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of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationSun, 20 Apr 2008 14:34:43 -0600
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2008/Apr/20/t1208723827uapdriq3a9vwo4z.htm/, Retrieved Sun, 12 May 2024 20:53:01 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=10446, Retrieved Sun, 12 May 2024 20:53:01 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact159
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [Rekenkundig gemid...] [2008-04-20 20:34:43] [bd1a672bbeeae91e7f15e9efb6f60992] [Current]
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Dataseries X:
47,87
47,87
47,89
47,88
47,91
47,92
47,92
47,91
47,93
48,05
48,03
48,04
48,04
48,06
48,04
48,09
48,12
48,16
48,16
48,16
48,08
48,13
48,16
48,15
48,15
48,15
48,27
48,47
48,51
48,53
48,53
48,53
48,68
48,64
48,67
48,66
48,66
48,67
48,71
48,96
49,01
49,04
49,04
49,04
49,06
49,13
49,19
49,26
49,26
49,26
49,29
49,43
49,43
49,45
49,45
49,46
49,57
49,68
49,71
49,7
49,7
49,8
49,84
50,09
50,2
50,16
50,16
50,29
50,36
51,02
51,03
51,04




Summary of compuational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Sir Ronald Aylmer Fisher' @ 193.190.124.24

\begin{tabular}{lllllllll}
\hline
Summary of compuational 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 & 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=10446&T=0

[TABLE]
[ROW][C]Summary of compuational 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]'Sir Ronald Aylmer Fisher' @ 193.190.124.24[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=10446&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=10446&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 compuational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Sir Ronald Aylmer Fisher' @ 193.190.124.24







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean48.88208333333330.101062032094085483.683954502575
Geometric Mean48.8747256851132
Harmonic Mean48.8674276757827
Quadratic Mean48.8895002218722
Winsorized Mean ( 1 / 24 )48.88194444444440.101020349769937483.882153999346
Winsorized Mean ( 2 / 24 )48.88194444444440.100898281354622484.467562659879
Winsorized Mean ( 3 / 24 )48.85486111111110.093583248791879522.047072973071
Winsorized Mean ( 4 / 24 )48.85208333333330.0925569100193593527.805901505521
Winsorized Mean ( 5 / 24 )48.84583333333330.0912195133113728535.475706459875
Winsorized Mean ( 6 / 24 )48.84333333333330.0904089993720157540.248577825227
Winsorized Mean ( 7 / 24 )48.84333333333330.0904089993720157540.248577825227
Winsorized Mean ( 8 / 24 )48.83666666666670.0886770264695101550.725127025523
Winsorized Mean ( 9 / 24 )48.81791666666670.081017091238639602.563186610484
Winsorized Mean ( 10 / 24 )48.813750.0798503190639623611.31565374083
Winsorized Mean ( 11 / 24 )48.80.0775167203932938629.541597637325
Winsorized Mean ( 12 / 24 )48.79833333333330.0772419222572214631.759696125004
Winsorized Mean ( 13 / 24 )48.80013888888890.0769932046509558633.823973298962
Winsorized Mean ( 14 / 24 )48.79819444444440.0760894597415394641.326599113755
Winsorized Mean ( 15 / 24 )48.77944444444440.0718710615411081678.707721835221
Winsorized Mean ( 16 / 24 )48.75722222222220.0678862110124497718.2198195342
Winsorized Mean ( 17 / 24 )48.76194444444440.0665708345513811732.482096297121
Winsorized Mean ( 18 / 24 )48.76444444444440.066232414587812736.262519612535
Winsorized Mean ( 19 / 24 )48.76444444444440.0647569456244468753.03805598322
Winsorized Mean ( 20 / 24 )48.76444444444440.0647569456244468753.03805598322
Winsorized Mean ( 21 / 24 )48.72361111111110.0590334596363252825.355847535825
Winsorized Mean ( 22 / 24 )48.71750.0573855771086595848.950249428589
Winsorized Mean ( 23 / 24 )48.71750.0573855771086595848.950249428589
Winsorized Mean ( 24 / 24 )48.71750.0573855771086595848.950249428589
Trimmed Mean ( 1 / 24 )48.86571428571430.0981315235710083497.961434893599
Trimmed Mean ( 2 / 24 )48.84852941176470.094650891445119516.091593707687
Trimmed Mean ( 3 / 24 )48.8303030303030.0905062090612938539.52434354237
Trimmed Mean ( 4 / 24 )48.821093750.088963697894314548.775454545492
Trimmed Mean ( 5 / 24 )48.81209677419350.0874436094175137558.212282170699
Trimmed Mean ( 6 / 24 )48.8040.085988174196775567.566417776439
Trimmed Mean ( 7 / 24 )48.79586206896550.0844013954416394578.140465730879
Trimmed Mean ( 8 / 24 )48.78714285714290.0824115875275597591.993727105763
Trimmed Mean ( 9 / 24 )48.77888888888890.080361111382858606.99619566603
Trimmed Mean ( 10 / 24 )48.77288461538460.0795771898895252612.90031330705
Trimmed Mean ( 11 / 24 )48.7670.078766122418311619.136736743347
Trimmed Mean ( 12 / 24 )48.76250.0781583793940455623.893437633316
Trimmed Mean ( 13 / 24 )48.75782608695650.0773329041988833630.492629134451
Trimmed Mean ( 14 / 24 )48.75250.076212624708147639.690604892504
Trimmed Mean ( 15 / 24 )48.74690476190480.0748529243904805651.235808872475
Trimmed Mean ( 16 / 24 )48.7430.0739258117373468659.350216852274
Trimmed Mean ( 17 / 24 )48.74131578947370.0734480695893748663.61602234029
Trimmed Mean ( 18 / 24 )48.73888888888890.072901082990821668.561931995243
Trimmed Mean ( 19 / 24 )48.73588235294120.0720196517633725676.702554923031
Trimmed Mean ( 20 / 24 )48.73250.0709540400995716686.817832101067
Trimmed Mean ( 21 / 24 )48.72866666666670.0692151955499597704.016889347574
Trimmed Mean ( 22 / 24 )48.72928571428570.0682159824160855714.338253124611
Trimmed Mean ( 23 / 24 )48.73076923076920.0669349237966896728.032041670589
Trimmed Mean ( 24 / 24 )48.73250.064637366363697753.936967756319
Median48.67
Midrange49.455
Midmean - Weighted Average at Xnp48.7413157894737
Midmean - Weighted Average at X(n+1)p48.7581081081081
Midmean - Empirical Distribution Function48.7413157894737
Midmean - Empirical Distribution Function - Averaging48.7581081081081
Midmean - Empirical Distribution Function - Interpolation48.7581081081081
Midmean - Closest Observation48.7413157894737
Midmean - True Basic - Statistics Graphics Toolkit48.7581081081081
Midmean - MS Excel (old versions)48.7413157894737
Number of observations72

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 48.8820833333333 & 0.101062032094085 & 483.683954502575 \tabularnewline
Geometric Mean & 48.8747256851132 &  &  \tabularnewline
Harmonic Mean & 48.8674276757827 &  &  \tabularnewline
Quadratic Mean & 48.8895002218722 &  &  \tabularnewline
Winsorized Mean ( 1 / 24 ) & 48.8819444444444 & 0.101020349769937 & 483.882153999346 \tabularnewline
Winsorized Mean ( 2 / 24 ) & 48.8819444444444 & 0.100898281354622 & 484.467562659879 \tabularnewline
Winsorized Mean ( 3 / 24 ) & 48.8548611111111 & 0.093583248791879 & 522.047072973071 \tabularnewline
Winsorized Mean ( 4 / 24 ) & 48.8520833333333 & 0.0925569100193593 & 527.805901505521 \tabularnewline
Winsorized Mean ( 5 / 24 ) & 48.8458333333333 & 0.0912195133113728 & 535.475706459875 \tabularnewline
Winsorized Mean ( 6 / 24 ) & 48.8433333333333 & 0.0904089993720157 & 540.248577825227 \tabularnewline
Winsorized Mean ( 7 / 24 ) & 48.8433333333333 & 0.0904089993720157 & 540.248577825227 \tabularnewline
Winsorized Mean ( 8 / 24 ) & 48.8366666666667 & 0.0886770264695101 & 550.725127025523 \tabularnewline
Winsorized Mean ( 9 / 24 ) & 48.8179166666667 & 0.081017091238639 & 602.563186610484 \tabularnewline
Winsorized Mean ( 10 / 24 ) & 48.81375 & 0.0798503190639623 & 611.31565374083 \tabularnewline
Winsorized Mean ( 11 / 24 ) & 48.8 & 0.0775167203932938 & 629.541597637325 \tabularnewline
Winsorized Mean ( 12 / 24 ) & 48.7983333333333 & 0.0772419222572214 & 631.759696125004 \tabularnewline
Winsorized Mean ( 13 / 24 ) & 48.8001388888889 & 0.0769932046509558 & 633.823973298962 \tabularnewline
Winsorized Mean ( 14 / 24 ) & 48.7981944444444 & 0.0760894597415394 & 641.326599113755 \tabularnewline
Winsorized Mean ( 15 / 24 ) & 48.7794444444444 & 0.0718710615411081 & 678.707721835221 \tabularnewline
Winsorized Mean ( 16 / 24 ) & 48.7572222222222 & 0.0678862110124497 & 718.2198195342 \tabularnewline
Winsorized Mean ( 17 / 24 ) & 48.7619444444444 & 0.0665708345513811 & 732.482096297121 \tabularnewline
Winsorized Mean ( 18 / 24 ) & 48.7644444444444 & 0.066232414587812 & 736.262519612535 \tabularnewline
Winsorized Mean ( 19 / 24 ) & 48.7644444444444 & 0.0647569456244468 & 753.03805598322 \tabularnewline
Winsorized Mean ( 20 / 24 ) & 48.7644444444444 & 0.0647569456244468 & 753.03805598322 \tabularnewline
Winsorized Mean ( 21 / 24 ) & 48.7236111111111 & 0.0590334596363252 & 825.355847535825 \tabularnewline
Winsorized Mean ( 22 / 24 ) & 48.7175 & 0.0573855771086595 & 848.950249428589 \tabularnewline
Winsorized Mean ( 23 / 24 ) & 48.7175 & 0.0573855771086595 & 848.950249428589 \tabularnewline
Winsorized Mean ( 24 / 24 ) & 48.7175 & 0.0573855771086595 & 848.950249428589 \tabularnewline
Trimmed Mean ( 1 / 24 ) & 48.8657142857143 & 0.0981315235710083 & 497.961434893599 \tabularnewline
Trimmed Mean ( 2 / 24 ) & 48.8485294117647 & 0.094650891445119 & 516.091593707687 \tabularnewline
Trimmed Mean ( 3 / 24 ) & 48.830303030303 & 0.0905062090612938 & 539.52434354237 \tabularnewline
Trimmed Mean ( 4 / 24 ) & 48.82109375 & 0.088963697894314 & 548.775454545492 \tabularnewline
Trimmed Mean ( 5 / 24 ) & 48.8120967741935 & 0.0874436094175137 & 558.212282170699 \tabularnewline
Trimmed Mean ( 6 / 24 ) & 48.804 & 0.085988174196775 & 567.566417776439 \tabularnewline
Trimmed Mean ( 7 / 24 ) & 48.7958620689655 & 0.0844013954416394 & 578.140465730879 \tabularnewline
Trimmed Mean ( 8 / 24 ) & 48.7871428571429 & 0.0824115875275597 & 591.993727105763 \tabularnewline
Trimmed Mean ( 9 / 24 ) & 48.7788888888889 & 0.080361111382858 & 606.99619566603 \tabularnewline
Trimmed Mean ( 10 / 24 ) & 48.7728846153846 & 0.0795771898895252 & 612.90031330705 \tabularnewline
Trimmed Mean ( 11 / 24 ) & 48.767 & 0.078766122418311 & 619.136736743347 \tabularnewline
Trimmed Mean ( 12 / 24 ) & 48.7625 & 0.0781583793940455 & 623.893437633316 \tabularnewline
Trimmed Mean ( 13 / 24 ) & 48.7578260869565 & 0.0773329041988833 & 630.492629134451 \tabularnewline
Trimmed Mean ( 14 / 24 ) & 48.7525 & 0.076212624708147 & 639.690604892504 \tabularnewline
Trimmed Mean ( 15 / 24 ) & 48.7469047619048 & 0.0748529243904805 & 651.235808872475 \tabularnewline
Trimmed Mean ( 16 / 24 ) & 48.743 & 0.0739258117373468 & 659.350216852274 \tabularnewline
Trimmed Mean ( 17 / 24 ) & 48.7413157894737 & 0.0734480695893748 & 663.61602234029 \tabularnewline
Trimmed Mean ( 18 / 24 ) & 48.7388888888889 & 0.072901082990821 & 668.561931995243 \tabularnewline
Trimmed Mean ( 19 / 24 ) & 48.7358823529412 & 0.0720196517633725 & 676.702554923031 \tabularnewline
Trimmed Mean ( 20 / 24 ) & 48.7325 & 0.0709540400995716 & 686.817832101067 \tabularnewline
Trimmed Mean ( 21 / 24 ) & 48.7286666666667 & 0.0692151955499597 & 704.016889347574 \tabularnewline
Trimmed Mean ( 22 / 24 ) & 48.7292857142857 & 0.0682159824160855 & 714.338253124611 \tabularnewline
Trimmed Mean ( 23 / 24 ) & 48.7307692307692 & 0.0669349237966896 & 728.032041670589 \tabularnewline
Trimmed Mean ( 24 / 24 ) & 48.7325 & 0.064637366363697 & 753.936967756319 \tabularnewline
Median & 48.67 &  &  \tabularnewline
Midrange & 49.455 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 48.7413157894737 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 48.7581081081081 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 48.7413157894737 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 48.7581081081081 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 48.7581081081081 &  &  \tabularnewline
Midmean - Closest Observation & 48.7413157894737 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 48.7581081081081 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 48.7413157894737 &  &  \tabularnewline
Number of observations & 72 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=10446&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]48.8820833333333[/C][C]0.101062032094085[/C][C]483.683954502575[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]48.8747256851132[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]48.8674276757827[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]48.8895002218722[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 24 )[/C][C]48.8819444444444[/C][C]0.101020349769937[/C][C]483.882153999346[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 24 )[/C][C]48.8819444444444[/C][C]0.100898281354622[/C][C]484.467562659879[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 24 )[/C][C]48.8548611111111[/C][C]0.093583248791879[/C][C]522.047072973071[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 24 )[/C][C]48.8520833333333[/C][C]0.0925569100193593[/C][C]527.805901505521[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 24 )[/C][C]48.8458333333333[/C][C]0.0912195133113728[/C][C]535.475706459875[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 24 )[/C][C]48.8433333333333[/C][C]0.0904089993720157[/C][C]540.248577825227[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 24 )[/C][C]48.8433333333333[/C][C]0.0904089993720157[/C][C]540.248577825227[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 24 )[/C][C]48.8366666666667[/C][C]0.0886770264695101[/C][C]550.725127025523[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 24 )[/C][C]48.8179166666667[/C][C]0.081017091238639[/C][C]602.563186610484[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 24 )[/C][C]48.81375[/C][C]0.0798503190639623[/C][C]611.31565374083[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 24 )[/C][C]48.8[/C][C]0.0775167203932938[/C][C]629.541597637325[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 24 )[/C][C]48.7983333333333[/C][C]0.0772419222572214[/C][C]631.759696125004[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 24 )[/C][C]48.8001388888889[/C][C]0.0769932046509558[/C][C]633.823973298962[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 24 )[/C][C]48.7981944444444[/C][C]0.0760894597415394[/C][C]641.326599113755[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 24 )[/C][C]48.7794444444444[/C][C]0.0718710615411081[/C][C]678.707721835221[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 24 )[/C][C]48.7572222222222[/C][C]0.0678862110124497[/C][C]718.2198195342[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 24 )[/C][C]48.7619444444444[/C][C]0.0665708345513811[/C][C]732.482096297121[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 24 )[/C][C]48.7644444444444[/C][C]0.066232414587812[/C][C]736.262519612535[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 24 )[/C][C]48.7644444444444[/C][C]0.0647569456244468[/C][C]753.03805598322[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 24 )[/C][C]48.7644444444444[/C][C]0.0647569456244468[/C][C]753.03805598322[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 24 )[/C][C]48.7236111111111[/C][C]0.0590334596363252[/C][C]825.355847535825[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 24 )[/C][C]48.7175[/C][C]0.0573855771086595[/C][C]848.950249428589[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 24 )[/C][C]48.7175[/C][C]0.0573855771086595[/C][C]848.950249428589[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 24 )[/C][C]48.7175[/C][C]0.0573855771086595[/C][C]848.950249428589[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 24 )[/C][C]48.8657142857143[/C][C]0.0981315235710083[/C][C]497.961434893599[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 24 )[/C][C]48.8485294117647[/C][C]0.094650891445119[/C][C]516.091593707687[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 24 )[/C][C]48.830303030303[/C][C]0.0905062090612938[/C][C]539.52434354237[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 24 )[/C][C]48.82109375[/C][C]0.088963697894314[/C][C]548.775454545492[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 24 )[/C][C]48.8120967741935[/C][C]0.0874436094175137[/C][C]558.212282170699[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 24 )[/C][C]48.804[/C][C]0.085988174196775[/C][C]567.566417776439[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 24 )[/C][C]48.7958620689655[/C][C]0.0844013954416394[/C][C]578.140465730879[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 24 )[/C][C]48.7871428571429[/C][C]0.0824115875275597[/C][C]591.993727105763[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 24 )[/C][C]48.7788888888889[/C][C]0.080361111382858[/C][C]606.99619566603[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 24 )[/C][C]48.7728846153846[/C][C]0.0795771898895252[/C][C]612.90031330705[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 24 )[/C][C]48.767[/C][C]0.078766122418311[/C][C]619.136736743347[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 24 )[/C][C]48.7625[/C][C]0.0781583793940455[/C][C]623.893437633316[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 24 )[/C][C]48.7578260869565[/C][C]0.0773329041988833[/C][C]630.492629134451[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 24 )[/C][C]48.7525[/C][C]0.076212624708147[/C][C]639.690604892504[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 24 )[/C][C]48.7469047619048[/C][C]0.0748529243904805[/C][C]651.235808872475[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 24 )[/C][C]48.743[/C][C]0.0739258117373468[/C][C]659.350216852274[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 24 )[/C][C]48.7413157894737[/C][C]0.0734480695893748[/C][C]663.61602234029[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 24 )[/C][C]48.7388888888889[/C][C]0.072901082990821[/C][C]668.561931995243[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 24 )[/C][C]48.7358823529412[/C][C]0.0720196517633725[/C][C]676.702554923031[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 24 )[/C][C]48.7325[/C][C]0.0709540400995716[/C][C]686.817832101067[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 24 )[/C][C]48.7286666666667[/C][C]0.0692151955499597[/C][C]704.016889347574[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 24 )[/C][C]48.7292857142857[/C][C]0.0682159824160855[/C][C]714.338253124611[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 24 )[/C][C]48.7307692307692[/C][C]0.0669349237966896[/C][C]728.032041670589[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 24 )[/C][C]48.7325[/C][C]0.064637366363697[/C][C]753.936967756319[/C][/ROW]
[ROW][C]Median[/C][C]48.67[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]49.455[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]48.7413157894737[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]48.7581081081081[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]48.7413157894737[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]48.7581081081081[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]48.7581081081081[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]48.7413157894737[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]48.7581081081081[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]48.7413157894737[/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=10446&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=10446&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 Mean48.88208333333330.101062032094085483.683954502575
Geometric Mean48.8747256851132
Harmonic Mean48.8674276757827
Quadratic Mean48.8895002218722
Winsorized Mean ( 1 / 24 )48.88194444444440.101020349769937483.882153999346
Winsorized Mean ( 2 / 24 )48.88194444444440.100898281354622484.467562659879
Winsorized Mean ( 3 / 24 )48.85486111111110.093583248791879522.047072973071
Winsorized Mean ( 4 / 24 )48.85208333333330.0925569100193593527.805901505521
Winsorized Mean ( 5 / 24 )48.84583333333330.0912195133113728535.475706459875
Winsorized Mean ( 6 / 24 )48.84333333333330.0904089993720157540.248577825227
Winsorized Mean ( 7 / 24 )48.84333333333330.0904089993720157540.248577825227
Winsorized Mean ( 8 / 24 )48.83666666666670.0886770264695101550.725127025523
Winsorized Mean ( 9 / 24 )48.81791666666670.081017091238639602.563186610484
Winsorized Mean ( 10 / 24 )48.813750.0798503190639623611.31565374083
Winsorized Mean ( 11 / 24 )48.80.0775167203932938629.541597637325
Winsorized Mean ( 12 / 24 )48.79833333333330.0772419222572214631.759696125004
Winsorized Mean ( 13 / 24 )48.80013888888890.0769932046509558633.823973298962
Winsorized Mean ( 14 / 24 )48.79819444444440.0760894597415394641.326599113755
Winsorized Mean ( 15 / 24 )48.77944444444440.0718710615411081678.707721835221
Winsorized Mean ( 16 / 24 )48.75722222222220.0678862110124497718.2198195342
Winsorized Mean ( 17 / 24 )48.76194444444440.0665708345513811732.482096297121
Winsorized Mean ( 18 / 24 )48.76444444444440.066232414587812736.262519612535
Winsorized Mean ( 19 / 24 )48.76444444444440.0647569456244468753.03805598322
Winsorized Mean ( 20 / 24 )48.76444444444440.0647569456244468753.03805598322
Winsorized Mean ( 21 / 24 )48.72361111111110.0590334596363252825.355847535825
Winsorized Mean ( 22 / 24 )48.71750.0573855771086595848.950249428589
Winsorized Mean ( 23 / 24 )48.71750.0573855771086595848.950249428589
Winsorized Mean ( 24 / 24 )48.71750.0573855771086595848.950249428589
Trimmed Mean ( 1 / 24 )48.86571428571430.0981315235710083497.961434893599
Trimmed Mean ( 2 / 24 )48.84852941176470.094650891445119516.091593707687
Trimmed Mean ( 3 / 24 )48.8303030303030.0905062090612938539.52434354237
Trimmed Mean ( 4 / 24 )48.821093750.088963697894314548.775454545492
Trimmed Mean ( 5 / 24 )48.81209677419350.0874436094175137558.212282170699
Trimmed Mean ( 6 / 24 )48.8040.085988174196775567.566417776439
Trimmed Mean ( 7 / 24 )48.79586206896550.0844013954416394578.140465730879
Trimmed Mean ( 8 / 24 )48.78714285714290.0824115875275597591.993727105763
Trimmed Mean ( 9 / 24 )48.77888888888890.080361111382858606.99619566603
Trimmed Mean ( 10 / 24 )48.77288461538460.0795771898895252612.90031330705
Trimmed Mean ( 11 / 24 )48.7670.078766122418311619.136736743347
Trimmed Mean ( 12 / 24 )48.76250.0781583793940455623.893437633316
Trimmed Mean ( 13 / 24 )48.75782608695650.0773329041988833630.492629134451
Trimmed Mean ( 14 / 24 )48.75250.076212624708147639.690604892504
Trimmed Mean ( 15 / 24 )48.74690476190480.0748529243904805651.235808872475
Trimmed Mean ( 16 / 24 )48.7430.0739258117373468659.350216852274
Trimmed Mean ( 17 / 24 )48.74131578947370.0734480695893748663.61602234029
Trimmed Mean ( 18 / 24 )48.73888888888890.072901082990821668.561931995243
Trimmed Mean ( 19 / 24 )48.73588235294120.0720196517633725676.702554923031
Trimmed Mean ( 20 / 24 )48.73250.0709540400995716686.817832101067
Trimmed Mean ( 21 / 24 )48.72866666666670.0692151955499597704.016889347574
Trimmed Mean ( 22 / 24 )48.72928571428570.0682159824160855714.338253124611
Trimmed Mean ( 23 / 24 )48.73076923076920.0669349237966896728.032041670589
Trimmed Mean ( 24 / 24 )48.73250.064637366363697753.936967756319
Median48.67
Midrange49.455
Midmean - Weighted Average at Xnp48.7413157894737
Midmean - Weighted Average at X(n+1)p48.7581081081081
Midmean - Empirical Distribution Function48.7413157894737
Midmean - Empirical Distribution Function - Averaging48.7581081081081
Midmean - Empirical Distribution Function - Interpolation48.7581081081081
Midmean - Closest Observation48.7413157894737
Midmean - True Basic - Statistics Graphics Toolkit48.7581081081081
Midmean - MS Excel (old versions)48.7413157894737
Number of observations72



Parameters (Session):
Parameters (R input):
R code (references can be found in the software module):
geomean <- function(x) {
return(exp(mean(log(x))))
}
harmean <- function(x) {
return(1/mean(1/x))
}
quamean <- function(x) {
return(sqrt(mean(x*x)))
}
winmean <- function(x) {
x <-sort(x[!is.na(x)])
n<-length(x)
denom <- 3
nodenom <- n/denom
if (nodenom>40) denom <- n/40
sqrtn = sqrt(n)
roundnodenom = floor(nodenom)
win <- array(NA,dim=c(roundnodenom,2))
for (j in 1:roundnodenom) {
win[j,1] <- (j*x[j+1]+sum(x[(j+1):(n-j)])+j*x[n-j])/n
win[j,2] <- sd(c(rep(x[j+1],j),x[(j+1):(n-j)],rep(x[n-j],j)))/sqrtn
}
return(win)
}
trimean <- function(x) {
x <-sort(x[!is.na(x)])
n<-length(x)
denom <- 3
nodenom <- n/denom
if (nodenom>40) denom <- n/40
sqrtn = sqrt(n)
roundnodenom = floor(nodenom)
tri <- array(NA,dim=c(roundnodenom,2))
for (j in 1:roundnodenom) {
tri[j,1] <- mean(x,trim=j/n)
tri[j,2] <- sd(x[(j+1):(n-j)]) / sqrt(n-j*2)
}
return(tri)
}
midrange <- function(x) {
return((max(x)+min(x))/2)
}
q1 <- function(data,n,p,i,f) {
np <- n*p;
i <<- floor(np)
f <<- np - i
qvalue <- (1-f)*data[i] + f*data[i+1]
}
q2 <- function(data,n,p,i,f) {
np <- (n+1)*p
i <<- floor(np)
f <<- np - i
qvalue <- (1-f)*data[i] + f*data[i+1]
}
q3 <- function(data,n,p,i,f) {
np <- n*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- data[i]
} else {
qvalue <- data[i+1]
}
}
q4 <- function(data,n,p,i,f) {
np <- n*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- (data[i]+data[i+1])/2
} else {
qvalue <- data[i+1]
}
}
q5 <- function(data,n,p,i,f) {
np <- (n-1)*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- data[i+1]
} else {
qvalue <- data[i+1] + f*(data[i+2]-data[i+1])
}
}
q6 <- function(data,n,p,i,f) {
np <- n*p+0.5
i <<- floor(np)
f <<- np - i
qvalue <- data[i]
}
q7 <- function(data,n,p,i,f) {
np <- (n+1)*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- data[i]
} else {
qvalue <- f*data[i] + (1-f)*data[i+1]
}
}
q8 <- function(data,n,p,i,f) {
np <- (n+1)*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- data[i]
} else {
if (f == 0.5) {
qvalue <- (data[i]+data[i+1])/2
} else {
if (f < 0.5) {
qvalue <- data[i]
} else {
qvalue <- data[i+1]
}
}
}
}
midmean <- function(x,def) {
x <-sort(x[!is.na(x)])
n<-length(x)
if (def==1) {
qvalue1 <- q1(x,n,0.25,i,f)
qvalue3 <- q1(x,n,0.75,i,f)
}
if (def==2) {
qvalue1 <- q2(x,n,0.25,i,f)
qvalue3 <- q2(x,n,0.75,i,f)
}
if (def==3) {
qvalue1 <- q3(x,n,0.25,i,f)
qvalue3 <- q3(x,n,0.75,i,f)
}
if (def==4) {
qvalue1 <- q4(x,n,0.25,i,f)
qvalue3 <- q4(x,n,0.75,i,f)
}
if (def==5) {
qvalue1 <- q5(x,n,0.25,i,f)
qvalue3 <- q5(x,n,0.75,i,f)
}
if (def==6) {
qvalue1 <- q6(x,n,0.25,i,f)
qvalue3 <- q6(x,n,0.75,i,f)
}
if (def==7) {
qvalue1 <- q7(x,n,0.25,i,f)
qvalue3 <- q7(x,n,0.75,i,f)
}
if (def==8) {
qvalue1 <- q8(x,n,0.25,i,f)
qvalue3 <- q8(x,n,0.75,i,f)
}
midm <- 0
myn <- 0
roundno4 <- round(n/4)
round3no4 <- round(3*n/4)
for (i in 1:n) {
if ((x[i]>=qvalue1) & (x[i]<=qvalue3)){
midm = midm + x[i]
myn = myn + 1
}
}
midm = midm / myn
return(midm)
}
(arm <- mean(x))
sqrtn <- sqrt(length(x))
(armse <- sd(x) / sqrtn)
(armose <- arm / armse)
(geo <- geomean(x))
(har <- harmean(x))
(qua <- quamean(x))
(win <- winmean(x))
(tri <- trimean(x))
(midr <- midrange(x))
midm <- array(NA,dim=8)
for (j in 1:8) midm[j] <- midmean(x,j)
midm
bitmap(file='test1.png')
lb <- win[,1] - 2*win[,2]
ub <- win[,1] + 2*win[,2]
if ((ylimmin == '') | (ylimmax == '')) plot(win[,1],type='b',main=main, xlab='j', pch=19, ylab='Winsorized Mean(j/n)', ylim=c(min(lb),max(ub))) else plot(win[,1],type='l',main=main, xlab='j', pch=19, ylab='Winsorized Mean(j/n)', ylim=c(ylimmin,ylimmax))
lines(ub,lty=3)
lines(lb,lty=3)
grid()
dev.off()
bitmap(file='test2.png')
lb <- tri[,1] - 2*tri[,2]
ub <- tri[,1] + 2*tri[,2]
if ((ylimmin == '') | (ylimmax == '')) plot(tri[,1],type='b',main=main, xlab='j', pch=19, ylab='Trimmed Mean(j/n)', ylim=c(min(lb),max(ub))) else plot(tri[,1],type='l',main=main, xlab='j', pch=19, ylab='Trimmed Mean(j/n)', ylim=c(ylimmin,ylimmax))
lines(ub,lty=3)
lines(lb,lty=3)
grid()
dev.off()
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Central Tendency - Ungrouped Data',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Measure',header=TRUE)
a<-table.element(a,'Value',header=TRUE)
a<-table.element(a,'S.E.',header=TRUE)
a<-table.element(a,'Value/S.E.',header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('arithmetic_mean.htm', 'Arithmetic Mean', 'click to view the definition of the Arithmetic Mean'),header=TRUE)
a<-table.element(a,arm)
a<-table.element(a,hyperlink('arithmetic_mean_standard_error.htm', armse, 'click to view the definition of the Standard Error of the Arithmetic Mean'))
a<-table.element(a,armose)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('geometric_mean.htm', 'Geometric Mean', 'click to view the definition of the Geometric Mean'),header=TRUE)
a<-table.element(a,geo)
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('harmonic_mean.htm', 'Harmonic Mean', 'click to view the definition of the Harmonic Mean'),header=TRUE)
a<-table.element(a,har)
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('quadratic_mean.htm', 'Quadratic Mean', 'click to view the definition of the Quadratic Mean'),header=TRUE)
a<-table.element(a,qua)
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
for (j in 1:length(win[,1])) {
a<-table.row.start(a)
mylabel <- paste('Winsorized Mean (',j)
mylabel <- paste(mylabel,'/')
mylabel <- paste(mylabel,length(win[,1]))
mylabel <- paste(mylabel,')')
a<-table.element(a,hyperlink('winsorized_mean.htm', mylabel, 'click to view the definition of the Winsorized Mean'),header=TRUE)
a<-table.element(a,win[j,1])
a<-table.element(a,win[j,2])
a<-table.element(a,win[j,1]/win[j,2])
a<-table.row.end(a)
}
for (j in 1:length(tri[,1])) {
a<-table.row.start(a)
mylabel <- paste('Trimmed Mean (',j)
mylabel <- paste(mylabel,'/')
mylabel <- paste(mylabel,length(tri[,1]))
mylabel <- paste(mylabel,')')
a<-table.element(a,hyperlink('arithmetic_mean.htm', mylabel, 'click to view the definition of the Trimmed Mean'),header=TRUE)
a<-table.element(a,tri[j,1])
a<-table.element(a,tri[j,2])
a<-table.element(a,tri[j,1]/tri[j,2])
a<-table.row.end(a)
}
a<-table.row.start(a)
a<-table.element(a,hyperlink('median_1.htm', 'Median', 'click to view the definition of the Median'),header=TRUE)
a<-table.element(a,median(x))
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('midrange.htm', 'Midrange', 'click to view the definition of the Midrange'),header=TRUE)
a<-table.element(a,midr)
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_1.htm','Weighted Average at Xnp',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[1])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_2.htm','Weighted Average at X(n+1)p',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[2])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_3.htm','Empirical Distribution Function',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[3])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_4.htm','Empirical Distribution Function - Averaging',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[4])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_5.htm','Empirical Distribution Function - Interpolation',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[5])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_6.htm','Closest Observation',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[6])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_7.htm','True Basic - Statistics Graphics Toolkit',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[7])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_8.htm','MS Excel (old versions)',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[8])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Number of observations',header=TRUE)
a<-table.element(a,length(x))
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable.tab')