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of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationMon, 04 Apr 2011 11:23:56 +0000
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2011/Apr/04/t1301916065plq7gnn7xq2q9in.htm/, Retrieved Wed, 08 May 2024 09:06:21 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=120067, Retrieved Wed, 08 May 2024 09:06:21 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsKDGP1W52
Estimated Impact138
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [] [2011-04-04 11:23:56] [697c881a84403defd656157daf408edb] [Current]
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Dataseries X:
12 544
12 264
13 783
11 214
11 453
10 883
10 381
10 348
10 024
10 805
10 796
11 907
12 261
11 377
12 689
11 474
10 992
10 764
12 164
10 409
10 398
10 349
10 865
11 630
12 221
10 884
12 019
11 021
10 799
10 423
10 484
10 450
9 906
11 049
11 281
12 485
12 849
11 380
12 079
11 366
11 328
10 444
10 854
10 434
10 137
10 992
10 906
12 367
14 371
11 695
11 546
10 922
10 670
10 254
10 573
10 239
10 253
11 176
10 719
11 817
12 503
11 510
12 012
10 941
11 252
10 662
11 114
10 415
10 626
11 411
10 936
12 513




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'RServer@AstonUniversity' @ vre.aston.ac.uk

\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 & 'RServer@AstonUniversity' @ vre.aston.ac.uk \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=120067&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]'RServer@AstonUniversity' @ vre.aston.ac.uk[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=120067&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=120067&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'RServer@AstonUniversity' @ vre.aston.ac.uk







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean11250.8611111111103.442406665237108.76449488962
Geometric Mean11218.6602819691
Harmonic Mean11187.9057193693
Quadratic Mean11284.5735089004
Winsorized Mean ( 1 / 24 )11244.333333333399.9511069832018112.498337164221
Winsorized Mean ( 2 / 24 )11221.527777777891.465611717451122.685756614656
Winsorized Mean ( 3 / 24 )11219.111111111189.1713998909491125.815128223078
Winsorized Mean ( 4 / 24 )11211.833333333387.2489602468864128.503919148234
Winsorized Mean ( 5 / 24 )11209.7586.7790323172698129.175789365989
Winsorized Mean ( 6 / 24 )11216.7585.4336740196424131.291907186634
Winsorized Mean ( 7 / 24 )11215.097222222285.0501811730887131.86447186277
Winsorized Mean ( 8 / 24 )11205.541666666781.8528273385218136.898651286943
Winsorized Mean ( 9 / 24 )11194.791666666779.0370471796482141.639801411373
Winsorized Mean ( 10 / 24 )11195.902777777878.7416765597124142.185222196629
Winsorized Mean ( 11 / 24 )11190.708333333377.457877485924144.474760948194
Winsorized Mean ( 12 / 24 )11182.541666666775.5096946213366148.094118546559
Winsorized Mean ( 13 / 24 )11169.180555555672.4643815327156154.133386904199
Winsorized Mean ( 14 / 24 )11159.458333333370.1471205406799159.086477781532
Winsorized Mean ( 15 / 24 )11159.2569.7163203052299160.066537521529
Winsorized Mean ( 16 / 24 )11143.472222222264.6802898512028172.285440400125
Winsorized Mean ( 17 / 24 )11143.236111111158.2186178975123191.403309002072
Winsorized Mean ( 18 / 24 )11125.986111111151.53458618426215.893576235008
Winsorized Mean ( 19 / 24 )11118.333333333347.6106650905019233.526108324653
Winsorized Mean ( 20 / 24 )11097.222222222243.8575203365545253.028947762304
Winsorized Mean ( 21 / 24 )11101.013888888940.4195209439625274.644865392623
Winsorized Mean ( 22 / 24 )11103.763888888937.0571477050127299.638924648993
Winsorized Mean ( 23 / 24 )11107.277777777834.8116675788084319.067673291794
Winsorized Mean ( 24 / 24 )11094.277777777832.751890257257338.737022218727
Trimmed Mean ( 1 / 24 )11225.594.4759475125023118.818601935847
Trimmed Mean ( 2 / 24 )11205.558823529487.7727840806288127.665527998245
Trimmed Mean ( 3 / 24 )11196.848484848585.3512972125328131.185451780156
Trimmed Mean ( 4 / 24 )11188.583.4872536844863134.014469349817
Trimmed Mean ( 5 / 24 )11181.725806451681.9322189885296136.475320020529
Trimmed Mean ( 6 / 24 )1117580.1701298334618139.391067760698
Trimmed Mean ( 7 / 24 )11166.362068965578.3615941797584142.497893079489
Trimmed Mean ( 8 / 24 )11157.410714285776.2115339499456146.400552987343
Trimmed Mean ( 9 / 24 )11149.388888888974.3475107361849149.963176688611
Trimmed Mean ( 10 / 24 )11142.403846153872.6838816471276153.299515568651
Trimmed Mean ( 11 / 24 )11134.770.6190368622154157.672781940157
Trimmed Mean ( 12 / 24 )11127.062568.2787777783294162.965168124781
Trimmed Mean ( 13 / 24 )11119.826086956565.732956346832169.16668144795
Trimmed Mean ( 14 / 24 )11113.613636363663.1787893588588175.907353546104
Trimmed Mean ( 15 / 24 )1110860.4022520751431183.900427854596
Trimmed Mean ( 16 / 24 )11101.8556.7885591357797195.494482849192
Trimmed Mean ( 17 / 24 )11096.921052631653.3379331145447208.049326335924
Trimmed Mean ( 18 / 24 )11091.472222222250.4417231889594219.886861927229
Trimmed Mean ( 19 / 24 )11087.411764705948.3638931783179229.249777800694
Trimmed Mean ( 20 / 24 )11083.7546.5398069294691238.156338224552
Trimmed Mean ( 21 / 24 )11082.133333333345.0246862896226246.134604071358
Trimmed Mean ( 22 / 24 )11079.821428571443.7736800184572253.116060242128
Trimmed Mean ( 23 / 24 )11076.807692307742.8457347031011258.527663700116
Trimmed Mean ( 24 / 24 )11072.833333333341.9732776733881263.806734834857
Median11006.5
Midrange12138.5
Midmean - Weighted Average at Xnp11077.4594594595
Midmean - Weighted Average at X(n+1)p11091.4722222222
Midmean - Empirical Distribution Function11077.4594594595
Midmean - Empirical Distribution Function - Averaging11091.4722222222
Midmean - Empirical Distribution Function - Interpolation11091.4722222222
Midmean - Closest Observation11077.4594594595
Midmean - True Basic - Statistics Graphics Toolkit11091.4722222222
Midmean - MS Excel (old versions)11096.9210526316
Number of observations72

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 11250.8611111111 & 103.442406665237 & 108.76449488962 \tabularnewline
Geometric Mean & 11218.6602819691 &  &  \tabularnewline
Harmonic Mean & 11187.9057193693 &  &  \tabularnewline
Quadratic Mean & 11284.5735089004 &  &  \tabularnewline
Winsorized Mean ( 1 / 24 ) & 11244.3333333333 & 99.9511069832018 & 112.498337164221 \tabularnewline
Winsorized Mean ( 2 / 24 ) & 11221.5277777778 & 91.465611717451 & 122.685756614656 \tabularnewline
Winsorized Mean ( 3 / 24 ) & 11219.1111111111 & 89.1713998909491 & 125.815128223078 \tabularnewline
Winsorized Mean ( 4 / 24 ) & 11211.8333333333 & 87.2489602468864 & 128.503919148234 \tabularnewline
Winsorized Mean ( 5 / 24 ) & 11209.75 & 86.7790323172698 & 129.175789365989 \tabularnewline
Winsorized Mean ( 6 / 24 ) & 11216.75 & 85.4336740196424 & 131.291907186634 \tabularnewline
Winsorized Mean ( 7 / 24 ) & 11215.0972222222 & 85.0501811730887 & 131.86447186277 \tabularnewline
Winsorized Mean ( 8 / 24 ) & 11205.5416666667 & 81.8528273385218 & 136.898651286943 \tabularnewline
Winsorized Mean ( 9 / 24 ) & 11194.7916666667 & 79.0370471796482 & 141.639801411373 \tabularnewline
Winsorized Mean ( 10 / 24 ) & 11195.9027777778 & 78.7416765597124 & 142.185222196629 \tabularnewline
Winsorized Mean ( 11 / 24 ) & 11190.7083333333 & 77.457877485924 & 144.474760948194 \tabularnewline
Winsorized Mean ( 12 / 24 ) & 11182.5416666667 & 75.5096946213366 & 148.094118546559 \tabularnewline
Winsorized Mean ( 13 / 24 ) & 11169.1805555556 & 72.4643815327156 & 154.133386904199 \tabularnewline
Winsorized Mean ( 14 / 24 ) & 11159.4583333333 & 70.1471205406799 & 159.086477781532 \tabularnewline
Winsorized Mean ( 15 / 24 ) & 11159.25 & 69.7163203052299 & 160.066537521529 \tabularnewline
Winsorized Mean ( 16 / 24 ) & 11143.4722222222 & 64.6802898512028 & 172.285440400125 \tabularnewline
Winsorized Mean ( 17 / 24 ) & 11143.2361111111 & 58.2186178975123 & 191.403309002072 \tabularnewline
Winsorized Mean ( 18 / 24 ) & 11125.9861111111 & 51.53458618426 & 215.893576235008 \tabularnewline
Winsorized Mean ( 19 / 24 ) & 11118.3333333333 & 47.6106650905019 & 233.526108324653 \tabularnewline
Winsorized Mean ( 20 / 24 ) & 11097.2222222222 & 43.8575203365545 & 253.028947762304 \tabularnewline
Winsorized Mean ( 21 / 24 ) & 11101.0138888889 & 40.4195209439625 & 274.644865392623 \tabularnewline
Winsorized Mean ( 22 / 24 ) & 11103.7638888889 & 37.0571477050127 & 299.638924648993 \tabularnewline
Winsorized Mean ( 23 / 24 ) & 11107.2777777778 & 34.8116675788084 & 319.067673291794 \tabularnewline
Winsorized Mean ( 24 / 24 ) & 11094.2777777778 & 32.751890257257 & 338.737022218727 \tabularnewline
Trimmed Mean ( 1 / 24 ) & 11225.5 & 94.4759475125023 & 118.818601935847 \tabularnewline
Trimmed Mean ( 2 / 24 ) & 11205.5588235294 & 87.7727840806288 & 127.665527998245 \tabularnewline
Trimmed Mean ( 3 / 24 ) & 11196.8484848485 & 85.3512972125328 & 131.185451780156 \tabularnewline
Trimmed Mean ( 4 / 24 ) & 11188.5 & 83.4872536844863 & 134.014469349817 \tabularnewline
Trimmed Mean ( 5 / 24 ) & 11181.7258064516 & 81.9322189885296 & 136.475320020529 \tabularnewline
Trimmed Mean ( 6 / 24 ) & 11175 & 80.1701298334618 & 139.391067760698 \tabularnewline
Trimmed Mean ( 7 / 24 ) & 11166.3620689655 & 78.3615941797584 & 142.497893079489 \tabularnewline
Trimmed Mean ( 8 / 24 ) & 11157.4107142857 & 76.2115339499456 & 146.400552987343 \tabularnewline
Trimmed Mean ( 9 / 24 ) & 11149.3888888889 & 74.3475107361849 & 149.963176688611 \tabularnewline
Trimmed Mean ( 10 / 24 ) & 11142.4038461538 & 72.6838816471276 & 153.299515568651 \tabularnewline
Trimmed Mean ( 11 / 24 ) & 11134.7 & 70.6190368622154 & 157.672781940157 \tabularnewline
Trimmed Mean ( 12 / 24 ) & 11127.0625 & 68.2787777783294 & 162.965168124781 \tabularnewline
Trimmed Mean ( 13 / 24 ) & 11119.8260869565 & 65.732956346832 & 169.16668144795 \tabularnewline
Trimmed Mean ( 14 / 24 ) & 11113.6136363636 & 63.1787893588588 & 175.907353546104 \tabularnewline
Trimmed Mean ( 15 / 24 ) & 11108 & 60.4022520751431 & 183.900427854596 \tabularnewline
Trimmed Mean ( 16 / 24 ) & 11101.85 & 56.7885591357797 & 195.494482849192 \tabularnewline
Trimmed Mean ( 17 / 24 ) & 11096.9210526316 & 53.3379331145447 & 208.049326335924 \tabularnewline
Trimmed Mean ( 18 / 24 ) & 11091.4722222222 & 50.4417231889594 & 219.886861927229 \tabularnewline
Trimmed Mean ( 19 / 24 ) & 11087.4117647059 & 48.3638931783179 & 229.249777800694 \tabularnewline
Trimmed Mean ( 20 / 24 ) & 11083.75 & 46.5398069294691 & 238.156338224552 \tabularnewline
Trimmed Mean ( 21 / 24 ) & 11082.1333333333 & 45.0246862896226 & 246.134604071358 \tabularnewline
Trimmed Mean ( 22 / 24 ) & 11079.8214285714 & 43.7736800184572 & 253.116060242128 \tabularnewline
Trimmed Mean ( 23 / 24 ) & 11076.8076923077 & 42.8457347031011 & 258.527663700116 \tabularnewline
Trimmed Mean ( 24 / 24 ) & 11072.8333333333 & 41.9732776733881 & 263.806734834857 \tabularnewline
Median & 11006.5 &  &  \tabularnewline
Midrange & 12138.5 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 11077.4594594595 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 11091.4722222222 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 11077.4594594595 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 11091.4722222222 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 11091.4722222222 &  &  \tabularnewline
Midmean - Closest Observation & 11077.4594594595 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 11091.4722222222 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 11096.9210526316 &  &  \tabularnewline
Number of observations & 72 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=120067&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]11250.8611111111[/C][C]103.442406665237[/C][C]108.76449488962[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]11218.6602819691[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]11187.9057193693[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]11284.5735089004[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 24 )[/C][C]11244.3333333333[/C][C]99.9511069832018[/C][C]112.498337164221[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 24 )[/C][C]11221.5277777778[/C][C]91.465611717451[/C][C]122.685756614656[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 24 )[/C][C]11219.1111111111[/C][C]89.1713998909491[/C][C]125.815128223078[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 24 )[/C][C]11211.8333333333[/C][C]87.2489602468864[/C][C]128.503919148234[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 24 )[/C][C]11209.75[/C][C]86.7790323172698[/C][C]129.175789365989[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 24 )[/C][C]11216.75[/C][C]85.4336740196424[/C][C]131.291907186634[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 24 )[/C][C]11215.0972222222[/C][C]85.0501811730887[/C][C]131.86447186277[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 24 )[/C][C]11205.5416666667[/C][C]81.8528273385218[/C][C]136.898651286943[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 24 )[/C][C]11194.7916666667[/C][C]79.0370471796482[/C][C]141.639801411373[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 24 )[/C][C]11195.9027777778[/C][C]78.7416765597124[/C][C]142.185222196629[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 24 )[/C][C]11190.7083333333[/C][C]77.457877485924[/C][C]144.474760948194[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 24 )[/C][C]11182.5416666667[/C][C]75.5096946213366[/C][C]148.094118546559[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 24 )[/C][C]11169.1805555556[/C][C]72.4643815327156[/C][C]154.133386904199[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 24 )[/C][C]11159.4583333333[/C][C]70.1471205406799[/C][C]159.086477781532[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 24 )[/C][C]11159.25[/C][C]69.7163203052299[/C][C]160.066537521529[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 24 )[/C][C]11143.4722222222[/C][C]64.6802898512028[/C][C]172.285440400125[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 24 )[/C][C]11143.2361111111[/C][C]58.2186178975123[/C][C]191.403309002072[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 24 )[/C][C]11125.9861111111[/C][C]51.53458618426[/C][C]215.893576235008[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 24 )[/C][C]11118.3333333333[/C][C]47.6106650905019[/C][C]233.526108324653[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 24 )[/C][C]11097.2222222222[/C][C]43.8575203365545[/C][C]253.028947762304[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 24 )[/C][C]11101.0138888889[/C][C]40.4195209439625[/C][C]274.644865392623[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 24 )[/C][C]11103.7638888889[/C][C]37.0571477050127[/C][C]299.638924648993[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 24 )[/C][C]11107.2777777778[/C][C]34.8116675788084[/C][C]319.067673291794[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 24 )[/C][C]11094.2777777778[/C][C]32.751890257257[/C][C]338.737022218727[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 24 )[/C][C]11225.5[/C][C]94.4759475125023[/C][C]118.818601935847[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 24 )[/C][C]11205.5588235294[/C][C]87.7727840806288[/C][C]127.665527998245[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 24 )[/C][C]11196.8484848485[/C][C]85.3512972125328[/C][C]131.185451780156[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 24 )[/C][C]11188.5[/C][C]83.4872536844863[/C][C]134.014469349817[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 24 )[/C][C]11181.7258064516[/C][C]81.9322189885296[/C][C]136.475320020529[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 24 )[/C][C]11175[/C][C]80.1701298334618[/C][C]139.391067760698[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 24 )[/C][C]11166.3620689655[/C][C]78.3615941797584[/C][C]142.497893079489[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 24 )[/C][C]11157.4107142857[/C][C]76.2115339499456[/C][C]146.400552987343[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 24 )[/C][C]11149.3888888889[/C][C]74.3475107361849[/C][C]149.963176688611[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 24 )[/C][C]11142.4038461538[/C][C]72.6838816471276[/C][C]153.299515568651[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 24 )[/C][C]11134.7[/C][C]70.6190368622154[/C][C]157.672781940157[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 24 )[/C][C]11127.0625[/C][C]68.2787777783294[/C][C]162.965168124781[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 24 )[/C][C]11119.8260869565[/C][C]65.732956346832[/C][C]169.16668144795[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 24 )[/C][C]11113.6136363636[/C][C]63.1787893588588[/C][C]175.907353546104[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 24 )[/C][C]11108[/C][C]60.4022520751431[/C][C]183.900427854596[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 24 )[/C][C]11101.85[/C][C]56.7885591357797[/C][C]195.494482849192[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 24 )[/C][C]11096.9210526316[/C][C]53.3379331145447[/C][C]208.049326335924[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 24 )[/C][C]11091.4722222222[/C][C]50.4417231889594[/C][C]219.886861927229[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 24 )[/C][C]11087.4117647059[/C][C]48.3638931783179[/C][C]229.249777800694[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 24 )[/C][C]11083.75[/C][C]46.5398069294691[/C][C]238.156338224552[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 24 )[/C][C]11082.1333333333[/C][C]45.0246862896226[/C][C]246.134604071358[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 24 )[/C][C]11079.8214285714[/C][C]43.7736800184572[/C][C]253.116060242128[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 24 )[/C][C]11076.8076923077[/C][C]42.8457347031011[/C][C]258.527663700116[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 24 )[/C][C]11072.8333333333[/C][C]41.9732776733881[/C][C]263.806734834857[/C][/ROW]
[ROW][C]Median[/C][C]11006.5[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]12138.5[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]11077.4594594595[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]11091.4722222222[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]11077.4594594595[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]11091.4722222222[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]11091.4722222222[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]11077.4594594595[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]11091.4722222222[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]11096.9210526316[/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=120067&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=120067&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 Mean11250.8611111111103.442406665237108.76449488962
Geometric Mean11218.6602819691
Harmonic Mean11187.9057193693
Quadratic Mean11284.5735089004
Winsorized Mean ( 1 / 24 )11244.333333333399.9511069832018112.498337164221
Winsorized Mean ( 2 / 24 )11221.527777777891.465611717451122.685756614656
Winsorized Mean ( 3 / 24 )11219.111111111189.1713998909491125.815128223078
Winsorized Mean ( 4 / 24 )11211.833333333387.2489602468864128.503919148234
Winsorized Mean ( 5 / 24 )11209.7586.7790323172698129.175789365989
Winsorized Mean ( 6 / 24 )11216.7585.4336740196424131.291907186634
Winsorized Mean ( 7 / 24 )11215.097222222285.0501811730887131.86447186277
Winsorized Mean ( 8 / 24 )11205.541666666781.8528273385218136.898651286943
Winsorized Mean ( 9 / 24 )11194.791666666779.0370471796482141.639801411373
Winsorized Mean ( 10 / 24 )11195.902777777878.7416765597124142.185222196629
Winsorized Mean ( 11 / 24 )11190.708333333377.457877485924144.474760948194
Winsorized Mean ( 12 / 24 )11182.541666666775.5096946213366148.094118546559
Winsorized Mean ( 13 / 24 )11169.180555555672.4643815327156154.133386904199
Winsorized Mean ( 14 / 24 )11159.458333333370.1471205406799159.086477781532
Winsorized Mean ( 15 / 24 )11159.2569.7163203052299160.066537521529
Winsorized Mean ( 16 / 24 )11143.472222222264.6802898512028172.285440400125
Winsorized Mean ( 17 / 24 )11143.236111111158.2186178975123191.403309002072
Winsorized Mean ( 18 / 24 )11125.986111111151.53458618426215.893576235008
Winsorized Mean ( 19 / 24 )11118.333333333347.6106650905019233.526108324653
Winsorized Mean ( 20 / 24 )11097.222222222243.8575203365545253.028947762304
Winsorized Mean ( 21 / 24 )11101.013888888940.4195209439625274.644865392623
Winsorized Mean ( 22 / 24 )11103.763888888937.0571477050127299.638924648993
Winsorized Mean ( 23 / 24 )11107.277777777834.8116675788084319.067673291794
Winsorized Mean ( 24 / 24 )11094.277777777832.751890257257338.737022218727
Trimmed Mean ( 1 / 24 )11225.594.4759475125023118.818601935847
Trimmed Mean ( 2 / 24 )11205.558823529487.7727840806288127.665527998245
Trimmed Mean ( 3 / 24 )11196.848484848585.3512972125328131.185451780156
Trimmed Mean ( 4 / 24 )11188.583.4872536844863134.014469349817
Trimmed Mean ( 5 / 24 )11181.725806451681.9322189885296136.475320020529
Trimmed Mean ( 6 / 24 )1117580.1701298334618139.391067760698
Trimmed Mean ( 7 / 24 )11166.362068965578.3615941797584142.497893079489
Trimmed Mean ( 8 / 24 )11157.410714285776.2115339499456146.400552987343
Trimmed Mean ( 9 / 24 )11149.388888888974.3475107361849149.963176688611
Trimmed Mean ( 10 / 24 )11142.403846153872.6838816471276153.299515568651
Trimmed Mean ( 11 / 24 )11134.770.6190368622154157.672781940157
Trimmed Mean ( 12 / 24 )11127.062568.2787777783294162.965168124781
Trimmed Mean ( 13 / 24 )11119.826086956565.732956346832169.16668144795
Trimmed Mean ( 14 / 24 )11113.613636363663.1787893588588175.907353546104
Trimmed Mean ( 15 / 24 )1110860.4022520751431183.900427854596
Trimmed Mean ( 16 / 24 )11101.8556.7885591357797195.494482849192
Trimmed Mean ( 17 / 24 )11096.921052631653.3379331145447208.049326335924
Trimmed Mean ( 18 / 24 )11091.472222222250.4417231889594219.886861927229
Trimmed Mean ( 19 / 24 )11087.411764705948.3638931783179229.249777800694
Trimmed Mean ( 20 / 24 )11083.7546.5398069294691238.156338224552
Trimmed Mean ( 21 / 24 )11082.133333333345.0246862896226246.134604071358
Trimmed Mean ( 22 / 24 )11079.821428571443.7736800184572253.116060242128
Trimmed Mean ( 23 / 24 )11076.807692307742.8457347031011258.527663700116
Trimmed Mean ( 24 / 24 )11072.833333333341.9732776733881263.806734834857
Median11006.5
Midrange12138.5
Midmean - Weighted Average at Xnp11077.4594594595
Midmean - Weighted Average at X(n+1)p11091.4722222222
Midmean - Empirical Distribution Function11077.4594594595
Midmean - Empirical Distribution Function - Averaging11091.4722222222
Midmean - Empirical Distribution Function - Interpolation11091.4722222222
Midmean - Closest Observation11077.4594594595
Midmean - True Basic - Statistics Graphics Toolkit11091.4722222222
Midmean - MS Excel (old versions)11096.9210526316
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')