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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 14:46:47 -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/t13238056660xyo9izz958b516.htm/, Retrieved Thu, 02 May 2024 19:39:47 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=154668, Retrieved Thu, 02 May 2024 19:39:47 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact93
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] [76a85a4cc6ea7903d92a0f5b9d2872d3] [Current]
-   PD        [Central Tendency] [central tendency ...] [2011-12-13 20:31:23] [22f8bc702946f784836540059d0d9516]
-    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:
2
8
7
4
11
9
2
13
11
13
9
1
3
10
1
5
6
12
2
4
7
5
9
8
15
3
3
14
11
9
13
8
11
2
13
10
1
15
12
14
10
3
11
3
13
3
13
5
2
10
15
1
1
4
8
8
10
15
8
11
5
8
14
12
9
1
5
9
6
7




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Gertrude Mary Cox' @ cox.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 & 2 seconds \tabularnewline
R Server & 'Gertrude Mary Cox' @ cox.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=154668&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]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gertrude Mary Cox' @ cox.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=154668&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=154668&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 time2 seconds
R Server'Gertrude Mary Cox' @ cox.wessa.net







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean7.80.5202324691387214.9932971560069
Geometric Mean6.12952918280997
Harmonic Mean4.16877169376058
Quadratic Mean8.91707831715555
Winsorized Mean ( 1 / 23 )7.80.5202324691387214.9932971560069
Winsorized Mean ( 2 / 23 )7.80.5202324691387214.9932971560069
Winsorized Mean ( 3 / 23 )7.80.5202324691387214.9932971560069
Winsorized Mean ( 4 / 23 )7.742857142857140.50940866716264315.1996965147533
Winsorized Mean ( 5 / 23 )7.742857142857140.50940866716264315.1996965147533
Winsorized Mean ( 6 / 23 )7.828571428571430.49384259509000415.8523616763853
Winsorized Mean ( 7 / 23 )7.728571428571430.4767563925041316.2107347695489
Winsorized Mean ( 8 / 23 )7.728571428571430.4767563925041316.2107347695489
Winsorized Mean ( 9 / 23 )7.728571428571430.4767563925041316.2107347695489
Winsorized Mean ( 10 / 23 )7.728571428571430.4767563925041316.2107347695489
Winsorized Mean ( 11 / 23 )7.885714285714290.45069206370984417.4969007015644
Winsorized Mean ( 12 / 23 )7.885714285714290.45069206370984417.4969007015644
Winsorized Mean ( 13 / 23 )7.70.42164520522475618.2617990305274
Winsorized Mean ( 14 / 23 )7.70.42164520522475618.2617990305274
Winsorized Mean ( 15 / 23 )7.70.42164520522475618.2617990305274
Winsorized Mean ( 16 / 23 )7.471428571428570.38968130981352319.1731766016798
Winsorized Mean ( 17 / 23 )7.714285714285710.35077132231134421.9923500685684
Winsorized Mean ( 18 / 23 )7.714285714285710.35077132231134421.9923500685684
Winsorized Mean ( 19 / 23 )7.714285714285710.35077132231134421.9923500685684
Winsorized Mean ( 20 / 23 )80.30860669992418425.9229627936314
Winsorized Mean ( 21 / 23 )80.30860669992418425.9229627936314
Winsorized Mean ( 22 / 23 )7.685714285714290.26651874039652428.8374253693364
Winsorized Mean ( 23 / 23 )7.685714285714290.26651874039652428.8374253693364
Trimmed Mean ( 1 / 23 )7.794117647058820.51516034119676915.1294985731089
Trimmed Mean ( 2 / 23 )7.787878787878790.50890217391733215.3032924342427
Trimmed Mean ( 3 / 23 )7.781250.50122308244235515.5245244534302
Trimmed Mean ( 4 / 23 )7.77419354838710.49182602314021715.8067958640137
Trimmed Mean ( 5 / 23 )7.783333333333330.48426755612302916.0723823740031
Trimmed Mean ( 6 / 23 )7.793103448275860.47487293851854616.4109234621537
Trimmed Mean ( 7 / 23 )7.785714285714290.46759559458383616.6505295941542
Trimmed Mean ( 8 / 23 )7.79629629629630.46271132224702516.8491582579735
Trimmed Mean ( 9 / 23 )7.807692307692310.4562606733712717.1123499424177
Trimmed Mean ( 10 / 23 )7.820.44784290248492517.4614802570489
Trimmed Mean ( 11 / 23 )7.833333333333330.43691915173595317.9285648207688
Trimmed Mean ( 12 / 23 )7.826086956521740.4287994112608718.2511606849212
Trimmed Mean ( 13 / 23 )7.818181818181820.41797954479311818.7046995853624
Trimmed Mean ( 14 / 23 )7.833333333333330.41025850419370919.0936525465288
Trimmed Mean ( 15 / 23 )7.850.39959915813160519.6446860316324
Trimmed Mean ( 16 / 23 )7.868421052631580.38494250116823920.4405100209828
Trimmed Mean ( 17 / 23 )7.916666666666670.37241170254232921.2578353811716
Trimmed Mean ( 18 / 23 )7.941176470588240.36549279718765721.7273131828942
Trimmed Mean ( 19 / 23 )7.968750.35493177161251722.4514981113034
Trimmed Mean ( 20 / 23 )80.33903175181040523.5966099260042
Trimmed Mean ( 21 / 23 )80.32934117335311824.2909197126787
Trimmed Mean ( 22 / 23 )80.31378581622109425.4950975679639
Trimmed Mean ( 23 / 23 )8.041666666666670.30383518765284426.4671999605751
Median8
Midrange8
Midmean - Weighted Average at Xnp8
Midmean - Weighted Average at X(n+1)p8
Midmean - Empirical Distribution Function8
Midmean - Empirical Distribution Function - Averaging8
Midmean - Empirical Distribution Function - Interpolation8
Midmean - Closest Observation8
Midmean - True Basic - Statistics Graphics Toolkit8
Midmean - MS Excel (old versions)8
Number of observations70

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 7.8 & 0.52023246913872 & 14.9932971560069 \tabularnewline
Geometric Mean & 6.12952918280997 &  &  \tabularnewline
Harmonic Mean & 4.16877169376058 &  &  \tabularnewline
Quadratic Mean & 8.91707831715555 &  &  \tabularnewline
Winsorized Mean ( 1 / 23 ) & 7.8 & 0.52023246913872 & 14.9932971560069 \tabularnewline
Winsorized Mean ( 2 / 23 ) & 7.8 & 0.52023246913872 & 14.9932971560069 \tabularnewline
Winsorized Mean ( 3 / 23 ) & 7.8 & 0.52023246913872 & 14.9932971560069 \tabularnewline
Winsorized Mean ( 4 / 23 ) & 7.74285714285714 & 0.509408667162643 & 15.1996965147533 \tabularnewline
Winsorized Mean ( 5 / 23 ) & 7.74285714285714 & 0.509408667162643 & 15.1996965147533 \tabularnewline
Winsorized Mean ( 6 / 23 ) & 7.82857142857143 & 0.493842595090004 & 15.8523616763853 \tabularnewline
Winsorized Mean ( 7 / 23 ) & 7.72857142857143 & 0.47675639250413 & 16.2107347695489 \tabularnewline
Winsorized Mean ( 8 / 23 ) & 7.72857142857143 & 0.47675639250413 & 16.2107347695489 \tabularnewline
Winsorized Mean ( 9 / 23 ) & 7.72857142857143 & 0.47675639250413 & 16.2107347695489 \tabularnewline
Winsorized Mean ( 10 / 23 ) & 7.72857142857143 & 0.47675639250413 & 16.2107347695489 \tabularnewline
Winsorized Mean ( 11 / 23 ) & 7.88571428571429 & 0.450692063709844 & 17.4969007015644 \tabularnewline
Winsorized Mean ( 12 / 23 ) & 7.88571428571429 & 0.450692063709844 & 17.4969007015644 \tabularnewline
Winsorized Mean ( 13 / 23 ) & 7.7 & 0.421645205224756 & 18.2617990305274 \tabularnewline
Winsorized Mean ( 14 / 23 ) & 7.7 & 0.421645205224756 & 18.2617990305274 \tabularnewline
Winsorized Mean ( 15 / 23 ) & 7.7 & 0.421645205224756 & 18.2617990305274 \tabularnewline
Winsorized Mean ( 16 / 23 ) & 7.47142857142857 & 0.389681309813523 & 19.1731766016798 \tabularnewline
Winsorized Mean ( 17 / 23 ) & 7.71428571428571 & 0.350771322311344 & 21.9923500685684 \tabularnewline
Winsorized Mean ( 18 / 23 ) & 7.71428571428571 & 0.350771322311344 & 21.9923500685684 \tabularnewline
Winsorized Mean ( 19 / 23 ) & 7.71428571428571 & 0.350771322311344 & 21.9923500685684 \tabularnewline
Winsorized Mean ( 20 / 23 ) & 8 & 0.308606699924184 & 25.9229627936314 \tabularnewline
Winsorized Mean ( 21 / 23 ) & 8 & 0.308606699924184 & 25.9229627936314 \tabularnewline
Winsorized Mean ( 22 / 23 ) & 7.68571428571429 & 0.266518740396524 & 28.8374253693364 \tabularnewline
Winsorized Mean ( 23 / 23 ) & 7.68571428571429 & 0.266518740396524 & 28.8374253693364 \tabularnewline
Trimmed Mean ( 1 / 23 ) & 7.79411764705882 & 0.515160341196769 & 15.1294985731089 \tabularnewline
Trimmed Mean ( 2 / 23 ) & 7.78787878787879 & 0.508902173917332 & 15.3032924342427 \tabularnewline
Trimmed Mean ( 3 / 23 ) & 7.78125 & 0.501223082442355 & 15.5245244534302 \tabularnewline
Trimmed Mean ( 4 / 23 ) & 7.7741935483871 & 0.491826023140217 & 15.8067958640137 \tabularnewline
Trimmed Mean ( 5 / 23 ) & 7.78333333333333 & 0.484267556123029 & 16.0723823740031 \tabularnewline
Trimmed Mean ( 6 / 23 ) & 7.79310344827586 & 0.474872938518546 & 16.4109234621537 \tabularnewline
Trimmed Mean ( 7 / 23 ) & 7.78571428571429 & 0.467595594583836 & 16.6505295941542 \tabularnewline
Trimmed Mean ( 8 / 23 ) & 7.7962962962963 & 0.462711322247025 & 16.8491582579735 \tabularnewline
Trimmed Mean ( 9 / 23 ) & 7.80769230769231 & 0.45626067337127 & 17.1123499424177 \tabularnewline
Trimmed Mean ( 10 / 23 ) & 7.82 & 0.447842902484925 & 17.4614802570489 \tabularnewline
Trimmed Mean ( 11 / 23 ) & 7.83333333333333 & 0.436919151735953 & 17.9285648207688 \tabularnewline
Trimmed Mean ( 12 / 23 ) & 7.82608695652174 & 0.42879941126087 & 18.2511606849212 \tabularnewline
Trimmed Mean ( 13 / 23 ) & 7.81818181818182 & 0.417979544793118 & 18.7046995853624 \tabularnewline
Trimmed Mean ( 14 / 23 ) & 7.83333333333333 & 0.410258504193709 & 19.0936525465288 \tabularnewline
Trimmed Mean ( 15 / 23 ) & 7.85 & 0.399599158131605 & 19.6446860316324 \tabularnewline
Trimmed Mean ( 16 / 23 ) & 7.86842105263158 & 0.384942501168239 & 20.4405100209828 \tabularnewline
Trimmed Mean ( 17 / 23 ) & 7.91666666666667 & 0.372411702542329 & 21.2578353811716 \tabularnewline
Trimmed Mean ( 18 / 23 ) & 7.94117647058824 & 0.365492797187657 & 21.7273131828942 \tabularnewline
Trimmed Mean ( 19 / 23 ) & 7.96875 & 0.354931771612517 & 22.4514981113034 \tabularnewline
Trimmed Mean ( 20 / 23 ) & 8 & 0.339031751810405 & 23.5966099260042 \tabularnewline
Trimmed Mean ( 21 / 23 ) & 8 & 0.329341173353118 & 24.2909197126787 \tabularnewline
Trimmed Mean ( 22 / 23 ) & 8 & 0.313785816221094 & 25.4950975679639 \tabularnewline
Trimmed Mean ( 23 / 23 ) & 8.04166666666667 & 0.303835187652844 & 26.4671999605751 \tabularnewline
Median & 8 &  &  \tabularnewline
Midrange & 8 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 8 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 8 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 8 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 8 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 8 &  &  \tabularnewline
Midmean - Closest Observation & 8 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 8 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 8 &  &  \tabularnewline
Number of observations & 70 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=154668&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]7.8[/C][C]0.52023246913872[/C][C]14.9932971560069[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]6.12952918280997[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]4.16877169376058[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]8.91707831715555[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 23 )[/C][C]7.8[/C][C]0.52023246913872[/C][C]14.9932971560069[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 23 )[/C][C]7.8[/C][C]0.52023246913872[/C][C]14.9932971560069[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 23 )[/C][C]7.8[/C][C]0.52023246913872[/C][C]14.9932971560069[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 23 )[/C][C]7.74285714285714[/C][C]0.509408667162643[/C][C]15.1996965147533[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 23 )[/C][C]7.74285714285714[/C][C]0.509408667162643[/C][C]15.1996965147533[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 23 )[/C][C]7.82857142857143[/C][C]0.493842595090004[/C][C]15.8523616763853[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 23 )[/C][C]7.72857142857143[/C][C]0.47675639250413[/C][C]16.2107347695489[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 23 )[/C][C]7.72857142857143[/C][C]0.47675639250413[/C][C]16.2107347695489[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 23 )[/C][C]7.72857142857143[/C][C]0.47675639250413[/C][C]16.2107347695489[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 23 )[/C][C]7.72857142857143[/C][C]0.47675639250413[/C][C]16.2107347695489[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 23 )[/C][C]7.88571428571429[/C][C]0.450692063709844[/C][C]17.4969007015644[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 23 )[/C][C]7.88571428571429[/C][C]0.450692063709844[/C][C]17.4969007015644[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 23 )[/C][C]7.7[/C][C]0.421645205224756[/C][C]18.2617990305274[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 23 )[/C][C]7.7[/C][C]0.421645205224756[/C][C]18.2617990305274[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 23 )[/C][C]7.7[/C][C]0.421645205224756[/C][C]18.2617990305274[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 23 )[/C][C]7.47142857142857[/C][C]0.389681309813523[/C][C]19.1731766016798[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 23 )[/C][C]7.71428571428571[/C][C]0.350771322311344[/C][C]21.9923500685684[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 23 )[/C][C]7.71428571428571[/C][C]0.350771322311344[/C][C]21.9923500685684[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 23 )[/C][C]7.71428571428571[/C][C]0.350771322311344[/C][C]21.9923500685684[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 23 )[/C][C]8[/C][C]0.308606699924184[/C][C]25.9229627936314[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 23 )[/C][C]8[/C][C]0.308606699924184[/C][C]25.9229627936314[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 23 )[/C][C]7.68571428571429[/C][C]0.266518740396524[/C][C]28.8374253693364[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 23 )[/C][C]7.68571428571429[/C][C]0.266518740396524[/C][C]28.8374253693364[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 23 )[/C][C]7.79411764705882[/C][C]0.515160341196769[/C][C]15.1294985731089[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 23 )[/C][C]7.78787878787879[/C][C]0.508902173917332[/C][C]15.3032924342427[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 23 )[/C][C]7.78125[/C][C]0.501223082442355[/C][C]15.5245244534302[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 23 )[/C][C]7.7741935483871[/C][C]0.491826023140217[/C][C]15.8067958640137[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 23 )[/C][C]7.78333333333333[/C][C]0.484267556123029[/C][C]16.0723823740031[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 23 )[/C][C]7.79310344827586[/C][C]0.474872938518546[/C][C]16.4109234621537[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 23 )[/C][C]7.78571428571429[/C][C]0.467595594583836[/C][C]16.6505295941542[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 23 )[/C][C]7.7962962962963[/C][C]0.462711322247025[/C][C]16.8491582579735[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 23 )[/C][C]7.80769230769231[/C][C]0.45626067337127[/C][C]17.1123499424177[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 23 )[/C][C]7.82[/C][C]0.447842902484925[/C][C]17.4614802570489[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 23 )[/C][C]7.83333333333333[/C][C]0.436919151735953[/C][C]17.9285648207688[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 23 )[/C][C]7.82608695652174[/C][C]0.42879941126087[/C][C]18.2511606849212[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 23 )[/C][C]7.81818181818182[/C][C]0.417979544793118[/C][C]18.7046995853624[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 23 )[/C][C]7.83333333333333[/C][C]0.410258504193709[/C][C]19.0936525465288[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 23 )[/C][C]7.85[/C][C]0.399599158131605[/C][C]19.6446860316324[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 23 )[/C][C]7.86842105263158[/C][C]0.384942501168239[/C][C]20.4405100209828[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 23 )[/C][C]7.91666666666667[/C][C]0.372411702542329[/C][C]21.2578353811716[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 23 )[/C][C]7.94117647058824[/C][C]0.365492797187657[/C][C]21.7273131828942[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 23 )[/C][C]7.96875[/C][C]0.354931771612517[/C][C]22.4514981113034[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 23 )[/C][C]8[/C][C]0.339031751810405[/C][C]23.5966099260042[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 23 )[/C][C]8[/C][C]0.329341173353118[/C][C]24.2909197126787[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 23 )[/C][C]8[/C][C]0.313785816221094[/C][C]25.4950975679639[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 23 )[/C][C]8.04166666666667[/C][C]0.303835187652844[/C][C]26.4671999605751[/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]8[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]8[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]8[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]8[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]8[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]8[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]8[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]8[/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=154668&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=154668&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 Mean7.80.5202324691387214.9932971560069
Geometric Mean6.12952918280997
Harmonic Mean4.16877169376058
Quadratic Mean8.91707831715555
Winsorized Mean ( 1 / 23 )7.80.5202324691387214.9932971560069
Winsorized Mean ( 2 / 23 )7.80.5202324691387214.9932971560069
Winsorized Mean ( 3 / 23 )7.80.5202324691387214.9932971560069
Winsorized Mean ( 4 / 23 )7.742857142857140.50940866716264315.1996965147533
Winsorized Mean ( 5 / 23 )7.742857142857140.50940866716264315.1996965147533
Winsorized Mean ( 6 / 23 )7.828571428571430.49384259509000415.8523616763853
Winsorized Mean ( 7 / 23 )7.728571428571430.4767563925041316.2107347695489
Winsorized Mean ( 8 / 23 )7.728571428571430.4767563925041316.2107347695489
Winsorized Mean ( 9 / 23 )7.728571428571430.4767563925041316.2107347695489
Winsorized Mean ( 10 / 23 )7.728571428571430.4767563925041316.2107347695489
Winsorized Mean ( 11 / 23 )7.885714285714290.45069206370984417.4969007015644
Winsorized Mean ( 12 / 23 )7.885714285714290.45069206370984417.4969007015644
Winsorized Mean ( 13 / 23 )7.70.42164520522475618.2617990305274
Winsorized Mean ( 14 / 23 )7.70.42164520522475618.2617990305274
Winsorized Mean ( 15 / 23 )7.70.42164520522475618.2617990305274
Winsorized Mean ( 16 / 23 )7.471428571428570.38968130981352319.1731766016798
Winsorized Mean ( 17 / 23 )7.714285714285710.35077132231134421.9923500685684
Winsorized Mean ( 18 / 23 )7.714285714285710.35077132231134421.9923500685684
Winsorized Mean ( 19 / 23 )7.714285714285710.35077132231134421.9923500685684
Winsorized Mean ( 20 / 23 )80.30860669992418425.9229627936314
Winsorized Mean ( 21 / 23 )80.30860669992418425.9229627936314
Winsorized Mean ( 22 / 23 )7.685714285714290.26651874039652428.8374253693364
Winsorized Mean ( 23 / 23 )7.685714285714290.26651874039652428.8374253693364
Trimmed Mean ( 1 / 23 )7.794117647058820.51516034119676915.1294985731089
Trimmed Mean ( 2 / 23 )7.787878787878790.50890217391733215.3032924342427
Trimmed Mean ( 3 / 23 )7.781250.50122308244235515.5245244534302
Trimmed Mean ( 4 / 23 )7.77419354838710.49182602314021715.8067958640137
Trimmed Mean ( 5 / 23 )7.783333333333330.48426755612302916.0723823740031
Trimmed Mean ( 6 / 23 )7.793103448275860.47487293851854616.4109234621537
Trimmed Mean ( 7 / 23 )7.785714285714290.46759559458383616.6505295941542
Trimmed Mean ( 8 / 23 )7.79629629629630.46271132224702516.8491582579735
Trimmed Mean ( 9 / 23 )7.807692307692310.4562606733712717.1123499424177
Trimmed Mean ( 10 / 23 )7.820.44784290248492517.4614802570489
Trimmed Mean ( 11 / 23 )7.833333333333330.43691915173595317.9285648207688
Trimmed Mean ( 12 / 23 )7.826086956521740.4287994112608718.2511606849212
Trimmed Mean ( 13 / 23 )7.818181818181820.41797954479311818.7046995853624
Trimmed Mean ( 14 / 23 )7.833333333333330.41025850419370919.0936525465288
Trimmed Mean ( 15 / 23 )7.850.39959915813160519.6446860316324
Trimmed Mean ( 16 / 23 )7.868421052631580.38494250116823920.4405100209828
Trimmed Mean ( 17 / 23 )7.916666666666670.37241170254232921.2578353811716
Trimmed Mean ( 18 / 23 )7.941176470588240.36549279718765721.7273131828942
Trimmed Mean ( 19 / 23 )7.968750.35493177161251722.4514981113034
Trimmed Mean ( 20 / 23 )80.33903175181040523.5966099260042
Trimmed Mean ( 21 / 23 )80.32934117335311824.2909197126787
Trimmed Mean ( 22 / 23 )80.31378581622109425.4950975679639
Trimmed Mean ( 23 / 23 )8.041666666666670.30383518765284426.4671999605751
Median8
Midrange8
Midmean - Weighted Average at Xnp8
Midmean - Weighted Average at X(n+1)p8
Midmean - Empirical Distribution Function8
Midmean - Empirical Distribution Function - Averaging8
Midmean - Empirical Distribution Function - Interpolation8
Midmean - Closest Observation8
Midmean - True Basic - Statistics Graphics Toolkit8
Midmean - MS Excel (old versions)8
Number of observations70



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')