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Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationTue, 11 Dec 2007 15:04:14 -0700
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2007/Dec/11/t11974097915enc632k2qpsheo.htm/, Retrieved Mon, 29 Apr 2024 00:40:59 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=3169, Retrieved Mon, 29 Apr 2024 00:40:59 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact220
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Central Tendency] [Workshop2: the se...] [2007-11-22 16:20:38] [74be16979710d4c4e7c6647856088456]
-    D    [Central Tendency] [tijdreeks 1: indu...] [2007-12-11 22:04:14] [d41d8cd98f00b204e9800998ecf8427e] [Current]
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Dataseries X:
98,8
100,5
110,4
96,4
101,9
106,2
81,0
94,7
101,0
109,4
102,3
90,7
96,2
96,1
106,0
103,1
102,0
104,7
86,0
92,1
106,9
112,6
101,7
92,0
97,4
97,0
105,4
102,7
98,1
104,5
87,4
89,9
109,8
111,7
98,6
96,9
95,1
97,0
112,7
102,9
97,4
111,4
87,4
96,8
114,1
110,3
103,9
101,6
94,6
95,9
104,7
102,8
98,1
113,9
80,9
95,7
113,2
105,9
108,8
102,3
99,0
100,7
115,5
100,7
109,9
114,6
85,4
100,5
114,8
116,5
112,9
102,0
106,0
105,3
118,8
106,1
109,3
117,2
91,9
103,9
115,9




Summary of compuational 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 compuational 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=3169&T=0

[TABLE]
[ROW][C]Summary of compuational 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=3169&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=3169&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 compuational 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 Mean102.3012345679010.954085584177688107.224379305629
Geometric Mean101.93702045347
Harmonic Mean101.563946346377
Quadratic Mean102.656538701982
Winsorized Mean ( 1 / 27 )102.2827160493830.949664967114064107.704000454191
Winsorized Mean ( 2 / 27 )102.3740740740740.91849611681165111.458363514309
Winsorized Mean ( 3 / 27 )102.3740740740740.909225314294337112.594834816635
Winsorized Mean ( 4 / 27 )102.4234567901230.890499013254835115.018046360050
Winsorized Mean ( 5 / 27 )102.3802469135800.882732884239017115.981004833461
Winsorized Mean ( 6 / 27 )102.5506172839510.843045484942213121.643041942132
Winsorized Mean ( 7 / 27 )102.5765432098770.822676810529592124.6863189736
Winsorized Mean ( 8 / 27 )102.6753086419750.798512372377608128.583240778417
Winsorized Mean ( 9 / 27 )102.6086419753090.783225362004993131.007813271826
Winsorized Mean ( 10 / 27 )102.5839506172840.774924243191273132.379328068026
Winsorized Mean ( 11 / 27 )102.8962962962960.716921669629317143.525158542772
Winsorized Mean ( 12 / 27 )102.8962962962960.712256985727357144.465127556760
Winsorized Mean ( 13 / 27 )102.8160493827160.678954935844632151.432803496466
Winsorized Mean ( 14 / 27 )102.8679012345680.656046960737478156.799600319666
Winsorized Mean ( 15 / 27 )102.7197530864200.621605398016185165.249132993767
Winsorized Mean ( 16 / 27 )102.7395061728390.613174997206016167.553319429169
Winsorized Mean ( 17 / 27 )102.6765432098770.59751871607894171.838204305406
Winsorized Mean ( 18 / 27 )102.6987654320990.588176964392395174.605215180757
Winsorized Mean ( 19 / 27 )102.6987654320990.561656758422223182.849692257945
Winsorized Mean ( 20 / 27 )102.6987654320990.554745225214822185.127804195754
Winsorized Mean ( 21 / 27 )102.5950617283950.532258469058472192.754211896108
Winsorized Mean ( 22 / 27 )102.0790123456790.460624629753047221.60997426561
Winsorized Mean ( 23 / 27 )101.9938271604940.419539524466461243.108983093314
Winsorized Mean ( 24 / 27 )101.9641975308640.415841065919254245.199923450232
Winsorized Mean ( 25 / 27 )102.1493827160490.382858495991739266.807146205405
Winsorized Mean ( 26 / 27 )102.1493827160490.382858495991739266.807146205405
Winsorized Mean ( 27 / 27 )102.2827160493830.35687597753842286.605774798533
Trimmed Mean ( 1 / 27 )102.3632911392410.915806909456328111.773879496071
Trimmed Mean ( 2 / 27 )102.4480519480520.876031976911496116.945562089227
Trimmed Mean ( 3 / 27 )102.4880.849249716562261120.680640807122
Trimmed Mean ( 4 / 27 )102.5301369863010.821946600206004124.740630304456
Trimmed Mean ( 5 / 27 )102.5605633802820.796588497847146128.749741751809
Trimmed Mean ( 6 / 27 )102.6028985507250.768902105363296133.440782428663
Trimmed Mean ( 7 / 27 )102.6134328358210.747172857920301137.335600119948
Trimmed Mean ( 8 / 27 )102.620.72635549677297141.280682057088
Trimmed Mean ( 9 / 27 )102.6111111111110.707038388419598145.128062056817
Trimmed Mean ( 10 / 27 )102.6114754098360.68709851013267149.340267656850
Trimmed Mean ( 11 / 27 )102.6152542372880.664618088631765154.397323805225
Trimmed Mean ( 12 / 27 )102.5789473684210.649256065709292157.994592251297
Trimmed Mean ( 13 / 27 )102.540.631110399771971162.475535242406
Trimmed Mean ( 14 / 27 )102.5075471698110.615368304272153166.579179425004
Trimmed Mean ( 15 / 27 )102.4666666666670.600043571402693170.765376966101
Trimmed Mean ( 16 / 27 )102.4387755102040.587582794329094174.339304177838
Trimmed Mean ( 17 / 27 )102.4063829787230.57306489127709178.699453652636
Trimmed Mean ( 18 / 27 )102.3777777777780.557455337603938183.651982269682
Trimmed Mean ( 19 / 27 )102.3441860465120.538869066392929189.924032439978
Trimmed Mean ( 20 / 27 )102.3073170731710.520229666025924196.657983491608
Trimmed Mean ( 21 / 27 )102.2666666666670.496714350707558205.886273511104
Trimmed Mean ( 22 / 27 )102.2324324324320.470751971030436217.168357699394
Trimmed Mean ( 23 / 27 )102.2485714285710.454674533675056224.882996199752
Trimmed Mean ( 24 / 27 )102.2757575757580.442595442177368231.081813840213
Trimmed Mean ( 25 / 27 )102.3096774193550.425563632296678240.409822773650
Trimmed Mean ( 26 / 27 )102.3275862068970.410871252344403249.050245357938
Trimmed Mean ( 27 / 27 )102.3481481481480.388046843090115263.752044297343
Median102.3
Midrange99.85
Midmean - Weighted Average at Xnp102.1325
Midmean - Weighted Average at X(n+1)p102.307317073171
Midmean - Empirical Distribution Function102.307317073171
Midmean - Empirical Distribution Function - Averaging102.307317073171
Midmean - Empirical Distribution Function - Interpolation102.307317073171
Midmean - Closest Observation102.176190476190
Midmean - True Basic - Statistics Graphics Toolkit102.307317073171
Midmean - MS Excel (old versions)102.307317073171
Number of observations81

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 102.301234567901 & 0.954085584177688 & 107.224379305629 \tabularnewline
Geometric Mean & 101.93702045347 &  &  \tabularnewline
Harmonic Mean & 101.563946346377 &  &  \tabularnewline
Quadratic Mean & 102.656538701982 &  &  \tabularnewline
Winsorized Mean ( 1 / 27 ) & 102.282716049383 & 0.949664967114064 & 107.704000454191 \tabularnewline
Winsorized Mean ( 2 / 27 ) & 102.374074074074 & 0.91849611681165 & 111.458363514309 \tabularnewline
Winsorized Mean ( 3 / 27 ) & 102.374074074074 & 0.909225314294337 & 112.594834816635 \tabularnewline
Winsorized Mean ( 4 / 27 ) & 102.423456790123 & 0.890499013254835 & 115.018046360050 \tabularnewline
Winsorized Mean ( 5 / 27 ) & 102.380246913580 & 0.882732884239017 & 115.981004833461 \tabularnewline
Winsorized Mean ( 6 / 27 ) & 102.550617283951 & 0.843045484942213 & 121.643041942132 \tabularnewline
Winsorized Mean ( 7 / 27 ) & 102.576543209877 & 0.822676810529592 & 124.6863189736 \tabularnewline
Winsorized Mean ( 8 / 27 ) & 102.675308641975 & 0.798512372377608 & 128.583240778417 \tabularnewline
Winsorized Mean ( 9 / 27 ) & 102.608641975309 & 0.783225362004993 & 131.007813271826 \tabularnewline
Winsorized Mean ( 10 / 27 ) & 102.583950617284 & 0.774924243191273 & 132.379328068026 \tabularnewline
Winsorized Mean ( 11 / 27 ) & 102.896296296296 & 0.716921669629317 & 143.525158542772 \tabularnewline
Winsorized Mean ( 12 / 27 ) & 102.896296296296 & 0.712256985727357 & 144.465127556760 \tabularnewline
Winsorized Mean ( 13 / 27 ) & 102.816049382716 & 0.678954935844632 & 151.432803496466 \tabularnewline
Winsorized Mean ( 14 / 27 ) & 102.867901234568 & 0.656046960737478 & 156.799600319666 \tabularnewline
Winsorized Mean ( 15 / 27 ) & 102.719753086420 & 0.621605398016185 & 165.249132993767 \tabularnewline
Winsorized Mean ( 16 / 27 ) & 102.739506172839 & 0.613174997206016 & 167.553319429169 \tabularnewline
Winsorized Mean ( 17 / 27 ) & 102.676543209877 & 0.59751871607894 & 171.838204305406 \tabularnewline
Winsorized Mean ( 18 / 27 ) & 102.698765432099 & 0.588176964392395 & 174.605215180757 \tabularnewline
Winsorized Mean ( 19 / 27 ) & 102.698765432099 & 0.561656758422223 & 182.849692257945 \tabularnewline
Winsorized Mean ( 20 / 27 ) & 102.698765432099 & 0.554745225214822 & 185.127804195754 \tabularnewline
Winsorized Mean ( 21 / 27 ) & 102.595061728395 & 0.532258469058472 & 192.754211896108 \tabularnewline
Winsorized Mean ( 22 / 27 ) & 102.079012345679 & 0.460624629753047 & 221.60997426561 \tabularnewline
Winsorized Mean ( 23 / 27 ) & 101.993827160494 & 0.419539524466461 & 243.108983093314 \tabularnewline
Winsorized Mean ( 24 / 27 ) & 101.964197530864 & 0.415841065919254 & 245.199923450232 \tabularnewline
Winsorized Mean ( 25 / 27 ) & 102.149382716049 & 0.382858495991739 & 266.807146205405 \tabularnewline
Winsorized Mean ( 26 / 27 ) & 102.149382716049 & 0.382858495991739 & 266.807146205405 \tabularnewline
Winsorized Mean ( 27 / 27 ) & 102.282716049383 & 0.35687597753842 & 286.605774798533 \tabularnewline
Trimmed Mean ( 1 / 27 ) & 102.363291139241 & 0.915806909456328 & 111.773879496071 \tabularnewline
Trimmed Mean ( 2 / 27 ) & 102.448051948052 & 0.876031976911496 & 116.945562089227 \tabularnewline
Trimmed Mean ( 3 / 27 ) & 102.488 & 0.849249716562261 & 120.680640807122 \tabularnewline
Trimmed Mean ( 4 / 27 ) & 102.530136986301 & 0.821946600206004 & 124.740630304456 \tabularnewline
Trimmed Mean ( 5 / 27 ) & 102.560563380282 & 0.796588497847146 & 128.749741751809 \tabularnewline
Trimmed Mean ( 6 / 27 ) & 102.602898550725 & 0.768902105363296 & 133.440782428663 \tabularnewline
Trimmed Mean ( 7 / 27 ) & 102.613432835821 & 0.747172857920301 & 137.335600119948 \tabularnewline
Trimmed Mean ( 8 / 27 ) & 102.62 & 0.72635549677297 & 141.280682057088 \tabularnewline
Trimmed Mean ( 9 / 27 ) & 102.611111111111 & 0.707038388419598 & 145.128062056817 \tabularnewline
Trimmed Mean ( 10 / 27 ) & 102.611475409836 & 0.68709851013267 & 149.340267656850 \tabularnewline
Trimmed Mean ( 11 / 27 ) & 102.615254237288 & 0.664618088631765 & 154.397323805225 \tabularnewline
Trimmed Mean ( 12 / 27 ) & 102.578947368421 & 0.649256065709292 & 157.994592251297 \tabularnewline
Trimmed Mean ( 13 / 27 ) & 102.54 & 0.631110399771971 & 162.475535242406 \tabularnewline
Trimmed Mean ( 14 / 27 ) & 102.507547169811 & 0.615368304272153 & 166.579179425004 \tabularnewline
Trimmed Mean ( 15 / 27 ) & 102.466666666667 & 0.600043571402693 & 170.765376966101 \tabularnewline
Trimmed Mean ( 16 / 27 ) & 102.438775510204 & 0.587582794329094 & 174.339304177838 \tabularnewline
Trimmed Mean ( 17 / 27 ) & 102.406382978723 & 0.57306489127709 & 178.699453652636 \tabularnewline
Trimmed Mean ( 18 / 27 ) & 102.377777777778 & 0.557455337603938 & 183.651982269682 \tabularnewline
Trimmed Mean ( 19 / 27 ) & 102.344186046512 & 0.538869066392929 & 189.924032439978 \tabularnewline
Trimmed Mean ( 20 / 27 ) & 102.307317073171 & 0.520229666025924 & 196.657983491608 \tabularnewline
Trimmed Mean ( 21 / 27 ) & 102.266666666667 & 0.496714350707558 & 205.886273511104 \tabularnewline
Trimmed Mean ( 22 / 27 ) & 102.232432432432 & 0.470751971030436 & 217.168357699394 \tabularnewline
Trimmed Mean ( 23 / 27 ) & 102.248571428571 & 0.454674533675056 & 224.882996199752 \tabularnewline
Trimmed Mean ( 24 / 27 ) & 102.275757575758 & 0.442595442177368 & 231.081813840213 \tabularnewline
Trimmed Mean ( 25 / 27 ) & 102.309677419355 & 0.425563632296678 & 240.409822773650 \tabularnewline
Trimmed Mean ( 26 / 27 ) & 102.327586206897 & 0.410871252344403 & 249.050245357938 \tabularnewline
Trimmed Mean ( 27 / 27 ) & 102.348148148148 & 0.388046843090115 & 263.752044297343 \tabularnewline
Median & 102.3 &  &  \tabularnewline
Midrange & 99.85 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 102.1325 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 102.307317073171 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 102.307317073171 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 102.307317073171 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 102.307317073171 &  &  \tabularnewline
Midmean - Closest Observation & 102.176190476190 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 102.307317073171 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 102.307317073171 &  &  \tabularnewline
Number of observations & 81 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=3169&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]102.301234567901[/C][C]0.954085584177688[/C][C]107.224379305629[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]101.93702045347[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]101.563946346377[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]102.656538701982[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 27 )[/C][C]102.282716049383[/C][C]0.949664967114064[/C][C]107.704000454191[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 27 )[/C][C]102.374074074074[/C][C]0.91849611681165[/C][C]111.458363514309[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 27 )[/C][C]102.374074074074[/C][C]0.909225314294337[/C][C]112.594834816635[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 27 )[/C][C]102.423456790123[/C][C]0.890499013254835[/C][C]115.018046360050[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 27 )[/C][C]102.380246913580[/C][C]0.882732884239017[/C][C]115.981004833461[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 27 )[/C][C]102.550617283951[/C][C]0.843045484942213[/C][C]121.643041942132[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 27 )[/C][C]102.576543209877[/C][C]0.822676810529592[/C][C]124.6863189736[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 27 )[/C][C]102.675308641975[/C][C]0.798512372377608[/C][C]128.583240778417[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 27 )[/C][C]102.608641975309[/C][C]0.783225362004993[/C][C]131.007813271826[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 27 )[/C][C]102.583950617284[/C][C]0.774924243191273[/C][C]132.379328068026[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 27 )[/C][C]102.896296296296[/C][C]0.716921669629317[/C][C]143.525158542772[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 27 )[/C][C]102.896296296296[/C][C]0.712256985727357[/C][C]144.465127556760[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 27 )[/C][C]102.816049382716[/C][C]0.678954935844632[/C][C]151.432803496466[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 27 )[/C][C]102.867901234568[/C][C]0.656046960737478[/C][C]156.799600319666[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 27 )[/C][C]102.719753086420[/C][C]0.621605398016185[/C][C]165.249132993767[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 27 )[/C][C]102.739506172839[/C][C]0.613174997206016[/C][C]167.553319429169[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 27 )[/C][C]102.676543209877[/C][C]0.59751871607894[/C][C]171.838204305406[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 27 )[/C][C]102.698765432099[/C][C]0.588176964392395[/C][C]174.605215180757[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 27 )[/C][C]102.698765432099[/C][C]0.561656758422223[/C][C]182.849692257945[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 27 )[/C][C]102.698765432099[/C][C]0.554745225214822[/C][C]185.127804195754[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 27 )[/C][C]102.595061728395[/C][C]0.532258469058472[/C][C]192.754211896108[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 27 )[/C][C]102.079012345679[/C][C]0.460624629753047[/C][C]221.60997426561[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 27 )[/C][C]101.993827160494[/C][C]0.419539524466461[/C][C]243.108983093314[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 27 )[/C][C]101.964197530864[/C][C]0.415841065919254[/C][C]245.199923450232[/C][/ROW]
[ROW][C]Winsorized Mean ( 25 / 27 )[/C][C]102.149382716049[/C][C]0.382858495991739[/C][C]266.807146205405[/C][/ROW]
[ROW][C]Winsorized Mean ( 26 / 27 )[/C][C]102.149382716049[/C][C]0.382858495991739[/C][C]266.807146205405[/C][/ROW]
[ROW][C]Winsorized Mean ( 27 / 27 )[/C][C]102.282716049383[/C][C]0.35687597753842[/C][C]286.605774798533[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 27 )[/C][C]102.363291139241[/C][C]0.915806909456328[/C][C]111.773879496071[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 27 )[/C][C]102.448051948052[/C][C]0.876031976911496[/C][C]116.945562089227[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 27 )[/C][C]102.488[/C][C]0.849249716562261[/C][C]120.680640807122[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 27 )[/C][C]102.530136986301[/C][C]0.821946600206004[/C][C]124.740630304456[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 27 )[/C][C]102.560563380282[/C][C]0.796588497847146[/C][C]128.749741751809[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 27 )[/C][C]102.602898550725[/C][C]0.768902105363296[/C][C]133.440782428663[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 27 )[/C][C]102.613432835821[/C][C]0.747172857920301[/C][C]137.335600119948[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 27 )[/C][C]102.62[/C][C]0.72635549677297[/C][C]141.280682057088[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 27 )[/C][C]102.611111111111[/C][C]0.707038388419598[/C][C]145.128062056817[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 27 )[/C][C]102.611475409836[/C][C]0.68709851013267[/C][C]149.340267656850[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 27 )[/C][C]102.615254237288[/C][C]0.664618088631765[/C][C]154.397323805225[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 27 )[/C][C]102.578947368421[/C][C]0.649256065709292[/C][C]157.994592251297[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 27 )[/C][C]102.54[/C][C]0.631110399771971[/C][C]162.475535242406[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 27 )[/C][C]102.507547169811[/C][C]0.615368304272153[/C][C]166.579179425004[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 27 )[/C][C]102.466666666667[/C][C]0.600043571402693[/C][C]170.765376966101[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 27 )[/C][C]102.438775510204[/C][C]0.587582794329094[/C][C]174.339304177838[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 27 )[/C][C]102.406382978723[/C][C]0.57306489127709[/C][C]178.699453652636[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 27 )[/C][C]102.377777777778[/C][C]0.557455337603938[/C][C]183.651982269682[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 27 )[/C][C]102.344186046512[/C][C]0.538869066392929[/C][C]189.924032439978[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 27 )[/C][C]102.307317073171[/C][C]0.520229666025924[/C][C]196.657983491608[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 27 )[/C][C]102.266666666667[/C][C]0.496714350707558[/C][C]205.886273511104[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 27 )[/C][C]102.232432432432[/C][C]0.470751971030436[/C][C]217.168357699394[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 27 )[/C][C]102.248571428571[/C][C]0.454674533675056[/C][C]224.882996199752[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 27 )[/C][C]102.275757575758[/C][C]0.442595442177368[/C][C]231.081813840213[/C][/ROW]
[ROW][C]Trimmed Mean ( 25 / 27 )[/C][C]102.309677419355[/C][C]0.425563632296678[/C][C]240.409822773650[/C][/ROW]
[ROW][C]Trimmed Mean ( 26 / 27 )[/C][C]102.327586206897[/C][C]0.410871252344403[/C][C]249.050245357938[/C][/ROW]
[ROW][C]Trimmed Mean ( 27 / 27 )[/C][C]102.348148148148[/C][C]0.388046843090115[/C][C]263.752044297343[/C][/ROW]
[ROW][C]Median[/C][C]102.3[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]99.85[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]102.1325[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]102.307317073171[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]102.307317073171[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]102.307317073171[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]102.307317073171[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]102.176190476190[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]102.307317073171[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]102.307317073171[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]81[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=3169&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=3169&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 Mean102.3012345679010.954085584177688107.224379305629
Geometric Mean101.93702045347
Harmonic Mean101.563946346377
Quadratic Mean102.656538701982
Winsorized Mean ( 1 / 27 )102.2827160493830.949664967114064107.704000454191
Winsorized Mean ( 2 / 27 )102.3740740740740.91849611681165111.458363514309
Winsorized Mean ( 3 / 27 )102.3740740740740.909225314294337112.594834816635
Winsorized Mean ( 4 / 27 )102.4234567901230.890499013254835115.018046360050
Winsorized Mean ( 5 / 27 )102.3802469135800.882732884239017115.981004833461
Winsorized Mean ( 6 / 27 )102.5506172839510.843045484942213121.643041942132
Winsorized Mean ( 7 / 27 )102.5765432098770.822676810529592124.6863189736
Winsorized Mean ( 8 / 27 )102.6753086419750.798512372377608128.583240778417
Winsorized Mean ( 9 / 27 )102.6086419753090.783225362004993131.007813271826
Winsorized Mean ( 10 / 27 )102.5839506172840.774924243191273132.379328068026
Winsorized Mean ( 11 / 27 )102.8962962962960.716921669629317143.525158542772
Winsorized Mean ( 12 / 27 )102.8962962962960.712256985727357144.465127556760
Winsorized Mean ( 13 / 27 )102.8160493827160.678954935844632151.432803496466
Winsorized Mean ( 14 / 27 )102.8679012345680.656046960737478156.799600319666
Winsorized Mean ( 15 / 27 )102.7197530864200.621605398016185165.249132993767
Winsorized Mean ( 16 / 27 )102.7395061728390.613174997206016167.553319429169
Winsorized Mean ( 17 / 27 )102.6765432098770.59751871607894171.838204305406
Winsorized Mean ( 18 / 27 )102.6987654320990.588176964392395174.605215180757
Winsorized Mean ( 19 / 27 )102.6987654320990.561656758422223182.849692257945
Winsorized Mean ( 20 / 27 )102.6987654320990.554745225214822185.127804195754
Winsorized Mean ( 21 / 27 )102.5950617283950.532258469058472192.754211896108
Winsorized Mean ( 22 / 27 )102.0790123456790.460624629753047221.60997426561
Winsorized Mean ( 23 / 27 )101.9938271604940.419539524466461243.108983093314
Winsorized Mean ( 24 / 27 )101.9641975308640.415841065919254245.199923450232
Winsorized Mean ( 25 / 27 )102.1493827160490.382858495991739266.807146205405
Winsorized Mean ( 26 / 27 )102.1493827160490.382858495991739266.807146205405
Winsorized Mean ( 27 / 27 )102.2827160493830.35687597753842286.605774798533
Trimmed Mean ( 1 / 27 )102.3632911392410.915806909456328111.773879496071
Trimmed Mean ( 2 / 27 )102.4480519480520.876031976911496116.945562089227
Trimmed Mean ( 3 / 27 )102.4880.849249716562261120.680640807122
Trimmed Mean ( 4 / 27 )102.5301369863010.821946600206004124.740630304456
Trimmed Mean ( 5 / 27 )102.5605633802820.796588497847146128.749741751809
Trimmed Mean ( 6 / 27 )102.6028985507250.768902105363296133.440782428663
Trimmed Mean ( 7 / 27 )102.6134328358210.747172857920301137.335600119948
Trimmed Mean ( 8 / 27 )102.620.72635549677297141.280682057088
Trimmed Mean ( 9 / 27 )102.6111111111110.707038388419598145.128062056817
Trimmed Mean ( 10 / 27 )102.6114754098360.68709851013267149.340267656850
Trimmed Mean ( 11 / 27 )102.6152542372880.664618088631765154.397323805225
Trimmed Mean ( 12 / 27 )102.5789473684210.649256065709292157.994592251297
Trimmed Mean ( 13 / 27 )102.540.631110399771971162.475535242406
Trimmed Mean ( 14 / 27 )102.5075471698110.615368304272153166.579179425004
Trimmed Mean ( 15 / 27 )102.4666666666670.600043571402693170.765376966101
Trimmed Mean ( 16 / 27 )102.4387755102040.587582794329094174.339304177838
Trimmed Mean ( 17 / 27 )102.4063829787230.57306489127709178.699453652636
Trimmed Mean ( 18 / 27 )102.3777777777780.557455337603938183.651982269682
Trimmed Mean ( 19 / 27 )102.3441860465120.538869066392929189.924032439978
Trimmed Mean ( 20 / 27 )102.3073170731710.520229666025924196.657983491608
Trimmed Mean ( 21 / 27 )102.2666666666670.496714350707558205.886273511104
Trimmed Mean ( 22 / 27 )102.2324324324320.470751971030436217.168357699394
Trimmed Mean ( 23 / 27 )102.2485714285710.454674533675056224.882996199752
Trimmed Mean ( 24 / 27 )102.2757575757580.442595442177368231.081813840213
Trimmed Mean ( 25 / 27 )102.3096774193550.425563632296678240.409822773650
Trimmed Mean ( 26 / 27 )102.3275862068970.410871252344403249.050245357938
Trimmed Mean ( 27 / 27 )102.3481481481480.388046843090115263.752044297343
Median102.3
Midrange99.85
Midmean - Weighted Average at Xnp102.1325
Midmean - Weighted Average at X(n+1)p102.307317073171
Midmean - Empirical Distribution Function102.307317073171
Midmean - Empirical Distribution Function - Averaging102.307317073171
Midmean - Empirical Distribution Function - Interpolation102.307317073171
Midmean - Closest Observation102.176190476190
Midmean - True Basic - Statistics Graphics Toolkit102.307317073171
Midmean - MS Excel (old versions)102.307317073171
Number of observations81



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')