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 computationThu, 26 Nov 2015 17:19:48 +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/2015/Nov/26/t14485585794pnsxjz755fz9jj.htm/, Retrieved Tue, 14 May 2024 16:31:52 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=284262, Retrieved Tue, 14 May 2024 16:31:52 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsData afiek
Estimated Impact104
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [Werkloosheid - ce...] [2015-11-26 17:19:48] [acc3abca1b515ed7734f46e1e7706f6a] [Current]
- RM D    [Skewness and Kurtosis Test] [Skweness and Kurt...] [2015-12-09 16:46:42] [9378e2688aa9dcfd1390615d31e9d404]
- RM        [Skewness and Kurtosis Test] [Skewness and Kurt...] [2015-12-09 16:57:40] [9378e2688aa9dcfd1390615d31e9d404]
- RM        [Skewness and Kurtosis Test] [Skewness and Kurt...] [2015-12-09 16:58:09] [9378e2688aa9dcfd1390615d31e9d404]
- RM      [Skewness and Kurtosis Test] [Skewness and Kurt...] [2015-12-09 16:55:17] [9378e2688aa9dcfd1390615d31e9d404]
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Dataseries X:
8.5
8.4
8.5
8.7
8.7
8.6
8.5
8.3
8
8.2
8.1
8.1
8
7.9
7.9
8
8
7.9
8
7.7
7.2
7.5
7.3
7
7
7
7.2
7.3
7.1
6.8
6.4
6.1
6.5
7.7
7.9
7.5
6.9
6.6
6.9
7.7
8
8
7.7
7.3
7.4
8.1
8.3
8.1
7.9
7.9
8.3
8.6
8.7
8.5
8.3
8
8
8.8
8.7
8.5
8.1
7.8
7.7
7.5
7.2
6.9
6.6
6.5
6.6
7.7
8
7.7
7.3
7
7
7.3
7.3
7.1
7.1
7
7
7.5
7.8
7.9
8.1
8.3
8.4
8.6
8.5
8.4
8.3
8
8
8.7
8.7
8.6
8.5
8.5
8.6
8.8
8.7
8.6
8.4
8.1
8.1
8.7
8.7
8.6
8.6
8.5
8.6
8.8
8.8
8.7
8.5
8.3
8.3
8.9
9
8.8




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' @ fisher.wessa.net

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 2 seconds \tabularnewline
R Server & 'Sir Ronald Aylmer Fisher' @ fisher.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=284262&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' @ fisher.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=284262&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=284262&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' @ fisher.wessa.net







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean7.9250.0617808769013542128.275939052369
Geometric Mean7.89516429581835
Harmonic Mean7.86413897159824
Quadratic Mean7.95360505263703
Winsorized Mean ( 1 / 40 )7.926666666666670.061091075571416129.751630537268
Winsorized Mean ( 2 / 40 )7.926666666666670.0605383566321068130.936270946984
Winsorized Mean ( 3 / 40 )7.926666666666670.0605383566321068130.936270946984
Winsorized Mean ( 4 / 40 )7.930.0598972041920824132.393491598866
Winsorized Mean ( 5 / 40 )7.930.0598972041920824132.393491598866
Winsorized Mean ( 6 / 40 )7.930.0598972041920824132.393491598866
Winsorized Mean ( 7 / 40 )7.935833333333330.0571473577242606138.866146211417
Winsorized Mean ( 8 / 40 )7.94250.0560694659686143141.654639700794
Winsorized Mean ( 9 / 40 )7.94250.0560694659686143141.654639700794
Winsorized Mean ( 10 / 40 )7.94250.0560694659686143141.654639700794
Winsorized Mean ( 11 / 40 )7.951666666666670.0546824719243833145.415274526406
Winsorized Mean ( 12 / 40 )7.951666666666670.0546824719243833145.415274526406
Winsorized Mean ( 13 / 40 )7.951666666666670.0546824719243833145.415274526406
Winsorized Mean ( 14 / 40 )7.951666666666670.0546824719243833145.415274526406
Winsorized Mean ( 15 / 40 )7.951666666666670.0546824719243833145.415274526406
Winsorized Mean ( 16 / 40 )7.951666666666670.0546824719243833145.415274526406
Winsorized Mean ( 17 / 40 )7.93750.0531245365773163149.413068073506
Winsorized Mean ( 18 / 40 )7.95250.0509567084342561156.063848006593
Winsorized Mean ( 19 / 40 )7.95250.0509567084342561156.063848006593
Winsorized Mean ( 20 / 40 )7.95250.0509567084342561156.063848006593
Winsorized Mean ( 21 / 40 )7.970.0485590691146083164.129999716208
Winsorized Mean ( 22 / 40 )7.970.0485590691146083164.129999716208
Winsorized Mean ( 23 / 40 )7.970.0485590691146083164.129999716208
Winsorized Mean ( 24 / 40 )7.990.0459630834694193173.835160674457
Winsorized Mean ( 25 / 40 )7.990.0459630834694193173.835160674457
Winsorized Mean ( 26 / 40 )7.968333333333330.0436433106224941182.578572057877
Winsorized Mean ( 27 / 40 )7.968333333333330.0436433106224941182.578572057877
Winsorized Mean ( 28 / 40 )7.968333333333330.0436433106224941182.578572057877
Winsorized Mean ( 29 / 40 )7.968333333333330.0436433106224941182.578572057877
Winsorized Mean ( 30 / 40 )7.993333333333330.0404929937110426197.400404385352
Winsorized Mean ( 31 / 40 )8.019166666666670.0373921574135685214.461192435951
Winsorized Mean ( 32 / 40 )8.019166666666670.0373921574135685214.461192435951
Winsorized Mean ( 33 / 40 )8.019166666666670.0373921574135685214.461192435951
Winsorized Mean ( 34 / 40 )8.019166666666670.0373921574135685214.461192435951
Winsorized Mean ( 35 / 40 )8.07750.030961765976458260.886281685024
Winsorized Mean ( 36 / 40 )8.04750.027627030262416291.290809166264
Winsorized Mean ( 37 / 40 )8.04750.027627030262416291.290809166264
Winsorized Mean ( 38 / 40 )8.04750.027627030262416291.290809166264
Winsorized Mean ( 39 / 40 )8.04750.027627030262416291.290809166264
Winsorized Mean ( 40 / 40 )8.014166666666670.0241753582361256331.501464772132
Trimmed Mean ( 1 / 40 )7.931355932203390.0601882597796375131.775797493429
Trimmed Mean ( 2 / 40 )7.936206896551720.0591848241180395134.091923306616
Trimmed Mean ( 3 / 40 )7.941228070175440.058387632857626136.008734752778
Trimmed Mean ( 4 / 40 )7.946428571428570.0574966924714401138.206707722809
Trimmed Mean ( 5 / 40 )7.950909090909090.0567061614659224140.212436979837
Trimmed Mean ( 6 / 40 )7.955555555555560.0558197249939143142.522299356059
Trimmed Mean ( 7 / 40 )7.960377358490570.0548243826187695145.197756513637
Trimmed Mean ( 8 / 40 )7.964423076923080.0542777664619343146.734539685022
Trimmed Mean ( 9 / 40 )7.967647058823530.0538583487778168147.937083843633
Trimmed Mean ( 10 / 40 )7.9710.0533767815447954149.334593980915
Trimmed Mean ( 11 / 40 )7.974489795918370.0528249160302959150.960766153322
Trimmed Mean ( 12 / 40 )7.977083333333330.0524086332504606152.209337251954
Trimmed Mean ( 13 / 40 )7.979787234042550.0519265048092227153.674645797174
Trimmed Mean ( 14 / 40 )7.982608695652170.05136941463361155.396138978569
Trimmed Mean ( 15 / 40 )7.985555555555560.050726583710212157.423484324807
Trimmed Mean ( 16 / 40 )7.988636363636360.0499851550110441159.820177848229
Trimmed Mean ( 17 / 40 )7.991860465116280.0491296371691217162.668827323219
Trimmed Mean ( 18 / 40 )7.996428571428570.0483356507814287165.435417588314
Trimmed Mean ( 19 / 40 )80.0477118723613698167.673151441385
Trimmed Mean ( 20 / 40 )8.003750.0469797879378307170.365817968176
Trimmed Mean ( 21 / 40 )8.007692307692310.0461205340988719173.625316014894
Trimmed Mean ( 22 / 40 )8.010526315789470.0454443537638286176.271101959545
Trimmed Mean ( 23 / 40 )8.013513513513510.0446436515648505179.499508499498
Trimmed Mean ( 24 / 40 )8.016666666666670.0436947728777575183.469695313315
Trimmed Mean ( 25 / 40 )8.018571428571430.0429402231304904186.738000969485
Trimmed Mean ( 26 / 40 )8.020588235294120.0420375904948833190.795622224598
Trimmed Mean ( 27 / 40 )8.024242424242420.0412542633841497194.50698584829
Trimmed Mean ( 28 / 40 )8.0281250.0403032127544856199.193177201649
Trimmed Mean ( 29 / 40 )8.032258064516130.039145702254721205.188758966444
Trimmed Mean ( 30 / 40 )8.036666666666670.0377298355369088213.005610872724
Trimmed Mean ( 31 / 40 )8.039655172413790.0365595136034498219.905966463819
Trimmed Mean ( 32 / 40 )8.041071428571430.0356549832325517225.52447651217
Trimmed Mean ( 33 / 40 )8.042592592592590.0345280501381729232.929243337174
Trimmed Mean ( 34 / 40 )8.044230769230770.0331154411107301242.914800450122
Trimmed Mean ( 35 / 40 )8.0460.0313258060143547256.848937783533
Trimmed Mean ( 36 / 40 )8.043750.0303505304497559265.028316830116
Trimmed Mean ( 37 / 40 )8.043478260869560.0297578267077347270.297906492576
Trimmed Mean ( 38 / 40 )8.043181818181820.0289706652086081277.631934243331
Trimmed Mean ( 39 / 40 )8.042857142857140.0279253312383553288.012954052639
Trimmed Mean ( 40 / 40 )8.04250.0265270785695654303.180765982545
Median8
Midrange7.55
Midmean - Weighted Average at Xnp8
Midmean - Weighted Average at X(n+1)p8.065625
Midmean - Empirical Distribution Function8
Midmean - Empirical Distribution Function - Averaging8.065625
Midmean - Empirical Distribution Function - Interpolation8.065625
Midmean - Closest Observation8
Midmean - True Basic - Statistics Graphics Toolkit8.065625
Midmean - MS Excel (old versions)8
Number of observations120

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 7.925 & 0.0617808769013542 & 128.275939052369 \tabularnewline
Geometric Mean & 7.89516429581835 &  &  \tabularnewline
Harmonic Mean & 7.86413897159824 &  &  \tabularnewline
Quadratic Mean & 7.95360505263703 &  &  \tabularnewline
Winsorized Mean ( 1 / 40 ) & 7.92666666666667 & 0.061091075571416 & 129.751630537268 \tabularnewline
Winsorized Mean ( 2 / 40 ) & 7.92666666666667 & 0.0605383566321068 & 130.936270946984 \tabularnewline
Winsorized Mean ( 3 / 40 ) & 7.92666666666667 & 0.0605383566321068 & 130.936270946984 \tabularnewline
Winsorized Mean ( 4 / 40 ) & 7.93 & 0.0598972041920824 & 132.393491598866 \tabularnewline
Winsorized Mean ( 5 / 40 ) & 7.93 & 0.0598972041920824 & 132.393491598866 \tabularnewline
Winsorized Mean ( 6 / 40 ) & 7.93 & 0.0598972041920824 & 132.393491598866 \tabularnewline
Winsorized Mean ( 7 / 40 ) & 7.93583333333333 & 0.0571473577242606 & 138.866146211417 \tabularnewline
Winsorized Mean ( 8 / 40 ) & 7.9425 & 0.0560694659686143 & 141.654639700794 \tabularnewline
Winsorized Mean ( 9 / 40 ) & 7.9425 & 0.0560694659686143 & 141.654639700794 \tabularnewline
Winsorized Mean ( 10 / 40 ) & 7.9425 & 0.0560694659686143 & 141.654639700794 \tabularnewline
Winsorized Mean ( 11 / 40 ) & 7.95166666666667 & 0.0546824719243833 & 145.415274526406 \tabularnewline
Winsorized Mean ( 12 / 40 ) & 7.95166666666667 & 0.0546824719243833 & 145.415274526406 \tabularnewline
Winsorized Mean ( 13 / 40 ) & 7.95166666666667 & 0.0546824719243833 & 145.415274526406 \tabularnewline
Winsorized Mean ( 14 / 40 ) & 7.95166666666667 & 0.0546824719243833 & 145.415274526406 \tabularnewline
Winsorized Mean ( 15 / 40 ) & 7.95166666666667 & 0.0546824719243833 & 145.415274526406 \tabularnewline
Winsorized Mean ( 16 / 40 ) & 7.95166666666667 & 0.0546824719243833 & 145.415274526406 \tabularnewline
Winsorized Mean ( 17 / 40 ) & 7.9375 & 0.0531245365773163 & 149.413068073506 \tabularnewline
Winsorized Mean ( 18 / 40 ) & 7.9525 & 0.0509567084342561 & 156.063848006593 \tabularnewline
Winsorized Mean ( 19 / 40 ) & 7.9525 & 0.0509567084342561 & 156.063848006593 \tabularnewline
Winsorized Mean ( 20 / 40 ) & 7.9525 & 0.0509567084342561 & 156.063848006593 \tabularnewline
Winsorized Mean ( 21 / 40 ) & 7.97 & 0.0485590691146083 & 164.129999716208 \tabularnewline
Winsorized Mean ( 22 / 40 ) & 7.97 & 0.0485590691146083 & 164.129999716208 \tabularnewline
Winsorized Mean ( 23 / 40 ) & 7.97 & 0.0485590691146083 & 164.129999716208 \tabularnewline
Winsorized Mean ( 24 / 40 ) & 7.99 & 0.0459630834694193 & 173.835160674457 \tabularnewline
Winsorized Mean ( 25 / 40 ) & 7.99 & 0.0459630834694193 & 173.835160674457 \tabularnewline
Winsorized Mean ( 26 / 40 ) & 7.96833333333333 & 0.0436433106224941 & 182.578572057877 \tabularnewline
Winsorized Mean ( 27 / 40 ) & 7.96833333333333 & 0.0436433106224941 & 182.578572057877 \tabularnewline
Winsorized Mean ( 28 / 40 ) & 7.96833333333333 & 0.0436433106224941 & 182.578572057877 \tabularnewline
Winsorized Mean ( 29 / 40 ) & 7.96833333333333 & 0.0436433106224941 & 182.578572057877 \tabularnewline
Winsorized Mean ( 30 / 40 ) & 7.99333333333333 & 0.0404929937110426 & 197.400404385352 \tabularnewline
Winsorized Mean ( 31 / 40 ) & 8.01916666666667 & 0.0373921574135685 & 214.461192435951 \tabularnewline
Winsorized Mean ( 32 / 40 ) & 8.01916666666667 & 0.0373921574135685 & 214.461192435951 \tabularnewline
Winsorized Mean ( 33 / 40 ) & 8.01916666666667 & 0.0373921574135685 & 214.461192435951 \tabularnewline
Winsorized Mean ( 34 / 40 ) & 8.01916666666667 & 0.0373921574135685 & 214.461192435951 \tabularnewline
Winsorized Mean ( 35 / 40 ) & 8.0775 & 0.030961765976458 & 260.886281685024 \tabularnewline
Winsorized Mean ( 36 / 40 ) & 8.0475 & 0.027627030262416 & 291.290809166264 \tabularnewline
Winsorized Mean ( 37 / 40 ) & 8.0475 & 0.027627030262416 & 291.290809166264 \tabularnewline
Winsorized Mean ( 38 / 40 ) & 8.0475 & 0.027627030262416 & 291.290809166264 \tabularnewline
Winsorized Mean ( 39 / 40 ) & 8.0475 & 0.027627030262416 & 291.290809166264 \tabularnewline
Winsorized Mean ( 40 / 40 ) & 8.01416666666667 & 0.0241753582361256 & 331.501464772132 \tabularnewline
Trimmed Mean ( 1 / 40 ) & 7.93135593220339 & 0.0601882597796375 & 131.775797493429 \tabularnewline
Trimmed Mean ( 2 / 40 ) & 7.93620689655172 & 0.0591848241180395 & 134.091923306616 \tabularnewline
Trimmed Mean ( 3 / 40 ) & 7.94122807017544 & 0.058387632857626 & 136.008734752778 \tabularnewline
Trimmed Mean ( 4 / 40 ) & 7.94642857142857 & 0.0574966924714401 & 138.206707722809 \tabularnewline
Trimmed Mean ( 5 / 40 ) & 7.95090909090909 & 0.0567061614659224 & 140.212436979837 \tabularnewline
Trimmed Mean ( 6 / 40 ) & 7.95555555555556 & 0.0558197249939143 & 142.522299356059 \tabularnewline
Trimmed Mean ( 7 / 40 ) & 7.96037735849057 & 0.0548243826187695 & 145.197756513637 \tabularnewline
Trimmed Mean ( 8 / 40 ) & 7.96442307692308 & 0.0542777664619343 & 146.734539685022 \tabularnewline
Trimmed Mean ( 9 / 40 ) & 7.96764705882353 & 0.0538583487778168 & 147.937083843633 \tabularnewline
Trimmed Mean ( 10 / 40 ) & 7.971 & 0.0533767815447954 & 149.334593980915 \tabularnewline
Trimmed Mean ( 11 / 40 ) & 7.97448979591837 & 0.0528249160302959 & 150.960766153322 \tabularnewline
Trimmed Mean ( 12 / 40 ) & 7.97708333333333 & 0.0524086332504606 & 152.209337251954 \tabularnewline
Trimmed Mean ( 13 / 40 ) & 7.97978723404255 & 0.0519265048092227 & 153.674645797174 \tabularnewline
Trimmed Mean ( 14 / 40 ) & 7.98260869565217 & 0.05136941463361 & 155.396138978569 \tabularnewline
Trimmed Mean ( 15 / 40 ) & 7.98555555555556 & 0.050726583710212 & 157.423484324807 \tabularnewline
Trimmed Mean ( 16 / 40 ) & 7.98863636363636 & 0.0499851550110441 & 159.820177848229 \tabularnewline
Trimmed Mean ( 17 / 40 ) & 7.99186046511628 & 0.0491296371691217 & 162.668827323219 \tabularnewline
Trimmed Mean ( 18 / 40 ) & 7.99642857142857 & 0.0483356507814287 & 165.435417588314 \tabularnewline
Trimmed Mean ( 19 / 40 ) & 8 & 0.0477118723613698 & 167.673151441385 \tabularnewline
Trimmed Mean ( 20 / 40 ) & 8.00375 & 0.0469797879378307 & 170.365817968176 \tabularnewline
Trimmed Mean ( 21 / 40 ) & 8.00769230769231 & 0.0461205340988719 & 173.625316014894 \tabularnewline
Trimmed Mean ( 22 / 40 ) & 8.01052631578947 & 0.0454443537638286 & 176.271101959545 \tabularnewline
Trimmed Mean ( 23 / 40 ) & 8.01351351351351 & 0.0446436515648505 & 179.499508499498 \tabularnewline
Trimmed Mean ( 24 / 40 ) & 8.01666666666667 & 0.0436947728777575 & 183.469695313315 \tabularnewline
Trimmed Mean ( 25 / 40 ) & 8.01857142857143 & 0.0429402231304904 & 186.738000969485 \tabularnewline
Trimmed Mean ( 26 / 40 ) & 8.02058823529412 & 0.0420375904948833 & 190.795622224598 \tabularnewline
Trimmed Mean ( 27 / 40 ) & 8.02424242424242 & 0.0412542633841497 & 194.50698584829 \tabularnewline
Trimmed Mean ( 28 / 40 ) & 8.028125 & 0.0403032127544856 & 199.193177201649 \tabularnewline
Trimmed Mean ( 29 / 40 ) & 8.03225806451613 & 0.039145702254721 & 205.188758966444 \tabularnewline
Trimmed Mean ( 30 / 40 ) & 8.03666666666667 & 0.0377298355369088 & 213.005610872724 \tabularnewline
Trimmed Mean ( 31 / 40 ) & 8.03965517241379 & 0.0365595136034498 & 219.905966463819 \tabularnewline
Trimmed Mean ( 32 / 40 ) & 8.04107142857143 & 0.0356549832325517 & 225.52447651217 \tabularnewline
Trimmed Mean ( 33 / 40 ) & 8.04259259259259 & 0.0345280501381729 & 232.929243337174 \tabularnewline
Trimmed Mean ( 34 / 40 ) & 8.04423076923077 & 0.0331154411107301 & 242.914800450122 \tabularnewline
Trimmed Mean ( 35 / 40 ) & 8.046 & 0.0313258060143547 & 256.848937783533 \tabularnewline
Trimmed Mean ( 36 / 40 ) & 8.04375 & 0.0303505304497559 & 265.028316830116 \tabularnewline
Trimmed Mean ( 37 / 40 ) & 8.04347826086956 & 0.0297578267077347 & 270.297906492576 \tabularnewline
Trimmed Mean ( 38 / 40 ) & 8.04318181818182 & 0.0289706652086081 & 277.631934243331 \tabularnewline
Trimmed Mean ( 39 / 40 ) & 8.04285714285714 & 0.0279253312383553 & 288.012954052639 \tabularnewline
Trimmed Mean ( 40 / 40 ) & 8.0425 & 0.0265270785695654 & 303.180765982545 \tabularnewline
Median & 8 &  &  \tabularnewline
Midrange & 7.55 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 8 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 8.065625 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 8 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 8.065625 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 8.065625 &  &  \tabularnewline
Midmean - Closest Observation & 8 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 8.065625 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 8 &  &  \tabularnewline
Number of observations & 120 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=284262&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]7.925[/C][C]0.0617808769013542[/C][C]128.275939052369[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]7.89516429581835[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]7.86413897159824[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]7.95360505263703[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 40 )[/C][C]7.92666666666667[/C][C]0.061091075571416[/C][C]129.751630537268[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 40 )[/C][C]7.92666666666667[/C][C]0.0605383566321068[/C][C]130.936270946984[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 40 )[/C][C]7.92666666666667[/C][C]0.0605383566321068[/C][C]130.936270946984[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 40 )[/C][C]7.93[/C][C]0.0598972041920824[/C][C]132.393491598866[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 40 )[/C][C]7.93[/C][C]0.0598972041920824[/C][C]132.393491598866[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 40 )[/C][C]7.93[/C][C]0.0598972041920824[/C][C]132.393491598866[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 40 )[/C][C]7.93583333333333[/C][C]0.0571473577242606[/C][C]138.866146211417[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 40 )[/C][C]7.9425[/C][C]0.0560694659686143[/C][C]141.654639700794[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 40 )[/C][C]7.9425[/C][C]0.0560694659686143[/C][C]141.654639700794[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 40 )[/C][C]7.9425[/C][C]0.0560694659686143[/C][C]141.654639700794[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 40 )[/C][C]7.95166666666667[/C][C]0.0546824719243833[/C][C]145.415274526406[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 40 )[/C][C]7.95166666666667[/C][C]0.0546824719243833[/C][C]145.415274526406[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 40 )[/C][C]7.95166666666667[/C][C]0.0546824719243833[/C][C]145.415274526406[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 40 )[/C][C]7.95166666666667[/C][C]0.0546824719243833[/C][C]145.415274526406[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 40 )[/C][C]7.95166666666667[/C][C]0.0546824719243833[/C][C]145.415274526406[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 40 )[/C][C]7.95166666666667[/C][C]0.0546824719243833[/C][C]145.415274526406[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 40 )[/C][C]7.9375[/C][C]0.0531245365773163[/C][C]149.413068073506[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 40 )[/C][C]7.9525[/C][C]0.0509567084342561[/C][C]156.063848006593[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 40 )[/C][C]7.9525[/C][C]0.0509567084342561[/C][C]156.063848006593[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 40 )[/C][C]7.9525[/C][C]0.0509567084342561[/C][C]156.063848006593[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 40 )[/C][C]7.97[/C][C]0.0485590691146083[/C][C]164.129999716208[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 40 )[/C][C]7.97[/C][C]0.0485590691146083[/C][C]164.129999716208[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 40 )[/C][C]7.97[/C][C]0.0485590691146083[/C][C]164.129999716208[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 40 )[/C][C]7.99[/C][C]0.0459630834694193[/C][C]173.835160674457[/C][/ROW]
[ROW][C]Winsorized Mean ( 25 / 40 )[/C][C]7.99[/C][C]0.0459630834694193[/C][C]173.835160674457[/C][/ROW]
[ROW][C]Winsorized Mean ( 26 / 40 )[/C][C]7.96833333333333[/C][C]0.0436433106224941[/C][C]182.578572057877[/C][/ROW]
[ROW][C]Winsorized Mean ( 27 / 40 )[/C][C]7.96833333333333[/C][C]0.0436433106224941[/C][C]182.578572057877[/C][/ROW]
[ROW][C]Winsorized Mean ( 28 / 40 )[/C][C]7.96833333333333[/C][C]0.0436433106224941[/C][C]182.578572057877[/C][/ROW]
[ROW][C]Winsorized Mean ( 29 / 40 )[/C][C]7.96833333333333[/C][C]0.0436433106224941[/C][C]182.578572057877[/C][/ROW]
[ROW][C]Winsorized Mean ( 30 / 40 )[/C][C]7.99333333333333[/C][C]0.0404929937110426[/C][C]197.400404385352[/C][/ROW]
[ROW][C]Winsorized Mean ( 31 / 40 )[/C][C]8.01916666666667[/C][C]0.0373921574135685[/C][C]214.461192435951[/C][/ROW]
[ROW][C]Winsorized Mean ( 32 / 40 )[/C][C]8.01916666666667[/C][C]0.0373921574135685[/C][C]214.461192435951[/C][/ROW]
[ROW][C]Winsorized Mean ( 33 / 40 )[/C][C]8.01916666666667[/C][C]0.0373921574135685[/C][C]214.461192435951[/C][/ROW]
[ROW][C]Winsorized Mean ( 34 / 40 )[/C][C]8.01916666666667[/C][C]0.0373921574135685[/C][C]214.461192435951[/C][/ROW]
[ROW][C]Winsorized Mean ( 35 / 40 )[/C][C]8.0775[/C][C]0.030961765976458[/C][C]260.886281685024[/C][/ROW]
[ROW][C]Winsorized Mean ( 36 / 40 )[/C][C]8.0475[/C][C]0.027627030262416[/C][C]291.290809166264[/C][/ROW]
[ROW][C]Winsorized Mean ( 37 / 40 )[/C][C]8.0475[/C][C]0.027627030262416[/C][C]291.290809166264[/C][/ROW]
[ROW][C]Winsorized Mean ( 38 / 40 )[/C][C]8.0475[/C][C]0.027627030262416[/C][C]291.290809166264[/C][/ROW]
[ROW][C]Winsorized Mean ( 39 / 40 )[/C][C]8.0475[/C][C]0.027627030262416[/C][C]291.290809166264[/C][/ROW]
[ROW][C]Winsorized Mean ( 40 / 40 )[/C][C]8.01416666666667[/C][C]0.0241753582361256[/C][C]331.501464772132[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 40 )[/C][C]7.93135593220339[/C][C]0.0601882597796375[/C][C]131.775797493429[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 40 )[/C][C]7.93620689655172[/C][C]0.0591848241180395[/C][C]134.091923306616[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 40 )[/C][C]7.94122807017544[/C][C]0.058387632857626[/C][C]136.008734752778[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 40 )[/C][C]7.94642857142857[/C][C]0.0574966924714401[/C][C]138.206707722809[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 40 )[/C][C]7.95090909090909[/C][C]0.0567061614659224[/C][C]140.212436979837[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 40 )[/C][C]7.95555555555556[/C][C]0.0558197249939143[/C][C]142.522299356059[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 40 )[/C][C]7.96037735849057[/C][C]0.0548243826187695[/C][C]145.197756513637[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 40 )[/C][C]7.96442307692308[/C][C]0.0542777664619343[/C][C]146.734539685022[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 40 )[/C][C]7.96764705882353[/C][C]0.0538583487778168[/C][C]147.937083843633[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 40 )[/C][C]7.971[/C][C]0.0533767815447954[/C][C]149.334593980915[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 40 )[/C][C]7.97448979591837[/C][C]0.0528249160302959[/C][C]150.960766153322[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 40 )[/C][C]7.97708333333333[/C][C]0.0524086332504606[/C][C]152.209337251954[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 40 )[/C][C]7.97978723404255[/C][C]0.0519265048092227[/C][C]153.674645797174[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 40 )[/C][C]7.98260869565217[/C][C]0.05136941463361[/C][C]155.396138978569[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 40 )[/C][C]7.98555555555556[/C][C]0.050726583710212[/C][C]157.423484324807[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 40 )[/C][C]7.98863636363636[/C][C]0.0499851550110441[/C][C]159.820177848229[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 40 )[/C][C]7.99186046511628[/C][C]0.0491296371691217[/C][C]162.668827323219[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 40 )[/C][C]7.99642857142857[/C][C]0.0483356507814287[/C][C]165.435417588314[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 40 )[/C][C]8[/C][C]0.0477118723613698[/C][C]167.673151441385[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 40 )[/C][C]8.00375[/C][C]0.0469797879378307[/C][C]170.365817968176[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 40 )[/C][C]8.00769230769231[/C][C]0.0461205340988719[/C][C]173.625316014894[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 40 )[/C][C]8.01052631578947[/C][C]0.0454443537638286[/C][C]176.271101959545[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 40 )[/C][C]8.01351351351351[/C][C]0.0446436515648505[/C][C]179.499508499498[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 40 )[/C][C]8.01666666666667[/C][C]0.0436947728777575[/C][C]183.469695313315[/C][/ROW]
[ROW][C]Trimmed Mean ( 25 / 40 )[/C][C]8.01857142857143[/C][C]0.0429402231304904[/C][C]186.738000969485[/C][/ROW]
[ROW][C]Trimmed Mean ( 26 / 40 )[/C][C]8.02058823529412[/C][C]0.0420375904948833[/C][C]190.795622224598[/C][/ROW]
[ROW][C]Trimmed Mean ( 27 / 40 )[/C][C]8.02424242424242[/C][C]0.0412542633841497[/C][C]194.50698584829[/C][/ROW]
[ROW][C]Trimmed Mean ( 28 / 40 )[/C][C]8.028125[/C][C]0.0403032127544856[/C][C]199.193177201649[/C][/ROW]
[ROW][C]Trimmed Mean ( 29 / 40 )[/C][C]8.03225806451613[/C][C]0.039145702254721[/C][C]205.188758966444[/C][/ROW]
[ROW][C]Trimmed Mean ( 30 / 40 )[/C][C]8.03666666666667[/C][C]0.0377298355369088[/C][C]213.005610872724[/C][/ROW]
[ROW][C]Trimmed Mean ( 31 / 40 )[/C][C]8.03965517241379[/C][C]0.0365595136034498[/C][C]219.905966463819[/C][/ROW]
[ROW][C]Trimmed Mean ( 32 / 40 )[/C][C]8.04107142857143[/C][C]0.0356549832325517[/C][C]225.52447651217[/C][/ROW]
[ROW][C]Trimmed Mean ( 33 / 40 )[/C][C]8.04259259259259[/C][C]0.0345280501381729[/C][C]232.929243337174[/C][/ROW]
[ROW][C]Trimmed Mean ( 34 / 40 )[/C][C]8.04423076923077[/C][C]0.0331154411107301[/C][C]242.914800450122[/C][/ROW]
[ROW][C]Trimmed Mean ( 35 / 40 )[/C][C]8.046[/C][C]0.0313258060143547[/C][C]256.848937783533[/C][/ROW]
[ROW][C]Trimmed Mean ( 36 / 40 )[/C][C]8.04375[/C][C]0.0303505304497559[/C][C]265.028316830116[/C][/ROW]
[ROW][C]Trimmed Mean ( 37 / 40 )[/C][C]8.04347826086956[/C][C]0.0297578267077347[/C][C]270.297906492576[/C][/ROW]
[ROW][C]Trimmed Mean ( 38 / 40 )[/C][C]8.04318181818182[/C][C]0.0289706652086081[/C][C]277.631934243331[/C][/ROW]
[ROW][C]Trimmed Mean ( 39 / 40 )[/C][C]8.04285714285714[/C][C]0.0279253312383553[/C][C]288.012954052639[/C][/ROW]
[ROW][C]Trimmed Mean ( 40 / 40 )[/C][C]8.0425[/C][C]0.0265270785695654[/C][C]303.180765982545[/C][/ROW]
[ROW][C]Median[/C][C]8[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]7.55[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]8[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]8.065625[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]8[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]8.065625[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]8.065625[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]8[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]8.065625[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]8[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]120[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=284262&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=284262&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 Mean7.9250.0617808769013542128.275939052369
Geometric Mean7.89516429581835
Harmonic Mean7.86413897159824
Quadratic Mean7.95360505263703
Winsorized Mean ( 1 / 40 )7.926666666666670.061091075571416129.751630537268
Winsorized Mean ( 2 / 40 )7.926666666666670.0605383566321068130.936270946984
Winsorized Mean ( 3 / 40 )7.926666666666670.0605383566321068130.936270946984
Winsorized Mean ( 4 / 40 )7.930.0598972041920824132.393491598866
Winsorized Mean ( 5 / 40 )7.930.0598972041920824132.393491598866
Winsorized Mean ( 6 / 40 )7.930.0598972041920824132.393491598866
Winsorized Mean ( 7 / 40 )7.935833333333330.0571473577242606138.866146211417
Winsorized Mean ( 8 / 40 )7.94250.0560694659686143141.654639700794
Winsorized Mean ( 9 / 40 )7.94250.0560694659686143141.654639700794
Winsorized Mean ( 10 / 40 )7.94250.0560694659686143141.654639700794
Winsorized Mean ( 11 / 40 )7.951666666666670.0546824719243833145.415274526406
Winsorized Mean ( 12 / 40 )7.951666666666670.0546824719243833145.415274526406
Winsorized Mean ( 13 / 40 )7.951666666666670.0546824719243833145.415274526406
Winsorized Mean ( 14 / 40 )7.951666666666670.0546824719243833145.415274526406
Winsorized Mean ( 15 / 40 )7.951666666666670.0546824719243833145.415274526406
Winsorized Mean ( 16 / 40 )7.951666666666670.0546824719243833145.415274526406
Winsorized Mean ( 17 / 40 )7.93750.0531245365773163149.413068073506
Winsorized Mean ( 18 / 40 )7.95250.0509567084342561156.063848006593
Winsorized Mean ( 19 / 40 )7.95250.0509567084342561156.063848006593
Winsorized Mean ( 20 / 40 )7.95250.0509567084342561156.063848006593
Winsorized Mean ( 21 / 40 )7.970.0485590691146083164.129999716208
Winsorized Mean ( 22 / 40 )7.970.0485590691146083164.129999716208
Winsorized Mean ( 23 / 40 )7.970.0485590691146083164.129999716208
Winsorized Mean ( 24 / 40 )7.990.0459630834694193173.835160674457
Winsorized Mean ( 25 / 40 )7.990.0459630834694193173.835160674457
Winsorized Mean ( 26 / 40 )7.968333333333330.0436433106224941182.578572057877
Winsorized Mean ( 27 / 40 )7.968333333333330.0436433106224941182.578572057877
Winsorized Mean ( 28 / 40 )7.968333333333330.0436433106224941182.578572057877
Winsorized Mean ( 29 / 40 )7.968333333333330.0436433106224941182.578572057877
Winsorized Mean ( 30 / 40 )7.993333333333330.0404929937110426197.400404385352
Winsorized Mean ( 31 / 40 )8.019166666666670.0373921574135685214.461192435951
Winsorized Mean ( 32 / 40 )8.019166666666670.0373921574135685214.461192435951
Winsorized Mean ( 33 / 40 )8.019166666666670.0373921574135685214.461192435951
Winsorized Mean ( 34 / 40 )8.019166666666670.0373921574135685214.461192435951
Winsorized Mean ( 35 / 40 )8.07750.030961765976458260.886281685024
Winsorized Mean ( 36 / 40 )8.04750.027627030262416291.290809166264
Winsorized Mean ( 37 / 40 )8.04750.027627030262416291.290809166264
Winsorized Mean ( 38 / 40 )8.04750.027627030262416291.290809166264
Winsorized Mean ( 39 / 40 )8.04750.027627030262416291.290809166264
Winsorized Mean ( 40 / 40 )8.014166666666670.0241753582361256331.501464772132
Trimmed Mean ( 1 / 40 )7.931355932203390.0601882597796375131.775797493429
Trimmed Mean ( 2 / 40 )7.936206896551720.0591848241180395134.091923306616
Trimmed Mean ( 3 / 40 )7.941228070175440.058387632857626136.008734752778
Trimmed Mean ( 4 / 40 )7.946428571428570.0574966924714401138.206707722809
Trimmed Mean ( 5 / 40 )7.950909090909090.0567061614659224140.212436979837
Trimmed Mean ( 6 / 40 )7.955555555555560.0558197249939143142.522299356059
Trimmed Mean ( 7 / 40 )7.960377358490570.0548243826187695145.197756513637
Trimmed Mean ( 8 / 40 )7.964423076923080.0542777664619343146.734539685022
Trimmed Mean ( 9 / 40 )7.967647058823530.0538583487778168147.937083843633
Trimmed Mean ( 10 / 40 )7.9710.0533767815447954149.334593980915
Trimmed Mean ( 11 / 40 )7.974489795918370.0528249160302959150.960766153322
Trimmed Mean ( 12 / 40 )7.977083333333330.0524086332504606152.209337251954
Trimmed Mean ( 13 / 40 )7.979787234042550.0519265048092227153.674645797174
Trimmed Mean ( 14 / 40 )7.982608695652170.05136941463361155.396138978569
Trimmed Mean ( 15 / 40 )7.985555555555560.050726583710212157.423484324807
Trimmed Mean ( 16 / 40 )7.988636363636360.0499851550110441159.820177848229
Trimmed Mean ( 17 / 40 )7.991860465116280.0491296371691217162.668827323219
Trimmed Mean ( 18 / 40 )7.996428571428570.0483356507814287165.435417588314
Trimmed Mean ( 19 / 40 )80.0477118723613698167.673151441385
Trimmed Mean ( 20 / 40 )8.003750.0469797879378307170.365817968176
Trimmed Mean ( 21 / 40 )8.007692307692310.0461205340988719173.625316014894
Trimmed Mean ( 22 / 40 )8.010526315789470.0454443537638286176.271101959545
Trimmed Mean ( 23 / 40 )8.013513513513510.0446436515648505179.499508499498
Trimmed Mean ( 24 / 40 )8.016666666666670.0436947728777575183.469695313315
Trimmed Mean ( 25 / 40 )8.018571428571430.0429402231304904186.738000969485
Trimmed Mean ( 26 / 40 )8.020588235294120.0420375904948833190.795622224598
Trimmed Mean ( 27 / 40 )8.024242424242420.0412542633841497194.50698584829
Trimmed Mean ( 28 / 40 )8.0281250.0403032127544856199.193177201649
Trimmed Mean ( 29 / 40 )8.032258064516130.039145702254721205.188758966444
Trimmed Mean ( 30 / 40 )8.036666666666670.0377298355369088213.005610872724
Trimmed Mean ( 31 / 40 )8.039655172413790.0365595136034498219.905966463819
Trimmed Mean ( 32 / 40 )8.041071428571430.0356549832325517225.52447651217
Trimmed Mean ( 33 / 40 )8.042592592592590.0345280501381729232.929243337174
Trimmed Mean ( 34 / 40 )8.044230769230770.0331154411107301242.914800450122
Trimmed Mean ( 35 / 40 )8.0460.0313258060143547256.848937783533
Trimmed Mean ( 36 / 40 )8.043750.0303505304497559265.028316830116
Trimmed Mean ( 37 / 40 )8.043478260869560.0297578267077347270.297906492576
Trimmed Mean ( 38 / 40 )8.043181818181820.0289706652086081277.631934243331
Trimmed Mean ( 39 / 40 )8.042857142857140.0279253312383553288.012954052639
Trimmed Mean ( 40 / 40 )8.04250.0265270785695654303.180765982545
Median8
Midrange7.55
Midmean - Weighted Average at Xnp8
Midmean - Weighted Average at X(n+1)p8.065625
Midmean - Empirical Distribution Function8
Midmean - Empirical Distribution Function - Averaging8.065625
Midmean - Empirical Distribution Function - Interpolation8.065625
Midmean - Closest Observation8
Midmean - True Basic - Statistics Graphics Toolkit8.065625
Midmean - MS Excel (old versions)8
Number of observations120



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')