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Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationMon, 20 Oct 2008 13:51:36 -0600
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2008/Oct/20/t1224532327m3b9m6v789mnrpf.htm/, Retrieved Sat, 18 May 2024 15:26:44 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=18012, Retrieved Sat, 18 May 2024 15:26:44 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact156
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Pearson Correlation] [investigating Ass...] [2007-10-22 22:15:01] [8cd6641b921d30ebe00b648d1481bba0]
- RM D    [Central Tendency] [Centrale tendens ...] [2008-10-20 19:51:36] [84a986a411c52e49a8807521f8b9f7a0] [Current]
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Dataseries X:
118.76
119.28
119.89
120.38
121.39
121.86
122.21
122.61
123.7
125.53
126.03
126.17
126.39
127.55
128.86
129.59
130.4
130.52
130.55
130.67
131.13
132.15
132.69
132.8
132.96
133.05
133.23
135.32
136.22
136.33
136.53
136.6
136.77
137.49
138.06
138.46
138.34
139.06
139.95
140.41
141.39
141.87
141.91
141.99
142.26
142.38
143.17
143.28
143.8
144.16
145.36
146.83
147.56
148.04
148.69
148.93
149.21
149.86
150.64
150.69




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 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 & 2 seconds \tabularnewline
R Server & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=18012&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]'George Udny Yule' @ 72.249.76.132[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=18012&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=18012&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'George Udny Yule' @ 72.249.76.132







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean135.5318333333331.17487247755330115.358760991304
Geometric Mean135.228603453567
Harmonic Mean134.922900099097
Quadratic Mean135.831944113550
Winsorized Mean ( 1 / 20 )135.5396666666671.17262350045655115.586687981177
Winsorized Mean ( 2 / 20 )135.5341.16236108337108116.602320861366
Winsorized Mean ( 3 / 20 )135.5261.15016015097088117.832286126066
Winsorized Mean ( 4 / 20 )135.5746666666671.13174208164215119.792900578504
Winsorized Mean ( 5 / 20 )135.5938333333331.11952671324810121.117103976852
Winsorized Mean ( 6 / 20 )135.5638333333331.09959001326372123.285798977897
Winsorized Mean ( 7 / 20 )135.55451.07937964567224125.58556254373
Winsorized Mean ( 8 / 20 )135.60251.03224391155281131.366723002524
Winsorized Mean ( 9 / 20 )135.65650.94064417238377144.216595374445
Winsorized Mean ( 10 / 20 )135.5398333333330.891606640093676152.017523466506
Winsorized Mean ( 11 / 20 )135.49950.876263975685835154.633197027125
Winsorized Mean ( 12 / 20 )135.43950.851868681194467158.991054595516
Winsorized Mean ( 13 / 20 )135.6670.803961951344116168.748035616839
Winsorized Mean ( 14 / 20 )135.7883333333330.724135493403013187.517853454756
Winsorized Mean ( 15 / 20 )135.9408333333330.6904578146994196.885067326694
Winsorized Mean ( 16 / 20 )136.0848333333330.64633689644796210.547833616196
Winsorized Mean ( 17 / 20 )136.0961666666670.63777721752208213.391389544195
Winsorized Mean ( 18 / 20 )136.0931666666670.634591353525927214.457959300113
Winsorized Mean ( 19 / 20 )135.9791666666670.605717825620934224.492595256333
Winsorized Mean ( 20 / 20 )135.8058333333330.534316464536657254.167412660772
Trimmed Mean ( 1 / 20 )135.5596551724141.15040201725384117.836767616257
Trimmed Mean ( 2 / 20 )135.5810714285711.12278248054044120.754530622273
Trimmed Mean ( 3 / 20 )135.6072222222221.09516411811615123.823653440625
Trimmed Mean ( 4 / 20 )135.6384615384621.0663656149663127.196957248802
Trimmed Mean ( 5 / 20 )135.65761.03726125101497130.784409296363
Trimmed Mean ( 6 / 20 )135.6735416666671.00436818508164135.083472059241
Trimmed Mean ( 7 / 20 )135.6973913043480.968471550153775140.115000056328
Trimmed Mean ( 8 / 20 )135.7252272727270.928038264265229146.249602520632
Trimmed Mean ( 9 / 20 )135.7471428571430.889202312905741152.661706888219
Trimmed Mean ( 10 / 20 )135.762250.864078765959476157.117910251213
Trimmed Mean ( 11 / 20 )135.7973684210530.843121417494993161.065020533486
Trimmed Mean ( 12 / 20 )135.84250.817787702396212166.109736795951
Trimmed Mean ( 13 / 20 )135.9017647058820.788663603802186172.31905219246
Trimmed Mean ( 14 / 20 )135.9356250.761509263480711178.508169918597
Trimmed Mean ( 15 / 20 )135.9566666666670.745599709765947182.345385715540
Trimmed Mean ( 16 / 20 )135.9589285714290.730462334438441186.127226773369
Trimmed Mean ( 17 / 20 )135.9407692307690.719079309432859189.048367054235
Trimmed Mean ( 18 / 20 )135.9179166666670.700762777773306193.957100716094
Trimmed Mean ( 19 / 20 )135.8913636363640.669063536107213203.106814678641
Trimmed Mean ( 20 / 20 )135.87750.626836197440011216.767156323967
Median136.43
Midrange134.725
Midmean - Weighted Average at Xnp135.727741935484
Midmean - Weighted Average at X(n+1)p135.956666666667
Midmean - Empirical Distribution Function135.727741935484
Midmean - Empirical Distribution Function - Averaging135.956666666667
Midmean - Empirical Distribution Function - Interpolation135.956666666667
Midmean - Closest Observation135.727741935484
Midmean - True Basic - Statistics Graphics Toolkit135.956666666667
Midmean - MS Excel (old versions)135.935625
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 135.531833333333 & 1.17487247755330 & 115.358760991304 \tabularnewline
Geometric Mean & 135.228603453567 &  &  \tabularnewline
Harmonic Mean & 134.922900099097 &  &  \tabularnewline
Quadratic Mean & 135.831944113550 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 135.539666666667 & 1.17262350045655 & 115.586687981177 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 135.534 & 1.16236108337108 & 116.602320861366 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 135.526 & 1.15016015097088 & 117.832286126066 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 135.574666666667 & 1.13174208164215 & 119.792900578504 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 135.593833333333 & 1.11952671324810 & 121.117103976852 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 135.563833333333 & 1.09959001326372 & 123.285798977897 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 135.5545 & 1.07937964567224 & 125.58556254373 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 135.6025 & 1.03224391155281 & 131.366723002524 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 135.6565 & 0.94064417238377 & 144.216595374445 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 135.539833333333 & 0.891606640093676 & 152.017523466506 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 135.4995 & 0.876263975685835 & 154.633197027125 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 135.4395 & 0.851868681194467 & 158.991054595516 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 135.667 & 0.803961951344116 & 168.748035616839 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 135.788333333333 & 0.724135493403013 & 187.517853454756 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 135.940833333333 & 0.6904578146994 & 196.885067326694 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 136.084833333333 & 0.64633689644796 & 210.547833616196 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 136.096166666667 & 0.63777721752208 & 213.391389544195 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 136.093166666667 & 0.634591353525927 & 214.457959300113 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 135.979166666667 & 0.605717825620934 & 224.492595256333 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 135.805833333333 & 0.534316464536657 & 254.167412660772 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 135.559655172414 & 1.15040201725384 & 117.836767616257 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 135.581071428571 & 1.12278248054044 & 120.754530622273 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 135.607222222222 & 1.09516411811615 & 123.823653440625 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 135.638461538462 & 1.0663656149663 & 127.196957248802 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 135.6576 & 1.03726125101497 & 130.784409296363 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 135.673541666667 & 1.00436818508164 & 135.083472059241 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 135.697391304348 & 0.968471550153775 & 140.115000056328 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 135.725227272727 & 0.928038264265229 & 146.249602520632 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 135.747142857143 & 0.889202312905741 & 152.661706888219 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 135.76225 & 0.864078765959476 & 157.117910251213 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 135.797368421053 & 0.843121417494993 & 161.065020533486 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 135.8425 & 0.817787702396212 & 166.109736795951 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 135.901764705882 & 0.788663603802186 & 172.31905219246 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 135.935625 & 0.761509263480711 & 178.508169918597 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 135.956666666667 & 0.745599709765947 & 182.345385715540 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 135.958928571429 & 0.730462334438441 & 186.127226773369 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 135.940769230769 & 0.719079309432859 & 189.048367054235 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 135.917916666667 & 0.700762777773306 & 193.957100716094 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 135.891363636364 & 0.669063536107213 & 203.106814678641 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 135.8775 & 0.626836197440011 & 216.767156323967 \tabularnewline
Median & 136.43 &  &  \tabularnewline
Midrange & 134.725 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 135.727741935484 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 135.956666666667 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 135.727741935484 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 135.956666666667 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 135.956666666667 &  &  \tabularnewline
Midmean - Closest Observation & 135.727741935484 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 135.956666666667 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 135.935625 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=18012&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]135.531833333333[/C][C]1.17487247755330[/C][C]115.358760991304[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]135.228603453567[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]134.922900099097[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]135.831944113550[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]135.539666666667[/C][C]1.17262350045655[/C][C]115.586687981177[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]135.534[/C][C]1.16236108337108[/C][C]116.602320861366[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]135.526[/C][C]1.15016015097088[/C][C]117.832286126066[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]135.574666666667[/C][C]1.13174208164215[/C][C]119.792900578504[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]135.593833333333[/C][C]1.11952671324810[/C][C]121.117103976852[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]135.563833333333[/C][C]1.09959001326372[/C][C]123.285798977897[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]135.5545[/C][C]1.07937964567224[/C][C]125.58556254373[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]135.6025[/C][C]1.03224391155281[/C][C]131.366723002524[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]135.6565[/C][C]0.94064417238377[/C][C]144.216595374445[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]135.539833333333[/C][C]0.891606640093676[/C][C]152.017523466506[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]135.4995[/C][C]0.876263975685835[/C][C]154.633197027125[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]135.4395[/C][C]0.851868681194467[/C][C]158.991054595516[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]135.667[/C][C]0.803961951344116[/C][C]168.748035616839[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]135.788333333333[/C][C]0.724135493403013[/C][C]187.517853454756[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]135.940833333333[/C][C]0.6904578146994[/C][C]196.885067326694[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]136.084833333333[/C][C]0.64633689644796[/C][C]210.547833616196[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]136.096166666667[/C][C]0.63777721752208[/C][C]213.391389544195[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]136.093166666667[/C][C]0.634591353525927[/C][C]214.457959300113[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]135.979166666667[/C][C]0.605717825620934[/C][C]224.492595256333[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]135.805833333333[/C][C]0.534316464536657[/C][C]254.167412660772[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]135.559655172414[/C][C]1.15040201725384[/C][C]117.836767616257[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]135.581071428571[/C][C]1.12278248054044[/C][C]120.754530622273[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]135.607222222222[/C][C]1.09516411811615[/C][C]123.823653440625[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]135.638461538462[/C][C]1.0663656149663[/C][C]127.196957248802[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]135.6576[/C][C]1.03726125101497[/C][C]130.784409296363[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]135.673541666667[/C][C]1.00436818508164[/C][C]135.083472059241[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]135.697391304348[/C][C]0.968471550153775[/C][C]140.115000056328[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]135.725227272727[/C][C]0.928038264265229[/C][C]146.249602520632[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]135.747142857143[/C][C]0.889202312905741[/C][C]152.661706888219[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]135.76225[/C][C]0.864078765959476[/C][C]157.117910251213[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]135.797368421053[/C][C]0.843121417494993[/C][C]161.065020533486[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]135.8425[/C][C]0.817787702396212[/C][C]166.109736795951[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]135.901764705882[/C][C]0.788663603802186[/C][C]172.31905219246[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]135.935625[/C][C]0.761509263480711[/C][C]178.508169918597[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]135.956666666667[/C][C]0.745599709765947[/C][C]182.345385715540[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]135.958928571429[/C][C]0.730462334438441[/C][C]186.127226773369[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]135.940769230769[/C][C]0.719079309432859[/C][C]189.048367054235[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]135.917916666667[/C][C]0.700762777773306[/C][C]193.957100716094[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]135.891363636364[/C][C]0.669063536107213[/C][C]203.106814678641[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]135.8775[/C][C]0.626836197440011[/C][C]216.767156323967[/C][/ROW]
[ROW][C]Median[/C][C]136.43[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]134.725[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]135.727741935484[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]135.956666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]135.727741935484[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]135.956666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]135.956666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]135.727741935484[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]135.956666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]135.935625[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]60[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=18012&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=18012&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 Mean135.5318333333331.17487247755330115.358760991304
Geometric Mean135.228603453567
Harmonic Mean134.922900099097
Quadratic Mean135.831944113550
Winsorized Mean ( 1 / 20 )135.5396666666671.17262350045655115.586687981177
Winsorized Mean ( 2 / 20 )135.5341.16236108337108116.602320861366
Winsorized Mean ( 3 / 20 )135.5261.15016015097088117.832286126066
Winsorized Mean ( 4 / 20 )135.5746666666671.13174208164215119.792900578504
Winsorized Mean ( 5 / 20 )135.5938333333331.11952671324810121.117103976852
Winsorized Mean ( 6 / 20 )135.5638333333331.09959001326372123.285798977897
Winsorized Mean ( 7 / 20 )135.55451.07937964567224125.58556254373
Winsorized Mean ( 8 / 20 )135.60251.03224391155281131.366723002524
Winsorized Mean ( 9 / 20 )135.65650.94064417238377144.216595374445
Winsorized Mean ( 10 / 20 )135.5398333333330.891606640093676152.017523466506
Winsorized Mean ( 11 / 20 )135.49950.876263975685835154.633197027125
Winsorized Mean ( 12 / 20 )135.43950.851868681194467158.991054595516
Winsorized Mean ( 13 / 20 )135.6670.803961951344116168.748035616839
Winsorized Mean ( 14 / 20 )135.7883333333330.724135493403013187.517853454756
Winsorized Mean ( 15 / 20 )135.9408333333330.6904578146994196.885067326694
Winsorized Mean ( 16 / 20 )136.0848333333330.64633689644796210.547833616196
Winsorized Mean ( 17 / 20 )136.0961666666670.63777721752208213.391389544195
Winsorized Mean ( 18 / 20 )136.0931666666670.634591353525927214.457959300113
Winsorized Mean ( 19 / 20 )135.9791666666670.605717825620934224.492595256333
Winsorized Mean ( 20 / 20 )135.8058333333330.534316464536657254.167412660772
Trimmed Mean ( 1 / 20 )135.5596551724141.15040201725384117.836767616257
Trimmed Mean ( 2 / 20 )135.5810714285711.12278248054044120.754530622273
Trimmed Mean ( 3 / 20 )135.6072222222221.09516411811615123.823653440625
Trimmed Mean ( 4 / 20 )135.6384615384621.0663656149663127.196957248802
Trimmed Mean ( 5 / 20 )135.65761.03726125101497130.784409296363
Trimmed Mean ( 6 / 20 )135.6735416666671.00436818508164135.083472059241
Trimmed Mean ( 7 / 20 )135.6973913043480.968471550153775140.115000056328
Trimmed Mean ( 8 / 20 )135.7252272727270.928038264265229146.249602520632
Trimmed Mean ( 9 / 20 )135.7471428571430.889202312905741152.661706888219
Trimmed Mean ( 10 / 20 )135.762250.864078765959476157.117910251213
Trimmed Mean ( 11 / 20 )135.7973684210530.843121417494993161.065020533486
Trimmed Mean ( 12 / 20 )135.84250.817787702396212166.109736795951
Trimmed Mean ( 13 / 20 )135.9017647058820.788663603802186172.31905219246
Trimmed Mean ( 14 / 20 )135.9356250.761509263480711178.508169918597
Trimmed Mean ( 15 / 20 )135.9566666666670.745599709765947182.345385715540
Trimmed Mean ( 16 / 20 )135.9589285714290.730462334438441186.127226773369
Trimmed Mean ( 17 / 20 )135.9407692307690.719079309432859189.048367054235
Trimmed Mean ( 18 / 20 )135.9179166666670.700762777773306193.957100716094
Trimmed Mean ( 19 / 20 )135.8913636363640.669063536107213203.106814678641
Trimmed Mean ( 20 / 20 )135.87750.626836197440011216.767156323967
Median136.43
Midrange134.725
Midmean - Weighted Average at Xnp135.727741935484
Midmean - Weighted Average at X(n+1)p135.956666666667
Midmean - Empirical Distribution Function135.727741935484
Midmean - Empirical Distribution Function - Averaging135.956666666667
Midmean - Empirical Distribution Function - Interpolation135.956666666667
Midmean - Closest Observation135.727741935484
Midmean - True Basic - Statistics Graphics Toolkit135.956666666667
Midmean - MS Excel (old versions)135.935625
Number of observations60



Parameters (Session):
Parameters (R input):
R code (references can be found in the software module):
geomean <- function(x) {
return(exp(mean(log(x))))
}
harmean <- function(x) {
return(1/mean(1/x))
}
quamean <- function(x) {
return(sqrt(mean(x*x)))
}
winmean <- function(x) {
x <-sort(x[!is.na(x)])
n<-length(x)
denom <- 3
nodenom <- n/denom
if (nodenom>40) denom <- n/40
sqrtn = sqrt(n)
roundnodenom = floor(nodenom)
win <- array(NA,dim=c(roundnodenom,2))
for (j in 1:roundnodenom) {
win[j,1] <- (j*x[j+1]+sum(x[(j+1):(n-j)])+j*x[n-j])/n
win[j,2] <- sd(c(rep(x[j+1],j),x[(j+1):(n-j)],rep(x[n-j],j)))/sqrtn
}
return(win)
}
trimean <- function(x) {
x <-sort(x[!is.na(x)])
n<-length(x)
denom <- 3
nodenom <- n/denom
if (nodenom>40) denom <- n/40
sqrtn = sqrt(n)
roundnodenom = floor(nodenom)
tri <- array(NA,dim=c(roundnodenom,2))
for (j in 1:roundnodenom) {
tri[j,1] <- mean(x,trim=j/n)
tri[j,2] <- sd(x[(j+1):(n-j)]) / sqrt(n-j*2)
}
return(tri)
}
midrange <- function(x) {
return((max(x)+min(x))/2)
}
q1 <- function(data,n,p,i,f) {
np <- n*p;
i <<- floor(np)
f <<- np - i
qvalue <- (1-f)*data[i] + f*data[i+1]
}
q2 <- function(data,n,p,i,f) {
np <- (n+1)*p
i <<- floor(np)
f <<- np - i
qvalue <- (1-f)*data[i] + f*data[i+1]
}
q3 <- function(data,n,p,i,f) {
np <- n*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- data[i]
} else {
qvalue <- data[i+1]
}
}
q4 <- function(data,n,p,i,f) {
np <- n*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- (data[i]+data[i+1])/2
} else {
qvalue <- data[i+1]
}
}
q5 <- function(data,n,p,i,f) {
np <- (n-1)*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- data[i+1]
} else {
qvalue <- data[i+1] + f*(data[i+2]-data[i+1])
}
}
q6 <- function(data,n,p,i,f) {
np <- n*p+0.5
i <<- floor(np)
f <<- np - i
qvalue <- data[i]
}
q7 <- function(data,n,p,i,f) {
np <- (n+1)*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- data[i]
} else {
qvalue <- f*data[i] + (1-f)*data[i+1]
}
}
q8 <- function(data,n,p,i,f) {
np <- (n+1)*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- data[i]
} else {
if (f == 0.5) {
qvalue <- (data[i]+data[i+1])/2
} else {
if (f < 0.5) {
qvalue <- data[i]
} else {
qvalue <- data[i+1]
}
}
}
}
midmean <- function(x,def) {
x <-sort(x[!is.na(x)])
n<-length(x)
if (def==1) {
qvalue1 <- q1(x,n,0.25,i,f)
qvalue3 <- q1(x,n,0.75,i,f)
}
if (def==2) {
qvalue1 <- q2(x,n,0.25,i,f)
qvalue3 <- q2(x,n,0.75,i,f)
}
if (def==3) {
qvalue1 <- q3(x,n,0.25,i,f)
qvalue3 <- q3(x,n,0.75,i,f)
}
if (def==4) {
qvalue1 <- q4(x,n,0.25,i,f)
qvalue3 <- q4(x,n,0.75,i,f)
}
if (def==5) {
qvalue1 <- q5(x,n,0.25,i,f)
qvalue3 <- q5(x,n,0.75,i,f)
}
if (def==6) {
qvalue1 <- q6(x,n,0.25,i,f)
qvalue3 <- q6(x,n,0.75,i,f)
}
if (def==7) {
qvalue1 <- q7(x,n,0.25,i,f)
qvalue3 <- q7(x,n,0.75,i,f)
}
if (def==8) {
qvalue1 <- q8(x,n,0.25,i,f)
qvalue3 <- q8(x,n,0.75,i,f)
}
midm <- 0
myn <- 0
roundno4 <- round(n/4)
round3no4 <- round(3*n/4)
for (i in 1:n) {
if ((x[i]>=qvalue1) & (x[i]<=qvalue3)){
midm = midm + x[i]
myn = myn + 1
}
}
midm = midm / myn
return(midm)
}
(arm <- mean(x))
sqrtn <- sqrt(length(x))
(armse <- sd(x) / sqrtn)
(armose <- arm / armse)
(geo <- geomean(x))
(har <- harmean(x))
(qua <- quamean(x))
(win <- winmean(x))
(tri <- trimean(x))
(midr <- midrange(x))
midm <- array(NA,dim=8)
for (j in 1:8) midm[j] <- midmean(x,j)
midm
bitmap(file='test1.png')
lb <- win[,1] - 2*win[,2]
ub <- win[,1] + 2*win[,2]
if ((ylimmin == '') | (ylimmax == '')) plot(win[,1],type='b',main=main, xlab='j', pch=19, ylab='Winsorized Mean(j/n)', ylim=c(min(lb),max(ub))) else plot(win[,1],type='l',main=main, xlab='j', pch=19, ylab='Winsorized Mean(j/n)', ylim=c(ylimmin,ylimmax))
lines(ub,lty=3)
lines(lb,lty=3)
grid()
dev.off()
bitmap(file='test2.png')
lb <- tri[,1] - 2*tri[,2]
ub <- tri[,1] + 2*tri[,2]
if ((ylimmin == '') | (ylimmax == '')) plot(tri[,1],type='b',main=main, xlab='j', pch=19, ylab='Trimmed Mean(j/n)', ylim=c(min(lb),max(ub))) else plot(tri[,1],type='l',main=main, xlab='j', pch=19, ylab='Trimmed Mean(j/n)', ylim=c(ylimmin,ylimmax))
lines(ub,lty=3)
lines(lb,lty=3)
grid()
dev.off()
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Central Tendency - Ungrouped Data',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Measure',header=TRUE)
a<-table.element(a,'Value',header=TRUE)
a<-table.element(a,'S.E.',header=TRUE)
a<-table.element(a,'Value/S.E.',header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('arithmetic_mean.htm', 'Arithmetic Mean', 'click to view the definition of the Arithmetic Mean'),header=TRUE)
a<-table.element(a,arm)
a<-table.element(a,hyperlink('arithmetic_mean_standard_error.htm', armse, 'click to view the definition of the Standard Error of the Arithmetic Mean'))
a<-table.element(a,armose)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('geometric_mean.htm', 'Geometric Mean', 'click to view the definition of the Geometric Mean'),header=TRUE)
a<-table.element(a,geo)
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('harmonic_mean.htm', 'Harmonic Mean', 'click to view the definition of the Harmonic Mean'),header=TRUE)
a<-table.element(a,har)
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('quadratic_mean.htm', 'Quadratic Mean', 'click to view the definition of the Quadratic Mean'),header=TRUE)
a<-table.element(a,qua)
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
for (j in 1:length(win[,1])) {
a<-table.row.start(a)
mylabel <- paste('Winsorized Mean (',j)
mylabel <- paste(mylabel,'/')
mylabel <- paste(mylabel,length(win[,1]))
mylabel <- paste(mylabel,')')
a<-table.element(a,hyperlink('winsorized_mean.htm', mylabel, 'click to view the definition of the Winsorized Mean'),header=TRUE)
a<-table.element(a,win[j,1])
a<-table.element(a,win[j,2])
a<-table.element(a,win[j,1]/win[j,2])
a<-table.row.end(a)
}
for (j in 1:length(tri[,1])) {
a<-table.row.start(a)
mylabel <- paste('Trimmed Mean (',j)
mylabel <- paste(mylabel,'/')
mylabel <- paste(mylabel,length(tri[,1]))
mylabel <- paste(mylabel,')')
a<-table.element(a,hyperlink('arithmetic_mean.htm', mylabel, 'click to view the definition of the Trimmed Mean'),header=TRUE)
a<-table.element(a,tri[j,1])
a<-table.element(a,tri[j,2])
a<-table.element(a,tri[j,1]/tri[j,2])
a<-table.row.end(a)
}
a<-table.row.start(a)
a<-table.element(a,hyperlink('median_1.htm', 'Median', 'click to view the definition of the Median'),header=TRUE)
a<-table.element(a,median(x))
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('midrange.htm', 'Midrange', 'click to view the definition of the Midrange'),header=TRUE)
a<-table.element(a,midr)
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_1.htm','Weighted Average at Xnp',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[1])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_2.htm','Weighted Average at X(n+1)p',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[2])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_3.htm','Empirical Distribution Function',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[3])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_4.htm','Empirical Distribution Function - Averaging',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[4])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_5.htm','Empirical Distribution Function - Interpolation',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[5])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_6.htm','Closest Observation',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[6])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_7.htm','True Basic - Statistics Graphics Toolkit',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[7])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_8.htm','MS Excel (old versions)',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[8])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Number of observations',header=TRUE)
a<-table.element(a,length(x))
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable.tab')