Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationThu, 13 Oct 2016 13:05:50 +0100
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2016/Oct/13/t14763605115pxelij3pcgyolm.htm/, Retrieved Tue, 30 Apr 2024 10:33:17 +0200
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=, Retrieved Tue, 30 Apr 2024 10:33:17 +0200
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact0
Dataseries X:
98,98
98,97
98,91
98,98
98,95
98,96
98,96
99,04
99,33
100,04
100,14
100,21
100,21
100,27
100,44
100,57
100,51
100,47
100,47
100,49
101
101,61
101,65
101,74
101,74
101,73
101,77
101,82
101,97
102,09
102,09
102,08
102,42
102,78
103,04
103,08
99,16
99,19
99,23
99,31
99,46
99,49
99,95
100,14
100,43
101,1
101,26
101,28
101,04
101,12
101,07
100,97
101,01
100,99
101,19
101,25
101,33
101,79
102,06
102,09
102,27
102,26
102,46
102,46
102,51
102,56
102,59
102,26
102,33
102,84
102,93
102,95




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 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 & 2 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=&T=0

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

As an alternative you can also use a QR Code:  

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

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Gwilym Jenkins' @ jenkins.wessa.net







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean101.0255555555560.149576722674081675.409607520846
Geometric Mean101.017678078951
Harmonic Mean101.00978536658
Quadratic Mean101.033417106531
Winsorized Mean ( 1 / 24 )101.0255555555560.149360515960703676.387296239227
Winsorized Mean ( 2 / 24 )101.0233333333330.148840852503679678.73390694827
Winsorized Mean ( 3 / 24 )101.02250.148689600906857679.418731262068
Winsorized Mean ( 4 / 24 )101.0180555555560.147694944103208683.964208584992
Winsorized Mean ( 5 / 24 )101.0145833333330.146844607367218687.901211657867
Winsorized Mean ( 6 / 24 )100.998750.144273304138941700.051548710175
Winsorized Mean ( 7 / 24 )101.0016666666670.142682768605617707.875713750978
Winsorized Mean ( 8 / 24 )101.0094444444440.139295804536738725.143479951716
Winsorized Mean ( 9 / 24 )101.0069444444440.137657810831703733.75381922885
Winsorized Mean ( 10 / 24 )101.01250.136630985551713739.308873401691
Winsorized Mean ( 11 / 24 )101.0186111111110.133498475423348756.70235776673
Winsorized Mean ( 12 / 24 )101.0069444444440.130718437168153772.706181565741
Winsorized Mean ( 13 / 24 )101.0195833333330.124998660008467808.165330144262
Winsorized Mean ( 14 / 24 )101.0234722222220.123702998807689816.661464927583
Winsorized Mean ( 15 / 24 )101.1193055555560.107955159065662936.678769506989
Winsorized Mean ( 16 / 24 )101.1015277777780.09946367518264191016.46684171008
Winsorized Mean ( 17 / 24 )101.1251388888890.09598125816653721053.59255359444
Winsorized Mean ( 18 / 24 )101.1251388888890.09598125816653721053.59255359444
Winsorized Mean ( 19 / 24 )101.1409722222220.09296838435680611087.90717319611
Winsorized Mean ( 20 / 24 )101.1354166666670.09218078988735511097.14200529475
Winsorized Mean ( 21 / 24 )101.1266666666670.08604894520135651175.22261812772
Winsorized Mean ( 22 / 24 )101.1297222222220.07309392531481151383.55850758681
Winsorized Mean ( 23 / 24 )101.1233333333330.07139565528177671416.37937118485
Winsorized Mean ( 24 / 24 )101.1266666666670.06917804929247681461.83171831161
Trimmed Mean ( 1 / 24 )101.0264285714290.147915402450742683.001410925219
Trimmed Mean ( 2 / 24 )101.0273529411760.146145473613549691.27938377566
Trimmed Mean ( 3 / 24 )101.0295454545450.144308080148638700.096247905763
Trimmed Mean ( 4 / 24 )101.03218750.142123993754378710.873546620187
Trimmed Mean ( 5 / 24 )101.0362903225810.13980556753752722.69146431143
Trimmed Mean ( 6 / 24 )101.04150.137214999962429736.373574519306
Trimmed Mean ( 7 / 24 )101.0503448275860.13471620267882750.097930450894
Trimmed Mean ( 8 / 24 )101.0592857142860.132009655575343765.544651062342
Trimmed Mean ( 9 / 24 )101.0675925925930.129448363330927780.756048141139
Trimmed Mean ( 10 / 24 )101.0769230769230.126576793489926798.542294286886
Trimmed Mean ( 11 / 24 )101.08620.123157735262963820.786447429904
Trimmed Mean ( 12 / 24 )101.0954166666670.119512884826197845.895543511358
Trimmed Mean ( 13 / 24 )101.1069565217390.115420202505445875.990115482337
Trimmed Mean ( 14 / 24 )101.1179545454550.111461831627098907.198034245037
Trimmed Mean ( 15 / 24 )101.1295238095240.106538805687956949.227121108568
Trimmed Mean ( 16 / 24 )101.130750.104010223548285972.315475824857
Trimmed Mean ( 17 / 24 )101.1342105263160.102479662888216986.871030563712
Trimmed Mean ( 18 / 24 )101.1352777777780.1010417846232881000.92529199517
Trimmed Mean ( 19 / 24 )101.1364705882350.09884257307385921023.20758599295
Trimmed Mean ( 20 / 24 )101.13593750.0963715292406711049.43792317989
Trimmed Mean ( 21 / 24 )101.1360.09285955282965851089.1286563217
Trimmed Mean ( 22 / 24 )101.1371428571430.08950459942492441129.96587334013
Trimmed Mean ( 23 / 24 )101.1380769230770.08849166711012411142.91074206134
Trimmed Mean ( 24 / 24 )101.140.08699491905869561162.59663316384
Median101.11
Midrange100.995
Midmean - Weighted Average at Xnp101.158717948718
Midmean - Weighted Average at X(n+1)p101.158717948718
Midmean - Empirical Distribution Function101.158717948718
Midmean - Empirical Distribution Function - Averaging101.158717948718
Midmean - Empirical Distribution Function - Interpolation101.158717948718
Midmean - Closest Observation101.158717948718
Midmean - True Basic - Statistics Graphics Toolkit101.158717948718
Midmean - MS Excel (old versions)101.158717948718
Number of observations72

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 101.025555555556 & 0.149576722674081 & 675.409607520846 \tabularnewline
Geometric Mean & 101.017678078951 &  &  \tabularnewline
Harmonic Mean & 101.00978536658 &  &  \tabularnewline
Quadratic Mean & 101.033417106531 &  &  \tabularnewline
Winsorized Mean ( 1 / 24 ) & 101.025555555556 & 0.149360515960703 & 676.387296239227 \tabularnewline
Winsorized Mean ( 2 / 24 ) & 101.023333333333 & 0.148840852503679 & 678.73390694827 \tabularnewline
Winsorized Mean ( 3 / 24 ) & 101.0225 & 0.148689600906857 & 679.418731262068 \tabularnewline
Winsorized Mean ( 4 / 24 ) & 101.018055555556 & 0.147694944103208 & 683.964208584992 \tabularnewline
Winsorized Mean ( 5 / 24 ) & 101.014583333333 & 0.146844607367218 & 687.901211657867 \tabularnewline
Winsorized Mean ( 6 / 24 ) & 100.99875 & 0.144273304138941 & 700.051548710175 \tabularnewline
Winsorized Mean ( 7 / 24 ) & 101.001666666667 & 0.142682768605617 & 707.875713750978 \tabularnewline
Winsorized Mean ( 8 / 24 ) & 101.009444444444 & 0.139295804536738 & 725.143479951716 \tabularnewline
Winsorized Mean ( 9 / 24 ) & 101.006944444444 & 0.137657810831703 & 733.75381922885 \tabularnewline
Winsorized Mean ( 10 / 24 ) & 101.0125 & 0.136630985551713 & 739.308873401691 \tabularnewline
Winsorized Mean ( 11 / 24 ) & 101.018611111111 & 0.133498475423348 & 756.70235776673 \tabularnewline
Winsorized Mean ( 12 / 24 ) & 101.006944444444 & 0.130718437168153 & 772.706181565741 \tabularnewline
Winsorized Mean ( 13 / 24 ) & 101.019583333333 & 0.124998660008467 & 808.165330144262 \tabularnewline
Winsorized Mean ( 14 / 24 ) & 101.023472222222 & 0.123702998807689 & 816.661464927583 \tabularnewline
Winsorized Mean ( 15 / 24 ) & 101.119305555556 & 0.107955159065662 & 936.678769506989 \tabularnewline
Winsorized Mean ( 16 / 24 ) & 101.101527777778 & 0.0994636751826419 & 1016.46684171008 \tabularnewline
Winsorized Mean ( 17 / 24 ) & 101.125138888889 & 0.0959812581665372 & 1053.59255359444 \tabularnewline
Winsorized Mean ( 18 / 24 ) & 101.125138888889 & 0.0959812581665372 & 1053.59255359444 \tabularnewline
Winsorized Mean ( 19 / 24 ) & 101.140972222222 & 0.0929683843568061 & 1087.90717319611 \tabularnewline
Winsorized Mean ( 20 / 24 ) & 101.135416666667 & 0.0921807898873551 & 1097.14200529475 \tabularnewline
Winsorized Mean ( 21 / 24 ) & 101.126666666667 & 0.0860489452013565 & 1175.22261812772 \tabularnewline
Winsorized Mean ( 22 / 24 ) & 101.129722222222 & 0.0730939253148115 & 1383.55850758681 \tabularnewline
Winsorized Mean ( 23 / 24 ) & 101.123333333333 & 0.0713956552817767 & 1416.37937118485 \tabularnewline
Winsorized Mean ( 24 / 24 ) & 101.126666666667 & 0.0691780492924768 & 1461.83171831161 \tabularnewline
Trimmed Mean ( 1 / 24 ) & 101.026428571429 & 0.147915402450742 & 683.001410925219 \tabularnewline
Trimmed Mean ( 2 / 24 ) & 101.027352941176 & 0.146145473613549 & 691.27938377566 \tabularnewline
Trimmed Mean ( 3 / 24 ) & 101.029545454545 & 0.144308080148638 & 700.096247905763 \tabularnewline
Trimmed Mean ( 4 / 24 ) & 101.0321875 & 0.142123993754378 & 710.873546620187 \tabularnewline
Trimmed Mean ( 5 / 24 ) & 101.036290322581 & 0.13980556753752 & 722.69146431143 \tabularnewline
Trimmed Mean ( 6 / 24 ) & 101.0415 & 0.137214999962429 & 736.373574519306 \tabularnewline
Trimmed Mean ( 7 / 24 ) & 101.050344827586 & 0.13471620267882 & 750.097930450894 \tabularnewline
Trimmed Mean ( 8 / 24 ) & 101.059285714286 & 0.132009655575343 & 765.544651062342 \tabularnewline
Trimmed Mean ( 9 / 24 ) & 101.067592592593 & 0.129448363330927 & 780.756048141139 \tabularnewline
Trimmed Mean ( 10 / 24 ) & 101.076923076923 & 0.126576793489926 & 798.542294286886 \tabularnewline
Trimmed Mean ( 11 / 24 ) & 101.0862 & 0.123157735262963 & 820.786447429904 \tabularnewline
Trimmed Mean ( 12 / 24 ) & 101.095416666667 & 0.119512884826197 & 845.895543511358 \tabularnewline
Trimmed Mean ( 13 / 24 ) & 101.106956521739 & 0.115420202505445 & 875.990115482337 \tabularnewline
Trimmed Mean ( 14 / 24 ) & 101.117954545455 & 0.111461831627098 & 907.198034245037 \tabularnewline
Trimmed Mean ( 15 / 24 ) & 101.129523809524 & 0.106538805687956 & 949.227121108568 \tabularnewline
Trimmed Mean ( 16 / 24 ) & 101.13075 & 0.104010223548285 & 972.315475824857 \tabularnewline
Trimmed Mean ( 17 / 24 ) & 101.134210526316 & 0.102479662888216 & 986.871030563712 \tabularnewline
Trimmed Mean ( 18 / 24 ) & 101.135277777778 & 0.101041784623288 & 1000.92529199517 \tabularnewline
Trimmed Mean ( 19 / 24 ) & 101.136470588235 & 0.0988425730738592 & 1023.20758599295 \tabularnewline
Trimmed Mean ( 20 / 24 ) & 101.1359375 & 0.096371529240671 & 1049.43792317989 \tabularnewline
Trimmed Mean ( 21 / 24 ) & 101.136 & 0.0928595528296585 & 1089.1286563217 \tabularnewline
Trimmed Mean ( 22 / 24 ) & 101.137142857143 & 0.0895045994249244 & 1129.96587334013 \tabularnewline
Trimmed Mean ( 23 / 24 ) & 101.138076923077 & 0.0884916671101241 & 1142.91074206134 \tabularnewline
Trimmed Mean ( 24 / 24 ) & 101.14 & 0.0869949190586956 & 1162.59663316384 \tabularnewline
Median & 101.11 &  &  \tabularnewline
Midrange & 100.995 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 101.158717948718 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 101.158717948718 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 101.158717948718 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 101.158717948718 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 101.158717948718 &  &  \tabularnewline
Midmean - Closest Observation & 101.158717948718 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 101.158717948718 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 101.158717948718 &  &  \tabularnewline
Number of observations & 72 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&T=1

[TABLE]
[ROW][C]Central Tendency - Ungrouped Data[/C][/ROW]
[ROW][C]Measure[/C][C]Value[/C][C]S.E.[/C][C]Value/S.E.[/C][/ROW]
[ROW][C]Arithmetic Mean[/C][C]101.025555555556[/C][C]0.149576722674081[/C][C]675.409607520846[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]101.017678078951[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]101.00978536658[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]101.033417106531[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 24 )[/C][C]101.025555555556[/C][C]0.149360515960703[/C][C]676.387296239227[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 24 )[/C][C]101.023333333333[/C][C]0.148840852503679[/C][C]678.73390694827[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 24 )[/C][C]101.0225[/C][C]0.148689600906857[/C][C]679.418731262068[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 24 )[/C][C]101.018055555556[/C][C]0.147694944103208[/C][C]683.964208584992[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 24 )[/C][C]101.014583333333[/C][C]0.146844607367218[/C][C]687.901211657867[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 24 )[/C][C]100.99875[/C][C]0.144273304138941[/C][C]700.051548710175[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 24 )[/C][C]101.001666666667[/C][C]0.142682768605617[/C][C]707.875713750978[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 24 )[/C][C]101.009444444444[/C][C]0.139295804536738[/C][C]725.143479951716[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 24 )[/C][C]101.006944444444[/C][C]0.137657810831703[/C][C]733.75381922885[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 24 )[/C][C]101.0125[/C][C]0.136630985551713[/C][C]739.308873401691[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 24 )[/C][C]101.018611111111[/C][C]0.133498475423348[/C][C]756.70235776673[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 24 )[/C][C]101.006944444444[/C][C]0.130718437168153[/C][C]772.706181565741[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 24 )[/C][C]101.019583333333[/C][C]0.124998660008467[/C][C]808.165330144262[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 24 )[/C][C]101.023472222222[/C][C]0.123702998807689[/C][C]816.661464927583[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 24 )[/C][C]101.119305555556[/C][C]0.107955159065662[/C][C]936.678769506989[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 24 )[/C][C]101.101527777778[/C][C]0.0994636751826419[/C][C]1016.46684171008[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 24 )[/C][C]101.125138888889[/C][C]0.0959812581665372[/C][C]1053.59255359444[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 24 )[/C][C]101.125138888889[/C][C]0.0959812581665372[/C][C]1053.59255359444[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 24 )[/C][C]101.140972222222[/C][C]0.0929683843568061[/C][C]1087.90717319611[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 24 )[/C][C]101.135416666667[/C][C]0.0921807898873551[/C][C]1097.14200529475[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 24 )[/C][C]101.126666666667[/C][C]0.0860489452013565[/C][C]1175.22261812772[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 24 )[/C][C]101.129722222222[/C][C]0.0730939253148115[/C][C]1383.55850758681[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 24 )[/C][C]101.123333333333[/C][C]0.0713956552817767[/C][C]1416.37937118485[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 24 )[/C][C]101.126666666667[/C][C]0.0691780492924768[/C][C]1461.83171831161[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 24 )[/C][C]101.026428571429[/C][C]0.147915402450742[/C][C]683.001410925219[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 24 )[/C][C]101.027352941176[/C][C]0.146145473613549[/C][C]691.27938377566[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 24 )[/C][C]101.029545454545[/C][C]0.144308080148638[/C][C]700.096247905763[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 24 )[/C][C]101.0321875[/C][C]0.142123993754378[/C][C]710.873546620187[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 24 )[/C][C]101.036290322581[/C][C]0.13980556753752[/C][C]722.69146431143[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 24 )[/C][C]101.0415[/C][C]0.137214999962429[/C][C]736.373574519306[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 24 )[/C][C]101.050344827586[/C][C]0.13471620267882[/C][C]750.097930450894[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 24 )[/C][C]101.059285714286[/C][C]0.132009655575343[/C][C]765.544651062342[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 24 )[/C][C]101.067592592593[/C][C]0.129448363330927[/C][C]780.756048141139[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 24 )[/C][C]101.076923076923[/C][C]0.126576793489926[/C][C]798.542294286886[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 24 )[/C][C]101.0862[/C][C]0.123157735262963[/C][C]820.786447429904[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 24 )[/C][C]101.095416666667[/C][C]0.119512884826197[/C][C]845.895543511358[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 24 )[/C][C]101.106956521739[/C][C]0.115420202505445[/C][C]875.990115482337[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 24 )[/C][C]101.117954545455[/C][C]0.111461831627098[/C][C]907.198034245037[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 24 )[/C][C]101.129523809524[/C][C]0.106538805687956[/C][C]949.227121108568[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 24 )[/C][C]101.13075[/C][C]0.104010223548285[/C][C]972.315475824857[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 24 )[/C][C]101.134210526316[/C][C]0.102479662888216[/C][C]986.871030563712[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 24 )[/C][C]101.135277777778[/C][C]0.101041784623288[/C][C]1000.92529199517[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 24 )[/C][C]101.136470588235[/C][C]0.0988425730738592[/C][C]1023.20758599295[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 24 )[/C][C]101.1359375[/C][C]0.096371529240671[/C][C]1049.43792317989[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 24 )[/C][C]101.136[/C][C]0.0928595528296585[/C][C]1089.1286563217[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 24 )[/C][C]101.137142857143[/C][C]0.0895045994249244[/C][C]1129.96587334013[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 24 )[/C][C]101.138076923077[/C][C]0.0884916671101241[/C][C]1142.91074206134[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 24 )[/C][C]101.14[/C][C]0.0869949190586956[/C][C]1162.59663316384[/C][/ROW]
[ROW][C]Median[/C][C]101.11[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]100.995[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]101.158717948718[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]101.158717948718[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]101.158717948718[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]101.158717948718[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]101.158717948718[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]101.158717948718[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]101.158717948718[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]101.158717948718[/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=&T=1

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

As an alternative you can also use a QR Code:  

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

Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean101.0255555555560.149576722674081675.409607520846
Geometric Mean101.017678078951
Harmonic Mean101.00978536658
Quadratic Mean101.033417106531
Winsorized Mean ( 1 / 24 )101.0255555555560.149360515960703676.387296239227
Winsorized Mean ( 2 / 24 )101.0233333333330.148840852503679678.73390694827
Winsorized Mean ( 3 / 24 )101.02250.148689600906857679.418731262068
Winsorized Mean ( 4 / 24 )101.0180555555560.147694944103208683.964208584992
Winsorized Mean ( 5 / 24 )101.0145833333330.146844607367218687.901211657867
Winsorized Mean ( 6 / 24 )100.998750.144273304138941700.051548710175
Winsorized Mean ( 7 / 24 )101.0016666666670.142682768605617707.875713750978
Winsorized Mean ( 8 / 24 )101.0094444444440.139295804536738725.143479951716
Winsorized Mean ( 9 / 24 )101.0069444444440.137657810831703733.75381922885
Winsorized Mean ( 10 / 24 )101.01250.136630985551713739.308873401691
Winsorized Mean ( 11 / 24 )101.0186111111110.133498475423348756.70235776673
Winsorized Mean ( 12 / 24 )101.0069444444440.130718437168153772.706181565741
Winsorized Mean ( 13 / 24 )101.0195833333330.124998660008467808.165330144262
Winsorized Mean ( 14 / 24 )101.0234722222220.123702998807689816.661464927583
Winsorized Mean ( 15 / 24 )101.1193055555560.107955159065662936.678769506989
Winsorized Mean ( 16 / 24 )101.1015277777780.09946367518264191016.46684171008
Winsorized Mean ( 17 / 24 )101.1251388888890.09598125816653721053.59255359444
Winsorized Mean ( 18 / 24 )101.1251388888890.09598125816653721053.59255359444
Winsorized Mean ( 19 / 24 )101.1409722222220.09296838435680611087.90717319611
Winsorized Mean ( 20 / 24 )101.1354166666670.09218078988735511097.14200529475
Winsorized Mean ( 21 / 24 )101.1266666666670.08604894520135651175.22261812772
Winsorized Mean ( 22 / 24 )101.1297222222220.07309392531481151383.55850758681
Winsorized Mean ( 23 / 24 )101.1233333333330.07139565528177671416.37937118485
Winsorized Mean ( 24 / 24 )101.1266666666670.06917804929247681461.83171831161
Trimmed Mean ( 1 / 24 )101.0264285714290.147915402450742683.001410925219
Trimmed Mean ( 2 / 24 )101.0273529411760.146145473613549691.27938377566
Trimmed Mean ( 3 / 24 )101.0295454545450.144308080148638700.096247905763
Trimmed Mean ( 4 / 24 )101.03218750.142123993754378710.873546620187
Trimmed Mean ( 5 / 24 )101.0362903225810.13980556753752722.69146431143
Trimmed Mean ( 6 / 24 )101.04150.137214999962429736.373574519306
Trimmed Mean ( 7 / 24 )101.0503448275860.13471620267882750.097930450894
Trimmed Mean ( 8 / 24 )101.0592857142860.132009655575343765.544651062342
Trimmed Mean ( 9 / 24 )101.0675925925930.129448363330927780.756048141139
Trimmed Mean ( 10 / 24 )101.0769230769230.126576793489926798.542294286886
Trimmed Mean ( 11 / 24 )101.08620.123157735262963820.786447429904
Trimmed Mean ( 12 / 24 )101.0954166666670.119512884826197845.895543511358
Trimmed Mean ( 13 / 24 )101.1069565217390.115420202505445875.990115482337
Trimmed Mean ( 14 / 24 )101.1179545454550.111461831627098907.198034245037
Trimmed Mean ( 15 / 24 )101.1295238095240.106538805687956949.227121108568
Trimmed Mean ( 16 / 24 )101.130750.104010223548285972.315475824857
Trimmed Mean ( 17 / 24 )101.1342105263160.102479662888216986.871030563712
Trimmed Mean ( 18 / 24 )101.1352777777780.1010417846232881000.92529199517
Trimmed Mean ( 19 / 24 )101.1364705882350.09884257307385921023.20758599295
Trimmed Mean ( 20 / 24 )101.13593750.0963715292406711049.43792317989
Trimmed Mean ( 21 / 24 )101.1360.09285955282965851089.1286563217
Trimmed Mean ( 22 / 24 )101.1371428571430.08950459942492441129.96587334013
Trimmed Mean ( 23 / 24 )101.1380769230770.08849166711012411142.91074206134
Trimmed Mean ( 24 / 24 )101.140.08699491905869561162.59663316384
Median101.11
Midrange100.995
Midmean - Weighted Average at Xnp101.158717948718
Midmean - Weighted Average at X(n+1)p101.158717948718
Midmean - Empirical Distribution Function101.158717948718
Midmean - Empirical Distribution Function - Averaging101.158717948718
Midmean - Empirical Distribution Function - Interpolation101.158717948718
Midmean - Closest Observation101.158717948718
Midmean - True Basic - Statistics Graphics Toolkit101.158717948718
Midmean - MS Excel (old versions)101.158717948718
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')