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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 computationSun, 24 Jan 2010 07:11:25 -0700
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2010/Jan/24/t1264342415vf771skjf38gkys.htm/, Retrieved Thu, 02 May 2024 14:27:56 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=72407, Retrieved Thu, 02 May 2024 14:27:56 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsKDGP1W52
Estimated Impact201
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Harrell-Davis Quantiles] [] [2009-10-19 20:22:48] [ea88de511753f4b18fc5981c22c607f8]
- RMPD    [Central Tendency] [Central Tendency ...] [2010-01-24 14:11:25] [3588db8f96a346e7899895ad48978494] [Current]
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Dataseries X:
8,2
8,21
8,22
8,2
8,18
8,2
8,19
8,24
8,31
8,27
8,36
8,32
8,29
8,27
8,27
8,43
8,46
8,48
8,46
8,46
8,43
8,4
8,38
8,3
8,39
8,53
8,52
8,54
8,62
8,52
8,49
8,44
8,31
8,26
8,21
8,03
7,89
7,83
7,85
7,84
7,88
8,01
8,08
8,11
8,11
8,07
8,06
7,95
7,95
8,07
8,17
8,21
8,2
8,19
8,18
8,16
8,17
8,17
8,19
8,01
8,04
8,13
8,14
8,17
8,25
8,27
8,27
8,26
8,24
8,21
8,25
8,06
8,16
8,32
8,43
8,39
8,41




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

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 1 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=72407&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=72407&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=72407&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 time1 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean8.230389610389610.0202576041252532406.286427531161
Geometric Mean8.22848906438038
Harmonic Mean8.22658255430908
Quadratic Mean8.23228408758476
Winsorized Mean ( 1 / 25 )8.229480519480520.0199862359540495411.757398361602
Winsorized Mean ( 2 / 25 )8.229480519480520.0198678959961959414.209965718374
Winsorized Mean ( 3 / 25 )8.230259740259740.0195060097526919421.934565019066
Winsorized Mean ( 4 / 25 )8.230779220779220.0193845551560415424.605009221166
Winsorized Mean ( 5 / 25 )8.232727272727270.0181601032322665453.341435752389
Winsorized Mean ( 6 / 25 )8.231948051948050.0180168893963829456.901736522881
Winsorized Mean ( 7 / 25 )8.235584415584420.0166396958302660494.935995200387
Winsorized Mean ( 8 / 25 )8.235584415584420.0166396958302660494.935995200387
Winsorized Mean ( 9 / 25 )8.237922077922080.0162340806531411507.446171664063
Winsorized Mean ( 10 / 25 )8.236623376623380.0155593042163481529.369646746103
Winsorized Mean ( 11 / 25 )8.238051948051950.0148517842101725554.684328257978
Winsorized Mean ( 12 / 25 )8.238051948051950.0148517842101725554.684328257978
Winsorized Mean ( 13 / 25 )8.239740259740260.0145893598176804564.777369446654
Winsorized Mean ( 14 / 25 )8.23610389610390.0139794740705432589.156920678337
Winsorized Mean ( 15 / 25 )8.23610389610390.0133607036512269616.44237542441
Winsorized Mean ( 16 / 25 )8.240259740259740.0121014367703242680.932346848845
Winsorized Mean ( 17 / 25 )8.240259740259740.0121014367703242680.932346848845
Winsorized Mean ( 18 / 25 )8.24259740259740.0110757699207354744.200851190135
Winsorized Mean ( 19 / 25 )8.240129870129870.00995288543346042827.913666365286
Winsorized Mean ( 20 / 25 )8.234935064935070.007686223876428821071.38891571829
Winsorized Mean ( 21 / 25 )8.234935064935070.007686223876428821071.38891571829
Winsorized Mean ( 22 / 25 )8.234935064935070.006913742979737011191.09649998130
Winsorized Mean ( 23 / 25 )8.234935064935070.006913742979737011191.09649998130
Winsorized Mean ( 24 / 25 )8.231818181818180.006474956415710311271.33182886686
Winsorized Mean ( 25 / 25 )8.228571428571430.006032250661418421364.09640288996
Trimmed Mean ( 1 / 25 )8.230533333333330.0194026963235687424.195338424981
Trimmed Mean ( 2 / 25 )8.231643835616440.0187154183364818439.832211475101
Trimmed Mean ( 3 / 25 )8.232816901408450.0179773869791819457.954034751669
Trimmed Mean ( 4 / 25 )8.233768115942030.0172688749784436476.798177427312
Trimmed Mean ( 5 / 25 )8.233768115942030.0164669101450306500.019010453325
Trimmed Mean ( 6 / 25 )8.235076923076920.0159085775679879517.650109689757
Trimmed Mean ( 7 / 25 )8.235714285714290.0152764494272271539.111808993774
Trimmed Mean ( 8 / 25 )8.235737704918030.0148792205132396553.505991633759
Trimmed Mean ( 9 / 25 )8.23576271186440.0143944664952429572.147826012596
Trimmed Mean ( 10 / 25 )8.23576271186440.0138964803594602592.650980595801
Trimmed Mean ( 11 / 25 )8.235272727272730.0134386110028966612.806838853929
Trimmed Mean ( 12 / 25 )8.234905660377360.0130273315497986632.125284360686
Trimmed Mean ( 13 / 25 )8.234509803921570.0125098039215686658.244514106583
Trimmed Mean ( 14 / 25 )8.23387755102040.0119124367874582691.20010438916
Trimmed Mean ( 15 / 25 )8.23361702127660.0112963017038561728.87722346031
Trimmed Mean ( 16 / 25 )8.233333333333330.0106505560152672773.042583084973
Trimmed Mean ( 17 / 25 )8.232558139534880.0101161199564886813.805903344835
Trimmed Mean ( 18 / 25 )8.231707317073170.00940227294149607875.501846021007
Trimmed Mean ( 19 / 25 )8.230512820512820.0087161623953814944.281720229774
Trimmed Mean ( 20 / 25 )8.230512820512820.008109109047326561014.97128383374
Trimmed Mean ( 21 / 25 )8.228857142857140.00791521700676021039.62495732323
Trimmed Mean ( 22 / 25 )8.228181818181820.007630860210239051078.27710002357
Trimmed Mean ( 23 / 25 )8.227419354838710.00743383346505191106.75325099999
Trimmed Mean ( 24 / 25 )8.226551724137930.007127893277719791154.13508642902
Trimmed Mean ( 25 / 25 )8.225925925925930.006820015357429361206.14478044614
Median8.21
Midrange8.225
Midmean - Weighted Average at Xnp8.2271052631579
Midmean - Weighted Average at X(n+1)p8.23051282051282
Midmean - Empirical Distribution Function8.23051282051282
Midmean - Empirical Distribution Function - Averaging8.23051282051282
Midmean - Empirical Distribution Function - Interpolation8.23051282051282
Midmean - Closest Observation8.228
Midmean - True Basic - Statistics Graphics Toolkit8.23051282051282
Midmean - MS Excel (old versions)8.23051282051282
Number of observations77

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 8.23038961038961 & 0.0202576041252532 & 406.286427531161 \tabularnewline
Geometric Mean & 8.22848906438038 &  &  \tabularnewline
Harmonic Mean & 8.22658255430908 &  &  \tabularnewline
Quadratic Mean & 8.23228408758476 &  &  \tabularnewline
Winsorized Mean ( 1 / 25 ) & 8.22948051948052 & 0.0199862359540495 & 411.757398361602 \tabularnewline
Winsorized Mean ( 2 / 25 ) & 8.22948051948052 & 0.0198678959961959 & 414.209965718374 \tabularnewline
Winsorized Mean ( 3 / 25 ) & 8.23025974025974 & 0.0195060097526919 & 421.934565019066 \tabularnewline
Winsorized Mean ( 4 / 25 ) & 8.23077922077922 & 0.0193845551560415 & 424.605009221166 \tabularnewline
Winsorized Mean ( 5 / 25 ) & 8.23272727272727 & 0.0181601032322665 & 453.341435752389 \tabularnewline
Winsorized Mean ( 6 / 25 ) & 8.23194805194805 & 0.0180168893963829 & 456.901736522881 \tabularnewline
Winsorized Mean ( 7 / 25 ) & 8.23558441558442 & 0.0166396958302660 & 494.935995200387 \tabularnewline
Winsorized Mean ( 8 / 25 ) & 8.23558441558442 & 0.0166396958302660 & 494.935995200387 \tabularnewline
Winsorized Mean ( 9 / 25 ) & 8.23792207792208 & 0.0162340806531411 & 507.446171664063 \tabularnewline
Winsorized Mean ( 10 / 25 ) & 8.23662337662338 & 0.0155593042163481 & 529.369646746103 \tabularnewline
Winsorized Mean ( 11 / 25 ) & 8.23805194805195 & 0.0148517842101725 & 554.684328257978 \tabularnewline
Winsorized Mean ( 12 / 25 ) & 8.23805194805195 & 0.0148517842101725 & 554.684328257978 \tabularnewline
Winsorized Mean ( 13 / 25 ) & 8.23974025974026 & 0.0145893598176804 & 564.777369446654 \tabularnewline
Winsorized Mean ( 14 / 25 ) & 8.2361038961039 & 0.0139794740705432 & 589.156920678337 \tabularnewline
Winsorized Mean ( 15 / 25 ) & 8.2361038961039 & 0.0133607036512269 & 616.44237542441 \tabularnewline
Winsorized Mean ( 16 / 25 ) & 8.24025974025974 & 0.0121014367703242 & 680.932346848845 \tabularnewline
Winsorized Mean ( 17 / 25 ) & 8.24025974025974 & 0.0121014367703242 & 680.932346848845 \tabularnewline
Winsorized Mean ( 18 / 25 ) & 8.2425974025974 & 0.0110757699207354 & 744.200851190135 \tabularnewline
Winsorized Mean ( 19 / 25 ) & 8.24012987012987 & 0.00995288543346042 & 827.913666365286 \tabularnewline
Winsorized Mean ( 20 / 25 ) & 8.23493506493507 & 0.00768622387642882 & 1071.38891571829 \tabularnewline
Winsorized Mean ( 21 / 25 ) & 8.23493506493507 & 0.00768622387642882 & 1071.38891571829 \tabularnewline
Winsorized Mean ( 22 / 25 ) & 8.23493506493507 & 0.00691374297973701 & 1191.09649998130 \tabularnewline
Winsorized Mean ( 23 / 25 ) & 8.23493506493507 & 0.00691374297973701 & 1191.09649998130 \tabularnewline
Winsorized Mean ( 24 / 25 ) & 8.23181818181818 & 0.00647495641571031 & 1271.33182886686 \tabularnewline
Winsorized Mean ( 25 / 25 ) & 8.22857142857143 & 0.00603225066141842 & 1364.09640288996 \tabularnewline
Trimmed Mean ( 1 / 25 ) & 8.23053333333333 & 0.0194026963235687 & 424.195338424981 \tabularnewline
Trimmed Mean ( 2 / 25 ) & 8.23164383561644 & 0.0187154183364818 & 439.832211475101 \tabularnewline
Trimmed Mean ( 3 / 25 ) & 8.23281690140845 & 0.0179773869791819 & 457.954034751669 \tabularnewline
Trimmed Mean ( 4 / 25 ) & 8.23376811594203 & 0.0172688749784436 & 476.798177427312 \tabularnewline
Trimmed Mean ( 5 / 25 ) & 8.23376811594203 & 0.0164669101450306 & 500.019010453325 \tabularnewline
Trimmed Mean ( 6 / 25 ) & 8.23507692307692 & 0.0159085775679879 & 517.650109689757 \tabularnewline
Trimmed Mean ( 7 / 25 ) & 8.23571428571429 & 0.0152764494272271 & 539.111808993774 \tabularnewline
Trimmed Mean ( 8 / 25 ) & 8.23573770491803 & 0.0148792205132396 & 553.505991633759 \tabularnewline
Trimmed Mean ( 9 / 25 ) & 8.2357627118644 & 0.0143944664952429 & 572.147826012596 \tabularnewline
Trimmed Mean ( 10 / 25 ) & 8.2357627118644 & 0.0138964803594602 & 592.650980595801 \tabularnewline
Trimmed Mean ( 11 / 25 ) & 8.23527272727273 & 0.0134386110028966 & 612.806838853929 \tabularnewline
Trimmed Mean ( 12 / 25 ) & 8.23490566037736 & 0.0130273315497986 & 632.125284360686 \tabularnewline
Trimmed Mean ( 13 / 25 ) & 8.23450980392157 & 0.0125098039215686 & 658.244514106583 \tabularnewline
Trimmed Mean ( 14 / 25 ) & 8.2338775510204 & 0.0119124367874582 & 691.20010438916 \tabularnewline
Trimmed Mean ( 15 / 25 ) & 8.2336170212766 & 0.0112963017038561 & 728.87722346031 \tabularnewline
Trimmed Mean ( 16 / 25 ) & 8.23333333333333 & 0.0106505560152672 & 773.042583084973 \tabularnewline
Trimmed Mean ( 17 / 25 ) & 8.23255813953488 & 0.0101161199564886 & 813.805903344835 \tabularnewline
Trimmed Mean ( 18 / 25 ) & 8.23170731707317 & 0.00940227294149607 & 875.501846021007 \tabularnewline
Trimmed Mean ( 19 / 25 ) & 8.23051282051282 & 0.0087161623953814 & 944.281720229774 \tabularnewline
Trimmed Mean ( 20 / 25 ) & 8.23051282051282 & 0.00810910904732656 & 1014.97128383374 \tabularnewline
Trimmed Mean ( 21 / 25 ) & 8.22885714285714 & 0.0079152170067602 & 1039.62495732323 \tabularnewline
Trimmed Mean ( 22 / 25 ) & 8.22818181818182 & 0.00763086021023905 & 1078.27710002357 \tabularnewline
Trimmed Mean ( 23 / 25 ) & 8.22741935483871 & 0.0074338334650519 & 1106.75325099999 \tabularnewline
Trimmed Mean ( 24 / 25 ) & 8.22655172413793 & 0.00712789327771979 & 1154.13508642902 \tabularnewline
Trimmed Mean ( 25 / 25 ) & 8.22592592592593 & 0.00682001535742936 & 1206.14478044614 \tabularnewline
Median & 8.21 &  &  \tabularnewline
Midrange & 8.225 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 8.2271052631579 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 8.23051282051282 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 8.23051282051282 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 8.23051282051282 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 8.23051282051282 &  &  \tabularnewline
Midmean - Closest Observation & 8.228 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 8.23051282051282 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 8.23051282051282 &  &  \tabularnewline
Number of observations & 77 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=72407&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]8.23038961038961[/C][C]0.0202576041252532[/C][C]406.286427531161[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]8.22848906438038[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]8.22658255430908[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]8.23228408758476[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 25 )[/C][C]8.22948051948052[/C][C]0.0199862359540495[/C][C]411.757398361602[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 25 )[/C][C]8.22948051948052[/C][C]0.0198678959961959[/C][C]414.209965718374[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 25 )[/C][C]8.23025974025974[/C][C]0.0195060097526919[/C][C]421.934565019066[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 25 )[/C][C]8.23077922077922[/C][C]0.0193845551560415[/C][C]424.605009221166[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 25 )[/C][C]8.23272727272727[/C][C]0.0181601032322665[/C][C]453.341435752389[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 25 )[/C][C]8.23194805194805[/C][C]0.0180168893963829[/C][C]456.901736522881[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 25 )[/C][C]8.23558441558442[/C][C]0.0166396958302660[/C][C]494.935995200387[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 25 )[/C][C]8.23558441558442[/C][C]0.0166396958302660[/C][C]494.935995200387[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 25 )[/C][C]8.23792207792208[/C][C]0.0162340806531411[/C][C]507.446171664063[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 25 )[/C][C]8.23662337662338[/C][C]0.0155593042163481[/C][C]529.369646746103[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 25 )[/C][C]8.23805194805195[/C][C]0.0148517842101725[/C][C]554.684328257978[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 25 )[/C][C]8.23805194805195[/C][C]0.0148517842101725[/C][C]554.684328257978[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 25 )[/C][C]8.23974025974026[/C][C]0.0145893598176804[/C][C]564.777369446654[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 25 )[/C][C]8.2361038961039[/C][C]0.0139794740705432[/C][C]589.156920678337[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 25 )[/C][C]8.2361038961039[/C][C]0.0133607036512269[/C][C]616.44237542441[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 25 )[/C][C]8.24025974025974[/C][C]0.0121014367703242[/C][C]680.932346848845[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 25 )[/C][C]8.24025974025974[/C][C]0.0121014367703242[/C][C]680.932346848845[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 25 )[/C][C]8.2425974025974[/C][C]0.0110757699207354[/C][C]744.200851190135[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 25 )[/C][C]8.24012987012987[/C][C]0.00995288543346042[/C][C]827.913666365286[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 25 )[/C][C]8.23493506493507[/C][C]0.00768622387642882[/C][C]1071.38891571829[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 25 )[/C][C]8.23493506493507[/C][C]0.00768622387642882[/C][C]1071.38891571829[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 25 )[/C][C]8.23493506493507[/C][C]0.00691374297973701[/C][C]1191.09649998130[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 25 )[/C][C]8.23493506493507[/C][C]0.00691374297973701[/C][C]1191.09649998130[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 25 )[/C][C]8.23181818181818[/C][C]0.00647495641571031[/C][C]1271.33182886686[/C][/ROW]
[ROW][C]Winsorized Mean ( 25 / 25 )[/C][C]8.22857142857143[/C][C]0.00603225066141842[/C][C]1364.09640288996[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 25 )[/C][C]8.23053333333333[/C][C]0.0194026963235687[/C][C]424.195338424981[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 25 )[/C][C]8.23164383561644[/C][C]0.0187154183364818[/C][C]439.832211475101[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 25 )[/C][C]8.23281690140845[/C][C]0.0179773869791819[/C][C]457.954034751669[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 25 )[/C][C]8.23376811594203[/C][C]0.0172688749784436[/C][C]476.798177427312[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 25 )[/C][C]8.23376811594203[/C][C]0.0164669101450306[/C][C]500.019010453325[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 25 )[/C][C]8.23507692307692[/C][C]0.0159085775679879[/C][C]517.650109689757[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 25 )[/C][C]8.23571428571429[/C][C]0.0152764494272271[/C][C]539.111808993774[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 25 )[/C][C]8.23573770491803[/C][C]0.0148792205132396[/C][C]553.505991633759[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 25 )[/C][C]8.2357627118644[/C][C]0.0143944664952429[/C][C]572.147826012596[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 25 )[/C][C]8.2357627118644[/C][C]0.0138964803594602[/C][C]592.650980595801[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 25 )[/C][C]8.23527272727273[/C][C]0.0134386110028966[/C][C]612.806838853929[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 25 )[/C][C]8.23490566037736[/C][C]0.0130273315497986[/C][C]632.125284360686[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 25 )[/C][C]8.23450980392157[/C][C]0.0125098039215686[/C][C]658.244514106583[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 25 )[/C][C]8.2338775510204[/C][C]0.0119124367874582[/C][C]691.20010438916[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 25 )[/C][C]8.2336170212766[/C][C]0.0112963017038561[/C][C]728.87722346031[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 25 )[/C][C]8.23333333333333[/C][C]0.0106505560152672[/C][C]773.042583084973[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 25 )[/C][C]8.23255813953488[/C][C]0.0101161199564886[/C][C]813.805903344835[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 25 )[/C][C]8.23170731707317[/C][C]0.00940227294149607[/C][C]875.501846021007[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 25 )[/C][C]8.23051282051282[/C][C]0.0087161623953814[/C][C]944.281720229774[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 25 )[/C][C]8.23051282051282[/C][C]0.00810910904732656[/C][C]1014.97128383374[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 25 )[/C][C]8.22885714285714[/C][C]0.0079152170067602[/C][C]1039.62495732323[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 25 )[/C][C]8.22818181818182[/C][C]0.00763086021023905[/C][C]1078.27710002357[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 25 )[/C][C]8.22741935483871[/C][C]0.0074338334650519[/C][C]1106.75325099999[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 25 )[/C][C]8.22655172413793[/C][C]0.00712789327771979[/C][C]1154.13508642902[/C][/ROW]
[ROW][C]Trimmed Mean ( 25 / 25 )[/C][C]8.22592592592593[/C][C]0.00682001535742936[/C][C]1206.14478044614[/C][/ROW]
[ROW][C]Median[/C][C]8.21[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]8.225[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]8.2271052631579[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]8.23051282051282[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]8.23051282051282[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]8.23051282051282[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]8.23051282051282[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]8.228[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]8.23051282051282[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]8.23051282051282[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]77[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=72407&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=72407&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 Mean8.230389610389610.0202576041252532406.286427531161
Geometric Mean8.22848906438038
Harmonic Mean8.22658255430908
Quadratic Mean8.23228408758476
Winsorized Mean ( 1 / 25 )8.229480519480520.0199862359540495411.757398361602
Winsorized Mean ( 2 / 25 )8.229480519480520.0198678959961959414.209965718374
Winsorized Mean ( 3 / 25 )8.230259740259740.0195060097526919421.934565019066
Winsorized Mean ( 4 / 25 )8.230779220779220.0193845551560415424.605009221166
Winsorized Mean ( 5 / 25 )8.232727272727270.0181601032322665453.341435752389
Winsorized Mean ( 6 / 25 )8.231948051948050.0180168893963829456.901736522881
Winsorized Mean ( 7 / 25 )8.235584415584420.0166396958302660494.935995200387
Winsorized Mean ( 8 / 25 )8.235584415584420.0166396958302660494.935995200387
Winsorized Mean ( 9 / 25 )8.237922077922080.0162340806531411507.446171664063
Winsorized Mean ( 10 / 25 )8.236623376623380.0155593042163481529.369646746103
Winsorized Mean ( 11 / 25 )8.238051948051950.0148517842101725554.684328257978
Winsorized Mean ( 12 / 25 )8.238051948051950.0148517842101725554.684328257978
Winsorized Mean ( 13 / 25 )8.239740259740260.0145893598176804564.777369446654
Winsorized Mean ( 14 / 25 )8.23610389610390.0139794740705432589.156920678337
Winsorized Mean ( 15 / 25 )8.23610389610390.0133607036512269616.44237542441
Winsorized Mean ( 16 / 25 )8.240259740259740.0121014367703242680.932346848845
Winsorized Mean ( 17 / 25 )8.240259740259740.0121014367703242680.932346848845
Winsorized Mean ( 18 / 25 )8.24259740259740.0110757699207354744.200851190135
Winsorized Mean ( 19 / 25 )8.240129870129870.00995288543346042827.913666365286
Winsorized Mean ( 20 / 25 )8.234935064935070.007686223876428821071.38891571829
Winsorized Mean ( 21 / 25 )8.234935064935070.007686223876428821071.38891571829
Winsorized Mean ( 22 / 25 )8.234935064935070.006913742979737011191.09649998130
Winsorized Mean ( 23 / 25 )8.234935064935070.006913742979737011191.09649998130
Winsorized Mean ( 24 / 25 )8.231818181818180.006474956415710311271.33182886686
Winsorized Mean ( 25 / 25 )8.228571428571430.006032250661418421364.09640288996
Trimmed Mean ( 1 / 25 )8.230533333333330.0194026963235687424.195338424981
Trimmed Mean ( 2 / 25 )8.231643835616440.0187154183364818439.832211475101
Trimmed Mean ( 3 / 25 )8.232816901408450.0179773869791819457.954034751669
Trimmed Mean ( 4 / 25 )8.233768115942030.0172688749784436476.798177427312
Trimmed Mean ( 5 / 25 )8.233768115942030.0164669101450306500.019010453325
Trimmed Mean ( 6 / 25 )8.235076923076920.0159085775679879517.650109689757
Trimmed Mean ( 7 / 25 )8.235714285714290.0152764494272271539.111808993774
Trimmed Mean ( 8 / 25 )8.235737704918030.0148792205132396553.505991633759
Trimmed Mean ( 9 / 25 )8.23576271186440.0143944664952429572.147826012596
Trimmed Mean ( 10 / 25 )8.23576271186440.0138964803594602592.650980595801
Trimmed Mean ( 11 / 25 )8.235272727272730.0134386110028966612.806838853929
Trimmed Mean ( 12 / 25 )8.234905660377360.0130273315497986632.125284360686
Trimmed Mean ( 13 / 25 )8.234509803921570.0125098039215686658.244514106583
Trimmed Mean ( 14 / 25 )8.23387755102040.0119124367874582691.20010438916
Trimmed Mean ( 15 / 25 )8.23361702127660.0112963017038561728.87722346031
Trimmed Mean ( 16 / 25 )8.233333333333330.0106505560152672773.042583084973
Trimmed Mean ( 17 / 25 )8.232558139534880.0101161199564886813.805903344835
Trimmed Mean ( 18 / 25 )8.231707317073170.00940227294149607875.501846021007
Trimmed Mean ( 19 / 25 )8.230512820512820.0087161623953814944.281720229774
Trimmed Mean ( 20 / 25 )8.230512820512820.008109109047326561014.97128383374
Trimmed Mean ( 21 / 25 )8.228857142857140.00791521700676021039.62495732323
Trimmed Mean ( 22 / 25 )8.228181818181820.007630860210239051078.27710002357
Trimmed Mean ( 23 / 25 )8.227419354838710.00743383346505191106.75325099999
Trimmed Mean ( 24 / 25 )8.226551724137930.007127893277719791154.13508642902
Trimmed Mean ( 25 / 25 )8.225925925925930.006820015357429361206.14478044614
Median8.21
Midrange8.225
Midmean - Weighted Average at Xnp8.2271052631579
Midmean - Weighted Average at X(n+1)p8.23051282051282
Midmean - Empirical Distribution Function8.23051282051282
Midmean - Empirical Distribution Function - Averaging8.23051282051282
Midmean - Empirical Distribution Function - Interpolation8.23051282051282
Midmean - Closest Observation8.228
Midmean - True Basic - Statistics Graphics Toolkit8.23051282051282
Midmean - MS Excel (old versions)8.23051282051282
Number of observations77



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')