FreeStatistics.org

Free Statistics

of Irreproducible Research!

Description of Statistical Computation

Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationThu, 11 Oct 2012 03:48:19 -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/2012/Oct/11/t13499417974mzzuwahjeq6g3x.htm/, Retrieved Sun, 28 Apr 2024 04:17:54 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=174871, Retrieved Sun, 28 Apr 2024 04:17:54 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact107

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [Gemiddelde consum...] [2012-10-11 07:48:19] [004c7a2610af8d0adb90cce3a555dd4b] [Current]
Feedback Forum

Post a new message

Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
98,01
99,2
100,7
106,41
107,51
107,1
99,75
98,96
107,26
107,11
107,2
107,65
104,78
105,56
107,95
107,11
107,47
107,06
99,71
99,6
107,19
107,26
113,24
113,52
110,48
111,41
115,5
118,32
118,42
117,5
110,23
109,19
118,41
118,3
116,1
114,11
113,41
114,33
116,61
123,64
123,77
123,39
116,03
114,95
123,4
123,53
114,45
114,26
114,35
112,77
115,31
114,93
116,38
115,07
105
103,43
114,52
115,04
117,16
115
116,22
112,92
116,56
114,32
113,22
111,56
103,87
102,85
112,27
112,76
118,55
122,73

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'Sir Maurice George Kendall' @ kendall.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 & 3 seconds \tabularnewline
R Server & 'Sir Maurice George Kendall' @ kendall.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=174871&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]3 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Sir Maurice George Kendall' @ kendall.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=174871&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=174871&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 time3 seconds
R Server'Sir Maurice George Kendall' @ kendall.wessa.net






Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean111.720.772710105840626144.582035559714
Geometric Mean111.527938344484
Harmonic Mean111.333547558184
Quadratic Mean111.909566813765
Winsorized Mean ( 1 / 24 )111.7313888888890.769123139159621145.271131760477
Winsorized Mean ( 2 / 24 )111.7350.766912060135463145.694670625291
Winsorized Mean ( 3 / 24 )111.746250.76195239803166146.657783725955
Winsorized Mean ( 4 / 24 )111.7518055555560.760465179850349146.951903277869
Winsorized Mean ( 5 / 24 )111.708750.750160466336572148.913139272098
Winsorized Mean ( 6 / 24 )111.4395833333330.669683299285521166.406394563262
Winsorized Mean ( 7 / 24 )111.6359722222220.623312170428646179.101223301081
Winsorized Mean ( 8 / 24 )111.6993055555560.610595072837114182.935157069885
Winsorized Mean ( 9 / 24 )111.7430555555560.598511705234227186.701537460867
Winsorized Mean ( 10 / 24 )111.8666666666670.575392973151763194.417853339271
Winsorized Mean ( 11 / 24 )111.7780555555560.550989103460135202.867996578526
Winsorized Mean ( 12 / 24 )111.8147222222220.52690009283869212.212379048592
Winsorized Mean ( 13 / 24 )111.8688888888890.488053548155124229.214374758182
Winsorized Mean ( 14 / 24 )111.9855555555560.467370356811397239.607741320116
Winsorized Mean ( 15 / 24 )111.9563888888890.46101457758886242.847828097821
Winsorized Mean ( 16 / 24 )111.9230555555560.455921809477409245.487391102972
Winsorized Mean ( 17 / 24 )111.8947222222220.452185571171303247.453101903229
Winsorized Mean ( 18 / 24 )111.8972222222220.446925999545481250.370804867071
Winsorized Mean ( 19 / 24 )111.760.428824000580866260.619741079359
Winsorized Mean ( 20 / 24 )111.7238888888890.419911755557314266.065161097019
Winsorized Mean ( 21 / 24 )111.6538888888890.411609381672968271.261768706721
Winsorized Mean ( 22 / 24 )111.7088888888890.400935455232806278.620629407854
Winsorized Mean ( 23 / 24 )111.7088888888890.397541080423444280.999610832423
Winsorized Mean ( 24 / 24 )111.7388888888890.388671071349607287.489594995817
Trimmed Mean ( 1 / 24 )111.7437142857140.750303131878834148.931424564225
Trimmed Mean ( 2 / 24 )111.7567647058820.727925825256495153.527682118577
Trimmed Mean ( 3 / 24 )111.7686363636360.702613233584188159.075620869649
Trimmed Mean ( 4 / 24 )111.777031250.674517673048186165.714014200507
Trimmed Mean ( 5 / 24 )111.784354838710.641005358761747174.389111277708
Trimmed Mean ( 6 / 24 )111.80250.60350326718488185.255832203722
Trimmed Mean ( 7 / 24 )111.8775862068970.582099393742245192.196706283526
Trimmed Mean ( 8 / 24 )111.9219642857140.568603119732047196.836704551423
Trimmed Mean ( 9 / 24 )111.9590740740740.554982152842181201.734548580901
Trimmed Mean ( 10 / 24 )111.9923076923080.540780022591844207.094017925352
Trimmed Mean ( 11 / 24 )112.01040.528277212324386212.029588607772
Trimmed Mean ( 12 / 24 )112.0420833333330.517601786879956216.463865027805
Trimmed Mean ( 13 / 24 )112.0717391304350.508933554345673220.208980471966
Trimmed Mean ( 14 / 24 )112.0972727272730.505507653452847221.751880434643
Trimmed Mean ( 15 / 24 )112.1109523809520.504440192878124222.248254528043
Trimmed Mean ( 16 / 24 )112.12950.503087766977146222.882581052888
Trimmed Mean ( 17 / 24 )112.1539473684210.500981616723584223.868388828131
Trimmed Mean ( 18 / 24 )112.1844444444440.497481984110974225.504536902827
Trimmed Mean ( 19 / 24 )112.2182352941180.492423609100987227.889632462979
Trimmed Mean ( 20 / 24 )112.27250.487770603142832230.174797900077
Trimmed Mean ( 21 / 24 )112.3383333333330.481299983720654233.406060945422
Trimmed Mean ( 22 / 24 )112.4221428571430.471526665279429238.421601863218
Trimmed Mean ( 23 / 24 )112.5119230769230.458258583110107245.520601738276
Trimmed Mean ( 24 / 24 )112.6166666666670.436196366939708258.178827707276
Median113.23
Midrange110.89
Midmean - Weighted Average at Xnp111.917368421053
Midmean - Weighted Average at X(n+1)p112.184444444444
Midmean - Empirical Distribution Function111.917368421053
Midmean - Empirical Distribution Function - Averaging112.184444444444
Midmean - Empirical Distribution Function - Interpolation112.184444444444
Midmean - Closest Observation111.917368421053
Midmean - True Basic - Statistics Graphics Toolkit112.184444444444
Midmean - MS Excel (old versions)112.024615384615
Number of observations72

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 111.72 & 0.772710105840626 & 144.582035559714 \tabularnewline
Geometric Mean & 111.527938344484 &  &  \tabularnewline
Harmonic Mean & 111.333547558184 &  &  \tabularnewline
Quadratic Mean & 111.909566813765 &  &  \tabularnewline
Winsorized Mean ( 1 / 24 ) & 111.731388888889 & 0.769123139159621 & 145.271131760477 \tabularnewline
Winsorized Mean ( 2 / 24 ) & 111.735 & 0.766912060135463 & 145.694670625291 \tabularnewline
Winsorized Mean ( 3 / 24 ) & 111.74625 & 0.76195239803166 & 146.657783725955 \tabularnewline
Winsorized Mean ( 4 / 24 ) & 111.751805555556 & 0.760465179850349 & 146.951903277869 \tabularnewline
Winsorized Mean ( 5 / 24 ) & 111.70875 & 0.750160466336572 & 148.913139272098 \tabularnewline
Winsorized Mean ( 6 / 24 ) & 111.439583333333 & 0.669683299285521 & 166.406394563262 \tabularnewline
Winsorized Mean ( 7 / 24 ) & 111.635972222222 & 0.623312170428646 & 179.101223301081 \tabularnewline
Winsorized Mean ( 8 / 24 ) & 111.699305555556 & 0.610595072837114 & 182.935157069885 \tabularnewline
Winsorized Mean ( 9 / 24 ) & 111.743055555556 & 0.598511705234227 & 186.701537460867 \tabularnewline
Winsorized Mean ( 10 / 24 ) & 111.866666666667 & 0.575392973151763 & 194.417853339271 \tabularnewline
Winsorized Mean ( 11 / 24 ) & 111.778055555556 & 0.550989103460135 & 202.867996578526 \tabularnewline
Winsorized Mean ( 12 / 24 ) & 111.814722222222 & 0.52690009283869 & 212.212379048592 \tabularnewline
Winsorized Mean ( 13 / 24 ) & 111.868888888889 & 0.488053548155124 & 229.214374758182 \tabularnewline
Winsorized Mean ( 14 / 24 ) & 111.985555555556 & 0.467370356811397 & 239.607741320116 \tabularnewline
Winsorized Mean ( 15 / 24 ) & 111.956388888889 & 0.46101457758886 & 242.847828097821 \tabularnewline
Winsorized Mean ( 16 / 24 ) & 111.923055555556 & 0.455921809477409 & 245.487391102972 \tabularnewline
Winsorized Mean ( 17 / 24 ) & 111.894722222222 & 0.452185571171303 & 247.453101903229 \tabularnewline
Winsorized Mean ( 18 / 24 ) & 111.897222222222 & 0.446925999545481 & 250.370804867071 \tabularnewline
Winsorized Mean ( 19 / 24 ) & 111.76 & 0.428824000580866 & 260.619741079359 \tabularnewline
Winsorized Mean ( 20 / 24 ) & 111.723888888889 & 0.419911755557314 & 266.065161097019 \tabularnewline
Winsorized Mean ( 21 / 24 ) & 111.653888888889 & 0.411609381672968 & 271.261768706721 \tabularnewline
Winsorized Mean ( 22 / 24 ) & 111.708888888889 & 0.400935455232806 & 278.620629407854 \tabularnewline
Winsorized Mean ( 23 / 24 ) & 111.708888888889 & 0.397541080423444 & 280.999610832423 \tabularnewline
Winsorized Mean ( 24 / 24 ) & 111.738888888889 & 0.388671071349607 & 287.489594995817 \tabularnewline
Trimmed Mean ( 1 / 24 ) & 111.743714285714 & 0.750303131878834 & 148.931424564225 \tabularnewline
Trimmed Mean ( 2 / 24 ) & 111.756764705882 & 0.727925825256495 & 153.527682118577 \tabularnewline
Trimmed Mean ( 3 / 24 ) & 111.768636363636 & 0.702613233584188 & 159.075620869649 \tabularnewline
Trimmed Mean ( 4 / 24 ) & 111.77703125 & 0.674517673048186 & 165.714014200507 \tabularnewline
Trimmed Mean ( 5 / 24 ) & 111.78435483871 & 0.641005358761747 & 174.389111277708 \tabularnewline
Trimmed Mean ( 6 / 24 ) & 111.8025 & 0.60350326718488 & 185.255832203722 \tabularnewline
Trimmed Mean ( 7 / 24 ) & 111.877586206897 & 0.582099393742245 & 192.196706283526 \tabularnewline
Trimmed Mean ( 8 / 24 ) & 111.921964285714 & 0.568603119732047 & 196.836704551423 \tabularnewline
Trimmed Mean ( 9 / 24 ) & 111.959074074074 & 0.554982152842181 & 201.734548580901 \tabularnewline
Trimmed Mean ( 10 / 24 ) & 111.992307692308 & 0.540780022591844 & 207.094017925352 \tabularnewline
Trimmed Mean ( 11 / 24 ) & 112.0104 & 0.528277212324386 & 212.029588607772 \tabularnewline
Trimmed Mean ( 12 / 24 ) & 112.042083333333 & 0.517601786879956 & 216.463865027805 \tabularnewline
Trimmed Mean ( 13 / 24 ) & 112.071739130435 & 0.508933554345673 & 220.208980471966 \tabularnewline
Trimmed Mean ( 14 / 24 ) & 112.097272727273 & 0.505507653452847 & 221.751880434643 \tabularnewline
Trimmed Mean ( 15 / 24 ) & 112.110952380952 & 0.504440192878124 & 222.248254528043 \tabularnewline
Trimmed Mean ( 16 / 24 ) & 112.1295 & 0.503087766977146 & 222.882581052888 \tabularnewline
Trimmed Mean ( 17 / 24 ) & 112.153947368421 & 0.500981616723584 & 223.868388828131 \tabularnewline
Trimmed Mean ( 18 / 24 ) & 112.184444444444 & 0.497481984110974 & 225.504536902827 \tabularnewline
Trimmed Mean ( 19 / 24 ) & 112.218235294118 & 0.492423609100987 & 227.889632462979 \tabularnewline
Trimmed Mean ( 20 / 24 ) & 112.2725 & 0.487770603142832 & 230.174797900077 \tabularnewline
Trimmed Mean ( 21 / 24 ) & 112.338333333333 & 0.481299983720654 & 233.406060945422 \tabularnewline
Trimmed Mean ( 22 / 24 ) & 112.422142857143 & 0.471526665279429 & 238.421601863218 \tabularnewline
Trimmed Mean ( 23 / 24 ) & 112.511923076923 & 0.458258583110107 & 245.520601738276 \tabularnewline
Trimmed Mean ( 24 / 24 ) & 112.616666666667 & 0.436196366939708 & 258.178827707276 \tabularnewline
Median & 113.23 &  &  \tabularnewline
Midrange & 110.89 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 111.917368421053 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 112.184444444444 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 111.917368421053 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 112.184444444444 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 112.184444444444 &  &  \tabularnewline
Midmean - Closest Observation & 111.917368421053 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 112.184444444444 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 112.024615384615 &  &  \tabularnewline
Number of observations & 72 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=174871&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]111.72[/C][C]0.772710105840626[/C][C]144.582035559714[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]111.527938344484[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]111.333547558184[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]111.909566813765[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 24 )[/C][C]111.731388888889[/C][C]0.769123139159621[/C][C]145.271131760477[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 24 )[/C][C]111.735[/C][C]0.766912060135463[/C][C]145.694670625291[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 24 )[/C][C]111.74625[/C][C]0.76195239803166[/C][C]146.657783725955[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 24 )[/C][C]111.751805555556[/C][C]0.760465179850349[/C][C]146.951903277869[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 24 )[/C][C]111.70875[/C][C]0.750160466336572[/C][C]148.913139272098[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 24 )[/C][C]111.439583333333[/C][C]0.669683299285521[/C][C]166.406394563262[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 24 )[/C][C]111.635972222222[/C][C]0.623312170428646[/C][C]179.101223301081[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 24 )[/C][C]111.699305555556[/C][C]0.610595072837114[/C][C]182.935157069885[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 24 )[/C][C]111.743055555556[/C][C]0.598511705234227[/C][C]186.701537460867[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 24 )[/C][C]111.866666666667[/C][C]0.575392973151763[/C][C]194.417853339271[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 24 )[/C][C]111.778055555556[/C][C]0.550989103460135[/C][C]202.867996578526[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 24 )[/C][C]111.814722222222[/C][C]0.52690009283869[/C][C]212.212379048592[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 24 )[/C][C]111.868888888889[/C][C]0.488053548155124[/C][C]229.214374758182[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 24 )[/C][C]111.985555555556[/C][C]0.467370356811397[/C][C]239.607741320116[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 24 )[/C][C]111.956388888889[/C][C]0.46101457758886[/C][C]242.847828097821[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 24 )[/C][C]111.923055555556[/C][C]0.455921809477409[/C][C]245.487391102972[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 24 )[/C][C]111.894722222222[/C][C]0.452185571171303[/C][C]247.453101903229[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 24 )[/C][C]111.897222222222[/C][C]0.446925999545481[/C][C]250.370804867071[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 24 )[/C][C]111.76[/C][C]0.428824000580866[/C][C]260.619741079359[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 24 )[/C][C]111.723888888889[/C][C]0.419911755557314[/C][C]266.065161097019[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 24 )[/C][C]111.653888888889[/C][C]0.411609381672968[/C][C]271.261768706721[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 24 )[/C][C]111.708888888889[/C][C]0.400935455232806[/C][C]278.620629407854[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 24 )[/C][C]111.708888888889[/C][C]0.397541080423444[/C][C]280.999610832423[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 24 )[/C][C]111.738888888889[/C][C]0.388671071349607[/C][C]287.489594995817[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 24 )[/C][C]111.743714285714[/C][C]0.750303131878834[/C][C]148.931424564225[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 24 )[/C][C]111.756764705882[/C][C]0.727925825256495[/C][C]153.527682118577[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 24 )[/C][C]111.768636363636[/C][C]0.702613233584188[/C][C]159.075620869649[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 24 )[/C][C]111.77703125[/C][C]0.674517673048186[/C][C]165.714014200507[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 24 )[/C][C]111.78435483871[/C][C]0.641005358761747[/C][C]174.389111277708[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 24 )[/C][C]111.8025[/C][C]0.60350326718488[/C][C]185.255832203722[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 24 )[/C][C]111.877586206897[/C][C]0.582099393742245[/C][C]192.196706283526[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 24 )[/C][C]111.921964285714[/C][C]0.568603119732047[/C][C]196.836704551423[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 24 )[/C][C]111.959074074074[/C][C]0.554982152842181[/C][C]201.734548580901[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 24 )[/C][C]111.992307692308[/C][C]0.540780022591844[/C][C]207.094017925352[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 24 )[/C][C]112.0104[/C][C]0.528277212324386[/C][C]212.029588607772[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 24 )[/C][C]112.042083333333[/C][C]0.517601786879956[/C][C]216.463865027805[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 24 )[/C][C]112.071739130435[/C][C]0.508933554345673[/C][C]220.208980471966[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 24 )[/C][C]112.097272727273[/C][C]0.505507653452847[/C][C]221.751880434643[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 24 )[/C][C]112.110952380952[/C][C]0.504440192878124[/C][C]222.248254528043[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 24 )[/C][C]112.1295[/C][C]0.503087766977146[/C][C]222.882581052888[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 24 )[/C][C]112.153947368421[/C][C]0.500981616723584[/C][C]223.868388828131[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 24 )[/C][C]112.184444444444[/C][C]0.497481984110974[/C][C]225.504536902827[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 24 )[/C][C]112.218235294118[/C][C]0.492423609100987[/C][C]227.889632462979[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 24 )[/C][C]112.2725[/C][C]0.487770603142832[/C][C]230.174797900077[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 24 )[/C][C]112.338333333333[/C][C]0.481299983720654[/C][C]233.406060945422[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 24 )[/C][C]112.422142857143[/C][C]0.471526665279429[/C][C]238.421601863218[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 24 )[/C][C]112.511923076923[/C][C]0.458258583110107[/C][C]245.520601738276[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 24 )[/C][C]112.616666666667[/C][C]0.436196366939708[/C][C]258.178827707276[/C][/ROW]
[ROW][C]Median[/C][C]113.23[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]110.89[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]111.917368421053[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]112.184444444444[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]111.917368421053[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]112.184444444444[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]112.184444444444[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]111.917368421053[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]112.184444444444[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]112.024615384615[/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=174871&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=174871&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 Mean111.720.772710105840626144.582035559714
Geometric Mean111.527938344484
Harmonic Mean111.333547558184
Quadratic Mean111.909566813765
Winsorized Mean ( 1 / 24 )111.7313888888890.769123139159621145.271131760477
Winsorized Mean ( 2 / 24 )111.7350.766912060135463145.694670625291
Winsorized Mean ( 3 / 24 )111.746250.76195239803166146.657783725955
Winsorized Mean ( 4 / 24 )111.7518055555560.760465179850349146.951903277869
Winsorized Mean ( 5 / 24 )111.708750.750160466336572148.913139272098
Winsorized Mean ( 6 / 24 )111.4395833333330.669683299285521166.406394563262
Winsorized Mean ( 7 / 24 )111.6359722222220.623312170428646179.101223301081
Winsorized Mean ( 8 / 24 )111.6993055555560.610595072837114182.935157069885
Winsorized Mean ( 9 / 24 )111.7430555555560.598511705234227186.701537460867
Winsorized Mean ( 10 / 24 )111.8666666666670.575392973151763194.417853339271
Winsorized Mean ( 11 / 24 )111.7780555555560.550989103460135202.867996578526
Winsorized Mean ( 12 / 24 )111.8147222222220.52690009283869212.212379048592
Winsorized Mean ( 13 / 24 )111.8688888888890.488053548155124229.214374758182
Winsorized Mean ( 14 / 24 )111.9855555555560.467370356811397239.607741320116
Winsorized Mean ( 15 / 24 )111.9563888888890.46101457758886242.847828097821
Winsorized Mean ( 16 / 24 )111.9230555555560.455921809477409245.487391102972
Winsorized Mean ( 17 / 24 )111.8947222222220.452185571171303247.453101903229
Winsorized Mean ( 18 / 24 )111.8972222222220.446925999545481250.370804867071
Winsorized Mean ( 19 / 24 )111.760.428824000580866260.619741079359
Winsorized Mean ( 20 / 24 )111.7238888888890.419911755557314266.065161097019
Winsorized Mean ( 21 / 24 )111.6538888888890.411609381672968271.261768706721
Winsorized Mean ( 22 / 24 )111.7088888888890.400935455232806278.620629407854
Winsorized Mean ( 23 / 24 )111.7088888888890.397541080423444280.999610832423
Winsorized Mean ( 24 / 24 )111.7388888888890.388671071349607287.489594995817
Trimmed Mean ( 1 / 24 )111.7437142857140.750303131878834148.931424564225
Trimmed Mean ( 2 / 24 )111.7567647058820.727925825256495153.527682118577
Trimmed Mean ( 3 / 24 )111.7686363636360.702613233584188159.075620869649
Trimmed Mean ( 4 / 24 )111.777031250.674517673048186165.714014200507
Trimmed Mean ( 5 / 24 )111.784354838710.641005358761747174.389111277708
Trimmed Mean ( 6 / 24 )111.80250.60350326718488185.255832203722
Trimmed Mean ( 7 / 24 )111.8775862068970.582099393742245192.196706283526
Trimmed Mean ( 8 / 24 )111.9219642857140.568603119732047196.836704551423
Trimmed Mean ( 9 / 24 )111.9590740740740.554982152842181201.734548580901
Trimmed Mean ( 10 / 24 )111.9923076923080.540780022591844207.094017925352
Trimmed Mean ( 11 / 24 )112.01040.528277212324386212.029588607772
Trimmed Mean ( 12 / 24 )112.0420833333330.517601786879956216.463865027805
Trimmed Mean ( 13 / 24 )112.0717391304350.508933554345673220.208980471966
Trimmed Mean ( 14 / 24 )112.0972727272730.505507653452847221.751880434643
Trimmed Mean ( 15 / 24 )112.1109523809520.504440192878124222.248254528043
Trimmed Mean ( 16 / 24 )112.12950.503087766977146222.882581052888
Trimmed Mean ( 17 / 24 )112.1539473684210.500981616723584223.868388828131
Trimmed Mean ( 18 / 24 )112.1844444444440.497481984110974225.504536902827
Trimmed Mean ( 19 / 24 )112.2182352941180.492423609100987227.889632462979
Trimmed Mean ( 20 / 24 )112.27250.487770603142832230.174797900077
Trimmed Mean ( 21 / 24 )112.3383333333330.481299983720654233.406060945422
Trimmed Mean ( 22 / 24 )112.4221428571430.471526665279429238.421601863218
Trimmed Mean ( 23 / 24 )112.5119230769230.458258583110107245.520601738276
Trimmed Mean ( 24 / 24 )112.6166666666670.436196366939708258.178827707276
Median113.23
Midrange110.89
Midmean - Weighted Average at Xnp111.917368421053
Midmean - Weighted Average at X(n+1)p112.184444444444
Midmean - Empirical Distribution Function111.917368421053
Midmean - Empirical Distribution Function - Averaging112.184444444444
Midmean - Empirical Distribution Function - Interpolation112.184444444444
Midmean - Closest Observation111.917368421053
Midmean - True Basic - Statistics Graphics Toolkit112.184444444444
Midmean - MS Excel (old versions)112.024615384615
Number of observations72


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')