 )101.8912962962960.157994738100312644.903099441228
Trimmed Mean ( 4 / 20 )101.8919230769230.148635330330439685.516174723746
Trimmed Mean ( 5 / 20 )101.8930.137670487996906740.122312941102
Trimmed Mean ( 6 / 20 )101.8983333333330.12656934484453805.079092875918
Trimmed Mean ( 7 / 20 )101.890.117413345577949867.788916996297
Trimmed Mean ( 8 / 20 )101.8738636363640.108280924233025940.8292767905
Trimmed Mean ( 9 / 20 )101.8542857142860.100054075307961017.99237463127
Trimmed Mean ( 10 / 20 )101.83450.09515503543812481070.19559743865
Trimmed Mean ( 11 / 20 )101.8202631578950.09188130666917781108.17169290488
Trimmed Mean ( 12 / 20 )101.8033333333330.08771164878927631160.65921389657
Trimmed Mean ( 13 / 20 )101.7838235294120.08186878626828081243.25555769045
Trimmed Mean ( 14 / 20 )101.7631250.07640279178630811331.92940494403
Trimmed Mean ( 15 / 20 )101.7440.0715984973835781421.03540881483
Trimmed Mean ( 16 / 20 )101.7278571428570.06731501625532221511.22086574278
Trimmed Mean ( 17 / 20 )101.7119230769230.06203229737128721639.66074749961
Trimmed Mean ( 18 / 20 )101.6933333333330.05486038493985271853.67516915579
Trimmed Mean ( 19 / 20 )101.6895454545450.05364415894633311895.63127564882
Trimmed Mean ( 20 / 20 )101.6840.05272271057643321928.65652938285
Median101.645
Midrange101.82
Midmean - Weighted Average at Xnp101.72935483871
Midmean - Weighted Average at X(n+1)p101.72935483871
Midmean - Empirical Distribution Function101.72935483871
Midmean - Empirical Distribution Function - Averaging101.72935483871
Midmean - Empirical Distribution Function - Interpolation101.72935483871
Midmean - Closest Observation101.72935483871
Midmean - True Basic - Statistics Graphics Toolkit101.72935483871
Midmean - MS Excel (old versions)101.763125
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 101.882333333333 & 0.188007748167458 & 541.904971079103 \tabularnewline
Geometric Mean & 101.872100531527 &  &  \tabularnewline
Harmonic Mean & 101.861869096943 &  &  \tabularnewline
Quadratic Mean & 101.892567507809 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 101.880833333333 & 0.187605230985258 & 543.059662026903 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 101.883166666667 & 0.184278175204971 & 552.877010819882 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 101.889666666667 & 0.176277414691503 & 578.007493727885 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 101.888333333333 & 0.174021910216515 & 585.491408562092 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 101.871666666667 & 0.166276973796933 & 612.662501249741 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 101.936666666667 & 0.151877639321265 & 671.17626480249 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 101.972833333333 & 0.143128698687395 & 712.455533156563 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 101.9835 & 0.131151102099528 & 777.603072848038 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 101.973 & 0.111834800482096 & 911.818142120488 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 101.924666666667 & 0.101002172227764 & 1009.1334118718 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 101.932 & 0.0993540720776866 & 1025.9468773489 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 101.936 & 0.0988107819090049 & 1031.6283105003 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 101.927333333333 & 0.0898680346590712 & 1134.18896629943 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 101.897 & 0.0809415985317892 & 1258.8953251273 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 101.857 & 0.0734502022011501 & 1386.74907553086 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 101.838333333333 & 0.0700670246782983 & 1453.44166961432 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 101.838333333333 & 0.0665519493220807 & 1530.20812118489 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 101.718333333333 & 0.046307841623821 & 2196.56822184969 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 101.724666666667 & 0.0426352727016348 & 2385.92743099228 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 101.728 & 0.0421805374564264 & 2411.72839737018 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 101.884482758621 & 0.179185522424917 & 568.597738142113 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 101.888392857143 & 0.168742441251725 & 603.810114997381 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 101.891296296296 & 0.157994738100312 & 644.903099441228 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 101.891923076923 & 0.148635330330439 & 685.516174723746 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 101.893 & 0.137670487996906 & 740.122312941102 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 101.898333333333 & 0.12656934484453 & 805.079092875918 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 101.89 & 0.117413345577949 & 867.788916996297 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 101.873863636364 & 0.108280924233025 & 940.8292767905 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 101.854285714286 & 0.10005407530796 & 1017.99237463127 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 101.8345 & 0.0951550354381248 & 1070.19559743865 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 101.820263157895 & 0.0918813066691778 & 1108.17169290488 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 101.803333333333 & 0.0877116487892763 & 1160.65921389657 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 101.783823529412 & 0.0818687862682808 & 1243.25555769045 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 101.763125 & 0.0764027917863081 & 1331.92940494403 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 101.744 & 0.071598497383578 & 1421.03540881483 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 101.727857142857 & 0.0673150162553222 & 1511.22086574278 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 101.711923076923 & 0.0620322973712872 & 1639.66074749961 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 101.693333333333 & 0.0548603849398527 & 1853.67516915579 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 101.689545454545 & 0.0536441589463331 & 1895.63127564882 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 101.684 & 0.0527227105764332 & 1928.65652938285 \tabularnewline
Median & 101.645 &  &  \tabularnewline
Midrange & 101.82 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 101.72935483871 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 101.72935483871 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 101.72935483871 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 101.72935483871 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 101.72935483871 &  &  \tabularnewline
Midmean - Closest Observation & 101.72935483871 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 101.72935483871 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 101.763125 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&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]101.882333333333[/C][C]0.188007748167458[/C][C]541.904971079103[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]101.872100531527[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]101.861869096943[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]101.892567507809[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]101.880833333333[/C][C]0.187605230985258[/C][C]543.059662026903[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]101.883166666667[/C][C]0.184278175204971[/C][C]552.877010819882[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]101.889666666667[/C][C]0.176277414691503[/C][C]578.007493727885[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]101.888333333333[/C][C]0.174021910216515[/C][C]585.491408562092[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]101.871666666667[/C][C]0.166276973796933[/C][C]612.662501249741[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]101.936666666667[/C][C]0.151877639321265[/C][C]671.17626480249[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]101.972833333333[/C][C]0.143128698687395[/C][C]712.455533156563[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]101.9835[/C][C]0.131151102099528[/C][C]777.603072848038[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]101.973[/C][C]0.111834800482096[/C][C]911.818142120488[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]101.924666666667[/C][C]0.101002172227764[/C][C]1009.1334118718[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]101.932[/C][C]0.0993540720776866[/C][C]1025.9468773489[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]101.936[/C][C]0.0988107819090049[/C][C]1031.6283105003[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]101.927333333333[/C][C]0.0898680346590712[/C][C]1134.18896629943[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]101.897[/C][C]0.0809415985317892[/C][C]1258.8953251273[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]101.857[/C][C]0.0734502022011501[/C][C]1386.74907553086[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]101.838333333333[/C][C]0.0700670246782983[/C][C]1453.44166961432[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]101.838333333333[/C][C]0.0665519493220807[/C][C]1530.20812118489[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]101.718333333333[/C][C]0.046307841623821[/C][C]2196.56822184969[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]101.724666666667[/C][C]0.0426352727016348[/C][C]2385.92743099228[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]101.728[/C][C]0.0421805374564264[/C][C]2411.72839737018[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]101.884482758621[/C][C]0.179185522424917[/C][C]568.597738142113[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]101.888392857143[/C][C]0.168742441251725[/C][C]603.810114997381[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]101.891296296296[/C][C]0.157994738100312[/C][C]644.903099441228[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]101.891923076923[/C][C]0.148635330330439[/C][C]685.516174723746[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]101.893[/C][C]0.137670487996906[/C][C]740.122312941102[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]101.898333333333[/C][C]0.12656934484453[/C][C]805.079092875918[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]101.89[/C][C]0.117413345577949[/C][C]867.788916996297[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]101.873863636364[/C][C]0.108280924233025[/C][C]940.8292767905[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]101.854285714286[/C][C]0.10005407530796[/C][C]1017.99237463127[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]101.8345[/C][C]0.0951550354381248[/C][C]1070.19559743865[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]101.820263157895[/C][C]0.0918813066691778[/C][C]1108.17169290488[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]101.803333333333[/C][C]0.0877116487892763[/C][C]1160.65921389657[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]101.783823529412[/C][C]0.0818687862682808[/C][C]1243.25555769045[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]101.763125[/C][C]0.0764027917863081[/C][C]1331.92940494403[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]101.744[/C][C]0.071598497383578[/C][C]1421.03540881483[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]101.727857142857[/C][C]0.0673150162553222[/C][C]1511.22086574278[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]101.711923076923[/C][C]0.0620322973712872[/C][C]1639.66074749961[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]101.693333333333[/C][C]0.0548603849398527[/C][C]1853.67516915579[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]101.689545454545[/C][C]0.0536441589463331[/C][C]1895.63127564882[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]101.684[/C][C]0.0527227105764332[/C][C]1928.65652938285[/C][/ROW]
[ROW][C]Median[/C][C]101.645[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]101.82[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]101.72935483871[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]101.72935483871[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]101.72935483871[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]101.72935483871[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]101.72935483871[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]101.72935483871[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]101.72935483871[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]101.763125[/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=&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&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 Mean101.8823333333330.188007748167458541.904971079103
Geometric Mean101.872100531527
Harmonic Mean101.861869096943
Quadratic Mean101.892567507809
Winsorized Mean ( 1 / 20 )101.8808333333330.187605230985258543.059662026903
Winsorized Mean ( 2 / 20 )101.8831666666670.184278175204971552.877010819882
Winsorized Mean ( 3 / 20 )101.8896666666670.176277414691503578.007493727885
Winsorized Mean ( 4 / 20 )101.8883333333330.174021910216515585.491408562092
Winsorized Mean ( 5 / 20 )101.8716666666670.166276973796933612.662501249741
Winsorized Mean ( 6 / 20 )101.9366666666670.151877639321265671.17626480249
Winsorized Mean ( 7 / 20 )101.9728333333330.143128698687395712.455533156563
Winsorized Mean ( 8 / 20 )101.98350.131151102099528777.603072848038
Winsorized Mean ( 9 / 20 )101.9730.111834800482096911.818142120488
Winsorized Mean ( 10 / 20 )101.9246666666670.1010021722277641009.1334118718
Winsorized Mean ( 11 / 20 )101.9320.09935407207768661025.9468773489
Winsorized Mean ( 12 / 20 )101.9360.09881078190900491031.6283105003
Winsorized Mean ( 13 / 20 )101.9273333333330.08986803465907121134.18896629943
Winsorized Mean ( 14 / 20 )101.8970.08094159853178921258.8953251273
Winsorized Mean ( 15 / 20 )101.8570.07345020220115011386.74907553086
Winsorized Mean ( 16 / 20 )101.8383333333330.07006702467829831453.44166961432
Winsorized Mean ( 17 / 20 )101.8383333333330.06655194932208071530.20812118489
Winsorized Mean ( 18 / 20 )101.7183333333330.0463078416238212196.56822184969
Winsorized Mean ( 19 / 20 )101.7246666666670.04263527270163482385.92743099228
Winsorized Mean ( 20 / 20 )101.7280.04218053745642642411.72839737018
Trimmed Mean ( 1 / 20 )101.8844827586210.179185522424917568.597738142113
Trimmed Mean ( 2 / 20 )101.8883928571430.168742441251725603.810114997381
Trimmed Mean ( 3 / 20 )101.8912962962960.157994738100312644.903099441228
Trimmed Mean ( 4 / 20 )101.8919230769230.148635330330439685.516174723746
Trimmed Mean ( 5 / 20 )101.8930.137670487996906740.122312941102
Trimmed Mean ( 6 / 20 )101.8983333333330.12656934484453805.079092875918
Trimmed Mean ( 7 / 20 )101.890.117413345577949867.788916996297
Trimmed Mean ( 8 / 20 )101.8738636363640.108280924233025940.8292767905
Trimmed Mean ( 9 / 20 )101.8542857142860.100054075307961017.99237463127
Trimmed Mean ( 10 / 20 )101.83450.09515503543812481070.19559743865
Trimmed Mean ( 11 / 20 )101.8202631578950.09188130666917781108.17169290488
Trimmed Mean ( 12 / 20 )101.8033333333330.08771164878927631160.65921389657
Trimmed Mean ( 13 / 20 )101.7838235294120.08186878626828081243.25555769045
Trimmed Mean ( 14 / 20 )101.7631250.07640279178630811331.92940494403
Trimmed Mean ( 15 / 20 )101.7440.0715984973835781421.03540881483
Trimmed Mean ( 16 / 20 )101.7278571428570.06731501625532221511.22086574278
Trimmed Mean ( 17 / 20 )101.7119230769230.06203229737128721639.66074749961
Trimmed Mean ( 18 / 20 )101.6933333333330.05486038493985271853.67516915579
Trimmed Mean ( 19 / 20 )101.6895454545450.05364415894633311895.63127564882
Trimmed Mean ( 20 / 20 )101.6840.05272271057643321928.65652938285
Median101.645
Midrange101.82
Midmean - Weighted Average at Xnp101.72935483871
Midmean - Weighted Average at X(n+1)p101.72935483871
Midmean - Empirical Distribution Function101.72935483871
Midmean - Empirical Distribution Function - Averaging101.72935483871
Midmean - Empirical Distribution Function - Interpolation101.72935483871
Midmean - Closest Observation101.72935483871
Midmean - True Basic - Statistics Graphics Toolkit101.72935483871
Midmean - MS Excel (old versions)101.763125
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')