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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 computationWed, 23 Dec 2009 02:32:44 -0700
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/Dec/23/t1261560872m1daxp6fgt2qa25.htm/, Retrieved Mon, 29 Apr 2024 15:26:54 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=70490, Retrieved Mon, 29 Apr 2024 15:26:54 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact132
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Univariate Data Series] [intermediair goed] [2009-12-17 10:48:19] [bd8e774728cf1f2f4e6868fd314defe3]
- RMPD    [Central Tendency] [central tendency ...] [2009-12-23 09:32:44] [a315839f8c359622c3a1e6ed387dd5cd] [Current]
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Dataseries X:
111.9
106.5
96.3
96.6
96.1
102.9
101.9
98.2
110.9
87.2
91.7
108.5
102.8
105.4
129.8
110.9
106
109.1
104.2
105
106.2
105.2
105.6
108.5
112.5
107
108.9
109.9
106.2
112
104.1
105
108.3
102.4
106.7
107.1
115.7
109.7
108.1
114
111.7
109.5
103.3
102.1
104.4
101.5
103.9
106
109.8
106.9
106.7
107
100.7
102.7
96.7
98.4
102
101.6
101.6
105.5




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 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 & 1 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=70490&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' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=70490&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=70490&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' @ 72.249.127.135







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean105.450.796863555085643132.331312339497
Geometric Mean105.273260818069
Harmonic Mean105.096359964446
Quadratic Mean105.627491686587
Winsorized Mean ( 1 / 20 )105.290.675326662952763155.909733431278
Winsorized Mean ( 2 / 20 )105.380.6172007154596170.738622558998
Winsorized Mean ( 3 / 20 )105.3150.598117692441295176.077386325329
Winsorized Mean ( 4 / 20 )105.3016666666670.58642598266534179.565145098218
Winsorized Mean ( 5 / 20 )105.3016666666670.582729267539141180.704269602511
Winsorized Mean ( 6 / 20 )105.4316666666670.543099972415452194.129390575655
Winsorized Mean ( 7 / 20 )105.3616666666670.520256844796336202.518559285678
Winsorized Mean ( 8 / 20 )105.6683333333330.456791139372707231.327458493270
Winsorized Mean ( 9 / 20 )105.6383333333330.407431611305225259.278687274451
Winsorized Mean ( 10 / 20 )105.6383333333330.401635720963722263.020263934330
Winsorized Mean ( 11 / 20 )105.620.398434790757378265.087292701595
Winsorized Mean ( 12 / 20 )105.640.381412776679923276.97027068564
Winsorized Mean ( 13 / 20 )105.5750.363237366168172290.650163868661
Winsorized Mean ( 14 / 20 )105.5516666666670.351746985231695300.078383321865
Winsorized Mean ( 15 / 20 )105.5266666666670.323494921472433326.208109191783
Winsorized Mean ( 16 / 20 )105.6066666666670.310593260161910340.015963680650
Winsorized Mean ( 17 / 20 )105.5783333333330.297229121485654355.208577159655
Winsorized Mean ( 18 / 20 )105.5483333333330.283236856289623372.650419567591
Winsorized Mean ( 19 / 20 )105.3583333333330.216967956532661485.593979023688
Winsorized Mean ( 20 / 20 )105.5250.181030087707450582.914151654897
Trimmed Mean ( 1 / 20 )105.3448275862070.632178903351471166.637682826373
Trimmed Mean ( 2 / 20 )105.4035714285710.57762368263291182.477925676668
Trimmed Mean ( 3 / 20 )105.4166666666670.550450866593825191.509675184966
Trimmed Mean ( 4 / 20 )105.4557692307690.526022766323222200.477576223327
Trimmed Mean ( 5 / 20 )105.5020.499979509784233211.012647389349
Trimmed Mean ( 6 / 20 )105.5520833333330.467906056667821225.583921877437
Trimmed Mean ( 7 / 20 )105.5782608695650.440705550297012239.56644248844
Trimmed Mean ( 8 / 20 )105.6204545454550.412612718220565255.979638729881
Trimmed Mean ( 9 / 20 )105.6119047619050.395990391326198266.703200570608
Trimmed Mean ( 10 / 20 )105.60750.38790012427203272.254359799943
Trimmed Mean ( 11 / 20 )105.6026315789470.378183252450356279.236668717396
Trimmed Mean ( 12 / 20 )105.60.365452535297753288.956813267042
Trimmed Mean ( 13 / 20 )105.5941176470590.352453614512208299.597204566053
Trimmed Mean ( 14 / 20 )105.5968750.339249776398291311.265864700308
Trimmed Mean ( 15 / 20 )105.6033333333330.323468392221378326.471877539922
Trimmed Mean ( 16 / 20 )105.6142857142860.30940779266488341.343328183969
Trimmed Mean ( 17 / 20 )105.6153846153850.292348175334312361.265756130029
Trimmed Mean ( 18 / 20 )105.6208333333330.270599118347125390.322163569811
Trimmed Mean ( 19 / 20 )105.6318181818180.241154004397754438.026390835258
Trimmed Mean ( 20 / 20 )105.6750.225469.666666666667
Median105.8
Midrange108.5
Midmean - Weighted Average at Xnp105.490322580645
Midmean - Weighted Average at X(n+1)p105.603333333333
Midmean - Empirical Distribution Function105.490322580645
Midmean - Empirical Distribution Function - Averaging105.603333333333
Midmean - Empirical Distribution Function - Interpolation105.603333333333
Midmean - Closest Observation105.490322580645
Midmean - True Basic - Statistics Graphics Toolkit105.603333333333
Midmean - MS Excel (old versions)105.596875
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 105.45 & 0.796863555085643 & 132.331312339497 \tabularnewline
Geometric Mean & 105.273260818069 &  &  \tabularnewline
Harmonic Mean & 105.096359964446 &  &  \tabularnewline
Quadratic Mean & 105.627491686587 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 105.29 & 0.675326662952763 & 155.909733431278 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 105.38 & 0.6172007154596 & 170.738622558998 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 105.315 & 0.598117692441295 & 176.077386325329 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 105.301666666667 & 0.58642598266534 & 179.565145098218 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 105.301666666667 & 0.582729267539141 & 180.704269602511 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 105.431666666667 & 0.543099972415452 & 194.129390575655 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 105.361666666667 & 0.520256844796336 & 202.518559285678 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 105.668333333333 & 0.456791139372707 & 231.327458493270 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 105.638333333333 & 0.407431611305225 & 259.278687274451 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 105.638333333333 & 0.401635720963722 & 263.020263934330 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 105.62 & 0.398434790757378 & 265.087292701595 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 105.64 & 0.381412776679923 & 276.97027068564 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 105.575 & 0.363237366168172 & 290.650163868661 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 105.551666666667 & 0.351746985231695 & 300.078383321865 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 105.526666666667 & 0.323494921472433 & 326.208109191783 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 105.606666666667 & 0.310593260161910 & 340.015963680650 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 105.578333333333 & 0.297229121485654 & 355.208577159655 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 105.548333333333 & 0.283236856289623 & 372.650419567591 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 105.358333333333 & 0.216967956532661 & 485.593979023688 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 105.525 & 0.181030087707450 & 582.914151654897 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 105.344827586207 & 0.632178903351471 & 166.637682826373 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 105.403571428571 & 0.57762368263291 & 182.477925676668 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 105.416666666667 & 0.550450866593825 & 191.509675184966 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 105.455769230769 & 0.526022766323222 & 200.477576223327 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 105.502 & 0.499979509784233 & 211.012647389349 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 105.552083333333 & 0.467906056667821 & 225.583921877437 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 105.578260869565 & 0.440705550297012 & 239.56644248844 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 105.620454545455 & 0.412612718220565 & 255.979638729881 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 105.611904761905 & 0.395990391326198 & 266.703200570608 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 105.6075 & 0.38790012427203 & 272.254359799943 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 105.602631578947 & 0.378183252450356 & 279.236668717396 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 105.6 & 0.365452535297753 & 288.956813267042 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 105.594117647059 & 0.352453614512208 & 299.597204566053 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 105.596875 & 0.339249776398291 & 311.265864700308 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 105.603333333333 & 0.323468392221378 & 326.471877539922 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 105.614285714286 & 0.30940779266488 & 341.343328183969 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 105.615384615385 & 0.292348175334312 & 361.265756130029 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 105.620833333333 & 0.270599118347125 & 390.322163569811 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 105.631818181818 & 0.241154004397754 & 438.026390835258 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 105.675 & 0.225 & 469.666666666667 \tabularnewline
Median & 105.8 &  &  \tabularnewline
Midrange & 108.5 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 105.490322580645 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 105.603333333333 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 105.490322580645 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 105.603333333333 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 105.603333333333 &  &  \tabularnewline
Midmean - Closest Observation & 105.490322580645 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 105.603333333333 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 105.596875 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=70490&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]105.45[/C][C]0.796863555085643[/C][C]132.331312339497[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]105.273260818069[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]105.096359964446[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]105.627491686587[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]105.29[/C][C]0.675326662952763[/C][C]155.909733431278[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]105.38[/C][C]0.6172007154596[/C][C]170.738622558998[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]105.315[/C][C]0.598117692441295[/C][C]176.077386325329[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]105.301666666667[/C][C]0.58642598266534[/C][C]179.565145098218[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]105.301666666667[/C][C]0.582729267539141[/C][C]180.704269602511[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]105.431666666667[/C][C]0.543099972415452[/C][C]194.129390575655[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]105.361666666667[/C][C]0.520256844796336[/C][C]202.518559285678[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]105.668333333333[/C][C]0.456791139372707[/C][C]231.327458493270[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]105.638333333333[/C][C]0.407431611305225[/C][C]259.278687274451[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]105.638333333333[/C][C]0.401635720963722[/C][C]263.020263934330[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]105.62[/C][C]0.398434790757378[/C][C]265.087292701595[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]105.64[/C][C]0.381412776679923[/C][C]276.97027068564[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]105.575[/C][C]0.363237366168172[/C][C]290.650163868661[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]105.551666666667[/C][C]0.351746985231695[/C][C]300.078383321865[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]105.526666666667[/C][C]0.323494921472433[/C][C]326.208109191783[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]105.606666666667[/C][C]0.310593260161910[/C][C]340.015963680650[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]105.578333333333[/C][C]0.297229121485654[/C][C]355.208577159655[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]105.548333333333[/C][C]0.283236856289623[/C][C]372.650419567591[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]105.358333333333[/C][C]0.216967956532661[/C][C]485.593979023688[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]105.525[/C][C]0.181030087707450[/C][C]582.914151654897[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]105.344827586207[/C][C]0.632178903351471[/C][C]166.637682826373[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]105.403571428571[/C][C]0.57762368263291[/C][C]182.477925676668[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]105.416666666667[/C][C]0.550450866593825[/C][C]191.509675184966[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]105.455769230769[/C][C]0.526022766323222[/C][C]200.477576223327[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]105.502[/C][C]0.499979509784233[/C][C]211.012647389349[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]105.552083333333[/C][C]0.467906056667821[/C][C]225.583921877437[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]105.578260869565[/C][C]0.440705550297012[/C][C]239.56644248844[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]105.620454545455[/C][C]0.412612718220565[/C][C]255.979638729881[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]105.611904761905[/C][C]0.395990391326198[/C][C]266.703200570608[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]105.6075[/C][C]0.38790012427203[/C][C]272.254359799943[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]105.602631578947[/C][C]0.378183252450356[/C][C]279.236668717396[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]105.6[/C][C]0.365452535297753[/C][C]288.956813267042[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]105.594117647059[/C][C]0.352453614512208[/C][C]299.597204566053[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]105.596875[/C][C]0.339249776398291[/C][C]311.265864700308[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]105.603333333333[/C][C]0.323468392221378[/C][C]326.471877539922[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]105.614285714286[/C][C]0.30940779266488[/C][C]341.343328183969[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]105.615384615385[/C][C]0.292348175334312[/C][C]361.265756130029[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]105.620833333333[/C][C]0.270599118347125[/C][C]390.322163569811[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]105.631818181818[/C][C]0.241154004397754[/C][C]438.026390835258[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]105.675[/C][C]0.225[/C][C]469.666666666667[/C][/ROW]
[ROW][C]Median[/C][C]105.8[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]108.5[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]105.490322580645[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]105.603333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]105.490322580645[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]105.603333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]105.603333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]105.490322580645[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]105.603333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]105.596875[/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=70490&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=70490&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 Mean105.450.796863555085643132.331312339497
Geometric Mean105.273260818069
Harmonic Mean105.096359964446
Quadratic Mean105.627491686587
Winsorized Mean ( 1 / 20 )105.290.675326662952763155.909733431278
Winsorized Mean ( 2 / 20 )105.380.6172007154596170.738622558998
Winsorized Mean ( 3 / 20 )105.3150.598117692441295176.077386325329
Winsorized Mean ( 4 / 20 )105.3016666666670.58642598266534179.565145098218
Winsorized Mean ( 5 / 20 )105.3016666666670.582729267539141180.704269602511
Winsorized Mean ( 6 / 20 )105.4316666666670.543099972415452194.129390575655
Winsorized Mean ( 7 / 20 )105.3616666666670.520256844796336202.518559285678
Winsorized Mean ( 8 / 20 )105.6683333333330.456791139372707231.327458493270
Winsorized Mean ( 9 / 20 )105.6383333333330.407431611305225259.278687274451
Winsorized Mean ( 10 / 20 )105.6383333333330.401635720963722263.020263934330
Winsorized Mean ( 11 / 20 )105.620.398434790757378265.087292701595
Winsorized Mean ( 12 / 20 )105.640.381412776679923276.97027068564
Winsorized Mean ( 13 / 20 )105.5750.363237366168172290.650163868661
Winsorized Mean ( 14 / 20 )105.5516666666670.351746985231695300.078383321865
Winsorized Mean ( 15 / 20 )105.5266666666670.323494921472433326.208109191783
Winsorized Mean ( 16 / 20 )105.6066666666670.310593260161910340.015963680650
Winsorized Mean ( 17 / 20 )105.5783333333330.297229121485654355.208577159655
Winsorized Mean ( 18 / 20 )105.5483333333330.283236856289623372.650419567591
Winsorized Mean ( 19 / 20 )105.3583333333330.216967956532661485.593979023688
Winsorized Mean ( 20 / 20 )105.5250.181030087707450582.914151654897
Trimmed Mean ( 1 / 20 )105.3448275862070.632178903351471166.637682826373
Trimmed Mean ( 2 / 20 )105.4035714285710.57762368263291182.477925676668
Trimmed Mean ( 3 / 20 )105.4166666666670.550450866593825191.509675184966
Trimmed Mean ( 4 / 20 )105.4557692307690.526022766323222200.477576223327
Trimmed Mean ( 5 / 20 )105.5020.499979509784233211.012647389349
Trimmed Mean ( 6 / 20 )105.5520833333330.467906056667821225.583921877437
Trimmed Mean ( 7 / 20 )105.5782608695650.440705550297012239.56644248844
Trimmed Mean ( 8 / 20 )105.6204545454550.412612718220565255.979638729881
Trimmed Mean ( 9 / 20 )105.6119047619050.395990391326198266.703200570608
Trimmed Mean ( 10 / 20 )105.60750.38790012427203272.254359799943
Trimmed Mean ( 11 / 20 )105.6026315789470.378183252450356279.236668717396
Trimmed Mean ( 12 / 20 )105.60.365452535297753288.956813267042
Trimmed Mean ( 13 / 20 )105.5941176470590.352453614512208299.597204566053
Trimmed Mean ( 14 / 20 )105.5968750.339249776398291311.265864700308
Trimmed Mean ( 15 / 20 )105.6033333333330.323468392221378326.471877539922
Trimmed Mean ( 16 / 20 )105.6142857142860.30940779266488341.343328183969
Trimmed Mean ( 17 / 20 )105.6153846153850.292348175334312361.265756130029
Trimmed Mean ( 18 / 20 )105.6208333333330.270599118347125390.322163569811
Trimmed Mean ( 19 / 20 )105.6318181818180.241154004397754438.026390835258
Trimmed Mean ( 20 / 20 )105.6750.225469.666666666667
Median105.8
Midrange108.5
Midmean - Weighted Average at Xnp105.490322580645
Midmean - Weighted Average at X(n+1)p105.603333333333
Midmean - Empirical Distribution Function105.490322580645
Midmean - Empirical Distribution Function - Averaging105.603333333333
Midmean - Empirical Distribution Function - Interpolation105.603333333333
Midmean - Closest Observation105.490322580645
Midmean - True Basic - Statistics Graphics Toolkit105.603333333333
Midmean - MS Excel (old versions)105.596875
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')