Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationMon, 10 Oct 2016 16:22:11 +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/10/t1476113030p1ko9toyi6mhx94.htm/, Retrieved Wed, 08 May 2024 16:29:27 +0200
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=, Retrieved Wed, 08 May 2024 16:29:27 +0200
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact0
Dataseries X:
2884
2505
3128
2765
2398
3015
2769
2840
2895
2761
2712
3051
2980
2790
3164
2629
2919
2653
2788
3031
2794
2448
2856
2703
2918
2766
2907
2516
2754
3000
3117
3265
2748
2970
3081
2679
3034
2958
3029
2697
2844
2604
3289
3217
2834
3141
2674
2883
3237
2905
3211
3058
2784
3125
3370
3021
3152
3210
2930
3229
2961
2927
3342
2999
2593
3168
3547
3037
2911
2869
2827
2988




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 Mean2927.8333333333326.8909727073146108.877925882426
Geometric Mean2919.03489499142
Harmonic Mean2910.19560022397
Quadratic Mean2936.58813269943
Winsorized Mean ( 1 / 24 )2926.0694444444426.0087887396058112.503103229435
Winsorized Mean ( 2 / 24 )2926.87525.4357481478713115.069349758637
Winsorized Mean ( 3 / 24 )2925.12524.8472007905986117.724528595864
Winsorized Mean ( 4 / 24 )2928.0694444444423.6513152485163123.801548187817
Winsorized Mean ( 5 / 24 )2926.8888888888923.1211052259266126.589488706918
Winsorized Mean ( 6 / 24 )2928.3055555555622.5963130664613129.59218377541
Winsorized Mean ( 7 / 24 )2929.4722222222221.9546228945208133.433046711694
Winsorized Mean ( 8 / 24 )2931.1388888888921.4275839947288136.792784926661
Winsorized Mean ( 9 / 24 )2931.6388888888921.2995560942116137.638497061711
Winsorized Mean ( 10 / 24 )2928.3055555555619.8511345419169147.513259223157
Winsorized Mean ( 11 / 24 )2928.6111111111119.5979398684521149.434641129064
Winsorized Mean ( 12 / 24 )2928.1111111111119.0212955729132153.938573736314
Winsorized Mean ( 13 / 24 )2932.62517.6926732744888165.753640193457
Winsorized Mean ( 14 / 24 )2931.2638888888917.1073430620144171.345361945628
Winsorized Mean ( 15 / 24 )2932.0972222222216.7951172169961174.58033691215
Winsorized Mean ( 16 / 24 )2931.2083333333316.3820287988549178.928285948211
Winsorized Mean ( 17 / 24 )2922.9444444444415.0376664389246194.374869020799
Winsorized Mean ( 18 / 24 )2917.9444444444414.0981342744041206.973801472591
Winsorized Mean ( 19 / 24 )2920.0555555555613.2596244445446220.221588308782
Winsorized Mean ( 20 / 24 )2917.2777777777812.5672404668165232.133520917402
Winsorized Mean ( 21 / 24 )2916.9861111111112.3657816561885235.891769094217
Winsorized Mean ( 22 / 24 )2917.2916666666712.0675335832985241.747134700682
Winsorized Mean ( 23 / 24 )2927.1944444444410.5120960003035278.459637769664
Winsorized Mean ( 24 / 24 )2926.861111111119.8387091527135297.484259945207
Trimmed Mean ( 1 / 24 )2926.5571428571425.0564880306135116.798377301781
Trimmed Mean ( 2 / 24 )2927.0735294117623.919727075388122.370690944194
Trimmed Mean ( 3 / 24 )2927.1818181818222.9340791310697127.634591363045
Trimmed Mean ( 4 / 24 )2927.95312522.0276637679793132.921636894433
Trimmed Mean ( 5 / 24 )2927.9193548387121.3913485527907136.873995934059
Trimmed Mean ( 6 / 24 )2928.1666666666720.7904960722519140.841596876313
Trimmed Mean ( 7 / 24 )2928.1379310344820.2087180619733144.894788578616
Trimmed Mean ( 8 / 24 )2927.8928571428619.6643866664704148.893169505011
Trimmed Mean ( 9 / 24 )2927.3518518518519.1208989136816153.096978602676
Trimmed Mean ( 10 / 24 )2926.6923076923118.4707697508712158.449937234168
Trimmed Mean ( 11 / 24 )2926.4617.9998913828922162.58209217759
Trimmed Mean ( 12 / 24 )2926.1666666666717.4559560577831167.631418008868
Trimmed Mean ( 13 / 24 )2925.9130434782616.890606430536173.227234647336
Trimmed Mean ( 14 / 24 )2925.0681818181816.4600996752289177.706589846486
Trimmed Mean ( 15 / 24 )2924.3095238095216.0237008002138182.499009452954
Trimmed Mean ( 16 / 24 )2923.37515.5075948101204188.512469908756
Trimmed Mean ( 17 / 24 )2922.4473684210514.9096709986008196.010184845482
Trimmed Mean ( 18 / 24 )2922.3888888888914.4457539088991202.300891135118
Trimmed Mean ( 19 / 24 )2922.9117647058814.0348666697203208.26074329669
Trimmed Mean ( 20 / 24 )2923.2513.6673468883958213.885695875765
Trimmed Mean ( 21 / 24 )2923.9666666666713.30694083287219.732446652507
Trimmed Mean ( 22 / 24 )2924.8214285714312.8060474276049228.393768265035
Trimmed Mean ( 23 / 24 )2925.7692307692312.1255366501139241.289875672576
Trimmed Mean ( 24 / 24 )2925.5833333333311.6684134303116250.726746254414
Median2918.5
Midrange2972.5
Midmean - Weighted Average at Xnp2918.16216216216
Midmean - Weighted Average at X(n+1)p2922.38888888889
Midmean - Empirical Distribution Function2918.16216216216
Midmean - Empirical Distribution Function - Averaging2922.38888888889
Midmean - Empirical Distribution Function - Interpolation2922.38888888889
Midmean - Closest Observation2918.16216216216
Midmean - True Basic - Statistics Graphics Toolkit2922.38888888889
Midmean - MS Excel (old versions)2922.44736842105
Number of observations72

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 2927.83333333333 & 26.8909727073146 & 108.877925882426 \tabularnewline
Geometric Mean & 2919.03489499142 &  &  \tabularnewline
Harmonic Mean & 2910.19560022397 &  &  \tabularnewline
Quadratic Mean & 2936.58813269943 &  &  \tabularnewline
Winsorized Mean ( 1 / 24 ) & 2926.06944444444 & 26.0087887396058 & 112.503103229435 \tabularnewline
Winsorized Mean ( 2 / 24 ) & 2926.875 & 25.4357481478713 & 115.069349758637 \tabularnewline
Winsorized Mean ( 3 / 24 ) & 2925.125 & 24.8472007905986 & 117.724528595864 \tabularnewline
Winsorized Mean ( 4 / 24 ) & 2928.06944444444 & 23.6513152485163 & 123.801548187817 \tabularnewline
Winsorized Mean ( 5 / 24 ) & 2926.88888888889 & 23.1211052259266 & 126.589488706918 \tabularnewline
Winsorized Mean ( 6 / 24 ) & 2928.30555555556 & 22.5963130664613 & 129.59218377541 \tabularnewline
Winsorized Mean ( 7 / 24 ) & 2929.47222222222 & 21.9546228945208 & 133.433046711694 \tabularnewline
Winsorized Mean ( 8 / 24 ) & 2931.13888888889 & 21.4275839947288 & 136.792784926661 \tabularnewline
Winsorized Mean ( 9 / 24 ) & 2931.63888888889 & 21.2995560942116 & 137.638497061711 \tabularnewline
Winsorized Mean ( 10 / 24 ) & 2928.30555555556 & 19.8511345419169 & 147.513259223157 \tabularnewline
Winsorized Mean ( 11 / 24 ) & 2928.61111111111 & 19.5979398684521 & 149.434641129064 \tabularnewline
Winsorized Mean ( 12 / 24 ) & 2928.11111111111 & 19.0212955729132 & 153.938573736314 \tabularnewline
Winsorized Mean ( 13 / 24 ) & 2932.625 & 17.6926732744888 & 165.753640193457 \tabularnewline
Winsorized Mean ( 14 / 24 ) & 2931.26388888889 & 17.1073430620144 & 171.345361945628 \tabularnewline
Winsorized Mean ( 15 / 24 ) & 2932.09722222222 & 16.7951172169961 & 174.58033691215 \tabularnewline
Winsorized Mean ( 16 / 24 ) & 2931.20833333333 & 16.3820287988549 & 178.928285948211 \tabularnewline
Winsorized Mean ( 17 / 24 ) & 2922.94444444444 & 15.0376664389246 & 194.374869020799 \tabularnewline
Winsorized Mean ( 18 / 24 ) & 2917.94444444444 & 14.0981342744041 & 206.973801472591 \tabularnewline
Winsorized Mean ( 19 / 24 ) & 2920.05555555556 & 13.2596244445446 & 220.221588308782 \tabularnewline
Winsorized Mean ( 20 / 24 ) & 2917.27777777778 & 12.5672404668165 & 232.133520917402 \tabularnewline
Winsorized Mean ( 21 / 24 ) & 2916.98611111111 & 12.3657816561885 & 235.891769094217 \tabularnewline
Winsorized Mean ( 22 / 24 ) & 2917.29166666667 & 12.0675335832985 & 241.747134700682 \tabularnewline
Winsorized Mean ( 23 / 24 ) & 2927.19444444444 & 10.5120960003035 & 278.459637769664 \tabularnewline
Winsorized Mean ( 24 / 24 ) & 2926.86111111111 & 9.8387091527135 & 297.484259945207 \tabularnewline
Trimmed Mean ( 1 / 24 ) & 2926.55714285714 & 25.0564880306135 & 116.798377301781 \tabularnewline
Trimmed Mean ( 2 / 24 ) & 2927.07352941176 & 23.919727075388 & 122.370690944194 \tabularnewline
Trimmed Mean ( 3 / 24 ) & 2927.18181818182 & 22.9340791310697 & 127.634591363045 \tabularnewline
Trimmed Mean ( 4 / 24 ) & 2927.953125 & 22.0276637679793 & 132.921636894433 \tabularnewline
Trimmed Mean ( 5 / 24 ) & 2927.91935483871 & 21.3913485527907 & 136.873995934059 \tabularnewline
Trimmed Mean ( 6 / 24 ) & 2928.16666666667 & 20.7904960722519 & 140.841596876313 \tabularnewline
Trimmed Mean ( 7 / 24 ) & 2928.13793103448 & 20.2087180619733 & 144.894788578616 \tabularnewline
Trimmed Mean ( 8 / 24 ) & 2927.89285714286 & 19.6643866664704 & 148.893169505011 \tabularnewline
Trimmed Mean ( 9 / 24 ) & 2927.35185185185 & 19.1208989136816 & 153.096978602676 \tabularnewline
Trimmed Mean ( 10 / 24 ) & 2926.69230769231 & 18.4707697508712 & 158.449937234168 \tabularnewline
Trimmed Mean ( 11 / 24 ) & 2926.46 & 17.9998913828922 & 162.58209217759 \tabularnewline
Trimmed Mean ( 12 / 24 ) & 2926.16666666667 & 17.4559560577831 & 167.631418008868 \tabularnewline
Trimmed Mean ( 13 / 24 ) & 2925.91304347826 & 16.890606430536 & 173.227234647336 \tabularnewline
Trimmed Mean ( 14 / 24 ) & 2925.06818181818 & 16.4600996752289 & 177.706589846486 \tabularnewline
Trimmed Mean ( 15 / 24 ) & 2924.30952380952 & 16.0237008002138 & 182.499009452954 \tabularnewline
Trimmed Mean ( 16 / 24 ) & 2923.375 & 15.5075948101204 & 188.512469908756 \tabularnewline
Trimmed Mean ( 17 / 24 ) & 2922.44736842105 & 14.9096709986008 & 196.010184845482 \tabularnewline
Trimmed Mean ( 18 / 24 ) & 2922.38888888889 & 14.4457539088991 & 202.300891135118 \tabularnewline
Trimmed Mean ( 19 / 24 ) & 2922.91176470588 & 14.0348666697203 & 208.26074329669 \tabularnewline
Trimmed Mean ( 20 / 24 ) & 2923.25 & 13.6673468883958 & 213.885695875765 \tabularnewline
Trimmed Mean ( 21 / 24 ) & 2923.96666666667 & 13.30694083287 & 219.732446652507 \tabularnewline
Trimmed Mean ( 22 / 24 ) & 2924.82142857143 & 12.8060474276049 & 228.393768265035 \tabularnewline
Trimmed Mean ( 23 / 24 ) & 2925.76923076923 & 12.1255366501139 & 241.289875672576 \tabularnewline
Trimmed Mean ( 24 / 24 ) & 2925.58333333333 & 11.6684134303116 & 250.726746254414 \tabularnewline
Median & 2918.5 &  &  \tabularnewline
Midrange & 2972.5 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 2918.16216216216 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 2922.38888888889 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 2918.16216216216 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 2922.38888888889 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 2922.38888888889 &  &  \tabularnewline
Midmean - Closest Observation & 2918.16216216216 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 2922.38888888889 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 2922.44736842105 &  &  \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]2927.83333333333[/C][C]26.8909727073146[/C][C]108.877925882426[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]2919.03489499142[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]2910.19560022397[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]2936.58813269943[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 24 )[/C][C]2926.06944444444[/C][C]26.0087887396058[/C][C]112.503103229435[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 24 )[/C][C]2926.875[/C][C]25.4357481478713[/C][C]115.069349758637[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 24 )[/C][C]2925.125[/C][C]24.8472007905986[/C][C]117.724528595864[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 24 )[/C][C]2928.06944444444[/C][C]23.6513152485163[/C][C]123.801548187817[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 24 )[/C][C]2926.88888888889[/C][C]23.1211052259266[/C][C]126.589488706918[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 24 )[/C][C]2928.30555555556[/C][C]22.5963130664613[/C][C]129.59218377541[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 24 )[/C][C]2929.47222222222[/C][C]21.9546228945208[/C][C]133.433046711694[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 24 )[/C][C]2931.13888888889[/C][C]21.4275839947288[/C][C]136.792784926661[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 24 )[/C][C]2931.63888888889[/C][C]21.2995560942116[/C][C]137.638497061711[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 24 )[/C][C]2928.30555555556[/C][C]19.8511345419169[/C][C]147.513259223157[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 24 )[/C][C]2928.61111111111[/C][C]19.5979398684521[/C][C]149.434641129064[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 24 )[/C][C]2928.11111111111[/C][C]19.0212955729132[/C][C]153.938573736314[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 24 )[/C][C]2932.625[/C][C]17.6926732744888[/C][C]165.753640193457[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 24 )[/C][C]2931.26388888889[/C][C]17.1073430620144[/C][C]171.345361945628[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 24 )[/C][C]2932.09722222222[/C][C]16.7951172169961[/C][C]174.58033691215[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 24 )[/C][C]2931.20833333333[/C][C]16.3820287988549[/C][C]178.928285948211[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 24 )[/C][C]2922.94444444444[/C][C]15.0376664389246[/C][C]194.374869020799[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 24 )[/C][C]2917.94444444444[/C][C]14.0981342744041[/C][C]206.973801472591[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 24 )[/C][C]2920.05555555556[/C][C]13.2596244445446[/C][C]220.221588308782[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 24 )[/C][C]2917.27777777778[/C][C]12.5672404668165[/C][C]232.133520917402[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 24 )[/C][C]2916.98611111111[/C][C]12.3657816561885[/C][C]235.891769094217[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 24 )[/C][C]2917.29166666667[/C][C]12.0675335832985[/C][C]241.747134700682[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 24 )[/C][C]2927.19444444444[/C][C]10.5120960003035[/C][C]278.459637769664[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 24 )[/C][C]2926.86111111111[/C][C]9.8387091527135[/C][C]297.484259945207[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 24 )[/C][C]2926.55714285714[/C][C]25.0564880306135[/C][C]116.798377301781[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 24 )[/C][C]2927.07352941176[/C][C]23.919727075388[/C][C]122.370690944194[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 24 )[/C][C]2927.18181818182[/C][C]22.9340791310697[/C][C]127.634591363045[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 24 )[/C][C]2927.953125[/C][C]22.0276637679793[/C][C]132.921636894433[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 24 )[/C][C]2927.91935483871[/C][C]21.3913485527907[/C][C]136.873995934059[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 24 )[/C][C]2928.16666666667[/C][C]20.7904960722519[/C][C]140.841596876313[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 24 )[/C][C]2928.13793103448[/C][C]20.2087180619733[/C][C]144.894788578616[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 24 )[/C][C]2927.89285714286[/C][C]19.6643866664704[/C][C]148.893169505011[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 24 )[/C][C]2927.35185185185[/C][C]19.1208989136816[/C][C]153.096978602676[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 24 )[/C][C]2926.69230769231[/C][C]18.4707697508712[/C][C]158.449937234168[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 24 )[/C][C]2926.46[/C][C]17.9998913828922[/C][C]162.58209217759[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 24 )[/C][C]2926.16666666667[/C][C]17.4559560577831[/C][C]167.631418008868[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 24 )[/C][C]2925.91304347826[/C][C]16.890606430536[/C][C]173.227234647336[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 24 )[/C][C]2925.06818181818[/C][C]16.4600996752289[/C][C]177.706589846486[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 24 )[/C][C]2924.30952380952[/C][C]16.0237008002138[/C][C]182.499009452954[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 24 )[/C][C]2923.375[/C][C]15.5075948101204[/C][C]188.512469908756[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 24 )[/C][C]2922.44736842105[/C][C]14.9096709986008[/C][C]196.010184845482[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 24 )[/C][C]2922.38888888889[/C][C]14.4457539088991[/C][C]202.300891135118[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 24 )[/C][C]2922.91176470588[/C][C]14.0348666697203[/C][C]208.26074329669[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 24 )[/C][C]2923.25[/C][C]13.6673468883958[/C][C]213.885695875765[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 24 )[/C][C]2923.96666666667[/C][C]13.30694083287[/C][C]219.732446652507[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 24 )[/C][C]2924.82142857143[/C][C]12.8060474276049[/C][C]228.393768265035[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 24 )[/C][C]2925.76923076923[/C][C]12.1255366501139[/C][C]241.289875672576[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 24 )[/C][C]2925.58333333333[/C][C]11.6684134303116[/C][C]250.726746254414[/C][/ROW]
[ROW][C]Median[/C][C]2918.5[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]2972.5[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]2918.16216216216[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]2922.38888888889[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]2918.16216216216[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]2922.38888888889[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]2922.38888888889[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]2918.16216216216[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]2922.38888888889[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]2922.44736842105[/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 Mean2927.8333333333326.8909727073146108.877925882426
Geometric Mean2919.03489499142
Harmonic Mean2910.19560022397
Quadratic Mean2936.58813269943
Winsorized Mean ( 1 / 24 )2926.0694444444426.0087887396058112.503103229435
Winsorized Mean ( 2 / 24 )2926.87525.4357481478713115.069349758637
Winsorized Mean ( 3 / 24 )2925.12524.8472007905986117.724528595864
Winsorized Mean ( 4 / 24 )2928.0694444444423.6513152485163123.801548187817
Winsorized Mean ( 5 / 24 )2926.8888888888923.1211052259266126.589488706918
Winsorized Mean ( 6 / 24 )2928.3055555555622.5963130664613129.59218377541
Winsorized Mean ( 7 / 24 )2929.4722222222221.9546228945208133.433046711694
Winsorized Mean ( 8 / 24 )2931.1388888888921.4275839947288136.792784926661
Winsorized Mean ( 9 / 24 )2931.6388888888921.2995560942116137.638497061711
Winsorized Mean ( 10 / 24 )2928.3055555555619.8511345419169147.513259223157
Winsorized Mean ( 11 / 24 )2928.6111111111119.5979398684521149.434641129064
Winsorized Mean ( 12 / 24 )2928.1111111111119.0212955729132153.938573736314
Winsorized Mean ( 13 / 24 )2932.62517.6926732744888165.753640193457
Winsorized Mean ( 14 / 24 )2931.2638888888917.1073430620144171.345361945628
Winsorized Mean ( 15 / 24 )2932.0972222222216.7951172169961174.58033691215
Winsorized Mean ( 16 / 24 )2931.2083333333316.3820287988549178.928285948211
Winsorized Mean ( 17 / 24 )2922.9444444444415.0376664389246194.374869020799
Winsorized Mean ( 18 / 24 )2917.9444444444414.0981342744041206.973801472591
Winsorized Mean ( 19 / 24 )2920.0555555555613.2596244445446220.221588308782
Winsorized Mean ( 20 / 24 )2917.2777777777812.5672404668165232.133520917402
Winsorized Mean ( 21 / 24 )2916.9861111111112.3657816561885235.891769094217
Winsorized Mean ( 22 / 24 )2917.2916666666712.0675335832985241.747134700682
Winsorized Mean ( 23 / 24 )2927.1944444444410.5120960003035278.459637769664
Winsorized Mean ( 24 / 24 )2926.861111111119.8387091527135297.484259945207
Trimmed Mean ( 1 / 24 )2926.5571428571425.0564880306135116.798377301781
Trimmed Mean ( 2 / 24 )2927.0735294117623.919727075388122.370690944194
Trimmed Mean ( 3 / 24 )2927.1818181818222.9340791310697127.634591363045
Trimmed Mean ( 4 / 24 )2927.95312522.0276637679793132.921636894433
Trimmed Mean ( 5 / 24 )2927.9193548387121.3913485527907136.873995934059
Trimmed Mean ( 6 / 24 )2928.1666666666720.7904960722519140.841596876313
Trimmed Mean ( 7 / 24 )2928.1379310344820.2087180619733144.894788578616
Trimmed Mean ( 8 / 24 )2927.8928571428619.6643866664704148.893169505011
Trimmed Mean ( 9 / 24 )2927.3518518518519.1208989136816153.096978602676
Trimmed Mean ( 10 / 24 )2926.6923076923118.4707697508712158.449937234168
Trimmed Mean ( 11 / 24 )2926.4617.9998913828922162.58209217759
Trimmed Mean ( 12 / 24 )2926.1666666666717.4559560577831167.631418008868
Trimmed Mean ( 13 / 24 )2925.9130434782616.890606430536173.227234647336
Trimmed Mean ( 14 / 24 )2925.0681818181816.4600996752289177.706589846486
Trimmed Mean ( 15 / 24 )2924.3095238095216.0237008002138182.499009452954
Trimmed Mean ( 16 / 24 )2923.37515.5075948101204188.512469908756
Trimmed Mean ( 17 / 24 )2922.4473684210514.9096709986008196.010184845482
Trimmed Mean ( 18 / 24 )2922.3888888888914.4457539088991202.300891135118
Trimmed Mean ( 19 / 24 )2922.9117647058814.0348666697203208.26074329669
Trimmed Mean ( 20 / 24 )2923.2513.6673468883958213.885695875765
Trimmed Mean ( 21 / 24 )2923.9666666666713.30694083287219.732446652507
Trimmed Mean ( 22 / 24 )2924.8214285714312.8060474276049228.393768265035
Trimmed Mean ( 23 / 24 )2925.7692307692312.1255366501139241.289875672576
Trimmed Mean ( 24 / 24 )2925.5833333333311.6684134303116250.726746254414
Median2918.5
Midrange2972.5
Midmean - Weighted Average at Xnp2918.16216216216
Midmean - Weighted Average at X(n+1)p2922.38888888889
Midmean - Empirical Distribution Function2918.16216216216
Midmean - Empirical Distribution Function - Averaging2922.38888888889
Midmean - Empirical Distribution Function - Interpolation2922.38888888889
Midmean - Closest Observation2918.16216216216
Midmean - True Basic - Statistics Graphics Toolkit2922.38888888889
Midmean - MS Excel (old versions)2922.44736842105
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')