Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationTue, 14 Mar 2017 12:31:15 +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/2017/Mar/14/t1489494705wuc54iqfczpus1c.htm/, Retrieved Tue, 14 May 2024 02:30:12 +0200
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=, Retrieved Tue, 14 May 2024 02:30:12 +0200
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact0
Dataseries X:
96,16
96,4
96,87
97
97,26
97,42
97,64
97,93
98,1
98,29
98,42
98,49
98,67
99,1
99,37
99,54
99,58
99,77
100,06
100,26
100,57
100,94
101,03
101,12
101,26
101,94
102,26
102,51
102,61
102,76
103,04
103,22
103,47
103,64
103,76
103,85
103,98
104,68
105,07
105,19
105,39
105,66
105,76
105,89
106,04
106,37
106,57
106,67
107,08
107,64
108,47
108,7
108,82
108,99
109,18
109,31
109,5
109,7
109,9
110,09




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 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 & 1 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]1 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 time1 seconds
R Server'Gwilym Jenkins' @ jenkins.wessa.net







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean102.9826666666670.535152434414965192.4361360315
Geometric Mean102.900799658507
Harmonic Mean102.819147644112
Quadratic Mean103.064671606392
Winsorized Mean ( 1 / 20 )102.98350.53359773592596192.99838261362
Winsorized Mean ( 2 / 20 )102.99250.528973722553911194.702488249789
Winsorized Mean ( 3 / 20 )102.9890.525583920632204195.95158062697
Winsorized Mean ( 4 / 20 )102.9936666666670.519654327015264198.196495847982
Winsorized Mean ( 5 / 20 )102.9961666666670.514965529627306200.005943584627
Winsorized Mean ( 6 / 20 )102.9991666666670.507140275876602203.097982089138
Winsorized Mean ( 7 / 20 )103.0131666666670.49722958421256207.17425096458
Winsorized Mean ( 8 / 20 )103.0198333333330.490182802962477210.166151710588
Winsorized Mean ( 9 / 20 )103.0138333333330.478653188890876215.216018036012
Winsorized Mean ( 10 / 20 )102.8971666666670.449240545059994229.046927749866
Winsorized Mean ( 11 / 20 )102.8073333333330.429204089751174239.530181068253
Winsorized Mean ( 12 / 20 )102.7613333333330.40952994045376250.92508064117
Winsorized Mean ( 13 / 20 )102.8328333333330.390578890348272263.283131460687
Winsorized Mean ( 14 / 20 )102.8491666666670.372974703529198275.753732608344
Winsorized Mean ( 15 / 20 )102.8091666666670.353281972468966291.011641347473
Winsorized Mean ( 16 / 20 )102.7798333333330.345455687892893297.519586260799
Winsorized Mean ( 17 / 20 )102.7968333333330.331461452426138310.132091019665
Winsorized Mean ( 18 / 20 )102.8538333333330.313608224020445327.969184018044
Winsorized Mean ( 19 / 20 )102.8316666666670.291232833122421353.090912051942
Winsorized Mean ( 20 / 20 )102.8683333333330.266032066231974386.676443897685
Trimmed Mean ( 1 / 20 )102.977758620690.526591618040172195.555255900093
Trimmed Mean ( 2 / 20 )102.9716071428570.517725782152643198.89217553492
Trimmed Mean ( 3 / 20 )102.960.509536929573883202.065824916957
Trimmed Mean ( 4 / 20 )102.9488461538460.500661451911697205.625669323556
Trimmed Mean ( 5 / 20 )102.93540.49152783133775209.419270766112
Trimmed Mean ( 6 / 20 )102.9202083333330.481250079633717213.860137772168
Trimmed Mean ( 7 / 20 )102.9030434782610.470253695490257218.824529110783
Trimmed Mean ( 8 / 20 )102.8815909090910.458646660645802224.315578280299
Trimmed Mean ( 9 / 20 )102.8569047619050.445164951105572231.053465701777
Trimmed Mean ( 10 / 20 )102.830750.430310768366067238.968572388878
Trimmed Mean ( 11 / 20 )102.8202631578950.418519793407652245.675986602011
Trimmed Mean ( 12 / 20 )102.8222222222220.407641904615545252.236634796405
Trimmed Mean ( 13 / 20 )102.8311764705880.397549930653877258.662292561478
Trimmed Mean ( 14 / 20 )102.83093750.388113551562233264.950649329521
Trimmed Mean ( 15 / 20 )102.8283333333330.378933495312478271.362480766021
Trimmed Mean ( 16 / 20 )102.8310714285710.370534555681238277.520867762289
Trimmed Mean ( 17 / 20 )102.8384615384620.359203688651479286.295672309317
Trimmed Mean ( 18 / 20 )102.8445833333330.345561913309253297.615504985629
Trimmed Mean ( 19 / 20 )102.8431818181820.329749600896828311.882657442122
Trimmed Mean ( 20 / 20 )102.8450.312360705797505329.250760710829
Median102.9
Midrange103.125
Midmean - Weighted Average at Xnp102.716774193548
Midmean - Weighted Average at X(n+1)p102.828333333333
Midmean - Empirical Distribution Function102.716774193548
Midmean - Empirical Distribution Function - Averaging102.828333333333
Midmean - Empirical Distribution Function - Interpolation102.828333333333
Midmean - Closest Observation102.716774193548
Midmean - True Basic - Statistics Graphics Toolkit102.828333333333
Midmean - MS Excel (old versions)102.8309375
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 102.982666666667 & 0.535152434414965 & 192.4361360315 \tabularnewline
Geometric Mean & 102.900799658507 &  &  \tabularnewline
Harmonic Mean & 102.819147644112 &  &  \tabularnewline
Quadratic Mean & 103.064671606392 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 102.9835 & 0.53359773592596 & 192.99838261362 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 102.9925 & 0.528973722553911 & 194.702488249789 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 102.989 & 0.525583920632204 & 195.95158062697 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 102.993666666667 & 0.519654327015264 & 198.196495847982 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 102.996166666667 & 0.514965529627306 & 200.005943584627 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 102.999166666667 & 0.507140275876602 & 203.097982089138 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 103.013166666667 & 0.49722958421256 & 207.17425096458 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 103.019833333333 & 0.490182802962477 & 210.166151710588 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 103.013833333333 & 0.478653188890876 & 215.216018036012 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 102.897166666667 & 0.449240545059994 & 229.046927749866 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 102.807333333333 & 0.429204089751174 & 239.530181068253 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 102.761333333333 & 0.40952994045376 & 250.92508064117 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 102.832833333333 & 0.390578890348272 & 263.283131460687 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 102.849166666667 & 0.372974703529198 & 275.753732608344 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 102.809166666667 & 0.353281972468966 & 291.011641347473 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 102.779833333333 & 0.345455687892893 & 297.519586260799 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 102.796833333333 & 0.331461452426138 & 310.132091019665 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 102.853833333333 & 0.313608224020445 & 327.969184018044 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 102.831666666667 & 0.291232833122421 & 353.090912051942 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 102.868333333333 & 0.266032066231974 & 386.676443897685 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 102.97775862069 & 0.526591618040172 & 195.555255900093 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 102.971607142857 & 0.517725782152643 & 198.89217553492 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 102.96 & 0.509536929573883 & 202.065824916957 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 102.948846153846 & 0.500661451911697 & 205.625669323556 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 102.9354 & 0.49152783133775 & 209.419270766112 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 102.920208333333 & 0.481250079633717 & 213.860137772168 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 102.903043478261 & 0.470253695490257 & 218.824529110783 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 102.881590909091 & 0.458646660645802 & 224.315578280299 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 102.856904761905 & 0.445164951105572 & 231.053465701777 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 102.83075 & 0.430310768366067 & 238.968572388878 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 102.820263157895 & 0.418519793407652 & 245.675986602011 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 102.822222222222 & 0.407641904615545 & 252.236634796405 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 102.831176470588 & 0.397549930653877 & 258.662292561478 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 102.8309375 & 0.388113551562233 & 264.950649329521 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 102.828333333333 & 0.378933495312478 & 271.362480766021 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 102.831071428571 & 0.370534555681238 & 277.520867762289 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 102.838461538462 & 0.359203688651479 & 286.295672309317 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 102.844583333333 & 0.345561913309253 & 297.615504985629 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 102.843181818182 & 0.329749600896828 & 311.882657442122 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 102.845 & 0.312360705797505 & 329.250760710829 \tabularnewline
Median & 102.9 &  &  \tabularnewline
Midrange & 103.125 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 102.716774193548 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 102.828333333333 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 102.716774193548 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 102.828333333333 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 102.828333333333 &  &  \tabularnewline
Midmean - Closest Observation & 102.716774193548 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 102.828333333333 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 102.8309375 &  &  \tabularnewline
Number of observations & 60 &  &  \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]102.982666666667[/C][C]0.535152434414965[/C][C]192.4361360315[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]102.900799658507[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]102.819147644112[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]103.064671606392[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]102.9835[/C][C]0.53359773592596[/C][C]192.99838261362[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]102.9925[/C][C]0.528973722553911[/C][C]194.702488249789[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]102.989[/C][C]0.525583920632204[/C][C]195.95158062697[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]102.993666666667[/C][C]0.519654327015264[/C][C]198.196495847982[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]102.996166666667[/C][C]0.514965529627306[/C][C]200.005943584627[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]102.999166666667[/C][C]0.507140275876602[/C][C]203.097982089138[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]103.013166666667[/C][C]0.49722958421256[/C][C]207.17425096458[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]103.019833333333[/C][C]0.490182802962477[/C][C]210.166151710588[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]103.013833333333[/C][C]0.478653188890876[/C][C]215.216018036012[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]102.897166666667[/C][C]0.449240545059994[/C][C]229.046927749866[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]102.807333333333[/C][C]0.429204089751174[/C][C]239.530181068253[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]102.761333333333[/C][C]0.40952994045376[/C][C]250.92508064117[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]102.832833333333[/C][C]0.390578890348272[/C][C]263.283131460687[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]102.849166666667[/C][C]0.372974703529198[/C][C]275.753732608344[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]102.809166666667[/C][C]0.353281972468966[/C][C]291.011641347473[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]102.779833333333[/C][C]0.345455687892893[/C][C]297.519586260799[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]102.796833333333[/C][C]0.331461452426138[/C][C]310.132091019665[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]102.853833333333[/C][C]0.313608224020445[/C][C]327.969184018044[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]102.831666666667[/C][C]0.291232833122421[/C][C]353.090912051942[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]102.868333333333[/C][C]0.266032066231974[/C][C]386.676443897685[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]102.97775862069[/C][C]0.526591618040172[/C][C]195.555255900093[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]102.971607142857[/C][C]0.517725782152643[/C][C]198.89217553492[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]102.96[/C][C]0.509536929573883[/C][C]202.065824916957[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]102.948846153846[/C][C]0.500661451911697[/C][C]205.625669323556[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]102.9354[/C][C]0.49152783133775[/C][C]209.419270766112[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]102.920208333333[/C][C]0.481250079633717[/C][C]213.860137772168[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]102.903043478261[/C][C]0.470253695490257[/C][C]218.824529110783[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]102.881590909091[/C][C]0.458646660645802[/C][C]224.315578280299[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]102.856904761905[/C][C]0.445164951105572[/C][C]231.053465701777[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]102.83075[/C][C]0.430310768366067[/C][C]238.968572388878[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]102.820263157895[/C][C]0.418519793407652[/C][C]245.675986602011[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]102.822222222222[/C][C]0.407641904615545[/C][C]252.236634796405[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]102.831176470588[/C][C]0.397549930653877[/C][C]258.662292561478[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]102.8309375[/C][C]0.388113551562233[/C][C]264.950649329521[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]102.828333333333[/C][C]0.378933495312478[/C][C]271.362480766021[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]102.831071428571[/C][C]0.370534555681238[/C][C]277.520867762289[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]102.838461538462[/C][C]0.359203688651479[/C][C]286.295672309317[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]102.844583333333[/C][C]0.345561913309253[/C][C]297.615504985629[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]102.843181818182[/C][C]0.329749600896828[/C][C]311.882657442122[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]102.845[/C][C]0.312360705797505[/C][C]329.250760710829[/C][/ROW]
[ROW][C]Median[/C][C]102.9[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]103.125[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]102.716774193548[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]102.828333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]102.716774193548[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]102.828333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]102.828333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]102.716774193548[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]102.828333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]102.8309375[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]60[/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 Mean102.9826666666670.535152434414965192.4361360315
Geometric Mean102.900799658507
Harmonic Mean102.819147644112
Quadratic Mean103.064671606392
Winsorized Mean ( 1 / 20 )102.98350.53359773592596192.99838261362
Winsorized Mean ( 2 / 20 )102.99250.528973722553911194.702488249789
Winsorized Mean ( 3 / 20 )102.9890.525583920632204195.95158062697
Winsorized Mean ( 4 / 20 )102.9936666666670.519654327015264198.196495847982
Winsorized Mean ( 5 / 20 )102.9961666666670.514965529627306200.005943584627
Winsorized Mean ( 6 / 20 )102.9991666666670.507140275876602203.097982089138
Winsorized Mean ( 7 / 20 )103.0131666666670.49722958421256207.17425096458
Winsorized Mean ( 8 / 20 )103.0198333333330.490182802962477210.166151710588
Winsorized Mean ( 9 / 20 )103.0138333333330.478653188890876215.216018036012
Winsorized Mean ( 10 / 20 )102.8971666666670.449240545059994229.046927749866
Winsorized Mean ( 11 / 20 )102.8073333333330.429204089751174239.530181068253
Winsorized Mean ( 12 / 20 )102.7613333333330.40952994045376250.92508064117
Winsorized Mean ( 13 / 20 )102.8328333333330.390578890348272263.283131460687
Winsorized Mean ( 14 / 20 )102.8491666666670.372974703529198275.753732608344
Winsorized Mean ( 15 / 20 )102.8091666666670.353281972468966291.011641347473
Winsorized Mean ( 16 / 20 )102.7798333333330.345455687892893297.519586260799
Winsorized Mean ( 17 / 20 )102.7968333333330.331461452426138310.132091019665
Winsorized Mean ( 18 / 20 )102.8538333333330.313608224020445327.969184018044
Winsorized Mean ( 19 / 20 )102.8316666666670.291232833122421353.090912051942
Winsorized Mean ( 20 / 20 )102.8683333333330.266032066231974386.676443897685
Trimmed Mean ( 1 / 20 )102.977758620690.526591618040172195.555255900093
Trimmed Mean ( 2 / 20 )102.9716071428570.517725782152643198.89217553492
Trimmed Mean ( 3 / 20 )102.960.509536929573883202.065824916957
Trimmed Mean ( 4 / 20 )102.9488461538460.500661451911697205.625669323556
Trimmed Mean ( 5 / 20 )102.93540.49152783133775209.419270766112
Trimmed Mean ( 6 / 20 )102.9202083333330.481250079633717213.860137772168
Trimmed Mean ( 7 / 20 )102.9030434782610.470253695490257218.824529110783
Trimmed Mean ( 8 / 20 )102.8815909090910.458646660645802224.315578280299
Trimmed Mean ( 9 / 20 )102.8569047619050.445164951105572231.053465701777
Trimmed Mean ( 10 / 20 )102.830750.430310768366067238.968572388878
Trimmed Mean ( 11 / 20 )102.8202631578950.418519793407652245.675986602011
Trimmed Mean ( 12 / 20 )102.8222222222220.407641904615545252.236634796405
Trimmed Mean ( 13 / 20 )102.8311764705880.397549930653877258.662292561478
Trimmed Mean ( 14 / 20 )102.83093750.388113551562233264.950649329521
Trimmed Mean ( 15 / 20 )102.8283333333330.378933495312478271.362480766021
Trimmed Mean ( 16 / 20 )102.8310714285710.370534555681238277.520867762289
Trimmed Mean ( 17 / 20 )102.8384615384620.359203688651479286.295672309317
Trimmed Mean ( 18 / 20 )102.8445833333330.345561913309253297.615504985629
Trimmed Mean ( 19 / 20 )102.8431818181820.329749600896828311.882657442122
Trimmed Mean ( 20 / 20 )102.8450.312360705797505329.250760710829
Median102.9
Midrange103.125
Midmean - Weighted Average at Xnp102.716774193548
Midmean - Weighted Average at X(n+1)p102.828333333333
Midmean - Empirical Distribution Function102.716774193548
Midmean - Empirical Distribution Function - Averaging102.828333333333
Midmean - Empirical Distribution Function - Interpolation102.828333333333
Midmean - Closest Observation102.716774193548
Midmean - True Basic - Statistics Graphics Toolkit102.828333333333
Midmean - MS Excel (old versions)102.8309375
Number of observations60



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')