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of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationMon, 21 Apr 2008 14:34:55 -0600
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2008/Apr/21/t1208810191ed6yh3l0x34fhun.htm/, Retrieved Thu, 16 May 2024 10:59:31 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=10604, Retrieved Thu, 16 May 2024 10:59:31 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsrobuustheid eigen reeks
Estimated Impact175
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [] [Stephanie De Coni...] [-0001-11-30 00:00:00] [cd00afdb012dd785c94e77d4cae74ef4]
- RM D    [Central Tendency] [stephanie De Coni...] [2008-04-21 20:34:55] [80d88a38ebee1e39f846defee1b12cef] [Current]
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Dataseries X:
68,64
68,61
68,61
68,61
68,58
68,75
68,54
68,5
68,47
68,47
68,47
68,59
68,32
67,86
67,91
67,91
68,05
68,15
68,25
68,25
68,31
68,31
69,65
69,65
70,18
70,08
70,08
70,09
70,04
70,14
70,26
70,23
70,54
70,54
70,57
70,61
70,63
70,45
70,4
70,4
70,33
70,51
70,45
70,39
70,59
70,59
70,32
70,94
70,44
70,57
70,61
70,61
70,68
69,96
70,11
70,22
70,49
70,49
70,58
70,85
70,69
70,7
70,7
70,7
70,67
70,64
70,98
70,75
70,88
70,88
70,92
70,89
71,02
71,01
71,02




Summary of compuational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'George Udny Yule' @ 72.249.76.132

\begin{tabular}{lllllllll}
\hline
Summary of compuational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 1 seconds \tabularnewline
R Server & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=10604&T=0

[TABLE]
[ROW][C]Summary of compuational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'George Udny Yule' @ 72.249.76.132[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=10604&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=10604&T=0

As an alternative you can also use a QR Code:  

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

Summary of compuational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'George Udny Yule' @ 72.249.76.132







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean69.87840.118318556113235590.595442469091
Geometric Mean69.8709319864616
Harmonic Mean69.8634089121463
Quadratic Mean69.8858121032684
Winsorized Mean ( 1 / 25 )69.87906666666670.118166651799895591.360300070115
Winsorized Mean ( 2 / 25 )69.87880.118132001294017591.531500647986
Winsorized Mean ( 3 / 25 )69.88320.116753248696047598.554650774063
Winsorized Mean ( 4 / 25 )69.88640.115377896926140605.717402222525
Winsorized Mean ( 5 / 25 )69.89173333333330.113886837042968613.69456864417
Winsorized Mean ( 6 / 25 )69.88933333333330.113597572194164615.23615323289
Winsorized Mean ( 7 / 25 )69.8940.112407399326839621.791807466111
Winsorized Mean ( 8 / 25 )69.8940.112407399326839621.791807466111
Winsorized Mean ( 9 / 25 )69.89160.111757143391817625.388211248048
Winsorized Mean ( 10 / 25 )69.89826666666670.10654921010582656.018628361926
Winsorized Mean ( 11 / 25 )69.89093333333330.105774053483784660.756877810759
Winsorized Mean ( 12 / 25 )69.89093333333330.105774053483784660.756877810759
Winsorized Mean ( 13 / 25 )69.89613333333340.1048341278132666.730718243573
Winsorized Mean ( 14 / 25 )69.90173333333330.103304216763892676.659051518662
Winsorized Mean ( 15 / 25 )69.90773333333330.101680044607934687.52658009631
Winsorized Mean ( 16 / 25 )69.90773333333330.101085740670813691.568690790806
Winsorized Mean ( 17 / 25 )69.90546666666670.0996026869881293701.843180947498
Winsorized Mean ( 18 / 25 )69.90306666666670.099364462139823703.50168622964
Winsorized Mean ( 19 / 25 )69.8980.0988674606469428706.986904919171
Winsorized Mean ( 20 / 25 )69.9060.0974611033523972717.270763365317
Winsorized Mean ( 21 / 25 )69.93680.0920748148601534759.56492669817
Winsorized Mean ( 22 / 25 )70.19493333333330.04706383372021911491.48354021948
Winsorized Mean ( 23 / 25 )70.19493333333330.04706383372021911491.48354021948
Winsorized Mean ( 24 / 25 )70.29093333333330.03180071580209382210.35695456595
Winsorized Mean ( 25 / 25 )70.31426666666670.02772462614526772536.16644993673
Trimmed Mean ( 1 / 25 )69.89041095890410.117291451370260595.869606372911
Trimmed Mean ( 2 / 25 )69.90239436619720.116193910081334601.601188197095
Trimmed Mean ( 3 / 25 )69.91521739130440.114852217713506608.740682445547
Trimmed Mean ( 4 / 25 )69.92716417910450.113803095514258614.45748784877
Trimmed Mean ( 5 / 25 )69.93892307692310.112955088734443619.174610551182
Trimmed Mean ( 6 / 25 )69.95015873015870.112293388145394622.923218236049
Trimmed Mean ( 7 / 25 )69.96262295081970.111461454446309627.684460949869
Trimmed Mean ( 8 / 25 )69.97508474576270.110639016563111632.463003734739
Trimmed Mean ( 9 / 25 )69.98842105263160.109520425726133639.044457584971
Trimmed Mean ( 10 / 25 )70.00309090909090.108167121204092647.175316582641
Trimmed Mean ( 11 / 25 )70.01792452830190.107466995807990651.529560325682
Trimmed Mean ( 12 / 25 )70.03490196078430.106556575251529657.255563961822
Trimmed Mean ( 13 / 25 )70.05326530612250.105232326288941665.701004402147
Trimmed Mean ( 14 / 25 )70.07255319148940.103583555713967676.483373335689
Trimmed Mean ( 15 / 25 )70.09288888888890.101624990077762689.720991217363
Trimmed Mean ( 16 / 25 )70.11441860465120.099264349644032706.340381577935
Trimmed Mean ( 17 / 25 )70.13804878048780.0960812787989083729.986628584347
Trimmed Mean ( 18 / 25 )70.1643589743590.0919351080124588763.19439321103
Trimmed Mean ( 19 / 25 )70.19378378378380.0860418846179656815.809464140064
Trimmed Mean ( 20 / 25 )70.22714285714290.0774624565377909906.595865868026
Trimmed Mean ( 21 / 25 )70.26363636363640.06477644859060281084.70961116923
Trimmed Mean ( 22 / 25 )70.30129032258060.04609420446271181525.16549839690
Trimmed Mean ( 23 / 25 )70.31379310344830.04245952518681181656.01929823954
Trimmed Mean ( 24 / 25 )70.32814814814810.03662016101668641920.47621298285
Trimmed Mean ( 25 / 25 )70.33280.03516399673908892000.13668872335
Median70.39
Midrange69.44
Midmean - Weighted Average at Xnp70.1125641025641
Midmean - Weighted Average at X(n+1)p70.1255
Midmean - Empirical Distribution Function70.1255
Midmean - Empirical Distribution Function - Averaging70.1255
Midmean - Empirical Distribution Function - Interpolation70.1125641025641
Midmean - Closest Observation70.1125641025641
Midmean - True Basic - Statistics Graphics Toolkit70.1255
Midmean - MS Excel (old versions)70.1255
Number of observations75

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 69.8784 & 0.118318556113235 & 590.595442469091 \tabularnewline
Geometric Mean & 69.8709319864616 &  &  \tabularnewline
Harmonic Mean & 69.8634089121463 &  &  \tabularnewline
Quadratic Mean & 69.8858121032684 &  &  \tabularnewline
Winsorized Mean ( 1 / 25 ) & 69.8790666666667 & 0.118166651799895 & 591.360300070115 \tabularnewline
Winsorized Mean ( 2 / 25 ) & 69.8788 & 0.118132001294017 & 591.531500647986 \tabularnewline
Winsorized Mean ( 3 / 25 ) & 69.8832 & 0.116753248696047 & 598.554650774063 \tabularnewline
Winsorized Mean ( 4 / 25 ) & 69.8864 & 0.115377896926140 & 605.717402222525 \tabularnewline
Winsorized Mean ( 5 / 25 ) & 69.8917333333333 & 0.113886837042968 & 613.69456864417 \tabularnewline
Winsorized Mean ( 6 / 25 ) & 69.8893333333333 & 0.113597572194164 & 615.23615323289 \tabularnewline
Winsorized Mean ( 7 / 25 ) & 69.894 & 0.112407399326839 & 621.791807466111 \tabularnewline
Winsorized Mean ( 8 / 25 ) & 69.894 & 0.112407399326839 & 621.791807466111 \tabularnewline
Winsorized Mean ( 9 / 25 ) & 69.8916 & 0.111757143391817 & 625.388211248048 \tabularnewline
Winsorized Mean ( 10 / 25 ) & 69.8982666666667 & 0.10654921010582 & 656.018628361926 \tabularnewline
Winsorized Mean ( 11 / 25 ) & 69.8909333333333 & 0.105774053483784 & 660.756877810759 \tabularnewline
Winsorized Mean ( 12 / 25 ) & 69.8909333333333 & 0.105774053483784 & 660.756877810759 \tabularnewline
Winsorized Mean ( 13 / 25 ) & 69.8961333333334 & 0.1048341278132 & 666.730718243573 \tabularnewline
Winsorized Mean ( 14 / 25 ) & 69.9017333333333 & 0.103304216763892 & 676.659051518662 \tabularnewline
Winsorized Mean ( 15 / 25 ) & 69.9077333333333 & 0.101680044607934 & 687.52658009631 \tabularnewline
Winsorized Mean ( 16 / 25 ) & 69.9077333333333 & 0.101085740670813 & 691.568690790806 \tabularnewline
Winsorized Mean ( 17 / 25 ) & 69.9054666666667 & 0.0996026869881293 & 701.843180947498 \tabularnewline
Winsorized Mean ( 18 / 25 ) & 69.9030666666667 & 0.099364462139823 & 703.50168622964 \tabularnewline
Winsorized Mean ( 19 / 25 ) & 69.898 & 0.0988674606469428 & 706.986904919171 \tabularnewline
Winsorized Mean ( 20 / 25 ) & 69.906 & 0.0974611033523972 & 717.270763365317 \tabularnewline
Winsorized Mean ( 21 / 25 ) & 69.9368 & 0.0920748148601534 & 759.56492669817 \tabularnewline
Winsorized Mean ( 22 / 25 ) & 70.1949333333333 & 0.0470638337202191 & 1491.48354021948 \tabularnewline
Winsorized Mean ( 23 / 25 ) & 70.1949333333333 & 0.0470638337202191 & 1491.48354021948 \tabularnewline
Winsorized Mean ( 24 / 25 ) & 70.2909333333333 & 0.0318007158020938 & 2210.35695456595 \tabularnewline
Winsorized Mean ( 25 / 25 ) & 70.3142666666667 & 0.0277246261452677 & 2536.16644993673 \tabularnewline
Trimmed Mean ( 1 / 25 ) & 69.8904109589041 & 0.117291451370260 & 595.869606372911 \tabularnewline
Trimmed Mean ( 2 / 25 ) & 69.9023943661972 & 0.116193910081334 & 601.601188197095 \tabularnewline
Trimmed Mean ( 3 / 25 ) & 69.9152173913044 & 0.114852217713506 & 608.740682445547 \tabularnewline
Trimmed Mean ( 4 / 25 ) & 69.9271641791045 & 0.113803095514258 & 614.45748784877 \tabularnewline
Trimmed Mean ( 5 / 25 ) & 69.9389230769231 & 0.112955088734443 & 619.174610551182 \tabularnewline
Trimmed Mean ( 6 / 25 ) & 69.9501587301587 & 0.112293388145394 & 622.923218236049 \tabularnewline
Trimmed Mean ( 7 / 25 ) & 69.9626229508197 & 0.111461454446309 & 627.684460949869 \tabularnewline
Trimmed Mean ( 8 / 25 ) & 69.9750847457627 & 0.110639016563111 & 632.463003734739 \tabularnewline
Trimmed Mean ( 9 / 25 ) & 69.9884210526316 & 0.109520425726133 & 639.044457584971 \tabularnewline
Trimmed Mean ( 10 / 25 ) & 70.0030909090909 & 0.108167121204092 & 647.175316582641 \tabularnewline
Trimmed Mean ( 11 / 25 ) & 70.0179245283019 & 0.107466995807990 & 651.529560325682 \tabularnewline
Trimmed Mean ( 12 / 25 ) & 70.0349019607843 & 0.106556575251529 & 657.255563961822 \tabularnewline
Trimmed Mean ( 13 / 25 ) & 70.0532653061225 & 0.105232326288941 & 665.701004402147 \tabularnewline
Trimmed Mean ( 14 / 25 ) & 70.0725531914894 & 0.103583555713967 & 676.483373335689 \tabularnewline
Trimmed Mean ( 15 / 25 ) & 70.0928888888889 & 0.101624990077762 & 689.720991217363 \tabularnewline
Trimmed Mean ( 16 / 25 ) & 70.1144186046512 & 0.099264349644032 & 706.340381577935 \tabularnewline
Trimmed Mean ( 17 / 25 ) & 70.1380487804878 & 0.0960812787989083 & 729.986628584347 \tabularnewline
Trimmed Mean ( 18 / 25 ) & 70.164358974359 & 0.0919351080124588 & 763.19439321103 \tabularnewline
Trimmed Mean ( 19 / 25 ) & 70.1937837837838 & 0.0860418846179656 & 815.809464140064 \tabularnewline
Trimmed Mean ( 20 / 25 ) & 70.2271428571429 & 0.0774624565377909 & 906.595865868026 \tabularnewline
Trimmed Mean ( 21 / 25 ) & 70.2636363636364 & 0.0647764485906028 & 1084.70961116923 \tabularnewline
Trimmed Mean ( 22 / 25 ) & 70.3012903225806 & 0.0460942044627118 & 1525.16549839690 \tabularnewline
Trimmed Mean ( 23 / 25 ) & 70.3137931034483 & 0.0424595251868118 & 1656.01929823954 \tabularnewline
Trimmed Mean ( 24 / 25 ) & 70.3281481481481 & 0.0366201610166864 & 1920.47621298285 \tabularnewline
Trimmed Mean ( 25 / 25 ) & 70.3328 & 0.0351639967390889 & 2000.13668872335 \tabularnewline
Median & 70.39 &  &  \tabularnewline
Midrange & 69.44 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 70.1125641025641 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 70.1255 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 70.1255 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 70.1255 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 70.1125641025641 &  &  \tabularnewline
Midmean - Closest Observation & 70.1125641025641 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 70.1255 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 70.1255 &  &  \tabularnewline
Number of observations & 75 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=10604&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]69.8784[/C][C]0.118318556113235[/C][C]590.595442469091[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]69.8709319864616[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]69.8634089121463[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]69.8858121032684[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 25 )[/C][C]69.8790666666667[/C][C]0.118166651799895[/C][C]591.360300070115[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 25 )[/C][C]69.8788[/C][C]0.118132001294017[/C][C]591.531500647986[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 25 )[/C][C]69.8832[/C][C]0.116753248696047[/C][C]598.554650774063[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 25 )[/C][C]69.8864[/C][C]0.115377896926140[/C][C]605.717402222525[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 25 )[/C][C]69.8917333333333[/C][C]0.113886837042968[/C][C]613.69456864417[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 25 )[/C][C]69.8893333333333[/C][C]0.113597572194164[/C][C]615.23615323289[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 25 )[/C][C]69.894[/C][C]0.112407399326839[/C][C]621.791807466111[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 25 )[/C][C]69.894[/C][C]0.112407399326839[/C][C]621.791807466111[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 25 )[/C][C]69.8916[/C][C]0.111757143391817[/C][C]625.388211248048[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 25 )[/C][C]69.8982666666667[/C][C]0.10654921010582[/C][C]656.018628361926[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 25 )[/C][C]69.8909333333333[/C][C]0.105774053483784[/C][C]660.756877810759[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 25 )[/C][C]69.8909333333333[/C][C]0.105774053483784[/C][C]660.756877810759[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 25 )[/C][C]69.8961333333334[/C][C]0.1048341278132[/C][C]666.730718243573[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 25 )[/C][C]69.9017333333333[/C][C]0.103304216763892[/C][C]676.659051518662[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 25 )[/C][C]69.9077333333333[/C][C]0.101680044607934[/C][C]687.52658009631[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 25 )[/C][C]69.9077333333333[/C][C]0.101085740670813[/C][C]691.568690790806[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 25 )[/C][C]69.9054666666667[/C][C]0.0996026869881293[/C][C]701.843180947498[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 25 )[/C][C]69.9030666666667[/C][C]0.099364462139823[/C][C]703.50168622964[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 25 )[/C][C]69.898[/C][C]0.0988674606469428[/C][C]706.986904919171[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 25 )[/C][C]69.906[/C][C]0.0974611033523972[/C][C]717.270763365317[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 25 )[/C][C]69.9368[/C][C]0.0920748148601534[/C][C]759.56492669817[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 25 )[/C][C]70.1949333333333[/C][C]0.0470638337202191[/C][C]1491.48354021948[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 25 )[/C][C]70.1949333333333[/C][C]0.0470638337202191[/C][C]1491.48354021948[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 25 )[/C][C]70.2909333333333[/C][C]0.0318007158020938[/C][C]2210.35695456595[/C][/ROW]
[ROW][C]Winsorized Mean ( 25 / 25 )[/C][C]70.3142666666667[/C][C]0.0277246261452677[/C][C]2536.16644993673[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 25 )[/C][C]69.8904109589041[/C][C]0.117291451370260[/C][C]595.869606372911[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 25 )[/C][C]69.9023943661972[/C][C]0.116193910081334[/C][C]601.601188197095[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 25 )[/C][C]69.9152173913044[/C][C]0.114852217713506[/C][C]608.740682445547[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 25 )[/C][C]69.9271641791045[/C][C]0.113803095514258[/C][C]614.45748784877[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 25 )[/C][C]69.9389230769231[/C][C]0.112955088734443[/C][C]619.174610551182[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 25 )[/C][C]69.9501587301587[/C][C]0.112293388145394[/C][C]622.923218236049[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 25 )[/C][C]69.9626229508197[/C][C]0.111461454446309[/C][C]627.684460949869[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 25 )[/C][C]69.9750847457627[/C][C]0.110639016563111[/C][C]632.463003734739[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 25 )[/C][C]69.9884210526316[/C][C]0.109520425726133[/C][C]639.044457584971[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 25 )[/C][C]70.0030909090909[/C][C]0.108167121204092[/C][C]647.175316582641[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 25 )[/C][C]70.0179245283019[/C][C]0.107466995807990[/C][C]651.529560325682[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 25 )[/C][C]70.0349019607843[/C][C]0.106556575251529[/C][C]657.255563961822[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 25 )[/C][C]70.0532653061225[/C][C]0.105232326288941[/C][C]665.701004402147[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 25 )[/C][C]70.0725531914894[/C][C]0.103583555713967[/C][C]676.483373335689[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 25 )[/C][C]70.0928888888889[/C][C]0.101624990077762[/C][C]689.720991217363[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 25 )[/C][C]70.1144186046512[/C][C]0.099264349644032[/C][C]706.340381577935[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 25 )[/C][C]70.1380487804878[/C][C]0.0960812787989083[/C][C]729.986628584347[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 25 )[/C][C]70.164358974359[/C][C]0.0919351080124588[/C][C]763.19439321103[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 25 )[/C][C]70.1937837837838[/C][C]0.0860418846179656[/C][C]815.809464140064[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 25 )[/C][C]70.2271428571429[/C][C]0.0774624565377909[/C][C]906.595865868026[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 25 )[/C][C]70.2636363636364[/C][C]0.0647764485906028[/C][C]1084.70961116923[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 25 )[/C][C]70.3012903225806[/C][C]0.0460942044627118[/C][C]1525.16549839690[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 25 )[/C][C]70.3137931034483[/C][C]0.0424595251868118[/C][C]1656.01929823954[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 25 )[/C][C]70.3281481481481[/C][C]0.0366201610166864[/C][C]1920.47621298285[/C][/ROW]
[ROW][C]Trimmed Mean ( 25 / 25 )[/C][C]70.3328[/C][C]0.0351639967390889[/C][C]2000.13668872335[/C][/ROW]
[ROW][C]Median[/C][C]70.39[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]69.44[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]70.1125641025641[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]70.1255[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]70.1255[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]70.1255[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]70.1125641025641[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]70.1125641025641[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]70.1255[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]70.1255[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]75[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=10604&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=10604&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 Mean69.87840.118318556113235590.595442469091
Geometric Mean69.8709319864616
Harmonic Mean69.8634089121463
Quadratic Mean69.8858121032684
Winsorized Mean ( 1 / 25 )69.87906666666670.118166651799895591.360300070115
Winsorized Mean ( 2 / 25 )69.87880.118132001294017591.531500647986
Winsorized Mean ( 3 / 25 )69.88320.116753248696047598.554650774063
Winsorized Mean ( 4 / 25 )69.88640.115377896926140605.717402222525
Winsorized Mean ( 5 / 25 )69.89173333333330.113886837042968613.69456864417
Winsorized Mean ( 6 / 25 )69.88933333333330.113597572194164615.23615323289
Winsorized Mean ( 7 / 25 )69.8940.112407399326839621.791807466111
Winsorized Mean ( 8 / 25 )69.8940.112407399326839621.791807466111
Winsorized Mean ( 9 / 25 )69.89160.111757143391817625.388211248048
Winsorized Mean ( 10 / 25 )69.89826666666670.10654921010582656.018628361926
Winsorized Mean ( 11 / 25 )69.89093333333330.105774053483784660.756877810759
Winsorized Mean ( 12 / 25 )69.89093333333330.105774053483784660.756877810759
Winsorized Mean ( 13 / 25 )69.89613333333340.1048341278132666.730718243573
Winsorized Mean ( 14 / 25 )69.90173333333330.103304216763892676.659051518662
Winsorized Mean ( 15 / 25 )69.90773333333330.101680044607934687.52658009631
Winsorized Mean ( 16 / 25 )69.90773333333330.101085740670813691.568690790806
Winsorized Mean ( 17 / 25 )69.90546666666670.0996026869881293701.843180947498
Winsorized Mean ( 18 / 25 )69.90306666666670.099364462139823703.50168622964
Winsorized Mean ( 19 / 25 )69.8980.0988674606469428706.986904919171
Winsorized Mean ( 20 / 25 )69.9060.0974611033523972717.270763365317
Winsorized Mean ( 21 / 25 )69.93680.0920748148601534759.56492669817
Winsorized Mean ( 22 / 25 )70.19493333333330.04706383372021911491.48354021948
Winsorized Mean ( 23 / 25 )70.19493333333330.04706383372021911491.48354021948
Winsorized Mean ( 24 / 25 )70.29093333333330.03180071580209382210.35695456595
Winsorized Mean ( 25 / 25 )70.31426666666670.02772462614526772536.16644993673
Trimmed Mean ( 1 / 25 )69.89041095890410.117291451370260595.869606372911
Trimmed Mean ( 2 / 25 )69.90239436619720.116193910081334601.601188197095
Trimmed Mean ( 3 / 25 )69.91521739130440.114852217713506608.740682445547
Trimmed Mean ( 4 / 25 )69.92716417910450.113803095514258614.45748784877
Trimmed Mean ( 5 / 25 )69.93892307692310.112955088734443619.174610551182
Trimmed Mean ( 6 / 25 )69.95015873015870.112293388145394622.923218236049
Trimmed Mean ( 7 / 25 )69.96262295081970.111461454446309627.684460949869
Trimmed Mean ( 8 / 25 )69.97508474576270.110639016563111632.463003734739
Trimmed Mean ( 9 / 25 )69.98842105263160.109520425726133639.044457584971
Trimmed Mean ( 10 / 25 )70.00309090909090.108167121204092647.175316582641
Trimmed Mean ( 11 / 25 )70.01792452830190.107466995807990651.529560325682
Trimmed Mean ( 12 / 25 )70.03490196078430.106556575251529657.255563961822
Trimmed Mean ( 13 / 25 )70.05326530612250.105232326288941665.701004402147
Trimmed Mean ( 14 / 25 )70.07255319148940.103583555713967676.483373335689
Trimmed Mean ( 15 / 25 )70.09288888888890.101624990077762689.720991217363
Trimmed Mean ( 16 / 25 )70.11441860465120.099264349644032706.340381577935
Trimmed Mean ( 17 / 25 )70.13804878048780.0960812787989083729.986628584347
Trimmed Mean ( 18 / 25 )70.1643589743590.0919351080124588763.19439321103
Trimmed Mean ( 19 / 25 )70.19378378378380.0860418846179656815.809464140064
Trimmed Mean ( 20 / 25 )70.22714285714290.0774624565377909906.595865868026
Trimmed Mean ( 21 / 25 )70.26363636363640.06477644859060281084.70961116923
Trimmed Mean ( 22 / 25 )70.30129032258060.04609420446271181525.16549839690
Trimmed Mean ( 23 / 25 )70.31379310344830.04245952518681181656.01929823954
Trimmed Mean ( 24 / 25 )70.32814814814810.03662016101668641920.47621298285
Trimmed Mean ( 25 / 25 )70.33280.03516399673908892000.13668872335
Median70.39
Midrange69.44
Midmean - Weighted Average at Xnp70.1125641025641
Midmean - Weighted Average at X(n+1)p70.1255
Midmean - Empirical Distribution Function70.1255
Midmean - Empirical Distribution Function - Averaging70.1255
Midmean - Empirical Distribution Function - Interpolation70.1125641025641
Midmean - Closest Observation70.1125641025641
Midmean - True Basic - Statistics Graphics Toolkit70.1255
Midmean - MS Excel (old versions)70.1255
Number of observations75



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')