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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 computationMon, 08 Dec 2014 13:27:52 +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/2014/Dec/08/t1418045288kfr0lc8xkoyeln0.htm/, Retrieved Sun, 19 May 2024 11:37:30 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=263983, Retrieved Sun, 19 May 2024 11:37:30 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact80

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [] [2014-12-08 13:27:52] [58179e1d3a5a39b9daf58e365d8a3352] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
12.9
12.8
7.4
6.7
12.6
14.8
13.3
11.1
8.2
11.4
6.4
12
6.3
11.3
11.9
9.3
10
13.8
10.8
11.7
10.9
16.1
9.9
11.5
8.3
11.7
9
10.8
10.4
12.7
11.8
13
10.8
12.3
11.3
11.6
10.9
12.1
13.3
10.1
14.3
9.3
12.5
7.6
9.2
14.5
12.3
12.6
13
12.6
13.2
7.7
10.5
10.9
4.3
10.3
11.4
5.6
8.8
9
9.6
6.4
11.6

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'Herman Ole Andreas Wold' @ wold.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 & 1 seconds \tabularnewline
R Server & 'Herman Ole Andreas Wold' @ wold.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=263983&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]'Herman Ole Andreas Wold' @ wold.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=263983&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=263983&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'Herman Ole Andreas Wold' @ wold.wessa.net






Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean10.80.30235464404101635.7196431834363
Geometric Mean10.4936446274374
Harmonic Mean10.1292697422042
Quadratic Mean11.0592918628607
Winsorized Mean ( 1 / 21 )10.80.29056683131655237.1687296552929
Winsorized Mean ( 2 / 21 )10.81269841269840.28243049490464838.2844579738067
Winsorized Mean ( 3 / 21 )10.80793650793650.27924722878469238.7038272679502
Winsorized Mean ( 4 / 21 )10.77619047619050.27320811531506739.4431565979043
Winsorized Mean ( 5 / 21 )10.76031746031750.26046494017745941.3119610377746
Winsorized Mean ( 6 / 21 )10.82698412698410.24452223444876644.2781170857191
Winsorized Mean ( 7 / 21 )10.83809523809520.23777243863113945.5817978756931
Winsorized Mean ( 8 / 21 )10.82539682539680.23102842553429546.8574237146842
Winsorized Mean ( 9 / 21 )10.89682539682540.2160243137162650.4425877317587
Winsorized Mean ( 10 / 21 )10.89682539682540.21038048886986651.7957984381613
Winsorized Mean ( 11 / 21 )10.96666666666670.19097668500115357.4241126166812
Winsorized Mean ( 12 / 21 )10.98571428571430.1811927419717860.6299908382934
Winsorized Mean ( 13 / 21 )10.96507936507940.17809020896796861.5703661005393
Winsorized Mean ( 14 / 21 )11.00952380952380.17032414333540864.6386565869496
Winsorized Mean ( 15 / 21 )11.03333333333330.16628219864210866.3530637881483
Winsorized Mean ( 16 / 21 )11.00793650793650.16247102364523267.7532292279586
Winsorized Mean ( 17 / 21 )11.03492063492060.14104356018162778.2376779252491
Winsorized Mean ( 18 / 21 )11.12063492063490.127365658272287.3126639589805
Winsorized Mean ( 19 / 21 )11.09047619047620.11387856302128497.3886207925136
Winsorized Mean ( 20 / 21 )11.09047619047620.10449974179587106.129220990234
Winsorized Mean ( 21 / 21 )11.12380952380950.0897945052787783123.880737348842
Trimmed Mean ( 1 / 21 )10.81967213114750.27988892871283338.6570207721527
Trimmed Mean ( 2 / 21 )10.84067796610170.26680917168908540.6308295081191
Trimmed Mean ( 3 / 21 )10.85614035087720.25623817955327242.3673801062898
Trimmed Mean ( 4 / 21 )10.87454545454550.24470442806909144.4395123551875
Trimmed Mean ( 5 / 21 )10.90377358490570.23268737107354746.8601864149268
Trimmed Mean ( 6 / 21 )10.93921568627450.22205949443693849.2625443195409
Trimmed Mean ( 7 / 21 )10.96326530612240.21390231330922851.2536079508097
Trimmed Mean ( 8 / 21 )10.98723404255320.20546684329493553.4744870089899
Trimmed Mean ( 9 / 21 )11.01555555555560.19640597914008556.0856426254662
Trimmed Mean ( 10 / 21 )11.03488372093020.18897882954697958.3921688338483
Trimmed Mean ( 11 / 21 )11.05609756097560.18065088216076161.2014590171601
Trimmed Mean ( 12 / 21 )11.06923076923080.17499388252865963.2549584550074
Trimmed Mean ( 13 / 21 )11.08108108108110.16987178692048665.2320275306689
Trimmed Mean ( 14 / 21 )11.09714285714290.16344431962673867.8955553945569
Trimmed Mean ( 15 / 21 )11.10909090909090.15669186832058770.8976861923814
Trimmed Mean ( 16 / 21 )11.11935483870970.14820933719216275.0246580233524
Trimmed Mean ( 17 / 21 )11.13448275862070.13684299929079581.3668424130312
Trimmed Mean ( 18 / 21 )11.14814814814810.12792117969937687.1485720687309
Trimmed Mean ( 19 / 21 )11.1520.11973860418984993.1362117961404
Trimmed Mean ( 20 / 21 )11.16086956521740.11224252581871799.4353030084456
Trimmed Mean ( 21 / 21 )11.17142857142860.104001569846865107.415961007875
Median11.3
Midrange10.2
Midmean - Weighted Average at Xnp11.0625
Midmean - Weighted Average at X(n+1)p11.1942857142857
Midmean - Empirical Distribution Function11.1942857142857
Midmean - Empirical Distribution Function - Averaging11.1942857142857
Midmean - Empirical Distribution Function - Interpolation11.0625
Midmean - Closest Observation11.0625
Midmean - True Basic - Statistics Graphics Toolkit11.1942857142857
Midmean - MS Excel (old versions)11.1942857142857
Number of observations63

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 10.8 & 0.302354644041016 & 35.7196431834363 \tabularnewline
Geometric Mean & 10.4936446274374 &  &  \tabularnewline
Harmonic Mean & 10.1292697422042 &  &  \tabularnewline
Quadratic Mean & 11.0592918628607 &  &  \tabularnewline
Winsorized Mean ( 1 / 21 ) & 10.8 & 0.290566831316552 & 37.1687296552929 \tabularnewline
Winsorized Mean ( 2 / 21 ) & 10.8126984126984 & 0.282430494904648 & 38.2844579738067 \tabularnewline
Winsorized Mean ( 3 / 21 ) & 10.8079365079365 & 0.279247228784692 & 38.7038272679502 \tabularnewline
Winsorized Mean ( 4 / 21 ) & 10.7761904761905 & 0.273208115315067 & 39.4431565979043 \tabularnewline
Winsorized Mean ( 5 / 21 ) & 10.7603174603175 & 0.260464940177459 & 41.3119610377746 \tabularnewline
Winsorized Mean ( 6 / 21 ) & 10.8269841269841 & 0.244522234448766 & 44.2781170857191 \tabularnewline
Winsorized Mean ( 7 / 21 ) & 10.8380952380952 & 0.237772438631139 & 45.5817978756931 \tabularnewline
Winsorized Mean ( 8 / 21 ) & 10.8253968253968 & 0.231028425534295 & 46.8574237146842 \tabularnewline
Winsorized Mean ( 9 / 21 ) & 10.8968253968254 & 0.21602431371626 & 50.4425877317587 \tabularnewline
Winsorized Mean ( 10 / 21 ) & 10.8968253968254 & 0.210380488869866 & 51.7957984381613 \tabularnewline
Winsorized Mean ( 11 / 21 ) & 10.9666666666667 & 0.190976685001153 & 57.4241126166812 \tabularnewline
Winsorized Mean ( 12 / 21 ) & 10.9857142857143 & 0.18119274197178 & 60.6299908382934 \tabularnewline
Winsorized Mean ( 13 / 21 ) & 10.9650793650794 & 0.178090208967968 & 61.5703661005393 \tabularnewline
Winsorized Mean ( 14 / 21 ) & 11.0095238095238 & 0.170324143335408 & 64.6386565869496 \tabularnewline
Winsorized Mean ( 15 / 21 ) & 11.0333333333333 & 0.166282198642108 & 66.3530637881483 \tabularnewline
Winsorized Mean ( 16 / 21 ) & 11.0079365079365 & 0.162471023645232 & 67.7532292279586 \tabularnewline
Winsorized Mean ( 17 / 21 ) & 11.0349206349206 & 0.141043560181627 & 78.2376779252491 \tabularnewline
Winsorized Mean ( 18 / 21 ) & 11.1206349206349 & 0.1273656582722 & 87.3126639589805 \tabularnewline
Winsorized Mean ( 19 / 21 ) & 11.0904761904762 & 0.113878563021284 & 97.3886207925136 \tabularnewline
Winsorized Mean ( 20 / 21 ) & 11.0904761904762 & 0.10449974179587 & 106.129220990234 \tabularnewline
Winsorized Mean ( 21 / 21 ) & 11.1238095238095 & 0.0897945052787783 & 123.880737348842 \tabularnewline
Trimmed Mean ( 1 / 21 ) & 10.8196721311475 & 0.279888928712833 & 38.6570207721527 \tabularnewline
Trimmed Mean ( 2 / 21 ) & 10.8406779661017 & 0.266809171689085 & 40.6308295081191 \tabularnewline
Trimmed Mean ( 3 / 21 ) & 10.8561403508772 & 0.256238179553272 & 42.3673801062898 \tabularnewline
Trimmed Mean ( 4 / 21 ) & 10.8745454545455 & 0.244704428069091 & 44.4395123551875 \tabularnewline
Trimmed Mean ( 5 / 21 ) & 10.9037735849057 & 0.232687371073547 & 46.8601864149268 \tabularnewline
Trimmed Mean ( 6 / 21 ) & 10.9392156862745 & 0.222059494436938 & 49.2625443195409 \tabularnewline
Trimmed Mean ( 7 / 21 ) & 10.9632653061224 & 0.213902313309228 & 51.2536079508097 \tabularnewline
Trimmed Mean ( 8 / 21 ) & 10.9872340425532 & 0.205466843294935 & 53.4744870089899 \tabularnewline
Trimmed Mean ( 9 / 21 ) & 11.0155555555556 & 0.196405979140085 & 56.0856426254662 \tabularnewline
Trimmed Mean ( 10 / 21 ) & 11.0348837209302 & 0.188978829546979 & 58.3921688338483 \tabularnewline
Trimmed Mean ( 11 / 21 ) & 11.0560975609756 & 0.180650882160761 & 61.2014590171601 \tabularnewline
Trimmed Mean ( 12 / 21 ) & 11.0692307692308 & 0.174993882528659 & 63.2549584550074 \tabularnewline
Trimmed Mean ( 13 / 21 ) & 11.0810810810811 & 0.169871786920486 & 65.2320275306689 \tabularnewline
Trimmed Mean ( 14 / 21 ) & 11.0971428571429 & 0.163444319626738 & 67.8955553945569 \tabularnewline
Trimmed Mean ( 15 / 21 ) & 11.1090909090909 & 0.156691868320587 & 70.8976861923814 \tabularnewline
Trimmed Mean ( 16 / 21 ) & 11.1193548387097 & 0.148209337192162 & 75.0246580233524 \tabularnewline
Trimmed Mean ( 17 / 21 ) & 11.1344827586207 & 0.136842999290795 & 81.3668424130312 \tabularnewline
Trimmed Mean ( 18 / 21 ) & 11.1481481481481 & 0.127921179699376 & 87.1485720687309 \tabularnewline
Trimmed Mean ( 19 / 21 ) & 11.152 & 0.119738604189849 & 93.1362117961404 \tabularnewline
Trimmed Mean ( 20 / 21 ) & 11.1608695652174 & 0.112242525818717 & 99.4353030084456 \tabularnewline
Trimmed Mean ( 21 / 21 ) & 11.1714285714286 & 0.104001569846865 & 107.415961007875 \tabularnewline
Median & 11.3 &  &  \tabularnewline
Midrange & 10.2 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 11.0625 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 11.1942857142857 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 11.1942857142857 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 11.1942857142857 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 11.0625 &  &  \tabularnewline
Midmean - Closest Observation & 11.0625 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 11.1942857142857 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 11.1942857142857 &  &  \tabularnewline
Number of observations & 63 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=263983&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]10.8[/C][C]0.302354644041016[/C][C]35.7196431834363[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]10.4936446274374[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]10.1292697422042[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]11.0592918628607[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 21 )[/C][C]10.8[/C][C]0.290566831316552[/C][C]37.1687296552929[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 21 )[/C][C]10.8126984126984[/C][C]0.282430494904648[/C][C]38.2844579738067[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 21 )[/C][C]10.8079365079365[/C][C]0.279247228784692[/C][C]38.7038272679502[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 21 )[/C][C]10.7761904761905[/C][C]0.273208115315067[/C][C]39.4431565979043[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 21 )[/C][C]10.7603174603175[/C][C]0.260464940177459[/C][C]41.3119610377746[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 21 )[/C][C]10.8269841269841[/C][C]0.244522234448766[/C][C]44.2781170857191[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 21 )[/C][C]10.8380952380952[/C][C]0.237772438631139[/C][C]45.5817978756931[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 21 )[/C][C]10.8253968253968[/C][C]0.231028425534295[/C][C]46.8574237146842[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 21 )[/C][C]10.8968253968254[/C][C]0.21602431371626[/C][C]50.4425877317587[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 21 )[/C][C]10.8968253968254[/C][C]0.210380488869866[/C][C]51.7957984381613[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 21 )[/C][C]10.9666666666667[/C][C]0.190976685001153[/C][C]57.4241126166812[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 21 )[/C][C]10.9857142857143[/C][C]0.18119274197178[/C][C]60.6299908382934[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 21 )[/C][C]10.9650793650794[/C][C]0.178090208967968[/C][C]61.5703661005393[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 21 )[/C][C]11.0095238095238[/C][C]0.170324143335408[/C][C]64.6386565869496[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 21 )[/C][C]11.0333333333333[/C][C]0.166282198642108[/C][C]66.3530637881483[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 21 )[/C][C]11.0079365079365[/C][C]0.162471023645232[/C][C]67.7532292279586[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 21 )[/C][C]11.0349206349206[/C][C]0.141043560181627[/C][C]78.2376779252491[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 21 )[/C][C]11.1206349206349[/C][C]0.1273656582722[/C][C]87.3126639589805[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 21 )[/C][C]11.0904761904762[/C][C]0.113878563021284[/C][C]97.3886207925136[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 21 )[/C][C]11.0904761904762[/C][C]0.10449974179587[/C][C]106.129220990234[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 21 )[/C][C]11.1238095238095[/C][C]0.0897945052787783[/C][C]123.880737348842[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 21 )[/C][C]10.8196721311475[/C][C]0.279888928712833[/C][C]38.6570207721527[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 21 )[/C][C]10.8406779661017[/C][C]0.266809171689085[/C][C]40.6308295081191[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 21 )[/C][C]10.8561403508772[/C][C]0.256238179553272[/C][C]42.3673801062898[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 21 )[/C][C]10.8745454545455[/C][C]0.244704428069091[/C][C]44.4395123551875[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 21 )[/C][C]10.9037735849057[/C][C]0.232687371073547[/C][C]46.8601864149268[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 21 )[/C][C]10.9392156862745[/C][C]0.222059494436938[/C][C]49.2625443195409[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 21 )[/C][C]10.9632653061224[/C][C]0.213902313309228[/C][C]51.2536079508097[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 21 )[/C][C]10.9872340425532[/C][C]0.205466843294935[/C][C]53.4744870089899[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 21 )[/C][C]11.0155555555556[/C][C]0.196405979140085[/C][C]56.0856426254662[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 21 )[/C][C]11.0348837209302[/C][C]0.188978829546979[/C][C]58.3921688338483[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 21 )[/C][C]11.0560975609756[/C][C]0.180650882160761[/C][C]61.2014590171601[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 21 )[/C][C]11.0692307692308[/C][C]0.174993882528659[/C][C]63.2549584550074[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 21 )[/C][C]11.0810810810811[/C][C]0.169871786920486[/C][C]65.2320275306689[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 21 )[/C][C]11.0971428571429[/C][C]0.163444319626738[/C][C]67.8955553945569[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 21 )[/C][C]11.1090909090909[/C][C]0.156691868320587[/C][C]70.8976861923814[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 21 )[/C][C]11.1193548387097[/C][C]0.148209337192162[/C][C]75.0246580233524[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 21 )[/C][C]11.1344827586207[/C][C]0.136842999290795[/C][C]81.3668424130312[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 21 )[/C][C]11.1481481481481[/C][C]0.127921179699376[/C][C]87.1485720687309[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 21 )[/C][C]11.152[/C][C]0.119738604189849[/C][C]93.1362117961404[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 21 )[/C][C]11.1608695652174[/C][C]0.112242525818717[/C][C]99.4353030084456[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 21 )[/C][C]11.1714285714286[/C][C]0.104001569846865[/C][C]107.415961007875[/C][/ROW]
[ROW][C]Median[/C][C]11.3[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]10.2[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]11.0625[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]11.1942857142857[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]11.1942857142857[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]11.1942857142857[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]11.0625[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]11.0625[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]11.1942857142857[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]11.1942857142857[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]63[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=263983&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=263983&T=1

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


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

Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean10.80.30235464404101635.7196431834363
Geometric Mean10.4936446274374
Harmonic Mean10.1292697422042
Quadratic Mean11.0592918628607
Winsorized Mean ( 1 / 21 )10.80.29056683131655237.1687296552929
Winsorized Mean ( 2 / 21 )10.81269841269840.28243049490464838.2844579738067
Winsorized Mean ( 3 / 21 )10.80793650793650.27924722878469238.7038272679502
Winsorized Mean ( 4 / 21 )10.77619047619050.27320811531506739.4431565979043
Winsorized Mean ( 5 / 21 )10.76031746031750.26046494017745941.3119610377746
Winsorized Mean ( 6 / 21 )10.82698412698410.24452223444876644.2781170857191
Winsorized Mean ( 7 / 21 )10.83809523809520.23777243863113945.5817978756931
Winsorized Mean ( 8 / 21 )10.82539682539680.23102842553429546.8574237146842
Winsorized Mean ( 9 / 21 )10.89682539682540.2160243137162650.4425877317587
Winsorized Mean ( 10 / 21 )10.89682539682540.21038048886986651.7957984381613
Winsorized Mean ( 11 / 21 )10.96666666666670.19097668500115357.4241126166812
Winsorized Mean ( 12 / 21 )10.98571428571430.1811927419717860.6299908382934
Winsorized Mean ( 13 / 21 )10.96507936507940.17809020896796861.5703661005393
Winsorized Mean ( 14 / 21 )11.00952380952380.17032414333540864.6386565869496
Winsorized Mean ( 15 / 21 )11.03333333333330.16628219864210866.3530637881483
Winsorized Mean ( 16 / 21 )11.00793650793650.16247102364523267.7532292279586
Winsorized Mean ( 17 / 21 )11.03492063492060.14104356018162778.2376779252491
Winsorized Mean ( 18 / 21 )11.12063492063490.127365658272287.3126639589805
Winsorized Mean ( 19 / 21 )11.09047619047620.11387856302128497.3886207925136
Winsorized Mean ( 20 / 21 )11.09047619047620.10449974179587106.129220990234
Winsorized Mean ( 21 / 21 )11.12380952380950.0897945052787783123.880737348842
Trimmed Mean ( 1 / 21 )10.81967213114750.27988892871283338.6570207721527
Trimmed Mean ( 2 / 21 )10.84067796610170.26680917168908540.6308295081191
Trimmed Mean ( 3 / 21 )10.85614035087720.25623817955327242.3673801062898
Trimmed Mean ( 4 / 21 )10.87454545454550.24470442806909144.4395123551875
Trimmed Mean ( 5 / 21 )10.90377358490570.23268737107354746.8601864149268
Trimmed Mean ( 6 / 21 )10.93921568627450.22205949443693849.2625443195409
Trimmed Mean ( 7 / 21 )10.96326530612240.21390231330922851.2536079508097
Trimmed Mean ( 8 / 21 )10.98723404255320.20546684329493553.4744870089899
Trimmed Mean ( 9 / 21 )11.01555555555560.19640597914008556.0856426254662
Trimmed Mean ( 10 / 21 )11.03488372093020.18897882954697958.3921688338483
Trimmed Mean ( 11 / 21 )11.05609756097560.18065088216076161.2014590171601
Trimmed Mean ( 12 / 21 )11.06923076923080.17499388252865963.2549584550074
Trimmed Mean ( 13 / 21 )11.08108108108110.16987178692048665.2320275306689
Trimmed Mean ( 14 / 21 )11.09714285714290.16344431962673867.8955553945569
Trimmed Mean ( 15 / 21 )11.10909090909090.15669186832058770.8976861923814
Trimmed Mean ( 16 / 21 )11.11935483870970.14820933719216275.0246580233524
Trimmed Mean ( 17 / 21 )11.13448275862070.13684299929079581.3668424130312
Trimmed Mean ( 18 / 21 )11.14814814814810.12792117969937687.1485720687309
Trimmed Mean ( 19 / 21 )11.1520.11973860418984993.1362117961404
Trimmed Mean ( 20 / 21 )11.16086956521740.11224252581871799.4353030084456
Trimmed Mean ( 21 / 21 )11.17142857142860.104001569846865107.415961007875
Median11.3
Midrange10.2
Midmean - Weighted Average at Xnp11.0625
Midmean - Weighted Average at X(n+1)p11.1942857142857
Midmean - Empirical Distribution Function11.1942857142857
Midmean - Empirical Distribution Function - Averaging11.1942857142857
Midmean - Empirical Distribution Function - Interpolation11.0625
Midmean - Closest Observation11.0625
Midmean - True Basic - Statistics Graphics Toolkit11.1942857142857
Midmean - MS Excel (old versions)11.1942857142857
Number of observations63


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
par1 = grey ;
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')