Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationTue, 11 Oct 2016 13:38:30 +0100
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2016/Oct/11/t1476189527kn2xg62knf0parf.htm/, Retrieved Mon, 29 Apr 2024 05:18:38 +0200
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=, Retrieved Mon, 29 Apr 2024 05:18:38 +0200
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact0
Dataseries X:
2322
2347
2963
1900
2723
2555
2176
2444
1944
2089
1978
2081
2435
2246
2641
1966
2398
2334
2333
2421
1531
2215
1927
1698
2482
1974
2369
2097
2264
1938
2360
2176
1478
2158
1690
1886
2450
1811
2196
1997
2199
1970
2239
1937
1311
2149
1673
2378
2770
1764
2310
1971
1899
2554
1948
2138
1469
2059
1771
1761




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 Mean2121.0543.06557491707149.2516355368387
Geometric Mean2094.31667837541
Harmonic Mean2066.42041432362
Quadratic Mean2146.68979671804
Winsorized Mean ( 1 / 20 )2120.4666666666741.329128636144551.3068321699918
Winsorized Mean ( 2 / 20 )2119.240.844135317454251.8850499228071
Winsorized Mean ( 3 / 20 )2117.7539.176131504540154.0571495619616
Winsorized Mean ( 4 / 20 )2121.4833333333335.716804284345759.3973446348659
Winsorized Mean ( 5 / 20 )2122.8166666666735.402085000894359.9630407817235
Winsorized Mean ( 6 / 20 )2116.4166666666733.830946382639262.5586007180908
Winsorized Mean ( 7 / 20 )2120.0333333333331.680734014875466.9186936242669
Winsorized Mean ( 8 / 20 )2119.6333333333331.463493029175767.3680233586215
Winsorized Mean ( 9 / 20 )2119.3333333333331.028669690296668.3024233551367
Winsorized Mean ( 10 / 20 )2123.6666666666729.391259574228872.2550410370559
Winsorized Mean ( 11 / 20 )2133.226.32857140667581.0222464048762
Winsorized Mean ( 12 / 20 )2131.825.246723790363284.4386787648747
Winsorized Mean ( 13 / 20 )2130.0666666666724.893035200766385.5687805640147
Winsorized Mean ( 14 / 20 )2134.2666666666723.588681891343590.4784199684295
Winsorized Mean ( 15 / 20 )2133.5166666666722.696306124038894.0028150398865
Winsorized Mean ( 16 / 20 )2130.3166666666722.110029061998396.3506950032985
Winsorized Mean ( 17 / 20 )2131.7333333333321.816464350596197.7121360764899
Winsorized Mean ( 18 / 20 )2129.6333333333321.1288616524159100.792620462344
Winsorized Mean ( 19 / 20 )2131.5333333333319.7232041876439108.072365577835
Winsorized Mean ( 20 / 20 )2117.5333333333317.2477209935891122.771775709986
Trimmed Mean ( 1 / 20 )2120.539.661149829620753.4654191597924
Trimmed Mean ( 2 / 20 )2120.5357142857137.59860597966556.3993174489659
Trimmed Mean ( 3 / 20 )2121.2777777777835.358861240863559.9928194329477
Trimmed Mean ( 4 / 20 )2122.6346153846233.406281741063563.5399842412105
Trimmed Mean ( 5 / 20 )2122.9832.390859002792465.5425655681741
Trimmed Mean ( 6 / 20 )2123.0208333333331.208028403996668.0280345124735
Trimmed Mean ( 7 / 20 )2124.4565217391330.197477364035570.3521190239986
Trimmed Mean ( 8 / 20 )2125.3181818181829.526706525310171.9795206416393
Trimmed Mean ( 9 / 20 )2126.3333333333328.689366535810774.1157296268357
Trimmed Mean ( 10 / 20 )2127.527.685875321320376.8442382734296
Trimmed Mean ( 11 / 20 )2128.1052631578926.794401590203179.4235040478009
Trimmed Mean ( 12 / 20 )2127.3333333333326.396608728792380.591160599086
Trimmed Mean ( 13 / 20 )2126.6764705882426.076800070940781.5543496442321
Trimmed Mean ( 14 / 20 )2126.187525.653728486952182.8802527118587
Trimmed Mean ( 15 / 20 )2125.0333333333325.336016947998683.8740097819992
Trimmed Mean ( 16 / 20 )2123.8214285714325.034317904434484.8364008429895
Trimmed Mean ( 17 / 20 )2122.8846153846224.653620543789586.1084322935031
Trimmed Mean ( 18 / 20 )2121.5833333333324.03506772772588.2703288947273
Trimmed Mean ( 19 / 20 )2120.3636363636423.194597954310491.4162703117513
Trimmed Mean ( 20 / 20 )2118.622.283980557200495.0727808508808
Median2143.5
Midrange2137
Midmean - Weighted Average at Xnp2118.64516129032
Midmean - Weighted Average at X(n+1)p2125.03333333333
Midmean - Empirical Distribution Function2118.64516129032
Midmean - Empirical Distribution Function - Averaging2125.03333333333
Midmean - Empirical Distribution Function - Interpolation2125.03333333333
Midmean - Closest Observation2118.64516129032
Midmean - True Basic - Statistics Graphics Toolkit2125.03333333333
Midmean - MS Excel (old versions)2126.1875
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 2121.05 & 43.065574917071 & 49.2516355368387 \tabularnewline
Geometric Mean & 2094.31667837541 &  &  \tabularnewline
Harmonic Mean & 2066.42041432362 &  &  \tabularnewline
Quadratic Mean & 2146.68979671804 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 2120.46666666667 & 41.3291286361445 & 51.3068321699918 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 2119.2 & 40.8441353174542 & 51.8850499228071 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 2117.75 & 39.1761315045401 & 54.0571495619616 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 2121.48333333333 & 35.7168042843457 & 59.3973446348659 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 2122.81666666667 & 35.4020850008943 & 59.9630407817235 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 2116.41666666667 & 33.8309463826392 & 62.5586007180908 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 2120.03333333333 & 31.6807340148754 & 66.9186936242669 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 2119.63333333333 & 31.4634930291757 & 67.3680233586215 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 2119.33333333333 & 31.0286696902966 & 68.3024233551367 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 2123.66666666667 & 29.3912595742288 & 72.2550410370559 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 2133.2 & 26.328571406675 & 81.0222464048762 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 2131.8 & 25.2467237903632 & 84.4386787648747 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 2130.06666666667 & 24.8930352007663 & 85.5687805640147 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 2134.26666666667 & 23.5886818913435 & 90.4784199684295 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 2133.51666666667 & 22.6963061240388 & 94.0028150398865 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 2130.31666666667 & 22.1100290619983 & 96.3506950032985 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 2131.73333333333 & 21.8164643505961 & 97.7121360764899 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 2129.63333333333 & 21.1288616524159 & 100.792620462344 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 2131.53333333333 & 19.7232041876439 & 108.072365577835 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 2117.53333333333 & 17.2477209935891 & 122.771775709986 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 2120.5 & 39.6611498296207 & 53.4654191597924 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 2120.53571428571 & 37.598605979665 & 56.3993174489659 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 2121.27777777778 & 35.3588612408635 & 59.9928194329477 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 2122.63461538462 & 33.4062817410635 & 63.5399842412105 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 2122.98 & 32.3908590027924 & 65.5425655681741 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 2123.02083333333 & 31.2080284039966 & 68.0280345124735 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 2124.45652173913 & 30.1974773640355 & 70.3521190239986 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 2125.31818181818 & 29.5267065253101 & 71.9795206416393 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 2126.33333333333 & 28.6893665358107 & 74.1157296268357 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 2127.5 & 27.6858753213203 & 76.8442382734296 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 2128.10526315789 & 26.7944015902031 & 79.4235040478009 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 2127.33333333333 & 26.3966087287923 & 80.591160599086 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 2126.67647058824 & 26.0768000709407 & 81.5543496442321 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 2126.1875 & 25.6537284869521 & 82.8802527118587 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 2125.03333333333 & 25.3360169479986 & 83.8740097819992 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 2123.82142857143 & 25.0343179044344 & 84.8364008429895 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 2122.88461538462 & 24.6536205437895 & 86.1084322935031 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 2121.58333333333 & 24.035067727725 & 88.2703288947273 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 2120.36363636364 & 23.1945979543104 & 91.4162703117513 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 2118.6 & 22.2839805572004 & 95.0727808508808 \tabularnewline
Median & 2143.5 &  &  \tabularnewline
Midrange & 2137 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 2118.64516129032 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 2125.03333333333 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 2118.64516129032 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 2125.03333333333 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 2125.03333333333 &  &  \tabularnewline
Midmean - Closest Observation & 2118.64516129032 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 2125.03333333333 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 2126.1875 &  &  \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]2121.05[/C][C]43.065574917071[/C][C]49.2516355368387[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]2094.31667837541[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]2066.42041432362[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]2146.68979671804[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]2120.46666666667[/C][C]41.3291286361445[/C][C]51.3068321699918[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]2119.2[/C][C]40.8441353174542[/C][C]51.8850499228071[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]2117.75[/C][C]39.1761315045401[/C][C]54.0571495619616[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]2121.48333333333[/C][C]35.7168042843457[/C][C]59.3973446348659[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]2122.81666666667[/C][C]35.4020850008943[/C][C]59.9630407817235[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]2116.41666666667[/C][C]33.8309463826392[/C][C]62.5586007180908[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]2120.03333333333[/C][C]31.6807340148754[/C][C]66.9186936242669[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]2119.63333333333[/C][C]31.4634930291757[/C][C]67.3680233586215[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]2119.33333333333[/C][C]31.0286696902966[/C][C]68.3024233551367[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]2123.66666666667[/C][C]29.3912595742288[/C][C]72.2550410370559[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]2133.2[/C][C]26.328571406675[/C][C]81.0222464048762[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]2131.8[/C][C]25.2467237903632[/C][C]84.4386787648747[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]2130.06666666667[/C][C]24.8930352007663[/C][C]85.5687805640147[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]2134.26666666667[/C][C]23.5886818913435[/C][C]90.4784199684295[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]2133.51666666667[/C][C]22.6963061240388[/C][C]94.0028150398865[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]2130.31666666667[/C][C]22.1100290619983[/C][C]96.3506950032985[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]2131.73333333333[/C][C]21.8164643505961[/C][C]97.7121360764899[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]2129.63333333333[/C][C]21.1288616524159[/C][C]100.792620462344[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]2131.53333333333[/C][C]19.7232041876439[/C][C]108.072365577835[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]2117.53333333333[/C][C]17.2477209935891[/C][C]122.771775709986[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]2120.5[/C][C]39.6611498296207[/C][C]53.4654191597924[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]2120.53571428571[/C][C]37.598605979665[/C][C]56.3993174489659[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]2121.27777777778[/C][C]35.3588612408635[/C][C]59.9928194329477[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]2122.63461538462[/C][C]33.4062817410635[/C][C]63.5399842412105[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]2122.98[/C][C]32.3908590027924[/C][C]65.5425655681741[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]2123.02083333333[/C][C]31.2080284039966[/C][C]68.0280345124735[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]2124.45652173913[/C][C]30.1974773640355[/C][C]70.3521190239986[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]2125.31818181818[/C][C]29.5267065253101[/C][C]71.9795206416393[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]2126.33333333333[/C][C]28.6893665358107[/C][C]74.1157296268357[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]2127.5[/C][C]27.6858753213203[/C][C]76.8442382734296[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]2128.10526315789[/C][C]26.7944015902031[/C][C]79.4235040478009[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]2127.33333333333[/C][C]26.3966087287923[/C][C]80.591160599086[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]2126.67647058824[/C][C]26.0768000709407[/C][C]81.5543496442321[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]2126.1875[/C][C]25.6537284869521[/C][C]82.8802527118587[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]2125.03333333333[/C][C]25.3360169479986[/C][C]83.8740097819992[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]2123.82142857143[/C][C]25.0343179044344[/C][C]84.8364008429895[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]2122.88461538462[/C][C]24.6536205437895[/C][C]86.1084322935031[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]2121.58333333333[/C][C]24.035067727725[/C][C]88.2703288947273[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]2120.36363636364[/C][C]23.1945979543104[/C][C]91.4162703117513[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]2118.6[/C][C]22.2839805572004[/C][C]95.0727808508808[/C][/ROW]
[ROW][C]Median[/C][C]2143.5[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]2137[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]2118.64516129032[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]2125.03333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]2118.64516129032[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]2125.03333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]2125.03333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]2118.64516129032[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]2125.03333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]2126.1875[/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 Mean2121.0543.06557491707149.2516355368387
Geometric Mean2094.31667837541
Harmonic Mean2066.42041432362
Quadratic Mean2146.68979671804
Winsorized Mean ( 1 / 20 )2120.4666666666741.329128636144551.3068321699918
Winsorized Mean ( 2 / 20 )2119.240.844135317454251.8850499228071
Winsorized Mean ( 3 / 20 )2117.7539.176131504540154.0571495619616
Winsorized Mean ( 4 / 20 )2121.4833333333335.716804284345759.3973446348659
Winsorized Mean ( 5 / 20 )2122.8166666666735.402085000894359.9630407817235
Winsorized Mean ( 6 / 20 )2116.4166666666733.830946382639262.5586007180908
Winsorized Mean ( 7 / 20 )2120.0333333333331.680734014875466.9186936242669
Winsorized Mean ( 8 / 20 )2119.6333333333331.463493029175767.3680233586215
Winsorized Mean ( 9 / 20 )2119.3333333333331.028669690296668.3024233551367
Winsorized Mean ( 10 / 20 )2123.6666666666729.391259574228872.2550410370559
Winsorized Mean ( 11 / 20 )2133.226.32857140667581.0222464048762
Winsorized Mean ( 12 / 20 )2131.825.246723790363284.4386787648747
Winsorized Mean ( 13 / 20 )2130.0666666666724.893035200766385.5687805640147
Winsorized Mean ( 14 / 20 )2134.2666666666723.588681891343590.4784199684295
Winsorized Mean ( 15 / 20 )2133.5166666666722.696306124038894.0028150398865
Winsorized Mean ( 16 / 20 )2130.3166666666722.110029061998396.3506950032985
Winsorized Mean ( 17 / 20 )2131.7333333333321.816464350596197.7121360764899
Winsorized Mean ( 18 / 20 )2129.6333333333321.1288616524159100.792620462344
Winsorized Mean ( 19 / 20 )2131.5333333333319.7232041876439108.072365577835
Winsorized Mean ( 20 / 20 )2117.5333333333317.2477209935891122.771775709986
Trimmed Mean ( 1 / 20 )2120.539.661149829620753.4654191597924
Trimmed Mean ( 2 / 20 )2120.5357142857137.59860597966556.3993174489659
Trimmed Mean ( 3 / 20 )2121.2777777777835.358861240863559.9928194329477
Trimmed Mean ( 4 / 20 )2122.6346153846233.406281741063563.5399842412105
Trimmed Mean ( 5 / 20 )2122.9832.390859002792465.5425655681741
Trimmed Mean ( 6 / 20 )2123.0208333333331.208028403996668.0280345124735
Trimmed Mean ( 7 / 20 )2124.4565217391330.197477364035570.3521190239986
Trimmed Mean ( 8 / 20 )2125.3181818181829.526706525310171.9795206416393
Trimmed Mean ( 9 / 20 )2126.3333333333328.689366535810774.1157296268357
Trimmed Mean ( 10 / 20 )2127.527.685875321320376.8442382734296
Trimmed Mean ( 11 / 20 )2128.1052631578926.794401590203179.4235040478009
Trimmed Mean ( 12 / 20 )2127.3333333333326.396608728792380.591160599086
Trimmed Mean ( 13 / 20 )2126.6764705882426.076800070940781.5543496442321
Trimmed Mean ( 14 / 20 )2126.187525.653728486952182.8802527118587
Trimmed Mean ( 15 / 20 )2125.0333333333325.336016947998683.8740097819992
Trimmed Mean ( 16 / 20 )2123.8214285714325.034317904434484.8364008429895
Trimmed Mean ( 17 / 20 )2122.8846153846224.653620543789586.1084322935031
Trimmed Mean ( 18 / 20 )2121.5833333333324.03506772772588.2703288947273
Trimmed Mean ( 19 / 20 )2120.3636363636423.194597954310491.4162703117513
Trimmed Mean ( 20 / 20 )2118.622.283980557200495.0727808508808
Median2143.5
Midrange2137
Midmean - Weighted Average at Xnp2118.64516129032
Midmean - Weighted Average at X(n+1)p2125.03333333333
Midmean - Empirical Distribution Function2118.64516129032
Midmean - Empirical Distribution Function - Averaging2125.03333333333
Midmean - Empirical Distribution Function - Interpolation2125.03333333333
Midmean - Closest Observation2118.64516129032
Midmean - True Basic - Statistics Graphics Toolkit2125.03333333333
Midmean - MS Excel (old versions)2126.1875
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')