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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, 13 Oct 2014 09:57:09 +0100
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2014/Oct/13/t1413190826x24bccxbs4uh585.htm/, Retrieved Fri, 10 May 2024 12:14:54 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=240705, Retrieved Fri, 10 May 2024 12:14:54 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsTessa Bertels
Estimated Impact114
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [] [2014-10-13 08:57:09] [929039938a2aac5a4cd000b15aa01fe0] [Current]
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Dataseries X:
44,91
44,86
44,76
44,89
44,89
45
45,01
45,11
45,05
44,67
44,48
44,48
44,48
44,58
44,79
44,79
44,41
44,41
44,44
44,43
44,36
44,39
44,39
44,41
44,32
44,43
44,82
44,97
44,91
44,79
44,76
44,8
44,65
44,49
44,56
44,4
44,45
44,46
44,39
44,5
44,44
44,41
44,4
44,42
44,49
44,46
44,49
44,5
44,5
44,5
44,55
44,53
44,49
44,49
44,62
44,59
44,56
44,57
44,04
44,06
44,07
44,1
44,21
44,48
44,51
44,24
44,25
44,27
44,45
44,39
44,23
44,23




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

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 1 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=240705&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' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=240705&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=240705&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' @ jenkins.wessa.net







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean44.53097222222220.02842993730181651566.34085223174
Geometric Mean44.5303287808498
Harmonic Mean44.5296862389906
Quadratic Mean44.5316165618441
Winsorized Mean ( 1 / 24 )44.53041666666670.02813548535202011582.71364824597
Winsorized Mean ( 2 / 24 )44.52958333333330.02779060247767191602.32522375541
Winsorized Mean ( 3 / 24 )44.53041666666670.0274057193778341624.8585214181
Winsorized Mean ( 4 / 24 )44.53486111111110.02578425070334911727.21176285051
Winsorized Mean ( 5 / 24 )44.53208333333330.02459367571097341810.71279692704
Winsorized Mean ( 6 / 24 )44.53208333333330.02459367571097341810.71279692704
Winsorized Mean ( 7 / 24 )44.53111111111110.02401140472664221854.58167142137
Winsorized Mean ( 8 / 24 )44.53222222222220.02382383689316841869.22964684131
Winsorized Mean ( 9 / 24 )44.53097222222220.02263125489345451967.67578430225
Winsorized Mean ( 10 / 24 )44.53236111111110.02043587345640682179.12687735644
Winsorized Mean ( 11 / 24 )44.53541666666670.01898638164036072345.65055681777
Winsorized Mean ( 12 / 24 )44.538750.01804287354061162468.49538127895
Winsorized Mean ( 13 / 24 )44.538750.01804287354061162468.49538127895
Winsorized Mean ( 14 / 24 )44.538750.01804287354061162468.49538127895
Winsorized Mean ( 15 / 24 )44.53250.01683454186151222645.30513312108
Winsorized Mean ( 16 / 24 )44.53472222222220.01657483175835492686.88834200526
Winsorized Mean ( 17 / 24 )44.51347222222220.01266697510469283514.13592071647
Winsorized Mean ( 18 / 24 )44.51097222222220.01149293809541473872.89758743073
Winsorized Mean ( 19 / 24 )44.50305555555560.01017576151516414373.4373579055
Winsorized Mean ( 20 / 24 )44.49472222222220.008867773727665175017.57527748031
Winsorized Mean ( 21 / 24 )44.49180555555550.008432105694964535276.47626406357
Winsorized Mean ( 22 / 24 )44.49180555555560.007571584276370515876.15536346946
Winsorized Mean ( 23 / 24 )44.49180555555560.006688129736892166652.35384267979
Winsorized Mean ( 24 / 24 )44.49180555555560.006688129736892166652.35384267979
Trimmed Mean ( 1 / 24 )44.52971428571430.02713128226556121641.26832819242
Trimmed Mean ( 2 / 24 )44.52897058823530.02593310407569791717.0706005057
Trimmed Mean ( 3 / 24 )44.52863636363640.0247221259898141801.1653359417
Trimmed Mean ( 4 / 24 )44.527968750.02344380702176181899.34888598369
Trimmed Mean ( 5 / 24 )44.52596774193550.02252733186563891976.53090954155
Trimmed Mean ( 6 / 24 )44.52450.02181124081726442041.35566486237
Trimmed Mean ( 7 / 24 )44.52293103448280.02093259516332382126.9666129354
Trimmed Mean ( 8 / 24 )44.52142857142860.02001367806858662224.55005116273
Trimmed Mean ( 9 / 24 )44.51962962962960.01891531564170962353.62869290221
Trimmed Mean ( 10 / 24 )44.51788461538460.01785718553688562492.99558003857
Trimmed Mean ( 11 / 24 )44.51580.01708344466530832605.78594493879
Trimmed Mean ( 12 / 24 )44.5131250.01643857104214972707.84637459456
Trimmed Mean ( 13 / 24 )44.50978260869570.01580829944816882815.59586814707
Trimmed Mean ( 14 / 24 )44.50613636363640.01496725075093362973.56789862428
Trimmed Mean ( 15 / 24 )44.50214285714290.01382458428232333219.05830572027
Trimmed Mean ( 16 / 24 )44.49850.01264682994636643518.54972263505
Trimmed Mean ( 17 / 24 )44.49421052631580.01101939050643644037.81048510141
Trimmed Mean ( 18 / 24 )44.49194444444440.01018728934494024367.39773829459
Trimmed Mean ( 19 / 24 )44.48970588235290.009388479439639334738.75521253334
Trimmed Mean ( 20 / 24 )44.4881250.008723317612083845099.90888539625
Trimmed Mean ( 21 / 24 )44.48733333333330.008234122071206235402.8022597455
Trimmed Mean ( 22 / 24 )44.48678571428570.007664485048961875804.27588156249
Trimmed Mean ( 23 / 24 )44.48615384615380.007126913736554196241.99414930235
Trimmed Mean ( 24 / 24 )44.48541666666670.00664795835136976691.59075846213
Median44.49
Midrange44.575
Midmean - Weighted Average at Xnp44.4871052631579
Midmean - Weighted Average at X(n+1)p44.4919444444444
Midmean - Empirical Distribution Function44.4871052631579
Midmean - Empirical Distribution Function - Averaging44.4919444444444
Midmean - Empirical Distribution Function - Interpolation44.4919444444444
Midmean - Closest Observation44.4871052631579
Midmean - True Basic - Statistics Graphics Toolkit44.4919444444444
Midmean - MS Excel (old versions)44.4917948717949
Number of observations72

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 44.5309722222222 & 0.0284299373018165 & 1566.34085223174 \tabularnewline
Geometric Mean & 44.5303287808498 &  &  \tabularnewline
Harmonic Mean & 44.5296862389906 &  &  \tabularnewline
Quadratic Mean & 44.5316165618441 &  &  \tabularnewline
Winsorized Mean ( 1 / 24 ) & 44.5304166666667 & 0.0281354853520201 & 1582.71364824597 \tabularnewline
Winsorized Mean ( 2 / 24 ) & 44.5295833333333 & 0.0277906024776719 & 1602.32522375541 \tabularnewline
Winsorized Mean ( 3 / 24 ) & 44.5304166666667 & 0.027405719377834 & 1624.8585214181 \tabularnewline
Winsorized Mean ( 4 / 24 ) & 44.5348611111111 & 0.0257842507033491 & 1727.21176285051 \tabularnewline
Winsorized Mean ( 5 / 24 ) & 44.5320833333333 & 0.0245936757109734 & 1810.71279692704 \tabularnewline
Winsorized Mean ( 6 / 24 ) & 44.5320833333333 & 0.0245936757109734 & 1810.71279692704 \tabularnewline
Winsorized Mean ( 7 / 24 ) & 44.5311111111111 & 0.0240114047266422 & 1854.58167142137 \tabularnewline
Winsorized Mean ( 8 / 24 ) & 44.5322222222222 & 0.0238238368931684 & 1869.22964684131 \tabularnewline
Winsorized Mean ( 9 / 24 ) & 44.5309722222222 & 0.0226312548934545 & 1967.67578430225 \tabularnewline
Winsorized Mean ( 10 / 24 ) & 44.5323611111111 & 0.0204358734564068 & 2179.12687735644 \tabularnewline
Winsorized Mean ( 11 / 24 ) & 44.5354166666667 & 0.0189863816403607 & 2345.65055681777 \tabularnewline
Winsorized Mean ( 12 / 24 ) & 44.53875 & 0.0180428735406116 & 2468.49538127895 \tabularnewline
Winsorized Mean ( 13 / 24 ) & 44.53875 & 0.0180428735406116 & 2468.49538127895 \tabularnewline
Winsorized Mean ( 14 / 24 ) & 44.53875 & 0.0180428735406116 & 2468.49538127895 \tabularnewline
Winsorized Mean ( 15 / 24 ) & 44.5325 & 0.0168345418615122 & 2645.30513312108 \tabularnewline
Winsorized Mean ( 16 / 24 ) & 44.5347222222222 & 0.0165748317583549 & 2686.88834200526 \tabularnewline
Winsorized Mean ( 17 / 24 ) & 44.5134722222222 & 0.0126669751046928 & 3514.13592071647 \tabularnewline
Winsorized Mean ( 18 / 24 ) & 44.5109722222222 & 0.0114929380954147 & 3872.89758743073 \tabularnewline
Winsorized Mean ( 19 / 24 ) & 44.5030555555556 & 0.0101757615151641 & 4373.4373579055 \tabularnewline
Winsorized Mean ( 20 / 24 ) & 44.4947222222222 & 0.00886777372766517 & 5017.57527748031 \tabularnewline
Winsorized Mean ( 21 / 24 ) & 44.4918055555555 & 0.00843210569496453 & 5276.47626406357 \tabularnewline
Winsorized Mean ( 22 / 24 ) & 44.4918055555556 & 0.00757158427637051 & 5876.15536346946 \tabularnewline
Winsorized Mean ( 23 / 24 ) & 44.4918055555556 & 0.00668812973689216 & 6652.35384267979 \tabularnewline
Winsorized Mean ( 24 / 24 ) & 44.4918055555556 & 0.00668812973689216 & 6652.35384267979 \tabularnewline
Trimmed Mean ( 1 / 24 ) & 44.5297142857143 & 0.0271312822655612 & 1641.26832819242 \tabularnewline
Trimmed Mean ( 2 / 24 ) & 44.5289705882353 & 0.0259331040756979 & 1717.0706005057 \tabularnewline
Trimmed Mean ( 3 / 24 ) & 44.5286363636364 & 0.024722125989814 & 1801.1653359417 \tabularnewline
Trimmed Mean ( 4 / 24 ) & 44.52796875 & 0.0234438070217618 & 1899.34888598369 \tabularnewline
Trimmed Mean ( 5 / 24 ) & 44.5259677419355 & 0.0225273318656389 & 1976.53090954155 \tabularnewline
Trimmed Mean ( 6 / 24 ) & 44.5245 & 0.0218112408172644 & 2041.35566486237 \tabularnewline
Trimmed Mean ( 7 / 24 ) & 44.5229310344828 & 0.0209325951633238 & 2126.9666129354 \tabularnewline
Trimmed Mean ( 8 / 24 ) & 44.5214285714286 & 0.0200136780685866 & 2224.55005116273 \tabularnewline
Trimmed Mean ( 9 / 24 ) & 44.5196296296296 & 0.0189153156417096 & 2353.62869290221 \tabularnewline
Trimmed Mean ( 10 / 24 ) & 44.5178846153846 & 0.0178571855368856 & 2492.99558003857 \tabularnewline
Trimmed Mean ( 11 / 24 ) & 44.5158 & 0.0170834446653083 & 2605.78594493879 \tabularnewline
Trimmed Mean ( 12 / 24 ) & 44.513125 & 0.0164385710421497 & 2707.84637459456 \tabularnewline
Trimmed Mean ( 13 / 24 ) & 44.5097826086957 & 0.0158082994481688 & 2815.59586814707 \tabularnewline
Trimmed Mean ( 14 / 24 ) & 44.5061363636364 & 0.0149672507509336 & 2973.56789862428 \tabularnewline
Trimmed Mean ( 15 / 24 ) & 44.5021428571429 & 0.0138245842823233 & 3219.05830572027 \tabularnewline
Trimmed Mean ( 16 / 24 ) & 44.4985 & 0.0126468299463664 & 3518.54972263505 \tabularnewline
Trimmed Mean ( 17 / 24 ) & 44.4942105263158 & 0.0110193905064364 & 4037.81048510141 \tabularnewline
Trimmed Mean ( 18 / 24 ) & 44.4919444444444 & 0.0101872893449402 & 4367.39773829459 \tabularnewline
Trimmed Mean ( 19 / 24 ) & 44.4897058823529 & 0.00938847943963933 & 4738.75521253334 \tabularnewline
Trimmed Mean ( 20 / 24 ) & 44.488125 & 0.00872331761208384 & 5099.90888539625 \tabularnewline
Trimmed Mean ( 21 / 24 ) & 44.4873333333333 & 0.00823412207120623 & 5402.8022597455 \tabularnewline
Trimmed Mean ( 22 / 24 ) & 44.4867857142857 & 0.00766448504896187 & 5804.27588156249 \tabularnewline
Trimmed Mean ( 23 / 24 ) & 44.4861538461538 & 0.00712691373655419 & 6241.99414930235 \tabularnewline
Trimmed Mean ( 24 / 24 ) & 44.4854166666667 & 0.0066479583513697 & 6691.59075846213 \tabularnewline
Median & 44.49 &  &  \tabularnewline
Midrange & 44.575 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 44.4871052631579 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 44.4919444444444 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 44.4871052631579 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 44.4919444444444 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 44.4919444444444 &  &  \tabularnewline
Midmean - Closest Observation & 44.4871052631579 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 44.4919444444444 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 44.4917948717949 &  &  \tabularnewline
Number of observations & 72 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=240705&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]44.5309722222222[/C][C]0.0284299373018165[/C][C]1566.34085223174[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]44.5303287808498[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]44.5296862389906[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]44.5316165618441[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 24 )[/C][C]44.5304166666667[/C][C]0.0281354853520201[/C][C]1582.71364824597[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 24 )[/C][C]44.5295833333333[/C][C]0.0277906024776719[/C][C]1602.32522375541[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 24 )[/C][C]44.5304166666667[/C][C]0.027405719377834[/C][C]1624.8585214181[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 24 )[/C][C]44.5348611111111[/C][C]0.0257842507033491[/C][C]1727.21176285051[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 24 )[/C][C]44.5320833333333[/C][C]0.0245936757109734[/C][C]1810.71279692704[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 24 )[/C][C]44.5320833333333[/C][C]0.0245936757109734[/C][C]1810.71279692704[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 24 )[/C][C]44.5311111111111[/C][C]0.0240114047266422[/C][C]1854.58167142137[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 24 )[/C][C]44.5322222222222[/C][C]0.0238238368931684[/C][C]1869.22964684131[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 24 )[/C][C]44.5309722222222[/C][C]0.0226312548934545[/C][C]1967.67578430225[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 24 )[/C][C]44.5323611111111[/C][C]0.0204358734564068[/C][C]2179.12687735644[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 24 )[/C][C]44.5354166666667[/C][C]0.0189863816403607[/C][C]2345.65055681777[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 24 )[/C][C]44.53875[/C][C]0.0180428735406116[/C][C]2468.49538127895[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 24 )[/C][C]44.53875[/C][C]0.0180428735406116[/C][C]2468.49538127895[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 24 )[/C][C]44.53875[/C][C]0.0180428735406116[/C][C]2468.49538127895[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 24 )[/C][C]44.5325[/C][C]0.0168345418615122[/C][C]2645.30513312108[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 24 )[/C][C]44.5347222222222[/C][C]0.0165748317583549[/C][C]2686.88834200526[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 24 )[/C][C]44.5134722222222[/C][C]0.0126669751046928[/C][C]3514.13592071647[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 24 )[/C][C]44.5109722222222[/C][C]0.0114929380954147[/C][C]3872.89758743073[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 24 )[/C][C]44.5030555555556[/C][C]0.0101757615151641[/C][C]4373.4373579055[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 24 )[/C][C]44.4947222222222[/C][C]0.00886777372766517[/C][C]5017.57527748031[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 24 )[/C][C]44.4918055555555[/C][C]0.00843210569496453[/C][C]5276.47626406357[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 24 )[/C][C]44.4918055555556[/C][C]0.00757158427637051[/C][C]5876.15536346946[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 24 )[/C][C]44.4918055555556[/C][C]0.00668812973689216[/C][C]6652.35384267979[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 24 )[/C][C]44.4918055555556[/C][C]0.00668812973689216[/C][C]6652.35384267979[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 24 )[/C][C]44.5297142857143[/C][C]0.0271312822655612[/C][C]1641.26832819242[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 24 )[/C][C]44.5289705882353[/C][C]0.0259331040756979[/C][C]1717.0706005057[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 24 )[/C][C]44.5286363636364[/C][C]0.024722125989814[/C][C]1801.1653359417[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 24 )[/C][C]44.52796875[/C][C]0.0234438070217618[/C][C]1899.34888598369[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 24 )[/C][C]44.5259677419355[/C][C]0.0225273318656389[/C][C]1976.53090954155[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 24 )[/C][C]44.5245[/C][C]0.0218112408172644[/C][C]2041.35566486237[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 24 )[/C][C]44.5229310344828[/C][C]0.0209325951633238[/C][C]2126.9666129354[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 24 )[/C][C]44.5214285714286[/C][C]0.0200136780685866[/C][C]2224.55005116273[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 24 )[/C][C]44.5196296296296[/C][C]0.0189153156417096[/C][C]2353.62869290221[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 24 )[/C][C]44.5178846153846[/C][C]0.0178571855368856[/C][C]2492.99558003857[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 24 )[/C][C]44.5158[/C][C]0.0170834446653083[/C][C]2605.78594493879[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 24 )[/C][C]44.513125[/C][C]0.0164385710421497[/C][C]2707.84637459456[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 24 )[/C][C]44.5097826086957[/C][C]0.0158082994481688[/C][C]2815.59586814707[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 24 )[/C][C]44.5061363636364[/C][C]0.0149672507509336[/C][C]2973.56789862428[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 24 )[/C][C]44.5021428571429[/C][C]0.0138245842823233[/C][C]3219.05830572027[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 24 )[/C][C]44.4985[/C][C]0.0126468299463664[/C][C]3518.54972263505[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 24 )[/C][C]44.4942105263158[/C][C]0.0110193905064364[/C][C]4037.81048510141[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 24 )[/C][C]44.4919444444444[/C][C]0.0101872893449402[/C][C]4367.39773829459[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 24 )[/C][C]44.4897058823529[/C][C]0.00938847943963933[/C][C]4738.75521253334[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 24 )[/C][C]44.488125[/C][C]0.00872331761208384[/C][C]5099.90888539625[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 24 )[/C][C]44.4873333333333[/C][C]0.00823412207120623[/C][C]5402.8022597455[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 24 )[/C][C]44.4867857142857[/C][C]0.00766448504896187[/C][C]5804.27588156249[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 24 )[/C][C]44.4861538461538[/C][C]0.00712691373655419[/C][C]6241.99414930235[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 24 )[/C][C]44.4854166666667[/C][C]0.0066479583513697[/C][C]6691.59075846213[/C][/ROW]
[ROW][C]Median[/C][C]44.49[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]44.575[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]44.4871052631579[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]44.4919444444444[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]44.4871052631579[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]44.4919444444444[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]44.4919444444444[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]44.4871052631579[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]44.4919444444444[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]44.4917948717949[/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=240705&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=240705&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 Mean44.53097222222220.02842993730181651566.34085223174
Geometric Mean44.5303287808498
Harmonic Mean44.5296862389906
Quadratic Mean44.5316165618441
Winsorized Mean ( 1 / 24 )44.53041666666670.02813548535202011582.71364824597
Winsorized Mean ( 2 / 24 )44.52958333333330.02779060247767191602.32522375541
Winsorized Mean ( 3 / 24 )44.53041666666670.0274057193778341624.8585214181
Winsorized Mean ( 4 / 24 )44.53486111111110.02578425070334911727.21176285051
Winsorized Mean ( 5 / 24 )44.53208333333330.02459367571097341810.71279692704
Winsorized Mean ( 6 / 24 )44.53208333333330.02459367571097341810.71279692704
Winsorized Mean ( 7 / 24 )44.53111111111110.02401140472664221854.58167142137
Winsorized Mean ( 8 / 24 )44.53222222222220.02382383689316841869.22964684131
Winsorized Mean ( 9 / 24 )44.53097222222220.02263125489345451967.67578430225
Winsorized Mean ( 10 / 24 )44.53236111111110.02043587345640682179.12687735644
Winsorized Mean ( 11 / 24 )44.53541666666670.01898638164036072345.65055681777
Winsorized Mean ( 12 / 24 )44.538750.01804287354061162468.49538127895
Winsorized Mean ( 13 / 24 )44.538750.01804287354061162468.49538127895
Winsorized Mean ( 14 / 24 )44.538750.01804287354061162468.49538127895
Winsorized Mean ( 15 / 24 )44.53250.01683454186151222645.30513312108
Winsorized Mean ( 16 / 24 )44.53472222222220.01657483175835492686.88834200526
Winsorized Mean ( 17 / 24 )44.51347222222220.01266697510469283514.13592071647
Winsorized Mean ( 18 / 24 )44.51097222222220.01149293809541473872.89758743073
Winsorized Mean ( 19 / 24 )44.50305555555560.01017576151516414373.4373579055
Winsorized Mean ( 20 / 24 )44.49472222222220.008867773727665175017.57527748031
Winsorized Mean ( 21 / 24 )44.49180555555550.008432105694964535276.47626406357
Winsorized Mean ( 22 / 24 )44.49180555555560.007571584276370515876.15536346946
Winsorized Mean ( 23 / 24 )44.49180555555560.006688129736892166652.35384267979
Winsorized Mean ( 24 / 24 )44.49180555555560.006688129736892166652.35384267979
Trimmed Mean ( 1 / 24 )44.52971428571430.02713128226556121641.26832819242
Trimmed Mean ( 2 / 24 )44.52897058823530.02593310407569791717.0706005057
Trimmed Mean ( 3 / 24 )44.52863636363640.0247221259898141801.1653359417
Trimmed Mean ( 4 / 24 )44.527968750.02344380702176181899.34888598369
Trimmed Mean ( 5 / 24 )44.52596774193550.02252733186563891976.53090954155
Trimmed Mean ( 6 / 24 )44.52450.02181124081726442041.35566486237
Trimmed Mean ( 7 / 24 )44.52293103448280.02093259516332382126.9666129354
Trimmed Mean ( 8 / 24 )44.52142857142860.02001367806858662224.55005116273
Trimmed Mean ( 9 / 24 )44.51962962962960.01891531564170962353.62869290221
Trimmed Mean ( 10 / 24 )44.51788461538460.01785718553688562492.99558003857
Trimmed Mean ( 11 / 24 )44.51580.01708344466530832605.78594493879
Trimmed Mean ( 12 / 24 )44.5131250.01643857104214972707.84637459456
Trimmed Mean ( 13 / 24 )44.50978260869570.01580829944816882815.59586814707
Trimmed Mean ( 14 / 24 )44.50613636363640.01496725075093362973.56789862428
Trimmed Mean ( 15 / 24 )44.50214285714290.01382458428232333219.05830572027
Trimmed Mean ( 16 / 24 )44.49850.01264682994636643518.54972263505
Trimmed Mean ( 17 / 24 )44.49421052631580.01101939050643644037.81048510141
Trimmed Mean ( 18 / 24 )44.49194444444440.01018728934494024367.39773829459
Trimmed Mean ( 19 / 24 )44.48970588235290.009388479439639334738.75521253334
Trimmed Mean ( 20 / 24 )44.4881250.008723317612083845099.90888539625
Trimmed Mean ( 21 / 24 )44.48733333333330.008234122071206235402.8022597455
Trimmed Mean ( 22 / 24 )44.48678571428570.007664485048961875804.27588156249
Trimmed Mean ( 23 / 24 )44.48615384615380.007126913736554196241.99414930235
Trimmed Mean ( 24 / 24 )44.48541666666670.00664795835136976691.59075846213
Median44.49
Midrange44.575
Midmean - Weighted Average at Xnp44.4871052631579
Midmean - Weighted Average at X(n+1)p44.4919444444444
Midmean - Empirical Distribution Function44.4871052631579
Midmean - Empirical Distribution Function - Averaging44.4919444444444
Midmean - Empirical Distribution Function - Interpolation44.4919444444444
Midmean - Closest Observation44.4871052631579
Midmean - True Basic - Statistics Graphics Toolkit44.4919444444444
Midmean - MS Excel (old versions)44.4917948717949
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')