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Description of Statistical Computation

Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationThu, 09 Mar 2017 08:58:33 +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/2017/Mar/09/t14890499974j53bmnka8cn1a7.htm/, Retrieved Thu, 16 May 2024 00:09:14 +0200
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=, Retrieved Thu, 16 May 2024 00:09:14 +0200
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact0

Tree of Dependent Computations

Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
97,91	
98,51	
98,54	
98,52	
98,66	
98,53	
98,71	
98,92	
98,96	
99,25	
99,32	
99,41	
99,36	
99,58	
99,77	
99,77	
100,03	
100,2	
100,24	
100,1	
100,03	
100,18	
100,29	
100,41	
100,6	
100,75	
100,79	
100,44	
100,29	
100,34	
100,46	
100,12	
100,06	
100,28	
100,28	
100,4	
100,61	
100,89	
100,73	
101,12	
101,16	
101,33	
101,37	
101,61	
101,85	
102,27	
102,28	
102,23	
102,42	
102,53	
103,47	
103,53	
103,77	
103,74	
103,93	
103,97	
103,68	
103,86	
103,97	
104,05

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gwilym Jenkins' @ jenkins.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 & 1 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&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' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=&T=0

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

As an alternative you can also use a QR Code:  
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' @ jenkins.wessa.net






Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean100.8396666666670.217506408330383463.616991520982
Geometric Mean100.825905206869
Harmonic Mean100.812222544367
Quadratic Mean100.853505673659
Winsorized Mean ( 1 / 20 )100.8483333333330.21511173901871468.818362927938
Winsorized Mean ( 2 / 20 )100.8486666666670.215050442994231468.953540678695
Winsorized Mean ( 3 / 20 )100.8471666666670.214469137240362470.217617156002
Winsorized Mean ( 4 / 20 )100.8431666666670.213219005161263472.955807060429
Winsorized Mean ( 5 / 20 )100.8456666666670.20963370888784481.056540008182
Winsorized Mean ( 6 / 20 )100.8476666666670.208048419867627484.731711641128
Winsorized Mean ( 7 / 20 )100.8651666666670.20226618525765498.675379367951
Winsorized Mean ( 8 / 20 )100.85050.196729247679788512.636027379885
Winsorized Mean ( 9 / 20 )100.8850.187883017456575536.956460278894
Winsorized Mean ( 10 / 20 )100.740.151916755379293663.126326970854
Winsorized Mean ( 11 / 20 )100.7271666666670.14677129517897686.286555854414
Winsorized Mean ( 12 / 20 )100.7091666666670.139789246465869720.435721722387
Winsorized Mean ( 13 / 20 )100.7438333333330.133752256787902753.212213032699
Winsorized Mean ( 14 / 20 )100.7788333333330.125642774857224802.106077710039
Winsorized Mean ( 15 / 20 )100.6838333333330.10757209950232935.966052527977
Winsorized Mean ( 16 / 20 )100.6891666666670.08636778918911951165.81850261546
Winsorized Mean ( 17 / 20 )100.6211666666670.07439780525993571352.47493276327
Winsorized Mean ( 18 / 20 )100.6181666666670.07115213733848231414.12711452377
Winsorized Mean ( 19 / 20 )100.5770.06048920153899261662.72652706725
Winsorized Mean ( 20 / 20 )100.5703333333330.05742987208027121751.18504865836
Trimmed Mean ( 1 / 20 )100.8348275862070.211998990024205475.638245138309
Trimmed Mean ( 2 / 20 )100.8203571428570.208065918045986484.559691898093
Trimmed Mean ( 3 / 20 )100.804629629630.203148129037518496.212444127471
Trimmed Mean ( 4 / 20 )100.7882692307690.197224849125708511.032304892416
Trimmed Mean ( 5 / 20 )100.77180.190223003394459529.756118880287
Trimmed Mean ( 6 / 20 )100.7533333333330.182558970685578551.89472724877
Trimmed Mean ( 7 / 20 )100.7328260869570.173167050408546581.708967435211
Trimmed Mean ( 8 / 20 )100.7070454545450.162679914890628619.050271339596
Trimmed Mean ( 9 / 20 )100.6814285714290.150536235245157668.818563234711
Trimmed Mean ( 10 / 20 )100.64750.13669953482186736.268050444787
Trimmed Mean ( 11 / 20 )100.6328947368420.130207137687605772.867728482611
Trimmed Mean ( 12 / 20 )100.6186111111110.122849212501935819.041563734289
Trimmed Mean ( 13 / 20 )100.6052941176470.114807624333108876.294537945898
Trimmed Mean ( 14 / 20 )100.58531250.105080599225877957.220583447435
Trimmed Mean ( 15 / 20 )100.5576666666670.09322409452907691078.6660591839
Trimmed Mean ( 16 / 20 )100.5396428571430.08342293935291211205.17981788942
Trimmed Mean ( 17 / 20 )100.5180769230770.07689957333235491307.13439057255
Trimmed Mean ( 18 / 20 )100.5029166666670.07215994504627971392.7798393168
Trimmed Mean ( 19 / 20 )100.4854545454550.06558668720081211532.10138877407
Trimmed Mean ( 20 / 20 )100.4710.06025341222047531667.47402839798
Median100.405
Midrange100.98
Midmean - Weighted Average at Xnp100.532258064516
Midmean - Weighted Average at X(n+1)p100.532258064516
Midmean - Empirical Distribution Function100.532258064516
Midmean - Empirical Distribution Function - Averaging100.532258064516
Midmean - Empirical Distribution Function - Interpolation100.532258064516
Midmean - Closest Observation100.532258064516
Midmean - True Basic - Statistics Graphics Toolkit100.532258064516
Midmean - MS Excel (old versions)100.5853125
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 100.839666666667 & 0.217506408330383 & 463.616991520982 \tabularnewline
Geometric Mean & 100.825905206869 &  &  \tabularnewline
Harmonic Mean & 100.812222544367 &  &  \tabularnewline
Quadratic Mean & 100.853505673659 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 100.848333333333 & 0.21511173901871 & 468.818362927938 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 100.848666666667 & 0.215050442994231 & 468.953540678695 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 100.847166666667 & 0.214469137240362 & 470.217617156002 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 100.843166666667 & 0.213219005161263 & 472.955807060429 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 100.845666666667 & 0.20963370888784 & 481.056540008182 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 100.847666666667 & 0.208048419867627 & 484.731711641128 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 100.865166666667 & 0.20226618525765 & 498.675379367951 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 100.8505 & 0.196729247679788 & 512.636027379885 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 100.885 & 0.187883017456575 & 536.956460278894 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 100.74 & 0.151916755379293 & 663.126326970854 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 100.727166666667 & 0.14677129517897 & 686.286555854414 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 100.709166666667 & 0.139789246465869 & 720.435721722387 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 100.743833333333 & 0.133752256787902 & 753.212213032699 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 100.778833333333 & 0.125642774857224 & 802.106077710039 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 100.683833333333 & 0.10757209950232 & 935.966052527977 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 100.689166666667 & 0.0863677891891195 & 1165.81850261546 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 100.621166666667 & 0.0743978052599357 & 1352.47493276327 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 100.618166666667 & 0.0711521373384823 & 1414.12711452377 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 100.577 & 0.0604892015389926 & 1662.72652706725 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 100.570333333333 & 0.0574298720802712 & 1751.18504865836 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 100.834827586207 & 0.211998990024205 & 475.638245138309 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 100.820357142857 & 0.208065918045986 & 484.559691898093 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 100.80462962963 & 0.203148129037518 & 496.212444127471 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 100.788269230769 & 0.197224849125708 & 511.032304892416 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 100.7718 & 0.190223003394459 & 529.756118880287 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 100.753333333333 & 0.182558970685578 & 551.89472724877 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 100.732826086957 & 0.173167050408546 & 581.708967435211 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 100.707045454545 & 0.162679914890628 & 619.050271339596 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 100.681428571429 & 0.150536235245157 & 668.818563234711 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 100.6475 & 0.13669953482186 & 736.268050444787 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 100.632894736842 & 0.130207137687605 & 772.867728482611 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 100.618611111111 & 0.122849212501935 & 819.041563734289 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 100.605294117647 & 0.114807624333108 & 876.294537945898 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 100.5853125 & 0.105080599225877 & 957.220583447435 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 100.557666666667 & 0.0932240945290769 & 1078.6660591839 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 100.539642857143 & 0.0834229393529121 & 1205.17981788942 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 100.518076923077 & 0.0768995733323549 & 1307.13439057255 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 100.502916666667 & 0.0721599450462797 & 1392.7798393168 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 100.485454545455 & 0.0655866872008121 & 1532.10138877407 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 100.471 & 0.0602534122204753 & 1667.47402839798 \tabularnewline
Median & 100.405 &  &  \tabularnewline
Midrange & 100.98 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 100.532258064516 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 100.532258064516 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 100.532258064516 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 100.532258064516 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 100.532258064516 &  &  \tabularnewline
Midmean - Closest Observation & 100.532258064516 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 100.532258064516 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 100.5853125 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&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]100.839666666667[/C][C]0.217506408330383[/C][C]463.616991520982[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]100.825905206869[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]100.812222544367[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]100.853505673659[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]100.848333333333[/C][C]0.21511173901871[/C][C]468.818362927938[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]100.848666666667[/C][C]0.215050442994231[/C][C]468.953540678695[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]100.847166666667[/C][C]0.214469137240362[/C][C]470.217617156002[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]100.843166666667[/C][C]0.213219005161263[/C][C]472.955807060429[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]100.845666666667[/C][C]0.20963370888784[/C][C]481.056540008182[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]100.847666666667[/C][C]0.208048419867627[/C][C]484.731711641128[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]100.865166666667[/C][C]0.20226618525765[/C][C]498.675379367951[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]100.8505[/C][C]0.196729247679788[/C][C]512.636027379885[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]100.885[/C][C]0.187883017456575[/C][C]536.956460278894[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]100.74[/C][C]0.151916755379293[/C][C]663.126326970854[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]100.727166666667[/C][C]0.14677129517897[/C][C]686.286555854414[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]100.709166666667[/C][C]0.139789246465869[/C][C]720.435721722387[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]100.743833333333[/C][C]0.133752256787902[/C][C]753.212213032699[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]100.778833333333[/C][C]0.125642774857224[/C][C]802.106077710039[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]100.683833333333[/C][C]0.10757209950232[/C][C]935.966052527977[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]100.689166666667[/C][C]0.0863677891891195[/C][C]1165.81850261546[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]100.621166666667[/C][C]0.0743978052599357[/C][C]1352.47493276327[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]100.618166666667[/C][C]0.0711521373384823[/C][C]1414.12711452377[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]100.577[/C][C]0.0604892015389926[/C][C]1662.72652706725[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]100.570333333333[/C][C]0.0574298720802712[/C][C]1751.18504865836[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]100.834827586207[/C][C]0.211998990024205[/C][C]475.638245138309[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]100.820357142857[/C][C]0.208065918045986[/C][C]484.559691898093[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]100.80462962963[/C][C]0.203148129037518[/C][C]496.212444127471[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]100.788269230769[/C][C]0.197224849125708[/C][C]511.032304892416[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]100.7718[/C][C]0.190223003394459[/C][C]529.756118880287[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]100.753333333333[/C][C]0.182558970685578[/C][C]551.89472724877[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]100.732826086957[/C][C]0.173167050408546[/C][C]581.708967435211[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]100.707045454545[/C][C]0.162679914890628[/C][C]619.050271339596[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]100.681428571429[/C][C]0.150536235245157[/C][C]668.818563234711[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]100.6475[/C][C]0.13669953482186[/C][C]736.268050444787[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]100.632894736842[/C][C]0.130207137687605[/C][C]772.867728482611[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]100.618611111111[/C][C]0.122849212501935[/C][C]819.041563734289[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]100.605294117647[/C][C]0.114807624333108[/C][C]876.294537945898[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]100.5853125[/C][C]0.105080599225877[/C][C]957.220583447435[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]100.557666666667[/C][C]0.0932240945290769[/C][C]1078.6660591839[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]100.539642857143[/C][C]0.0834229393529121[/C][C]1205.17981788942[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]100.518076923077[/C][C]0.0768995733323549[/C][C]1307.13439057255[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]100.502916666667[/C][C]0.0721599450462797[/C][C]1392.7798393168[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]100.485454545455[/C][C]0.0655866872008121[/C][C]1532.10138877407[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]100.471[/C][C]0.0602534122204753[/C][C]1667.47402839798[/C][/ROW]
[ROW][C]Median[/C][C]100.405[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]100.98[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]100.532258064516[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]100.532258064516[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]100.532258064516[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]100.532258064516[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]100.532258064516[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]100.532258064516[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]100.532258064516[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]100.5853125[/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=&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&T=1

As an alternative you can also use a QR Code:  
QR Code


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

Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean100.8396666666670.217506408330383463.616991520982
Geometric Mean100.825905206869
Harmonic Mean100.812222544367
Quadratic Mean100.853505673659
Winsorized Mean ( 1 / 20 )100.8483333333330.21511173901871468.818362927938
Winsorized Mean ( 2 / 20 )100.8486666666670.215050442994231468.953540678695
Winsorized Mean ( 3 / 20 )100.8471666666670.214469137240362470.217617156002
Winsorized Mean ( 4 / 20 )100.8431666666670.213219005161263472.955807060429
Winsorized Mean ( 5 / 20 )100.8456666666670.20963370888784481.056540008182
Winsorized Mean ( 6 / 20 )100.8476666666670.208048419867627484.731711641128
Winsorized Mean ( 7 / 20 )100.8651666666670.20226618525765498.675379367951
Winsorized Mean ( 8 / 20 )100.85050.196729247679788512.636027379885
Winsorized Mean ( 9 / 20 )100.8850.187883017456575536.956460278894
Winsorized Mean ( 10 / 20 )100.740.151916755379293663.126326970854
Winsorized Mean ( 11 / 20 )100.7271666666670.14677129517897686.286555854414
Winsorized Mean ( 12 / 20 )100.7091666666670.139789246465869720.435721722387
Winsorized Mean ( 13 / 20 )100.7438333333330.133752256787902753.212213032699
Winsorized Mean ( 14 / 20 )100.7788333333330.125642774857224802.106077710039
Winsorized Mean ( 15 / 20 )100.6838333333330.10757209950232935.966052527977
Winsorized Mean ( 16 / 20 )100.6891666666670.08636778918911951165.81850261546
Winsorized Mean ( 17 / 20 )100.6211666666670.07439780525993571352.47493276327
Winsorized Mean ( 18 / 20 )100.6181666666670.07115213733848231414.12711452377
Winsorized Mean ( 19 / 20 )100.5770.06048920153899261662.72652706725
Winsorized Mean ( 20 / 20 )100.5703333333330.05742987208027121751.18504865836
Trimmed Mean ( 1 / 20 )100.8348275862070.211998990024205475.638245138309
Trimmed Mean ( 2 / 20 )100.8203571428570.208065918045986484.559691898093
Trimmed Mean ( 3 / 20 )100.804629629630.203148129037518496.212444127471
Trimmed Mean ( 4 / 20 )100.7882692307690.197224849125708511.032304892416
Trimmed Mean ( 5 / 20 )100.77180.190223003394459529.756118880287
Trimmed Mean ( 6 / 20 )100.7533333333330.182558970685578551.89472724877
Trimmed Mean ( 7 / 20 )100.7328260869570.173167050408546581.708967435211
Trimmed Mean ( 8 / 20 )100.7070454545450.162679914890628619.050271339596
Trimmed Mean ( 9 / 20 )100.6814285714290.150536235245157668.818563234711
Trimmed Mean ( 10 / 20 )100.64750.13669953482186736.268050444787
Trimmed Mean ( 11 / 20 )100.6328947368420.130207137687605772.867728482611
Trimmed Mean ( 12 / 20 )100.6186111111110.122849212501935819.041563734289
Trimmed Mean ( 13 / 20 )100.6052941176470.114807624333108876.294537945898
Trimmed Mean ( 14 / 20 )100.58531250.105080599225877957.220583447435
Trimmed Mean ( 15 / 20 )100.5576666666670.09322409452907691078.6660591839
Trimmed Mean ( 16 / 20 )100.5396428571430.08342293935291211205.17981788942
Trimmed Mean ( 17 / 20 )100.5180769230770.07689957333235491307.13439057255
Trimmed Mean ( 18 / 20 )100.5029166666670.07215994504627971392.7798393168
Trimmed Mean ( 19 / 20 )100.4854545454550.06558668720081211532.10138877407
Trimmed Mean ( 20 / 20 )100.4710.06025341222047531667.47402839798
Median100.405
Midrange100.98
Midmean - Weighted Average at Xnp100.532258064516
Midmean - Weighted Average at X(n+1)p100.532258064516
Midmean - Empirical Distribution Function100.532258064516
Midmean - Empirical Distribution Function - Averaging100.532258064516
Midmean - Empirical Distribution Function - Interpolation100.532258064516
Midmean - Closest Observation100.532258064516
Midmean - True Basic - Statistics Graphics Toolkit100.532258064516
Midmean - MS Excel (old versions)100.5853125
Number of observations60


Figures (Output of Computation)

Input Parameters & R Code

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')