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Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationThu, 10 Oct 2013 13:58:01 -0400
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2013/Oct/10/t1381427916guw3g96c1fi34g5.htm/, Retrieved Thu, 02 May 2024 13:34:36 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=214662, Retrieved Thu, 02 May 2024 13:34:36 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact71
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [] [2013-10-10 17:58:01] [ccf63754fa7d22a76bdef567828ba364] [Current]
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Dataseries X:
9,27
9,30
9,35
9,33
9,37
9,42
9,45
9,38
9,40
9,43
9,45
9,49
9,47
9,48
9,52
9,53
9,53
9,54
9,57
9,61
9,61
9,63
9,64
9,60
9,64
9,66
9,67
9,70
9,72
9,73
9,77
9,72
9,68
9,62
9,79
9,77
9,79
9,77
9,78
9,81
9,74
9,70
9,78
9,85
9,83
9,90
9,93
9,85
9,95
9,97
10,02
9,97
9,95
9,95
9,98
10,00
10,04
10,05
10,06
10,09
10,14
10,13
10,12
10,10
10,12
10,06
10,21
10,18
10,26
10,39
10,41
10,46




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'Gertrude Mary Cox' @ cox.wessa.net

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 3 seconds \tabularnewline
R Server & 'Gertrude Mary Cox' @ cox.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=214662&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]3 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gertrude Mary Cox' @ cox.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=214662&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=214662&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 time3 seconds
R Server'Gertrude Mary Cox' @ cox.wessa.net







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean9.780277777777780.0335794739812418291.257623131358
Geometric Mean9.77620443823705
Harmonic Mean9.77215083128011
Quadratic Mean9.78436976338623
Winsorized Mean ( 1 / 24 )9.780.0333010406958116293.684515428074
Winsorized Mean ( 2 / 24 )9.780277777777780.0329899995648977296.461894718673
Winsorized Mean ( 3 / 24 )9.775694444444440.0315371867272613309.973572753532
Winsorized Mean ( 4 / 24 )9.774027777777780.0307506884550985317.847445661244
Winsorized Mean ( 5 / 24 )9.772638888888890.0302169988740258323.41527130576
Winsorized Mean ( 6 / 24 )9.770972222222220.0293034416907404333.441113345732
Winsorized Mean ( 7 / 24 )9.771944444444450.0287912722664391339.406482423329
Winsorized Mean ( 8 / 24 )9.771944444444440.0284082404513793343.982741950144
Winsorized Mean ( 9 / 24 )9.774444444444440.027992208345311349.184470330716
Winsorized Mean ( 10 / 24 )9.771666666666670.0275172445576191355.110652384017
Winsorized Mean ( 11 / 24 )9.773194444444440.0267661191170038365.133040084089
Winsorized Mean ( 12 / 24 )9.769861111111110.0256858146485763380.360181087448
Winsorized Mean ( 13 / 24 )9.771666666666670.0254013172307639384.691336197009
Winsorized Mean ( 14 / 24 )9.775555555555560.0242007521392133403.936022290642
Winsorized Mean ( 15 / 24 )9.775555555555560.0235618329545634414.889434722957
Winsorized Mean ( 16 / 24 )9.771111111111110.0228697711004298427.25006158577
Winsorized Mean ( 17 / 24 )9.768750.0218052066796249448.000798319791
Winsorized Mean ( 18 / 24 )9.771250.0199764508268344489.138440291619
Winsorized Mean ( 19 / 24 )9.776527777777780.0184928609096939528.664971067455
Winsorized Mean ( 20 / 24 )9.779305555555560.0181233454146182539.5971511787
Winsorized Mean ( 21 / 24 )9.773472222222220.0172709238074755565.891687738899
Winsorized Mean ( 22 / 24 )9.776527777777780.0168675217849794579.606648943761
Winsorized Mean ( 23 / 24 )9.779722222222220.0164540097693277594.367109253384
Winsorized Mean ( 24 / 24 )9.776388888888890.015062864558742649.039155252512
Trimmed Mean ( 1 / 24 )9.777857142857140.0323073316661218302.651337594383
Trimmed Mean ( 2 / 24 )9.775588235294120.0311228148285273314.097175629943
Trimmed Mean ( 3 / 24 )9.77303030303030.0299050320445183326.802201331255
Trimmed Mean ( 4 / 24 )9.772031250.0291259747499363335.509157509702
Trimmed Mean ( 5 / 24 )9.771451612903230.0284769816906219343.135087807469
Trimmed Mean ( 6 / 24 )9.771166666666670.0278556526094355350.778594336608
Trimmed Mean ( 7 / 24 )9.771206896551720.027350293809361357.261496518454
Trimmed Mean ( 8 / 24 )9.771071428571430.026852989109571363.872766219862
Trimmed Mean ( 9 / 24 )9.770925925925930.0263214931300503371.214728497709
Trimmed Mean ( 10 / 24 )9.770384615384620.0257467090524847379.480911345511
Trimmed Mean ( 11 / 24 )9.77020.0251257896616693388.851460254996
Trimmed Mean ( 12 / 24 )9.769791666666670.0245012114032059398.747290731442
Trimmed Mean ( 13 / 24 )9.769782608695650.0239372955632542408.140618177983
Trimmed Mean ( 14 / 24 )9.769545454545450.0232596215410762420.021685963057
Trimmed Mean ( 15 / 24 )9.768809523809520.0226399438900379431.485588977455
Trimmed Mean ( 16 / 24 )9.7680.0219562502052815444.884709760246
Trimmed Mean ( 17 / 24 )9.767631578947370.0211995672495564460.746743740806
Trimmed Mean ( 18 / 24 )9.76750.0204333022605217478.018671454362
Trimmed Mean ( 19 / 24 )9.767058823529410.0198457932599956492.147564754567
Trimmed Mean ( 20 / 24 )9.76593750.0193849967706571503.788451220307
Trimmed Mean ( 21 / 24 )9.764333333333330.0187768709114712520.019196988147
Trimmed Mean ( 22 / 24 )9.763214285714290.0181269302670648538.602738680652
Trimmed Mean ( 23 / 24 )9.761538461538460.0172287086680013566.585612981458
Trimmed Mean ( 24 / 24 )9.759166666666670.0159246034540607612.83577294844
Median9.77
Midrange9.865
Midmean - Weighted Average at Xnp9.76135135135135
Midmean - Weighted Average at X(n+1)p9.7675
Midmean - Empirical Distribution Function9.76135135135135
Midmean - Empirical Distribution Function - Averaging9.7675
Midmean - Empirical Distribution Function - Interpolation9.7675
Midmean - Closest Observation9.76135135135135
Midmean - True Basic - Statistics Graphics Toolkit9.7675
Midmean - MS Excel (old versions)9.76763157894737
Number of observations72

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 9.78027777777778 & 0.0335794739812418 & 291.257623131358 \tabularnewline
Geometric Mean & 9.77620443823705 &  &  \tabularnewline
Harmonic Mean & 9.77215083128011 &  &  \tabularnewline
Quadratic Mean & 9.78436976338623 &  &  \tabularnewline
Winsorized Mean ( 1 / 24 ) & 9.78 & 0.0333010406958116 & 293.684515428074 \tabularnewline
Winsorized Mean ( 2 / 24 ) & 9.78027777777778 & 0.0329899995648977 & 296.461894718673 \tabularnewline
Winsorized Mean ( 3 / 24 ) & 9.77569444444444 & 0.0315371867272613 & 309.973572753532 \tabularnewline
Winsorized Mean ( 4 / 24 ) & 9.77402777777778 & 0.0307506884550985 & 317.847445661244 \tabularnewline
Winsorized Mean ( 5 / 24 ) & 9.77263888888889 & 0.0302169988740258 & 323.41527130576 \tabularnewline
Winsorized Mean ( 6 / 24 ) & 9.77097222222222 & 0.0293034416907404 & 333.441113345732 \tabularnewline
Winsorized Mean ( 7 / 24 ) & 9.77194444444445 & 0.0287912722664391 & 339.406482423329 \tabularnewline
Winsorized Mean ( 8 / 24 ) & 9.77194444444444 & 0.0284082404513793 & 343.982741950144 \tabularnewline
Winsorized Mean ( 9 / 24 ) & 9.77444444444444 & 0.027992208345311 & 349.184470330716 \tabularnewline
Winsorized Mean ( 10 / 24 ) & 9.77166666666667 & 0.0275172445576191 & 355.110652384017 \tabularnewline
Winsorized Mean ( 11 / 24 ) & 9.77319444444444 & 0.0267661191170038 & 365.133040084089 \tabularnewline
Winsorized Mean ( 12 / 24 ) & 9.76986111111111 & 0.0256858146485763 & 380.360181087448 \tabularnewline
Winsorized Mean ( 13 / 24 ) & 9.77166666666667 & 0.0254013172307639 & 384.691336197009 \tabularnewline
Winsorized Mean ( 14 / 24 ) & 9.77555555555556 & 0.0242007521392133 & 403.936022290642 \tabularnewline
Winsorized Mean ( 15 / 24 ) & 9.77555555555556 & 0.0235618329545634 & 414.889434722957 \tabularnewline
Winsorized Mean ( 16 / 24 ) & 9.77111111111111 & 0.0228697711004298 & 427.25006158577 \tabularnewline
Winsorized Mean ( 17 / 24 ) & 9.76875 & 0.0218052066796249 & 448.000798319791 \tabularnewline
Winsorized Mean ( 18 / 24 ) & 9.77125 & 0.0199764508268344 & 489.138440291619 \tabularnewline
Winsorized Mean ( 19 / 24 ) & 9.77652777777778 & 0.0184928609096939 & 528.664971067455 \tabularnewline
Winsorized Mean ( 20 / 24 ) & 9.77930555555556 & 0.0181233454146182 & 539.5971511787 \tabularnewline
Winsorized Mean ( 21 / 24 ) & 9.77347222222222 & 0.0172709238074755 & 565.891687738899 \tabularnewline
Winsorized Mean ( 22 / 24 ) & 9.77652777777778 & 0.0168675217849794 & 579.606648943761 \tabularnewline
Winsorized Mean ( 23 / 24 ) & 9.77972222222222 & 0.0164540097693277 & 594.367109253384 \tabularnewline
Winsorized Mean ( 24 / 24 ) & 9.77638888888889 & 0.015062864558742 & 649.039155252512 \tabularnewline
Trimmed Mean ( 1 / 24 ) & 9.77785714285714 & 0.0323073316661218 & 302.651337594383 \tabularnewline
Trimmed Mean ( 2 / 24 ) & 9.77558823529412 & 0.0311228148285273 & 314.097175629943 \tabularnewline
Trimmed Mean ( 3 / 24 ) & 9.7730303030303 & 0.0299050320445183 & 326.802201331255 \tabularnewline
Trimmed Mean ( 4 / 24 ) & 9.77203125 & 0.0291259747499363 & 335.509157509702 \tabularnewline
Trimmed Mean ( 5 / 24 ) & 9.77145161290323 & 0.0284769816906219 & 343.135087807469 \tabularnewline
Trimmed Mean ( 6 / 24 ) & 9.77116666666667 & 0.0278556526094355 & 350.778594336608 \tabularnewline
Trimmed Mean ( 7 / 24 ) & 9.77120689655172 & 0.027350293809361 & 357.261496518454 \tabularnewline
Trimmed Mean ( 8 / 24 ) & 9.77107142857143 & 0.026852989109571 & 363.872766219862 \tabularnewline
Trimmed Mean ( 9 / 24 ) & 9.77092592592593 & 0.0263214931300503 & 371.214728497709 \tabularnewline
Trimmed Mean ( 10 / 24 ) & 9.77038461538462 & 0.0257467090524847 & 379.480911345511 \tabularnewline
Trimmed Mean ( 11 / 24 ) & 9.7702 & 0.0251257896616693 & 388.851460254996 \tabularnewline
Trimmed Mean ( 12 / 24 ) & 9.76979166666667 & 0.0245012114032059 & 398.747290731442 \tabularnewline
Trimmed Mean ( 13 / 24 ) & 9.76978260869565 & 0.0239372955632542 & 408.140618177983 \tabularnewline
Trimmed Mean ( 14 / 24 ) & 9.76954545454545 & 0.0232596215410762 & 420.021685963057 \tabularnewline
Trimmed Mean ( 15 / 24 ) & 9.76880952380952 & 0.0226399438900379 & 431.485588977455 \tabularnewline
Trimmed Mean ( 16 / 24 ) & 9.768 & 0.0219562502052815 & 444.884709760246 \tabularnewline
Trimmed Mean ( 17 / 24 ) & 9.76763157894737 & 0.0211995672495564 & 460.746743740806 \tabularnewline
Trimmed Mean ( 18 / 24 ) & 9.7675 & 0.0204333022605217 & 478.018671454362 \tabularnewline
Trimmed Mean ( 19 / 24 ) & 9.76705882352941 & 0.0198457932599956 & 492.147564754567 \tabularnewline
Trimmed Mean ( 20 / 24 ) & 9.7659375 & 0.0193849967706571 & 503.788451220307 \tabularnewline
Trimmed Mean ( 21 / 24 ) & 9.76433333333333 & 0.0187768709114712 & 520.019196988147 \tabularnewline
Trimmed Mean ( 22 / 24 ) & 9.76321428571429 & 0.0181269302670648 & 538.602738680652 \tabularnewline
Trimmed Mean ( 23 / 24 ) & 9.76153846153846 & 0.0172287086680013 & 566.585612981458 \tabularnewline
Trimmed Mean ( 24 / 24 ) & 9.75916666666667 & 0.0159246034540607 & 612.83577294844 \tabularnewline
Median & 9.77 &  &  \tabularnewline
Midrange & 9.865 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 9.76135135135135 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 9.7675 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 9.76135135135135 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 9.7675 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 9.7675 &  &  \tabularnewline
Midmean - Closest Observation & 9.76135135135135 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 9.7675 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 9.76763157894737 &  &  \tabularnewline
Number of observations & 72 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=214662&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]9.78027777777778[/C][C]0.0335794739812418[/C][C]291.257623131358[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]9.77620443823705[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]9.77215083128011[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]9.78436976338623[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 24 )[/C][C]9.78[/C][C]0.0333010406958116[/C][C]293.684515428074[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 24 )[/C][C]9.78027777777778[/C][C]0.0329899995648977[/C][C]296.461894718673[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 24 )[/C][C]9.77569444444444[/C][C]0.0315371867272613[/C][C]309.973572753532[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 24 )[/C][C]9.77402777777778[/C][C]0.0307506884550985[/C][C]317.847445661244[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 24 )[/C][C]9.77263888888889[/C][C]0.0302169988740258[/C][C]323.41527130576[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 24 )[/C][C]9.77097222222222[/C][C]0.0293034416907404[/C][C]333.441113345732[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 24 )[/C][C]9.77194444444445[/C][C]0.0287912722664391[/C][C]339.406482423329[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 24 )[/C][C]9.77194444444444[/C][C]0.0284082404513793[/C][C]343.982741950144[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 24 )[/C][C]9.77444444444444[/C][C]0.027992208345311[/C][C]349.184470330716[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 24 )[/C][C]9.77166666666667[/C][C]0.0275172445576191[/C][C]355.110652384017[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 24 )[/C][C]9.77319444444444[/C][C]0.0267661191170038[/C][C]365.133040084089[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 24 )[/C][C]9.76986111111111[/C][C]0.0256858146485763[/C][C]380.360181087448[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 24 )[/C][C]9.77166666666667[/C][C]0.0254013172307639[/C][C]384.691336197009[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 24 )[/C][C]9.77555555555556[/C][C]0.0242007521392133[/C][C]403.936022290642[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 24 )[/C][C]9.77555555555556[/C][C]0.0235618329545634[/C][C]414.889434722957[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 24 )[/C][C]9.77111111111111[/C][C]0.0228697711004298[/C][C]427.25006158577[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 24 )[/C][C]9.76875[/C][C]0.0218052066796249[/C][C]448.000798319791[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 24 )[/C][C]9.77125[/C][C]0.0199764508268344[/C][C]489.138440291619[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 24 )[/C][C]9.77652777777778[/C][C]0.0184928609096939[/C][C]528.664971067455[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 24 )[/C][C]9.77930555555556[/C][C]0.0181233454146182[/C][C]539.5971511787[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 24 )[/C][C]9.77347222222222[/C][C]0.0172709238074755[/C][C]565.891687738899[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 24 )[/C][C]9.77652777777778[/C][C]0.0168675217849794[/C][C]579.606648943761[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 24 )[/C][C]9.77972222222222[/C][C]0.0164540097693277[/C][C]594.367109253384[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 24 )[/C][C]9.77638888888889[/C][C]0.015062864558742[/C][C]649.039155252512[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 24 )[/C][C]9.77785714285714[/C][C]0.0323073316661218[/C][C]302.651337594383[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 24 )[/C][C]9.77558823529412[/C][C]0.0311228148285273[/C][C]314.097175629943[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 24 )[/C][C]9.7730303030303[/C][C]0.0299050320445183[/C][C]326.802201331255[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 24 )[/C][C]9.77203125[/C][C]0.0291259747499363[/C][C]335.509157509702[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 24 )[/C][C]9.77145161290323[/C][C]0.0284769816906219[/C][C]343.135087807469[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 24 )[/C][C]9.77116666666667[/C][C]0.0278556526094355[/C][C]350.778594336608[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 24 )[/C][C]9.77120689655172[/C][C]0.027350293809361[/C][C]357.261496518454[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 24 )[/C][C]9.77107142857143[/C][C]0.026852989109571[/C][C]363.872766219862[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 24 )[/C][C]9.77092592592593[/C][C]0.0263214931300503[/C][C]371.214728497709[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 24 )[/C][C]9.77038461538462[/C][C]0.0257467090524847[/C][C]379.480911345511[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 24 )[/C][C]9.7702[/C][C]0.0251257896616693[/C][C]388.851460254996[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 24 )[/C][C]9.76979166666667[/C][C]0.0245012114032059[/C][C]398.747290731442[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 24 )[/C][C]9.76978260869565[/C][C]0.0239372955632542[/C][C]408.140618177983[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 24 )[/C][C]9.76954545454545[/C][C]0.0232596215410762[/C][C]420.021685963057[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 24 )[/C][C]9.76880952380952[/C][C]0.0226399438900379[/C][C]431.485588977455[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 24 )[/C][C]9.768[/C][C]0.0219562502052815[/C][C]444.884709760246[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 24 )[/C][C]9.76763157894737[/C][C]0.0211995672495564[/C][C]460.746743740806[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 24 )[/C][C]9.7675[/C][C]0.0204333022605217[/C][C]478.018671454362[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 24 )[/C][C]9.76705882352941[/C][C]0.0198457932599956[/C][C]492.147564754567[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 24 )[/C][C]9.7659375[/C][C]0.0193849967706571[/C][C]503.788451220307[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 24 )[/C][C]9.76433333333333[/C][C]0.0187768709114712[/C][C]520.019196988147[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 24 )[/C][C]9.76321428571429[/C][C]0.0181269302670648[/C][C]538.602738680652[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 24 )[/C][C]9.76153846153846[/C][C]0.0172287086680013[/C][C]566.585612981458[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 24 )[/C][C]9.75916666666667[/C][C]0.0159246034540607[/C][C]612.83577294844[/C][/ROW]
[ROW][C]Median[/C][C]9.77[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]9.865[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]9.76135135135135[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]9.7675[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]9.76135135135135[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]9.7675[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]9.7675[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]9.76135135135135[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]9.7675[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]9.76763157894737[/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=214662&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=214662&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 Mean9.780277777777780.0335794739812418291.257623131358
Geometric Mean9.77620443823705
Harmonic Mean9.77215083128011
Quadratic Mean9.78436976338623
Winsorized Mean ( 1 / 24 )9.780.0333010406958116293.684515428074
Winsorized Mean ( 2 / 24 )9.780277777777780.0329899995648977296.461894718673
Winsorized Mean ( 3 / 24 )9.775694444444440.0315371867272613309.973572753532
Winsorized Mean ( 4 / 24 )9.774027777777780.0307506884550985317.847445661244
Winsorized Mean ( 5 / 24 )9.772638888888890.0302169988740258323.41527130576
Winsorized Mean ( 6 / 24 )9.770972222222220.0293034416907404333.441113345732
Winsorized Mean ( 7 / 24 )9.771944444444450.0287912722664391339.406482423329
Winsorized Mean ( 8 / 24 )9.771944444444440.0284082404513793343.982741950144
Winsorized Mean ( 9 / 24 )9.774444444444440.027992208345311349.184470330716
Winsorized Mean ( 10 / 24 )9.771666666666670.0275172445576191355.110652384017
Winsorized Mean ( 11 / 24 )9.773194444444440.0267661191170038365.133040084089
Winsorized Mean ( 12 / 24 )9.769861111111110.0256858146485763380.360181087448
Winsorized Mean ( 13 / 24 )9.771666666666670.0254013172307639384.691336197009
Winsorized Mean ( 14 / 24 )9.775555555555560.0242007521392133403.936022290642
Winsorized Mean ( 15 / 24 )9.775555555555560.0235618329545634414.889434722957
Winsorized Mean ( 16 / 24 )9.771111111111110.0228697711004298427.25006158577
Winsorized Mean ( 17 / 24 )9.768750.0218052066796249448.000798319791
Winsorized Mean ( 18 / 24 )9.771250.0199764508268344489.138440291619
Winsorized Mean ( 19 / 24 )9.776527777777780.0184928609096939528.664971067455
Winsorized Mean ( 20 / 24 )9.779305555555560.0181233454146182539.5971511787
Winsorized Mean ( 21 / 24 )9.773472222222220.0172709238074755565.891687738899
Winsorized Mean ( 22 / 24 )9.776527777777780.0168675217849794579.606648943761
Winsorized Mean ( 23 / 24 )9.779722222222220.0164540097693277594.367109253384
Winsorized Mean ( 24 / 24 )9.776388888888890.015062864558742649.039155252512
Trimmed Mean ( 1 / 24 )9.777857142857140.0323073316661218302.651337594383
Trimmed Mean ( 2 / 24 )9.775588235294120.0311228148285273314.097175629943
Trimmed Mean ( 3 / 24 )9.77303030303030.0299050320445183326.802201331255
Trimmed Mean ( 4 / 24 )9.772031250.0291259747499363335.509157509702
Trimmed Mean ( 5 / 24 )9.771451612903230.0284769816906219343.135087807469
Trimmed Mean ( 6 / 24 )9.771166666666670.0278556526094355350.778594336608
Trimmed Mean ( 7 / 24 )9.771206896551720.027350293809361357.261496518454
Trimmed Mean ( 8 / 24 )9.771071428571430.026852989109571363.872766219862
Trimmed Mean ( 9 / 24 )9.770925925925930.0263214931300503371.214728497709
Trimmed Mean ( 10 / 24 )9.770384615384620.0257467090524847379.480911345511
Trimmed Mean ( 11 / 24 )9.77020.0251257896616693388.851460254996
Trimmed Mean ( 12 / 24 )9.769791666666670.0245012114032059398.747290731442
Trimmed Mean ( 13 / 24 )9.769782608695650.0239372955632542408.140618177983
Trimmed Mean ( 14 / 24 )9.769545454545450.0232596215410762420.021685963057
Trimmed Mean ( 15 / 24 )9.768809523809520.0226399438900379431.485588977455
Trimmed Mean ( 16 / 24 )9.7680.0219562502052815444.884709760246
Trimmed Mean ( 17 / 24 )9.767631578947370.0211995672495564460.746743740806
Trimmed Mean ( 18 / 24 )9.76750.0204333022605217478.018671454362
Trimmed Mean ( 19 / 24 )9.767058823529410.0198457932599956492.147564754567
Trimmed Mean ( 20 / 24 )9.76593750.0193849967706571503.788451220307
Trimmed Mean ( 21 / 24 )9.764333333333330.0187768709114712520.019196988147
Trimmed Mean ( 22 / 24 )9.763214285714290.0181269302670648538.602738680652
Trimmed Mean ( 23 / 24 )9.761538461538460.0172287086680013566.585612981458
Trimmed Mean ( 24 / 24 )9.759166666666670.0159246034540607612.83577294844
Median9.77
Midrange9.865
Midmean - Weighted Average at Xnp9.76135135135135
Midmean - Weighted Average at X(n+1)p9.7675
Midmean - Empirical Distribution Function9.76135135135135
Midmean - Empirical Distribution Function - Averaging9.7675
Midmean - Empirical Distribution Function - Interpolation9.7675
Midmean - Closest Observation9.76135135135135
Midmean - True Basic - Statistics Graphics Toolkit9.7675
Midmean - MS Excel (old versions)9.76763157894737
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')