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Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationMon, 22 Nov 2010 16:47:27 +0000
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2010/Nov/22/t1290444353ratgvlpbnjnp3ej.htm/, Retrieved Fri, 03 May 2024 21:10:35 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=98593, Retrieved Fri, 03 May 2024 21:10:35 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact140
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Central Tendency] [Arabica Price in ...] [2008-01-06 21:28:17] [74be16979710d4c4e7c6647856088456]
-  M D    [Central Tendency] [Xt1ceosalaris] [2010-11-22 16:47:27] [6e19356a8195a048e2417405f21c29e8] [Current]
-    D      [Central Tendency] [ws6Xtceosalary] [2010-11-22 20:32:12] [8b2514d8f13517d765015fc185a22b4b]
-    D        [Central Tendency] [ws6Yt] [2010-11-22 20:48:38] [8b2514d8f13517d765015fc185a22b4b]
-    D        [Central Tendency] [univariate analys...] [2010-12-06 20:42:47] [46df8573ee32a55e1a6edcfb6691f406]
-    D          [Central Tendency] [univariate analys...] [2010-12-06 20:52:17] [46df8573ee32a55e1a6edcfb6691f406]
-   PD            [Central Tendency] [univariate analys...] [2010-12-17 19:46:13] [46df8573ee32a55e1a6edcfb6691f406]
-    D          [Central Tendency] [univariate analys...] [2010-12-06 20:55:30] [46df8573ee32a55e1a6edcfb6691f406]
-    D          [Central Tendency] [univariate analys...] [2010-12-06 21:05:11] [46df8573ee32a55e1a6edcfb6691f406]
- RMPD          [Classical Decomposition] [ws8dollar] [2010-12-07 20:36:13] [8b2514d8f13517d765015fc185a22b4b]
-   P             [Classical Decomposition] [ws8dollar4] [2010-12-08 21:03:24] [8b2514d8f13517d765015fc185a22b4b]
-    D            [Classical Decomposition] [tijdreeks additie...] [2010-12-09 17:38:16] [916599f00c9c716123aa8433d9efa14f]
-    D            [Classical Decomposition] [TUM] [2010-12-09 17:41:47] [75b8170d590d2aca2c97c1862bb2167f]
-    D              [Classical Decomposition] [TUM CD] [2010-12-09 19:04:14] [75b8170d590d2aca2c97c1862bb2167f]
-                     [Classical Decomposition] [TUM CD] [2010-12-28 08:38:35] [75b8170d590d2aca2c97c1862bb2167f]
-                     [Classical Decomposition] [berekening 9] [2010-12-28 13:57:13] [916599f00c9c716123aa8433d9efa14f]
-    D            [Classical Decomposition] [] [2010-12-10 19:31:37] [8e42c8cdf50f15ce85eb45a67cf771d0]
-   PD            [Classical Decomposition] [Classical composi...] [2010-12-14 13:51:38] [46df8573ee32a55e1a6edcfb6691f406]
- RM D            [Central Tendency] [Classical Decompo...] [2010-12-17 19:46:13] [46df8573ee32a55e1a6edcfb6691f406]
- RM D            [Central Tendency] [Classical Decompo...] [2010-12-17 19:46:13] [46df8573ee32a55e1a6edcfb6691f406]
- RM D            [Central Tendency] [Classical Decompo...] [2010-12-17 19:46:13] [46df8573ee32a55e1a6edcfb6691f406]
- RM D            [Central Tendency] [Classical Decompo...] [2010-12-17 19:46:13] [46df8573ee32a55e1a6edcfb6691f406]
-    D            [Classical Decomposition] [CD] [2010-12-17 20:04:13] [2db53827eae1799a3d605fb62e1e92dc]
-   PD            [Classical Decomposition] [workshop8] [2010-12-19 00:13:34] [8b2514d8f13517d765015fc185a22b4b]
-   PD            [Classical Decomposition] [ws8dollar] [2010-12-26 01:10:21] [8b2514d8f13517d765015fc185a22b4b]
-    D          [Central Tendency] [Univariate analys...] [2010-12-14 13:41:06] [46df8573ee32a55e1a6edcfb6691f406]
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Dataseries X:
53
43
33
45
46
55
41
55
36
45
55
50
49
47
69
51
48
62
45
37
50
50
50
58
53
57
53
61
47
47
56
44
46
58
48
38
74
60
32
51
50
40
61
63
56
45
61
70
59
57
69
44
56
50
56
43
48
52
62
48




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'RServer@AstonUniversity' @ vre.aston.ac.uk

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 2 seconds \tabularnewline
R Server & 'RServer@AstonUniversity' @ vre.aston.ac.uk \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=98593&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'RServer@AstonUniversity' @ vre.aston.ac.uk[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=98593&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=98593&T=0

As an alternative you can also use a QR Code:  

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

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'RServer@AstonUniversity' @ vre.aston.ac.uk







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean51.46666666666671.1518755687140844.6807520400165
Geometric Mean50.6948684314599
Harmonic Mean49.9053806072266
Quadratic Mean52.2216430227928
Winsorized Mean ( 1 / 20 )51.41666666666671.1267902683513145.631088686893
Winsorized Mean ( 2 / 20 )51.48333333333331.0916973946596247.1589779229853
Winsorized Mean ( 3 / 20 )51.53333333333331.0799839574730947.7167581765835
Winsorized Mean ( 4 / 20 )51.20.96778622096593552.9042456803094
Winsorized Mean ( 5 / 20 )51.28333333333330.91413620944375556.1003194092255
Winsorized Mean ( 6 / 20 )51.38333333333330.893824281150657.4870636398339
Winsorized Mean ( 7 / 20 )51.50.82732295800138362.2489675910987
Winsorized Mean ( 8 / 20 )51.50.82732295800138362.2489675910987
Winsorized Mean ( 9 / 20 )51.650.80212465041429864.3914882472727
Winsorized Mean ( 10 / 20 )51.48333333333330.77002152243259866.8596030545884
Winsorized Mean ( 11 / 20 )51.48333333333330.70690367521067972.829347390208
Winsorized Mean ( 12 / 20 )51.28333333333330.67191087091648176.3246072553988
Winsorized Mean ( 13 / 20 )51.28333333333330.67191087091648176.3246072553988
Winsorized Mean ( 14 / 20 )51.050.63353773091835380.5792575700264
Winsorized Mean ( 15 / 20 )51.30.59437095837380286.3097351532058
Winsorized Mean ( 16 / 20 )51.03333333333330.55232772279779592.3968347538775
Winsorized Mean ( 17 / 20 )51.31666666666670.510063509209878100.608386485361
Winsorized Mean ( 18 / 20 )51.31666666666670.510063509209878100.608386485361
Winsorized Mean ( 19 / 20 )51.31666666666670.510063509209878100.608386485361
Winsorized Mean ( 20 / 20 )51.31666666666670.412030706624526124.545733707731
Trimmed Mean ( 1 / 20 )51.41379310344831.0735319983387247.8921850331529
Trimmed Mean ( 2 / 20 )51.41071428571431.0073679171949551.0346948797706
Trimmed Mean ( 3 / 20 )51.37037037037040.94919742342398354.1197954215521
Trimmed Mean ( 4 / 20 )51.30769230769230.88157718150601158.1998869571949
Trimmed Mean ( 5 / 20 )51.340.84448269396605360.7946146994266
Trimmed Mean ( 6 / 20 )51.35416666666670.81676232432969462.8752883634934
Trimmed Mean ( 7 / 20 )51.34782608695650.78771815707145365.1855306698216
Trimmed Mean ( 8 / 20 )51.31818181818180.76992402859115766.6535656928206
Trimmed Mean ( 9 / 20 )51.28571428571430.74609764043714268.7386094072966
Trimmed Mean ( 10 / 20 )51.2250.72101024211225371.0461474859672
Trimmed Mean ( 11 / 20 )51.18421052631580.69631754740555473.5069950729028
Trimmed Mean ( 12 / 20 )51.13888888888890.67981414100762375.2248089648306
Trimmed Mean ( 13 / 20 )51.11764705882350.66590603561999676.7640542726575
Trimmed Mean ( 14 / 20 )51.093750.64501715249761379.213009765952
Trimmed Mean ( 15 / 20 )51.10.6257868610016581.657195419872
Trimmed Mean ( 16 / 20 )51.07142857142860.60842534948479283.9403365008958
Trimmed Mean ( 17 / 20 )51.07692307692310.59465071046423785.8939915115008
Trimmed Mean ( 18 / 20 )51.04166666666670.58507761985572487.2391370554444
Trimmed Mean ( 19 / 20 )510.56599144900459490.1073683881503
Trimmed Mean ( 20 / 20 )50.950.53051613398750996.0385495103522
Median50
Midrange53
Midmean - Weighted Average at Xnp50.5714285714286
Midmean - Weighted Average at X(n+1)p51.2903225806452
Midmean - Empirical Distribution Function50.5714285714286
Midmean - Empirical Distribution Function - Averaging51.2903225806452
Midmean - Empirical Distribution Function - Interpolation51.2903225806452
Midmean - Closest Observation50.5714285714286
Midmean - True Basic - Statistics Graphics Toolkit51.2903225806452
Midmean - MS Excel (old versions)50.5714285714286
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 51.4666666666667 & 1.15187556871408 & 44.6807520400165 \tabularnewline
Geometric Mean & 50.6948684314599 &  &  \tabularnewline
Harmonic Mean & 49.9053806072266 &  &  \tabularnewline
Quadratic Mean & 52.2216430227928 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 51.4166666666667 & 1.12679026835131 & 45.631088686893 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 51.4833333333333 & 1.09169739465962 & 47.1589779229853 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 51.5333333333333 & 1.07998395747309 & 47.7167581765835 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 51.2 & 0.967786220965935 & 52.9042456803094 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 51.2833333333333 & 0.914136209443755 & 56.1003194092255 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 51.3833333333333 & 0.8938242811506 & 57.4870636398339 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 51.5 & 0.827322958001383 & 62.2489675910987 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 51.5 & 0.827322958001383 & 62.2489675910987 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 51.65 & 0.802124650414298 & 64.3914882472727 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 51.4833333333333 & 0.770021522432598 & 66.8596030545884 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 51.4833333333333 & 0.706903675210679 & 72.829347390208 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 51.2833333333333 & 0.671910870916481 & 76.3246072553988 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 51.2833333333333 & 0.671910870916481 & 76.3246072553988 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 51.05 & 0.633537730918353 & 80.5792575700264 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 51.3 & 0.594370958373802 & 86.3097351532058 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 51.0333333333333 & 0.552327722797795 & 92.3968347538775 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 51.3166666666667 & 0.510063509209878 & 100.608386485361 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 51.3166666666667 & 0.510063509209878 & 100.608386485361 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 51.3166666666667 & 0.510063509209878 & 100.608386485361 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 51.3166666666667 & 0.412030706624526 & 124.545733707731 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 51.4137931034483 & 1.07353199833872 & 47.8921850331529 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 51.4107142857143 & 1.00736791719495 & 51.0346948797706 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 51.3703703703704 & 0.949197423423983 & 54.1197954215521 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 51.3076923076923 & 0.881577181506011 & 58.1998869571949 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 51.34 & 0.844482693966053 & 60.7946146994266 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 51.3541666666667 & 0.816762324329694 & 62.8752883634934 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 51.3478260869565 & 0.787718157071453 & 65.1855306698216 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 51.3181818181818 & 0.769924028591157 & 66.6535656928206 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 51.2857142857143 & 0.746097640437142 & 68.7386094072966 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 51.225 & 0.721010242112253 & 71.0461474859672 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 51.1842105263158 & 0.696317547405554 & 73.5069950729028 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 51.1388888888889 & 0.679814141007623 & 75.2248089648306 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 51.1176470588235 & 0.665906035619996 & 76.7640542726575 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 51.09375 & 0.645017152497613 & 79.213009765952 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 51.1 & 0.62578686100165 & 81.657195419872 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 51.0714285714286 & 0.608425349484792 & 83.9403365008958 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 51.0769230769231 & 0.594650710464237 & 85.8939915115008 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 51.0416666666667 & 0.585077619855724 & 87.2391370554444 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 51 & 0.565991449004594 & 90.1073683881503 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 50.95 & 0.530516133987509 & 96.0385495103522 \tabularnewline
Median & 50 &  &  \tabularnewline
Midrange & 53 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 50.5714285714286 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 51.2903225806452 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 50.5714285714286 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 51.2903225806452 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 51.2903225806452 &  &  \tabularnewline
Midmean - Closest Observation & 50.5714285714286 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 51.2903225806452 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 50.5714285714286 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=98593&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]51.4666666666667[/C][C]1.15187556871408[/C][C]44.6807520400165[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]50.6948684314599[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]49.9053806072266[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]52.2216430227928[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]51.4166666666667[/C][C]1.12679026835131[/C][C]45.631088686893[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]51.4833333333333[/C][C]1.09169739465962[/C][C]47.1589779229853[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]51.5333333333333[/C][C]1.07998395747309[/C][C]47.7167581765835[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]51.2[/C][C]0.967786220965935[/C][C]52.9042456803094[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]51.2833333333333[/C][C]0.914136209443755[/C][C]56.1003194092255[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]51.3833333333333[/C][C]0.8938242811506[/C][C]57.4870636398339[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]51.5[/C][C]0.827322958001383[/C][C]62.2489675910987[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]51.5[/C][C]0.827322958001383[/C][C]62.2489675910987[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]51.65[/C][C]0.802124650414298[/C][C]64.3914882472727[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]51.4833333333333[/C][C]0.770021522432598[/C][C]66.8596030545884[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]51.4833333333333[/C][C]0.706903675210679[/C][C]72.829347390208[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]51.2833333333333[/C][C]0.671910870916481[/C][C]76.3246072553988[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]51.2833333333333[/C][C]0.671910870916481[/C][C]76.3246072553988[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]51.05[/C][C]0.633537730918353[/C][C]80.5792575700264[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]51.3[/C][C]0.594370958373802[/C][C]86.3097351532058[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]51.0333333333333[/C][C]0.552327722797795[/C][C]92.3968347538775[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]51.3166666666667[/C][C]0.510063509209878[/C][C]100.608386485361[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]51.3166666666667[/C][C]0.510063509209878[/C][C]100.608386485361[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]51.3166666666667[/C][C]0.510063509209878[/C][C]100.608386485361[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]51.3166666666667[/C][C]0.412030706624526[/C][C]124.545733707731[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]51.4137931034483[/C][C]1.07353199833872[/C][C]47.8921850331529[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]51.4107142857143[/C][C]1.00736791719495[/C][C]51.0346948797706[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]51.3703703703704[/C][C]0.949197423423983[/C][C]54.1197954215521[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]51.3076923076923[/C][C]0.881577181506011[/C][C]58.1998869571949[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]51.34[/C][C]0.844482693966053[/C][C]60.7946146994266[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]51.3541666666667[/C][C]0.816762324329694[/C][C]62.8752883634934[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]51.3478260869565[/C][C]0.787718157071453[/C][C]65.1855306698216[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]51.3181818181818[/C][C]0.769924028591157[/C][C]66.6535656928206[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]51.2857142857143[/C][C]0.746097640437142[/C][C]68.7386094072966[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]51.225[/C][C]0.721010242112253[/C][C]71.0461474859672[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]51.1842105263158[/C][C]0.696317547405554[/C][C]73.5069950729028[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]51.1388888888889[/C][C]0.679814141007623[/C][C]75.2248089648306[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]51.1176470588235[/C][C]0.665906035619996[/C][C]76.7640542726575[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]51.09375[/C][C]0.645017152497613[/C][C]79.213009765952[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]51.1[/C][C]0.62578686100165[/C][C]81.657195419872[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]51.0714285714286[/C][C]0.608425349484792[/C][C]83.9403365008958[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]51.0769230769231[/C][C]0.594650710464237[/C][C]85.8939915115008[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]51.0416666666667[/C][C]0.585077619855724[/C][C]87.2391370554444[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]51[/C][C]0.565991449004594[/C][C]90.1073683881503[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]50.95[/C][C]0.530516133987509[/C][C]96.0385495103522[/C][/ROW]
[ROW][C]Median[/C][C]50[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]53[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]50.5714285714286[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]51.2903225806452[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]50.5714285714286[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]51.2903225806452[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]51.2903225806452[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]50.5714285714286[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]51.2903225806452[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]50.5714285714286[/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=98593&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=98593&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 Mean51.46666666666671.1518755687140844.6807520400165
Geometric Mean50.6948684314599
Harmonic Mean49.9053806072266
Quadratic Mean52.2216430227928
Winsorized Mean ( 1 / 20 )51.41666666666671.1267902683513145.631088686893
Winsorized Mean ( 2 / 20 )51.48333333333331.0916973946596247.1589779229853
Winsorized Mean ( 3 / 20 )51.53333333333331.0799839574730947.7167581765835
Winsorized Mean ( 4 / 20 )51.20.96778622096593552.9042456803094
Winsorized Mean ( 5 / 20 )51.28333333333330.91413620944375556.1003194092255
Winsorized Mean ( 6 / 20 )51.38333333333330.893824281150657.4870636398339
Winsorized Mean ( 7 / 20 )51.50.82732295800138362.2489675910987
Winsorized Mean ( 8 / 20 )51.50.82732295800138362.2489675910987
Winsorized Mean ( 9 / 20 )51.650.80212465041429864.3914882472727
Winsorized Mean ( 10 / 20 )51.48333333333330.77002152243259866.8596030545884
Winsorized Mean ( 11 / 20 )51.48333333333330.70690367521067972.829347390208
Winsorized Mean ( 12 / 20 )51.28333333333330.67191087091648176.3246072553988
Winsorized Mean ( 13 / 20 )51.28333333333330.67191087091648176.3246072553988
Winsorized Mean ( 14 / 20 )51.050.63353773091835380.5792575700264
Winsorized Mean ( 15 / 20 )51.30.59437095837380286.3097351532058
Winsorized Mean ( 16 / 20 )51.03333333333330.55232772279779592.3968347538775
Winsorized Mean ( 17 / 20 )51.31666666666670.510063509209878100.608386485361
Winsorized Mean ( 18 / 20 )51.31666666666670.510063509209878100.608386485361
Winsorized Mean ( 19 / 20 )51.31666666666670.510063509209878100.608386485361
Winsorized Mean ( 20 / 20 )51.31666666666670.412030706624526124.545733707731
Trimmed Mean ( 1 / 20 )51.41379310344831.0735319983387247.8921850331529
Trimmed Mean ( 2 / 20 )51.41071428571431.0073679171949551.0346948797706
Trimmed Mean ( 3 / 20 )51.37037037037040.94919742342398354.1197954215521
Trimmed Mean ( 4 / 20 )51.30769230769230.88157718150601158.1998869571949
Trimmed Mean ( 5 / 20 )51.340.84448269396605360.7946146994266
Trimmed Mean ( 6 / 20 )51.35416666666670.81676232432969462.8752883634934
Trimmed Mean ( 7 / 20 )51.34782608695650.78771815707145365.1855306698216
Trimmed Mean ( 8 / 20 )51.31818181818180.76992402859115766.6535656928206
Trimmed Mean ( 9 / 20 )51.28571428571430.74609764043714268.7386094072966
Trimmed Mean ( 10 / 20 )51.2250.72101024211225371.0461474859672
Trimmed Mean ( 11 / 20 )51.18421052631580.69631754740555473.5069950729028
Trimmed Mean ( 12 / 20 )51.13888888888890.67981414100762375.2248089648306
Trimmed Mean ( 13 / 20 )51.11764705882350.66590603561999676.7640542726575
Trimmed Mean ( 14 / 20 )51.093750.64501715249761379.213009765952
Trimmed Mean ( 15 / 20 )51.10.6257868610016581.657195419872
Trimmed Mean ( 16 / 20 )51.07142857142860.60842534948479283.9403365008958
Trimmed Mean ( 17 / 20 )51.07692307692310.59465071046423785.8939915115008
Trimmed Mean ( 18 / 20 )51.04166666666670.58507761985572487.2391370554444
Trimmed Mean ( 19 / 20 )510.56599144900459490.1073683881503
Trimmed Mean ( 20 / 20 )50.950.53051613398750996.0385495103522
Median50
Midrange53
Midmean - Weighted Average at Xnp50.5714285714286
Midmean - Weighted Average at X(n+1)p51.2903225806452
Midmean - Empirical Distribution Function50.5714285714286
Midmean - Empirical Distribution Function - Averaging51.2903225806452
Midmean - Empirical Distribution Function - Interpolation51.2903225806452
Midmean - Closest Observation50.5714285714286
Midmean - True Basic - Statistics Graphics Toolkit51.2903225806452
Midmean - MS Excel (old versions)50.5714285714286
Number of observations60



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')