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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, 16 Dec 2009 10:46:26 -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/16/t1260985667e4so4xrjbahv10j.htm/, Retrieved Tue, 30 Apr 2024 14:32:35 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=68505, Retrieved Tue, 30 Apr 2024 14:32:35 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact113
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [FINALE PAPER - Ce...] [2009-12-16 17:46:26] [d41d8cd98f00b204e9800998ecf8427e] [Current]
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Dataseries X:
8.4
8.4
8.4
8.6
8.9
8.8
8.3
7.5
7.2
7.4
8.8
9.3
9.3
8.7
8.2
8.3
8.5
8.6
8.5
8.2
8.1
7.9
8.6
8.7
8.7
8.5
8.4
8.5
8.7
8.7
8.6
8.5
8.3
8
8.2
8.1
8.1
8
7.9
7.9
8
8
7.9
8
7.7
7.2
7.5
7.3
7
7
7
7.2
7.3
7.1
6.8
6.4
6.1
6.5
7.7
7.9
7.5
6.9
6.6
6.9
7.7
8
8
7.7
7.3
7.4
8.1
8.3




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=68505&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=68505&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=68505&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 Mean7.926388888888890.082388850899650196.2070571726174
Geometric Mean7.89488174905469
Harmonic Mean7.86222486663189
Quadratic Mean7.95673195057703
Winsorized Mean ( 1 / 24 )7.930555555555550.081184474935875697.685617377209
Winsorized Mean ( 2 / 24 )7.922222222222220.0781541308061114101.366647424895
Winsorized Mean ( 3 / 24 )7.922222222222220.076407559249171103.683749357668
Winsorized Mean ( 4 / 24 )7.933333333333330.0738500786445482107.424846106362
Winsorized Mean ( 5 / 24 )7.933333333333330.07128926724559111.283698652746
Winsorized Mean ( 6 / 24 )7.933333333333330.07128926724559111.283698652746
Winsorized Mean ( 7 / 24 )7.943055555555560.0693651738487749114.510713587664
Winsorized Mean ( 8 / 24 )7.943055555555560.0693651738487749114.510713587664
Winsorized Mean ( 9 / 24 )7.943055555555560.0693651738487749114.510713587664
Winsorized Mean ( 10 / 24 )7.943055555555560.0646958209802144122.775403962873
Winsorized Mean ( 11 / 24 )7.958333333333330.0619754987177558128.410960750418
Winsorized Mean ( 12 / 24 )7.958333333333330.0619754987177558128.410960750418
Winsorized Mean ( 13 / 24 )7.958333333333330.0619754987177558128.410960750418
Winsorized Mean ( 14 / 24 )7.958333333333330.0559366817309294142.273962041851
Winsorized Mean ( 15 / 24 )7.958333333333330.0559366817309294142.273962041851
Winsorized Mean ( 16 / 24 )7.958333333333330.0559366817309294142.273962041851
Winsorized Mean ( 17 / 24 )7.981944444444450.0521196404490242153.146575373083
Winsorized Mean ( 18 / 24 )7.981944444444450.0521196404490242153.146575373083
Winsorized Mean ( 19 / 24 )7.981944444444450.0444196796223246179.693876955224
Winsorized Mean ( 20 / 24 )7.981944444444450.0444196796223246179.693876955224
Winsorized Mean ( 21 / 24 )7.981944444444450.0444196796223246179.693876955224
Winsorized Mean ( 22 / 24 )8.043055555555560.0355389088329445226.316896598121
Winsorized Mean ( 23 / 24 )8.011111111111110.0311839634383759256.898425594369
Winsorized Mean ( 24 / 24 )8.011111111111110.0311839634383759256.898425594369
Trimmed Mean ( 1 / 24 )7.932857142857140.0781176431022906101.550134231130
Trimmed Mean ( 2 / 24 )7.935294117647060.0744533695681092106.580725139484
Trimmed Mean ( 3 / 24 )7.942424242424240.0720353644715447110.257292382572
Trimmed Mean ( 4 / 24 )7.950.0699347768701167113.677348463766
Trimmed Mean ( 5 / 24 )7.954838709677420.068359852090741116.367114123040
Trimmed Mean ( 6 / 24 )7.960.0672376676781866118.386021925957
Trimmed Mean ( 7 / 24 )7.965517241379310.0658396245841646120.983637007176
Trimmed Mean ( 8 / 24 )7.969642857142860.0646127145049311123.344807878868
Trimmed Mean ( 9 / 24 )7.974074074074070.0630676976563063126.436739732114
Trimmed Mean ( 10 / 24 )7.978846153846150.0611193068649804130.545429310452
Trimmed Mean ( 11 / 24 )7.9840.0597518678727763133.619253828174
Trimmed Mean ( 12 / 24 )7.98750.0586207458496702136.257222323365
Trimmed Mean ( 13 / 24 )7.991304347826090.0571316038968899139.875371996359
Trimmed Mean ( 14 / 24 )7.995454545454550.0551717044414823144.919476865807
Trimmed Mean ( 15 / 24 )80.0539927297553511148.168096635402
Trimmed Mean ( 16 / 24 )8.0050.0523731679197346152.845442007025
Trimmed Mean ( 17 / 24 )8.010526315789470.0501476445548387159.738834932309
Trimmed Mean ( 18 / 24 )8.013888888888890.0481651882748529166.383422881230
Trimmed Mean ( 19 / 24 )8.017647058823530.0453684830640290176.722837470853
Trimmed Mean ( 20 / 24 )8.0218750.0437031719432723183.553610488789
Trimmed Mean ( 21 / 24 )8.026666666666670.0412264097180139194.697203117336
Trimmed Mean ( 22 / 24 )8.032142857142860.0374637643020091214.397645479317
Trimmed Mean ( 23 / 24 )8.030769230769230.0354180444099118226.742310722322
Trimmed Mean ( 24 / 24 )8.033333333333330.0338724518623775237.164211376621
Median8
Midrange7.7
Midmean - Weighted Average at Xnp8.04634146341463
Midmean - Weighted Average at X(n+1)p8.04634146341463
Midmean - Empirical Distribution Function8.04634146341463
Midmean - Empirical Distribution Function - Averaging8.04634146341463
Midmean - Empirical Distribution Function - Interpolation8.04634146341463
Midmean - Closest Observation8.04634146341463
Midmean - True Basic - Statistics Graphics Toolkit8.04634146341463
Midmean - MS Excel (old versions)8.04634146341463
Number of observations72

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 7.92638888888889 & 0.0823888508996501 & 96.2070571726174 \tabularnewline
Geometric Mean & 7.89488174905469 &  &  \tabularnewline
Harmonic Mean & 7.86222486663189 &  &  \tabularnewline
Quadratic Mean & 7.95673195057703 &  &  \tabularnewline
Winsorized Mean ( 1 / 24 ) & 7.93055555555555 & 0.0811844749358756 & 97.685617377209 \tabularnewline
Winsorized Mean ( 2 / 24 ) & 7.92222222222222 & 0.0781541308061114 & 101.366647424895 \tabularnewline
Winsorized Mean ( 3 / 24 ) & 7.92222222222222 & 0.076407559249171 & 103.683749357668 \tabularnewline
Winsorized Mean ( 4 / 24 ) & 7.93333333333333 & 0.0738500786445482 & 107.424846106362 \tabularnewline
Winsorized Mean ( 5 / 24 ) & 7.93333333333333 & 0.07128926724559 & 111.283698652746 \tabularnewline
Winsorized Mean ( 6 / 24 ) & 7.93333333333333 & 0.07128926724559 & 111.283698652746 \tabularnewline
Winsorized Mean ( 7 / 24 ) & 7.94305555555556 & 0.0693651738487749 & 114.510713587664 \tabularnewline
Winsorized Mean ( 8 / 24 ) & 7.94305555555556 & 0.0693651738487749 & 114.510713587664 \tabularnewline
Winsorized Mean ( 9 / 24 ) & 7.94305555555556 & 0.0693651738487749 & 114.510713587664 \tabularnewline
Winsorized Mean ( 10 / 24 ) & 7.94305555555556 & 0.0646958209802144 & 122.775403962873 \tabularnewline
Winsorized Mean ( 11 / 24 ) & 7.95833333333333 & 0.0619754987177558 & 128.410960750418 \tabularnewline
Winsorized Mean ( 12 / 24 ) & 7.95833333333333 & 0.0619754987177558 & 128.410960750418 \tabularnewline
Winsorized Mean ( 13 / 24 ) & 7.95833333333333 & 0.0619754987177558 & 128.410960750418 \tabularnewline
Winsorized Mean ( 14 / 24 ) & 7.95833333333333 & 0.0559366817309294 & 142.273962041851 \tabularnewline
Winsorized Mean ( 15 / 24 ) & 7.95833333333333 & 0.0559366817309294 & 142.273962041851 \tabularnewline
Winsorized Mean ( 16 / 24 ) & 7.95833333333333 & 0.0559366817309294 & 142.273962041851 \tabularnewline
Winsorized Mean ( 17 / 24 ) & 7.98194444444445 & 0.0521196404490242 & 153.146575373083 \tabularnewline
Winsorized Mean ( 18 / 24 ) & 7.98194444444445 & 0.0521196404490242 & 153.146575373083 \tabularnewline
Winsorized Mean ( 19 / 24 ) & 7.98194444444445 & 0.0444196796223246 & 179.693876955224 \tabularnewline
Winsorized Mean ( 20 / 24 ) & 7.98194444444445 & 0.0444196796223246 & 179.693876955224 \tabularnewline
Winsorized Mean ( 21 / 24 ) & 7.98194444444445 & 0.0444196796223246 & 179.693876955224 \tabularnewline
Winsorized Mean ( 22 / 24 ) & 8.04305555555556 & 0.0355389088329445 & 226.316896598121 \tabularnewline
Winsorized Mean ( 23 / 24 ) & 8.01111111111111 & 0.0311839634383759 & 256.898425594369 \tabularnewline
Winsorized Mean ( 24 / 24 ) & 8.01111111111111 & 0.0311839634383759 & 256.898425594369 \tabularnewline
Trimmed Mean ( 1 / 24 ) & 7.93285714285714 & 0.0781176431022906 & 101.550134231130 \tabularnewline
Trimmed Mean ( 2 / 24 ) & 7.93529411764706 & 0.0744533695681092 & 106.580725139484 \tabularnewline
Trimmed Mean ( 3 / 24 ) & 7.94242424242424 & 0.0720353644715447 & 110.257292382572 \tabularnewline
Trimmed Mean ( 4 / 24 ) & 7.95 & 0.0699347768701167 & 113.677348463766 \tabularnewline
Trimmed Mean ( 5 / 24 ) & 7.95483870967742 & 0.068359852090741 & 116.367114123040 \tabularnewline
Trimmed Mean ( 6 / 24 ) & 7.96 & 0.0672376676781866 & 118.386021925957 \tabularnewline
Trimmed Mean ( 7 / 24 ) & 7.96551724137931 & 0.0658396245841646 & 120.983637007176 \tabularnewline
Trimmed Mean ( 8 / 24 ) & 7.96964285714286 & 0.0646127145049311 & 123.344807878868 \tabularnewline
Trimmed Mean ( 9 / 24 ) & 7.97407407407407 & 0.0630676976563063 & 126.436739732114 \tabularnewline
Trimmed Mean ( 10 / 24 ) & 7.97884615384615 & 0.0611193068649804 & 130.545429310452 \tabularnewline
Trimmed Mean ( 11 / 24 ) & 7.984 & 0.0597518678727763 & 133.619253828174 \tabularnewline
Trimmed Mean ( 12 / 24 ) & 7.9875 & 0.0586207458496702 & 136.257222323365 \tabularnewline
Trimmed Mean ( 13 / 24 ) & 7.99130434782609 & 0.0571316038968899 & 139.875371996359 \tabularnewline
Trimmed Mean ( 14 / 24 ) & 7.99545454545455 & 0.0551717044414823 & 144.919476865807 \tabularnewline
Trimmed Mean ( 15 / 24 ) & 8 & 0.0539927297553511 & 148.168096635402 \tabularnewline
Trimmed Mean ( 16 / 24 ) & 8.005 & 0.0523731679197346 & 152.845442007025 \tabularnewline
Trimmed Mean ( 17 / 24 ) & 8.01052631578947 & 0.0501476445548387 & 159.738834932309 \tabularnewline
Trimmed Mean ( 18 / 24 ) & 8.01388888888889 & 0.0481651882748529 & 166.383422881230 \tabularnewline
Trimmed Mean ( 19 / 24 ) & 8.01764705882353 & 0.0453684830640290 & 176.722837470853 \tabularnewline
Trimmed Mean ( 20 / 24 ) & 8.021875 & 0.0437031719432723 & 183.553610488789 \tabularnewline
Trimmed Mean ( 21 / 24 ) & 8.02666666666667 & 0.0412264097180139 & 194.697203117336 \tabularnewline
Trimmed Mean ( 22 / 24 ) & 8.03214285714286 & 0.0374637643020091 & 214.397645479317 \tabularnewline
Trimmed Mean ( 23 / 24 ) & 8.03076923076923 & 0.0354180444099118 & 226.742310722322 \tabularnewline
Trimmed Mean ( 24 / 24 ) & 8.03333333333333 & 0.0338724518623775 & 237.164211376621 \tabularnewline
Median & 8 &  &  \tabularnewline
Midrange & 7.7 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 8.04634146341463 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 8.04634146341463 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 8.04634146341463 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 8.04634146341463 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 8.04634146341463 &  &  \tabularnewline
Midmean - Closest Observation & 8.04634146341463 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 8.04634146341463 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 8.04634146341463 &  &  \tabularnewline
Number of observations & 72 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=68505&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]7.92638888888889[/C][C]0.0823888508996501[/C][C]96.2070571726174[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]7.89488174905469[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]7.86222486663189[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]7.95673195057703[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 24 )[/C][C]7.93055555555555[/C][C]0.0811844749358756[/C][C]97.685617377209[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 24 )[/C][C]7.92222222222222[/C][C]0.0781541308061114[/C][C]101.366647424895[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 24 )[/C][C]7.92222222222222[/C][C]0.076407559249171[/C][C]103.683749357668[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 24 )[/C][C]7.93333333333333[/C][C]0.0738500786445482[/C][C]107.424846106362[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 24 )[/C][C]7.93333333333333[/C][C]0.07128926724559[/C][C]111.283698652746[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 24 )[/C][C]7.93333333333333[/C][C]0.07128926724559[/C][C]111.283698652746[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 24 )[/C][C]7.94305555555556[/C][C]0.0693651738487749[/C][C]114.510713587664[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 24 )[/C][C]7.94305555555556[/C][C]0.0693651738487749[/C][C]114.510713587664[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 24 )[/C][C]7.94305555555556[/C][C]0.0693651738487749[/C][C]114.510713587664[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 24 )[/C][C]7.94305555555556[/C][C]0.0646958209802144[/C][C]122.775403962873[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 24 )[/C][C]7.95833333333333[/C][C]0.0619754987177558[/C][C]128.410960750418[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 24 )[/C][C]7.95833333333333[/C][C]0.0619754987177558[/C][C]128.410960750418[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 24 )[/C][C]7.95833333333333[/C][C]0.0619754987177558[/C][C]128.410960750418[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 24 )[/C][C]7.95833333333333[/C][C]0.0559366817309294[/C][C]142.273962041851[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 24 )[/C][C]7.95833333333333[/C][C]0.0559366817309294[/C][C]142.273962041851[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 24 )[/C][C]7.95833333333333[/C][C]0.0559366817309294[/C][C]142.273962041851[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 24 )[/C][C]7.98194444444445[/C][C]0.0521196404490242[/C][C]153.146575373083[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 24 )[/C][C]7.98194444444445[/C][C]0.0521196404490242[/C][C]153.146575373083[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 24 )[/C][C]7.98194444444445[/C][C]0.0444196796223246[/C][C]179.693876955224[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 24 )[/C][C]7.98194444444445[/C][C]0.0444196796223246[/C][C]179.693876955224[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 24 )[/C][C]7.98194444444445[/C][C]0.0444196796223246[/C][C]179.693876955224[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 24 )[/C][C]8.04305555555556[/C][C]0.0355389088329445[/C][C]226.316896598121[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 24 )[/C][C]8.01111111111111[/C][C]0.0311839634383759[/C][C]256.898425594369[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 24 )[/C][C]8.01111111111111[/C][C]0.0311839634383759[/C][C]256.898425594369[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 24 )[/C][C]7.93285714285714[/C][C]0.0781176431022906[/C][C]101.550134231130[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 24 )[/C][C]7.93529411764706[/C][C]0.0744533695681092[/C][C]106.580725139484[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 24 )[/C][C]7.94242424242424[/C][C]0.0720353644715447[/C][C]110.257292382572[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 24 )[/C][C]7.95[/C][C]0.0699347768701167[/C][C]113.677348463766[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 24 )[/C][C]7.95483870967742[/C][C]0.068359852090741[/C][C]116.367114123040[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 24 )[/C][C]7.96[/C][C]0.0672376676781866[/C][C]118.386021925957[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 24 )[/C][C]7.96551724137931[/C][C]0.0658396245841646[/C][C]120.983637007176[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 24 )[/C][C]7.96964285714286[/C][C]0.0646127145049311[/C][C]123.344807878868[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 24 )[/C][C]7.97407407407407[/C][C]0.0630676976563063[/C][C]126.436739732114[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 24 )[/C][C]7.97884615384615[/C][C]0.0611193068649804[/C][C]130.545429310452[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 24 )[/C][C]7.984[/C][C]0.0597518678727763[/C][C]133.619253828174[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 24 )[/C][C]7.9875[/C][C]0.0586207458496702[/C][C]136.257222323365[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 24 )[/C][C]7.99130434782609[/C][C]0.0571316038968899[/C][C]139.875371996359[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 24 )[/C][C]7.99545454545455[/C][C]0.0551717044414823[/C][C]144.919476865807[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 24 )[/C][C]8[/C][C]0.0539927297553511[/C][C]148.168096635402[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 24 )[/C][C]8.005[/C][C]0.0523731679197346[/C][C]152.845442007025[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 24 )[/C][C]8.01052631578947[/C][C]0.0501476445548387[/C][C]159.738834932309[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 24 )[/C][C]8.01388888888889[/C][C]0.0481651882748529[/C][C]166.383422881230[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 24 )[/C][C]8.01764705882353[/C][C]0.0453684830640290[/C][C]176.722837470853[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 24 )[/C][C]8.021875[/C][C]0.0437031719432723[/C][C]183.553610488789[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 24 )[/C][C]8.02666666666667[/C][C]0.0412264097180139[/C][C]194.697203117336[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 24 )[/C][C]8.03214285714286[/C][C]0.0374637643020091[/C][C]214.397645479317[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 24 )[/C][C]8.03076923076923[/C][C]0.0354180444099118[/C][C]226.742310722322[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 24 )[/C][C]8.03333333333333[/C][C]0.0338724518623775[/C][C]237.164211376621[/C][/ROW]
[ROW][C]Median[/C][C]8[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]7.7[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]8.04634146341463[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]8.04634146341463[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]8.04634146341463[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]8.04634146341463[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]8.04634146341463[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]8.04634146341463[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]8.04634146341463[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]8.04634146341463[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]72[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=68505&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=68505&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 Mean7.926388888888890.082388850899650196.2070571726174
Geometric Mean7.89488174905469
Harmonic Mean7.86222486663189
Quadratic Mean7.95673195057703
Winsorized Mean ( 1 / 24 )7.930555555555550.081184474935875697.685617377209
Winsorized Mean ( 2 / 24 )7.922222222222220.0781541308061114101.366647424895
Winsorized Mean ( 3 / 24 )7.922222222222220.076407559249171103.683749357668
Winsorized Mean ( 4 / 24 )7.933333333333330.0738500786445482107.424846106362
Winsorized Mean ( 5 / 24 )7.933333333333330.07128926724559111.283698652746
Winsorized Mean ( 6 / 24 )7.933333333333330.07128926724559111.283698652746
Winsorized Mean ( 7 / 24 )7.943055555555560.0693651738487749114.510713587664
Winsorized Mean ( 8 / 24 )7.943055555555560.0693651738487749114.510713587664
Winsorized Mean ( 9 / 24 )7.943055555555560.0693651738487749114.510713587664
Winsorized Mean ( 10 / 24 )7.943055555555560.0646958209802144122.775403962873
Winsorized Mean ( 11 / 24 )7.958333333333330.0619754987177558128.410960750418
Winsorized Mean ( 12 / 24 )7.958333333333330.0619754987177558128.410960750418
Winsorized Mean ( 13 / 24 )7.958333333333330.0619754987177558128.410960750418
Winsorized Mean ( 14 / 24 )7.958333333333330.0559366817309294142.273962041851
Winsorized Mean ( 15 / 24 )7.958333333333330.0559366817309294142.273962041851
Winsorized Mean ( 16 / 24 )7.958333333333330.0559366817309294142.273962041851
Winsorized Mean ( 17 / 24 )7.981944444444450.0521196404490242153.146575373083
Winsorized Mean ( 18 / 24 )7.981944444444450.0521196404490242153.146575373083
Winsorized Mean ( 19 / 24 )7.981944444444450.0444196796223246179.693876955224
Winsorized Mean ( 20 / 24 )7.981944444444450.0444196796223246179.693876955224
Winsorized Mean ( 21 / 24 )7.981944444444450.0444196796223246179.693876955224
Winsorized Mean ( 22 / 24 )8.043055555555560.0355389088329445226.316896598121
Winsorized Mean ( 23 / 24 )8.011111111111110.0311839634383759256.898425594369
Winsorized Mean ( 24 / 24 )8.011111111111110.0311839634383759256.898425594369
Trimmed Mean ( 1 / 24 )7.932857142857140.0781176431022906101.550134231130
Trimmed Mean ( 2 / 24 )7.935294117647060.0744533695681092106.580725139484
Trimmed Mean ( 3 / 24 )7.942424242424240.0720353644715447110.257292382572
Trimmed Mean ( 4 / 24 )7.950.0699347768701167113.677348463766
Trimmed Mean ( 5 / 24 )7.954838709677420.068359852090741116.367114123040
Trimmed Mean ( 6 / 24 )7.960.0672376676781866118.386021925957
Trimmed Mean ( 7 / 24 )7.965517241379310.0658396245841646120.983637007176
Trimmed Mean ( 8 / 24 )7.969642857142860.0646127145049311123.344807878868
Trimmed Mean ( 9 / 24 )7.974074074074070.0630676976563063126.436739732114
Trimmed Mean ( 10 / 24 )7.978846153846150.0611193068649804130.545429310452
Trimmed Mean ( 11 / 24 )7.9840.0597518678727763133.619253828174
Trimmed Mean ( 12 / 24 )7.98750.0586207458496702136.257222323365
Trimmed Mean ( 13 / 24 )7.991304347826090.0571316038968899139.875371996359
Trimmed Mean ( 14 / 24 )7.995454545454550.0551717044414823144.919476865807
Trimmed Mean ( 15 / 24 )80.0539927297553511148.168096635402
Trimmed Mean ( 16 / 24 )8.0050.0523731679197346152.845442007025
Trimmed Mean ( 17 / 24 )8.010526315789470.0501476445548387159.738834932309
Trimmed Mean ( 18 / 24 )8.013888888888890.0481651882748529166.383422881230
Trimmed Mean ( 19 / 24 )8.017647058823530.0453684830640290176.722837470853
Trimmed Mean ( 20 / 24 )8.0218750.0437031719432723183.553610488789
Trimmed Mean ( 21 / 24 )8.026666666666670.0412264097180139194.697203117336
Trimmed Mean ( 22 / 24 )8.032142857142860.0374637643020091214.397645479317
Trimmed Mean ( 23 / 24 )8.030769230769230.0354180444099118226.742310722322
Trimmed Mean ( 24 / 24 )8.033333333333330.0338724518623775237.164211376621
Median8
Midrange7.7
Midmean - Weighted Average at Xnp8.04634146341463
Midmean - Weighted Average at X(n+1)p8.04634146341463
Midmean - Empirical Distribution Function8.04634146341463
Midmean - Empirical Distribution Function - Averaging8.04634146341463
Midmean - Empirical Distribution Function - Interpolation8.04634146341463
Midmean - Closest Observation8.04634146341463
Midmean - True Basic - Statistics Graphics Toolkit8.04634146341463
Midmean - MS Excel (old versions)8.04634146341463
Number of observations72



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')