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Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationFri, 16 Oct 2009 07:22:51 -0600
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2009/Oct/16/t1255699424x9pcb67ravagtgp.htm/, Retrieved Tue, 30 Apr 2024 07:29:42 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=47002, Retrieved Tue, 30 Apr 2024 07:29:42 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact135
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Bivariate Data Series] [Bivariate dataset] [2008-01-05 23:51:08] [74be16979710d4c4e7c6647856088456]
F RMPD  [Univariate Explorative Data Analysis] [Colombia Coffee] [2008-01-07 14:21:11] [74be16979710d4c4e7c6647856088456]
F RMPD    [Univariate Data Series] [] [2009-10-14 08:30:28] [74be16979710d4c4e7c6647856088456]
- RMPD        [Central Tendency] [WS 2 Imp gem] [2009-10-16 13:22:51] [51118f1042b56b16d340924f16263174] [Current]
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Post a new message
Dataseries X:
1076,7
1035,9
1037
1154
1237,2
996,6
1238,2
1153,4
1268,1
1156
1144,5
1232,9
1055,2
1109,7
1079,8
1126,3
1196,8
1130,4
1183,6
1200,9
1426,6
1080,4
1325,4
1230
1125,9
1174,5
1151,9
1439,3
1344,3
1319,1
1257,6
1249,1
1397,1
1348
1548,2
1377,6
1402,9
1167,6
1392,9
1547
1420
1266,4
1280,8
1128,6
1449,5
1511,7
1548,3
1652
1650,5
1370,8
1653,3
1474,3
1418,8
1554,1
1156,6
1223,4
1337,5
1098,9
1037,6
1202,5




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 2 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=47002&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=47002&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=47002&T=0

As an alternative you can also use a QR Code:  

The GUIDs for individual cells are displayed in the table below:

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean1275.9033333333322.119314612069757.6827698195096
Geometric Mean1264.94665353107
Harmonic Mean1254.37047723341
Quadratic Mean1287.16583883611
Winsorized Mean ( 1 / 20 )1276.5366666666721.982160713682958.0714827488309
Winsorized Mean ( 2 / 20 )1276.5233333333321.960916795032558.1270511266668
Winsorized Mean ( 3 / 20 )1271.7333333333320.698335950291161.4413321142104
Winsorized Mean ( 4 / 20 )1272.5220.390810326289462.4065439105854
Winsorized Mean ( 5 / 20 )1274.3033333333320.077535576856263.4691109601246
Winsorized Mean ( 6 / 20 )1274.4933333333319.998372090056663.7298539898168
Winsorized Mean ( 7 / 20 )1270.44519.068735974538766.6245000033744
Winsorized Mean ( 8 / 20 )1267.92517.628702139530771.9238994433288
Winsorized Mean ( 9 / 20 )1265.82516.650835072626876.0217126936148
Winsorized Mean ( 10 / 20 )1266.82515.918371333272679.5825762244961
Winsorized Mean ( 11 / 20 )1264.5715.486990038480081.6536975137176
Winsorized Mean ( 12 / 20 )1263.7115.185311573050583.2192341869835
Winsorized Mean ( 13 / 20 )1263.8415.081343321607083.801553551884
Winsorized Mean ( 14 / 20 )1263.4213.959221037629690.5079156347064
Winsorized Mean ( 15 / 20 )1263.8213.450584554537393.960228633608
Winsorized Mean ( 16 / 20 )1263.113.206879092625695.6395520199229
Winsorized Mean ( 17 / 20 )1258.93512.4718625290492100.942020253006
Winsorized Mean ( 18 / 20 )1257.49512.0593287201565104.275704658267
Winsorized Mean ( 19 / 20 )1250.46510.9085831092758114.631294227085
Winsorized Mean ( 20 / 20 )1252.8983333333310.1937832754598122.908080295323
Trimmed Mean ( 1 / 20 )1274.2120689655221.381437335650159.5943129997615
Trimmed Mean ( 2 / 20 )1271.7214285714320.635414287579461.6281025836678
Trimmed Mean ( 3 / 20 )1269.0537037037019.716499901466364.3650602310669
Trimmed Mean ( 4 / 20 )1268.0230769230819.200630530941166.0406998030459
Trimmed Mean ( 5 / 20 )1266.67418.667418699379967.8548020162035
Trimmed Mean ( 6 / 20 )1264.7666666666718.089563018191669.9169275341127
Trimmed Mean ( 7 / 20 )1262.6521739130417.36454902083372.7143660568544
Trimmed Mean ( 8 / 20 )1261.1340909090916.718348006783475.434133228797
Trimmed Mean ( 9 / 20 )1259.9214285714316.290742023496877.339720115523
Trimmed Mean ( 10 / 20 )1258.937515.981828097152278.7730597743278
Trimmed Mean ( 11 / 20 )1257.6921052631615.736197131604279.9235097746228
Trimmed Mean ( 12 / 20 )1256.6515.490190700456581.1255344947412
Trimmed Mean ( 13 / 20 )1255.6117647058815.199660356409182.6078830226257
Trimmed Mean ( 14 / 20 )1254.42514.785490380993584.8416229476258
Trimmed Mean ( 15 / 20 )1253.1414.490741078754286.4786689093016
Trimmed Mean ( 16 / 20 )1251.6142857142914.162920806625888.3726106220085
Trimmed Mean ( 17 / 20 )1249.9576923076913.698159531711391.2500463594423
Trimmed Mean ( 18 / 20 )1248.637513.216662754490794.474492025284
Trimmed Mean ( 19 / 20 )1247.2954545454512.559680003355999.3094930931506
Trimmed Mean ( 20 / 20 )1246.79511.9765526957336104.102994549019
Median1237.7
Midrange1324.95
Midmean - Weighted Average at Xnp1249.63548387097
Midmean - Weighted Average at X(n+1)p1253.14
Midmean - Empirical Distribution Function1249.63548387097
Midmean - Empirical Distribution Function - Averaging1253.14
Midmean - Empirical Distribution Function - Interpolation1253.14
Midmean - Closest Observation1249.63548387097
Midmean - True Basic - Statistics Graphics Toolkit1253.14
Midmean - MS Excel (old versions)1254.425
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 1275.90333333333 & 22.1193146120697 & 57.6827698195096 \tabularnewline
Geometric Mean & 1264.94665353107 &  &  \tabularnewline
Harmonic Mean & 1254.37047723341 &  &  \tabularnewline
Quadratic Mean & 1287.16583883611 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 1276.53666666667 & 21.9821607136829 & 58.0714827488309 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 1276.52333333333 & 21.9609167950325 & 58.1270511266668 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 1271.73333333333 & 20.6983359502911 & 61.4413321142104 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 1272.52 & 20.3908103262894 & 62.4065439105854 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 1274.30333333333 & 20.0775355768562 & 63.4691109601246 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 1274.49333333333 & 19.9983720900566 & 63.7298539898168 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 1270.445 & 19.0687359745387 & 66.6245000033744 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 1267.925 & 17.6287021395307 & 71.9238994433288 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 1265.825 & 16.6508350726268 & 76.0217126936148 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 1266.825 & 15.9183713332726 & 79.5825762244961 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 1264.57 & 15.4869900384800 & 81.6536975137176 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 1263.71 & 15.1853115730505 & 83.2192341869835 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 1263.84 & 15.0813433216070 & 83.801553551884 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 1263.42 & 13.9592210376296 & 90.5079156347064 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 1263.82 & 13.4505845545373 & 93.960228633608 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 1263.1 & 13.2068790926256 & 95.6395520199229 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 1258.935 & 12.4718625290492 & 100.942020253006 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 1257.495 & 12.0593287201565 & 104.275704658267 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 1250.465 & 10.9085831092758 & 114.631294227085 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 1252.89833333333 & 10.1937832754598 & 122.908080295323 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 1274.21206896552 & 21.3814373356501 & 59.5943129997615 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 1271.72142857143 & 20.6354142875794 & 61.6281025836678 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 1269.05370370370 & 19.7164999014663 & 64.3650602310669 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 1268.02307692308 & 19.2006305309411 & 66.0406998030459 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 1266.674 & 18.6674186993799 & 67.8548020162035 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 1264.76666666667 & 18.0895630181916 & 69.9169275341127 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 1262.65217391304 & 17.364549020833 & 72.7143660568544 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 1261.13409090909 & 16.7183480067834 & 75.434133228797 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 1259.92142857143 & 16.2907420234968 & 77.339720115523 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 1258.9375 & 15.9818280971522 & 78.7730597743278 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 1257.69210526316 & 15.7361971316042 & 79.9235097746228 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 1256.65 & 15.4901907004565 & 81.1255344947412 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 1255.61176470588 & 15.1996603564091 & 82.6078830226257 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 1254.425 & 14.7854903809935 & 84.8416229476258 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 1253.14 & 14.4907410787542 & 86.4786689093016 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 1251.61428571429 & 14.1629208066258 & 88.3726106220085 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 1249.95769230769 & 13.6981595317113 & 91.2500463594423 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 1248.6375 & 13.2166627544907 & 94.474492025284 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 1247.29545454545 & 12.5596800033559 & 99.3094930931506 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 1246.795 & 11.9765526957336 & 104.102994549019 \tabularnewline
Median & 1237.7 &  &  \tabularnewline
Midrange & 1324.95 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 1249.63548387097 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 1253.14 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 1249.63548387097 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 1253.14 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 1253.14 &  &  \tabularnewline
Midmean - Closest Observation & 1249.63548387097 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 1253.14 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 1254.425 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=47002&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]1275.90333333333[/C][C]22.1193146120697[/C][C]57.6827698195096[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]1264.94665353107[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]1254.37047723341[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]1287.16583883611[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]1276.53666666667[/C][C]21.9821607136829[/C][C]58.0714827488309[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]1276.52333333333[/C][C]21.9609167950325[/C][C]58.1270511266668[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]1271.73333333333[/C][C]20.6983359502911[/C][C]61.4413321142104[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]1272.52[/C][C]20.3908103262894[/C][C]62.4065439105854[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]1274.30333333333[/C][C]20.0775355768562[/C][C]63.4691109601246[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]1274.49333333333[/C][C]19.9983720900566[/C][C]63.7298539898168[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]1270.445[/C][C]19.0687359745387[/C][C]66.6245000033744[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]1267.925[/C][C]17.6287021395307[/C][C]71.9238994433288[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]1265.825[/C][C]16.6508350726268[/C][C]76.0217126936148[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]1266.825[/C][C]15.9183713332726[/C][C]79.5825762244961[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]1264.57[/C][C]15.4869900384800[/C][C]81.6536975137176[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]1263.71[/C][C]15.1853115730505[/C][C]83.2192341869835[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]1263.84[/C][C]15.0813433216070[/C][C]83.801553551884[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]1263.42[/C][C]13.9592210376296[/C][C]90.5079156347064[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]1263.82[/C][C]13.4505845545373[/C][C]93.960228633608[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]1263.1[/C][C]13.2068790926256[/C][C]95.6395520199229[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]1258.935[/C][C]12.4718625290492[/C][C]100.942020253006[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]1257.495[/C][C]12.0593287201565[/C][C]104.275704658267[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]1250.465[/C][C]10.9085831092758[/C][C]114.631294227085[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]1252.89833333333[/C][C]10.1937832754598[/C][C]122.908080295323[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]1274.21206896552[/C][C]21.3814373356501[/C][C]59.5943129997615[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]1271.72142857143[/C][C]20.6354142875794[/C][C]61.6281025836678[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]1269.05370370370[/C][C]19.7164999014663[/C][C]64.3650602310669[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]1268.02307692308[/C][C]19.2006305309411[/C][C]66.0406998030459[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]1266.674[/C][C]18.6674186993799[/C][C]67.8548020162035[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]1264.76666666667[/C][C]18.0895630181916[/C][C]69.9169275341127[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]1262.65217391304[/C][C]17.364549020833[/C][C]72.7143660568544[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]1261.13409090909[/C][C]16.7183480067834[/C][C]75.434133228797[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]1259.92142857143[/C][C]16.2907420234968[/C][C]77.339720115523[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]1258.9375[/C][C]15.9818280971522[/C][C]78.7730597743278[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]1257.69210526316[/C][C]15.7361971316042[/C][C]79.9235097746228[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]1256.65[/C][C]15.4901907004565[/C][C]81.1255344947412[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]1255.61176470588[/C][C]15.1996603564091[/C][C]82.6078830226257[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]1254.425[/C][C]14.7854903809935[/C][C]84.8416229476258[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]1253.14[/C][C]14.4907410787542[/C][C]86.4786689093016[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]1251.61428571429[/C][C]14.1629208066258[/C][C]88.3726106220085[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]1249.95769230769[/C][C]13.6981595317113[/C][C]91.2500463594423[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]1248.6375[/C][C]13.2166627544907[/C][C]94.474492025284[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]1247.29545454545[/C][C]12.5596800033559[/C][C]99.3094930931506[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]1246.795[/C][C]11.9765526957336[/C][C]104.102994549019[/C][/ROW]
[ROW][C]Median[/C][C]1237.7[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]1324.95[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]1249.63548387097[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]1253.14[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]1249.63548387097[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]1253.14[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]1253.14[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]1249.63548387097[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]1253.14[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]1254.425[/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=47002&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=47002&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 Mean1275.9033333333322.119314612069757.6827698195096
Geometric Mean1264.94665353107
Harmonic Mean1254.37047723341
Quadratic Mean1287.16583883611
Winsorized Mean ( 1 / 20 )1276.5366666666721.982160713682958.0714827488309
Winsorized Mean ( 2 / 20 )1276.5233333333321.960916795032558.1270511266668
Winsorized Mean ( 3 / 20 )1271.7333333333320.698335950291161.4413321142104
Winsorized Mean ( 4 / 20 )1272.5220.390810326289462.4065439105854
Winsorized Mean ( 5 / 20 )1274.3033333333320.077535576856263.4691109601246
Winsorized Mean ( 6 / 20 )1274.4933333333319.998372090056663.7298539898168
Winsorized Mean ( 7 / 20 )1270.44519.068735974538766.6245000033744
Winsorized Mean ( 8 / 20 )1267.92517.628702139530771.9238994433288
Winsorized Mean ( 9 / 20 )1265.82516.650835072626876.0217126936148
Winsorized Mean ( 10 / 20 )1266.82515.918371333272679.5825762244961
Winsorized Mean ( 11 / 20 )1264.5715.486990038480081.6536975137176
Winsorized Mean ( 12 / 20 )1263.7115.185311573050583.2192341869835
Winsorized Mean ( 13 / 20 )1263.8415.081343321607083.801553551884
Winsorized Mean ( 14 / 20 )1263.4213.959221037629690.5079156347064
Winsorized Mean ( 15 / 20 )1263.8213.450584554537393.960228633608
Winsorized Mean ( 16 / 20 )1263.113.206879092625695.6395520199229
Winsorized Mean ( 17 / 20 )1258.93512.4718625290492100.942020253006
Winsorized Mean ( 18 / 20 )1257.49512.0593287201565104.275704658267
Winsorized Mean ( 19 / 20 )1250.46510.9085831092758114.631294227085
Winsorized Mean ( 20 / 20 )1252.8983333333310.1937832754598122.908080295323
Trimmed Mean ( 1 / 20 )1274.2120689655221.381437335650159.5943129997615
Trimmed Mean ( 2 / 20 )1271.7214285714320.635414287579461.6281025836678
Trimmed Mean ( 3 / 20 )1269.0537037037019.716499901466364.3650602310669
Trimmed Mean ( 4 / 20 )1268.0230769230819.200630530941166.0406998030459
Trimmed Mean ( 5 / 20 )1266.67418.667418699379967.8548020162035
Trimmed Mean ( 6 / 20 )1264.7666666666718.089563018191669.9169275341127
Trimmed Mean ( 7 / 20 )1262.6521739130417.36454902083372.7143660568544
Trimmed Mean ( 8 / 20 )1261.1340909090916.718348006783475.434133228797
Trimmed Mean ( 9 / 20 )1259.9214285714316.290742023496877.339720115523
Trimmed Mean ( 10 / 20 )1258.937515.981828097152278.7730597743278
Trimmed Mean ( 11 / 20 )1257.6921052631615.736197131604279.9235097746228
Trimmed Mean ( 12 / 20 )1256.6515.490190700456581.1255344947412
Trimmed Mean ( 13 / 20 )1255.6117647058815.199660356409182.6078830226257
Trimmed Mean ( 14 / 20 )1254.42514.785490380993584.8416229476258
Trimmed Mean ( 15 / 20 )1253.1414.490741078754286.4786689093016
Trimmed Mean ( 16 / 20 )1251.6142857142914.162920806625888.3726106220085
Trimmed Mean ( 17 / 20 )1249.9576923076913.698159531711391.2500463594423
Trimmed Mean ( 18 / 20 )1248.637513.216662754490794.474492025284
Trimmed Mean ( 19 / 20 )1247.2954545454512.559680003355999.3094930931506
Trimmed Mean ( 20 / 20 )1246.79511.9765526957336104.102994549019
Median1237.7
Midrange1324.95
Midmean - Weighted Average at Xnp1249.63548387097
Midmean - Weighted Average at X(n+1)p1253.14
Midmean - Empirical Distribution Function1249.63548387097
Midmean - Empirical Distribution Function - Averaging1253.14
Midmean - Empirical Distribution Function - Interpolation1253.14
Midmean - Closest Observation1249.63548387097
Midmean - True Basic - Statistics Graphics Toolkit1253.14
Midmean - MS Excel (old versions)1254.425
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')