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Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationMon, 07 Oct 2013 06:25:06 -0400
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2013/Oct/07/t1381141544jg21slhew380ju5.htm/, Retrieved Fri, 03 May 2024 12:20:45 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=213619, Retrieved Fri, 03 May 2024 12:20:45 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact75
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [] [2013-10-07 10:25:06] [5e7911d8fd88d8bc3975d02d8918deef] [Current]
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Dataseries X:
51,02
51,06
50,9
51,23
51,29
51,3
51,3
51,3
51,46
51,47
51,77
51,82
51,82
51,84
51,9
51,94
52,22
52,27
52,27
52,28
52,53
52,73
52,72
52,67
52,67
52,65
52,69
52,73
52,84
52,83
52,83
52,84
52,82
53,09
53,4
53,43
53,43
53,42
53,6
53,69
54,05
54,04
54,04
54,08
54,05
54,39
54,38
54,46
54,46
54,69
54,91
55,52
56,01
56,07
56,07
56,09
56,29
56,45
56,87
56,87
56,87
56,87
56,8
56,89
57,01
57,03
57,03
57,03
57,06
57,25
57,24
57,31




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time5 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 & 5 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=213619&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]5 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=213619&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=213619&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 time5 seconds
R Server'Gwilym Jenkins' @ jenkins.wessa.net







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean53.89236111111110.241845853357487222.837647877508
Geometric Mean53.8541560217161
Harmonic Mean53.8162940366291
Quadratic Mean53.9308755234163
Winsorized Mean ( 1 / 24 )53.89319444444440.241396386530381223.256011488232
Winsorized Mean ( 2 / 24 )53.89402777777780.241156954757567223.481125941224
Winsorized Mean ( 3 / 24 )53.89361111111110.238579709940161225.893522649635
Winsorized Mean ( 4 / 24 )53.89527777777780.237749866273848226.688993026391
Winsorized Mean ( 5 / 24 )53.89597222222220.237642853810551226.793995098157
Winsorized Mean ( 6 / 24 )53.89597222222220.237642853810551226.793995098157
Winsorized Mean ( 7 / 24 )53.89402777777780.237282447903399227.130275559695
Winsorized Mean ( 8 / 24 )53.89847222222220.232154943581884232.165946546865
Winsorized Mean ( 9 / 24 )53.89722222222220.231517263796729232.800013866541
Winsorized Mean ( 10 / 24 )53.93888888888890.225616921198924239.072887805838
Winsorized Mean ( 11 / 24 )53.94652777777780.224590407896989240.199607289199
Winsorized Mean ( 12 / 24 )53.94652777777780.224590407896989240.199607289199
Winsorized Mean ( 13 / 24 )53.93750.22180180056166243.178819393784
Winsorized Mean ( 14 / 24 )53.88111111111110.208133853377049258.87720924237
Winsorized Mean ( 15 / 24 )53.85611111111110.201279801548897267.568383398013
Winsorized Mean ( 16 / 24 )53.87388888888890.18567208161661290.156109738307
Winsorized Mean ( 17 / 24 )53.88097222222220.183407385782883293.777548773343
Winsorized Mean ( 18 / 24 )53.88097222222220.183407385782883293.777548773343
Winsorized Mean ( 19 / 24 )53.86777777777780.180425859280952298.559075691567
Winsorized Mean ( 20 / 24 )53.80111111111110.149516769299837359.833290694102
Winsorized Mean ( 21 / 24 )53.65819444444440.117420156735132456.976007666918
Winsorized Mean ( 22 / 24 )53.59708333333330.106775259698699501.961629356604
Winsorized Mean ( 23 / 24 )53.52361111111110.0964416406186121554.984452439745
Winsorized Mean ( 24 / 24 )53.53027777777780.0956134898710108559.861143547776
Trimmed Mean ( 1 / 24 )53.88628571428570.240065913259791224.464543852054
Trimmed Mean ( 2 / 24 )53.87897058823530.238348791914142226.050948928844
Trimmed Mean ( 3 / 24 )53.87075757575760.236317643155315227.959101387754
Trimmed Mean ( 4 / 24 )53.86218750.234874741688488229.323030278994
Trimmed Mean ( 5 / 24 )53.85258064516130.233256319532832230.872975930589
Trimmed Mean ( 6 / 24 )53.84216666666670.231157012657937232.924651722946
Trimmed Mean ( 7 / 24 )53.83103448275860.228439786850461235.646492342409
Trimmed Mean ( 8 / 24 )53.81946428571430.225056474823378239.137595698819
Trimmed Mean ( 9 / 24 )53.80629629629630.221958957729988242.415520628599
Trimmed Mean ( 10 / 24 )53.79230769230770.218095350372362246.645825325786
Trimmed Mean ( 11 / 24 )53.77120.214342590547117250.865681257034
Trimmed Mean ( 12 / 24 )53.74729166666670.209612260157777256.412919865521
Trimmed Mean ( 13 / 24 )53.72130434782610.203384077463708264.137217710232
Trimmed Mean ( 14 / 24 )53.69409090909090.195854855807898274.152461972942
Trimmed Mean ( 15 / 24 )53.67119047619050.18935007196694283.449538300473
Trimmed Mean ( 16 / 24 )53.6490.182336614605079294.23053683539
Trimmed Mean ( 17 / 24 )53.62236842105260.176574983049033303.680439296219
Trimmed Mean ( 18 / 24 )53.59194444444440.16899366919881317.1239768834
Trimmed Mean ( 19 / 24 )53.55794117647060.158132359219738338.690584525129
Trimmed Mean ( 20 / 24 )53.521250.1432899370102373.517157706547
Trimmed Mean ( 21 / 24 )53.48766666666670.132856921858907402.5960101911
Trimmed Mean ( 22 / 24 )53.46678571428570.129198847574828413.833302060372
Trimmed Mean ( 23 / 24 )53.45038461538460.126984530577221420.920441036562
Trimmed Mean ( 24 / 24 )53.44083333333330.126625541569534422.038339745124
Median53.425
Midrange54.105
Midmean - Weighted Average at Xnp53.6223684210526
Midmean - Weighted Average at X(n+1)p53.6223684210526
Midmean - Empirical Distribution Function53.6223684210526
Midmean - Empirical Distribution Function - Averaging53.6223684210526
Midmean - Empirical Distribution Function - Interpolation53.6223684210526
Midmean - Closest Observation53.6223684210526
Midmean - True Basic - Statistics Graphics Toolkit53.6223684210526
Midmean - MS Excel (old versions)53.6223684210526
Number of observations72

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 53.8923611111111 & 0.241845853357487 & 222.837647877508 \tabularnewline
Geometric Mean & 53.8541560217161 &  &  \tabularnewline
Harmonic Mean & 53.8162940366291 &  &  \tabularnewline
Quadratic Mean & 53.9308755234163 &  &  \tabularnewline
Winsorized Mean ( 1 / 24 ) & 53.8931944444444 & 0.241396386530381 & 223.256011488232 \tabularnewline
Winsorized Mean ( 2 / 24 ) & 53.8940277777778 & 0.241156954757567 & 223.481125941224 \tabularnewline
Winsorized Mean ( 3 / 24 ) & 53.8936111111111 & 0.238579709940161 & 225.893522649635 \tabularnewline
Winsorized Mean ( 4 / 24 ) & 53.8952777777778 & 0.237749866273848 & 226.688993026391 \tabularnewline
Winsorized Mean ( 5 / 24 ) & 53.8959722222222 & 0.237642853810551 & 226.793995098157 \tabularnewline
Winsorized Mean ( 6 / 24 ) & 53.8959722222222 & 0.237642853810551 & 226.793995098157 \tabularnewline
Winsorized Mean ( 7 / 24 ) & 53.8940277777778 & 0.237282447903399 & 227.130275559695 \tabularnewline
Winsorized Mean ( 8 / 24 ) & 53.8984722222222 & 0.232154943581884 & 232.165946546865 \tabularnewline
Winsorized Mean ( 9 / 24 ) & 53.8972222222222 & 0.231517263796729 & 232.800013866541 \tabularnewline
Winsorized Mean ( 10 / 24 ) & 53.9388888888889 & 0.225616921198924 & 239.072887805838 \tabularnewline
Winsorized Mean ( 11 / 24 ) & 53.9465277777778 & 0.224590407896989 & 240.199607289199 \tabularnewline
Winsorized Mean ( 12 / 24 ) & 53.9465277777778 & 0.224590407896989 & 240.199607289199 \tabularnewline
Winsorized Mean ( 13 / 24 ) & 53.9375 & 0.22180180056166 & 243.178819393784 \tabularnewline
Winsorized Mean ( 14 / 24 ) & 53.8811111111111 & 0.208133853377049 & 258.87720924237 \tabularnewline
Winsorized Mean ( 15 / 24 ) & 53.8561111111111 & 0.201279801548897 & 267.568383398013 \tabularnewline
Winsorized Mean ( 16 / 24 ) & 53.8738888888889 & 0.18567208161661 & 290.156109738307 \tabularnewline
Winsorized Mean ( 17 / 24 ) & 53.8809722222222 & 0.183407385782883 & 293.777548773343 \tabularnewline
Winsorized Mean ( 18 / 24 ) & 53.8809722222222 & 0.183407385782883 & 293.777548773343 \tabularnewline
Winsorized Mean ( 19 / 24 ) & 53.8677777777778 & 0.180425859280952 & 298.559075691567 \tabularnewline
Winsorized Mean ( 20 / 24 ) & 53.8011111111111 & 0.149516769299837 & 359.833290694102 \tabularnewline
Winsorized Mean ( 21 / 24 ) & 53.6581944444444 & 0.117420156735132 & 456.976007666918 \tabularnewline
Winsorized Mean ( 22 / 24 ) & 53.5970833333333 & 0.106775259698699 & 501.961629356604 \tabularnewline
Winsorized Mean ( 23 / 24 ) & 53.5236111111111 & 0.0964416406186121 & 554.984452439745 \tabularnewline
Winsorized Mean ( 24 / 24 ) & 53.5302777777778 & 0.0956134898710108 & 559.861143547776 \tabularnewline
Trimmed Mean ( 1 / 24 ) & 53.8862857142857 & 0.240065913259791 & 224.464543852054 \tabularnewline
Trimmed Mean ( 2 / 24 ) & 53.8789705882353 & 0.238348791914142 & 226.050948928844 \tabularnewline
Trimmed Mean ( 3 / 24 ) & 53.8707575757576 & 0.236317643155315 & 227.959101387754 \tabularnewline
Trimmed Mean ( 4 / 24 ) & 53.8621875 & 0.234874741688488 & 229.323030278994 \tabularnewline
Trimmed Mean ( 5 / 24 ) & 53.8525806451613 & 0.233256319532832 & 230.872975930589 \tabularnewline
Trimmed Mean ( 6 / 24 ) & 53.8421666666667 & 0.231157012657937 & 232.924651722946 \tabularnewline
Trimmed Mean ( 7 / 24 ) & 53.8310344827586 & 0.228439786850461 & 235.646492342409 \tabularnewline
Trimmed Mean ( 8 / 24 ) & 53.8194642857143 & 0.225056474823378 & 239.137595698819 \tabularnewline
Trimmed Mean ( 9 / 24 ) & 53.8062962962963 & 0.221958957729988 & 242.415520628599 \tabularnewline
Trimmed Mean ( 10 / 24 ) & 53.7923076923077 & 0.218095350372362 & 246.645825325786 \tabularnewline
Trimmed Mean ( 11 / 24 ) & 53.7712 & 0.214342590547117 & 250.865681257034 \tabularnewline
Trimmed Mean ( 12 / 24 ) & 53.7472916666667 & 0.209612260157777 & 256.412919865521 \tabularnewline
Trimmed Mean ( 13 / 24 ) & 53.7213043478261 & 0.203384077463708 & 264.137217710232 \tabularnewline
Trimmed Mean ( 14 / 24 ) & 53.6940909090909 & 0.195854855807898 & 274.152461972942 \tabularnewline
Trimmed Mean ( 15 / 24 ) & 53.6711904761905 & 0.18935007196694 & 283.449538300473 \tabularnewline
Trimmed Mean ( 16 / 24 ) & 53.649 & 0.182336614605079 & 294.23053683539 \tabularnewline
Trimmed Mean ( 17 / 24 ) & 53.6223684210526 & 0.176574983049033 & 303.680439296219 \tabularnewline
Trimmed Mean ( 18 / 24 ) & 53.5919444444444 & 0.16899366919881 & 317.1239768834 \tabularnewline
Trimmed Mean ( 19 / 24 ) & 53.5579411764706 & 0.158132359219738 & 338.690584525129 \tabularnewline
Trimmed Mean ( 20 / 24 ) & 53.52125 & 0.1432899370102 & 373.517157706547 \tabularnewline
Trimmed Mean ( 21 / 24 ) & 53.4876666666667 & 0.132856921858907 & 402.5960101911 \tabularnewline
Trimmed Mean ( 22 / 24 ) & 53.4667857142857 & 0.129198847574828 & 413.833302060372 \tabularnewline
Trimmed Mean ( 23 / 24 ) & 53.4503846153846 & 0.126984530577221 & 420.920441036562 \tabularnewline
Trimmed Mean ( 24 / 24 ) & 53.4408333333333 & 0.126625541569534 & 422.038339745124 \tabularnewline
Median & 53.425 &  &  \tabularnewline
Midrange & 54.105 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 53.6223684210526 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 53.6223684210526 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 53.6223684210526 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 53.6223684210526 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 53.6223684210526 &  &  \tabularnewline
Midmean - Closest Observation & 53.6223684210526 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 53.6223684210526 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 53.6223684210526 &  &  \tabularnewline
Number of observations & 72 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=213619&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]53.8923611111111[/C][C]0.241845853357487[/C][C]222.837647877508[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]53.8541560217161[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]53.8162940366291[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]53.9308755234163[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 24 )[/C][C]53.8931944444444[/C][C]0.241396386530381[/C][C]223.256011488232[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 24 )[/C][C]53.8940277777778[/C][C]0.241156954757567[/C][C]223.481125941224[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 24 )[/C][C]53.8936111111111[/C][C]0.238579709940161[/C][C]225.893522649635[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 24 )[/C][C]53.8952777777778[/C][C]0.237749866273848[/C][C]226.688993026391[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 24 )[/C][C]53.8959722222222[/C][C]0.237642853810551[/C][C]226.793995098157[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 24 )[/C][C]53.8959722222222[/C][C]0.237642853810551[/C][C]226.793995098157[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 24 )[/C][C]53.8940277777778[/C][C]0.237282447903399[/C][C]227.130275559695[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 24 )[/C][C]53.8984722222222[/C][C]0.232154943581884[/C][C]232.165946546865[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 24 )[/C][C]53.8972222222222[/C][C]0.231517263796729[/C][C]232.800013866541[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 24 )[/C][C]53.9388888888889[/C][C]0.225616921198924[/C][C]239.072887805838[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 24 )[/C][C]53.9465277777778[/C][C]0.224590407896989[/C][C]240.199607289199[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 24 )[/C][C]53.9465277777778[/C][C]0.224590407896989[/C][C]240.199607289199[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 24 )[/C][C]53.9375[/C][C]0.22180180056166[/C][C]243.178819393784[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 24 )[/C][C]53.8811111111111[/C][C]0.208133853377049[/C][C]258.87720924237[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 24 )[/C][C]53.8561111111111[/C][C]0.201279801548897[/C][C]267.568383398013[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 24 )[/C][C]53.8738888888889[/C][C]0.18567208161661[/C][C]290.156109738307[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 24 )[/C][C]53.8809722222222[/C][C]0.183407385782883[/C][C]293.777548773343[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 24 )[/C][C]53.8809722222222[/C][C]0.183407385782883[/C][C]293.777548773343[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 24 )[/C][C]53.8677777777778[/C][C]0.180425859280952[/C][C]298.559075691567[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 24 )[/C][C]53.8011111111111[/C][C]0.149516769299837[/C][C]359.833290694102[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 24 )[/C][C]53.6581944444444[/C][C]0.117420156735132[/C][C]456.976007666918[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 24 )[/C][C]53.5970833333333[/C][C]0.106775259698699[/C][C]501.961629356604[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 24 )[/C][C]53.5236111111111[/C][C]0.0964416406186121[/C][C]554.984452439745[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 24 )[/C][C]53.5302777777778[/C][C]0.0956134898710108[/C][C]559.861143547776[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 24 )[/C][C]53.8862857142857[/C][C]0.240065913259791[/C][C]224.464543852054[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 24 )[/C][C]53.8789705882353[/C][C]0.238348791914142[/C][C]226.050948928844[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 24 )[/C][C]53.8707575757576[/C][C]0.236317643155315[/C][C]227.959101387754[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 24 )[/C][C]53.8621875[/C][C]0.234874741688488[/C][C]229.323030278994[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 24 )[/C][C]53.8525806451613[/C][C]0.233256319532832[/C][C]230.872975930589[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 24 )[/C][C]53.8421666666667[/C][C]0.231157012657937[/C][C]232.924651722946[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 24 )[/C][C]53.8310344827586[/C][C]0.228439786850461[/C][C]235.646492342409[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 24 )[/C][C]53.8194642857143[/C][C]0.225056474823378[/C][C]239.137595698819[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 24 )[/C][C]53.8062962962963[/C][C]0.221958957729988[/C][C]242.415520628599[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 24 )[/C][C]53.7923076923077[/C][C]0.218095350372362[/C][C]246.645825325786[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 24 )[/C][C]53.7712[/C][C]0.214342590547117[/C][C]250.865681257034[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 24 )[/C][C]53.7472916666667[/C][C]0.209612260157777[/C][C]256.412919865521[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 24 )[/C][C]53.7213043478261[/C][C]0.203384077463708[/C][C]264.137217710232[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 24 )[/C][C]53.6940909090909[/C][C]0.195854855807898[/C][C]274.152461972942[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 24 )[/C][C]53.6711904761905[/C][C]0.18935007196694[/C][C]283.449538300473[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 24 )[/C][C]53.649[/C][C]0.182336614605079[/C][C]294.23053683539[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 24 )[/C][C]53.6223684210526[/C][C]0.176574983049033[/C][C]303.680439296219[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 24 )[/C][C]53.5919444444444[/C][C]0.16899366919881[/C][C]317.1239768834[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 24 )[/C][C]53.5579411764706[/C][C]0.158132359219738[/C][C]338.690584525129[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 24 )[/C][C]53.52125[/C][C]0.1432899370102[/C][C]373.517157706547[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 24 )[/C][C]53.4876666666667[/C][C]0.132856921858907[/C][C]402.5960101911[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 24 )[/C][C]53.4667857142857[/C][C]0.129198847574828[/C][C]413.833302060372[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 24 )[/C][C]53.4503846153846[/C][C]0.126984530577221[/C][C]420.920441036562[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 24 )[/C][C]53.4408333333333[/C][C]0.126625541569534[/C][C]422.038339745124[/C][/ROW]
[ROW][C]Median[/C][C]53.425[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]54.105[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]53.6223684210526[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]53.6223684210526[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]53.6223684210526[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]53.6223684210526[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]53.6223684210526[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]53.6223684210526[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]53.6223684210526[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]53.6223684210526[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]72[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=213619&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=213619&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 Mean53.89236111111110.241845853357487222.837647877508
Geometric Mean53.8541560217161
Harmonic Mean53.8162940366291
Quadratic Mean53.9308755234163
Winsorized Mean ( 1 / 24 )53.89319444444440.241396386530381223.256011488232
Winsorized Mean ( 2 / 24 )53.89402777777780.241156954757567223.481125941224
Winsorized Mean ( 3 / 24 )53.89361111111110.238579709940161225.893522649635
Winsorized Mean ( 4 / 24 )53.89527777777780.237749866273848226.688993026391
Winsorized Mean ( 5 / 24 )53.89597222222220.237642853810551226.793995098157
Winsorized Mean ( 6 / 24 )53.89597222222220.237642853810551226.793995098157
Winsorized Mean ( 7 / 24 )53.89402777777780.237282447903399227.130275559695
Winsorized Mean ( 8 / 24 )53.89847222222220.232154943581884232.165946546865
Winsorized Mean ( 9 / 24 )53.89722222222220.231517263796729232.800013866541
Winsorized Mean ( 10 / 24 )53.93888888888890.225616921198924239.072887805838
Winsorized Mean ( 11 / 24 )53.94652777777780.224590407896989240.199607289199
Winsorized Mean ( 12 / 24 )53.94652777777780.224590407896989240.199607289199
Winsorized Mean ( 13 / 24 )53.93750.22180180056166243.178819393784
Winsorized Mean ( 14 / 24 )53.88111111111110.208133853377049258.87720924237
Winsorized Mean ( 15 / 24 )53.85611111111110.201279801548897267.568383398013
Winsorized Mean ( 16 / 24 )53.87388888888890.18567208161661290.156109738307
Winsorized Mean ( 17 / 24 )53.88097222222220.183407385782883293.777548773343
Winsorized Mean ( 18 / 24 )53.88097222222220.183407385782883293.777548773343
Winsorized Mean ( 19 / 24 )53.86777777777780.180425859280952298.559075691567
Winsorized Mean ( 20 / 24 )53.80111111111110.149516769299837359.833290694102
Winsorized Mean ( 21 / 24 )53.65819444444440.117420156735132456.976007666918
Winsorized Mean ( 22 / 24 )53.59708333333330.106775259698699501.961629356604
Winsorized Mean ( 23 / 24 )53.52361111111110.0964416406186121554.984452439745
Winsorized Mean ( 24 / 24 )53.53027777777780.0956134898710108559.861143547776
Trimmed Mean ( 1 / 24 )53.88628571428570.240065913259791224.464543852054
Trimmed Mean ( 2 / 24 )53.87897058823530.238348791914142226.050948928844
Trimmed Mean ( 3 / 24 )53.87075757575760.236317643155315227.959101387754
Trimmed Mean ( 4 / 24 )53.86218750.234874741688488229.323030278994
Trimmed Mean ( 5 / 24 )53.85258064516130.233256319532832230.872975930589
Trimmed Mean ( 6 / 24 )53.84216666666670.231157012657937232.924651722946
Trimmed Mean ( 7 / 24 )53.83103448275860.228439786850461235.646492342409
Trimmed Mean ( 8 / 24 )53.81946428571430.225056474823378239.137595698819
Trimmed Mean ( 9 / 24 )53.80629629629630.221958957729988242.415520628599
Trimmed Mean ( 10 / 24 )53.79230769230770.218095350372362246.645825325786
Trimmed Mean ( 11 / 24 )53.77120.214342590547117250.865681257034
Trimmed Mean ( 12 / 24 )53.74729166666670.209612260157777256.412919865521
Trimmed Mean ( 13 / 24 )53.72130434782610.203384077463708264.137217710232
Trimmed Mean ( 14 / 24 )53.69409090909090.195854855807898274.152461972942
Trimmed Mean ( 15 / 24 )53.67119047619050.18935007196694283.449538300473
Trimmed Mean ( 16 / 24 )53.6490.182336614605079294.23053683539
Trimmed Mean ( 17 / 24 )53.62236842105260.176574983049033303.680439296219
Trimmed Mean ( 18 / 24 )53.59194444444440.16899366919881317.1239768834
Trimmed Mean ( 19 / 24 )53.55794117647060.158132359219738338.690584525129
Trimmed Mean ( 20 / 24 )53.521250.1432899370102373.517157706547
Trimmed Mean ( 21 / 24 )53.48766666666670.132856921858907402.5960101911
Trimmed Mean ( 22 / 24 )53.46678571428570.129198847574828413.833302060372
Trimmed Mean ( 23 / 24 )53.45038461538460.126984530577221420.920441036562
Trimmed Mean ( 24 / 24 )53.44083333333330.126625541569534422.038339745124
Median53.425
Midrange54.105
Midmean - Weighted Average at Xnp53.6223684210526
Midmean - Weighted Average at X(n+1)p53.6223684210526
Midmean - Empirical Distribution Function53.6223684210526
Midmean - Empirical Distribution Function - Averaging53.6223684210526
Midmean - Empirical Distribution Function - Interpolation53.6223684210526
Midmean - Closest Observation53.6223684210526
Midmean - True Basic - Statistics Graphics Toolkit53.6223684210526
Midmean - MS Excel (old versions)53.6223684210526
Number of observations72



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')