Free Statistics

of Irreproducible Research!

Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationTue, 20 Oct 2009 15:00:05 -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/20/t1256072565yx5cxrx3niyr0hx.htm/, Retrieved Fri, 03 May 2024 03:12:32 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=49174, Retrieved Fri, 03 May 2024 03:12:32 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact59
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] [Central Tendency ...] [2009-10-20 21:00:05] [557d56ec4b06cd0135c259898de8ce95] [Current]
Feedback Forum

Post a new message
Dataseries X:
-379,8571429
918,1538462
924,0769231
671,3333333
-149,8181818
233,7857143
186,4166667
450,5333333
863,3636364
541,8461538
177,0666667
1096,363636
-398,7142857
820,6153846
651,8666667
129,4375
-576,8823529
-533,0909091
-15,1875
-321,1538462
61,58823529
468,4375
495,4705882
618,9473684
-405,6666667
479,7894737
413,8125
359,4
-147,5
179,3125
292,5882353
456
259,7
136,8947368
556
229,2777778
-28,52631579
348,7058824
95,55
-222,4761905
-669,6666667
-504,88
118,92
-308,3846154
-264,3181818
-54,44
-160,1428571
-128,1071429
-708,3448276
-287,9
-327,1612903
-611,2758621
-618,0740741
-585,7727273
-160,44
-187,173913
39,26923077
106,0869565
-48,04545455
505,3888889




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 3 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=49174&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]3 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=49174&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=49174&T=0

As an alternative you can also use a QR Code:  

The GUIDs for individual cells are displayed in the table below:

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean84.716638845333358.25989387977981.45411591411662
Geometric MeanNaN
Harmonic Mean-864.311004002335
Quadratic Mean455.450993802143
Winsorized Mean ( 1 / 20 )82.489829645333357.33356687507661.43877023777483
Winsorized Mean ( 2 / 20 )84.012146835333356.91345617420971.47613855286131
Winsorized Mean ( 3 / 20 )81.612546945333356.17895531831551.45272453862676
Winsorized Mean ( 4 / 20 )80.462872478666755.16698587067861.45853305575342
Winsorized Mean ( 5 / 20 )68.763566070333352.3813853438311.31274813789230
Winsorized Mean ( 6 / 20 )71.196043790333351.10768809662961.39305937016213
Winsorized Mean ( 7 / 20 )70.64673171749.72615734038241.42071568557798
Winsorized Mean ( 8 / 20 )75.482193703666745.71016339263911.65132189651770
Winsorized Mean ( 9 / 20 )74.401973923666745.14908726647451.64791756441362
Winsorized Mean ( 10 / 20 )71.468620240333443.54730433214631.64117208484879
Winsorized Mean ( 11 / 20 )79.31117142241.58977223569681.90698739518287
Winsorized Mean ( 12 / 20 )77.37643734240.8632304676891.89354675233478
Winsorized Mean ( 13 / 20 )77.683509713666739.99932653731581.94212044148280
Winsorized Mean ( 14 / 20 )79.561169973666738.74486012167142.05346385878846
Winsorized Mean ( 15 / 20 )84.089957848666737.58223517241552.23749219446072
Winsorized Mean ( 16 / 20 )85.45559998234.24885227218382.49513762688641
Winsorized Mean ( 17 / 20 )80.041036940333330.27673840539152.64364793422002
Winsorized Mean ( 18 / 20 )84.852975560333328.59151772000632.96776744736986
Winsorized Mean ( 19 / 20 )67.176482563666725.87192276369492.59650135698198
Winsorized Mean ( 20 / 20 )59.65529589723.766023379872.51010844109194
Trimmed Mean ( 1 / 20 )80.947922798620755.98570059926111.44586781860669
Trimmed Mean ( 2 / 20 )79.295879748571454.31952244475881.45980443456978
Trimmed Mean ( 3 / 20 )76.67573136703752.53032180631631.4596470901082
Trimmed Mean ( 4 / 20 )74.776956144615450.65617475576831.47616665697997
Trimmed Mean ( 5 / 20 )73.071181244448.70742756656181.50020612656137
Trimmed Mean ( 6 / 20 )74.148085037916747.22813300150081.56999822617507
Trimmed Mean ( 7 / 20 )74.789833135217445.73333391077131.63534618493236
Trimmed Mean ( 8 / 20 )75.596930814090944.20623699695971.71009649202419
Trimmed Mean ( 9 / 20 )75.617419583809543.34267967640751.74464108237798
Trimmed Mean ( 10 / 20 )75.819993860542.3096558908381.79202577435565
Trimmed Mean ( 11 / 20 )76.507052853157941.31874731510811.85163050248581
Trimmed Mean ( 12 / 20 )76.082186403333340.45272364342101.88076795703488
Trimmed Mean ( 13 / 20 )75.891855382941239.39284660624791.92653900190357
Trimmed Mean ( 14 / 20 )75.63344370062538.09147645857381.98557395859622
Trimmed Mean ( 15 / 20 )75.072339947333336.55429228065152.05372160869518
Trimmed Mean ( 16 / 20 )73.784108818571434.62392084379352.13101540843540
Trimmed Mean ( 17 / 20 )72.1007206732.88304837699942.19264101805209
Trimmed Mean ( 18 / 20 )70.933027100833331.65268751611082.24097960290827
Trimmed Mean ( 19 / 20 )68.823944000909130.23199017366342.27652706968875
Trimmed Mean ( 20 / 20 )69.08406949129.00807622674662.38154605465707
Median100.81847825
Midrange194.0094042
Midmean - Weighted Average at Xnp63.363554787742
Midmean - Weighted Average at X(n+1)p75.0723399473333
Midmean - Empirical Distribution Function63.363554787742
Midmean - Empirical Distribution Function - Averaging75.0723399473333
Midmean - Empirical Distribution Function - Interpolation75.0723399473333
Midmean - Closest Observation63.363554787742
Midmean - True Basic - Statistics Graphics Toolkit75.0723399473333
Midmean - MS Excel (old versions)75.633443700625
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 84.7166388453333 & 58.2598938797798 & 1.45411591411662 \tabularnewline
Geometric Mean & NaN &  &  \tabularnewline
Harmonic Mean & -864.311004002335 &  &  \tabularnewline
Quadratic Mean & 455.450993802143 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 82.4898296453333 & 57.3335668750766 & 1.43877023777483 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 84.0121468353333 & 56.9134561742097 & 1.47613855286131 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 81.6125469453333 & 56.1789553183155 & 1.45272453862676 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 80.4628724786667 & 55.1669858706786 & 1.45853305575342 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 68.7635660703333 & 52.381385343831 & 1.31274813789230 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 71.1960437903333 & 51.1076880966296 & 1.39305937016213 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 70.646731717 & 49.7261573403824 & 1.42071568557798 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 75.4821937036667 & 45.7101633926391 & 1.65132189651770 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 74.4019739236667 & 45.1490872664745 & 1.64791756441362 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 71.4686202403334 & 43.5473043321463 & 1.64117208484879 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 79.311171422 & 41.5897722356968 & 1.90698739518287 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 77.376437342 & 40.863230467689 & 1.89354675233478 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 77.6835097136667 & 39.9993265373158 & 1.94212044148280 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 79.5611699736667 & 38.7448601216714 & 2.05346385878846 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 84.0899578486667 & 37.5822351724155 & 2.23749219446072 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 85.455599982 & 34.2488522721838 & 2.49513762688641 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 80.0410369403333 & 30.2767384053915 & 2.64364793422002 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 84.8529755603333 & 28.5915177200063 & 2.96776744736986 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 67.1764825636667 & 25.8719227636949 & 2.59650135698198 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 59.655295897 & 23.76602337987 & 2.51010844109194 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 80.9479227986207 & 55.9857005992611 & 1.44586781860669 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 79.2958797485714 & 54.3195224447588 & 1.45980443456978 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 76.675731367037 & 52.5303218063163 & 1.4596470901082 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 74.7769561446154 & 50.6561747557683 & 1.47616665697997 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 73.0711812444 & 48.7074275665618 & 1.50020612656137 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 74.1480850379167 & 47.2281330015008 & 1.56999822617507 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 74.7898331352174 & 45.7333339107713 & 1.63534618493236 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 75.5969308140909 & 44.2062369969597 & 1.71009649202419 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 75.6174195838095 & 43.3426796764075 & 1.74464108237798 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 75.8199938605 & 42.309655890838 & 1.79202577435565 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 76.5070528531579 & 41.3187473151081 & 1.85163050248581 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 76.0821864033333 & 40.4527236434210 & 1.88076795703488 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 75.8918553829412 & 39.3928466062479 & 1.92653900190357 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 75.633443700625 & 38.0914764585738 & 1.98557395859622 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 75.0723399473333 & 36.5542922806515 & 2.05372160869518 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 73.7841088185714 & 34.6239208437935 & 2.13101540843540 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 72.10072067 & 32.8830483769994 & 2.19264101805209 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 70.9330271008333 & 31.6526875161108 & 2.24097960290827 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 68.8239440009091 & 30.2319901736634 & 2.27652706968875 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 69.084069491 & 29.0080762267466 & 2.38154605465707 \tabularnewline
Median & 100.81847825 &  &  \tabularnewline
Midrange & 194.0094042 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 63.363554787742 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 75.0723399473333 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 63.363554787742 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 75.0723399473333 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 75.0723399473333 &  &  \tabularnewline
Midmean - Closest Observation & 63.363554787742 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 75.0723399473333 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 75.633443700625 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=49174&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]84.7166388453333[/C][C]58.2598938797798[/C][C]1.45411591411662[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]NaN[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]-864.311004002335[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]455.450993802143[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]82.4898296453333[/C][C]57.3335668750766[/C][C]1.43877023777483[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]84.0121468353333[/C][C]56.9134561742097[/C][C]1.47613855286131[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]81.6125469453333[/C][C]56.1789553183155[/C][C]1.45272453862676[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]80.4628724786667[/C][C]55.1669858706786[/C][C]1.45853305575342[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]68.7635660703333[/C][C]52.381385343831[/C][C]1.31274813789230[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]71.1960437903333[/C][C]51.1076880966296[/C][C]1.39305937016213[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]70.646731717[/C][C]49.7261573403824[/C][C]1.42071568557798[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]75.4821937036667[/C][C]45.7101633926391[/C][C]1.65132189651770[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]74.4019739236667[/C][C]45.1490872664745[/C][C]1.64791756441362[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]71.4686202403334[/C][C]43.5473043321463[/C][C]1.64117208484879[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]79.311171422[/C][C]41.5897722356968[/C][C]1.90698739518287[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]77.376437342[/C][C]40.863230467689[/C][C]1.89354675233478[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]77.6835097136667[/C][C]39.9993265373158[/C][C]1.94212044148280[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]79.5611699736667[/C][C]38.7448601216714[/C][C]2.05346385878846[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]84.0899578486667[/C][C]37.5822351724155[/C][C]2.23749219446072[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]85.455599982[/C][C]34.2488522721838[/C][C]2.49513762688641[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]80.0410369403333[/C][C]30.2767384053915[/C][C]2.64364793422002[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]84.8529755603333[/C][C]28.5915177200063[/C][C]2.96776744736986[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]67.1764825636667[/C][C]25.8719227636949[/C][C]2.59650135698198[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]59.655295897[/C][C]23.76602337987[/C][C]2.51010844109194[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]80.9479227986207[/C][C]55.9857005992611[/C][C]1.44586781860669[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]79.2958797485714[/C][C]54.3195224447588[/C][C]1.45980443456978[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]76.675731367037[/C][C]52.5303218063163[/C][C]1.4596470901082[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]74.7769561446154[/C][C]50.6561747557683[/C][C]1.47616665697997[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]73.0711812444[/C][C]48.7074275665618[/C][C]1.50020612656137[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]74.1480850379167[/C][C]47.2281330015008[/C][C]1.56999822617507[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]74.7898331352174[/C][C]45.7333339107713[/C][C]1.63534618493236[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]75.5969308140909[/C][C]44.2062369969597[/C][C]1.71009649202419[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]75.6174195838095[/C][C]43.3426796764075[/C][C]1.74464108237798[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]75.8199938605[/C][C]42.309655890838[/C][C]1.79202577435565[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]76.5070528531579[/C][C]41.3187473151081[/C][C]1.85163050248581[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]76.0821864033333[/C][C]40.4527236434210[/C][C]1.88076795703488[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]75.8918553829412[/C][C]39.3928466062479[/C][C]1.92653900190357[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]75.633443700625[/C][C]38.0914764585738[/C][C]1.98557395859622[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]75.0723399473333[/C][C]36.5542922806515[/C][C]2.05372160869518[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]73.7841088185714[/C][C]34.6239208437935[/C][C]2.13101540843540[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]72.10072067[/C][C]32.8830483769994[/C][C]2.19264101805209[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]70.9330271008333[/C][C]31.6526875161108[/C][C]2.24097960290827[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]68.8239440009091[/C][C]30.2319901736634[/C][C]2.27652706968875[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]69.084069491[/C][C]29.0080762267466[/C][C]2.38154605465707[/C][/ROW]
[ROW][C]Median[/C][C]100.81847825[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]194.0094042[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]63.363554787742[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]75.0723399473333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]63.363554787742[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]75.0723399473333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]75.0723399473333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]63.363554787742[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]75.0723399473333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]75.633443700625[/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=49174&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=49174&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 Mean84.716638845333358.25989387977981.45411591411662
Geometric MeanNaN
Harmonic Mean-864.311004002335
Quadratic Mean455.450993802143
Winsorized Mean ( 1 / 20 )82.489829645333357.33356687507661.43877023777483
Winsorized Mean ( 2 / 20 )84.012146835333356.91345617420971.47613855286131
Winsorized Mean ( 3 / 20 )81.612546945333356.17895531831551.45272453862676
Winsorized Mean ( 4 / 20 )80.462872478666755.16698587067861.45853305575342
Winsorized Mean ( 5 / 20 )68.763566070333352.3813853438311.31274813789230
Winsorized Mean ( 6 / 20 )71.196043790333351.10768809662961.39305937016213
Winsorized Mean ( 7 / 20 )70.64673171749.72615734038241.42071568557798
Winsorized Mean ( 8 / 20 )75.482193703666745.71016339263911.65132189651770
Winsorized Mean ( 9 / 20 )74.401973923666745.14908726647451.64791756441362
Winsorized Mean ( 10 / 20 )71.468620240333443.54730433214631.64117208484879
Winsorized Mean ( 11 / 20 )79.31117142241.58977223569681.90698739518287
Winsorized Mean ( 12 / 20 )77.37643734240.8632304676891.89354675233478
Winsorized Mean ( 13 / 20 )77.683509713666739.99932653731581.94212044148280
Winsorized Mean ( 14 / 20 )79.561169973666738.74486012167142.05346385878846
Winsorized Mean ( 15 / 20 )84.089957848666737.58223517241552.23749219446072
Winsorized Mean ( 16 / 20 )85.45559998234.24885227218382.49513762688641
Winsorized Mean ( 17 / 20 )80.041036940333330.27673840539152.64364793422002
Winsorized Mean ( 18 / 20 )84.852975560333328.59151772000632.96776744736986
Winsorized Mean ( 19 / 20 )67.176482563666725.87192276369492.59650135698198
Winsorized Mean ( 20 / 20 )59.65529589723.766023379872.51010844109194
Trimmed Mean ( 1 / 20 )80.947922798620755.98570059926111.44586781860669
Trimmed Mean ( 2 / 20 )79.295879748571454.31952244475881.45980443456978
Trimmed Mean ( 3 / 20 )76.67573136703752.53032180631631.4596470901082
Trimmed Mean ( 4 / 20 )74.776956144615450.65617475576831.47616665697997
Trimmed Mean ( 5 / 20 )73.071181244448.70742756656181.50020612656137
Trimmed Mean ( 6 / 20 )74.148085037916747.22813300150081.56999822617507
Trimmed Mean ( 7 / 20 )74.789833135217445.73333391077131.63534618493236
Trimmed Mean ( 8 / 20 )75.596930814090944.20623699695971.71009649202419
Trimmed Mean ( 9 / 20 )75.617419583809543.34267967640751.74464108237798
Trimmed Mean ( 10 / 20 )75.819993860542.3096558908381.79202577435565
Trimmed Mean ( 11 / 20 )76.507052853157941.31874731510811.85163050248581
Trimmed Mean ( 12 / 20 )76.082186403333340.45272364342101.88076795703488
Trimmed Mean ( 13 / 20 )75.891855382941239.39284660624791.92653900190357
Trimmed Mean ( 14 / 20 )75.63344370062538.09147645857381.98557395859622
Trimmed Mean ( 15 / 20 )75.072339947333336.55429228065152.05372160869518
Trimmed Mean ( 16 / 20 )73.784108818571434.62392084379352.13101540843540
Trimmed Mean ( 17 / 20 )72.1007206732.88304837699942.19264101805209
Trimmed Mean ( 18 / 20 )70.933027100833331.65268751611082.24097960290827
Trimmed Mean ( 19 / 20 )68.823944000909130.23199017366342.27652706968875
Trimmed Mean ( 20 / 20 )69.08406949129.00807622674662.38154605465707
Median100.81847825
Midrange194.0094042
Midmean - Weighted Average at Xnp63.363554787742
Midmean - Weighted Average at X(n+1)p75.0723399473333
Midmean - Empirical Distribution Function63.363554787742
Midmean - Empirical Distribution Function - Averaging75.0723399473333
Midmean - Empirical Distribution Function - Interpolation75.0723399473333
Midmean - Closest Observation63.363554787742
Midmean - True Basic - Statistics Graphics Toolkit75.0723399473333
Midmean - MS Excel (old versions)75.633443700625
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')