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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, 20 Apr 2008 03:57:48 -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/20/t120868554370nimad32qjztql.htm/, Retrieved Mon, 13 May 2024 07:23:38 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=10309, Retrieved Mon, 13 May 2024 07:23:38 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsCentrummaten - Blue Jeans (D) - Versluys Alexia
Estimated Impact216
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [Centrummaten - Bl...] [2008-04-20 09:57:48] [e8c1fcf34dff5578299591fe58b62c2d] [Current]
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Dataseries X:
44,13
44,13
44,17
44,14
44,15
44,14
44,14
44,14
44,19
44,29
44,29
44,29
44,29
44,27
44,26
44,33
44,32
44,34
44,34
44,34
44,37
44,47
44,51
44,51
44,51
44,52
44,7
44,84
44,9
44,95
44,94
44,94
44,91
45,28
45,36
45,34
45,34
45,34
45,44
45,62
45,75
45,77
45,77
45,77
46,09
46,25
46,35
46,34
46,34
46,28
46,59
46,42
46,29
46,29
46,29
46,3
46,52
46,66
46,67
46,72
46,72
46,72
46,76
46,89
47,04
47,02
47,02
47,18
47,22
47,8
47,88
47,91




Summary of compuational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'Sir Ronald Aylmer Fisher' @ 193.190.124.24

\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 & 3 seconds \tabularnewline
R Server & 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=10309&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]3 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Sir Ronald Aylmer Fisher' @ 193.190.124.24[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=10309&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=10309&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 time3 seconds
R Server'Sir Ronald Aylmer Fisher' @ 193.190.124.24







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean45.48750.133439181870304340.88563315842
Geometric Mean45.4736780107095
Harmonic Mean45.4599333154162
Quadratic Mean45.5013943009809
Winsorized Mean ( 1 / 24 )45.48708333333330.133333250806899341.153336156262
Winsorized Mean ( 2 / 24 )45.48513888888890.132739728073623342.664095738248
Winsorized Mean ( 3 / 24 )45.46097222222220.127409509408536356.809883604939
Winsorized Mean ( 4 / 24 )45.458750.126981314396215357.995585540695
Winsorized Mean ( 5 / 24 )45.44902777777780.125182677114444363.061637803347
Winsorized Mean ( 6 / 24 )45.44819444444440.124763207076209364.275618666034
Winsorized Mean ( 7 / 24 )45.45013888888890.124479902824437365.120295386078
Winsorized Mean ( 8 / 24 )45.43791666666670.121660707536230373.480621532105
Winsorized Mean ( 9 / 24 )45.43041666666670.117756718108244385.798936965161
Winsorized Mean ( 10 / 24 )45.426250.116687026643972389.299918821326
Winsorized Mean ( 11 / 24 )45.42930555555560.116262937656382390.746238408520
Winsorized Mean ( 12 / 24 )45.42930555555560.116262937656382390.746238408520
Winsorized Mean ( 13 / 24 )45.42027777777780.114865365194954395.42187238676
Winsorized Mean ( 14 / 24 )45.41833333333330.114567978057763396.431307449924
Winsorized Mean ( 15 / 24 )45.410.111503980714502407.25003456396
Winsorized Mean ( 16 / 24 )45.39666666666670.108908189500235416.834279175751
Winsorized Mean ( 17 / 24 )45.37541666666670.105214762388981431.264735445708
Winsorized Mean ( 18 / 24 )45.35791666666670.102801512242794441.218379740772
Winsorized Mean ( 19 / 24 )45.35527777777780.102443536152658442.734402590231
Winsorized Mean ( 20 / 24 )45.36361111111110.101286193622850447.875564166497
Winsorized Mean ( 21 / 24 )45.38111111111110.0957340382826197474.033185324743
Winsorized Mean ( 22 / 24 )45.39027777777780.0936929215334348484.457918857617
Winsorized Mean ( 23 / 24 )45.39027777777780.0936929215334348484.457918857617
Winsorized Mean ( 24 / 24 )45.39027777777780.0936929215334348484.457918857617
Trimmed Mean ( 1 / 24 )45.47228571428570.131322965943531346.263011862211
Trimmed Mean ( 2 / 24 )45.45661764705880.128885036040287352.691197082413
Trimmed Mean ( 3 / 24 )45.44106060606060.126307082927166359.766527363027
Trimmed Mean ( 4 / 24 )45.433593750.125573558564258361.808602618767
Trimmed Mean ( 5 / 24 )45.42629032258060.124744950559781364.153339423636
Trimmed Mean ( 6 / 24 )45.42083333333330.124183728399685365.755110743225
Trimmed Mean ( 7 / 24 )45.41517241379310.123493031459573367.754940315482
Trimmed Mean ( 8 / 24 )45.408750.122593738982308370.400237214015
Trimmed Mean ( 9 / 24 )45.40388888888890.122016145117066372.11377924886
Trimmed Mean ( 10 / 24 )45.39980769230770.121982273266644372.183649939586
Trimmed Mean ( 11 / 24 )45.3960.121958172823175372.225976735638
Trimmed Mean ( 12 / 24 )45.39145833333330.121791441016623372.698261507047
Trimmed Mean ( 13 / 24 )45.38652173913040.121353564721674374.002377624631
Trimmed Mean ( 14 / 24 )45.38227272727270.120853581338069375.514504616318
Trimmed Mean ( 15 / 24 )45.37785714285710.120025421094768378.068718517792
Trimmed Mean ( 16 / 24 )45.3740.119342106825456380.201097558651
Trimmed Mean ( 17 / 24 )45.37131578947370.118714170189528382.189554263303
Trimmed Mean ( 18 / 24 )45.37083333333330.118360074108025383.328868921831
Trimmed Mean ( 19 / 24 )45.37235294117650.118027504289890384.421861786862
Trimmed Mean ( 20 / 24 )45.3743750.117207888011417387.127315147768
Trimmed Mean ( 21 / 24 )45.37566666666670.115899960165151391.507180865368
Trimmed Mean ( 22 / 24 )45.3750.115079337712093394.293197215991
Trimmed Mean ( 23 / 24 )45.37307692307690.113857899601983398.506182545869
Trimmed Mean ( 24 / 24 )45.37083333333330.111320982348842407.567669418841
Median45.34
Midrange46.02
Midmean - Weighted Average at Xnp45.342972972973
Midmean - Weighted Average at X(n+1)p45.342972972973
Midmean - Empirical Distribution Function45.342972972973
Midmean - Empirical Distribution Function - Averaging45.342972972973
Midmean - Empirical Distribution Function - Interpolation45.342972972973
Midmean - Closest Observation45.342972972973
Midmean - True Basic - Statistics Graphics Toolkit45.342972972973
Midmean - MS Excel (old versions)45.3713157894737
Number of observations72

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 45.4875 & 0.133439181870304 & 340.88563315842 \tabularnewline
Geometric Mean & 45.4736780107095 &  &  \tabularnewline
Harmonic Mean & 45.4599333154162 &  &  \tabularnewline
Quadratic Mean & 45.5013943009809 &  &  \tabularnewline
Winsorized Mean ( 1 / 24 ) & 45.4870833333333 & 0.133333250806899 & 341.153336156262 \tabularnewline
Winsorized Mean ( 2 / 24 ) & 45.4851388888889 & 0.132739728073623 & 342.664095738248 \tabularnewline
Winsorized Mean ( 3 / 24 ) & 45.4609722222222 & 0.127409509408536 & 356.809883604939 \tabularnewline
Winsorized Mean ( 4 / 24 ) & 45.45875 & 0.126981314396215 & 357.995585540695 \tabularnewline
Winsorized Mean ( 5 / 24 ) & 45.4490277777778 & 0.125182677114444 & 363.061637803347 \tabularnewline
Winsorized Mean ( 6 / 24 ) & 45.4481944444444 & 0.124763207076209 & 364.275618666034 \tabularnewline
Winsorized Mean ( 7 / 24 ) & 45.4501388888889 & 0.124479902824437 & 365.120295386078 \tabularnewline
Winsorized Mean ( 8 / 24 ) & 45.4379166666667 & 0.121660707536230 & 373.480621532105 \tabularnewline
Winsorized Mean ( 9 / 24 ) & 45.4304166666667 & 0.117756718108244 & 385.798936965161 \tabularnewline
Winsorized Mean ( 10 / 24 ) & 45.42625 & 0.116687026643972 & 389.299918821326 \tabularnewline
Winsorized Mean ( 11 / 24 ) & 45.4293055555556 & 0.116262937656382 & 390.746238408520 \tabularnewline
Winsorized Mean ( 12 / 24 ) & 45.4293055555556 & 0.116262937656382 & 390.746238408520 \tabularnewline
Winsorized Mean ( 13 / 24 ) & 45.4202777777778 & 0.114865365194954 & 395.42187238676 \tabularnewline
Winsorized Mean ( 14 / 24 ) & 45.4183333333333 & 0.114567978057763 & 396.431307449924 \tabularnewline
Winsorized Mean ( 15 / 24 ) & 45.41 & 0.111503980714502 & 407.25003456396 \tabularnewline
Winsorized Mean ( 16 / 24 ) & 45.3966666666667 & 0.108908189500235 & 416.834279175751 \tabularnewline
Winsorized Mean ( 17 / 24 ) & 45.3754166666667 & 0.105214762388981 & 431.264735445708 \tabularnewline
Winsorized Mean ( 18 / 24 ) & 45.3579166666667 & 0.102801512242794 & 441.218379740772 \tabularnewline
Winsorized Mean ( 19 / 24 ) & 45.3552777777778 & 0.102443536152658 & 442.734402590231 \tabularnewline
Winsorized Mean ( 20 / 24 ) & 45.3636111111111 & 0.101286193622850 & 447.875564166497 \tabularnewline
Winsorized Mean ( 21 / 24 ) & 45.3811111111111 & 0.0957340382826197 & 474.033185324743 \tabularnewline
Winsorized Mean ( 22 / 24 ) & 45.3902777777778 & 0.0936929215334348 & 484.457918857617 \tabularnewline
Winsorized Mean ( 23 / 24 ) & 45.3902777777778 & 0.0936929215334348 & 484.457918857617 \tabularnewline
Winsorized Mean ( 24 / 24 ) & 45.3902777777778 & 0.0936929215334348 & 484.457918857617 \tabularnewline
Trimmed Mean ( 1 / 24 ) & 45.4722857142857 & 0.131322965943531 & 346.263011862211 \tabularnewline
Trimmed Mean ( 2 / 24 ) & 45.4566176470588 & 0.128885036040287 & 352.691197082413 \tabularnewline
Trimmed Mean ( 3 / 24 ) & 45.4410606060606 & 0.126307082927166 & 359.766527363027 \tabularnewline
Trimmed Mean ( 4 / 24 ) & 45.43359375 & 0.125573558564258 & 361.808602618767 \tabularnewline
Trimmed Mean ( 5 / 24 ) & 45.4262903225806 & 0.124744950559781 & 364.153339423636 \tabularnewline
Trimmed Mean ( 6 / 24 ) & 45.4208333333333 & 0.124183728399685 & 365.755110743225 \tabularnewline
Trimmed Mean ( 7 / 24 ) & 45.4151724137931 & 0.123493031459573 & 367.754940315482 \tabularnewline
Trimmed Mean ( 8 / 24 ) & 45.40875 & 0.122593738982308 & 370.400237214015 \tabularnewline
Trimmed Mean ( 9 / 24 ) & 45.4038888888889 & 0.122016145117066 & 372.11377924886 \tabularnewline
Trimmed Mean ( 10 / 24 ) & 45.3998076923077 & 0.121982273266644 & 372.183649939586 \tabularnewline
Trimmed Mean ( 11 / 24 ) & 45.396 & 0.121958172823175 & 372.225976735638 \tabularnewline
Trimmed Mean ( 12 / 24 ) & 45.3914583333333 & 0.121791441016623 & 372.698261507047 \tabularnewline
Trimmed Mean ( 13 / 24 ) & 45.3865217391304 & 0.121353564721674 & 374.002377624631 \tabularnewline
Trimmed Mean ( 14 / 24 ) & 45.3822727272727 & 0.120853581338069 & 375.514504616318 \tabularnewline
Trimmed Mean ( 15 / 24 ) & 45.3778571428571 & 0.120025421094768 & 378.068718517792 \tabularnewline
Trimmed Mean ( 16 / 24 ) & 45.374 & 0.119342106825456 & 380.201097558651 \tabularnewline
Trimmed Mean ( 17 / 24 ) & 45.3713157894737 & 0.118714170189528 & 382.189554263303 \tabularnewline
Trimmed Mean ( 18 / 24 ) & 45.3708333333333 & 0.118360074108025 & 383.328868921831 \tabularnewline
Trimmed Mean ( 19 / 24 ) & 45.3723529411765 & 0.118027504289890 & 384.421861786862 \tabularnewline
Trimmed Mean ( 20 / 24 ) & 45.374375 & 0.117207888011417 & 387.127315147768 \tabularnewline
Trimmed Mean ( 21 / 24 ) & 45.3756666666667 & 0.115899960165151 & 391.507180865368 \tabularnewline
Trimmed Mean ( 22 / 24 ) & 45.375 & 0.115079337712093 & 394.293197215991 \tabularnewline
Trimmed Mean ( 23 / 24 ) & 45.3730769230769 & 0.113857899601983 & 398.506182545869 \tabularnewline
Trimmed Mean ( 24 / 24 ) & 45.3708333333333 & 0.111320982348842 & 407.567669418841 \tabularnewline
Median & 45.34 &  &  \tabularnewline
Midrange & 46.02 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 45.342972972973 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 45.342972972973 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 45.342972972973 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 45.342972972973 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 45.342972972973 &  &  \tabularnewline
Midmean - Closest Observation & 45.342972972973 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 45.342972972973 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 45.3713157894737 &  &  \tabularnewline
Number of observations & 72 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=10309&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]45.4875[/C][C]0.133439181870304[/C][C]340.88563315842[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]45.4736780107095[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]45.4599333154162[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]45.5013943009809[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 24 )[/C][C]45.4870833333333[/C][C]0.133333250806899[/C][C]341.153336156262[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 24 )[/C][C]45.4851388888889[/C][C]0.132739728073623[/C][C]342.664095738248[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 24 )[/C][C]45.4609722222222[/C][C]0.127409509408536[/C][C]356.809883604939[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 24 )[/C][C]45.45875[/C][C]0.126981314396215[/C][C]357.995585540695[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 24 )[/C][C]45.4490277777778[/C][C]0.125182677114444[/C][C]363.061637803347[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 24 )[/C][C]45.4481944444444[/C][C]0.124763207076209[/C][C]364.275618666034[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 24 )[/C][C]45.4501388888889[/C][C]0.124479902824437[/C][C]365.120295386078[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 24 )[/C][C]45.4379166666667[/C][C]0.121660707536230[/C][C]373.480621532105[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 24 )[/C][C]45.4304166666667[/C][C]0.117756718108244[/C][C]385.798936965161[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 24 )[/C][C]45.42625[/C][C]0.116687026643972[/C][C]389.299918821326[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 24 )[/C][C]45.4293055555556[/C][C]0.116262937656382[/C][C]390.746238408520[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 24 )[/C][C]45.4293055555556[/C][C]0.116262937656382[/C][C]390.746238408520[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 24 )[/C][C]45.4202777777778[/C][C]0.114865365194954[/C][C]395.42187238676[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 24 )[/C][C]45.4183333333333[/C][C]0.114567978057763[/C][C]396.431307449924[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 24 )[/C][C]45.41[/C][C]0.111503980714502[/C][C]407.25003456396[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 24 )[/C][C]45.3966666666667[/C][C]0.108908189500235[/C][C]416.834279175751[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 24 )[/C][C]45.3754166666667[/C][C]0.105214762388981[/C][C]431.264735445708[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 24 )[/C][C]45.3579166666667[/C][C]0.102801512242794[/C][C]441.218379740772[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 24 )[/C][C]45.3552777777778[/C][C]0.102443536152658[/C][C]442.734402590231[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 24 )[/C][C]45.3636111111111[/C][C]0.101286193622850[/C][C]447.875564166497[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 24 )[/C][C]45.3811111111111[/C][C]0.0957340382826197[/C][C]474.033185324743[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 24 )[/C][C]45.3902777777778[/C][C]0.0936929215334348[/C][C]484.457918857617[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 24 )[/C][C]45.3902777777778[/C][C]0.0936929215334348[/C][C]484.457918857617[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 24 )[/C][C]45.3902777777778[/C][C]0.0936929215334348[/C][C]484.457918857617[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 24 )[/C][C]45.4722857142857[/C][C]0.131322965943531[/C][C]346.263011862211[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 24 )[/C][C]45.4566176470588[/C][C]0.128885036040287[/C][C]352.691197082413[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 24 )[/C][C]45.4410606060606[/C][C]0.126307082927166[/C][C]359.766527363027[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 24 )[/C][C]45.43359375[/C][C]0.125573558564258[/C][C]361.808602618767[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 24 )[/C][C]45.4262903225806[/C][C]0.124744950559781[/C][C]364.153339423636[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 24 )[/C][C]45.4208333333333[/C][C]0.124183728399685[/C][C]365.755110743225[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 24 )[/C][C]45.4151724137931[/C][C]0.123493031459573[/C][C]367.754940315482[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 24 )[/C][C]45.40875[/C][C]0.122593738982308[/C][C]370.400237214015[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 24 )[/C][C]45.4038888888889[/C][C]0.122016145117066[/C][C]372.11377924886[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 24 )[/C][C]45.3998076923077[/C][C]0.121982273266644[/C][C]372.183649939586[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 24 )[/C][C]45.396[/C][C]0.121958172823175[/C][C]372.225976735638[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 24 )[/C][C]45.3914583333333[/C][C]0.121791441016623[/C][C]372.698261507047[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 24 )[/C][C]45.3865217391304[/C][C]0.121353564721674[/C][C]374.002377624631[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 24 )[/C][C]45.3822727272727[/C][C]0.120853581338069[/C][C]375.514504616318[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 24 )[/C][C]45.3778571428571[/C][C]0.120025421094768[/C][C]378.068718517792[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 24 )[/C][C]45.374[/C][C]0.119342106825456[/C][C]380.201097558651[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 24 )[/C][C]45.3713157894737[/C][C]0.118714170189528[/C][C]382.189554263303[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 24 )[/C][C]45.3708333333333[/C][C]0.118360074108025[/C][C]383.328868921831[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 24 )[/C][C]45.3723529411765[/C][C]0.118027504289890[/C][C]384.421861786862[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 24 )[/C][C]45.374375[/C][C]0.117207888011417[/C][C]387.127315147768[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 24 )[/C][C]45.3756666666667[/C][C]0.115899960165151[/C][C]391.507180865368[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 24 )[/C][C]45.375[/C][C]0.115079337712093[/C][C]394.293197215991[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 24 )[/C][C]45.3730769230769[/C][C]0.113857899601983[/C][C]398.506182545869[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 24 )[/C][C]45.3708333333333[/C][C]0.111320982348842[/C][C]407.567669418841[/C][/ROW]
[ROW][C]Median[/C][C]45.34[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]46.02[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]45.342972972973[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]45.342972972973[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]45.342972972973[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]45.342972972973[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]45.342972972973[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]45.342972972973[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]45.342972972973[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]45.3713157894737[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]72[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=10309&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=10309&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 Mean45.48750.133439181870304340.88563315842
Geometric Mean45.4736780107095
Harmonic Mean45.4599333154162
Quadratic Mean45.5013943009809
Winsorized Mean ( 1 / 24 )45.48708333333330.133333250806899341.153336156262
Winsorized Mean ( 2 / 24 )45.48513888888890.132739728073623342.664095738248
Winsorized Mean ( 3 / 24 )45.46097222222220.127409509408536356.809883604939
Winsorized Mean ( 4 / 24 )45.458750.126981314396215357.995585540695
Winsorized Mean ( 5 / 24 )45.44902777777780.125182677114444363.061637803347
Winsorized Mean ( 6 / 24 )45.44819444444440.124763207076209364.275618666034
Winsorized Mean ( 7 / 24 )45.45013888888890.124479902824437365.120295386078
Winsorized Mean ( 8 / 24 )45.43791666666670.121660707536230373.480621532105
Winsorized Mean ( 9 / 24 )45.43041666666670.117756718108244385.798936965161
Winsorized Mean ( 10 / 24 )45.426250.116687026643972389.299918821326
Winsorized Mean ( 11 / 24 )45.42930555555560.116262937656382390.746238408520
Winsorized Mean ( 12 / 24 )45.42930555555560.116262937656382390.746238408520
Winsorized Mean ( 13 / 24 )45.42027777777780.114865365194954395.42187238676
Winsorized Mean ( 14 / 24 )45.41833333333330.114567978057763396.431307449924
Winsorized Mean ( 15 / 24 )45.410.111503980714502407.25003456396
Winsorized Mean ( 16 / 24 )45.39666666666670.108908189500235416.834279175751
Winsorized Mean ( 17 / 24 )45.37541666666670.105214762388981431.264735445708
Winsorized Mean ( 18 / 24 )45.35791666666670.102801512242794441.218379740772
Winsorized Mean ( 19 / 24 )45.35527777777780.102443536152658442.734402590231
Winsorized Mean ( 20 / 24 )45.36361111111110.101286193622850447.875564166497
Winsorized Mean ( 21 / 24 )45.38111111111110.0957340382826197474.033185324743
Winsorized Mean ( 22 / 24 )45.39027777777780.0936929215334348484.457918857617
Winsorized Mean ( 23 / 24 )45.39027777777780.0936929215334348484.457918857617
Winsorized Mean ( 24 / 24 )45.39027777777780.0936929215334348484.457918857617
Trimmed Mean ( 1 / 24 )45.47228571428570.131322965943531346.263011862211
Trimmed Mean ( 2 / 24 )45.45661764705880.128885036040287352.691197082413
Trimmed Mean ( 3 / 24 )45.44106060606060.126307082927166359.766527363027
Trimmed Mean ( 4 / 24 )45.433593750.125573558564258361.808602618767
Trimmed Mean ( 5 / 24 )45.42629032258060.124744950559781364.153339423636
Trimmed Mean ( 6 / 24 )45.42083333333330.124183728399685365.755110743225
Trimmed Mean ( 7 / 24 )45.41517241379310.123493031459573367.754940315482
Trimmed Mean ( 8 / 24 )45.408750.122593738982308370.400237214015
Trimmed Mean ( 9 / 24 )45.40388888888890.122016145117066372.11377924886
Trimmed Mean ( 10 / 24 )45.39980769230770.121982273266644372.183649939586
Trimmed Mean ( 11 / 24 )45.3960.121958172823175372.225976735638
Trimmed Mean ( 12 / 24 )45.39145833333330.121791441016623372.698261507047
Trimmed Mean ( 13 / 24 )45.38652173913040.121353564721674374.002377624631
Trimmed Mean ( 14 / 24 )45.38227272727270.120853581338069375.514504616318
Trimmed Mean ( 15 / 24 )45.37785714285710.120025421094768378.068718517792
Trimmed Mean ( 16 / 24 )45.3740.119342106825456380.201097558651
Trimmed Mean ( 17 / 24 )45.37131578947370.118714170189528382.189554263303
Trimmed Mean ( 18 / 24 )45.37083333333330.118360074108025383.328868921831
Trimmed Mean ( 19 / 24 )45.37235294117650.118027504289890384.421861786862
Trimmed Mean ( 20 / 24 )45.3743750.117207888011417387.127315147768
Trimmed Mean ( 21 / 24 )45.37566666666670.115899960165151391.507180865368
Trimmed Mean ( 22 / 24 )45.3750.115079337712093394.293197215991
Trimmed Mean ( 23 / 24 )45.37307692307690.113857899601983398.506182545869
Trimmed Mean ( 24 / 24 )45.37083333333330.111320982348842407.567669418841
Median45.34
Midrange46.02
Midmean - Weighted Average at Xnp45.342972972973
Midmean - Weighted Average at X(n+1)p45.342972972973
Midmean - Empirical Distribution Function45.342972972973
Midmean - Empirical Distribution Function - Averaging45.342972972973
Midmean - Empirical Distribution Function - Interpolation45.342972972973
Midmean - Closest Observation45.342972972973
Midmean - True Basic - Statistics Graphics Toolkit45.342972972973
Midmean - MS Excel (old versions)45.3713157894737
Number of observations72



Parameters (Session):
Parameters (R input):
R code (references can be found in the software module):
geomean <- function(x) {
return(exp(mean(log(x))))
}
harmean <- function(x) {
return(1/mean(1/x))
}
quamean <- function(x) {
return(sqrt(mean(x*x)))
}
winmean <- function(x) {
x <-sort(x[!is.na(x)])
n<-length(x)
denom <- 3
nodenom <- n/denom
if (nodenom>40) denom <- n/40
sqrtn = sqrt(n)
roundnodenom = floor(nodenom)
win <- array(NA,dim=c(roundnodenom,2))
for (j in 1:roundnodenom) {
win[j,1] <- (j*x[j+1]+sum(x[(j+1):(n-j)])+j*x[n-j])/n
win[j,2] <- sd(c(rep(x[j+1],j),x[(j+1):(n-j)],rep(x[n-j],j)))/sqrtn
}
return(win)
}
trimean <- function(x) {
x <-sort(x[!is.na(x)])
n<-length(x)
denom <- 3
nodenom <- n/denom
if (nodenom>40) denom <- n/40
sqrtn = sqrt(n)
roundnodenom = floor(nodenom)
tri <- array(NA,dim=c(roundnodenom,2))
for (j in 1:roundnodenom) {
tri[j,1] <- mean(x,trim=j/n)
tri[j,2] <- sd(x[(j+1):(n-j)]) / sqrt(n-j*2)
}
return(tri)
}
midrange <- function(x) {
return((max(x)+min(x))/2)
}
q1 <- function(data,n,p,i,f) {
np <- n*p;
i <<- floor(np)
f <<- np - i
qvalue <- (1-f)*data[i] + f*data[i+1]
}
q2 <- function(data,n,p,i,f) {
np <- (n+1)*p
i <<- floor(np)
f <<- np - i
qvalue <- (1-f)*data[i] + f*data[i+1]
}
q3 <- function(data,n,p,i,f) {
np <- n*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- data[i]
} else {
qvalue <- data[i+1]
}
}
q4 <- function(data,n,p,i,f) {
np <- n*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- (data[i]+data[i+1])/2
} else {
qvalue <- data[i+1]
}
}
q5 <- function(data,n,p,i,f) {
np <- (n-1)*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- data[i+1]
} else {
qvalue <- data[i+1] + f*(data[i+2]-data[i+1])
}
}
q6 <- function(data,n,p,i,f) {
np <- n*p+0.5
i <<- floor(np)
f <<- np - i
qvalue <- data[i]
}
q7 <- function(data,n,p,i,f) {
np <- (n+1)*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- data[i]
} else {
qvalue <- f*data[i] + (1-f)*data[i+1]
}
}
q8 <- function(data,n,p,i,f) {
np <- (n+1)*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- data[i]
} else {
if (f == 0.5) {
qvalue <- (data[i]+data[i+1])/2
} else {
if (f < 0.5) {
qvalue <- data[i]
} else {
qvalue <- data[i+1]
}
}
}
}
midmean <- function(x,def) {
x <-sort(x[!is.na(x)])
n<-length(x)
if (def==1) {
qvalue1 <- q1(x,n,0.25,i,f)
qvalue3 <- q1(x,n,0.75,i,f)
}
if (def==2) {
qvalue1 <- q2(x,n,0.25,i,f)
qvalue3 <- q2(x,n,0.75,i,f)
}
if (def==3) {
qvalue1 <- q3(x,n,0.25,i,f)
qvalue3 <- q3(x,n,0.75,i,f)
}
if (def==4) {
qvalue1 <- q4(x,n,0.25,i,f)
qvalue3 <- q4(x,n,0.75,i,f)
}
if (def==5) {
qvalue1 <- q5(x,n,0.25,i,f)
qvalue3 <- q5(x,n,0.75,i,f)
}
if (def==6) {
qvalue1 <- q6(x,n,0.25,i,f)
qvalue3 <- q6(x,n,0.75,i,f)
}
if (def==7) {
qvalue1 <- q7(x,n,0.25,i,f)
qvalue3 <- q7(x,n,0.75,i,f)
}
if (def==8) {
qvalue1 <- q8(x,n,0.25,i,f)
qvalue3 <- q8(x,n,0.75,i,f)
}
midm <- 0
myn <- 0
roundno4 <- round(n/4)
round3no4 <- round(3*n/4)
for (i in 1:n) {
if ((x[i]>=qvalue1) & (x[i]<=qvalue3)){
midm = midm + x[i]
myn = myn + 1
}
}
midm = midm / myn
return(midm)
}
(arm <- mean(x))
sqrtn <- sqrt(length(x))
(armse <- sd(x) / sqrtn)
(armose <- arm / armse)
(geo <- geomean(x))
(har <- harmean(x))
(qua <- quamean(x))
(win <- winmean(x))
(tri <- trimean(x))
(midr <- midrange(x))
midm <- array(NA,dim=8)
for (j in 1:8) midm[j] <- midmean(x,j)
midm
bitmap(file='test1.png')
lb <- win[,1] - 2*win[,2]
ub <- win[,1] + 2*win[,2]
if ((ylimmin == '') | (ylimmax == '')) plot(win[,1],type='b',main=main, xlab='j', pch=19, ylab='Winsorized Mean(j/n)', ylim=c(min(lb),max(ub))) else plot(win[,1],type='l',main=main, xlab='j', pch=19, ylab='Winsorized Mean(j/n)', ylim=c(ylimmin,ylimmax))
lines(ub,lty=3)
lines(lb,lty=3)
grid()
dev.off()
bitmap(file='test2.png')
lb <- tri[,1] - 2*tri[,2]
ub <- tri[,1] + 2*tri[,2]
if ((ylimmin == '') | (ylimmax == '')) plot(tri[,1],type='b',main=main, xlab='j', pch=19, ylab='Trimmed Mean(j/n)', ylim=c(min(lb),max(ub))) else plot(tri[,1],type='l',main=main, xlab='j', pch=19, ylab='Trimmed Mean(j/n)', ylim=c(ylimmin,ylimmax))
lines(ub,lty=3)
lines(lb,lty=3)
grid()
dev.off()
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Central Tendency - Ungrouped Data',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Measure',header=TRUE)
a<-table.element(a,'Value',header=TRUE)
a<-table.element(a,'S.E.',header=TRUE)
a<-table.element(a,'Value/S.E.',header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('arithmetic_mean.htm', 'Arithmetic Mean', 'click to view the definition of the Arithmetic Mean'),header=TRUE)
a<-table.element(a,arm)
a<-table.element(a,hyperlink('arithmetic_mean_standard_error.htm', armse, 'click to view the definition of the Standard Error of the Arithmetic Mean'))
a<-table.element(a,armose)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('geometric_mean.htm', 'Geometric Mean', 'click to view the definition of the Geometric Mean'),header=TRUE)
a<-table.element(a,geo)
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('harmonic_mean.htm', 'Harmonic Mean', 'click to view the definition of the Harmonic Mean'),header=TRUE)
a<-table.element(a,har)
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('quadratic_mean.htm', 'Quadratic Mean', 'click to view the definition of the Quadratic Mean'),header=TRUE)
a<-table.element(a,qua)
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
for (j in 1:length(win[,1])) {
a<-table.row.start(a)
mylabel <- paste('Winsorized Mean (',j)
mylabel <- paste(mylabel,'/')
mylabel <- paste(mylabel,length(win[,1]))
mylabel <- paste(mylabel,')')
a<-table.element(a,hyperlink('winsorized_mean.htm', mylabel, 'click to view the definition of the Winsorized Mean'),header=TRUE)
a<-table.element(a,win[j,1])
a<-table.element(a,win[j,2])
a<-table.element(a,win[j,1]/win[j,2])
a<-table.row.end(a)
}
for (j in 1:length(tri[,1])) {
a<-table.row.start(a)
mylabel <- paste('Trimmed Mean (',j)
mylabel <- paste(mylabel,'/')
mylabel <- paste(mylabel,length(tri[,1]))
mylabel <- paste(mylabel,')')
a<-table.element(a,hyperlink('arithmetic_mean.htm', mylabel, 'click to view the definition of the Trimmed Mean'),header=TRUE)
a<-table.element(a,tri[j,1])
a<-table.element(a,tri[j,2])
a<-table.element(a,tri[j,1]/tri[j,2])
a<-table.row.end(a)
}
a<-table.row.start(a)
a<-table.element(a,hyperlink('median_1.htm', 'Median', 'click to view the definition of the Median'),header=TRUE)
a<-table.element(a,median(x))
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('midrange.htm', 'Midrange', 'click to view the definition of the Midrange'),header=TRUE)
a<-table.element(a,midr)
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_1.htm','Weighted Average at Xnp',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[1])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_2.htm','Weighted Average at X(n+1)p',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[2])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_3.htm','Empirical Distribution Function',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[3])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_4.htm','Empirical Distribution Function - Averaging',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[4])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_5.htm','Empirical Distribution Function - Interpolation',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[5])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_6.htm','Closest Observation',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[6])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_7.htm','True Basic - Statistics Graphics Toolkit',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[7])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_8.htm','MS Excel (old versions)',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[8])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Number of observations',header=TRUE)
a<-table.element(a,length(x))
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable.tab')