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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 computationMon, 20 Oct 2008 08:12:16 -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/2008/Oct/20/t1224511963obiqjrzmv8g906c.htm/, Retrieved Sun, 19 May 2024 16:11:48 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=17329, Retrieved Sun, 19 May 2024 16:11:48 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact158
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
F     [Univariate Data Series] [Werkloosheid oude...] [2008-10-13 15:46:01] [7d3039e6253bb5fb3b26df1537d500b4]
- RMPD    [Central Tendency] [Central tendency ...] [2008-10-20 14:12:16] [35348cd8592af0baf5f138bd59921307] [Current]
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Dataseries X:
7.0
6.9
6.7
6.6
6.5
6.4
6.5
6.5
6.6
6.7
6.8
7.2
7.6
7.6
7.3
6.4
6.1
6.3
7.1
7.5
7.4
7.1
6.8
6.9
7.2
7.4
7.3
6.9
6.9
6.8
7.1
7.2
7.1
7.0
6.9
7.0
7.4
7.5
7.5
7.4
7.3
7.0
6.7
6.5
6.5
6.5
6.6
6.8
6.9
6.9
6.8
6.8
6.5
6.1
6.0
5.9
5.8
5.9
5.9
6.2




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=17329&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=17329&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=17329&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 Mean6.811666666666670.0600419658637476113.448428422952
Geometric Mean6.79575516609378
Harmonic Mean6.7795440799398
Quadratic Mean6.82726153007192
Winsorized Mean ( 1 / 20 )6.813333333333330.0595874075095568114.341831908706
Winsorized Mean ( 2 / 20 )6.810.058883203364101115.652675312020
Winsorized Mean ( 3 / 20 )6.810.058883203364101115.652675312020
Winsorized Mean ( 4 / 20 )6.816666666666670.0572025179538773119.167248409641
Winsorized Mean ( 5 / 20 )6.816666666666670.0536343904064822127.095071184827
Winsorized Mean ( 6 / 20 )6.816666666666670.0536343904064822127.095071184827
Winsorized Mean ( 7 / 20 )6.828333333333330.0510948860679575133.640249716018
Winsorized Mean ( 8 / 20 )6.841666666666670.0484384207281424141.244626968024
Winsorized Mean ( 9 / 20 )6.841666666666670.0428696399141088159.592352078866
Winsorized Mean ( 10 / 20 )6.841666666666670.0428696399141088159.592352078866
Winsorized Mean ( 11 / 20 )6.860.039858506808105172.108805606462
Winsorized Mean ( 12 / 20 )6.840.0362975773887705188.442328443554
Winsorized Mean ( 13 / 20 )6.840.0362975773887705188.442328443554
Winsorized Mean ( 14 / 20 )6.840.0362975773887705188.442328443554
Winsorized Mean ( 15 / 20 )6.8150.0323142234866942210.897842023224
Winsorized Mean ( 16 / 20 )6.8150.0323142234866942210.897842023224
Winsorized Mean ( 17 / 20 )6.8150.0323142234866942210.897842023224
Winsorized Mean ( 18 / 20 )6.8450.0275583612872057248.381967587379
Winsorized Mean ( 19 / 20 )6.813333333333330.0228563021099075298.094298043951
Winsorized Mean ( 20 / 20 )6.813333333333330.0228563021099075298.094298043951
Trimmed Mean ( 1 / 20 )6.815517241379310.0579860489791513117.537189744206
Trimmed Mean ( 2 / 20 )6.817857142857140.0560094578549215121.726890492622
Trimmed Mean ( 3 / 20 )6.822222222222220.0540250392724559126.278894270059
Trimmed Mean ( 4 / 20 )6.826923076923080.0515312572349303132.481205451659
Trimmed Mean ( 5 / 20 )6.830.0490938293641131139.121353711158
Trimmed Mean ( 6 / 20 )6.833333333333330.0472969093697866144.477375464590
Trimmed Mean ( 7 / 20 )6.836956521739130.0449754302922462152.015366552654
Trimmed Mean ( 8 / 20 )6.838636363636360.0427905945251913159.816343743726
Trimmed Mean ( 9 / 20 )6.838095238095240.0407468575350585167.818959589994
Trimmed Mean ( 10 / 20 )6.83750.039660013447636172.402866404161
Trimmed Mean ( 11 / 20 )6.836842105263160.0381695425396952179.117737608541
Trimmed Mean ( 12 / 20 )6.833333333333330.0369469804595635184.949710323745
Trimmed Mean ( 13 / 20 )6.832352941176470.0362504135412626188.476551678492
Trimmed Mean ( 14 / 20 )6.831250.0351945915474743194.099425497957
Trimmed Mean ( 15 / 20 )6.830.0336137629174608203.19058050035
Trimmed Mean ( 16 / 20 )6.832142857142860.0325517786266918209.885393222128
Trimmed Mean ( 17 / 20 )6.834615384615380.0308556478771255221.502896708973
Trimmed Mean ( 18 / 20 )6.83750.0281124166697652243.219929482395
Trimmed Mean ( 19 / 20 )6.836363636363640.0259415381239457263.529618162974
Trimmed Mean ( 20 / 20 )6.840.0244948974278318279.241830677282
Median6.85
Midrange6.7
Midmean - Weighted Average at Xnp6.79117647058824
Midmean - Weighted Average at X(n+1)p6.79117647058824
Midmean - Empirical Distribution Function6.79117647058824
Midmean - Empirical Distribution Function - Averaging6.79117647058824
Midmean - Empirical Distribution Function - Interpolation6.79117647058824
Midmean - Closest Observation6.79117647058824
Midmean - True Basic - Statistics Graphics Toolkit6.79117647058824
Midmean - MS Excel (old versions)6.82432432432432
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 6.81166666666667 & 0.0600419658637476 & 113.448428422952 \tabularnewline
Geometric Mean & 6.79575516609378 &  &  \tabularnewline
Harmonic Mean & 6.7795440799398 &  &  \tabularnewline
Quadratic Mean & 6.82726153007192 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 6.81333333333333 & 0.0595874075095568 & 114.341831908706 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 6.81 & 0.058883203364101 & 115.652675312020 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 6.81 & 0.058883203364101 & 115.652675312020 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 6.81666666666667 & 0.0572025179538773 & 119.167248409641 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 6.81666666666667 & 0.0536343904064822 & 127.095071184827 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 6.81666666666667 & 0.0536343904064822 & 127.095071184827 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 6.82833333333333 & 0.0510948860679575 & 133.640249716018 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 6.84166666666667 & 0.0484384207281424 & 141.244626968024 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 6.84166666666667 & 0.0428696399141088 & 159.592352078866 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 6.84166666666667 & 0.0428696399141088 & 159.592352078866 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 6.86 & 0.039858506808105 & 172.108805606462 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 6.84 & 0.0362975773887705 & 188.442328443554 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 6.84 & 0.0362975773887705 & 188.442328443554 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 6.84 & 0.0362975773887705 & 188.442328443554 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 6.815 & 0.0323142234866942 & 210.897842023224 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 6.815 & 0.0323142234866942 & 210.897842023224 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 6.815 & 0.0323142234866942 & 210.897842023224 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 6.845 & 0.0275583612872057 & 248.381967587379 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 6.81333333333333 & 0.0228563021099075 & 298.094298043951 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 6.81333333333333 & 0.0228563021099075 & 298.094298043951 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 6.81551724137931 & 0.0579860489791513 & 117.537189744206 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 6.81785714285714 & 0.0560094578549215 & 121.726890492622 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 6.82222222222222 & 0.0540250392724559 & 126.278894270059 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 6.82692307692308 & 0.0515312572349303 & 132.481205451659 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 6.83 & 0.0490938293641131 & 139.121353711158 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 6.83333333333333 & 0.0472969093697866 & 144.477375464590 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 6.83695652173913 & 0.0449754302922462 & 152.015366552654 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 6.83863636363636 & 0.0427905945251913 & 159.816343743726 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 6.83809523809524 & 0.0407468575350585 & 167.818959589994 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 6.8375 & 0.039660013447636 & 172.402866404161 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 6.83684210526316 & 0.0381695425396952 & 179.117737608541 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 6.83333333333333 & 0.0369469804595635 & 184.949710323745 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 6.83235294117647 & 0.0362504135412626 & 188.476551678492 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 6.83125 & 0.0351945915474743 & 194.099425497957 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 6.83 & 0.0336137629174608 & 203.19058050035 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 6.83214285714286 & 0.0325517786266918 & 209.885393222128 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 6.83461538461538 & 0.0308556478771255 & 221.502896708973 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 6.8375 & 0.0281124166697652 & 243.219929482395 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 6.83636363636364 & 0.0259415381239457 & 263.529618162974 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 6.84 & 0.0244948974278318 & 279.241830677282 \tabularnewline
Median & 6.85 &  &  \tabularnewline
Midrange & 6.7 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 6.79117647058824 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 6.79117647058824 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 6.79117647058824 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 6.79117647058824 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 6.79117647058824 &  &  \tabularnewline
Midmean - Closest Observation & 6.79117647058824 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 6.79117647058824 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 6.82432432432432 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=17329&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]6.81166666666667[/C][C]0.0600419658637476[/C][C]113.448428422952[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]6.79575516609378[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]6.7795440799398[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]6.82726153007192[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]6.81333333333333[/C][C]0.0595874075095568[/C][C]114.341831908706[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]6.81[/C][C]0.058883203364101[/C][C]115.652675312020[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]6.81[/C][C]0.058883203364101[/C][C]115.652675312020[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]6.81666666666667[/C][C]0.0572025179538773[/C][C]119.167248409641[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]6.81666666666667[/C][C]0.0536343904064822[/C][C]127.095071184827[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]6.81666666666667[/C][C]0.0536343904064822[/C][C]127.095071184827[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]6.82833333333333[/C][C]0.0510948860679575[/C][C]133.640249716018[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]6.84166666666667[/C][C]0.0484384207281424[/C][C]141.244626968024[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]6.84166666666667[/C][C]0.0428696399141088[/C][C]159.592352078866[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]6.84166666666667[/C][C]0.0428696399141088[/C][C]159.592352078866[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]6.86[/C][C]0.039858506808105[/C][C]172.108805606462[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]6.84[/C][C]0.0362975773887705[/C][C]188.442328443554[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]6.84[/C][C]0.0362975773887705[/C][C]188.442328443554[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]6.84[/C][C]0.0362975773887705[/C][C]188.442328443554[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]6.815[/C][C]0.0323142234866942[/C][C]210.897842023224[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]6.815[/C][C]0.0323142234866942[/C][C]210.897842023224[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]6.815[/C][C]0.0323142234866942[/C][C]210.897842023224[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]6.845[/C][C]0.0275583612872057[/C][C]248.381967587379[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]6.81333333333333[/C][C]0.0228563021099075[/C][C]298.094298043951[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]6.81333333333333[/C][C]0.0228563021099075[/C][C]298.094298043951[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]6.81551724137931[/C][C]0.0579860489791513[/C][C]117.537189744206[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]6.81785714285714[/C][C]0.0560094578549215[/C][C]121.726890492622[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]6.82222222222222[/C][C]0.0540250392724559[/C][C]126.278894270059[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]6.82692307692308[/C][C]0.0515312572349303[/C][C]132.481205451659[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]6.83[/C][C]0.0490938293641131[/C][C]139.121353711158[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]6.83333333333333[/C][C]0.0472969093697866[/C][C]144.477375464590[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]6.83695652173913[/C][C]0.0449754302922462[/C][C]152.015366552654[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]6.83863636363636[/C][C]0.0427905945251913[/C][C]159.816343743726[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]6.83809523809524[/C][C]0.0407468575350585[/C][C]167.818959589994[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]6.8375[/C][C]0.039660013447636[/C][C]172.402866404161[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]6.83684210526316[/C][C]0.0381695425396952[/C][C]179.117737608541[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]6.83333333333333[/C][C]0.0369469804595635[/C][C]184.949710323745[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]6.83235294117647[/C][C]0.0362504135412626[/C][C]188.476551678492[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]6.83125[/C][C]0.0351945915474743[/C][C]194.099425497957[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]6.83[/C][C]0.0336137629174608[/C][C]203.19058050035[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]6.83214285714286[/C][C]0.0325517786266918[/C][C]209.885393222128[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]6.83461538461538[/C][C]0.0308556478771255[/C][C]221.502896708973[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]6.8375[/C][C]0.0281124166697652[/C][C]243.219929482395[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]6.83636363636364[/C][C]0.0259415381239457[/C][C]263.529618162974[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]6.84[/C][C]0.0244948974278318[/C][C]279.241830677282[/C][/ROW]
[ROW][C]Median[/C][C]6.85[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]6.7[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]6.79117647058824[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]6.79117647058824[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]6.79117647058824[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]6.79117647058824[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]6.79117647058824[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]6.79117647058824[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]6.79117647058824[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]6.82432432432432[/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=17329&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=17329&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 Mean6.811666666666670.0600419658637476113.448428422952
Geometric Mean6.79575516609378
Harmonic Mean6.7795440799398
Quadratic Mean6.82726153007192
Winsorized Mean ( 1 / 20 )6.813333333333330.0595874075095568114.341831908706
Winsorized Mean ( 2 / 20 )6.810.058883203364101115.652675312020
Winsorized Mean ( 3 / 20 )6.810.058883203364101115.652675312020
Winsorized Mean ( 4 / 20 )6.816666666666670.0572025179538773119.167248409641
Winsorized Mean ( 5 / 20 )6.816666666666670.0536343904064822127.095071184827
Winsorized Mean ( 6 / 20 )6.816666666666670.0536343904064822127.095071184827
Winsorized Mean ( 7 / 20 )6.828333333333330.0510948860679575133.640249716018
Winsorized Mean ( 8 / 20 )6.841666666666670.0484384207281424141.244626968024
Winsorized Mean ( 9 / 20 )6.841666666666670.0428696399141088159.592352078866
Winsorized Mean ( 10 / 20 )6.841666666666670.0428696399141088159.592352078866
Winsorized Mean ( 11 / 20 )6.860.039858506808105172.108805606462
Winsorized Mean ( 12 / 20 )6.840.0362975773887705188.442328443554
Winsorized Mean ( 13 / 20 )6.840.0362975773887705188.442328443554
Winsorized Mean ( 14 / 20 )6.840.0362975773887705188.442328443554
Winsorized Mean ( 15 / 20 )6.8150.0323142234866942210.897842023224
Winsorized Mean ( 16 / 20 )6.8150.0323142234866942210.897842023224
Winsorized Mean ( 17 / 20 )6.8150.0323142234866942210.897842023224
Winsorized Mean ( 18 / 20 )6.8450.0275583612872057248.381967587379
Winsorized Mean ( 19 / 20 )6.813333333333330.0228563021099075298.094298043951
Winsorized Mean ( 20 / 20 )6.813333333333330.0228563021099075298.094298043951
Trimmed Mean ( 1 / 20 )6.815517241379310.0579860489791513117.537189744206
Trimmed Mean ( 2 / 20 )6.817857142857140.0560094578549215121.726890492622
Trimmed Mean ( 3 / 20 )6.822222222222220.0540250392724559126.278894270059
Trimmed Mean ( 4 / 20 )6.826923076923080.0515312572349303132.481205451659
Trimmed Mean ( 5 / 20 )6.830.0490938293641131139.121353711158
Trimmed Mean ( 6 / 20 )6.833333333333330.0472969093697866144.477375464590
Trimmed Mean ( 7 / 20 )6.836956521739130.0449754302922462152.015366552654
Trimmed Mean ( 8 / 20 )6.838636363636360.0427905945251913159.816343743726
Trimmed Mean ( 9 / 20 )6.838095238095240.0407468575350585167.818959589994
Trimmed Mean ( 10 / 20 )6.83750.039660013447636172.402866404161
Trimmed Mean ( 11 / 20 )6.836842105263160.0381695425396952179.117737608541
Trimmed Mean ( 12 / 20 )6.833333333333330.0369469804595635184.949710323745
Trimmed Mean ( 13 / 20 )6.832352941176470.0362504135412626188.476551678492
Trimmed Mean ( 14 / 20 )6.831250.0351945915474743194.099425497957
Trimmed Mean ( 15 / 20 )6.830.0336137629174608203.19058050035
Trimmed Mean ( 16 / 20 )6.832142857142860.0325517786266918209.885393222128
Trimmed Mean ( 17 / 20 )6.834615384615380.0308556478771255221.502896708973
Trimmed Mean ( 18 / 20 )6.83750.0281124166697652243.219929482395
Trimmed Mean ( 19 / 20 )6.836363636363640.0259415381239457263.529618162974
Trimmed Mean ( 20 / 20 )6.840.0244948974278318279.241830677282
Median6.85
Midrange6.7
Midmean - Weighted Average at Xnp6.79117647058824
Midmean - Weighted Average at X(n+1)p6.79117647058824
Midmean - Empirical Distribution Function6.79117647058824
Midmean - Empirical Distribution Function - Averaging6.79117647058824
Midmean - Empirical Distribution Function - Interpolation6.79117647058824
Midmean - Closest Observation6.79117647058824
Midmean - True Basic - Statistics Graphics Toolkit6.79117647058824
Midmean - MS Excel (old versions)6.82432432432432
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')