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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 computationWed, 09 Oct 2013 13:50:44 -0400
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2013/Oct/09/t13813411088gn922fcib8r517.htm/, Retrieved Mon, 29 Apr 2024 06:41:59 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=214483, Retrieved Mon, 29 Apr 2024 06:41:59 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact76
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [] [2013-10-09 17:50:44] [3c7daf9c150a57900c7784703a011e78] [Current]
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Dataseries X:
102,78
102,78
102,78
102,78
102,78
102,78
102,78
101,67
101,67
101,67
101,67
101,67
101,67
101,67
101,67
101,67
101,67
101,67
101,67
105,79
105,79
105,79
105,79
105,79
105,79
105,79
105,79
105,79
105,79
105,79
105,79
104,47
104,47
104,47
104,47
104,47
104,47
104,47
104,47
105,5
105,5
105,5
105,5
106,61
106,61
106,61
106,61
106,61
106,61
106,61
106,61
112,06
112,06
112,06
112,06
111,18
111,18
111,18
111,18
111,18
111,18
111,18
111,18
117,21
117,21
117,21
117,21
107,98
107,98
107,98
107,98
107,98




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'Gertrude Mary Cox' @ cox.wessa.net

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 3 seconds \tabularnewline
R Server & 'Gertrude Mary Cox' @ cox.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=214483&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]3 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gertrude Mary Cox' @ cox.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=214483&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=214483&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 time3 seconds
R Server'Gertrude Mary Cox' @ cox.wessa.net







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean106.4727777777780.482177962710734220.81635000323
Geometric Mean106.397038395498
Harmonic Mean106.323031895301
Quadratic Mean106.550267922913
Winsorized Mean ( 1 / 24 )106.4727777777780.482177962710734220.81635000323
Winsorized Mean ( 2 / 24 )106.4727777777780.482177962710734220.81635000323
Winsorized Mean ( 3 / 24 )106.4727777777780.482177962710734220.81635000323
Winsorized Mean ( 4 / 24 )106.1866666666670.406889994861784260.971437016378
Winsorized Mean ( 5 / 24 )106.1866666666670.406889994861784260.971437016378
Winsorized Mean ( 6 / 24 )106.1866666666670.406889994861784260.971437016378
Winsorized Mean ( 7 / 24 )106.1866666666670.406889994861784260.971437016378
Winsorized Mean ( 8 / 24 )106.0888888888890.387891432644997273.501500575762
Winsorized Mean ( 9 / 24 )106.0888888888890.387891432644997273.501500575762
Winsorized Mean ( 10 / 24 )106.0888888888890.387891432644997273.501500575762
Winsorized Mean ( 11 / 24 )106.0888888888890.387891432644997273.501500575762
Winsorized Mean ( 12 / 24 )106.2738888888890.360335901996223294.930059147985
Winsorized Mean ( 13 / 24 )106.2738888888890.360335901996223294.930059147986
Winsorized Mean ( 14 / 24 )106.2738888888890.360335901996223294.930059147985
Winsorized Mean ( 15 / 24 )106.2738888888890.360335901996223294.930059147985
Winsorized Mean ( 16 / 24 )105.5627777777780.23768471296793444.129437100235
Winsorized Mean ( 17 / 24 )105.5627777777780.23768471296793444.129437100235
Winsorized Mean ( 18 / 24 )105.5627777777780.23768471296793444.129437100235
Winsorized Mean ( 19 / 24 )106.008750.171316126159097618.79025855133
Winsorized Mean ( 20 / 24 )106.008750.171316126159097618.79025855133
Winsorized Mean ( 21 / 24 )105.6091666666670.11235001304121940.001374347234
Winsorized Mean ( 22 / 24 )105.6091666666670.11235001304121940.001374347234
Winsorized Mean ( 23 / 24 )105.6091666666670.11235001304121940.001374347234
Winsorized Mean ( 24 / 24 )105.6091666666670.11235001304121940.001374347234
Trimmed Mean ( 1 / 24 )106.3880.466176847346659228.213821869381
Trimmed Mean ( 2 / 24 )106.2982352941180.44685433265022237.881178556959
Trimmed Mean ( 3 / 24 )106.203030303030.423288049063572250.900138895913
Trimmed Mean ( 4 / 24 )106.1018750.394120534587745269.211740289005
Trimmed Mean ( 5 / 24 )106.0772580645160.388598831431998272.973692879154
Trimmed Mean ( 6 / 24 )106.0510.381736198733797277.812270232078
Trimmed Mean ( 7 / 24 )106.0229310344830.37322307446946284.073891157976
Trimmed Mean ( 8 / 24 )105.9928571428570.362649853870175292.27326582848
Trimmed Mean ( 9 / 24 )105.9768518518520.354396646166976299.034578904904
Trimmed Mean ( 10 / 24 )105.9596153846150.343996887102535308.024925100651
Trimmed Mean ( 11 / 24 )105.9410.330831265950805320.226686239968
Trimmed Mean ( 12 / 24 )105.9208333333330.314007192814878337.319767690094
Trimmed Mean ( 13 / 24 )105.8747826086960.298807248735134354.324679394053
Trimmed Mean ( 14 / 24 )105.8245454545450.278727373401774379.670443426465
Trimmed Mean ( 15 / 24 )105.7695238095240.251488242136183420.574428892182
Trimmed Mean ( 16 / 24 )105.7090.212664958597755497.068255612075
Trimmed Mean ( 17 / 24 )105.7263157894740.201002615303478525.994727132508
Trimmed Mean ( 18 / 24 )105.7455555555560.184803818951661572.204384927865
Trimmed Mean ( 19 / 24 )105.7670588235290.161402901176949655.298374764497
Trimmed Mean ( 20 / 24 )105.73843750.151016121078529700.179800307649
Trimmed Mean ( 21 / 24 )105.7060.135435949997496780.487012510006
Trimmed Mean ( 22 / 24 )105.7178571428570.134171332012801787.931785105711
Trimmed Mean ( 23 / 24 )105.7315384615380.131567698055403803.628398339957
Trimmed Mean ( 24 / 24 )105.74750.126850434010671833.639244711642
Median105.79
Midrange109.44
Midmean - Weighted Average at Xnp105.442727272727
Midmean - Weighted Average at X(n+1)p105.442727272727
Midmean - Empirical Distribution Function105.442727272727
Midmean - Empirical Distribution Function - Averaging105.442727272727
Midmean - Empirical Distribution Function - Interpolation105.442727272727
Midmean - Closest Observation105.442727272727
Midmean - True Basic - Statistics Graphics Toolkit105.442727272727
Midmean - MS Excel (old versions)105.442727272727
Number of observations72

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 106.472777777778 & 0.482177962710734 & 220.81635000323 \tabularnewline
Geometric Mean & 106.397038395498 &  &  \tabularnewline
Harmonic Mean & 106.323031895301 &  &  \tabularnewline
Quadratic Mean & 106.550267922913 &  &  \tabularnewline
Winsorized Mean ( 1 / 24 ) & 106.472777777778 & 0.482177962710734 & 220.81635000323 \tabularnewline
Winsorized Mean ( 2 / 24 ) & 106.472777777778 & 0.482177962710734 & 220.81635000323 \tabularnewline
Winsorized Mean ( 3 / 24 ) & 106.472777777778 & 0.482177962710734 & 220.81635000323 \tabularnewline
Winsorized Mean ( 4 / 24 ) & 106.186666666667 & 0.406889994861784 & 260.971437016378 \tabularnewline
Winsorized Mean ( 5 / 24 ) & 106.186666666667 & 0.406889994861784 & 260.971437016378 \tabularnewline
Winsorized Mean ( 6 / 24 ) & 106.186666666667 & 0.406889994861784 & 260.971437016378 \tabularnewline
Winsorized Mean ( 7 / 24 ) & 106.186666666667 & 0.406889994861784 & 260.971437016378 \tabularnewline
Winsorized Mean ( 8 / 24 ) & 106.088888888889 & 0.387891432644997 & 273.501500575762 \tabularnewline
Winsorized Mean ( 9 / 24 ) & 106.088888888889 & 0.387891432644997 & 273.501500575762 \tabularnewline
Winsorized Mean ( 10 / 24 ) & 106.088888888889 & 0.387891432644997 & 273.501500575762 \tabularnewline
Winsorized Mean ( 11 / 24 ) & 106.088888888889 & 0.387891432644997 & 273.501500575762 \tabularnewline
Winsorized Mean ( 12 / 24 ) & 106.273888888889 & 0.360335901996223 & 294.930059147985 \tabularnewline
Winsorized Mean ( 13 / 24 ) & 106.273888888889 & 0.360335901996223 & 294.930059147986 \tabularnewline
Winsorized Mean ( 14 / 24 ) & 106.273888888889 & 0.360335901996223 & 294.930059147985 \tabularnewline
Winsorized Mean ( 15 / 24 ) & 106.273888888889 & 0.360335901996223 & 294.930059147985 \tabularnewline
Winsorized Mean ( 16 / 24 ) & 105.562777777778 & 0.23768471296793 & 444.129437100235 \tabularnewline
Winsorized Mean ( 17 / 24 ) & 105.562777777778 & 0.23768471296793 & 444.129437100235 \tabularnewline
Winsorized Mean ( 18 / 24 ) & 105.562777777778 & 0.23768471296793 & 444.129437100235 \tabularnewline
Winsorized Mean ( 19 / 24 ) & 106.00875 & 0.171316126159097 & 618.79025855133 \tabularnewline
Winsorized Mean ( 20 / 24 ) & 106.00875 & 0.171316126159097 & 618.79025855133 \tabularnewline
Winsorized Mean ( 21 / 24 ) & 105.609166666667 & 0.11235001304121 & 940.001374347234 \tabularnewline
Winsorized Mean ( 22 / 24 ) & 105.609166666667 & 0.11235001304121 & 940.001374347234 \tabularnewline
Winsorized Mean ( 23 / 24 ) & 105.609166666667 & 0.11235001304121 & 940.001374347234 \tabularnewline
Winsorized Mean ( 24 / 24 ) & 105.609166666667 & 0.11235001304121 & 940.001374347234 \tabularnewline
Trimmed Mean ( 1 / 24 ) & 106.388 & 0.466176847346659 & 228.213821869381 \tabularnewline
Trimmed Mean ( 2 / 24 ) & 106.298235294118 & 0.44685433265022 & 237.881178556959 \tabularnewline
Trimmed Mean ( 3 / 24 ) & 106.20303030303 & 0.423288049063572 & 250.900138895913 \tabularnewline
Trimmed Mean ( 4 / 24 ) & 106.101875 & 0.394120534587745 & 269.211740289005 \tabularnewline
Trimmed Mean ( 5 / 24 ) & 106.077258064516 & 0.388598831431998 & 272.973692879154 \tabularnewline
Trimmed Mean ( 6 / 24 ) & 106.051 & 0.381736198733797 & 277.812270232078 \tabularnewline
Trimmed Mean ( 7 / 24 ) & 106.022931034483 & 0.37322307446946 & 284.073891157976 \tabularnewline
Trimmed Mean ( 8 / 24 ) & 105.992857142857 & 0.362649853870175 & 292.27326582848 \tabularnewline
Trimmed Mean ( 9 / 24 ) & 105.976851851852 & 0.354396646166976 & 299.034578904904 \tabularnewline
Trimmed Mean ( 10 / 24 ) & 105.959615384615 & 0.343996887102535 & 308.024925100651 \tabularnewline
Trimmed Mean ( 11 / 24 ) & 105.941 & 0.330831265950805 & 320.226686239968 \tabularnewline
Trimmed Mean ( 12 / 24 ) & 105.920833333333 & 0.314007192814878 & 337.319767690094 \tabularnewline
Trimmed Mean ( 13 / 24 ) & 105.874782608696 & 0.298807248735134 & 354.324679394053 \tabularnewline
Trimmed Mean ( 14 / 24 ) & 105.824545454545 & 0.278727373401774 & 379.670443426465 \tabularnewline
Trimmed Mean ( 15 / 24 ) & 105.769523809524 & 0.251488242136183 & 420.574428892182 \tabularnewline
Trimmed Mean ( 16 / 24 ) & 105.709 & 0.212664958597755 & 497.068255612075 \tabularnewline
Trimmed Mean ( 17 / 24 ) & 105.726315789474 & 0.201002615303478 & 525.994727132508 \tabularnewline
Trimmed Mean ( 18 / 24 ) & 105.745555555556 & 0.184803818951661 & 572.204384927865 \tabularnewline
Trimmed Mean ( 19 / 24 ) & 105.767058823529 & 0.161402901176949 & 655.298374764497 \tabularnewline
Trimmed Mean ( 20 / 24 ) & 105.7384375 & 0.151016121078529 & 700.179800307649 \tabularnewline
Trimmed Mean ( 21 / 24 ) & 105.706 & 0.135435949997496 & 780.487012510006 \tabularnewline
Trimmed Mean ( 22 / 24 ) & 105.717857142857 & 0.134171332012801 & 787.931785105711 \tabularnewline
Trimmed Mean ( 23 / 24 ) & 105.731538461538 & 0.131567698055403 & 803.628398339957 \tabularnewline
Trimmed Mean ( 24 / 24 ) & 105.7475 & 0.126850434010671 & 833.639244711642 \tabularnewline
Median & 105.79 &  &  \tabularnewline
Midrange & 109.44 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 105.442727272727 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 105.442727272727 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 105.442727272727 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 105.442727272727 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 105.442727272727 &  &  \tabularnewline
Midmean - Closest Observation & 105.442727272727 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 105.442727272727 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 105.442727272727 &  &  \tabularnewline
Number of observations & 72 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=214483&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]106.472777777778[/C][C]0.482177962710734[/C][C]220.81635000323[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]106.397038395498[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]106.323031895301[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]106.550267922913[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 24 )[/C][C]106.472777777778[/C][C]0.482177962710734[/C][C]220.81635000323[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 24 )[/C][C]106.472777777778[/C][C]0.482177962710734[/C][C]220.81635000323[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 24 )[/C][C]106.472777777778[/C][C]0.482177962710734[/C][C]220.81635000323[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 24 )[/C][C]106.186666666667[/C][C]0.406889994861784[/C][C]260.971437016378[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 24 )[/C][C]106.186666666667[/C][C]0.406889994861784[/C][C]260.971437016378[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 24 )[/C][C]106.186666666667[/C][C]0.406889994861784[/C][C]260.971437016378[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 24 )[/C][C]106.186666666667[/C][C]0.406889994861784[/C][C]260.971437016378[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 24 )[/C][C]106.088888888889[/C][C]0.387891432644997[/C][C]273.501500575762[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 24 )[/C][C]106.088888888889[/C][C]0.387891432644997[/C][C]273.501500575762[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 24 )[/C][C]106.088888888889[/C][C]0.387891432644997[/C][C]273.501500575762[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 24 )[/C][C]106.088888888889[/C][C]0.387891432644997[/C][C]273.501500575762[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 24 )[/C][C]106.273888888889[/C][C]0.360335901996223[/C][C]294.930059147985[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 24 )[/C][C]106.273888888889[/C][C]0.360335901996223[/C][C]294.930059147986[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 24 )[/C][C]106.273888888889[/C][C]0.360335901996223[/C][C]294.930059147985[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 24 )[/C][C]106.273888888889[/C][C]0.360335901996223[/C][C]294.930059147985[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 24 )[/C][C]105.562777777778[/C][C]0.23768471296793[/C][C]444.129437100235[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 24 )[/C][C]105.562777777778[/C][C]0.23768471296793[/C][C]444.129437100235[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 24 )[/C][C]105.562777777778[/C][C]0.23768471296793[/C][C]444.129437100235[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 24 )[/C][C]106.00875[/C][C]0.171316126159097[/C][C]618.79025855133[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 24 )[/C][C]106.00875[/C][C]0.171316126159097[/C][C]618.79025855133[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 24 )[/C][C]105.609166666667[/C][C]0.11235001304121[/C][C]940.001374347234[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 24 )[/C][C]105.609166666667[/C][C]0.11235001304121[/C][C]940.001374347234[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 24 )[/C][C]105.609166666667[/C][C]0.11235001304121[/C][C]940.001374347234[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 24 )[/C][C]105.609166666667[/C][C]0.11235001304121[/C][C]940.001374347234[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 24 )[/C][C]106.388[/C][C]0.466176847346659[/C][C]228.213821869381[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 24 )[/C][C]106.298235294118[/C][C]0.44685433265022[/C][C]237.881178556959[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 24 )[/C][C]106.20303030303[/C][C]0.423288049063572[/C][C]250.900138895913[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 24 )[/C][C]106.101875[/C][C]0.394120534587745[/C][C]269.211740289005[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 24 )[/C][C]106.077258064516[/C][C]0.388598831431998[/C][C]272.973692879154[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 24 )[/C][C]106.051[/C][C]0.381736198733797[/C][C]277.812270232078[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 24 )[/C][C]106.022931034483[/C][C]0.37322307446946[/C][C]284.073891157976[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 24 )[/C][C]105.992857142857[/C][C]0.362649853870175[/C][C]292.27326582848[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 24 )[/C][C]105.976851851852[/C][C]0.354396646166976[/C][C]299.034578904904[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 24 )[/C][C]105.959615384615[/C][C]0.343996887102535[/C][C]308.024925100651[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 24 )[/C][C]105.941[/C][C]0.330831265950805[/C][C]320.226686239968[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 24 )[/C][C]105.920833333333[/C][C]0.314007192814878[/C][C]337.319767690094[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 24 )[/C][C]105.874782608696[/C][C]0.298807248735134[/C][C]354.324679394053[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 24 )[/C][C]105.824545454545[/C][C]0.278727373401774[/C][C]379.670443426465[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 24 )[/C][C]105.769523809524[/C][C]0.251488242136183[/C][C]420.574428892182[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 24 )[/C][C]105.709[/C][C]0.212664958597755[/C][C]497.068255612075[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 24 )[/C][C]105.726315789474[/C][C]0.201002615303478[/C][C]525.994727132508[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 24 )[/C][C]105.745555555556[/C][C]0.184803818951661[/C][C]572.204384927865[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 24 )[/C][C]105.767058823529[/C][C]0.161402901176949[/C][C]655.298374764497[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 24 )[/C][C]105.7384375[/C][C]0.151016121078529[/C][C]700.179800307649[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 24 )[/C][C]105.706[/C][C]0.135435949997496[/C][C]780.487012510006[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 24 )[/C][C]105.717857142857[/C][C]0.134171332012801[/C][C]787.931785105711[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 24 )[/C][C]105.731538461538[/C][C]0.131567698055403[/C][C]803.628398339957[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 24 )[/C][C]105.7475[/C][C]0.126850434010671[/C][C]833.639244711642[/C][/ROW]
[ROW][C]Median[/C][C]105.79[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]109.44[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]105.442727272727[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]105.442727272727[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]105.442727272727[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]105.442727272727[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]105.442727272727[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]105.442727272727[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]105.442727272727[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]105.442727272727[/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=214483&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=214483&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 Mean106.4727777777780.482177962710734220.81635000323
Geometric Mean106.397038395498
Harmonic Mean106.323031895301
Quadratic Mean106.550267922913
Winsorized Mean ( 1 / 24 )106.4727777777780.482177962710734220.81635000323
Winsorized Mean ( 2 / 24 )106.4727777777780.482177962710734220.81635000323
Winsorized Mean ( 3 / 24 )106.4727777777780.482177962710734220.81635000323
Winsorized Mean ( 4 / 24 )106.1866666666670.406889994861784260.971437016378
Winsorized Mean ( 5 / 24 )106.1866666666670.406889994861784260.971437016378
Winsorized Mean ( 6 / 24 )106.1866666666670.406889994861784260.971437016378
Winsorized Mean ( 7 / 24 )106.1866666666670.406889994861784260.971437016378
Winsorized Mean ( 8 / 24 )106.0888888888890.387891432644997273.501500575762
Winsorized Mean ( 9 / 24 )106.0888888888890.387891432644997273.501500575762
Winsorized Mean ( 10 / 24 )106.0888888888890.387891432644997273.501500575762
Winsorized Mean ( 11 / 24 )106.0888888888890.387891432644997273.501500575762
Winsorized Mean ( 12 / 24 )106.2738888888890.360335901996223294.930059147985
Winsorized Mean ( 13 / 24 )106.2738888888890.360335901996223294.930059147986
Winsorized Mean ( 14 / 24 )106.2738888888890.360335901996223294.930059147985
Winsorized Mean ( 15 / 24 )106.2738888888890.360335901996223294.930059147985
Winsorized Mean ( 16 / 24 )105.5627777777780.23768471296793444.129437100235
Winsorized Mean ( 17 / 24 )105.5627777777780.23768471296793444.129437100235
Winsorized Mean ( 18 / 24 )105.5627777777780.23768471296793444.129437100235
Winsorized Mean ( 19 / 24 )106.008750.171316126159097618.79025855133
Winsorized Mean ( 20 / 24 )106.008750.171316126159097618.79025855133
Winsorized Mean ( 21 / 24 )105.6091666666670.11235001304121940.001374347234
Winsorized Mean ( 22 / 24 )105.6091666666670.11235001304121940.001374347234
Winsorized Mean ( 23 / 24 )105.6091666666670.11235001304121940.001374347234
Winsorized Mean ( 24 / 24 )105.6091666666670.11235001304121940.001374347234
Trimmed Mean ( 1 / 24 )106.3880.466176847346659228.213821869381
Trimmed Mean ( 2 / 24 )106.2982352941180.44685433265022237.881178556959
Trimmed Mean ( 3 / 24 )106.203030303030.423288049063572250.900138895913
Trimmed Mean ( 4 / 24 )106.1018750.394120534587745269.211740289005
Trimmed Mean ( 5 / 24 )106.0772580645160.388598831431998272.973692879154
Trimmed Mean ( 6 / 24 )106.0510.381736198733797277.812270232078
Trimmed Mean ( 7 / 24 )106.0229310344830.37322307446946284.073891157976
Trimmed Mean ( 8 / 24 )105.9928571428570.362649853870175292.27326582848
Trimmed Mean ( 9 / 24 )105.9768518518520.354396646166976299.034578904904
Trimmed Mean ( 10 / 24 )105.9596153846150.343996887102535308.024925100651
Trimmed Mean ( 11 / 24 )105.9410.330831265950805320.226686239968
Trimmed Mean ( 12 / 24 )105.9208333333330.314007192814878337.319767690094
Trimmed Mean ( 13 / 24 )105.8747826086960.298807248735134354.324679394053
Trimmed Mean ( 14 / 24 )105.8245454545450.278727373401774379.670443426465
Trimmed Mean ( 15 / 24 )105.7695238095240.251488242136183420.574428892182
Trimmed Mean ( 16 / 24 )105.7090.212664958597755497.068255612075
Trimmed Mean ( 17 / 24 )105.7263157894740.201002615303478525.994727132508
Trimmed Mean ( 18 / 24 )105.7455555555560.184803818951661572.204384927865
Trimmed Mean ( 19 / 24 )105.7670588235290.161402901176949655.298374764497
Trimmed Mean ( 20 / 24 )105.73843750.151016121078529700.179800307649
Trimmed Mean ( 21 / 24 )105.7060.135435949997496780.487012510006
Trimmed Mean ( 22 / 24 )105.7178571428570.134171332012801787.931785105711
Trimmed Mean ( 23 / 24 )105.7315384615380.131567698055403803.628398339957
Trimmed Mean ( 24 / 24 )105.74750.126850434010671833.639244711642
Median105.79
Midrange109.44
Midmean - Weighted Average at Xnp105.442727272727
Midmean - Weighted Average at X(n+1)p105.442727272727
Midmean - Empirical Distribution Function105.442727272727
Midmean - Empirical Distribution Function - Averaging105.442727272727
Midmean - Empirical Distribution Function - Interpolation105.442727272727
Midmean - Closest Observation105.442727272727
Midmean - True Basic - Statistics Graphics Toolkit105.442727272727
Midmean - MS Excel (old versions)105.442727272727
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')