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of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationMon, 10 Dec 2007 15:03:45 -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/2007/Dec/10/t11973233570cedj5cnqqwqnti.htm/, Retrieved Mon, 06 May 2024 20:16:52 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=3068, Retrieved Mon, 06 May 2024 20:16:52 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact195
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [Paper - inflatie ...] [2007-12-10 22:03:45] [3463f71ebce131edf0c83e066f45702c] [Current]
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Dataseries X:
1.7
1.4
1.3
1.4
1.3
1.3
1.4
2.0
1.7
1.8
1.7
1.6
1.7
1.9
1.8
1.7
1.6
1.8
1.6
1.5
1.5
1.3
1.4
1.4
1.3
1.3
1.2
1.1
1.4
1.2
1.5
1.1
1.3
1.5
1.1
1.4
1.3
1.5
1.6
1.7
1.1
1.6
1.3
1.7
1.6
1.7
1.9
1.8
1.9
1.6
1.5
1.6
1.6
1.7
2.0
2.0
1.9
1.7
1.8
1.9
1.7




Summary of compuational 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 compuational 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=3068&T=0

[TABLE]
[ROW][C]Summary of compuational 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=3068&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=3068&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 compuational 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 Mean1.555737704918030.031321058242345649.6706622388224
Geometric Mean1.53624594390677
Harmonic Mean1.51624172584771
Quadratic Mean1.57454130713324
Winsorized Mean ( 1 / 20 )1.555737704918030.031321058242345649.6706622388224
Winsorized Mean ( 2 / 20 )1.555737704918030.031321058242345649.6706622388224
Winsorized Mean ( 3 / 20 )1.550819672131150.030265036078793451.2412959989101
Winsorized Mean ( 4 / 20 )1.557377049180330.028768818160029254.1342032375914
Winsorized Mean ( 5 / 20 )1.557377049180330.028768818160029254.1342032375914
Winsorized Mean ( 6 / 20 )1.56721311475410.026930522983626658.194678050142
Winsorized Mean ( 7 / 20 )1.56721311475410.026930522983626658.194678050142
Winsorized Mean ( 8 / 20 )1.554098360655740.024469650042026663.5112622365492
Winsorized Mean ( 9 / 20 )1.554098360655740.024469650042026663.5112622365492
Winsorized Mean ( 10 / 20 )1.554098360655740.024469650042026663.5112622365491
Winsorized Mean ( 11 / 20 )1.554098360655740.024469650042026663.5112622365491
Winsorized Mean ( 12 / 20 )1.554098360655740.024469650042026663.5112622365492
Winsorized Mean ( 13 / 20 )1.53278688524590.021260974212293172.0939158262863
Winsorized Mean ( 14 / 20 )1.53278688524590.021260974212293172.0939158262863
Winsorized Mean ( 15 / 20 )1.557377049180330.017091687238004491.1189765816334
Winsorized Mean ( 16 / 20 )1.557377049180330.017091687238004491.1189765816334
Winsorized Mean ( 17 / 20 )1.557377049180330.017091687238004491.1189765816334
Winsorized Mean ( 18 / 20 )1.557377049180330.017091687238004491.1189765816334
Winsorized Mean ( 19 / 20 )1.557377049180330.017091687238004491.1189765816334
Winsorized Mean ( 20 / 20 )1.557377049180330.017091687238004491.1189765816334
Trimmed Mean ( 1 / 20 )1.555932203389830.030510098015121750.9972862957918
Trimmed Mean ( 2 / 20 )1.556140350877190.029513340072387252.7266770572377
Trimmed Mean ( 3 / 20 )1.556363636363640.028279942132682255.0341874485308
Trimmed Mean ( 4 / 20 )1.558490566037740.027264489931149357.1619190373037
Trimmed Mean ( 5 / 20 )1.558823529411760.026594481306958458.6145490645047
Trimmed Mean ( 6 / 20 )1.559183673469390.025740457472806260.5732697298254
Trimmed Mean ( 7 / 20 )1.557446808510640.025217771374009761.7598908885263
Trimmed Mean ( 8 / 20 )1.555555555555560.024526949835597963.4222993883184
Trimmed Mean ( 9 / 20 )1.555813953488370.02429568810469464.0366285072529
Trimmed Mean ( 10 / 20 )1.556097560975610.023953405096247564.9635220847738
Trimmed Mean ( 11 / 20 )1.556410256410260.023463547918046366.3331164513782
Trimmed Mean ( 12 / 20 )1.556756756756760.022773377765341568.358623511966
Trimmed Mean ( 13 / 20 )1.557142857142860.021803443674392971.4172898738764
Trimmed Mean ( 14 / 20 )1.560606060606060.021293135337204873.2915108973765
Trimmed Mean ( 15 / 20 )1.564516129032260.020503546557510676.3046590327157
Trimmed Mean ( 16 / 20 )1.565517241379310.020627986912522375.8928754423903
Trimmed Mean ( 17 / 20 )1.566666666666670.020672455764868175.7852228340064
Trimmed Mean ( 18 / 20 )1.5680.02059126028197476.1488116088095
Trimmed Mean ( 19 / 20 )1.569565217391300.020308668108561577.2854826816352
Trimmed Mean ( 20 / 20 )1.571428571428570.019691498217271879.8023875121013
Median1.6
Midrange1.55
Midmean - Weighted Average at Xnp1.57272727272727
Midmean - Weighted Average at X(n+1)p1.57272727272727
Midmean - Empirical Distribution Function1.57272727272727
Midmean - Empirical Distribution Function - Averaging1.57272727272727
Midmean - Empirical Distribution Function - Interpolation1.57272727272727
Midmean - Closest Observation1.51428571428572
Midmean - True Basic - Statistics Graphics Toolkit1.57272727272727
Midmean - MS Excel (old versions)1.57272727272727
Number of observations61

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 1.55573770491803 & 0.0313210582423456 & 49.6706622388224 \tabularnewline
Geometric Mean & 1.53624594390677 &  &  \tabularnewline
Harmonic Mean & 1.51624172584771 &  &  \tabularnewline
Quadratic Mean & 1.57454130713324 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 1.55573770491803 & 0.0313210582423456 & 49.6706622388224 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 1.55573770491803 & 0.0313210582423456 & 49.6706622388224 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 1.55081967213115 & 0.0302650360787934 & 51.2412959989101 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 1.55737704918033 & 0.0287688181600292 & 54.1342032375914 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 1.55737704918033 & 0.0287688181600292 & 54.1342032375914 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 1.5672131147541 & 0.0269305229836266 & 58.194678050142 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 1.5672131147541 & 0.0269305229836266 & 58.194678050142 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 1.55409836065574 & 0.0244696500420266 & 63.5112622365492 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 1.55409836065574 & 0.0244696500420266 & 63.5112622365492 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 1.55409836065574 & 0.0244696500420266 & 63.5112622365491 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 1.55409836065574 & 0.0244696500420266 & 63.5112622365491 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 1.55409836065574 & 0.0244696500420266 & 63.5112622365492 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 1.5327868852459 & 0.0212609742122931 & 72.0939158262863 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 1.5327868852459 & 0.0212609742122931 & 72.0939158262863 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 1.55737704918033 & 0.0170916872380044 & 91.1189765816334 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 1.55737704918033 & 0.0170916872380044 & 91.1189765816334 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 1.55737704918033 & 0.0170916872380044 & 91.1189765816334 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 1.55737704918033 & 0.0170916872380044 & 91.1189765816334 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 1.55737704918033 & 0.0170916872380044 & 91.1189765816334 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 1.55737704918033 & 0.0170916872380044 & 91.1189765816334 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 1.55593220338983 & 0.0305100980151217 & 50.9972862957918 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 1.55614035087719 & 0.0295133400723872 & 52.7266770572377 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 1.55636363636364 & 0.0282799421326822 & 55.0341874485308 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 1.55849056603774 & 0.0272644899311493 & 57.1619190373037 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 1.55882352941176 & 0.0265944813069584 & 58.6145490645047 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 1.55918367346939 & 0.0257404574728062 & 60.5732697298254 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 1.55744680851064 & 0.0252177713740097 & 61.7598908885263 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 1.55555555555556 & 0.0245269498355979 & 63.4222993883184 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 1.55581395348837 & 0.024295688104694 & 64.0366285072529 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 1.55609756097561 & 0.0239534050962475 & 64.9635220847738 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 1.55641025641026 & 0.0234635479180463 & 66.3331164513782 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 1.55675675675676 & 0.0227733777653415 & 68.358623511966 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 1.55714285714286 & 0.0218034436743929 & 71.4172898738764 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 1.56060606060606 & 0.0212931353372048 & 73.2915108973765 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 1.56451612903226 & 0.0205035465575106 & 76.3046590327157 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 1.56551724137931 & 0.0206279869125223 & 75.8928754423903 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 1.56666666666667 & 0.0206724557648681 & 75.7852228340064 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 1.568 & 0.020591260281974 & 76.1488116088095 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 1.56956521739130 & 0.0203086681085615 & 77.2854826816352 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 1.57142857142857 & 0.0196914982172718 & 79.8023875121013 \tabularnewline
Median & 1.6 &  &  \tabularnewline
Midrange & 1.55 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 1.57272727272727 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 1.57272727272727 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 1.57272727272727 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 1.57272727272727 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 1.57272727272727 &  &  \tabularnewline
Midmean - Closest Observation & 1.51428571428572 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 1.57272727272727 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 1.57272727272727 &  &  \tabularnewline
Number of observations & 61 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=3068&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]1.55573770491803[/C][C]0.0313210582423456[/C][C]49.6706622388224[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]1.53624594390677[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]1.51624172584771[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]1.57454130713324[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]1.55573770491803[/C][C]0.0313210582423456[/C][C]49.6706622388224[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]1.55573770491803[/C][C]0.0313210582423456[/C][C]49.6706622388224[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]1.55081967213115[/C][C]0.0302650360787934[/C][C]51.2412959989101[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]1.55737704918033[/C][C]0.0287688181600292[/C][C]54.1342032375914[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]1.55737704918033[/C][C]0.0287688181600292[/C][C]54.1342032375914[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]1.5672131147541[/C][C]0.0269305229836266[/C][C]58.194678050142[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]1.5672131147541[/C][C]0.0269305229836266[/C][C]58.194678050142[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]1.55409836065574[/C][C]0.0244696500420266[/C][C]63.5112622365492[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]1.55409836065574[/C][C]0.0244696500420266[/C][C]63.5112622365492[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]1.55409836065574[/C][C]0.0244696500420266[/C][C]63.5112622365491[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]1.55409836065574[/C][C]0.0244696500420266[/C][C]63.5112622365491[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]1.55409836065574[/C][C]0.0244696500420266[/C][C]63.5112622365492[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]1.5327868852459[/C][C]0.0212609742122931[/C][C]72.0939158262863[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]1.5327868852459[/C][C]0.0212609742122931[/C][C]72.0939158262863[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]1.55737704918033[/C][C]0.0170916872380044[/C][C]91.1189765816334[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]1.55737704918033[/C][C]0.0170916872380044[/C][C]91.1189765816334[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]1.55737704918033[/C][C]0.0170916872380044[/C][C]91.1189765816334[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]1.55737704918033[/C][C]0.0170916872380044[/C][C]91.1189765816334[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]1.55737704918033[/C][C]0.0170916872380044[/C][C]91.1189765816334[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]1.55737704918033[/C][C]0.0170916872380044[/C][C]91.1189765816334[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]1.55593220338983[/C][C]0.0305100980151217[/C][C]50.9972862957918[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]1.55614035087719[/C][C]0.0295133400723872[/C][C]52.7266770572377[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]1.55636363636364[/C][C]0.0282799421326822[/C][C]55.0341874485308[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]1.55849056603774[/C][C]0.0272644899311493[/C][C]57.1619190373037[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]1.55882352941176[/C][C]0.0265944813069584[/C][C]58.6145490645047[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]1.55918367346939[/C][C]0.0257404574728062[/C][C]60.5732697298254[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]1.55744680851064[/C][C]0.0252177713740097[/C][C]61.7598908885263[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]1.55555555555556[/C][C]0.0245269498355979[/C][C]63.4222993883184[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]1.55581395348837[/C][C]0.024295688104694[/C][C]64.0366285072529[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]1.55609756097561[/C][C]0.0239534050962475[/C][C]64.9635220847738[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]1.55641025641026[/C][C]0.0234635479180463[/C][C]66.3331164513782[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]1.55675675675676[/C][C]0.0227733777653415[/C][C]68.358623511966[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]1.55714285714286[/C][C]0.0218034436743929[/C][C]71.4172898738764[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]1.56060606060606[/C][C]0.0212931353372048[/C][C]73.2915108973765[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]1.56451612903226[/C][C]0.0205035465575106[/C][C]76.3046590327157[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]1.56551724137931[/C][C]0.0206279869125223[/C][C]75.8928754423903[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]1.56666666666667[/C][C]0.0206724557648681[/C][C]75.7852228340064[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]1.568[/C][C]0.020591260281974[/C][C]76.1488116088095[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]1.56956521739130[/C][C]0.0203086681085615[/C][C]77.2854826816352[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]1.57142857142857[/C][C]0.0196914982172718[/C][C]79.8023875121013[/C][/ROW]
[ROW][C]Median[/C][C]1.6[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]1.55[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]1.57272727272727[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]1.57272727272727[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]1.57272727272727[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]1.57272727272727[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]1.57272727272727[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]1.51428571428572[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]1.57272727272727[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]1.57272727272727[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]61[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=3068&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=3068&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 Mean1.555737704918030.031321058242345649.6706622388224
Geometric Mean1.53624594390677
Harmonic Mean1.51624172584771
Quadratic Mean1.57454130713324
Winsorized Mean ( 1 / 20 )1.555737704918030.031321058242345649.6706622388224
Winsorized Mean ( 2 / 20 )1.555737704918030.031321058242345649.6706622388224
Winsorized Mean ( 3 / 20 )1.550819672131150.030265036078793451.2412959989101
Winsorized Mean ( 4 / 20 )1.557377049180330.028768818160029254.1342032375914
Winsorized Mean ( 5 / 20 )1.557377049180330.028768818160029254.1342032375914
Winsorized Mean ( 6 / 20 )1.56721311475410.026930522983626658.194678050142
Winsorized Mean ( 7 / 20 )1.56721311475410.026930522983626658.194678050142
Winsorized Mean ( 8 / 20 )1.554098360655740.024469650042026663.5112622365492
Winsorized Mean ( 9 / 20 )1.554098360655740.024469650042026663.5112622365492
Winsorized Mean ( 10 / 20 )1.554098360655740.024469650042026663.5112622365491
Winsorized Mean ( 11 / 20 )1.554098360655740.024469650042026663.5112622365491
Winsorized Mean ( 12 / 20 )1.554098360655740.024469650042026663.5112622365492
Winsorized Mean ( 13 / 20 )1.53278688524590.021260974212293172.0939158262863
Winsorized Mean ( 14 / 20 )1.53278688524590.021260974212293172.0939158262863
Winsorized Mean ( 15 / 20 )1.557377049180330.017091687238004491.1189765816334
Winsorized Mean ( 16 / 20 )1.557377049180330.017091687238004491.1189765816334
Winsorized Mean ( 17 / 20 )1.557377049180330.017091687238004491.1189765816334
Winsorized Mean ( 18 / 20 )1.557377049180330.017091687238004491.1189765816334
Winsorized Mean ( 19 / 20 )1.557377049180330.017091687238004491.1189765816334
Winsorized Mean ( 20 / 20 )1.557377049180330.017091687238004491.1189765816334
Trimmed Mean ( 1 / 20 )1.555932203389830.030510098015121750.9972862957918
Trimmed Mean ( 2 / 20 )1.556140350877190.029513340072387252.7266770572377
Trimmed Mean ( 3 / 20 )1.556363636363640.028279942132682255.0341874485308
Trimmed Mean ( 4 / 20 )1.558490566037740.027264489931149357.1619190373037
Trimmed Mean ( 5 / 20 )1.558823529411760.026594481306958458.6145490645047
Trimmed Mean ( 6 / 20 )1.559183673469390.025740457472806260.5732697298254
Trimmed Mean ( 7 / 20 )1.557446808510640.025217771374009761.7598908885263
Trimmed Mean ( 8 / 20 )1.555555555555560.024526949835597963.4222993883184
Trimmed Mean ( 9 / 20 )1.555813953488370.02429568810469464.0366285072529
Trimmed Mean ( 10 / 20 )1.556097560975610.023953405096247564.9635220847738
Trimmed Mean ( 11 / 20 )1.556410256410260.023463547918046366.3331164513782
Trimmed Mean ( 12 / 20 )1.556756756756760.022773377765341568.358623511966
Trimmed Mean ( 13 / 20 )1.557142857142860.021803443674392971.4172898738764
Trimmed Mean ( 14 / 20 )1.560606060606060.021293135337204873.2915108973765
Trimmed Mean ( 15 / 20 )1.564516129032260.020503546557510676.3046590327157
Trimmed Mean ( 16 / 20 )1.565517241379310.020627986912522375.8928754423903
Trimmed Mean ( 17 / 20 )1.566666666666670.020672455764868175.7852228340064
Trimmed Mean ( 18 / 20 )1.5680.02059126028197476.1488116088095
Trimmed Mean ( 19 / 20 )1.569565217391300.020308668108561577.2854826816352
Trimmed Mean ( 20 / 20 )1.571428571428570.019691498217271879.8023875121013
Median1.6
Midrange1.55
Midmean - Weighted Average at Xnp1.57272727272727
Midmean - Weighted Average at X(n+1)p1.57272727272727
Midmean - Empirical Distribution Function1.57272727272727
Midmean - Empirical Distribution Function - Averaging1.57272727272727
Midmean - Empirical Distribution Function - Interpolation1.57272727272727
Midmean - Closest Observation1.51428571428572
Midmean - True Basic - Statistics Graphics Toolkit1.57272727272727
Midmean - MS Excel (old versions)1.57272727272727
Number of observations61



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')