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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 computationThu, 22 Oct 2009 14:08:54 -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/22/t1256242285huujq84bbilfc21.htm/, Retrieved Fri, 03 May 2024 00:34:07 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=49818, Retrieved Fri, 03 May 2024 00:34:07 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsKVN WS3
Estimated Impact157
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Central Tendency] [WS3 Q1.1 Central ...] [2009-10-22 07:58:17] [0f9a80199ae32669ca1a3c3995927a06]
-   PD  [Central Tendency] [WS3 Q2 Central Te...] [2009-10-22 18:39:51] [1b4c3bbe3f2ba180dd536c5a6a81a8e6]
-    D      [Central Tendency] [WS3 Q2 Central Te...] [2009-10-22 20:08:54] [f1100e00818182135823a11ccbd0f3b9] [Current]
-   PD        [Central Tendency] [WS3 Q2 Central Te...] [2009-10-23 07:18:30] [1b4c3bbe3f2ba180dd536c5a6a81a8e6]
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Dataseries X:
7,06
2,98
3,22
2,27
1,07
0,58
1,17
0,44
0,97
2,12
3,52
3,39
6,02
2,79
2,67
2,07
0,85
0,80
1,15
0,45
0,95
1,93
3,52
3,23
5,02
2,60
3,29
1,49
0,88
0,91
0,73
0,78
0,91
1,93
3,60
3,29
5,08
3,23
3,59
1,64
1,03
0,97
0,66
0,81
0,83
2,23
3,57
3,20
5,64
3,52
3,13
1,71
1,18
0,75
0,79
0,77
0,65
2,48
3,98
2,69




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=49818&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=49818&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=49818&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 Mean2.246333333333330.19816074720433411.3359147309685
Geometric Mean1.75992811634205
Harmonic Mean1.3675618812354
Quadratic Mean2.71344921947448
Winsorized Mean ( 1 / 20 )2.229166666666670.19164988258616811.6314533386912
Winsorized Mean ( 2 / 20 )2.220833333333330.1868972483748611.8826432847155
Winsorized Mean ( 3 / 20 )2.196333333333330.17818624273442612.3260544676663
Winsorized Mean ( 4 / 20 )2.1930.17699824442935412.3899533979576
Winsorized Mean ( 5 / 20 )2.112166666666670.15538272262269813.5933173972981
Winsorized Mean ( 6 / 20 )2.076166666666670.14787670304412914.0398495768945
Winsorized Mean ( 7 / 20 )2.077333333333330.14732048669610314.1007770196858
Winsorized Mean ( 8 / 20 )2.0760.14665810195845514.1553720679413
Winsorized Mean ( 9 / 20 )2.070.14515119722722614.2609915697735
Winsorized Mean ( 10 / 20 )2.071666666666670.14490268830222914.2969512225040
Winsorized Mean ( 11 / 20 )2.07350.14463060779746614.3365227566743
Winsorized Mean ( 12 / 20 )2.05150.13972204550463814.6827223477193
Winsorized Mean ( 13 / 20 )2.034166666666670.13562020991393514.9989936452506
Winsorized Mean ( 14 / 20 )2.041166666666670.13459042109338315.1657647705140
Winsorized Mean ( 15 / 20 )2.033666666666670.13115824027664815.5054433665556
Winsorized Mean ( 16 / 20 )2.033666666666670.13115824027664815.5054433665556
Winsorized Mean ( 17 / 20 )2.042166666666670.12908458481811415.8203759925647
Winsorized Mean ( 18 / 20 )2.042166666666670.12729965796898616.0422007352463
Winsorized Mean ( 19 / 20 )2.020.12390788450218916.3024331188893
Winsorized Mean ( 20 / 20 )1.990.11354359027552117.5263085760379
Trimmed Mean ( 1 / 20 )2.194482758620690.18440190798062811.9005425846853
Trimmed Mean ( 2 / 20 )2.157321428571430.17531261337175812.3055688183527
Trimmed Mean ( 3 / 20 )2.122037037037040.16716704334117112.6941111993359
Trimmed Mean ( 4 / 20 )2.093461538461540.16132368290121012.9767774998263
Trimmed Mean ( 5 / 20 )2.06360.15433220463582813.3711561036104
Trimmed Mean ( 6 / 20 )2.051458333333330.15312495175374413.3972831327483
Trimmed Mean ( 7 / 20 )2.046086956521740.15354726042696113.3254540057067
Trimmed Mean ( 8 / 20 )2.040.15386184462186813.2586477499572
Trimmed Mean ( 9 / 20 )2.033571428571430.15403961262127513.2016134938694
Trimmed Mean ( 10 / 20 )2.02750.15421960283127413.1468371256163
Trimmed Mean ( 11 / 20 )2.020526315789470.15405008670282113.1160349145878
Trimmed Mean ( 12 / 20 )2.01250.15340131774438713.1191832612119
Trimmed Mean ( 13 / 20 )2.006764705882350.15325739454218913.0940807905352
Trimmed Mean ( 14 / 20 )2.00281250.15348126552099913.0492310784731
Trimmed Mean ( 15 / 20 )1.997333333333330.15331429167123113.0277047988223
Trimmed Mean ( 16 / 20 )1.992142857142860.15321541112794513.0022354962667
Trimmed Mean ( 17 / 20 )1.986153846153850.15212755470133713.0558454716054
Trimmed Mean ( 18 / 20 )1.977916666666670.15015207166604113.1727564243391
Trimmed Mean ( 19 / 20 )1.968181818181820.14663415080871313.4223972200674
Trimmed Mean ( 20 / 20 )1.960.14129290219443513.8718928520756
Median2
Midrange3.75
Midmean - Weighted Average at Xnp1.96129032258065
Midmean - Weighted Average at X(n+1)p1.99733333333333
Midmean - Empirical Distribution Function1.96129032258065
Midmean - Empirical Distribution Function - Averaging1.99733333333333
Midmean - Empirical Distribution Function - Interpolation1.99733333333333
Midmean - Closest Observation1.96129032258065
Midmean - True Basic - Statistics Graphics Toolkit1.99733333333333
Midmean - MS Excel (old versions)2.04181818181818
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 2.24633333333333 & 0.198160747204334 & 11.3359147309685 \tabularnewline
Geometric Mean & 1.75992811634205 &  &  \tabularnewline
Harmonic Mean & 1.3675618812354 &  &  \tabularnewline
Quadratic Mean & 2.71344921947448 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 2.22916666666667 & 0.191649882586168 & 11.6314533386912 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 2.22083333333333 & 0.18689724837486 & 11.8826432847155 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 2.19633333333333 & 0.178186242734426 & 12.3260544676663 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 2.193 & 0.176998244429354 & 12.3899533979576 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 2.11216666666667 & 0.155382722622698 & 13.5933173972981 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 2.07616666666667 & 0.147876703044129 & 14.0398495768945 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 2.07733333333333 & 0.147320486696103 & 14.1007770196858 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 2.076 & 0.146658101958455 & 14.1553720679413 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 2.07 & 0.145151197227226 & 14.2609915697735 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 2.07166666666667 & 0.144902688302229 & 14.2969512225040 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 2.0735 & 0.144630607797466 & 14.3365227566743 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 2.0515 & 0.139722045504638 & 14.6827223477193 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 2.03416666666667 & 0.135620209913935 & 14.9989936452506 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 2.04116666666667 & 0.134590421093383 & 15.1657647705140 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 2.03366666666667 & 0.131158240276648 & 15.5054433665556 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 2.03366666666667 & 0.131158240276648 & 15.5054433665556 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 2.04216666666667 & 0.129084584818114 & 15.8203759925647 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 2.04216666666667 & 0.127299657968986 & 16.0422007352463 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 2.02 & 0.123907884502189 & 16.3024331188893 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 1.99 & 0.113543590275521 & 17.5263085760379 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 2.19448275862069 & 0.184401907980628 & 11.9005425846853 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 2.15732142857143 & 0.175312613371758 & 12.3055688183527 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 2.12203703703704 & 0.167167043341171 & 12.6941111993359 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 2.09346153846154 & 0.161323682901210 & 12.9767774998263 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 2.0636 & 0.154332204635828 & 13.3711561036104 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 2.05145833333333 & 0.153124951753744 & 13.3972831327483 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 2.04608695652174 & 0.153547260426961 & 13.3254540057067 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 2.04 & 0.153861844621868 & 13.2586477499572 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 2.03357142857143 & 0.154039612621275 & 13.2016134938694 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 2.0275 & 0.154219602831274 & 13.1468371256163 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 2.02052631578947 & 0.154050086702821 & 13.1160349145878 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 2.0125 & 0.153401317744387 & 13.1191832612119 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 2.00676470588235 & 0.153257394542189 & 13.0940807905352 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 2.0028125 & 0.153481265520999 & 13.0492310784731 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 1.99733333333333 & 0.153314291671231 & 13.0277047988223 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 1.99214285714286 & 0.153215411127945 & 13.0022354962667 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 1.98615384615385 & 0.152127554701337 & 13.0558454716054 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 1.97791666666667 & 0.150152071666041 & 13.1727564243391 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 1.96818181818182 & 0.146634150808713 & 13.4223972200674 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 1.96 & 0.141292902194435 & 13.8718928520756 \tabularnewline
Median & 2 &  &  \tabularnewline
Midrange & 3.75 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 1.96129032258065 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 1.99733333333333 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 1.96129032258065 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 1.99733333333333 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 1.99733333333333 &  &  \tabularnewline
Midmean - Closest Observation & 1.96129032258065 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 1.99733333333333 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 2.04181818181818 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=49818&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]2.24633333333333[/C][C]0.198160747204334[/C][C]11.3359147309685[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]1.75992811634205[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]1.3675618812354[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]2.71344921947448[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]2.22916666666667[/C][C]0.191649882586168[/C][C]11.6314533386912[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]2.22083333333333[/C][C]0.18689724837486[/C][C]11.8826432847155[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]2.19633333333333[/C][C]0.178186242734426[/C][C]12.3260544676663[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]2.193[/C][C]0.176998244429354[/C][C]12.3899533979576[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]2.11216666666667[/C][C]0.155382722622698[/C][C]13.5933173972981[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]2.07616666666667[/C][C]0.147876703044129[/C][C]14.0398495768945[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]2.07733333333333[/C][C]0.147320486696103[/C][C]14.1007770196858[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]2.076[/C][C]0.146658101958455[/C][C]14.1553720679413[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]2.07[/C][C]0.145151197227226[/C][C]14.2609915697735[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]2.07166666666667[/C][C]0.144902688302229[/C][C]14.2969512225040[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]2.0735[/C][C]0.144630607797466[/C][C]14.3365227566743[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]2.0515[/C][C]0.139722045504638[/C][C]14.6827223477193[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]2.03416666666667[/C][C]0.135620209913935[/C][C]14.9989936452506[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]2.04116666666667[/C][C]0.134590421093383[/C][C]15.1657647705140[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]2.03366666666667[/C][C]0.131158240276648[/C][C]15.5054433665556[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]2.03366666666667[/C][C]0.131158240276648[/C][C]15.5054433665556[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]2.04216666666667[/C][C]0.129084584818114[/C][C]15.8203759925647[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]2.04216666666667[/C][C]0.127299657968986[/C][C]16.0422007352463[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]2.02[/C][C]0.123907884502189[/C][C]16.3024331188893[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]1.99[/C][C]0.113543590275521[/C][C]17.5263085760379[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]2.19448275862069[/C][C]0.184401907980628[/C][C]11.9005425846853[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]2.15732142857143[/C][C]0.175312613371758[/C][C]12.3055688183527[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]2.12203703703704[/C][C]0.167167043341171[/C][C]12.6941111993359[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]2.09346153846154[/C][C]0.161323682901210[/C][C]12.9767774998263[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]2.0636[/C][C]0.154332204635828[/C][C]13.3711561036104[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]2.05145833333333[/C][C]0.153124951753744[/C][C]13.3972831327483[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]2.04608695652174[/C][C]0.153547260426961[/C][C]13.3254540057067[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]2.04[/C][C]0.153861844621868[/C][C]13.2586477499572[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]2.03357142857143[/C][C]0.154039612621275[/C][C]13.2016134938694[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]2.0275[/C][C]0.154219602831274[/C][C]13.1468371256163[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]2.02052631578947[/C][C]0.154050086702821[/C][C]13.1160349145878[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]2.0125[/C][C]0.153401317744387[/C][C]13.1191832612119[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]2.00676470588235[/C][C]0.153257394542189[/C][C]13.0940807905352[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]2.0028125[/C][C]0.153481265520999[/C][C]13.0492310784731[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]1.99733333333333[/C][C]0.153314291671231[/C][C]13.0277047988223[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]1.99214285714286[/C][C]0.153215411127945[/C][C]13.0022354962667[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]1.98615384615385[/C][C]0.152127554701337[/C][C]13.0558454716054[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]1.97791666666667[/C][C]0.150152071666041[/C][C]13.1727564243391[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]1.96818181818182[/C][C]0.146634150808713[/C][C]13.4223972200674[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]1.96[/C][C]0.141292902194435[/C][C]13.8718928520756[/C][/ROW]
[ROW][C]Median[/C][C]2[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]3.75[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]1.96129032258065[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]1.99733333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]1.96129032258065[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]1.99733333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]1.99733333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]1.96129032258065[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]1.99733333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]2.04181818181818[/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=49818&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=49818&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 Mean2.246333333333330.19816074720433411.3359147309685
Geometric Mean1.75992811634205
Harmonic Mean1.3675618812354
Quadratic Mean2.71344921947448
Winsorized Mean ( 1 / 20 )2.229166666666670.19164988258616811.6314533386912
Winsorized Mean ( 2 / 20 )2.220833333333330.1868972483748611.8826432847155
Winsorized Mean ( 3 / 20 )2.196333333333330.17818624273442612.3260544676663
Winsorized Mean ( 4 / 20 )2.1930.17699824442935412.3899533979576
Winsorized Mean ( 5 / 20 )2.112166666666670.15538272262269813.5933173972981
Winsorized Mean ( 6 / 20 )2.076166666666670.14787670304412914.0398495768945
Winsorized Mean ( 7 / 20 )2.077333333333330.14732048669610314.1007770196858
Winsorized Mean ( 8 / 20 )2.0760.14665810195845514.1553720679413
Winsorized Mean ( 9 / 20 )2.070.14515119722722614.2609915697735
Winsorized Mean ( 10 / 20 )2.071666666666670.14490268830222914.2969512225040
Winsorized Mean ( 11 / 20 )2.07350.14463060779746614.3365227566743
Winsorized Mean ( 12 / 20 )2.05150.13972204550463814.6827223477193
Winsorized Mean ( 13 / 20 )2.034166666666670.13562020991393514.9989936452506
Winsorized Mean ( 14 / 20 )2.041166666666670.13459042109338315.1657647705140
Winsorized Mean ( 15 / 20 )2.033666666666670.13115824027664815.5054433665556
Winsorized Mean ( 16 / 20 )2.033666666666670.13115824027664815.5054433665556
Winsorized Mean ( 17 / 20 )2.042166666666670.12908458481811415.8203759925647
Winsorized Mean ( 18 / 20 )2.042166666666670.12729965796898616.0422007352463
Winsorized Mean ( 19 / 20 )2.020.12390788450218916.3024331188893
Winsorized Mean ( 20 / 20 )1.990.11354359027552117.5263085760379
Trimmed Mean ( 1 / 20 )2.194482758620690.18440190798062811.9005425846853
Trimmed Mean ( 2 / 20 )2.157321428571430.17531261337175812.3055688183527
Trimmed Mean ( 3 / 20 )2.122037037037040.16716704334117112.6941111993359
Trimmed Mean ( 4 / 20 )2.093461538461540.16132368290121012.9767774998263
Trimmed Mean ( 5 / 20 )2.06360.15433220463582813.3711561036104
Trimmed Mean ( 6 / 20 )2.051458333333330.15312495175374413.3972831327483
Trimmed Mean ( 7 / 20 )2.046086956521740.15354726042696113.3254540057067
Trimmed Mean ( 8 / 20 )2.040.15386184462186813.2586477499572
Trimmed Mean ( 9 / 20 )2.033571428571430.15403961262127513.2016134938694
Trimmed Mean ( 10 / 20 )2.02750.15421960283127413.1468371256163
Trimmed Mean ( 11 / 20 )2.020526315789470.15405008670282113.1160349145878
Trimmed Mean ( 12 / 20 )2.01250.15340131774438713.1191832612119
Trimmed Mean ( 13 / 20 )2.006764705882350.15325739454218913.0940807905352
Trimmed Mean ( 14 / 20 )2.00281250.15348126552099913.0492310784731
Trimmed Mean ( 15 / 20 )1.997333333333330.15331429167123113.0277047988223
Trimmed Mean ( 16 / 20 )1.992142857142860.15321541112794513.0022354962667
Trimmed Mean ( 17 / 20 )1.986153846153850.15212755470133713.0558454716054
Trimmed Mean ( 18 / 20 )1.977916666666670.15015207166604113.1727564243391
Trimmed Mean ( 19 / 20 )1.968181818181820.14663415080871313.4223972200674
Trimmed Mean ( 20 / 20 )1.960.14129290219443513.8718928520756
Median2
Midrange3.75
Midmean - Weighted Average at Xnp1.96129032258065
Midmean - Weighted Average at X(n+1)p1.99733333333333
Midmean - Empirical Distribution Function1.96129032258065
Midmean - Empirical Distribution Function - Averaging1.99733333333333
Midmean - Empirical Distribution Function - Interpolation1.99733333333333
Midmean - Closest Observation1.96129032258065
Midmean - True Basic - Statistics Graphics Toolkit1.99733333333333
Midmean - MS Excel (old versions)2.04181818181818
Number of observations60



Parameters (Session):
par1 = 0 ; par2 = 36 ;
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')