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Description of Statistical Computation

Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationSun, 20 Dec 2009 17:48:00 -0700
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2009/Dec/21/t1261356596b09ubshiqbvjk7i.htm/, Retrieved Sun, 05 May 2024 16:38:44 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=70055, Retrieved Sun, 05 May 2024 16:38:44 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact155

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Bivariate Data Series] [Bivariate dataset] [2008-01-05 23:51:08] [74be16979710d4c4e7c6647856088456]
F RMPD  [Univariate Explorative Data Analysis] [Colombia Coffee] [2008-01-07 14:21:11] [74be16979710d4c4e7c6647856088456]
F RMPD    [Univariate Data Series] [] [2009-10-14 08:30:28] [74be16979710d4c4e7c6647856088456]
- RMPD      [Univariate Explorative Data Analysis] [WS 3 I] [2009-10-24 22:53:45] [4a2be4899cba879e4eea9daa25281df8]
-  M D        [Univariate Explorative Data Analysis] [PAPER 1] [2009-12-20 00:55:27] [4a2be4899cba879e4eea9daa25281df8]
- RMPD            [Central Tendency] [paper 13] [2009-12-21 00:48:00] [71c065898bd1c08eef04509b4bcee039] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
31,48
29,90
33,84
39,12
33,70
25,09
51,44
45,59
52,52
48,56
41,75
49,59
32,75
33,38
35,65
37,03
35,68
20,97
58,55
54,96
65,54
51,57
51,15
46,64
35,70
33,25
35,19
41,67
34,87
21,21
56,13
49,23
59,72
48,10
47,47
50,50
40,06
34,15
36,86
46,36
36,58
23,87
57,28
56,39
57,66
62,30
48,93
51,17
39,64
33,21
38,13
43,29
30,60
21,96
48,03
46,15
50,74
48,11
38,39
44,11

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 1 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=70055&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=70055&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=70055&T=0

As an alternative you can also use a QR Code:  
QR Code


The GUIDs for individual cells are displayed in the table below:

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135






Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean42.55766666666671.3805807417740730.8259164994431
Geometric Mean41.1331091226907
Harmonic Mean39.5950491451823
Quadratic Mean43.8589692081335
Winsorized Mean ( 1 / 20 )42.50766666666671.3652640804680231.1351241674026
Winsorized Mean ( 2 / 20 )42.44666666666671.3387355461492531.7065359090229
Winsorized Mean ( 3 / 20 )42.48366666666671.3022542811624932.6231729710596
Winsorized Mean ( 4 / 20 )42.50566666666671.2707484419178133.4493163749367
Winsorized Mean ( 5 / 20 )42.87483333333331.1800295766586036.3336938170132
Winsorized Mean ( 6 / 20 )42.85583333333331.1490819546543437.2957152096474
Winsorized Mean ( 7 / 20 )42.92816666666671.1248982500544338.1618218933042
Winsorized Mean ( 8 / 20 )42.94151.0661166614755240.2784250089183
Winsorized Mean ( 9 / 20 )42.64450.98885553962577743.125106035345
Winsorized Mean ( 10 / 20 )42.49283333333330.96169806541383644.1852124502797
Winsorized Mean ( 11 / 20 )42.49283333333330.95402688290975344.5404989047389
Winsorized Mean ( 12 / 20 )42.50283333333330.93520679883720745.4475238911644
Winsorized Mean ( 13 / 20 )42.52883333333330.92970377068403145.7444991344315
Winsorized Mean ( 14 / 20 )42.50550.90339470964381347.050862204804
Winsorized Mean ( 15 / 20 )42.62550.86636468310076849.2004127493297
Winsorized Mean ( 16 / 20 )42.46816666666670.81680127421735151.9932669147206
Winsorized Mean ( 17 / 20 )42.49650.7823100959071154.3218095002649
Winsorized Mean ( 18 / 20 )42.41550.76793778529930155.2329899790889
Winsorized Mean ( 19 / 20 )42.30466666666670.75029137340730256.3843170347918
Winsorized Mean ( 20 / 20 )42.4480.68602320792223261.8754577247654
Trimmed Mean ( 1 / 20 )42.53362068965521.3191551150950932.2430775599799
Trimmed Mean ( 2 / 20 )42.56142857142861.2622841702764933.7177868293364
Trimmed Mean ( 3 / 20 )42.62518518518521.2097464011305335.2348104903236
Trimmed Mean ( 4 / 20 )42.67961538461541.1623471845759336.7184744377272
Trimmed Mean ( 5 / 20 )42.73181.1155751766214038.3047246797084
Trimmed Mean ( 6 / 20 )42.69604166666671.0884381801227339.2268871548152
Trimmed Mean ( 7 / 20 )42.66130434782611.0629427118004240.1350927704901
Trimmed Mean ( 8 / 20 )42.60931818181821.0363982291572841.1128820786049
Trimmed Mean ( 9 / 20 )42.551.0173706745483241.8234976341254
Trimmed Mean ( 10 / 20 )42.534251.0113768786684542.0557864205869
Trimmed Mean ( 11 / 20 )42.54078947368421.0077417525186742.2139792931681
Trimmed Mean ( 12 / 20 )42.54805555555561.0018776672974042.4683141908238
Trimmed Mean ( 13 / 20 )42.55470588235290.9955823308065942.7435326698461
Trimmed Mean ( 14 / 20 )42.55843750.984907797118943.2105803451795
Trimmed Mean ( 15 / 20 )42.5660.9735829785344243.7209780147107
Trimmed Mean ( 16 / 20 )42.55750.96394164692539844.1494566976559
Trimmed Mean ( 17 / 20 )42.57038461538460.95974539584833244.3559143909787
Trimmed Mean ( 18 / 20 )42.581250.95787852708207644.4537055546203
Trimmed Mean ( 19 / 20 )42.60636363636360.95179200896797944.7643636791629
Trimmed Mean ( 20 / 20 )42.6540.93940137713781445.4055114651407
Median42.52
Midrange43.255
Midmean - Weighted Average at Xnp42.2945161290323
Midmean - Weighted Average at X(n+1)p42.566
Midmean - Empirical Distribution Function42.2945161290323
Midmean - Empirical Distribution Function - Averaging42.566
Midmean - Empirical Distribution Function - Interpolation42.566
Midmean - Closest Observation42.2945161290323
Midmean - True Basic - Statistics Graphics Toolkit42.566
Midmean - MS Excel (old versions)42.5584375
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 42.5576666666667 & 1.38058074177407 & 30.8259164994431 \tabularnewline
Geometric Mean & 41.1331091226907 &  &  \tabularnewline
Harmonic Mean & 39.5950491451823 &  &  \tabularnewline
Quadratic Mean & 43.8589692081335 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 42.5076666666667 & 1.36526408046802 & 31.1351241674026 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 42.4466666666667 & 1.33873554614925 & 31.7065359090229 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 42.4836666666667 & 1.30225428116249 & 32.6231729710596 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 42.5056666666667 & 1.27074844191781 & 33.4493163749367 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 42.8748333333333 & 1.18002957665860 & 36.3336938170132 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 42.8558333333333 & 1.14908195465434 & 37.2957152096474 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 42.9281666666667 & 1.12489825005443 & 38.1618218933042 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 42.9415 & 1.06611666147552 & 40.2784250089183 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 42.6445 & 0.988855539625777 & 43.125106035345 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 42.4928333333333 & 0.961698065413836 & 44.1852124502797 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 42.4928333333333 & 0.954026882909753 & 44.5404989047389 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 42.5028333333333 & 0.935206798837207 & 45.4475238911644 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 42.5288333333333 & 0.929703770684031 & 45.7444991344315 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 42.5055 & 0.903394709643813 & 47.050862204804 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 42.6255 & 0.866364683100768 & 49.2004127493297 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 42.4681666666667 & 0.816801274217351 & 51.9932669147206 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 42.4965 & 0.78231009590711 & 54.3218095002649 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 42.4155 & 0.767937785299301 & 55.2329899790889 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 42.3046666666667 & 0.750291373407302 & 56.3843170347918 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 42.448 & 0.686023207922232 & 61.8754577247654 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 42.5336206896552 & 1.31915511509509 & 32.2430775599799 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 42.5614285714286 & 1.26228417027649 & 33.7177868293364 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 42.6251851851852 & 1.20974640113053 & 35.2348104903236 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 42.6796153846154 & 1.16234718457593 & 36.7184744377272 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 42.7318 & 1.11557517662140 & 38.3047246797084 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 42.6960416666667 & 1.08843818012273 & 39.2268871548152 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 42.6613043478261 & 1.06294271180042 & 40.1350927704901 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 42.6093181818182 & 1.03639822915728 & 41.1128820786049 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 42.55 & 1.01737067454832 & 41.8234976341254 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 42.53425 & 1.01137687866845 & 42.0557864205869 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 42.5407894736842 & 1.00774175251867 & 42.2139792931681 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 42.5480555555556 & 1.00187766729740 & 42.4683141908238 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 42.5547058823529 & 0.99558233080659 & 42.7435326698461 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 42.5584375 & 0.9849077971189 & 43.2105803451795 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 42.566 & 0.97358297853442 & 43.7209780147107 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 42.5575 & 0.963941646925398 & 44.1494566976559 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 42.5703846153846 & 0.959745395848332 & 44.3559143909787 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 42.58125 & 0.957878527082076 & 44.4537055546203 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 42.6063636363636 & 0.951792008967979 & 44.7643636791629 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 42.654 & 0.939401377137814 & 45.4055114651407 \tabularnewline
Median & 42.52 &  &  \tabularnewline
Midrange & 43.255 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 42.2945161290323 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 42.566 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 42.2945161290323 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 42.566 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 42.566 &  &  \tabularnewline
Midmean - Closest Observation & 42.2945161290323 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 42.566 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 42.5584375 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=70055&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]42.5576666666667[/C][C]1.38058074177407[/C][C]30.8259164994431[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]41.1331091226907[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]39.5950491451823[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]43.8589692081335[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]42.5076666666667[/C][C]1.36526408046802[/C][C]31.1351241674026[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]42.4466666666667[/C][C]1.33873554614925[/C][C]31.7065359090229[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]42.4836666666667[/C][C]1.30225428116249[/C][C]32.6231729710596[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]42.5056666666667[/C][C]1.27074844191781[/C][C]33.4493163749367[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]42.8748333333333[/C][C]1.18002957665860[/C][C]36.3336938170132[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]42.8558333333333[/C][C]1.14908195465434[/C][C]37.2957152096474[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]42.9281666666667[/C][C]1.12489825005443[/C][C]38.1618218933042[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]42.9415[/C][C]1.06611666147552[/C][C]40.2784250089183[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]42.6445[/C][C]0.988855539625777[/C][C]43.125106035345[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]42.4928333333333[/C][C]0.961698065413836[/C][C]44.1852124502797[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]42.4928333333333[/C][C]0.954026882909753[/C][C]44.5404989047389[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]42.5028333333333[/C][C]0.935206798837207[/C][C]45.4475238911644[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]42.5288333333333[/C][C]0.929703770684031[/C][C]45.7444991344315[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]42.5055[/C][C]0.903394709643813[/C][C]47.050862204804[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]42.6255[/C][C]0.866364683100768[/C][C]49.2004127493297[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]42.4681666666667[/C][C]0.816801274217351[/C][C]51.9932669147206[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]42.4965[/C][C]0.78231009590711[/C][C]54.3218095002649[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]42.4155[/C][C]0.767937785299301[/C][C]55.2329899790889[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]42.3046666666667[/C][C]0.750291373407302[/C][C]56.3843170347918[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]42.448[/C][C]0.686023207922232[/C][C]61.8754577247654[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]42.5336206896552[/C][C]1.31915511509509[/C][C]32.2430775599799[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]42.5614285714286[/C][C]1.26228417027649[/C][C]33.7177868293364[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]42.6251851851852[/C][C]1.20974640113053[/C][C]35.2348104903236[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]42.6796153846154[/C][C]1.16234718457593[/C][C]36.7184744377272[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]42.7318[/C][C]1.11557517662140[/C][C]38.3047246797084[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]42.6960416666667[/C][C]1.08843818012273[/C][C]39.2268871548152[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]42.6613043478261[/C][C]1.06294271180042[/C][C]40.1350927704901[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]42.6093181818182[/C][C]1.03639822915728[/C][C]41.1128820786049[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]42.55[/C][C]1.01737067454832[/C][C]41.8234976341254[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]42.53425[/C][C]1.01137687866845[/C][C]42.0557864205869[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]42.5407894736842[/C][C]1.00774175251867[/C][C]42.2139792931681[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]42.5480555555556[/C][C]1.00187766729740[/C][C]42.4683141908238[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]42.5547058823529[/C][C]0.99558233080659[/C][C]42.7435326698461[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]42.5584375[/C][C]0.9849077971189[/C][C]43.2105803451795[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]42.566[/C][C]0.97358297853442[/C][C]43.7209780147107[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]42.5575[/C][C]0.963941646925398[/C][C]44.1494566976559[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]42.5703846153846[/C][C]0.959745395848332[/C][C]44.3559143909787[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]42.58125[/C][C]0.957878527082076[/C][C]44.4537055546203[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]42.6063636363636[/C][C]0.951792008967979[/C][C]44.7643636791629[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]42.654[/C][C]0.939401377137814[/C][C]45.4055114651407[/C][/ROW]
[ROW][C]Median[/C][C]42.52[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]43.255[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]42.2945161290323[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]42.566[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]42.2945161290323[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]42.566[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]42.566[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]42.2945161290323[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]42.566[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]42.5584375[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]60[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=70055&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=70055&T=1

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The GUIDs for individual cells are displayed in the table below:

Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean42.55766666666671.3805807417740730.8259164994431
Geometric Mean41.1331091226907
Harmonic Mean39.5950491451823
Quadratic Mean43.8589692081335
Winsorized Mean ( 1 / 20 )42.50766666666671.3652640804680231.1351241674026
Winsorized Mean ( 2 / 20 )42.44666666666671.3387355461492531.7065359090229
Winsorized Mean ( 3 / 20 )42.48366666666671.3022542811624932.6231729710596
Winsorized Mean ( 4 / 20 )42.50566666666671.2707484419178133.4493163749367
Winsorized Mean ( 5 / 20 )42.87483333333331.1800295766586036.3336938170132
Winsorized Mean ( 6 / 20 )42.85583333333331.1490819546543437.2957152096474
Winsorized Mean ( 7 / 20 )42.92816666666671.1248982500544338.1618218933042
Winsorized Mean ( 8 / 20 )42.94151.0661166614755240.2784250089183
Winsorized Mean ( 9 / 20 )42.64450.98885553962577743.125106035345
Winsorized Mean ( 10 / 20 )42.49283333333330.96169806541383644.1852124502797
Winsorized Mean ( 11 / 20 )42.49283333333330.95402688290975344.5404989047389
Winsorized Mean ( 12 / 20 )42.50283333333330.93520679883720745.4475238911644
Winsorized Mean ( 13 / 20 )42.52883333333330.92970377068403145.7444991344315
Winsorized Mean ( 14 / 20 )42.50550.90339470964381347.050862204804
Winsorized Mean ( 15 / 20 )42.62550.86636468310076849.2004127493297
Winsorized Mean ( 16 / 20 )42.46816666666670.81680127421735151.9932669147206
Winsorized Mean ( 17 / 20 )42.49650.7823100959071154.3218095002649
Winsorized Mean ( 18 / 20 )42.41550.76793778529930155.2329899790889
Winsorized Mean ( 19 / 20 )42.30466666666670.75029137340730256.3843170347918
Winsorized Mean ( 20 / 20 )42.4480.68602320792223261.8754577247654
Trimmed Mean ( 1 / 20 )42.53362068965521.3191551150950932.2430775599799
Trimmed Mean ( 2 / 20 )42.56142857142861.2622841702764933.7177868293364
Trimmed Mean ( 3 / 20 )42.62518518518521.2097464011305335.2348104903236
Trimmed Mean ( 4 / 20 )42.67961538461541.1623471845759336.7184744377272
Trimmed Mean ( 5 / 20 )42.73181.1155751766214038.3047246797084
Trimmed Mean ( 6 / 20 )42.69604166666671.0884381801227339.2268871548152
Trimmed Mean ( 7 / 20 )42.66130434782611.0629427118004240.1350927704901
Trimmed Mean ( 8 / 20 )42.60931818181821.0363982291572841.1128820786049
Trimmed Mean ( 9 / 20 )42.551.0173706745483241.8234976341254
Trimmed Mean ( 10 / 20 )42.534251.0113768786684542.0557864205869
Trimmed Mean ( 11 / 20 )42.54078947368421.0077417525186742.2139792931681
Trimmed Mean ( 12 / 20 )42.54805555555561.0018776672974042.4683141908238
Trimmed Mean ( 13 / 20 )42.55470588235290.9955823308065942.7435326698461
Trimmed Mean ( 14 / 20 )42.55843750.984907797118943.2105803451795
Trimmed Mean ( 15 / 20 )42.5660.9735829785344243.7209780147107
Trimmed Mean ( 16 / 20 )42.55750.96394164692539844.1494566976559
Trimmed Mean ( 17 / 20 )42.57038461538460.95974539584833244.3559143909787
Trimmed Mean ( 18 / 20 )42.581250.95787852708207644.4537055546203
Trimmed Mean ( 19 / 20 )42.60636363636360.95179200896797944.7643636791629
Trimmed Mean ( 20 / 20 )42.6540.93940137713781445.4055114651407
Median42.52
Midrange43.255
Midmean - Weighted Average at Xnp42.2945161290323
Midmean - Weighted Average at X(n+1)p42.566
Midmean - Empirical Distribution Function42.2945161290323
Midmean - Empirical Distribution Function - Averaging42.566
Midmean - Empirical Distribution Function - Interpolation42.566
Midmean - Closest Observation42.2945161290323
Midmean - True Basic - Statistics Graphics Toolkit42.566
Midmean - MS Excel (old versions)42.5584375
Number of observations60


Figures (Output of Computation)

Input Parameters & R Code

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')