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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 computationFri, 12 Nov 2010 13:56:15 +0000
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2010/Nov/12/t1289570066muasrr8msmtv5ja.htm/, Retrieved Tue, 30 Apr 2024 12:36:20 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=94137, Retrieved Tue, 30 Apr 2024 12:36:20 +0000
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Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact109
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Central Tendency] [Arabica Price in ...] [2008-01-06 21:28:17] [74be16979710d4c4e7c6647856088456]
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Dataseries X:
3
4
4
4
3
4
4
3
3
4
4
4
4
4
4
4
4
4
5
4
4
4
5
4
4
3
4
5
3
4
4
3
4
4
4
3
2
4
4
4
4
3
5
3
4
3
3
3
4
3
4
5
3
4
3
3
4
2
5
3
3
4
4
5
5
3
4
5
3
5
2
4
3
4
2
3
4
4
4
3
4
5
4
4
4
4
4
4
3
3
3
4
4
5
4
2
4
4
4
3
4
4
4
3
3
5
3
3
4
4
4
5
3
3
4
4
3
4
5
4
4
1
4
4
4
4
5
4
3
4
4
3
4
4
4
4
4
4
4
3
5
4
2
5
4
4
2
5
4
4
4
4
4
4
4
4




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time12 seconds
R Server'George Udny Yule' @ 72.249.76.132

\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 & 12 seconds \tabularnewline
R Server & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=94137&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]12 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'George Udny Yule' @ 72.249.76.132[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=94137&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=94137&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 time12 seconds
R Server'George Udny Yule' @ 72.249.76.132







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean3.769230769230770.059530944227420663.3154877374618
Geometric Mean3.68181721478552
Harmonic Mean3.56843309187953
Quadratic Mean3.84140732758325
Winsorized Mean ( 1 / 52 )3.775641025641030.057930763521438665.175060643621
Winsorized Mean ( 2 / 52 )3.775641025641030.057930763521438665.175060643621
Winsorized Mean ( 3 / 52 )3.775641025641030.057930763521438665.175060643621
Winsorized Mean ( 4 / 52 )3.775641025641030.057930763521438665.175060643621
Winsorized Mean ( 5 / 52 )3.775641025641030.057930763521438665.175060643621
Winsorized Mean ( 6 / 52 )3.775641025641030.057930763521438665.175060643621
Winsorized Mean ( 7 / 52 )3.775641025641030.057930763521438665.175060643621
Winsorized Mean ( 8 / 52 )3.826923076923080.049949073766147876.6164973316625
Winsorized Mean ( 9 / 52 )3.826923076923080.049949073766147876.6164973316625
Winsorized Mean ( 10 / 52 )3.826923076923080.049949073766147876.6164973316625
Winsorized Mean ( 11 / 52 )3.826923076923080.049949073766147876.6164973316625
Winsorized Mean ( 12 / 52 )3.826923076923080.049949073766147876.6164973316625
Winsorized Mean ( 13 / 52 )3.826923076923080.049949073766147876.6164973316625
Winsorized Mean ( 14 / 52 )3.826923076923080.049949073766147876.6164973316625
Winsorized Mean ( 15 / 52 )3.826923076923080.049949073766147876.6164973316625
Winsorized Mean ( 16 / 52 )3.826923076923080.049949073766147876.6164973316625
Winsorized Mean ( 17 / 52 )3.826923076923080.049949073766147876.6164973316625
Winsorized Mean ( 18 / 52 )3.826923076923080.049949073766147876.6164973316625
Winsorized Mean ( 19 / 52 )3.705128205128210.0366256053091788101.162238107766
Winsorized Mean ( 20 / 52 )3.705128205128210.0366256053091788101.162238107766
Winsorized Mean ( 21 / 52 )3.705128205128210.0366256053091788101.162238107766
Winsorized Mean ( 22 / 52 )3.705128205128210.0366256053091788101.162238107766
Winsorized Mean ( 23 / 52 )3.705128205128210.0366256053091788101.162238107766
Winsorized Mean ( 24 / 52 )3.705128205128210.0366256053091788101.162238107766
Winsorized Mean ( 25 / 52 )3.705128205128210.0366256053091788101.162238107766
Winsorized Mean ( 26 / 52 )3.705128205128210.0366256053091788101.162238107766
Winsorized Mean ( 27 / 52 )3.705128205128210.0366256053091788101.162238107766
Winsorized Mean ( 28 / 52 )3.705128205128210.0366256053091788101.162238107766
Winsorized Mean ( 29 / 52 )3.705128205128210.0366256053091788101.162238107766
Winsorized Mean ( 30 / 52 )3.705128205128210.0366256053091788101.162238107766
Winsorized Mean ( 31 / 52 )3.705128205128210.0366256053091788101.162238107766
Winsorized Mean ( 32 / 52 )3.705128205128210.0366256053091788101.162238107766
Winsorized Mean ( 33 / 52 )3.705128205128210.0366256053091788101.162238107766
Winsorized Mean ( 34 / 52 )3.705128205128210.0366256053091788101.162238107766
Winsorized Mean ( 35 / 52 )3.705128205128210.0366256053091788101.162238107766
Winsorized Mean ( 36 / 52 )3.705128205128210.0366256053091788101.162238107766
Winsorized Mean ( 37 / 52 )3.705128205128210.0366256053091788101.162238107766
Winsorized Mean ( 38 / 52 )3.705128205128210.0366256053091788101.162238107766
Winsorized Mean ( 39 / 52 )3.705128205128210.0366256053091788101.162238107766
Winsorized Mean ( 40 / 52 )3.705128205128210.0366256053091788101.162238107766
Winsorized Mean ( 41 / 52 )3.705128205128210.0366256053091788101.162238107766
Winsorized Mean ( 42 / 52 )3.705128205128210.0366256053091788101.162238107766
Winsorized Mean ( 43 / 52 )3.705128205128210.0366256053091788101.162238107766
Winsorized Mean ( 44 / 52 )3.705128205128210.0366256053091788101.162238107766
Winsorized Mean ( 45 / 52 )3.705128205128210.0366256053091788101.162238107766
Winsorized Mean ( 46 / 52 )40Inf
Winsorized Mean ( 47 / 52 )40Inf
Winsorized Mean ( 48 / 52 )40Inf
Winsorized Mean ( 49 / 52 )40Inf
Winsorized Mean ( 50 / 52 )40Inf
Winsorized Mean ( 51 / 52 )40Inf
Winsorized Mean ( 52 / 52 )40Inf
Trimmed Mean ( 1 / 52 )3.779220779220780.056977869865612366.3278705949245
Trimmed Mean ( 2 / 52 )3.782894736842110.055944754372659967.6183992451453
Trimmed Mean ( 3 / 52 )3.786666666666670.05482260728885369.071261910533
Trimmed Mean ( 4 / 52 )3.790540540540540.053601131515316270.7175470625544
Trimmed Mean ( 5 / 52 )3.794520547945210.052268165241399472.5971636926664
Trimmed Mean ( 6 / 52 )3.798611111111110.050809168385127774.7623161693589
Trimmed Mean ( 7 / 52 )3.802816901408450.049206506213028177.2828065651531
Trimmed Mean ( 8 / 52 )3.807142857142860.04743842070121880.2544182725102
Trimmed Mean ( 9 / 52 )3.804347826086960.046974129934723580.9881488251848
Trimmed Mean ( 10 / 52 )3.801470588235290.046465313674350981.8130835159674
Trimmed Mean ( 11 / 52 )3.798507462686570.045907415801008982.7427855915838
Trimmed Mean ( 12 / 52 )3.795454545454550.045295233191295683.7936859586346
Trimmed Mean ( 13 / 52 )3.792307692307690.044622786382501184.9859006965745
Trimmed Mean ( 14 / 52 )3.78906250.043883154723136486.344350671815
Trimmed Mean ( 15 / 52 )3.785714285714290.043068263065123987.9003241897607
Trimmed Mean ( 16 / 52 )3.782258064516130.04216860098296189.693705182309
Trimmed Mean ( 17 / 52 )3.778688524590160.041172845852582191.776228879578
Trimmed Mean ( 18 / 52 )3.7750.040067345268469594.2163743244225
Trimmed Mean ( 19 / 52 )3.771186440677970.038835387245388597.1069611550166
Trimmed Mean ( 20 / 52 )3.775862068965520.038886693701178297.0990770771317
Trimmed Mean ( 21 / 52 )3.780701754385960.038924311065187597.1295740611652
Trimmed Mean ( 22 / 52 )3.785714285714290.038946411200447997.2031611906452
Trimmed Mean ( 23 / 52 )3.790909090909090.038950910157241497.3253019147827
Trimmed Mean ( 24 / 52 )3.796296296296300.038935425188248597.5023716305041
Trimmed Mean ( 25 / 52 )3.801886792452830.038897222883185597.7418568896422
Trimmed Mean ( 26 / 52 )3.807692307692310.038833156160030998.0526097853305
Trimmed Mean ( 27 / 52 )3.813725490196080.038739587141493598.4451764100305
Trimmed Mean ( 28 / 52 )3.820.038612291966536998.9322261240171
Trimmed Mean ( 29 / 52 )3.82653061224490.03844634221296599.5291201188576
Trimmed Mean ( 30 / 52 )3.833333333333330.0382359556450936100.254675701435
Trimmed Mean ( 31 / 52 )3.833333333333330.0379743061437828100.945447661877
Trimmed Mean ( 32 / 52 )3.847826086956520.0376532784254104102.190997646564
Trimmed Mean ( 33 / 52 )3.855555555555560.0372631466754029103.468329959922
Trimmed Mean ( 34 / 52 )3.863636363636360.0367921460636536105.012530580628
Trimmed Mean ( 35 / 52 )3.872093023255810.0362258896767862106.887451427786
Trimmed Mean ( 36 / 52 )3.880952380952380.0355465558372129109.179420890321
Trimmed Mean ( 37 / 52 )3.890243902439020.0347317225419412112.008377866697
Trimmed Mean ( 38 / 52 )3.90.0337526370277807115.546527425103
Trimmed Mean ( 39 / 52 )3.910256410256410.032571535227231120.051338783297
Trimmed Mean ( 40 / 52 )3.921052631578950.0311372620163138125.927983954549
Trimmed Mean ( 41 / 52 )3.932432432432430.0293776057149328133.858166339048
Trimmed Mean ( 42 / 52 )3.944444444444440.0271845896182163145.098546633983
Trimmed Mean ( 43 / 52 )3.957142857142860.0243823433868205162.295428062990
Trimmed Mean ( 44 / 52 )3.970588235294120.0206414713705158192.359748199234
Trimmed Mean ( 45 / 52 )3.970588235294120.0151515151515152262.058823529412
Trimmed Mean ( 46 / 52 )40Inf
Trimmed Mean ( 47 / 52 )40Inf
Trimmed Mean ( 48 / 52 )40Inf
Trimmed Mean ( 49 / 52 )40Inf
Trimmed Mean ( 50 / 52 )40Inf
Trimmed Mean ( 51 / 52 )40Inf
Trimmed Mean ( 52 / 52 )40Inf
Median4
Midrange3
Midmean - Weighted Average at Xnp3.70542635658915
Midmean - Weighted Average at X(n+1)p3.70542635658915
Midmean - Empirical Distribution Function3.70542635658915
Midmean - Empirical Distribution Function - Averaging3.70542635658915
Midmean - Empirical Distribution Function - Interpolation3.70542635658915
Midmean - Closest Observation3.70542635658915
Midmean - True Basic - Statistics Graphics Toolkit3.70542635658915
Midmean - MS Excel (old versions)3.70542635658915
Number of observations156

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 3.76923076923077 & 0.0595309442274206 & 63.3154877374618 \tabularnewline
Geometric Mean & 3.68181721478552 &  &  \tabularnewline
Harmonic Mean & 3.56843309187953 &  &  \tabularnewline
Quadratic Mean & 3.84140732758325 &  &  \tabularnewline
Winsorized Mean ( 1 / 52 ) & 3.77564102564103 & 0.0579307635214386 & 65.175060643621 \tabularnewline
Winsorized Mean ( 2 / 52 ) & 3.77564102564103 & 0.0579307635214386 & 65.175060643621 \tabularnewline
Winsorized Mean ( 3 / 52 ) & 3.77564102564103 & 0.0579307635214386 & 65.175060643621 \tabularnewline
Winsorized Mean ( 4 / 52 ) & 3.77564102564103 & 0.0579307635214386 & 65.175060643621 \tabularnewline
Winsorized Mean ( 5 / 52 ) & 3.77564102564103 & 0.0579307635214386 & 65.175060643621 \tabularnewline
Winsorized Mean ( 6 / 52 ) & 3.77564102564103 & 0.0579307635214386 & 65.175060643621 \tabularnewline
Winsorized Mean ( 7 / 52 ) & 3.77564102564103 & 0.0579307635214386 & 65.175060643621 \tabularnewline
Winsorized Mean ( 8 / 52 ) & 3.82692307692308 & 0.0499490737661478 & 76.6164973316625 \tabularnewline
Winsorized Mean ( 9 / 52 ) & 3.82692307692308 & 0.0499490737661478 & 76.6164973316625 \tabularnewline
Winsorized Mean ( 10 / 52 ) & 3.82692307692308 & 0.0499490737661478 & 76.6164973316625 \tabularnewline
Winsorized Mean ( 11 / 52 ) & 3.82692307692308 & 0.0499490737661478 & 76.6164973316625 \tabularnewline
Winsorized Mean ( 12 / 52 ) & 3.82692307692308 & 0.0499490737661478 & 76.6164973316625 \tabularnewline
Winsorized Mean ( 13 / 52 ) & 3.82692307692308 & 0.0499490737661478 & 76.6164973316625 \tabularnewline
Winsorized Mean ( 14 / 52 ) & 3.82692307692308 & 0.0499490737661478 & 76.6164973316625 \tabularnewline
Winsorized Mean ( 15 / 52 ) & 3.82692307692308 & 0.0499490737661478 & 76.6164973316625 \tabularnewline
Winsorized Mean ( 16 / 52 ) & 3.82692307692308 & 0.0499490737661478 & 76.6164973316625 \tabularnewline
Winsorized Mean ( 17 / 52 ) & 3.82692307692308 & 0.0499490737661478 & 76.6164973316625 \tabularnewline
Winsorized Mean ( 18 / 52 ) & 3.82692307692308 & 0.0499490737661478 & 76.6164973316625 \tabularnewline
Winsorized Mean ( 19 / 52 ) & 3.70512820512821 & 0.0366256053091788 & 101.162238107766 \tabularnewline
Winsorized Mean ( 20 / 52 ) & 3.70512820512821 & 0.0366256053091788 & 101.162238107766 \tabularnewline
Winsorized Mean ( 21 / 52 ) & 3.70512820512821 & 0.0366256053091788 & 101.162238107766 \tabularnewline
Winsorized Mean ( 22 / 52 ) & 3.70512820512821 & 0.0366256053091788 & 101.162238107766 \tabularnewline
Winsorized Mean ( 23 / 52 ) & 3.70512820512821 & 0.0366256053091788 & 101.162238107766 \tabularnewline
Winsorized Mean ( 24 / 52 ) & 3.70512820512821 & 0.0366256053091788 & 101.162238107766 \tabularnewline
Winsorized Mean ( 25 / 52 ) & 3.70512820512821 & 0.0366256053091788 & 101.162238107766 \tabularnewline
Winsorized Mean ( 26 / 52 ) & 3.70512820512821 & 0.0366256053091788 & 101.162238107766 \tabularnewline
Winsorized Mean ( 27 / 52 ) & 3.70512820512821 & 0.0366256053091788 & 101.162238107766 \tabularnewline
Winsorized Mean ( 28 / 52 ) & 3.70512820512821 & 0.0366256053091788 & 101.162238107766 \tabularnewline
Winsorized Mean ( 29 / 52 ) & 3.70512820512821 & 0.0366256053091788 & 101.162238107766 \tabularnewline
Winsorized Mean ( 30 / 52 ) & 3.70512820512821 & 0.0366256053091788 & 101.162238107766 \tabularnewline
Winsorized Mean ( 31 / 52 ) & 3.70512820512821 & 0.0366256053091788 & 101.162238107766 \tabularnewline
Winsorized Mean ( 32 / 52 ) & 3.70512820512821 & 0.0366256053091788 & 101.162238107766 \tabularnewline
Winsorized Mean ( 33 / 52 ) & 3.70512820512821 & 0.0366256053091788 & 101.162238107766 \tabularnewline
Winsorized Mean ( 34 / 52 ) & 3.70512820512821 & 0.0366256053091788 & 101.162238107766 \tabularnewline
Winsorized Mean ( 35 / 52 ) & 3.70512820512821 & 0.0366256053091788 & 101.162238107766 \tabularnewline
Winsorized Mean ( 36 / 52 ) & 3.70512820512821 & 0.0366256053091788 & 101.162238107766 \tabularnewline
Winsorized Mean ( 37 / 52 ) & 3.70512820512821 & 0.0366256053091788 & 101.162238107766 \tabularnewline
Winsorized Mean ( 38 / 52 ) & 3.70512820512821 & 0.0366256053091788 & 101.162238107766 \tabularnewline
Winsorized Mean ( 39 / 52 ) & 3.70512820512821 & 0.0366256053091788 & 101.162238107766 \tabularnewline
Winsorized Mean ( 40 / 52 ) & 3.70512820512821 & 0.0366256053091788 & 101.162238107766 \tabularnewline
Winsorized Mean ( 41 / 52 ) & 3.70512820512821 & 0.0366256053091788 & 101.162238107766 \tabularnewline
Winsorized Mean ( 42 / 52 ) & 3.70512820512821 & 0.0366256053091788 & 101.162238107766 \tabularnewline
Winsorized Mean ( 43 / 52 ) & 3.70512820512821 & 0.0366256053091788 & 101.162238107766 \tabularnewline
Winsorized Mean ( 44 / 52 ) & 3.70512820512821 & 0.0366256053091788 & 101.162238107766 \tabularnewline
Winsorized Mean ( 45 / 52 ) & 3.70512820512821 & 0.0366256053091788 & 101.162238107766 \tabularnewline
Winsorized Mean ( 46 / 52 ) & 4 & 0 & Inf \tabularnewline
Winsorized Mean ( 47 / 52 ) & 4 & 0 & Inf \tabularnewline
Winsorized Mean ( 48 / 52 ) & 4 & 0 & Inf \tabularnewline
Winsorized Mean ( 49 / 52 ) & 4 & 0 & Inf \tabularnewline
Winsorized Mean ( 50 / 52 ) & 4 & 0 & Inf \tabularnewline
Winsorized Mean ( 51 / 52 ) & 4 & 0 & Inf \tabularnewline
Winsorized Mean ( 52 / 52 ) & 4 & 0 & Inf \tabularnewline
Trimmed Mean ( 1 / 52 ) & 3.77922077922078 & 0.0569778698656123 & 66.3278705949245 \tabularnewline
Trimmed Mean ( 2 / 52 ) & 3.78289473684211 & 0.0559447543726599 & 67.6183992451453 \tabularnewline
Trimmed Mean ( 3 / 52 ) & 3.78666666666667 & 0.054822607288853 & 69.071261910533 \tabularnewline
Trimmed Mean ( 4 / 52 ) & 3.79054054054054 & 0.0536011315153162 & 70.7175470625544 \tabularnewline
Trimmed Mean ( 5 / 52 ) & 3.79452054794521 & 0.0522681652413994 & 72.5971636926664 \tabularnewline
Trimmed Mean ( 6 / 52 ) & 3.79861111111111 & 0.0508091683851277 & 74.7623161693589 \tabularnewline
Trimmed Mean ( 7 / 52 ) & 3.80281690140845 & 0.0492065062130281 & 77.2828065651531 \tabularnewline
Trimmed Mean ( 8 / 52 ) & 3.80714285714286 & 0.047438420701218 & 80.2544182725102 \tabularnewline
Trimmed Mean ( 9 / 52 ) & 3.80434782608696 & 0.0469741299347235 & 80.9881488251848 \tabularnewline
Trimmed Mean ( 10 / 52 ) & 3.80147058823529 & 0.0464653136743509 & 81.8130835159674 \tabularnewline
Trimmed Mean ( 11 / 52 ) & 3.79850746268657 & 0.0459074158010089 & 82.7427855915838 \tabularnewline
Trimmed Mean ( 12 / 52 ) & 3.79545454545455 & 0.0452952331912956 & 83.7936859586346 \tabularnewline
Trimmed Mean ( 13 / 52 ) & 3.79230769230769 & 0.0446227863825011 & 84.9859006965745 \tabularnewline
Trimmed Mean ( 14 / 52 ) & 3.7890625 & 0.0438831547231364 & 86.344350671815 \tabularnewline
Trimmed Mean ( 15 / 52 ) & 3.78571428571429 & 0.0430682630651239 & 87.9003241897607 \tabularnewline
Trimmed Mean ( 16 / 52 ) & 3.78225806451613 & 0.042168600982961 & 89.693705182309 \tabularnewline
Trimmed Mean ( 17 / 52 ) & 3.77868852459016 & 0.0411728458525821 & 91.776228879578 \tabularnewline
Trimmed Mean ( 18 / 52 ) & 3.775 & 0.0400673452684695 & 94.2163743244225 \tabularnewline
Trimmed Mean ( 19 / 52 ) & 3.77118644067797 & 0.0388353872453885 & 97.1069611550166 \tabularnewline
Trimmed Mean ( 20 / 52 ) & 3.77586206896552 & 0.0388866937011782 & 97.0990770771317 \tabularnewline
Trimmed Mean ( 21 / 52 ) & 3.78070175438596 & 0.0389243110651875 & 97.1295740611652 \tabularnewline
Trimmed Mean ( 22 / 52 ) & 3.78571428571429 & 0.0389464112004479 & 97.2031611906452 \tabularnewline
Trimmed Mean ( 23 / 52 ) & 3.79090909090909 & 0.0389509101572414 & 97.3253019147827 \tabularnewline
Trimmed Mean ( 24 / 52 ) & 3.79629629629630 & 0.0389354251882485 & 97.5023716305041 \tabularnewline
Trimmed Mean ( 25 / 52 ) & 3.80188679245283 & 0.0388972228831855 & 97.7418568896422 \tabularnewline
Trimmed Mean ( 26 / 52 ) & 3.80769230769231 & 0.0388331561600309 & 98.0526097853305 \tabularnewline
Trimmed Mean ( 27 / 52 ) & 3.81372549019608 & 0.0387395871414935 & 98.4451764100305 \tabularnewline
Trimmed Mean ( 28 / 52 ) & 3.82 & 0.0386122919665369 & 98.9322261240171 \tabularnewline
Trimmed Mean ( 29 / 52 ) & 3.8265306122449 & 0.038446342212965 & 99.5291201188576 \tabularnewline
Trimmed Mean ( 30 / 52 ) & 3.83333333333333 & 0.0382359556450936 & 100.254675701435 \tabularnewline
Trimmed Mean ( 31 / 52 ) & 3.83333333333333 & 0.0379743061437828 & 100.945447661877 \tabularnewline
Trimmed Mean ( 32 / 52 ) & 3.84782608695652 & 0.0376532784254104 & 102.190997646564 \tabularnewline
Trimmed Mean ( 33 / 52 ) & 3.85555555555556 & 0.0372631466754029 & 103.468329959922 \tabularnewline
Trimmed Mean ( 34 / 52 ) & 3.86363636363636 & 0.0367921460636536 & 105.012530580628 \tabularnewline
Trimmed Mean ( 35 / 52 ) & 3.87209302325581 & 0.0362258896767862 & 106.887451427786 \tabularnewline
Trimmed Mean ( 36 / 52 ) & 3.88095238095238 & 0.0355465558372129 & 109.179420890321 \tabularnewline
Trimmed Mean ( 37 / 52 ) & 3.89024390243902 & 0.0347317225419412 & 112.008377866697 \tabularnewline
Trimmed Mean ( 38 / 52 ) & 3.9 & 0.0337526370277807 & 115.546527425103 \tabularnewline
Trimmed Mean ( 39 / 52 ) & 3.91025641025641 & 0.032571535227231 & 120.051338783297 \tabularnewline
Trimmed Mean ( 40 / 52 ) & 3.92105263157895 & 0.0311372620163138 & 125.927983954549 \tabularnewline
Trimmed Mean ( 41 / 52 ) & 3.93243243243243 & 0.0293776057149328 & 133.858166339048 \tabularnewline
Trimmed Mean ( 42 / 52 ) & 3.94444444444444 & 0.0271845896182163 & 145.098546633983 \tabularnewline
Trimmed Mean ( 43 / 52 ) & 3.95714285714286 & 0.0243823433868205 & 162.295428062990 \tabularnewline
Trimmed Mean ( 44 / 52 ) & 3.97058823529412 & 0.0206414713705158 & 192.359748199234 \tabularnewline
Trimmed Mean ( 45 / 52 ) & 3.97058823529412 & 0.0151515151515152 & 262.058823529412 \tabularnewline
Trimmed Mean ( 46 / 52 ) & 4 & 0 & Inf \tabularnewline
Trimmed Mean ( 47 / 52 ) & 4 & 0 & Inf \tabularnewline
Trimmed Mean ( 48 / 52 ) & 4 & 0 & Inf \tabularnewline
Trimmed Mean ( 49 / 52 ) & 4 & 0 & Inf \tabularnewline
Trimmed Mean ( 50 / 52 ) & 4 & 0 & Inf \tabularnewline
Trimmed Mean ( 51 / 52 ) & 4 & 0 & Inf \tabularnewline
Trimmed Mean ( 52 / 52 ) & 4 & 0 & Inf \tabularnewline
Median & 4 &  &  \tabularnewline
Midrange & 3 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 3.70542635658915 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 3.70542635658915 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 3.70542635658915 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 3.70542635658915 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 3.70542635658915 &  &  \tabularnewline
Midmean - Closest Observation & 3.70542635658915 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 3.70542635658915 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 3.70542635658915 &  &  \tabularnewline
Number of observations & 156 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=94137&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]3.76923076923077[/C][C]0.0595309442274206[/C][C]63.3154877374618[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]3.68181721478552[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]3.56843309187953[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]3.84140732758325[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 52 )[/C][C]3.77564102564103[/C][C]0.0579307635214386[/C][C]65.175060643621[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 52 )[/C][C]3.77564102564103[/C][C]0.0579307635214386[/C][C]65.175060643621[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 52 )[/C][C]3.77564102564103[/C][C]0.0579307635214386[/C][C]65.175060643621[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 52 )[/C][C]3.77564102564103[/C][C]0.0579307635214386[/C][C]65.175060643621[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 52 )[/C][C]3.77564102564103[/C][C]0.0579307635214386[/C][C]65.175060643621[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 52 )[/C][C]3.77564102564103[/C][C]0.0579307635214386[/C][C]65.175060643621[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 52 )[/C][C]3.77564102564103[/C][C]0.0579307635214386[/C][C]65.175060643621[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 52 )[/C][C]3.82692307692308[/C][C]0.0499490737661478[/C][C]76.6164973316625[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 52 )[/C][C]3.82692307692308[/C][C]0.0499490737661478[/C][C]76.6164973316625[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 52 )[/C][C]3.82692307692308[/C][C]0.0499490737661478[/C][C]76.6164973316625[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 52 )[/C][C]3.82692307692308[/C][C]0.0499490737661478[/C][C]76.6164973316625[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 52 )[/C][C]3.82692307692308[/C][C]0.0499490737661478[/C][C]76.6164973316625[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 52 )[/C][C]3.82692307692308[/C][C]0.0499490737661478[/C][C]76.6164973316625[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 52 )[/C][C]3.82692307692308[/C][C]0.0499490737661478[/C][C]76.6164973316625[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 52 )[/C][C]3.82692307692308[/C][C]0.0499490737661478[/C][C]76.6164973316625[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 52 )[/C][C]3.82692307692308[/C][C]0.0499490737661478[/C][C]76.6164973316625[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 52 )[/C][C]3.82692307692308[/C][C]0.0499490737661478[/C][C]76.6164973316625[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 52 )[/C][C]3.82692307692308[/C][C]0.0499490737661478[/C][C]76.6164973316625[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 52 )[/C][C]3.70512820512821[/C][C]0.0366256053091788[/C][C]101.162238107766[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 52 )[/C][C]3.70512820512821[/C][C]0.0366256053091788[/C][C]101.162238107766[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 52 )[/C][C]3.70512820512821[/C][C]0.0366256053091788[/C][C]101.162238107766[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 52 )[/C][C]3.70512820512821[/C][C]0.0366256053091788[/C][C]101.162238107766[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 52 )[/C][C]3.70512820512821[/C][C]0.0366256053091788[/C][C]101.162238107766[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 52 )[/C][C]3.70512820512821[/C][C]0.0366256053091788[/C][C]101.162238107766[/C][/ROW]
[ROW][C]Winsorized Mean ( 25 / 52 )[/C][C]3.70512820512821[/C][C]0.0366256053091788[/C][C]101.162238107766[/C][/ROW]
[ROW][C]Winsorized Mean ( 26 / 52 )[/C][C]3.70512820512821[/C][C]0.0366256053091788[/C][C]101.162238107766[/C][/ROW]
[ROW][C]Winsorized Mean ( 27 / 52 )[/C][C]3.70512820512821[/C][C]0.0366256053091788[/C][C]101.162238107766[/C][/ROW]
[ROW][C]Winsorized Mean ( 28 / 52 )[/C][C]3.70512820512821[/C][C]0.0366256053091788[/C][C]101.162238107766[/C][/ROW]
[ROW][C]Winsorized Mean ( 29 / 52 )[/C][C]3.70512820512821[/C][C]0.0366256053091788[/C][C]101.162238107766[/C][/ROW]
[ROW][C]Winsorized Mean ( 30 / 52 )[/C][C]3.70512820512821[/C][C]0.0366256053091788[/C][C]101.162238107766[/C][/ROW]
[ROW][C]Winsorized Mean ( 31 / 52 )[/C][C]3.70512820512821[/C][C]0.0366256053091788[/C][C]101.162238107766[/C][/ROW]
[ROW][C]Winsorized Mean ( 32 / 52 )[/C][C]3.70512820512821[/C][C]0.0366256053091788[/C][C]101.162238107766[/C][/ROW]
[ROW][C]Winsorized Mean ( 33 / 52 )[/C][C]3.70512820512821[/C][C]0.0366256053091788[/C][C]101.162238107766[/C][/ROW]
[ROW][C]Winsorized Mean ( 34 / 52 )[/C][C]3.70512820512821[/C][C]0.0366256053091788[/C][C]101.162238107766[/C][/ROW]
[ROW][C]Winsorized Mean ( 35 / 52 )[/C][C]3.70512820512821[/C][C]0.0366256053091788[/C][C]101.162238107766[/C][/ROW]
[ROW][C]Winsorized Mean ( 36 / 52 )[/C][C]3.70512820512821[/C][C]0.0366256053091788[/C][C]101.162238107766[/C][/ROW]
[ROW][C]Winsorized Mean ( 37 / 52 )[/C][C]3.70512820512821[/C][C]0.0366256053091788[/C][C]101.162238107766[/C][/ROW]
[ROW][C]Winsorized Mean ( 38 / 52 )[/C][C]3.70512820512821[/C][C]0.0366256053091788[/C][C]101.162238107766[/C][/ROW]
[ROW][C]Winsorized Mean ( 39 / 52 )[/C][C]3.70512820512821[/C][C]0.0366256053091788[/C][C]101.162238107766[/C][/ROW]
[ROW][C]Winsorized Mean ( 40 / 52 )[/C][C]3.70512820512821[/C][C]0.0366256053091788[/C][C]101.162238107766[/C][/ROW]
[ROW][C]Winsorized Mean ( 41 / 52 )[/C][C]3.70512820512821[/C][C]0.0366256053091788[/C][C]101.162238107766[/C][/ROW]
[ROW][C]Winsorized Mean ( 42 / 52 )[/C][C]3.70512820512821[/C][C]0.0366256053091788[/C][C]101.162238107766[/C][/ROW]
[ROW][C]Winsorized Mean ( 43 / 52 )[/C][C]3.70512820512821[/C][C]0.0366256053091788[/C][C]101.162238107766[/C][/ROW]
[ROW][C]Winsorized Mean ( 44 / 52 )[/C][C]3.70512820512821[/C][C]0.0366256053091788[/C][C]101.162238107766[/C][/ROW]
[ROW][C]Winsorized Mean ( 45 / 52 )[/C][C]3.70512820512821[/C][C]0.0366256053091788[/C][C]101.162238107766[/C][/ROW]
[ROW][C]Winsorized Mean ( 46 / 52 )[/C][C]4[/C][C]0[/C][C]Inf[/C][/ROW]
[ROW][C]Winsorized Mean ( 47 / 52 )[/C][C]4[/C][C]0[/C][C]Inf[/C][/ROW]
[ROW][C]Winsorized Mean ( 48 / 52 )[/C][C]4[/C][C]0[/C][C]Inf[/C][/ROW]
[ROW][C]Winsorized Mean ( 49 / 52 )[/C][C]4[/C][C]0[/C][C]Inf[/C][/ROW]
[ROW][C]Winsorized Mean ( 50 / 52 )[/C][C]4[/C][C]0[/C][C]Inf[/C][/ROW]
[ROW][C]Winsorized Mean ( 51 / 52 )[/C][C]4[/C][C]0[/C][C]Inf[/C][/ROW]
[ROW][C]Winsorized Mean ( 52 / 52 )[/C][C]4[/C][C]0[/C][C]Inf[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 52 )[/C][C]3.77922077922078[/C][C]0.0569778698656123[/C][C]66.3278705949245[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 52 )[/C][C]3.78289473684211[/C][C]0.0559447543726599[/C][C]67.6183992451453[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 52 )[/C][C]3.78666666666667[/C][C]0.054822607288853[/C][C]69.071261910533[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 52 )[/C][C]3.79054054054054[/C][C]0.0536011315153162[/C][C]70.7175470625544[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 52 )[/C][C]3.79452054794521[/C][C]0.0522681652413994[/C][C]72.5971636926664[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 52 )[/C][C]3.79861111111111[/C][C]0.0508091683851277[/C][C]74.7623161693589[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 52 )[/C][C]3.80281690140845[/C][C]0.0492065062130281[/C][C]77.2828065651531[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 52 )[/C][C]3.80714285714286[/C][C]0.047438420701218[/C][C]80.2544182725102[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 52 )[/C][C]3.80434782608696[/C][C]0.0469741299347235[/C][C]80.9881488251848[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 52 )[/C][C]3.80147058823529[/C][C]0.0464653136743509[/C][C]81.8130835159674[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 52 )[/C][C]3.79850746268657[/C][C]0.0459074158010089[/C][C]82.7427855915838[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 52 )[/C][C]3.79545454545455[/C][C]0.0452952331912956[/C][C]83.7936859586346[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 52 )[/C][C]3.79230769230769[/C][C]0.0446227863825011[/C][C]84.9859006965745[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 52 )[/C][C]3.7890625[/C][C]0.0438831547231364[/C][C]86.344350671815[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 52 )[/C][C]3.78571428571429[/C][C]0.0430682630651239[/C][C]87.9003241897607[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 52 )[/C][C]3.78225806451613[/C][C]0.042168600982961[/C][C]89.693705182309[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 52 )[/C][C]3.77868852459016[/C][C]0.0411728458525821[/C][C]91.776228879578[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 52 )[/C][C]3.775[/C][C]0.0400673452684695[/C][C]94.2163743244225[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 52 )[/C][C]3.77118644067797[/C][C]0.0388353872453885[/C][C]97.1069611550166[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 52 )[/C][C]3.77586206896552[/C][C]0.0388866937011782[/C][C]97.0990770771317[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 52 )[/C][C]3.78070175438596[/C][C]0.0389243110651875[/C][C]97.1295740611652[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 52 )[/C][C]3.78571428571429[/C][C]0.0389464112004479[/C][C]97.2031611906452[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 52 )[/C][C]3.79090909090909[/C][C]0.0389509101572414[/C][C]97.3253019147827[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 52 )[/C][C]3.79629629629630[/C][C]0.0389354251882485[/C][C]97.5023716305041[/C][/ROW]
[ROW][C]Trimmed Mean ( 25 / 52 )[/C][C]3.80188679245283[/C][C]0.0388972228831855[/C][C]97.7418568896422[/C][/ROW]
[ROW][C]Trimmed Mean ( 26 / 52 )[/C][C]3.80769230769231[/C][C]0.0388331561600309[/C][C]98.0526097853305[/C][/ROW]
[ROW][C]Trimmed Mean ( 27 / 52 )[/C][C]3.81372549019608[/C][C]0.0387395871414935[/C][C]98.4451764100305[/C][/ROW]
[ROW][C]Trimmed Mean ( 28 / 52 )[/C][C]3.82[/C][C]0.0386122919665369[/C][C]98.9322261240171[/C][/ROW]
[ROW][C]Trimmed Mean ( 29 / 52 )[/C][C]3.8265306122449[/C][C]0.038446342212965[/C][C]99.5291201188576[/C][/ROW]
[ROW][C]Trimmed Mean ( 30 / 52 )[/C][C]3.83333333333333[/C][C]0.0382359556450936[/C][C]100.254675701435[/C][/ROW]
[ROW][C]Trimmed Mean ( 31 / 52 )[/C][C]3.83333333333333[/C][C]0.0379743061437828[/C][C]100.945447661877[/C][/ROW]
[ROW][C]Trimmed Mean ( 32 / 52 )[/C][C]3.84782608695652[/C][C]0.0376532784254104[/C][C]102.190997646564[/C][/ROW]
[ROW][C]Trimmed Mean ( 33 / 52 )[/C][C]3.85555555555556[/C][C]0.0372631466754029[/C][C]103.468329959922[/C][/ROW]
[ROW][C]Trimmed Mean ( 34 / 52 )[/C][C]3.86363636363636[/C][C]0.0367921460636536[/C][C]105.012530580628[/C][/ROW]
[ROW][C]Trimmed Mean ( 35 / 52 )[/C][C]3.87209302325581[/C][C]0.0362258896767862[/C][C]106.887451427786[/C][/ROW]
[ROW][C]Trimmed Mean ( 36 / 52 )[/C][C]3.88095238095238[/C][C]0.0355465558372129[/C][C]109.179420890321[/C][/ROW]
[ROW][C]Trimmed Mean ( 37 / 52 )[/C][C]3.89024390243902[/C][C]0.0347317225419412[/C][C]112.008377866697[/C][/ROW]
[ROW][C]Trimmed Mean ( 38 / 52 )[/C][C]3.9[/C][C]0.0337526370277807[/C][C]115.546527425103[/C][/ROW]
[ROW][C]Trimmed Mean ( 39 / 52 )[/C][C]3.91025641025641[/C][C]0.032571535227231[/C][C]120.051338783297[/C][/ROW]
[ROW][C]Trimmed Mean ( 40 / 52 )[/C][C]3.92105263157895[/C][C]0.0311372620163138[/C][C]125.927983954549[/C][/ROW]
[ROW][C]Trimmed Mean ( 41 / 52 )[/C][C]3.93243243243243[/C][C]0.0293776057149328[/C][C]133.858166339048[/C][/ROW]
[ROW][C]Trimmed Mean ( 42 / 52 )[/C][C]3.94444444444444[/C][C]0.0271845896182163[/C][C]145.098546633983[/C][/ROW]
[ROW][C]Trimmed Mean ( 43 / 52 )[/C][C]3.95714285714286[/C][C]0.0243823433868205[/C][C]162.295428062990[/C][/ROW]
[ROW][C]Trimmed Mean ( 44 / 52 )[/C][C]3.97058823529412[/C][C]0.0206414713705158[/C][C]192.359748199234[/C][/ROW]
[ROW][C]Trimmed Mean ( 45 / 52 )[/C][C]3.97058823529412[/C][C]0.0151515151515152[/C][C]262.058823529412[/C][/ROW]
[ROW][C]Trimmed Mean ( 46 / 52 )[/C][C]4[/C][C]0[/C][C]Inf[/C][/ROW]
[ROW][C]Trimmed Mean ( 47 / 52 )[/C][C]4[/C][C]0[/C][C]Inf[/C][/ROW]
[ROW][C]Trimmed Mean ( 48 / 52 )[/C][C]4[/C][C]0[/C][C]Inf[/C][/ROW]
[ROW][C]Trimmed Mean ( 49 / 52 )[/C][C]4[/C][C]0[/C][C]Inf[/C][/ROW]
[ROW][C]Trimmed Mean ( 50 / 52 )[/C][C]4[/C][C]0[/C][C]Inf[/C][/ROW]
[ROW][C]Trimmed Mean ( 51 / 52 )[/C][C]4[/C][C]0[/C][C]Inf[/C][/ROW]
[ROW][C]Trimmed Mean ( 52 / 52 )[/C][C]4[/C][C]0[/C][C]Inf[/C][/ROW]
[ROW][C]Median[/C][C]4[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]3[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]3.70542635658915[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]3.70542635658915[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]3.70542635658915[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]3.70542635658915[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]3.70542635658915[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]3.70542635658915[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]3.70542635658915[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]3.70542635658915[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]156[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=94137&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=94137&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 Mean3.769230769230770.059530944227420663.3154877374618
Geometric Mean3.68181721478552
Harmonic Mean3.56843309187953
Quadratic Mean3.84140732758325
Winsorized Mean ( 1 / 52 )3.775641025641030.057930763521438665.175060643621
Winsorized Mean ( 2 / 52 )3.775641025641030.057930763521438665.175060643621
Winsorized Mean ( 3 / 52 )3.775641025641030.057930763521438665.175060643621
Winsorized Mean ( 4 / 52 )3.775641025641030.057930763521438665.175060643621
Winsorized Mean ( 5 / 52 )3.775641025641030.057930763521438665.175060643621
Winsorized Mean ( 6 / 52 )3.775641025641030.057930763521438665.175060643621
Winsorized Mean ( 7 / 52 )3.775641025641030.057930763521438665.175060643621
Winsorized Mean ( 8 / 52 )3.826923076923080.049949073766147876.6164973316625
Winsorized Mean ( 9 / 52 )3.826923076923080.049949073766147876.6164973316625
Winsorized Mean ( 10 / 52 )3.826923076923080.049949073766147876.6164973316625
Winsorized Mean ( 11 / 52 )3.826923076923080.049949073766147876.6164973316625
Winsorized Mean ( 12 / 52 )3.826923076923080.049949073766147876.6164973316625
Winsorized Mean ( 13 / 52 )3.826923076923080.049949073766147876.6164973316625
Winsorized Mean ( 14 / 52 )3.826923076923080.049949073766147876.6164973316625
Winsorized Mean ( 15 / 52 )3.826923076923080.049949073766147876.6164973316625
Winsorized Mean ( 16 / 52 )3.826923076923080.049949073766147876.6164973316625
Winsorized Mean ( 17 / 52 )3.826923076923080.049949073766147876.6164973316625
Winsorized Mean ( 18 / 52 )3.826923076923080.049949073766147876.6164973316625
Winsorized Mean ( 19 / 52 )3.705128205128210.0366256053091788101.162238107766
Winsorized Mean ( 20 / 52 )3.705128205128210.0366256053091788101.162238107766
Winsorized Mean ( 21 / 52 )3.705128205128210.0366256053091788101.162238107766
Winsorized Mean ( 22 / 52 )3.705128205128210.0366256053091788101.162238107766
Winsorized Mean ( 23 / 52 )3.705128205128210.0366256053091788101.162238107766
Winsorized Mean ( 24 / 52 )3.705128205128210.0366256053091788101.162238107766
Winsorized Mean ( 25 / 52 )3.705128205128210.0366256053091788101.162238107766
Winsorized Mean ( 26 / 52 )3.705128205128210.0366256053091788101.162238107766
Winsorized Mean ( 27 / 52 )3.705128205128210.0366256053091788101.162238107766
Winsorized Mean ( 28 / 52 )3.705128205128210.0366256053091788101.162238107766
Winsorized Mean ( 29 / 52 )3.705128205128210.0366256053091788101.162238107766
Winsorized Mean ( 30 / 52 )3.705128205128210.0366256053091788101.162238107766
Winsorized Mean ( 31 / 52 )3.705128205128210.0366256053091788101.162238107766
Winsorized Mean ( 32 / 52 )3.705128205128210.0366256053091788101.162238107766
Winsorized Mean ( 33 / 52 )3.705128205128210.0366256053091788101.162238107766
Winsorized Mean ( 34 / 52 )3.705128205128210.0366256053091788101.162238107766
Winsorized Mean ( 35 / 52 )3.705128205128210.0366256053091788101.162238107766
Winsorized Mean ( 36 / 52 )3.705128205128210.0366256053091788101.162238107766
Winsorized Mean ( 37 / 52 )3.705128205128210.0366256053091788101.162238107766
Winsorized Mean ( 38 / 52 )3.705128205128210.0366256053091788101.162238107766
Winsorized Mean ( 39 / 52 )3.705128205128210.0366256053091788101.162238107766
Winsorized Mean ( 40 / 52 )3.705128205128210.0366256053091788101.162238107766
Winsorized Mean ( 41 / 52 )3.705128205128210.0366256053091788101.162238107766
Winsorized Mean ( 42 / 52 )3.705128205128210.0366256053091788101.162238107766
Winsorized Mean ( 43 / 52 )3.705128205128210.0366256053091788101.162238107766
Winsorized Mean ( 44 / 52 )3.705128205128210.0366256053091788101.162238107766
Winsorized Mean ( 45 / 52 )3.705128205128210.0366256053091788101.162238107766
Winsorized Mean ( 46 / 52 )40Inf
Winsorized Mean ( 47 / 52 )40Inf
Winsorized Mean ( 48 / 52 )40Inf
Winsorized Mean ( 49 / 52 )40Inf
Winsorized Mean ( 50 / 52 )40Inf
Winsorized Mean ( 51 / 52 )40Inf
Winsorized Mean ( 52 / 52 )40Inf
Trimmed Mean ( 1 / 52 )3.779220779220780.056977869865612366.3278705949245
Trimmed Mean ( 2 / 52 )3.782894736842110.055944754372659967.6183992451453
Trimmed Mean ( 3 / 52 )3.786666666666670.05482260728885369.071261910533
Trimmed Mean ( 4 / 52 )3.790540540540540.053601131515316270.7175470625544
Trimmed Mean ( 5 / 52 )3.794520547945210.052268165241399472.5971636926664
Trimmed Mean ( 6 / 52 )3.798611111111110.050809168385127774.7623161693589
Trimmed Mean ( 7 / 52 )3.802816901408450.049206506213028177.2828065651531
Trimmed Mean ( 8 / 52 )3.807142857142860.04743842070121880.2544182725102
Trimmed Mean ( 9 / 52 )3.804347826086960.046974129934723580.9881488251848
Trimmed Mean ( 10 / 52 )3.801470588235290.046465313674350981.8130835159674
Trimmed Mean ( 11 / 52 )3.798507462686570.045907415801008982.7427855915838
Trimmed Mean ( 12 / 52 )3.795454545454550.045295233191295683.7936859586346
Trimmed Mean ( 13 / 52 )3.792307692307690.044622786382501184.9859006965745
Trimmed Mean ( 14 / 52 )3.78906250.043883154723136486.344350671815
Trimmed Mean ( 15 / 52 )3.785714285714290.043068263065123987.9003241897607
Trimmed Mean ( 16 / 52 )3.782258064516130.04216860098296189.693705182309
Trimmed Mean ( 17 / 52 )3.778688524590160.041172845852582191.776228879578
Trimmed Mean ( 18 / 52 )3.7750.040067345268469594.2163743244225
Trimmed Mean ( 19 / 52 )3.771186440677970.038835387245388597.1069611550166
Trimmed Mean ( 20 / 52 )3.775862068965520.038886693701178297.0990770771317
Trimmed Mean ( 21 / 52 )3.780701754385960.038924311065187597.1295740611652
Trimmed Mean ( 22 / 52 )3.785714285714290.038946411200447997.2031611906452
Trimmed Mean ( 23 / 52 )3.790909090909090.038950910157241497.3253019147827
Trimmed Mean ( 24 / 52 )3.796296296296300.038935425188248597.5023716305041
Trimmed Mean ( 25 / 52 )3.801886792452830.038897222883185597.7418568896422
Trimmed Mean ( 26 / 52 )3.807692307692310.038833156160030998.0526097853305
Trimmed Mean ( 27 / 52 )3.813725490196080.038739587141493598.4451764100305
Trimmed Mean ( 28 / 52 )3.820.038612291966536998.9322261240171
Trimmed Mean ( 29 / 52 )3.82653061224490.03844634221296599.5291201188576
Trimmed Mean ( 30 / 52 )3.833333333333330.0382359556450936100.254675701435
Trimmed Mean ( 31 / 52 )3.833333333333330.0379743061437828100.945447661877
Trimmed Mean ( 32 / 52 )3.847826086956520.0376532784254104102.190997646564
Trimmed Mean ( 33 / 52 )3.855555555555560.0372631466754029103.468329959922
Trimmed Mean ( 34 / 52 )3.863636363636360.0367921460636536105.012530580628
Trimmed Mean ( 35 / 52 )3.872093023255810.0362258896767862106.887451427786
Trimmed Mean ( 36 / 52 )3.880952380952380.0355465558372129109.179420890321
Trimmed Mean ( 37 / 52 )3.890243902439020.0347317225419412112.008377866697
Trimmed Mean ( 38 / 52 )3.90.0337526370277807115.546527425103
Trimmed Mean ( 39 / 52 )3.910256410256410.032571535227231120.051338783297
Trimmed Mean ( 40 / 52 )3.921052631578950.0311372620163138125.927983954549
Trimmed Mean ( 41 / 52 )3.932432432432430.0293776057149328133.858166339048
Trimmed Mean ( 42 / 52 )3.944444444444440.0271845896182163145.098546633983
Trimmed Mean ( 43 / 52 )3.957142857142860.0243823433868205162.295428062990
Trimmed Mean ( 44 / 52 )3.970588235294120.0206414713705158192.359748199234
Trimmed Mean ( 45 / 52 )3.970588235294120.0151515151515152262.058823529412
Trimmed Mean ( 46 / 52 )40Inf
Trimmed Mean ( 47 / 52 )40Inf
Trimmed Mean ( 48 / 52 )40Inf
Trimmed Mean ( 49 / 52 )40Inf
Trimmed Mean ( 50 / 52 )40Inf
Trimmed Mean ( 51 / 52 )40Inf
Trimmed Mean ( 52 / 52 )40Inf
Median4
Midrange3
Midmean - Weighted Average at Xnp3.70542635658915
Midmean - Weighted Average at X(n+1)p3.70542635658915
Midmean - Empirical Distribution Function3.70542635658915
Midmean - Empirical Distribution Function - Averaging3.70542635658915
Midmean - Empirical Distribution Function - Interpolation3.70542635658915
Midmean - Closest Observation3.70542635658915
Midmean - True Basic - Statistics Graphics Toolkit3.70542635658915
Midmean - MS Excel (old versions)3.70542635658915
Number of observations156



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')