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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 computationTue, 13 Dec 2011 15:31:23 -0500
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2011/Dec/13/t13238083206fl5z9c66mhmbmi.htm/, Retrieved Thu, 02 May 2024 18:13:10 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=154698, Retrieved Thu, 02 May 2024 18:13:10 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact94
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
F     [Central Tendency] [Time needed to su...] [2010-09-25 09:42:08] [b98453cac15ba1066b407e146608df68]
- R     [Central Tendency] [gemiddelde en med...] [2011-12-13 19:41:18] [22f8bc702946f784836540059d0d9516]
-    D    [Central Tendency] [gemiddelde en med...] [2011-12-13 19:46:47] [22f8bc702946f784836540059d0d9516]
-   PD        [Central Tendency] [central tendency ...] [2011-12-13 20:31:23] [76a85a4cc6ea7903d92a0f5b9d2872d3] [Current]
-    D          [Central Tendency] [gemiddelde en med...] [2011-12-13 20:41:51] [22f8bc702946f784836540059d0d9516]
- RM D            [Histogram] [gemiddelde en med...] [2011-12-13 20:50:34] [22f8bc702946f784836540059d0d9516]
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Dataseries X:
6
8
7
9
11
9
12
6
11
2
9
8
7
10
5
5
6
8
6
4
7
5
9
8
12
7
9
12
10
9
11
8
9
8
7
10
7
6
12
6
10
3
11
4
13
7
3
5
6
10
12
8
7
4
8
8
10
7
8
11
5
8
13
15
9
1
5
9
6
7




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'George Udny Yule' @ yule.wessa.net

\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 & 3 seconds \tabularnewline
R Server & 'George Udny Yule' @ yule.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=154698&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]3 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'George Udny Yule' @ yule.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=154698&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=154698&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 time3 seconds
R Server'George Udny Yule' @ yule.wessa.net







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean7.914285714285710.33296637594893923.7690237992661
Geometric Mean7.30669846773371
Harmonic Mean6.39544125913007
Quadratic Mean8.38365757206926
Winsorized Mean ( 1 / 23 )7.90.3211972942964424.5954749317063
Winsorized Mean ( 2 / 23 )7.928571428571430.31413981179504925.2389895545751
Winsorized Mean ( 3 / 23 )7.885714285714290.30492361134357325.861278013099
Winsorized Mean ( 4 / 23 )7.942857142857140.29268919084439927.1375144396083
Winsorized Mean ( 5 / 23 )7.942857142857140.29268919084439927.1375144396083
Winsorized Mean ( 6 / 23 )7.942857142857140.29268919084439927.1375144396083
Winsorized Mean ( 7 / 23 )8.042857142857140.27485039355013529.2626728270995
Winsorized Mean ( 8 / 23 )7.928571428571430.25278689178629631.3646462146232
Winsorized Mean ( 9 / 23 )7.928571428571430.25278689178629631.3646462146232
Winsorized Mean ( 10 / 23 )7.928571428571430.25278689178629631.3646462146232
Winsorized Mean ( 11 / 23 )7.928571428571430.25278689178629631.3646462146232
Winsorized Mean ( 12 / 23 )7.928571428571430.25278689178629631.3646462146232
Winsorized Mean ( 13 / 23 )7.928571428571430.1923177027403941.226425417915
Winsorized Mean ( 14 / 23 )7.928571428571430.1923177027403941.226425417915
Winsorized Mean ( 15 / 23 )7.928571428571430.1923177027403941.226425417915
Winsorized Mean ( 16 / 23 )7.928571428571430.1923177027403941.226425417915
Winsorized Mean ( 17 / 23 )7.928571428571430.1923177027403941.226425417915
Winsorized Mean ( 18 / 23 )7.928571428571430.1923177027403941.226425417915
Winsorized Mean ( 19 / 23 )7.657142857142860.15347690769269749.8911723741173
Winsorized Mean ( 20 / 23 )7.657142857142860.15347690769269749.8911723741173
Winsorized Mean ( 21 / 23 )7.957142857142860.11040245272449172.073968111921
Winsorized Mean ( 22 / 23 )7.957142857142860.11040245272449172.073968111921
Winsorized Mean ( 23 / 23 )7.957142857142860.11040245272449172.073968111921
Trimmed Mean ( 1 / 23 )7.911764705882350.30987216920155125.5323500857422
Trimmed Mean ( 2 / 23 )7.924242424242420.29629460396022526.7444709364541
Trimmed Mean ( 3 / 23 )7.9218750.2846125599403427.8338911032618
Trimmed Mean ( 4 / 23 )7.935483870967740.27486929516519128.8700266291972
Trimmed Mean ( 5 / 23 )7.933333333333330.26772389296161729.6325189566503
Trimmed Mean ( 6 / 23 )7.931034482758620.25897334294601630.6249067666083
Trimmed Mean ( 7 / 23 )7.928571428571430.2481845025577431.946279267485
Trimmed Mean ( 8 / 23 )7.90740740740740.23977120255086832.9789704655205
Trimmed Mean ( 9 / 23 )7.903846153846150.23505016213870133.6262101754356
Trimmed Mean ( 10 / 23 )7.90.22901742202687734.4951922438148
Trimmed Mean ( 11 / 23 )7.895833333333330.22129451376012735.6802037211463
Trimmed Mean ( 12 / 23 )7.891304347826090.2113409244500637.3392156221537
Trimmed Mean ( 13 / 23 )7.886363636363640.19834385407992439.7610688415169
Trimmed Mean ( 14 / 23 )7.880952380952380.19637357129549340.132449234187
Trimmed Mean ( 15 / 23 )7.8750.19344216653788740.7098418144402
Trimmed Mean ( 16 / 23 )7.868421052631580.18922260905477241.5828800370997
Trimmed Mean ( 17 / 23 )7.861111111111110.18323710798444842.9013052955316
Trimmed Mean ( 18 / 23 )7.852941176470590.1747539800672244.9371234546414
Trimmed Mean ( 19 / 23 )7.843750.16257364956307748.247363709189
Trimmed Mean ( 20 / 23 )7.866666666666670.15708064649063550.0804322010203
Trimmed Mean ( 21 / 23 )7.892857142857140.14853148628740453.1392860876966
Trimmed Mean ( 22 / 23 )7.884615384615390.1501478561226452.5123407568024
Trimmed Mean ( 23 / 23 )7.8750.15123285625681452.0720179127423
Median8
Midrange8
Midmean - Weighted Average at Xnp7.88636363636364
Midmean - Weighted Average at X(n+1)p7.88636363636364
Midmean - Empirical Distribution Function7.88636363636364
Midmean - Empirical Distribution Function - Averaging7.88636363636364
Midmean - Empirical Distribution Function - Interpolation7.88636363636364
Midmean - Closest Observation7.88636363636364
Midmean - True Basic - Statistics Graphics Toolkit7.88636363636364
Midmean - MS Excel (old versions)7.88636363636364
Number of observations70

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 7.91428571428571 & 0.332966375948939 & 23.7690237992661 \tabularnewline
Geometric Mean & 7.30669846773371 &  &  \tabularnewline
Harmonic Mean & 6.39544125913007 &  &  \tabularnewline
Quadratic Mean & 8.38365757206926 &  &  \tabularnewline
Winsorized Mean ( 1 / 23 ) & 7.9 & 0.32119729429644 & 24.5954749317063 \tabularnewline
Winsorized Mean ( 2 / 23 ) & 7.92857142857143 & 0.314139811795049 & 25.2389895545751 \tabularnewline
Winsorized Mean ( 3 / 23 ) & 7.88571428571429 & 0.304923611343573 & 25.861278013099 \tabularnewline
Winsorized Mean ( 4 / 23 ) & 7.94285714285714 & 0.292689190844399 & 27.1375144396083 \tabularnewline
Winsorized Mean ( 5 / 23 ) & 7.94285714285714 & 0.292689190844399 & 27.1375144396083 \tabularnewline
Winsorized Mean ( 6 / 23 ) & 7.94285714285714 & 0.292689190844399 & 27.1375144396083 \tabularnewline
Winsorized Mean ( 7 / 23 ) & 8.04285714285714 & 0.274850393550135 & 29.2626728270995 \tabularnewline
Winsorized Mean ( 8 / 23 ) & 7.92857142857143 & 0.252786891786296 & 31.3646462146232 \tabularnewline
Winsorized Mean ( 9 / 23 ) & 7.92857142857143 & 0.252786891786296 & 31.3646462146232 \tabularnewline
Winsorized Mean ( 10 / 23 ) & 7.92857142857143 & 0.252786891786296 & 31.3646462146232 \tabularnewline
Winsorized Mean ( 11 / 23 ) & 7.92857142857143 & 0.252786891786296 & 31.3646462146232 \tabularnewline
Winsorized Mean ( 12 / 23 ) & 7.92857142857143 & 0.252786891786296 & 31.3646462146232 \tabularnewline
Winsorized Mean ( 13 / 23 ) & 7.92857142857143 & 0.19231770274039 & 41.226425417915 \tabularnewline
Winsorized Mean ( 14 / 23 ) & 7.92857142857143 & 0.19231770274039 & 41.226425417915 \tabularnewline
Winsorized Mean ( 15 / 23 ) & 7.92857142857143 & 0.19231770274039 & 41.226425417915 \tabularnewline
Winsorized Mean ( 16 / 23 ) & 7.92857142857143 & 0.19231770274039 & 41.226425417915 \tabularnewline
Winsorized Mean ( 17 / 23 ) & 7.92857142857143 & 0.19231770274039 & 41.226425417915 \tabularnewline
Winsorized Mean ( 18 / 23 ) & 7.92857142857143 & 0.19231770274039 & 41.226425417915 \tabularnewline
Winsorized Mean ( 19 / 23 ) & 7.65714285714286 & 0.153476907692697 & 49.8911723741173 \tabularnewline
Winsorized Mean ( 20 / 23 ) & 7.65714285714286 & 0.153476907692697 & 49.8911723741173 \tabularnewline
Winsorized Mean ( 21 / 23 ) & 7.95714285714286 & 0.110402452724491 & 72.073968111921 \tabularnewline
Winsorized Mean ( 22 / 23 ) & 7.95714285714286 & 0.110402452724491 & 72.073968111921 \tabularnewline
Winsorized Mean ( 23 / 23 ) & 7.95714285714286 & 0.110402452724491 & 72.073968111921 \tabularnewline
Trimmed Mean ( 1 / 23 ) & 7.91176470588235 & 0.309872169201551 & 25.5323500857422 \tabularnewline
Trimmed Mean ( 2 / 23 ) & 7.92424242424242 & 0.296294603960225 & 26.7444709364541 \tabularnewline
Trimmed Mean ( 3 / 23 ) & 7.921875 & 0.28461255994034 & 27.8338911032618 \tabularnewline
Trimmed Mean ( 4 / 23 ) & 7.93548387096774 & 0.274869295165191 & 28.8700266291972 \tabularnewline
Trimmed Mean ( 5 / 23 ) & 7.93333333333333 & 0.267723892961617 & 29.6325189566503 \tabularnewline
Trimmed Mean ( 6 / 23 ) & 7.93103448275862 & 0.258973342946016 & 30.6249067666083 \tabularnewline
Trimmed Mean ( 7 / 23 ) & 7.92857142857143 & 0.24818450255774 & 31.946279267485 \tabularnewline
Trimmed Mean ( 8 / 23 ) & 7.9074074074074 & 0.239771202550868 & 32.9789704655205 \tabularnewline
Trimmed Mean ( 9 / 23 ) & 7.90384615384615 & 0.235050162138701 & 33.6262101754356 \tabularnewline
Trimmed Mean ( 10 / 23 ) & 7.9 & 0.229017422026877 & 34.4951922438148 \tabularnewline
Trimmed Mean ( 11 / 23 ) & 7.89583333333333 & 0.221294513760127 & 35.6802037211463 \tabularnewline
Trimmed Mean ( 12 / 23 ) & 7.89130434782609 & 0.21134092445006 & 37.3392156221537 \tabularnewline
Trimmed Mean ( 13 / 23 ) & 7.88636363636364 & 0.198343854079924 & 39.7610688415169 \tabularnewline
Trimmed Mean ( 14 / 23 ) & 7.88095238095238 & 0.196373571295493 & 40.132449234187 \tabularnewline
Trimmed Mean ( 15 / 23 ) & 7.875 & 0.193442166537887 & 40.7098418144402 \tabularnewline
Trimmed Mean ( 16 / 23 ) & 7.86842105263158 & 0.189222609054772 & 41.5828800370997 \tabularnewline
Trimmed Mean ( 17 / 23 ) & 7.86111111111111 & 0.183237107984448 & 42.9013052955316 \tabularnewline
Trimmed Mean ( 18 / 23 ) & 7.85294117647059 & 0.17475398006722 & 44.9371234546414 \tabularnewline
Trimmed Mean ( 19 / 23 ) & 7.84375 & 0.162573649563077 & 48.247363709189 \tabularnewline
Trimmed Mean ( 20 / 23 ) & 7.86666666666667 & 0.157080646490635 & 50.0804322010203 \tabularnewline
Trimmed Mean ( 21 / 23 ) & 7.89285714285714 & 0.148531486287404 & 53.1392860876966 \tabularnewline
Trimmed Mean ( 22 / 23 ) & 7.88461538461539 & 0.15014785612264 & 52.5123407568024 \tabularnewline
Trimmed Mean ( 23 / 23 ) & 7.875 & 0.151232856256814 & 52.0720179127423 \tabularnewline
Median & 8 &  &  \tabularnewline
Midrange & 8 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 7.88636363636364 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 7.88636363636364 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 7.88636363636364 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 7.88636363636364 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 7.88636363636364 &  &  \tabularnewline
Midmean - Closest Observation & 7.88636363636364 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 7.88636363636364 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 7.88636363636364 &  &  \tabularnewline
Number of observations & 70 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=154698&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]7.91428571428571[/C][C]0.332966375948939[/C][C]23.7690237992661[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]7.30669846773371[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]6.39544125913007[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]8.38365757206926[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 23 )[/C][C]7.9[/C][C]0.32119729429644[/C][C]24.5954749317063[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 23 )[/C][C]7.92857142857143[/C][C]0.314139811795049[/C][C]25.2389895545751[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 23 )[/C][C]7.88571428571429[/C][C]0.304923611343573[/C][C]25.861278013099[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 23 )[/C][C]7.94285714285714[/C][C]0.292689190844399[/C][C]27.1375144396083[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 23 )[/C][C]7.94285714285714[/C][C]0.292689190844399[/C][C]27.1375144396083[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 23 )[/C][C]7.94285714285714[/C][C]0.292689190844399[/C][C]27.1375144396083[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 23 )[/C][C]8.04285714285714[/C][C]0.274850393550135[/C][C]29.2626728270995[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 23 )[/C][C]7.92857142857143[/C][C]0.252786891786296[/C][C]31.3646462146232[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 23 )[/C][C]7.92857142857143[/C][C]0.252786891786296[/C][C]31.3646462146232[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 23 )[/C][C]7.92857142857143[/C][C]0.252786891786296[/C][C]31.3646462146232[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 23 )[/C][C]7.92857142857143[/C][C]0.252786891786296[/C][C]31.3646462146232[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 23 )[/C][C]7.92857142857143[/C][C]0.252786891786296[/C][C]31.3646462146232[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 23 )[/C][C]7.92857142857143[/C][C]0.19231770274039[/C][C]41.226425417915[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 23 )[/C][C]7.92857142857143[/C][C]0.19231770274039[/C][C]41.226425417915[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 23 )[/C][C]7.92857142857143[/C][C]0.19231770274039[/C][C]41.226425417915[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 23 )[/C][C]7.92857142857143[/C][C]0.19231770274039[/C][C]41.226425417915[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 23 )[/C][C]7.92857142857143[/C][C]0.19231770274039[/C][C]41.226425417915[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 23 )[/C][C]7.92857142857143[/C][C]0.19231770274039[/C][C]41.226425417915[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 23 )[/C][C]7.65714285714286[/C][C]0.153476907692697[/C][C]49.8911723741173[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 23 )[/C][C]7.65714285714286[/C][C]0.153476907692697[/C][C]49.8911723741173[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 23 )[/C][C]7.95714285714286[/C][C]0.110402452724491[/C][C]72.073968111921[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 23 )[/C][C]7.95714285714286[/C][C]0.110402452724491[/C][C]72.073968111921[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 23 )[/C][C]7.95714285714286[/C][C]0.110402452724491[/C][C]72.073968111921[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 23 )[/C][C]7.91176470588235[/C][C]0.309872169201551[/C][C]25.5323500857422[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 23 )[/C][C]7.92424242424242[/C][C]0.296294603960225[/C][C]26.7444709364541[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 23 )[/C][C]7.921875[/C][C]0.28461255994034[/C][C]27.8338911032618[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 23 )[/C][C]7.93548387096774[/C][C]0.274869295165191[/C][C]28.8700266291972[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 23 )[/C][C]7.93333333333333[/C][C]0.267723892961617[/C][C]29.6325189566503[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 23 )[/C][C]7.93103448275862[/C][C]0.258973342946016[/C][C]30.6249067666083[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 23 )[/C][C]7.92857142857143[/C][C]0.24818450255774[/C][C]31.946279267485[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 23 )[/C][C]7.9074074074074[/C][C]0.239771202550868[/C][C]32.9789704655205[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 23 )[/C][C]7.90384615384615[/C][C]0.235050162138701[/C][C]33.6262101754356[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 23 )[/C][C]7.9[/C][C]0.229017422026877[/C][C]34.4951922438148[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 23 )[/C][C]7.89583333333333[/C][C]0.221294513760127[/C][C]35.6802037211463[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 23 )[/C][C]7.89130434782609[/C][C]0.21134092445006[/C][C]37.3392156221537[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 23 )[/C][C]7.88636363636364[/C][C]0.198343854079924[/C][C]39.7610688415169[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 23 )[/C][C]7.88095238095238[/C][C]0.196373571295493[/C][C]40.132449234187[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 23 )[/C][C]7.875[/C][C]0.193442166537887[/C][C]40.7098418144402[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 23 )[/C][C]7.86842105263158[/C][C]0.189222609054772[/C][C]41.5828800370997[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 23 )[/C][C]7.86111111111111[/C][C]0.183237107984448[/C][C]42.9013052955316[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 23 )[/C][C]7.85294117647059[/C][C]0.17475398006722[/C][C]44.9371234546414[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 23 )[/C][C]7.84375[/C][C]0.162573649563077[/C][C]48.247363709189[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 23 )[/C][C]7.86666666666667[/C][C]0.157080646490635[/C][C]50.0804322010203[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 23 )[/C][C]7.89285714285714[/C][C]0.148531486287404[/C][C]53.1392860876966[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 23 )[/C][C]7.88461538461539[/C][C]0.15014785612264[/C][C]52.5123407568024[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 23 )[/C][C]7.875[/C][C]0.151232856256814[/C][C]52.0720179127423[/C][/ROW]
[ROW][C]Median[/C][C]8[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]8[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]7.88636363636364[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]7.88636363636364[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]7.88636363636364[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]7.88636363636364[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]7.88636363636364[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]7.88636363636364[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]7.88636363636364[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]7.88636363636364[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]70[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=154698&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=154698&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 Mean7.914285714285710.33296637594893923.7690237992661
Geometric Mean7.30669846773371
Harmonic Mean6.39544125913007
Quadratic Mean8.38365757206926
Winsorized Mean ( 1 / 23 )7.90.3211972942964424.5954749317063
Winsorized Mean ( 2 / 23 )7.928571428571430.31413981179504925.2389895545751
Winsorized Mean ( 3 / 23 )7.885714285714290.30492361134357325.861278013099
Winsorized Mean ( 4 / 23 )7.942857142857140.29268919084439927.1375144396083
Winsorized Mean ( 5 / 23 )7.942857142857140.29268919084439927.1375144396083
Winsorized Mean ( 6 / 23 )7.942857142857140.29268919084439927.1375144396083
Winsorized Mean ( 7 / 23 )8.042857142857140.27485039355013529.2626728270995
Winsorized Mean ( 8 / 23 )7.928571428571430.25278689178629631.3646462146232
Winsorized Mean ( 9 / 23 )7.928571428571430.25278689178629631.3646462146232
Winsorized Mean ( 10 / 23 )7.928571428571430.25278689178629631.3646462146232
Winsorized Mean ( 11 / 23 )7.928571428571430.25278689178629631.3646462146232
Winsorized Mean ( 12 / 23 )7.928571428571430.25278689178629631.3646462146232
Winsorized Mean ( 13 / 23 )7.928571428571430.1923177027403941.226425417915
Winsorized Mean ( 14 / 23 )7.928571428571430.1923177027403941.226425417915
Winsorized Mean ( 15 / 23 )7.928571428571430.1923177027403941.226425417915
Winsorized Mean ( 16 / 23 )7.928571428571430.1923177027403941.226425417915
Winsorized Mean ( 17 / 23 )7.928571428571430.1923177027403941.226425417915
Winsorized Mean ( 18 / 23 )7.928571428571430.1923177027403941.226425417915
Winsorized Mean ( 19 / 23 )7.657142857142860.15347690769269749.8911723741173
Winsorized Mean ( 20 / 23 )7.657142857142860.15347690769269749.8911723741173
Winsorized Mean ( 21 / 23 )7.957142857142860.11040245272449172.073968111921
Winsorized Mean ( 22 / 23 )7.957142857142860.11040245272449172.073968111921
Winsorized Mean ( 23 / 23 )7.957142857142860.11040245272449172.073968111921
Trimmed Mean ( 1 / 23 )7.911764705882350.30987216920155125.5323500857422
Trimmed Mean ( 2 / 23 )7.924242424242420.29629460396022526.7444709364541
Trimmed Mean ( 3 / 23 )7.9218750.2846125599403427.8338911032618
Trimmed Mean ( 4 / 23 )7.935483870967740.27486929516519128.8700266291972
Trimmed Mean ( 5 / 23 )7.933333333333330.26772389296161729.6325189566503
Trimmed Mean ( 6 / 23 )7.931034482758620.25897334294601630.6249067666083
Trimmed Mean ( 7 / 23 )7.928571428571430.2481845025577431.946279267485
Trimmed Mean ( 8 / 23 )7.90740740740740.23977120255086832.9789704655205
Trimmed Mean ( 9 / 23 )7.903846153846150.23505016213870133.6262101754356
Trimmed Mean ( 10 / 23 )7.90.22901742202687734.4951922438148
Trimmed Mean ( 11 / 23 )7.895833333333330.22129451376012735.6802037211463
Trimmed Mean ( 12 / 23 )7.891304347826090.2113409244500637.3392156221537
Trimmed Mean ( 13 / 23 )7.886363636363640.19834385407992439.7610688415169
Trimmed Mean ( 14 / 23 )7.880952380952380.19637357129549340.132449234187
Trimmed Mean ( 15 / 23 )7.8750.19344216653788740.7098418144402
Trimmed Mean ( 16 / 23 )7.868421052631580.18922260905477241.5828800370997
Trimmed Mean ( 17 / 23 )7.861111111111110.18323710798444842.9013052955316
Trimmed Mean ( 18 / 23 )7.852941176470590.1747539800672244.9371234546414
Trimmed Mean ( 19 / 23 )7.843750.16257364956307748.247363709189
Trimmed Mean ( 20 / 23 )7.866666666666670.15708064649063550.0804322010203
Trimmed Mean ( 21 / 23 )7.892857142857140.14853148628740453.1392860876966
Trimmed Mean ( 22 / 23 )7.884615384615390.1501478561226452.5123407568024
Trimmed Mean ( 23 / 23 )7.8750.15123285625681452.0720179127423
Median8
Midrange8
Midmean - Weighted Average at Xnp7.88636363636364
Midmean - Weighted Average at X(n+1)p7.88636363636364
Midmean - Empirical Distribution Function7.88636363636364
Midmean - Empirical Distribution Function - Averaging7.88636363636364
Midmean - Empirical Distribution Function - Interpolation7.88636363636364
Midmean - Closest Observation7.88636363636364
Midmean - True Basic - Statistics Graphics Toolkit7.88636363636364
Midmean - MS Excel (old versions)7.88636363636364
Number of observations70



Parameters (Session):
par1 = 5 ; par2 = grey ; par3 = FALSE ; par4 = Unknown ;
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')