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Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationSun, 18 Oct 2009 03:58:50 -0600
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2009/Oct/18/t1255859978nwk7aet2jekngqb.htm/, Retrieved Mon, 29 Apr 2024 14:09:20 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=47241, Retrieved Mon, 29 Apr 2024 14:09:20 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact164
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Bivariate Data Series] [Bivariate dataset] [2008-01-05 23:51:08] [74be16979710d4c4e7c6647856088456]
F RMPD  [Univariate Explorative Data Analysis] [Colombia Coffee] [2008-01-07 14:21:11] [74be16979710d4c4e7c6647856088456]
F RMPD    [Univariate Data Series] [] [2009-10-14 08:30:28] [74be16979710d4c4e7c6647856088456]
- RMPD        [Central Tendency] [WS3 gemiddelde 3] [2009-10-18 09:58:50] [9be6fbb216efe5bb8ca600257c6e1971] [Current]
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Dataseries X:
1.88
1.88
1.55
1.52
1.45
1.17
0.54
0.8
0.34
0.39
0.49
0.39
0.17
0.26
0.4
0.44
0.23
0.41
0.52
0.53
0.75
0.64
0.65
0.75
0.76
0.88
1.04
0.68
0.87
0.57
0.97
0.77
0.57
0.98
0.68
0.78
0.59
0.59
0.68
1.25
0.82
1.3
0.92
1.05
1.14
1.01
1.26
1.23
1.72
1.89
2.01
1.99
1.92
1.82
1.83
1.99
2.37
2.27
2.35
2.66




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Sir Ronald Aylmer Fisher' @ 193.190.124.24

\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 & 2 seconds \tabularnewline
R Server & 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=47241&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]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Sir Ronald Aylmer Fisher' @ 193.190.124.24[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=47241&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=47241&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 time2 seconds
R Server'Sir Ronald Aylmer Fisher' @ 193.190.124.24







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean1.072666666666670.081500707655818813.1614399128482
Geometric Mean0.893314845119609
Harmonic Mean0.725600026488088
Quadratic Mean1.24197960262370
Winsorized Mean ( 1 / 20 )1.068833333333330.079851235858772113.3853073385578
Winsorized Mean ( 2 / 20 )1.069166666666670.079492845738094513.4498476779817
Winsorized Mean ( 3 / 20 )1.069166666666670.07775969489818713.7496252790929
Winsorized Mean ( 4 / 20 )1.055166666666670.073037600279677414.446896702879
Winsorized Mean ( 5 / 20 )1.05350.072670926506561314.4968565923662
Winsorized Mean ( 6 / 20 )1.05450.072517064035102714.5414050338491
Winsorized Mean ( 7 / 20 )1.04750.070589777352437314.8392591574569
Winsorized Mean ( 8 / 20 )1.04750.069153732369012215.1474109077789
Winsorized Mean ( 9 / 20 )1.05350.06775655366805315.5483114616663
Winsorized Mean ( 10 / 20 )1.05850.067063855648652315.7834647257009
Winsorized Mean ( 11 / 20 )1.051166666666670.064930685191769616.1890585870470
Winsorized Mean ( 12 / 20 )1.051166666666670.06425368668297616.3596319671595
Winsorized Mean ( 13 / 20 )1.0360.059053839267260117.5433132350866
Winsorized Mean ( 14 / 20 )0.9963333333333330.051529140823896619.3353375857430
Winsorized Mean ( 15 / 20 )0.9938333333333330.049473551495236220.0881744547696
Winsorized Mean ( 16 / 20 )0.9751666666666670.046162016123432421.1248716706647
Winsorized Mean ( 17 / 20 )0.9468333333333330.036990983530092025.596327617596
Winsorized Mean ( 18 / 20 )0.9378333333333330.034651690322184227.0645767814947
Winsorized Mean ( 19 / 20 )0.9441666666666670.032835226077538928.7546875552817
Winsorized Mean ( 20 / 20 )0.93750.031789051343359329.4912858478818
Trimmed Mean ( 1 / 20 )1.060862068965520.078111901242476313.5813115810915
Trimmed Mean ( 2 / 20 )1.052321428571430.075942558210106113.8568077422416
Trimmed Mean ( 3 / 20 )1.042962962962960.07346549441741414.1966370911096
Trimmed Mean ( 4 / 20 )1.032884615384620.07119341262639614.5081486794982
Trimmed Mean ( 5 / 20 )1.02620.070193255097797614.6196382910329
Trimmed Mean ( 6 / 20 )1.0193750.068982862406912814.7772209565176
Trimmed Mean ( 7 / 20 )1.011739130434780.067412712822074615.0081355293491
Trimmed Mean ( 8 / 20 )1.004772727272730.065905217863895215.2457234774300
Trimmed Mean ( 9 / 20 )0.9971428571428570.064269581147636615.5150047555511
Trimmed Mean ( 10 / 20 )0.987750.062391945054568615.8313705260527
Trimmed Mean ( 11 / 20 )0.9765789473684210.059949334127031516.2900716344750
Trimmed Mean ( 12 / 20 )0.9652777777777780.057187364170866316.8792143469611
Trimmed Mean ( 13 / 20 )0.952647058823530.053436801634267717.8275463667088
Trimmed Mean ( 14 / 20 )0.9406250.049838322272479118.873528584236
Trimmed Mean ( 15 / 20 )0.9326666666666670.047384301521193119.6830308081997
Trimmed Mean ( 16 / 20 )0.9239285714285710.044377944155150320.8195442357224
Trimmed Mean ( 17 / 20 )0.9165384615384620.041122489851632722.2880099148975
Trimmed Mean ( 18 / 20 )0.9120833333333330.039818333692755622.9061150667707
Trimmed Mean ( 19 / 20 )0.9081818181818180.038509212726017223.5834948027447
Trimmed Mean ( 20 / 20 )0.90250.036834444692291424.5015231677667
Median0.875
Midrange1.415
Midmean - Weighted Average at Xnp0.91
Midmean - Weighted Average at X(n+1)p0.932666666666667
Midmean - Empirical Distribution Function0.91
Midmean - Empirical Distribution Function - Averaging0.932666666666667
Midmean - Empirical Distribution Function - Interpolation0.932666666666667
Midmean - Closest Observation0.91
Midmean - True Basic - Statistics Graphics Toolkit0.932666666666667
Midmean - MS Excel (old versions)0.92939393939394
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 1.07266666666667 & 0.0815007076558188 & 13.1614399128482 \tabularnewline
Geometric Mean & 0.893314845119609 &  &  \tabularnewline
Harmonic Mean & 0.725600026488088 &  &  \tabularnewline
Quadratic Mean & 1.24197960262370 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 1.06883333333333 & 0.0798512358587721 & 13.3853073385578 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 1.06916666666667 & 0.0794928457380945 & 13.4498476779817 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 1.06916666666667 & 0.077759694898187 & 13.7496252790929 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 1.05516666666667 & 0.0730376002796774 & 14.446896702879 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 1.0535 & 0.0726709265065613 & 14.4968565923662 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 1.0545 & 0.0725170640351027 & 14.5414050338491 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 1.0475 & 0.0705897773524373 & 14.8392591574569 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 1.0475 & 0.0691537323690122 & 15.1474109077789 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 1.0535 & 0.067756553668053 & 15.5483114616663 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 1.0585 & 0.0670638556486523 & 15.7834647257009 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 1.05116666666667 & 0.0649306851917696 & 16.1890585870470 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 1.05116666666667 & 0.064253686682976 & 16.3596319671595 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 1.036 & 0.0590538392672601 & 17.5433132350866 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 0.996333333333333 & 0.0515291408238966 & 19.3353375857430 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 0.993833333333333 & 0.0494735514952362 & 20.0881744547696 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 0.975166666666667 & 0.0461620161234324 & 21.1248716706647 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 0.946833333333333 & 0.0369909835300920 & 25.596327617596 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 0.937833333333333 & 0.0346516903221842 & 27.0645767814947 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 0.944166666666667 & 0.0328352260775389 & 28.7546875552817 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 0.9375 & 0.0317890513433593 & 29.4912858478818 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 1.06086206896552 & 0.0781119012424763 & 13.5813115810915 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 1.05232142857143 & 0.0759425582101061 & 13.8568077422416 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 1.04296296296296 & 0.073465494417414 & 14.1966370911096 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 1.03288461538462 & 0.071193412626396 & 14.5081486794982 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 1.0262 & 0.0701932550977976 & 14.6196382910329 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 1.019375 & 0.0689828624069128 & 14.7772209565176 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 1.01173913043478 & 0.0674127128220746 & 15.0081355293491 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 1.00477272727273 & 0.0659052178638952 & 15.2457234774300 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 0.997142857142857 & 0.0642695811476366 & 15.5150047555511 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 0.98775 & 0.0623919450545686 & 15.8313705260527 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 0.976578947368421 & 0.0599493341270315 & 16.2900716344750 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 0.965277777777778 & 0.0571873641708663 & 16.8792143469611 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 0.95264705882353 & 0.0534368016342677 & 17.8275463667088 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 0.940625 & 0.0498383222724791 & 18.873528584236 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 0.932666666666667 & 0.0473843015211931 & 19.6830308081997 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 0.923928571428571 & 0.0443779441551503 & 20.8195442357224 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 0.916538461538462 & 0.0411224898516327 & 22.2880099148975 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 0.912083333333333 & 0.0398183336927556 & 22.9061150667707 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 0.908181818181818 & 0.0385092127260172 & 23.5834948027447 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 0.9025 & 0.0368344446922914 & 24.5015231677667 \tabularnewline
Median & 0.875 &  &  \tabularnewline
Midrange & 1.415 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 0.91 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 0.932666666666667 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 0.91 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 0.932666666666667 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 0.932666666666667 &  &  \tabularnewline
Midmean - Closest Observation & 0.91 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 0.932666666666667 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 0.92939393939394 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=47241&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]1.07266666666667[/C][C]0.0815007076558188[/C][C]13.1614399128482[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]0.893314845119609[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]0.725600026488088[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]1.24197960262370[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]1.06883333333333[/C][C]0.0798512358587721[/C][C]13.3853073385578[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]1.06916666666667[/C][C]0.0794928457380945[/C][C]13.4498476779817[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]1.06916666666667[/C][C]0.077759694898187[/C][C]13.7496252790929[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]1.05516666666667[/C][C]0.0730376002796774[/C][C]14.446896702879[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]1.0535[/C][C]0.0726709265065613[/C][C]14.4968565923662[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]1.0545[/C][C]0.0725170640351027[/C][C]14.5414050338491[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]1.0475[/C][C]0.0705897773524373[/C][C]14.8392591574569[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]1.0475[/C][C]0.0691537323690122[/C][C]15.1474109077789[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]1.0535[/C][C]0.067756553668053[/C][C]15.5483114616663[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]1.0585[/C][C]0.0670638556486523[/C][C]15.7834647257009[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]1.05116666666667[/C][C]0.0649306851917696[/C][C]16.1890585870470[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]1.05116666666667[/C][C]0.064253686682976[/C][C]16.3596319671595[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]1.036[/C][C]0.0590538392672601[/C][C]17.5433132350866[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]0.996333333333333[/C][C]0.0515291408238966[/C][C]19.3353375857430[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]0.993833333333333[/C][C]0.0494735514952362[/C][C]20.0881744547696[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]0.975166666666667[/C][C]0.0461620161234324[/C][C]21.1248716706647[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]0.946833333333333[/C][C]0.0369909835300920[/C][C]25.596327617596[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]0.937833333333333[/C][C]0.0346516903221842[/C][C]27.0645767814947[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]0.944166666666667[/C][C]0.0328352260775389[/C][C]28.7546875552817[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]0.9375[/C][C]0.0317890513433593[/C][C]29.4912858478818[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]1.06086206896552[/C][C]0.0781119012424763[/C][C]13.5813115810915[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]1.05232142857143[/C][C]0.0759425582101061[/C][C]13.8568077422416[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]1.04296296296296[/C][C]0.073465494417414[/C][C]14.1966370911096[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]1.03288461538462[/C][C]0.071193412626396[/C][C]14.5081486794982[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]1.0262[/C][C]0.0701932550977976[/C][C]14.6196382910329[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]1.019375[/C][C]0.0689828624069128[/C][C]14.7772209565176[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]1.01173913043478[/C][C]0.0674127128220746[/C][C]15.0081355293491[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]1.00477272727273[/C][C]0.0659052178638952[/C][C]15.2457234774300[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]0.997142857142857[/C][C]0.0642695811476366[/C][C]15.5150047555511[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]0.98775[/C][C]0.0623919450545686[/C][C]15.8313705260527[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]0.976578947368421[/C][C]0.0599493341270315[/C][C]16.2900716344750[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]0.965277777777778[/C][C]0.0571873641708663[/C][C]16.8792143469611[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]0.95264705882353[/C][C]0.0534368016342677[/C][C]17.8275463667088[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]0.940625[/C][C]0.0498383222724791[/C][C]18.873528584236[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]0.932666666666667[/C][C]0.0473843015211931[/C][C]19.6830308081997[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]0.923928571428571[/C][C]0.0443779441551503[/C][C]20.8195442357224[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]0.916538461538462[/C][C]0.0411224898516327[/C][C]22.2880099148975[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]0.912083333333333[/C][C]0.0398183336927556[/C][C]22.9061150667707[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]0.908181818181818[/C][C]0.0385092127260172[/C][C]23.5834948027447[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]0.9025[/C][C]0.0368344446922914[/C][C]24.5015231677667[/C][/ROW]
[ROW][C]Median[/C][C]0.875[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]1.415[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]0.91[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]0.932666666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]0.91[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]0.932666666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]0.932666666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]0.91[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]0.932666666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]0.92939393939394[/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=47241&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=47241&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 Mean1.072666666666670.081500707655818813.1614399128482
Geometric Mean0.893314845119609
Harmonic Mean0.725600026488088
Quadratic Mean1.24197960262370
Winsorized Mean ( 1 / 20 )1.068833333333330.079851235858772113.3853073385578
Winsorized Mean ( 2 / 20 )1.069166666666670.079492845738094513.4498476779817
Winsorized Mean ( 3 / 20 )1.069166666666670.07775969489818713.7496252790929
Winsorized Mean ( 4 / 20 )1.055166666666670.073037600279677414.446896702879
Winsorized Mean ( 5 / 20 )1.05350.072670926506561314.4968565923662
Winsorized Mean ( 6 / 20 )1.05450.072517064035102714.5414050338491
Winsorized Mean ( 7 / 20 )1.04750.070589777352437314.8392591574569
Winsorized Mean ( 8 / 20 )1.04750.069153732369012215.1474109077789
Winsorized Mean ( 9 / 20 )1.05350.06775655366805315.5483114616663
Winsorized Mean ( 10 / 20 )1.05850.067063855648652315.7834647257009
Winsorized Mean ( 11 / 20 )1.051166666666670.064930685191769616.1890585870470
Winsorized Mean ( 12 / 20 )1.051166666666670.06425368668297616.3596319671595
Winsorized Mean ( 13 / 20 )1.0360.059053839267260117.5433132350866
Winsorized Mean ( 14 / 20 )0.9963333333333330.051529140823896619.3353375857430
Winsorized Mean ( 15 / 20 )0.9938333333333330.049473551495236220.0881744547696
Winsorized Mean ( 16 / 20 )0.9751666666666670.046162016123432421.1248716706647
Winsorized Mean ( 17 / 20 )0.9468333333333330.036990983530092025.596327617596
Winsorized Mean ( 18 / 20 )0.9378333333333330.034651690322184227.0645767814947
Winsorized Mean ( 19 / 20 )0.9441666666666670.032835226077538928.7546875552817
Winsorized Mean ( 20 / 20 )0.93750.031789051343359329.4912858478818
Trimmed Mean ( 1 / 20 )1.060862068965520.078111901242476313.5813115810915
Trimmed Mean ( 2 / 20 )1.052321428571430.075942558210106113.8568077422416
Trimmed Mean ( 3 / 20 )1.042962962962960.07346549441741414.1966370911096
Trimmed Mean ( 4 / 20 )1.032884615384620.07119341262639614.5081486794982
Trimmed Mean ( 5 / 20 )1.02620.070193255097797614.6196382910329
Trimmed Mean ( 6 / 20 )1.0193750.068982862406912814.7772209565176
Trimmed Mean ( 7 / 20 )1.011739130434780.067412712822074615.0081355293491
Trimmed Mean ( 8 / 20 )1.004772727272730.065905217863895215.2457234774300
Trimmed Mean ( 9 / 20 )0.9971428571428570.064269581147636615.5150047555511
Trimmed Mean ( 10 / 20 )0.987750.062391945054568615.8313705260527
Trimmed Mean ( 11 / 20 )0.9765789473684210.059949334127031516.2900716344750
Trimmed Mean ( 12 / 20 )0.9652777777777780.057187364170866316.8792143469611
Trimmed Mean ( 13 / 20 )0.952647058823530.053436801634267717.8275463667088
Trimmed Mean ( 14 / 20 )0.9406250.049838322272479118.873528584236
Trimmed Mean ( 15 / 20 )0.9326666666666670.047384301521193119.6830308081997
Trimmed Mean ( 16 / 20 )0.9239285714285710.044377944155150320.8195442357224
Trimmed Mean ( 17 / 20 )0.9165384615384620.041122489851632722.2880099148975
Trimmed Mean ( 18 / 20 )0.9120833333333330.039818333692755622.9061150667707
Trimmed Mean ( 19 / 20 )0.9081818181818180.038509212726017223.5834948027447
Trimmed Mean ( 20 / 20 )0.90250.036834444692291424.5015231677667
Median0.875
Midrange1.415
Midmean - Weighted Average at Xnp0.91
Midmean - Weighted Average at X(n+1)p0.932666666666667
Midmean - Empirical Distribution Function0.91
Midmean - Empirical Distribution Function - Averaging0.932666666666667
Midmean - Empirical Distribution Function - Interpolation0.932666666666667
Midmean - Closest Observation0.91
Midmean - True Basic - Statistics Graphics Toolkit0.932666666666667
Midmean - MS Excel (old versions)0.92939393939394
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')