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R Software Module

rwasp_centraltendency.wasp

Title produced by software

Central Tendency

Date of computation

Wed, 22 May 2013 09:25:12 -0400

Cite this page as follows

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2013/May/22/t1369229126bx9mqari0764t2a.htm/, Retrieved Sun, 28 Apr 2024 04:01:09 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=209569, Retrieved Sun, 28 Apr 2024 04:01:09 +0000

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User-defined keywords

Estimated Impact

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)

-     [Histogram] [] [2013-02-07 15:03:10] [f7b6cf1ee1276a04b9fb855631752c2b]
- R P   [Histogram] [] [2013-02-14 13:17:32] [f7b6cf1ee1276a04b9fb855631752c2b]
- RMPD      [Central Tendency] [Opnieuw] [2013-05-22 13:25:12] [c4c9b4129bedc71f03f13c4d5d04c320] [Current]

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Boxplots

2.39
2.4
2.42
2.42
2.44
2.44
2.44
2.45
2.46
2.47
2.48
2.48
2.49
2.5
2.51
2.52
2.52
2.52
2.54
2.54
2.54
2.56
2.57
2.58
2.58
2.58
2.58
2.59
2.6
2.61
2.61
2.62
2.63
2.65
2.67
2.68
2.67
2.68
2.68
2.68
2.68
2.69
2.69
2.69
2.7
2.71
2.72
2.71
2.72
2.73
2.74
2.74
2.75
2.75
2.76
2.75
2.78
2.79
2.8
2.81
2.81
2.82
2.82
2.83
2.83
2.84
2.84
2.84
2.86
2.87
2.88
2.88

Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	4 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 & 4 seconds \tabularnewline
R Server & 'Gertrude Mary Cox' @ cox.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=209569&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]4 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=209569&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=209569&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 Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	4 seconds
R Server	'Gertrude Mary Cox' @ cox.wessa.net

Central Tendency - Ungrouped Data
Measure	Value	S.E.	Value/S.E.
Arithmetic Mean	2.6475	0.0163535732600694	161.891224498588
Geometric Mean	2.64389467152583
Harmonic Mean	2.64027301258447
Quadratic Mean	2.65108363588259
Winsorized Mean ( 1 / 24 )	2.64763888888889	0.0163233334526403	162.19964485628
Winsorized Mean ( 2 / 24 )	2.64791666666667	0.0161540140943823	163.916946660799
Winsorized Mean ( 3 / 24 )	2.6475	0.0160748810162629	164.697953118379
Winsorized Mean ( 4 / 24 )	2.6475	0.0156606596215136	169.05418187897
Winsorized Mean ( 5 / 24 )	2.6475	0.0156606596215136	169.054181878969
Winsorized Mean ( 6 / 24 )	2.6475	0.0156606596215136	169.054181878969
Winsorized Mean ( 7 / 24 )	2.6475	0.0153158580760987	172.860050468317
Winsorized Mean ( 8 / 24 )	2.64861111111111	0.0151173106471776	175.20385556181
Winsorized Mean ( 9 / 24 )	2.64861111111111	0.0146920735386548	180.274833510915
Winsorized Mean ( 10 / 24 )	2.65	0.0144581312307451	183.287864642202
Winsorized Mean ( 11 / 24 )	2.64847222222222	0.0142092837610088	186.390268979623
Winsorized Mean ( 12 / 24 )	2.65013888888889	0.0139352025156863	190.175843221921
Winsorized Mean ( 13 / 24 )	2.65013888888889	0.0133575089740566	198.400681896309
Winsorized Mean ( 14 / 24 )	2.65013888888889	0.0127490725913218	207.869150473958
Winsorized Mean ( 15 / 24 )	2.65013888888889	0.0121117208321633	218.807791693094
Winsorized Mean ( 16 / 24 )	2.64569444444444	0.011463397538835	230.794965932353
Winsorized Mean ( 17 / 24 )	2.64333333333333	0.0111382688450158	237.319943531097
Winsorized Mean ( 18 / 24 )	2.64833333333333	0.0103801001379196	255.135624718945
Winsorized Mean ( 19 / 24 )	2.64833333333333	0.0103801001379196	255.135624718945
Winsorized Mean ( 20 / 24 )	2.64555555555556	0.0100036943271609	264.457856171459
Winsorized Mean ( 21 / 24 )	2.65138888888889	0.00915931321690988	289.474639211366
Winsorized Mean ( 22 / 24 )	2.65138888888889	0.00832230621485328	318.588239898792
Winsorized Mean ( 23 / 24 )	2.65138888888889	0.00746747133584227	355.05846218154
Winsorized Mean ( 24 / 24 )	2.65138888888889	0.00746747133584227	355.05846218154
Trimmed Mean ( 1 / 24 )	2.64785714285714	0.0160664933761385	164.806164037616
Trimmed Mean ( 2 / 24 )	2.64808823529412	0.015758907556715	168.037551192167
Trimmed Mean ( 3 / 24 )	2.64818181818182	0.0154963099463648	170.891123586686
Trimmed Mean ( 4 / 24 )	2.6484375	0.0152137853078337	174.081429861922
Trimmed Mean ( 5 / 24 )	2.64870967741936	0.0150189090598433	176.358327150493
Trimmed Mean ( 6 / 24 )	2.649	0.0147764891895322	179.271271140413
Trimmed Mean ( 7 / 24 )	2.64931034482759	0.0144758431333092	183.015961172684
Trimmed Mean ( 8 / 24 )	2.64964285714286	0.014192471677587	186.693545517319
Trimmed Mean ( 9 / 24 )	2.64981481481481	0.0138865593201223	190.818672482471
Trimmed Mean ( 10 / 24 )	2.65	0.0136011932756604	194.835846112284
Trimmed Mean ( 11 / 24 )	2.65	0.0132910895424149	199.381697906951
Trimmed Mean ( 12 / 24 )	2.65020833333333	0.0129493338341943	204.659820131838
Trimmed Mean ( 13 / 24 )	2.65021739130435	0.0125705319486472	210.827783750994
Trimmed Mean ( 14 / 24 )	2.65022727272727	0.0122106624998554	217.042054250428
Trimmed Mean ( 15 / 24 )	2.6502380952381	0.0118766800033603	223.146375459157
Trimmed Mean ( 16 / 24 )	2.65025	0.0115774288585315	228.915248142251
Trimmed Mean ( 17 / 24 )	2.65078947368421	0.0113171126289833	234.228425622936
Trimmed Mean ( 18 / 24 )	2.65166666666667	0.0110230638439563	240.556228667814
Trimmed Mean ( 19 / 24 )	2.65205882352941	0.0108035398219903	245.480543157828
Trimmed Mean ( 20 / 24 )	2.6525	0.0104726987617729	253.277599245199
Trimmed Mean ( 21 / 24 )	2.65333333333333	0.0100839389007862	263.124693578465
Trimmed Mean ( 22 / 24 )	2.65357142857143	0.00977544550621859	271.452736029614
Trimmed Mean ( 23 / 24 )	2.65384615384615	0.00956076796202422	277.576672123761
Trimmed Mean ( 24 / 24 )	2.65416666666667	0.00947759881125242	280.046319698136
Median	2.675
Midrange	2.635
Midmean - Weighted Average at Xnp	2.64425
Midmean - Weighted Average at X(n+1)p	2.65432432432432
Midmean - Empirical Distribution Function	2.64425
Midmean - Empirical Distribution Function - Averaging	2.65432432432432
Midmean - Empirical Distribution Function - Interpolation	2.65432432432432
Midmean - Closest Observation	2.64425
Midmean - True Basic - Statistics Graphics Toolkit	2.65432432432432
Midmean - MS Excel (old versions)	2.64425
Number of observations	72

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 2.6475 & 0.0163535732600694 & 161.891224498588 \tabularnewline
Geometric Mean & 2.64389467152583 &  &  \tabularnewline
Harmonic Mean & 2.64027301258447 &  &  \tabularnewline
Quadratic Mean & 2.65108363588259 &  &  \tabularnewline
Winsorized Mean ( 1 / 24 ) & 2.64763888888889 & 0.0163233334526403 & 162.19964485628 \tabularnewline
Winsorized Mean ( 2 / 24 ) & 2.64791666666667 & 0.0161540140943823 & 163.916946660799 \tabularnewline
Winsorized Mean ( 3 / 24 ) & 2.6475 & 0.0160748810162629 & 164.697953118379 \tabularnewline
Winsorized Mean ( 4 / 24 ) & 2.6475 & 0.0156606596215136 & 169.05418187897 \tabularnewline
Winsorized Mean ( 5 / 24 ) & 2.6475 & 0.0156606596215136 & 169.054181878969 \tabularnewline
Winsorized Mean ( 6 / 24 ) & 2.6475 & 0.0156606596215136 & 169.054181878969 \tabularnewline
Winsorized Mean ( 7 / 24 ) & 2.6475 & 0.0153158580760987 & 172.860050468317 \tabularnewline
Winsorized Mean ( 8 / 24 ) & 2.64861111111111 & 0.0151173106471776 & 175.20385556181 \tabularnewline
Winsorized Mean ( 9 / 24 ) & 2.64861111111111 & 0.0146920735386548 & 180.274833510915 \tabularnewline
Winsorized Mean ( 10 / 24 ) & 2.65 & 0.0144581312307451 & 183.287864642202 \tabularnewline
Winsorized Mean ( 11 / 24 ) & 2.64847222222222 & 0.0142092837610088 & 186.390268979623 \tabularnewline
Winsorized Mean ( 12 / 24 ) & 2.65013888888889 & 0.0139352025156863 & 190.175843221921 \tabularnewline
Winsorized Mean ( 13 / 24 ) & 2.65013888888889 & 0.0133575089740566 & 198.400681896309 \tabularnewline
Winsorized Mean ( 14 / 24 ) & 2.65013888888889 & 0.0127490725913218 & 207.869150473958 \tabularnewline
Winsorized Mean ( 15 / 24 ) & 2.65013888888889 & 0.0121117208321633 & 218.807791693094 \tabularnewline
Winsorized Mean ( 16 / 24 ) & 2.64569444444444 & 0.011463397538835 & 230.794965932353 \tabularnewline
Winsorized Mean ( 17 / 24 ) & 2.64333333333333 & 0.0111382688450158 & 237.319943531097 \tabularnewline
Winsorized Mean ( 18 / 24 ) & 2.64833333333333 & 0.0103801001379196 & 255.135624718945 \tabularnewline
Winsorized Mean ( 19 / 24 ) & 2.64833333333333 & 0.0103801001379196 & 255.135624718945 \tabularnewline
Winsorized Mean ( 20 / 24 ) & 2.64555555555556 & 0.0100036943271609 & 264.457856171459 \tabularnewline
Winsorized Mean ( 21 / 24 ) & 2.65138888888889 & 0.00915931321690988 & 289.474639211366 \tabularnewline
Winsorized Mean ( 22 / 24 ) & 2.65138888888889 & 0.00832230621485328 & 318.588239898792 \tabularnewline
Winsorized Mean ( 23 / 24 ) & 2.65138888888889 & 0.00746747133584227 & 355.05846218154 \tabularnewline
Winsorized Mean ( 24 / 24 ) & 2.65138888888889 & 0.00746747133584227 & 355.05846218154 \tabularnewline
Trimmed Mean ( 1 / 24 ) & 2.64785714285714 & 0.0160664933761385 & 164.806164037616 \tabularnewline
Trimmed Mean ( 2 / 24 ) & 2.64808823529412 & 0.015758907556715 & 168.037551192167 \tabularnewline
Trimmed Mean ( 3 / 24 ) & 2.64818181818182 & 0.0154963099463648 & 170.891123586686 \tabularnewline
Trimmed Mean ( 4 / 24 ) & 2.6484375 & 0.0152137853078337 & 174.081429861922 \tabularnewline
Trimmed Mean ( 5 / 24 ) & 2.64870967741936 & 0.0150189090598433 & 176.358327150493 \tabularnewline
Trimmed Mean ( 6 / 24 ) & 2.649 & 0.0147764891895322 & 179.271271140413 \tabularnewline
Trimmed Mean ( 7 / 24 ) & 2.64931034482759 & 0.0144758431333092 & 183.015961172684 \tabularnewline
Trimmed Mean ( 8 / 24 ) & 2.64964285714286 & 0.014192471677587 & 186.693545517319 \tabularnewline
Trimmed Mean ( 9 / 24 ) & 2.64981481481481 & 0.0138865593201223 & 190.818672482471 \tabularnewline
Trimmed Mean ( 10 / 24 ) & 2.65 & 0.0136011932756604 & 194.835846112284 \tabularnewline
Trimmed Mean ( 11 / 24 ) & 2.65 & 0.0132910895424149 & 199.381697906951 \tabularnewline
Trimmed Mean ( 12 / 24 ) & 2.65020833333333 & 0.0129493338341943 & 204.659820131838 \tabularnewline
Trimmed Mean ( 13 / 24 ) & 2.65021739130435 & 0.0125705319486472 & 210.827783750994 \tabularnewline
Trimmed Mean ( 14 / 24 ) & 2.65022727272727 & 0.0122106624998554 & 217.042054250428 \tabularnewline
Trimmed Mean ( 15 / 24 ) & 2.6502380952381 & 0.0118766800033603 & 223.146375459157 \tabularnewline
Trimmed Mean ( 16 / 24 ) & 2.65025 & 0.0115774288585315 & 228.915248142251 \tabularnewline
Trimmed Mean ( 17 / 24 ) & 2.65078947368421 & 0.0113171126289833 & 234.228425622936 \tabularnewline
Trimmed Mean ( 18 / 24 ) & 2.65166666666667 & 0.0110230638439563 & 240.556228667814 \tabularnewline
Trimmed Mean ( 19 / 24 ) & 2.65205882352941 & 0.0108035398219903 & 245.480543157828 \tabularnewline
Trimmed Mean ( 20 / 24 ) & 2.6525 & 0.0104726987617729 & 253.277599245199 \tabularnewline
Trimmed Mean ( 21 / 24 ) & 2.65333333333333 & 0.0100839389007862 & 263.124693578465 \tabularnewline
Trimmed Mean ( 22 / 24 ) & 2.65357142857143 & 0.00977544550621859 & 271.452736029614 \tabularnewline
Trimmed Mean ( 23 / 24 ) & 2.65384615384615 & 0.00956076796202422 & 277.576672123761 \tabularnewline
Trimmed Mean ( 24 / 24 ) & 2.65416666666667 & 0.00947759881125242 & 280.046319698136 \tabularnewline
Median & 2.675 &  &  \tabularnewline
Midrange & 2.635 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 2.64425 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 2.65432432432432 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 2.64425 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 2.65432432432432 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 2.65432432432432 &  &  \tabularnewline
Midmean - Closest Observation & 2.64425 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 2.65432432432432 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 2.64425 &  &  \tabularnewline
Number of observations & 72 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=209569&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]2.6475[/C][C]0.0163535732600694[/C][C]161.891224498588[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]2.64389467152583[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]2.64027301258447[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]2.65108363588259[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 24 )[/C][C]2.64763888888889[/C][C]0.0163233334526403[/C][C]162.19964485628[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 24 )[/C][C]2.64791666666667[/C][C]0.0161540140943823[/C][C]163.916946660799[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 24 )[/C][C]2.6475[/C][C]0.0160748810162629[/C][C]164.697953118379[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 24 )[/C][C]2.6475[/C][C]0.0156606596215136[/C][C]169.05418187897[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 24 )[/C][C]2.6475[/C][C]0.0156606596215136[/C][C]169.054181878969[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 24 )[/C][C]2.6475[/C][C]0.0156606596215136[/C][C]169.054181878969[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 24 )[/C][C]2.6475[/C][C]0.0153158580760987[/C][C]172.860050468317[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 24 )[/C][C]2.64861111111111[/C][C]0.0151173106471776[/C][C]175.20385556181[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 24 )[/C][C]2.64861111111111[/C][C]0.0146920735386548[/C][C]180.274833510915[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 24 )[/C][C]2.65[/C][C]0.0144581312307451[/C][C]183.287864642202[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 24 )[/C][C]2.64847222222222[/C][C]0.0142092837610088[/C][C]186.390268979623[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 24 )[/C][C]2.65013888888889[/C][C]0.0139352025156863[/C][C]190.175843221921[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 24 )[/C][C]2.65013888888889[/C][C]0.0133575089740566[/C][C]198.400681896309[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 24 )[/C][C]2.65013888888889[/C][C]0.0127490725913218[/C][C]207.869150473958[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 24 )[/C][C]2.65013888888889[/C][C]0.0121117208321633[/C][C]218.807791693094[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 24 )[/C][C]2.64569444444444[/C][C]0.011463397538835[/C][C]230.794965932353[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 24 )[/C][C]2.64333333333333[/C][C]0.0111382688450158[/C][C]237.319943531097[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 24 )[/C][C]2.64833333333333[/C][C]0.0103801001379196[/C][C]255.135624718945[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 24 )[/C][C]2.64833333333333[/C][C]0.0103801001379196[/C][C]255.135624718945[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 24 )[/C][C]2.64555555555556[/C][C]0.0100036943271609[/C][C]264.457856171459[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 24 )[/C][C]2.65138888888889[/C][C]0.00915931321690988[/C][C]289.474639211366[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 24 )[/C][C]2.65138888888889[/C][C]0.00832230621485328[/C][C]318.588239898792[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 24 )[/C][C]2.65138888888889[/C][C]0.00746747133584227[/C][C]355.05846218154[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 24 )[/C][C]2.65138888888889[/C][C]0.00746747133584227[/C][C]355.05846218154[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 24 )[/C][C]2.64785714285714[/C][C]0.0160664933761385[/C][C]164.806164037616[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 24 )[/C][C]2.64808823529412[/C][C]0.015758907556715[/C][C]168.037551192167[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 24 )[/C][C]2.64818181818182[/C][C]0.0154963099463648[/C][C]170.891123586686[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 24 )[/C][C]2.6484375[/C][C]0.0152137853078337[/C][C]174.081429861922[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 24 )[/C][C]2.64870967741936[/C][C]0.0150189090598433[/C][C]176.358327150493[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 24 )[/C][C]2.649[/C][C]0.0147764891895322[/C][C]179.271271140413[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 24 )[/C][C]2.64931034482759[/C][C]0.0144758431333092[/C][C]183.015961172684[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 24 )[/C][C]2.64964285714286[/C][C]0.014192471677587[/C][C]186.693545517319[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 24 )[/C][C]2.64981481481481[/C][C]0.0138865593201223[/C][C]190.818672482471[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 24 )[/C][C]2.65[/C][C]0.0136011932756604[/C][C]194.835846112284[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 24 )[/C][C]2.65[/C][C]0.0132910895424149[/C][C]199.381697906951[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 24 )[/C][C]2.65020833333333[/C][C]0.0129493338341943[/C][C]204.659820131838[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 24 )[/C][C]2.65021739130435[/C][C]0.0125705319486472[/C][C]210.827783750994[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 24 )[/C][C]2.65022727272727[/C][C]0.0122106624998554[/C][C]217.042054250428[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 24 )[/C][C]2.6502380952381[/C][C]0.0118766800033603[/C][C]223.146375459157[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 24 )[/C][C]2.65025[/C][C]0.0115774288585315[/C][C]228.915248142251[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 24 )[/C][C]2.65078947368421[/C][C]0.0113171126289833[/C][C]234.228425622936[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 24 )[/C][C]2.65166666666667[/C][C]0.0110230638439563[/C][C]240.556228667814[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 24 )[/C][C]2.65205882352941[/C][C]0.0108035398219903[/C][C]245.480543157828[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 24 )[/C][C]2.6525[/C][C]0.0104726987617729[/C][C]253.277599245199[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 24 )[/C][C]2.65333333333333[/C][C]0.0100839389007862[/C][C]263.124693578465[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 24 )[/C][C]2.65357142857143[/C][C]0.00977544550621859[/C][C]271.452736029614[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 24 )[/C][C]2.65384615384615[/C][C]0.00956076796202422[/C][C]277.576672123761[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 24 )[/C][C]2.65416666666667[/C][C]0.00947759881125242[/C][C]280.046319698136[/C][/ROW]
[ROW][C]Median[/C][C]2.675[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]2.635[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]2.64425[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]2.65432432432432[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]2.64425[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]2.65432432432432[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]2.65432432432432[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]2.64425[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]2.65432432432432[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]2.64425[/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=209569&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=209569&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
Measure	Value	S.E.	Value/S.E.
Arithmetic Mean	2.6475	0.0163535732600694	161.891224498588
Geometric Mean	2.64389467152583
Harmonic Mean	2.64027301258447
Quadratic Mean	2.65108363588259
Winsorized Mean ( 1 / 24 )	2.64763888888889	0.0163233334526403	162.19964485628
Winsorized Mean ( 2 / 24 )	2.64791666666667	0.0161540140943823	163.916946660799
Winsorized Mean ( 3 / 24 )	2.6475	0.0160748810162629	164.697953118379
Winsorized Mean ( 4 / 24 )	2.6475	0.0156606596215136	169.05418187897
Winsorized Mean ( 5 / 24 )	2.6475	0.0156606596215136	169.054181878969
Winsorized Mean ( 6 / 24 )	2.6475	0.0156606596215136	169.054181878969
Winsorized Mean ( 7 / 24 )	2.6475	0.0153158580760987	172.860050468317
Winsorized Mean ( 8 / 24 )	2.64861111111111	0.0151173106471776	175.20385556181
Winsorized Mean ( 9 / 24 )	2.64861111111111	0.0146920735386548	180.274833510915
Winsorized Mean ( 10 / 24 )	2.65	0.0144581312307451	183.287864642202
Winsorized Mean ( 11 / 24 )	2.64847222222222	0.0142092837610088	186.390268979623
Winsorized Mean ( 12 / 24 )	2.65013888888889	0.0139352025156863	190.175843221921
Winsorized Mean ( 13 / 24 )	2.65013888888889	0.0133575089740566	198.400681896309
Winsorized Mean ( 14 / 24 )	2.65013888888889	0.0127490725913218	207.869150473958
Winsorized Mean ( 15 / 24 )	2.65013888888889	0.0121117208321633	218.807791693094
Winsorized Mean ( 16 / 24 )	2.64569444444444	0.011463397538835	230.794965932353
Winsorized Mean ( 17 / 24 )	2.64333333333333	0.0111382688450158	237.319943531097
Winsorized Mean ( 18 / 24 )	2.64833333333333	0.0103801001379196	255.135624718945
Winsorized Mean ( 19 / 24 )	2.64833333333333	0.0103801001379196	255.135624718945
Winsorized Mean ( 20 / 24 )	2.64555555555556	0.0100036943271609	264.457856171459
Winsorized Mean ( 21 / 24 )	2.65138888888889	0.00915931321690988	289.474639211366
Winsorized Mean ( 22 / 24 )	2.65138888888889	0.00832230621485328	318.588239898792
Winsorized Mean ( 23 / 24 )	2.65138888888889	0.00746747133584227	355.05846218154
Winsorized Mean ( 24 / 24 )	2.65138888888889	0.00746747133584227	355.05846218154
Trimmed Mean ( 1 / 24 )	2.64785714285714	0.0160664933761385	164.806164037616
Trimmed Mean ( 2 / 24 )	2.64808823529412	0.015758907556715	168.037551192167
Trimmed Mean ( 3 / 24 )	2.64818181818182	0.0154963099463648	170.891123586686
Trimmed Mean ( 4 / 24 )	2.6484375	0.0152137853078337	174.081429861922
Trimmed Mean ( 5 / 24 )	2.64870967741936	0.0150189090598433	176.358327150493
Trimmed Mean ( 6 / 24 )	2.649	0.0147764891895322	179.271271140413
Trimmed Mean ( 7 / 24 )	2.64931034482759	0.0144758431333092	183.015961172684
Trimmed Mean ( 8 / 24 )	2.64964285714286	0.014192471677587	186.693545517319
Trimmed Mean ( 9 / 24 )	2.64981481481481	0.0138865593201223	190.818672482471
Trimmed Mean ( 10 / 24 )	2.65	0.0136011932756604	194.835846112284
Trimmed Mean ( 11 / 24 )	2.65	0.0132910895424149	199.381697906951
Trimmed Mean ( 12 / 24 )	2.65020833333333	0.0129493338341943	204.659820131838
Trimmed Mean ( 13 / 24 )	2.65021739130435	0.0125705319486472	210.827783750994
Trimmed Mean ( 14 / 24 )	2.65022727272727	0.0122106624998554	217.042054250428
Trimmed Mean ( 15 / 24 )	2.6502380952381	0.0118766800033603	223.146375459157
Trimmed Mean ( 16 / 24 )	2.65025	0.0115774288585315	228.915248142251
Trimmed Mean ( 17 / 24 )	2.65078947368421	0.0113171126289833	234.228425622936
Trimmed Mean ( 18 / 24 )	2.65166666666667	0.0110230638439563	240.556228667814
Trimmed Mean ( 19 / 24 )	2.65205882352941	0.0108035398219903	245.480543157828
Trimmed Mean ( 20 / 24 )	2.6525	0.0104726987617729	253.277599245199
Trimmed Mean ( 21 / 24 )	2.65333333333333	0.0100839389007862	263.124693578465
Trimmed Mean ( 22 / 24 )	2.65357142857143	0.00977544550621859	271.452736029614
Trimmed Mean ( 23 / 24 )	2.65384615384615	0.00956076796202422	277.576672123761
Trimmed Mean ( 24 / 24 )	2.65416666666667	0.00947759881125242	280.046319698136
Median	2.675
Midrange	2.635
Midmean - Weighted Average at Xnp	2.64425
Midmean - Weighted Average at X(n+1)p	2.65432432432432
Midmean - Empirical Distribution Function	2.64425
Midmean - Empirical Distribution Function - Averaging	2.65432432432432
Midmean - Empirical Distribution Function - Interpolation	2.65432432432432
Midmean - Closest Observation	2.64425
Midmean - True Basic - Statistics Graphics Toolkit	2.65432432432432
Midmean - MS Excel (old versions)	2.64425
Number of observations	72

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

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')

Free Statistics

Description of Statistical Computation

Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code