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Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationFri, 04 Mar 2016 17:17:58 +0000
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2016/Mar/04/t1457111964gpodjxgqguwb321.htm/, Retrieved Sat, 18 May 2024 14:50:34 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=293405, Retrieved Sat, 18 May 2024 14:50:34 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact51
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [] [2016-03-04 17:17:58] [3cc5eb308fa11ebf92933824162ee6d9] [Current]
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Dataseries X:
7,4361
7,4324
7,4367
7,4368
7,4456
7,4564
7,4597
7,4537
7,4639
7,4593
7,4438
7,4415
7,4317
7,4343
7,4281
7,4281
7,4305
7,425
7,4309
7,4361
7,4495
7,4393
7,4367
7,4343
7,4433
7,4463
7,4588
7,4586
7,4621
7,4581
7,4604
7,4557
7,4524
7,45
7,4446
7,4557
7,4534
7,4599
7,4592
7,4512
7,4514
7,4471
7,4442
7,4424
7,4426
7,4416
7,4498
7,4547
7,455
7,4573
7,4506
7,4398
7,435
7,4349
7,4457
7,459
7,4589
7,4555
7,458
7,4593
7,4625
7,4628
7,4522
7,4423
7,4501
7,4623
7,4617
7,4605




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'George Udny Yule' @ yule.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 & 'George Udny Yule' @ yule.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=293405&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]'George Udny Yule' @ yule.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=293405&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=293405&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'George Udny Yule' @ yule.wessa.net







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean7.448195588235290.001298840290824495734.49687452124
Geometric Mean7.44818799799495
Harmonic Mean7.44818040513286
Quadratic Mean7.4482031758456
Winsorized Mean ( 1 / 22 )7.4482250.001284600789305425798.08533671168
Winsorized Mean ( 2 / 22 )7.448216176470590.001283120664804485804.76675403365
Winsorized Mean ( 3 / 22 )7.448313235294120.001258067738844515920.438944039
Winsorized Mean ( 4 / 22 )7.4483250.001251193240830495952.97733150804
Winsorized Mean ( 5 / 22 )7.448354411764710.001234365675488116034.15548542321
Winsorized Mean ( 6 / 22 )7.448310294117650.001205522374480296178.49195650864
Winsorized Mean ( 7 / 22 )7.448495588235290.001166917466334966383.05261779092
Winsorized Mean ( 8 / 22 )7.448436764705880.001158093450801416431.63706655234
Winsorized Mean ( 9 / 22 )7.448489705882350.00113989460047916534.36703950674
Winsorized Mean ( 10 / 22 )7.448445588235290.001128739874474956598.90357085155
Winsorized Mean ( 11 / 22 )7.448623529411760.001097763145193826785.27381978799
Winsorized Mean ( 12 / 22 )7.448605882352940.001095208420944186801.08529108229
Winsorized Mean ( 13 / 22 )7.448682352941180.001070337841802616959.18808251841
Winsorized Mean ( 14 / 22 )7.448661764705880.001067383032581576978.43373684757
Winsorized Mean ( 15 / 22 )7.448661764705880.001060544341098997023.43266193585
Winsorized Mean ( 16 / 22 )7.449202941176470.0009591387767680987766.55383100787
Winsorized Mean ( 17 / 22 )7.449202941176470.0009218448564530268080.75555125263
Winsorized Mean ( 18 / 22 )7.449626470588240.0008516100994003378747.6962471839
Winsorized Mean ( 19 / 22 )7.449458823529410.000819291743461889092.55937579948
Winsorized Mean ( 20 / 22 )7.44940.0007527532140277779896.20484001695
Winsorized Mean ( 21 / 22 )7.449214705882350.00071882764979155110363.0052461706
Winsorized Mean ( 22 / 22 )7.449279411764710.0007097049518133210496.3046865201
Trimmed Mean ( 1 / 22 )7.448309090909090.001268260058911045872.85631095598
Trimmed Mean ( 2 / 22 )7.44839843750.001248162324154195967.49180243632
Trimmed Mean ( 3 / 22 )7.448498387096770.001224419896177316083.28761264931
Trimmed Mean ( 4 / 22 )7.448568333333330.001206768790353396172.32430344182
Trimmed Mean ( 5 / 22 )7.448639655172410.001187209867521866274.07155124179
Trimmed Mean ( 6 / 22 )7.448708928571430.001168013289334966377.24672877015
Trimmed Mean ( 7 / 22 )7.448792592592590.001151749047746816467.37464829237
Trimmed Mean ( 8 / 22 )7.448848076923080.001140834980342326529.29495086832
Trimmed Mean ( 9 / 22 )7.4489180.001128038536033026603.42511541819
Trimmed Mean ( 10 / 22 )7.448985416666670.001114973004727336680.86616006308
Trimmed Mean ( 11 / 22 )7.44906521739130.001099473819656126775.1183195259
Trimmed Mean ( 12 / 22 )7.449127272727270.001085481565349786862.50924061241
Trimmed Mean ( 13 / 22 )7.449197619047620.001066300866947476986.01853374895
Trimmed Mean ( 14 / 22 )7.4492650.001045580135863737124.52804379869
Trimmed Mean ( 15 / 22 )7.449342105263160.001017105700205467324.05894860129
Trimmed Mean ( 16 / 22 )7.449427777777780.0009789418575655177609.67336334295
Trimmed Mean ( 17 / 22 )7.449455882352940.0009538195210441927810.13149552408
Trimmed Mean ( 18 / 22 )7.44948750.000927174318961628034.61371572822
Trimmed Mean ( 19 / 22 )7.449470.0009075057391921358208.73045566802
Trimmed Mean ( 20 / 22 )7.449471428571430.0008858508172632448409.3972522212
Trimmed Mean ( 21 / 22 )7.449480769230770.000871621287394398546.69439235487
Trimmed Mean ( 22 / 22 )7.449516666666670.0008565321610979768697.2994185265
Median7.45005
Midrange7.44445
Midmean - Weighted Average at Xnp7.44916571428571
Midmean - Weighted Average at X(n+1)p7.44945588235294
Midmean - Empirical Distribution Function7.44916571428571
Midmean - Empirical Distribution Function - Averaging7.44945588235294
Midmean - Empirical Distribution Function - Interpolation7.44945588235294
Midmean - Closest Observation7.44916571428571
Midmean - True Basic - Statistics Graphics Toolkit7.44945588235294
Midmean - MS Excel (old versions)7.44942777777778
Number of observations68

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 7.44819558823529 & 0.00129884029082449 & 5734.49687452124 \tabularnewline
Geometric Mean & 7.44818799799495 &  &  \tabularnewline
Harmonic Mean & 7.44818040513286 &  &  \tabularnewline
Quadratic Mean & 7.4482031758456 &  &  \tabularnewline
Winsorized Mean ( 1 / 22 ) & 7.448225 & 0.00128460078930542 & 5798.08533671168 \tabularnewline
Winsorized Mean ( 2 / 22 ) & 7.44821617647059 & 0.00128312066480448 & 5804.76675403365 \tabularnewline
Winsorized Mean ( 3 / 22 ) & 7.44831323529412 & 0.00125806773884451 & 5920.438944039 \tabularnewline
Winsorized Mean ( 4 / 22 ) & 7.448325 & 0.00125119324083049 & 5952.97733150804 \tabularnewline
Winsorized Mean ( 5 / 22 ) & 7.44835441176471 & 0.00123436567548811 & 6034.15548542321 \tabularnewline
Winsorized Mean ( 6 / 22 ) & 7.44831029411765 & 0.00120552237448029 & 6178.49195650864 \tabularnewline
Winsorized Mean ( 7 / 22 ) & 7.44849558823529 & 0.00116691746633496 & 6383.05261779092 \tabularnewline
Winsorized Mean ( 8 / 22 ) & 7.44843676470588 & 0.00115809345080141 & 6431.63706655234 \tabularnewline
Winsorized Mean ( 9 / 22 ) & 7.44848970588235 & 0.0011398946004791 & 6534.36703950674 \tabularnewline
Winsorized Mean ( 10 / 22 ) & 7.44844558823529 & 0.00112873987447495 & 6598.90357085155 \tabularnewline
Winsorized Mean ( 11 / 22 ) & 7.44862352941176 & 0.00109776314519382 & 6785.27381978799 \tabularnewline
Winsorized Mean ( 12 / 22 ) & 7.44860588235294 & 0.00109520842094418 & 6801.08529108229 \tabularnewline
Winsorized Mean ( 13 / 22 ) & 7.44868235294118 & 0.00107033784180261 & 6959.18808251841 \tabularnewline
Winsorized Mean ( 14 / 22 ) & 7.44866176470588 & 0.00106738303258157 & 6978.43373684757 \tabularnewline
Winsorized Mean ( 15 / 22 ) & 7.44866176470588 & 0.00106054434109899 & 7023.43266193585 \tabularnewline
Winsorized Mean ( 16 / 22 ) & 7.44920294117647 & 0.000959138776768098 & 7766.55383100787 \tabularnewline
Winsorized Mean ( 17 / 22 ) & 7.44920294117647 & 0.000921844856453026 & 8080.75555125263 \tabularnewline
Winsorized Mean ( 18 / 22 ) & 7.44962647058824 & 0.000851610099400337 & 8747.6962471839 \tabularnewline
Winsorized Mean ( 19 / 22 ) & 7.44945882352941 & 0.00081929174346188 & 9092.55937579948 \tabularnewline
Winsorized Mean ( 20 / 22 ) & 7.4494 & 0.000752753214027777 & 9896.20484001695 \tabularnewline
Winsorized Mean ( 21 / 22 ) & 7.44921470588235 & 0.000718827649791551 & 10363.0052461706 \tabularnewline
Winsorized Mean ( 22 / 22 ) & 7.44927941176471 & 0.00070970495181332 & 10496.3046865201 \tabularnewline
Trimmed Mean ( 1 / 22 ) & 7.44830909090909 & 0.00126826005891104 & 5872.85631095598 \tabularnewline
Trimmed Mean ( 2 / 22 ) & 7.4483984375 & 0.00124816232415419 & 5967.49180243632 \tabularnewline
Trimmed Mean ( 3 / 22 ) & 7.44849838709677 & 0.00122441989617731 & 6083.28761264931 \tabularnewline
Trimmed Mean ( 4 / 22 ) & 7.44856833333333 & 0.00120676879035339 & 6172.32430344182 \tabularnewline
Trimmed Mean ( 5 / 22 ) & 7.44863965517241 & 0.00118720986752186 & 6274.07155124179 \tabularnewline
Trimmed Mean ( 6 / 22 ) & 7.44870892857143 & 0.00116801328933496 & 6377.24672877015 \tabularnewline
Trimmed Mean ( 7 / 22 ) & 7.44879259259259 & 0.00115174904774681 & 6467.37464829237 \tabularnewline
Trimmed Mean ( 8 / 22 ) & 7.44884807692308 & 0.00114083498034232 & 6529.29495086832 \tabularnewline
Trimmed Mean ( 9 / 22 ) & 7.448918 & 0.00112803853603302 & 6603.42511541819 \tabularnewline
Trimmed Mean ( 10 / 22 ) & 7.44898541666667 & 0.00111497300472733 & 6680.86616006308 \tabularnewline
Trimmed Mean ( 11 / 22 ) & 7.4490652173913 & 0.00109947381965612 & 6775.1183195259 \tabularnewline
Trimmed Mean ( 12 / 22 ) & 7.44912727272727 & 0.00108548156534978 & 6862.50924061241 \tabularnewline
Trimmed Mean ( 13 / 22 ) & 7.44919761904762 & 0.00106630086694747 & 6986.01853374895 \tabularnewline
Trimmed Mean ( 14 / 22 ) & 7.449265 & 0.00104558013586373 & 7124.52804379869 \tabularnewline
Trimmed Mean ( 15 / 22 ) & 7.44934210526316 & 0.00101710570020546 & 7324.05894860129 \tabularnewline
Trimmed Mean ( 16 / 22 ) & 7.44942777777778 & 0.000978941857565517 & 7609.67336334295 \tabularnewline
Trimmed Mean ( 17 / 22 ) & 7.44945588235294 & 0.000953819521044192 & 7810.13149552408 \tabularnewline
Trimmed Mean ( 18 / 22 ) & 7.4494875 & 0.00092717431896162 & 8034.61371572822 \tabularnewline
Trimmed Mean ( 19 / 22 ) & 7.44947 & 0.000907505739192135 & 8208.73045566802 \tabularnewline
Trimmed Mean ( 20 / 22 ) & 7.44947142857143 & 0.000885850817263244 & 8409.3972522212 \tabularnewline
Trimmed Mean ( 21 / 22 ) & 7.44948076923077 & 0.00087162128739439 & 8546.69439235487 \tabularnewline
Trimmed Mean ( 22 / 22 ) & 7.44951666666667 & 0.000856532161097976 & 8697.2994185265 \tabularnewline
Median & 7.45005 &  &  \tabularnewline
Midrange & 7.44445 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 7.44916571428571 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 7.44945588235294 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 7.44916571428571 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 7.44945588235294 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 7.44945588235294 &  &  \tabularnewline
Midmean - Closest Observation & 7.44916571428571 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 7.44945588235294 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 7.44942777777778 &  &  \tabularnewline
Number of observations & 68 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=293405&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]7.44819558823529[/C][C]0.00129884029082449[/C][C]5734.49687452124[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]7.44818799799495[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]7.44818040513286[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]7.4482031758456[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 22 )[/C][C]7.448225[/C][C]0.00128460078930542[/C][C]5798.08533671168[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 22 )[/C][C]7.44821617647059[/C][C]0.00128312066480448[/C][C]5804.76675403365[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 22 )[/C][C]7.44831323529412[/C][C]0.00125806773884451[/C][C]5920.438944039[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 22 )[/C][C]7.448325[/C][C]0.00125119324083049[/C][C]5952.97733150804[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 22 )[/C][C]7.44835441176471[/C][C]0.00123436567548811[/C][C]6034.15548542321[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 22 )[/C][C]7.44831029411765[/C][C]0.00120552237448029[/C][C]6178.49195650864[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 22 )[/C][C]7.44849558823529[/C][C]0.00116691746633496[/C][C]6383.05261779092[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 22 )[/C][C]7.44843676470588[/C][C]0.00115809345080141[/C][C]6431.63706655234[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 22 )[/C][C]7.44848970588235[/C][C]0.0011398946004791[/C][C]6534.36703950674[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 22 )[/C][C]7.44844558823529[/C][C]0.00112873987447495[/C][C]6598.90357085155[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 22 )[/C][C]7.44862352941176[/C][C]0.00109776314519382[/C][C]6785.27381978799[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 22 )[/C][C]7.44860588235294[/C][C]0.00109520842094418[/C][C]6801.08529108229[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 22 )[/C][C]7.44868235294118[/C][C]0.00107033784180261[/C][C]6959.18808251841[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 22 )[/C][C]7.44866176470588[/C][C]0.00106738303258157[/C][C]6978.43373684757[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 22 )[/C][C]7.44866176470588[/C][C]0.00106054434109899[/C][C]7023.43266193585[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 22 )[/C][C]7.44920294117647[/C][C]0.000959138776768098[/C][C]7766.55383100787[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 22 )[/C][C]7.44920294117647[/C][C]0.000921844856453026[/C][C]8080.75555125263[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 22 )[/C][C]7.44962647058824[/C][C]0.000851610099400337[/C][C]8747.6962471839[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 22 )[/C][C]7.44945882352941[/C][C]0.00081929174346188[/C][C]9092.55937579948[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 22 )[/C][C]7.4494[/C][C]0.000752753214027777[/C][C]9896.20484001695[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 22 )[/C][C]7.44921470588235[/C][C]0.000718827649791551[/C][C]10363.0052461706[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 22 )[/C][C]7.44927941176471[/C][C]0.00070970495181332[/C][C]10496.3046865201[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 22 )[/C][C]7.44830909090909[/C][C]0.00126826005891104[/C][C]5872.85631095598[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 22 )[/C][C]7.4483984375[/C][C]0.00124816232415419[/C][C]5967.49180243632[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 22 )[/C][C]7.44849838709677[/C][C]0.00122441989617731[/C][C]6083.28761264931[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 22 )[/C][C]7.44856833333333[/C][C]0.00120676879035339[/C][C]6172.32430344182[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 22 )[/C][C]7.44863965517241[/C][C]0.00118720986752186[/C][C]6274.07155124179[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 22 )[/C][C]7.44870892857143[/C][C]0.00116801328933496[/C][C]6377.24672877015[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 22 )[/C][C]7.44879259259259[/C][C]0.00115174904774681[/C][C]6467.37464829237[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 22 )[/C][C]7.44884807692308[/C][C]0.00114083498034232[/C][C]6529.29495086832[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 22 )[/C][C]7.448918[/C][C]0.00112803853603302[/C][C]6603.42511541819[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 22 )[/C][C]7.44898541666667[/C][C]0.00111497300472733[/C][C]6680.86616006308[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 22 )[/C][C]7.4490652173913[/C][C]0.00109947381965612[/C][C]6775.1183195259[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 22 )[/C][C]7.44912727272727[/C][C]0.00108548156534978[/C][C]6862.50924061241[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 22 )[/C][C]7.44919761904762[/C][C]0.00106630086694747[/C][C]6986.01853374895[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 22 )[/C][C]7.449265[/C][C]0.00104558013586373[/C][C]7124.52804379869[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 22 )[/C][C]7.44934210526316[/C][C]0.00101710570020546[/C][C]7324.05894860129[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 22 )[/C][C]7.44942777777778[/C][C]0.000978941857565517[/C][C]7609.67336334295[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 22 )[/C][C]7.44945588235294[/C][C]0.000953819521044192[/C][C]7810.13149552408[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 22 )[/C][C]7.4494875[/C][C]0.00092717431896162[/C][C]8034.61371572822[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 22 )[/C][C]7.44947[/C][C]0.000907505739192135[/C][C]8208.73045566802[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 22 )[/C][C]7.44947142857143[/C][C]0.000885850817263244[/C][C]8409.3972522212[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 22 )[/C][C]7.44948076923077[/C][C]0.00087162128739439[/C][C]8546.69439235487[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 22 )[/C][C]7.44951666666667[/C][C]0.000856532161097976[/C][C]8697.2994185265[/C][/ROW]
[ROW][C]Median[/C][C]7.45005[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]7.44445[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]7.44916571428571[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]7.44945588235294[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]7.44916571428571[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]7.44945588235294[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]7.44945588235294[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]7.44916571428571[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]7.44945588235294[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]7.44942777777778[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]68[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=293405&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=293405&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 Mean7.448195588235290.001298840290824495734.49687452124
Geometric Mean7.44818799799495
Harmonic Mean7.44818040513286
Quadratic Mean7.4482031758456
Winsorized Mean ( 1 / 22 )7.4482250.001284600789305425798.08533671168
Winsorized Mean ( 2 / 22 )7.448216176470590.001283120664804485804.76675403365
Winsorized Mean ( 3 / 22 )7.448313235294120.001258067738844515920.438944039
Winsorized Mean ( 4 / 22 )7.4483250.001251193240830495952.97733150804
Winsorized Mean ( 5 / 22 )7.448354411764710.001234365675488116034.15548542321
Winsorized Mean ( 6 / 22 )7.448310294117650.001205522374480296178.49195650864
Winsorized Mean ( 7 / 22 )7.448495588235290.001166917466334966383.05261779092
Winsorized Mean ( 8 / 22 )7.448436764705880.001158093450801416431.63706655234
Winsorized Mean ( 9 / 22 )7.448489705882350.00113989460047916534.36703950674
Winsorized Mean ( 10 / 22 )7.448445588235290.001128739874474956598.90357085155
Winsorized Mean ( 11 / 22 )7.448623529411760.001097763145193826785.27381978799
Winsorized Mean ( 12 / 22 )7.448605882352940.001095208420944186801.08529108229
Winsorized Mean ( 13 / 22 )7.448682352941180.001070337841802616959.18808251841
Winsorized Mean ( 14 / 22 )7.448661764705880.001067383032581576978.43373684757
Winsorized Mean ( 15 / 22 )7.448661764705880.001060544341098997023.43266193585
Winsorized Mean ( 16 / 22 )7.449202941176470.0009591387767680987766.55383100787
Winsorized Mean ( 17 / 22 )7.449202941176470.0009218448564530268080.75555125263
Winsorized Mean ( 18 / 22 )7.449626470588240.0008516100994003378747.6962471839
Winsorized Mean ( 19 / 22 )7.449458823529410.000819291743461889092.55937579948
Winsorized Mean ( 20 / 22 )7.44940.0007527532140277779896.20484001695
Winsorized Mean ( 21 / 22 )7.449214705882350.00071882764979155110363.0052461706
Winsorized Mean ( 22 / 22 )7.449279411764710.0007097049518133210496.3046865201
Trimmed Mean ( 1 / 22 )7.448309090909090.001268260058911045872.85631095598
Trimmed Mean ( 2 / 22 )7.44839843750.001248162324154195967.49180243632
Trimmed Mean ( 3 / 22 )7.448498387096770.001224419896177316083.28761264931
Trimmed Mean ( 4 / 22 )7.448568333333330.001206768790353396172.32430344182
Trimmed Mean ( 5 / 22 )7.448639655172410.001187209867521866274.07155124179
Trimmed Mean ( 6 / 22 )7.448708928571430.001168013289334966377.24672877015
Trimmed Mean ( 7 / 22 )7.448792592592590.001151749047746816467.37464829237
Trimmed Mean ( 8 / 22 )7.448848076923080.001140834980342326529.29495086832
Trimmed Mean ( 9 / 22 )7.4489180.001128038536033026603.42511541819
Trimmed Mean ( 10 / 22 )7.448985416666670.001114973004727336680.86616006308
Trimmed Mean ( 11 / 22 )7.44906521739130.001099473819656126775.1183195259
Trimmed Mean ( 12 / 22 )7.449127272727270.001085481565349786862.50924061241
Trimmed Mean ( 13 / 22 )7.449197619047620.001066300866947476986.01853374895
Trimmed Mean ( 14 / 22 )7.4492650.001045580135863737124.52804379869
Trimmed Mean ( 15 / 22 )7.449342105263160.001017105700205467324.05894860129
Trimmed Mean ( 16 / 22 )7.449427777777780.0009789418575655177609.67336334295
Trimmed Mean ( 17 / 22 )7.449455882352940.0009538195210441927810.13149552408
Trimmed Mean ( 18 / 22 )7.44948750.000927174318961628034.61371572822
Trimmed Mean ( 19 / 22 )7.449470.0009075057391921358208.73045566802
Trimmed Mean ( 20 / 22 )7.449471428571430.0008858508172632448409.3972522212
Trimmed Mean ( 21 / 22 )7.449480769230770.000871621287394398546.69439235487
Trimmed Mean ( 22 / 22 )7.449516666666670.0008565321610979768697.2994185265
Median7.45005
Midrange7.44445
Midmean - Weighted Average at Xnp7.44916571428571
Midmean - Weighted Average at X(n+1)p7.44945588235294
Midmean - Empirical Distribution Function7.44916571428571
Midmean - Empirical Distribution Function - Averaging7.44945588235294
Midmean - Empirical Distribution Function - Interpolation7.44945588235294
Midmean - Closest Observation7.44916571428571
Midmean - True Basic - Statistics Graphics Toolkit7.44945588235294
Midmean - MS Excel (old versions)7.44942777777778
Number of observations68



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')