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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 computationMon, 15 Nov 2010 20:50:41 +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/15/t1289854139a2u6hcy4k1iq0pc.htm/, Retrieved Sun, 28 Apr 2024 09:17:59 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=95063, Retrieved Sun, 28 Apr 2024 09:17:59 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact141
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]
-  M D    [Central Tendency] [] [2010-11-15 20:50:41] [6fde1c772c7be11768d9b6a0344566b2] [Current]
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Dataseries X:
53
43
33
45
46
55
41
55
36
45
55
50
49
47
69
51
48
62
45
37
50
50
50
58
53
57
53
61
47
56
44
46
58
48
38
74
60
32
51
50
40
61
63
56
45
61
70
59
57
69
44
56
50
56
43
48
52
62
48




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 1 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=95063&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=95063&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=95063&T=0

As an alternative you can also use a QR Code:  

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

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean51.54237288135591.1690340375230244.0897110152286
Geometric Mean50.7599345597894
Harmonic Mean49.9577232687362
Quadratic Mean52.3056531928644
Winsorized Mean ( 1 / 19 )51.49152542372881.1435210936985245.0289248772741
Winsorized Mean ( 2 / 19 )51.55932203389831.1076671286177946.5476682496093
Winsorized Mean ( 3 / 19 )51.61016949152541.0956630270392947.1040531786375
Winsorized Mean ( 4 / 19 )51.2711864406780.98166431169220652.2288381374444
Winsorized Mean ( 5 / 19 )51.35593220338980.9268268521938955.4104923501356
Winsorized Mean ( 6 / 19 )51.45762711864410.90595859635845656.7990936070153
Winsorized Mean ( 7 / 19 )51.57627118644070.8378827892815561.5554727298614
Winsorized Mean ( 8 / 19 )51.57627118644070.8378827892815561.5554727298614
Winsorized Mean ( 9 / 19 )51.7288135593220.811889480547363.7141073985234
Winsorized Mean ( 10 / 19 )51.55932203389830.7793623802313466.1557746969951
Winsorized Mean ( 11 / 19 )51.55932203389830.71482227601629572.1288686206569
Winsorized Mean ( 12 / 19 )51.35593220338980.67939650389576675.5905158606305
Winsorized Mean ( 13 / 19 )51.35593220338980.67939650389576675.5905158606305
Winsorized Mean ( 14 / 19 )51.11864406779660.64057467339357579.8012256666114
Winsorized Mean ( 15 / 19 )51.37288135593220.5999699510714185.6257571969928
Winsorized Mean ( 16 / 19 )51.10169491525420.5574504222473391.6703851604248
Winsorized Mean ( 17 / 19 )51.38983050847460.513418397316292100.093473036993
Winsorized Mean ( 18 / 19 )51.38983050847460.513418397316292100.093473036993
Winsorized Mean ( 19 / 19 )51.71186440677970.467563194038431110.598663594828
Trimmed Mean ( 1 / 19 )51.49122807017541.0896881687661147.2531771437701
Trimmed Mean ( 2 / 19 )51.49090909090911.0225974478019250.3530584802351
Trimmed Mean ( 3 / 19 )51.45283018867920.96362208178266953.3952377819043
Trimmed Mean ( 4 / 19 )51.39215686274510.89489989860737557.4278273388125
Trimmed Mean ( 5 / 19 )51.42857142857140.85714285714285760
Trimmed Mean ( 6 / 19 )51.44680851063830.82894475602784762.0630122050136
Trimmed Mean ( 7 / 19 )51.44444444444440.7993403565513764.3586227353683
Trimmed Mean ( 8 / 19 )51.41860465116280.7813103101962665.8107335589195
Trimmed Mean ( 9 / 19 )51.3902439024390.75698217330919567.8883145659605
Trimmed Mean ( 10 / 19 )51.33333333333330.73134314656028170.1904893411101
Trimmed Mean ( 11 / 19 )51.29729729729730.70590055453313572.6692973505653
Trimmed Mean ( 12 / 19 )51.25714285714290.68885833835711874.4088298029284
Trimmed Mean ( 13 / 19 )51.24242424242420.67424242424242476
Trimmed Mean ( 14 / 19 )51.22580645161290.65205989140347278.5599714488744
Trimmed Mean ( 15 / 19 )51.24137931034480.63100352558052981.2061695902607
Trimmed Mean ( 16 / 19 )51.22222222222220.61169358410539883.7383676291697
Trimmed Mean ( 17 / 19 )51.240.59520304658718586.0882690265168
Trimmed Mean ( 18 / 19 )51.21739130434780.58288000290207687.869528975679
Trimmed Mean ( 19 / 19 )51.19047619047620.55899164155539891.576460871648
Median50
Midrange53
Midmean - Weighted Average at Xnp50.6764705882353
Midmean - Weighted Average at X(n+1)p50.6764705882353
Midmean - Empirical Distribution Function50.6764705882353
Midmean - Empirical Distribution Function - Averaging50.6764705882353
Midmean - Empirical Distribution Function - Interpolation51.4333333333333
Midmean - Closest Observation50.6764705882353
Midmean - True Basic - Statistics Graphics Toolkit50.6764705882353
Midmean - MS Excel (old versions)50.6764705882353
Number of observations59

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 51.5423728813559 & 1.16903403752302 & 44.0897110152286 \tabularnewline
Geometric Mean & 50.7599345597894 &  &  \tabularnewline
Harmonic Mean & 49.9577232687362 &  &  \tabularnewline
Quadratic Mean & 52.3056531928644 &  &  \tabularnewline
Winsorized Mean ( 1 / 19 ) & 51.4915254237288 & 1.14352109369852 & 45.0289248772741 \tabularnewline
Winsorized Mean ( 2 / 19 ) & 51.5593220338983 & 1.10766712861779 & 46.5476682496093 \tabularnewline
Winsorized Mean ( 3 / 19 ) & 51.6101694915254 & 1.09566302703929 & 47.1040531786375 \tabularnewline
Winsorized Mean ( 4 / 19 ) & 51.271186440678 & 0.981664311692206 & 52.2288381374444 \tabularnewline
Winsorized Mean ( 5 / 19 ) & 51.3559322033898 & 0.92682685219389 & 55.4104923501356 \tabularnewline
Winsorized Mean ( 6 / 19 ) & 51.4576271186441 & 0.905958596358456 & 56.7990936070153 \tabularnewline
Winsorized Mean ( 7 / 19 ) & 51.5762711864407 & 0.83788278928155 & 61.5554727298614 \tabularnewline
Winsorized Mean ( 8 / 19 ) & 51.5762711864407 & 0.83788278928155 & 61.5554727298614 \tabularnewline
Winsorized Mean ( 9 / 19 ) & 51.728813559322 & 0.8118894805473 & 63.7141073985234 \tabularnewline
Winsorized Mean ( 10 / 19 ) & 51.5593220338983 & 0.77936238023134 & 66.1557746969951 \tabularnewline
Winsorized Mean ( 11 / 19 ) & 51.5593220338983 & 0.714822276016295 & 72.1288686206569 \tabularnewline
Winsorized Mean ( 12 / 19 ) & 51.3559322033898 & 0.679396503895766 & 75.5905158606305 \tabularnewline
Winsorized Mean ( 13 / 19 ) & 51.3559322033898 & 0.679396503895766 & 75.5905158606305 \tabularnewline
Winsorized Mean ( 14 / 19 ) & 51.1186440677966 & 0.640574673393575 & 79.8012256666114 \tabularnewline
Winsorized Mean ( 15 / 19 ) & 51.3728813559322 & 0.59996995107141 & 85.6257571969928 \tabularnewline
Winsorized Mean ( 16 / 19 ) & 51.1016949152542 & 0.55745042224733 & 91.6703851604248 \tabularnewline
Winsorized Mean ( 17 / 19 ) & 51.3898305084746 & 0.513418397316292 & 100.093473036993 \tabularnewline
Winsorized Mean ( 18 / 19 ) & 51.3898305084746 & 0.513418397316292 & 100.093473036993 \tabularnewline
Winsorized Mean ( 19 / 19 ) & 51.7118644067797 & 0.467563194038431 & 110.598663594828 \tabularnewline
Trimmed Mean ( 1 / 19 ) & 51.4912280701754 & 1.08968816876611 & 47.2531771437701 \tabularnewline
Trimmed Mean ( 2 / 19 ) & 51.4909090909091 & 1.02259744780192 & 50.3530584802351 \tabularnewline
Trimmed Mean ( 3 / 19 ) & 51.4528301886792 & 0.963622081782669 & 53.3952377819043 \tabularnewline
Trimmed Mean ( 4 / 19 ) & 51.3921568627451 & 0.894899898607375 & 57.4278273388125 \tabularnewline
Trimmed Mean ( 5 / 19 ) & 51.4285714285714 & 0.857142857142857 & 60 \tabularnewline
Trimmed Mean ( 6 / 19 ) & 51.4468085106383 & 0.828944756027847 & 62.0630122050136 \tabularnewline
Trimmed Mean ( 7 / 19 ) & 51.4444444444444 & 0.79934035655137 & 64.3586227353683 \tabularnewline
Trimmed Mean ( 8 / 19 ) & 51.4186046511628 & 0.78131031019626 & 65.8107335589195 \tabularnewline
Trimmed Mean ( 9 / 19 ) & 51.390243902439 & 0.756982173309195 & 67.8883145659605 \tabularnewline
Trimmed Mean ( 10 / 19 ) & 51.3333333333333 & 0.731343146560281 & 70.1904893411101 \tabularnewline
Trimmed Mean ( 11 / 19 ) & 51.2972972972973 & 0.705900554533135 & 72.6692973505653 \tabularnewline
Trimmed Mean ( 12 / 19 ) & 51.2571428571429 & 0.688858338357118 & 74.4088298029284 \tabularnewline
Trimmed Mean ( 13 / 19 ) & 51.2424242424242 & 0.674242424242424 & 76 \tabularnewline
Trimmed Mean ( 14 / 19 ) & 51.2258064516129 & 0.652059891403472 & 78.5599714488744 \tabularnewline
Trimmed Mean ( 15 / 19 ) & 51.2413793103448 & 0.631003525580529 & 81.2061695902607 \tabularnewline
Trimmed Mean ( 16 / 19 ) & 51.2222222222222 & 0.611693584105398 & 83.7383676291697 \tabularnewline
Trimmed Mean ( 17 / 19 ) & 51.24 & 0.595203046587185 & 86.0882690265168 \tabularnewline
Trimmed Mean ( 18 / 19 ) & 51.2173913043478 & 0.582880002902076 & 87.869528975679 \tabularnewline
Trimmed Mean ( 19 / 19 ) & 51.1904761904762 & 0.558991641555398 & 91.576460871648 \tabularnewline
Median & 50 &  &  \tabularnewline
Midrange & 53 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 50.6764705882353 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 50.6764705882353 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 50.6764705882353 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 50.6764705882353 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 51.4333333333333 &  &  \tabularnewline
Midmean - Closest Observation & 50.6764705882353 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 50.6764705882353 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 50.6764705882353 &  &  \tabularnewline
Number of observations & 59 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=95063&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]51.5423728813559[/C][C]1.16903403752302[/C][C]44.0897110152286[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]50.7599345597894[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]49.9577232687362[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]52.3056531928644[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 19 )[/C][C]51.4915254237288[/C][C]1.14352109369852[/C][C]45.0289248772741[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 19 )[/C][C]51.5593220338983[/C][C]1.10766712861779[/C][C]46.5476682496093[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 19 )[/C][C]51.6101694915254[/C][C]1.09566302703929[/C][C]47.1040531786375[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 19 )[/C][C]51.271186440678[/C][C]0.981664311692206[/C][C]52.2288381374444[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 19 )[/C][C]51.3559322033898[/C][C]0.92682685219389[/C][C]55.4104923501356[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 19 )[/C][C]51.4576271186441[/C][C]0.905958596358456[/C][C]56.7990936070153[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 19 )[/C][C]51.5762711864407[/C][C]0.83788278928155[/C][C]61.5554727298614[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 19 )[/C][C]51.5762711864407[/C][C]0.83788278928155[/C][C]61.5554727298614[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 19 )[/C][C]51.728813559322[/C][C]0.8118894805473[/C][C]63.7141073985234[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 19 )[/C][C]51.5593220338983[/C][C]0.77936238023134[/C][C]66.1557746969951[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 19 )[/C][C]51.5593220338983[/C][C]0.714822276016295[/C][C]72.1288686206569[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 19 )[/C][C]51.3559322033898[/C][C]0.679396503895766[/C][C]75.5905158606305[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 19 )[/C][C]51.3559322033898[/C][C]0.679396503895766[/C][C]75.5905158606305[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 19 )[/C][C]51.1186440677966[/C][C]0.640574673393575[/C][C]79.8012256666114[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 19 )[/C][C]51.3728813559322[/C][C]0.59996995107141[/C][C]85.6257571969928[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 19 )[/C][C]51.1016949152542[/C][C]0.55745042224733[/C][C]91.6703851604248[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 19 )[/C][C]51.3898305084746[/C][C]0.513418397316292[/C][C]100.093473036993[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 19 )[/C][C]51.3898305084746[/C][C]0.513418397316292[/C][C]100.093473036993[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 19 )[/C][C]51.7118644067797[/C][C]0.467563194038431[/C][C]110.598663594828[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 19 )[/C][C]51.4912280701754[/C][C]1.08968816876611[/C][C]47.2531771437701[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 19 )[/C][C]51.4909090909091[/C][C]1.02259744780192[/C][C]50.3530584802351[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 19 )[/C][C]51.4528301886792[/C][C]0.963622081782669[/C][C]53.3952377819043[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 19 )[/C][C]51.3921568627451[/C][C]0.894899898607375[/C][C]57.4278273388125[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 19 )[/C][C]51.4285714285714[/C][C]0.857142857142857[/C][C]60[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 19 )[/C][C]51.4468085106383[/C][C]0.828944756027847[/C][C]62.0630122050136[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 19 )[/C][C]51.4444444444444[/C][C]0.79934035655137[/C][C]64.3586227353683[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 19 )[/C][C]51.4186046511628[/C][C]0.78131031019626[/C][C]65.8107335589195[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 19 )[/C][C]51.390243902439[/C][C]0.756982173309195[/C][C]67.8883145659605[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 19 )[/C][C]51.3333333333333[/C][C]0.731343146560281[/C][C]70.1904893411101[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 19 )[/C][C]51.2972972972973[/C][C]0.705900554533135[/C][C]72.6692973505653[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 19 )[/C][C]51.2571428571429[/C][C]0.688858338357118[/C][C]74.4088298029284[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 19 )[/C][C]51.2424242424242[/C][C]0.674242424242424[/C][C]76[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 19 )[/C][C]51.2258064516129[/C][C]0.652059891403472[/C][C]78.5599714488744[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 19 )[/C][C]51.2413793103448[/C][C]0.631003525580529[/C][C]81.2061695902607[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 19 )[/C][C]51.2222222222222[/C][C]0.611693584105398[/C][C]83.7383676291697[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 19 )[/C][C]51.24[/C][C]0.595203046587185[/C][C]86.0882690265168[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 19 )[/C][C]51.2173913043478[/C][C]0.582880002902076[/C][C]87.869528975679[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 19 )[/C][C]51.1904761904762[/C][C]0.558991641555398[/C][C]91.576460871648[/C][/ROW]
[ROW][C]Median[/C][C]50[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]53[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]50.6764705882353[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]50.6764705882353[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]50.6764705882353[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]50.6764705882353[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]51.4333333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]50.6764705882353[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]50.6764705882353[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]50.6764705882353[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]59[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=95063&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=95063&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 Mean51.54237288135591.1690340375230244.0897110152286
Geometric Mean50.7599345597894
Harmonic Mean49.9577232687362
Quadratic Mean52.3056531928644
Winsorized Mean ( 1 / 19 )51.49152542372881.1435210936985245.0289248772741
Winsorized Mean ( 2 / 19 )51.55932203389831.1076671286177946.5476682496093
Winsorized Mean ( 3 / 19 )51.61016949152541.0956630270392947.1040531786375
Winsorized Mean ( 4 / 19 )51.2711864406780.98166431169220652.2288381374444
Winsorized Mean ( 5 / 19 )51.35593220338980.9268268521938955.4104923501356
Winsorized Mean ( 6 / 19 )51.45762711864410.90595859635845656.7990936070153
Winsorized Mean ( 7 / 19 )51.57627118644070.8378827892815561.5554727298614
Winsorized Mean ( 8 / 19 )51.57627118644070.8378827892815561.5554727298614
Winsorized Mean ( 9 / 19 )51.7288135593220.811889480547363.7141073985234
Winsorized Mean ( 10 / 19 )51.55932203389830.7793623802313466.1557746969951
Winsorized Mean ( 11 / 19 )51.55932203389830.71482227601629572.1288686206569
Winsorized Mean ( 12 / 19 )51.35593220338980.67939650389576675.5905158606305
Winsorized Mean ( 13 / 19 )51.35593220338980.67939650389576675.5905158606305
Winsorized Mean ( 14 / 19 )51.11864406779660.64057467339357579.8012256666114
Winsorized Mean ( 15 / 19 )51.37288135593220.5999699510714185.6257571969928
Winsorized Mean ( 16 / 19 )51.10169491525420.5574504222473391.6703851604248
Winsorized Mean ( 17 / 19 )51.38983050847460.513418397316292100.093473036993
Winsorized Mean ( 18 / 19 )51.38983050847460.513418397316292100.093473036993
Winsorized Mean ( 19 / 19 )51.71186440677970.467563194038431110.598663594828
Trimmed Mean ( 1 / 19 )51.49122807017541.0896881687661147.2531771437701
Trimmed Mean ( 2 / 19 )51.49090909090911.0225974478019250.3530584802351
Trimmed Mean ( 3 / 19 )51.45283018867920.96362208178266953.3952377819043
Trimmed Mean ( 4 / 19 )51.39215686274510.89489989860737557.4278273388125
Trimmed Mean ( 5 / 19 )51.42857142857140.85714285714285760
Trimmed Mean ( 6 / 19 )51.44680851063830.82894475602784762.0630122050136
Trimmed Mean ( 7 / 19 )51.44444444444440.7993403565513764.3586227353683
Trimmed Mean ( 8 / 19 )51.41860465116280.7813103101962665.8107335589195
Trimmed Mean ( 9 / 19 )51.3902439024390.75698217330919567.8883145659605
Trimmed Mean ( 10 / 19 )51.33333333333330.73134314656028170.1904893411101
Trimmed Mean ( 11 / 19 )51.29729729729730.70590055453313572.6692973505653
Trimmed Mean ( 12 / 19 )51.25714285714290.68885833835711874.4088298029284
Trimmed Mean ( 13 / 19 )51.24242424242420.67424242424242476
Trimmed Mean ( 14 / 19 )51.22580645161290.65205989140347278.5599714488744
Trimmed Mean ( 15 / 19 )51.24137931034480.63100352558052981.2061695902607
Trimmed Mean ( 16 / 19 )51.22222222222220.61169358410539883.7383676291697
Trimmed Mean ( 17 / 19 )51.240.59520304658718586.0882690265168
Trimmed Mean ( 18 / 19 )51.21739130434780.58288000290207687.869528975679
Trimmed Mean ( 19 / 19 )51.19047619047620.55899164155539891.576460871648
Median50
Midrange53
Midmean - Weighted Average at Xnp50.6764705882353
Midmean - Weighted Average at X(n+1)p50.6764705882353
Midmean - Empirical Distribution Function50.6764705882353
Midmean - Empirical Distribution Function - Averaging50.6764705882353
Midmean - Empirical Distribution Function - Interpolation51.4333333333333
Midmean - Closest Observation50.6764705882353
Midmean - True Basic - Statistics Graphics Toolkit50.6764705882353
Midmean - MS Excel (old versions)50.6764705882353
Number of observations59



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')