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Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationFri, 12 Oct 2012 10:09:59 -0400
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2012/Oct/12/t135005121010yxs9na5bb81uw.htm/, Retrieved Mon, 13 May 2024 08:29:29 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=175482, Retrieved Mon, 13 May 2024 08:29:29 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact66
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [] [2012-10-12 14:09:59] [db26a86bf4adac007852ad52c5e0cac3] [Current]
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Dataseries X:
3.65
3.66
3.69
3.7
3.7
3.71
3.71
3.71
3.72
3.72
3.73
3.74
3.78
3.78
3.79
3.79
3.8
3.81
3.83
3.84
3.88
3.91
3.96
3.96
3.97
3.98
3.99
3.99
4
4
4.02
4.02
4.02
4.03
4.03
4.03
4.04
4.04
4.05
4.05
4.05
4.05
4.06
4.06
4.06
4.06
4.07
4.07
4.08
4.08
4.08
4.09
4.09
4.09
4.09
4.1
4.1
4.11
4.11
4.12
4.12
4.12
4.12
4.12
4.15
4.15
4.15
4.15
4.16
4.16
4.16
4.2




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Sir Maurice George Kendall' @ kendall.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 & 2 seconds \tabularnewline
R Server & 'Sir Maurice George Kendall' @ kendall.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=175482&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]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Sir Maurice George Kendall' @ kendall.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=175482&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=175482&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 time2 seconds
R Server'Sir Maurice George Kendall' @ kendall.wessa.net







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean3.975138888888890.0186496328379525213.148372594198
Geometric Mean3.97197043338947
Harmonic Mean3.96874063240233
Quadratic Mean3.97824378477628
Winsorized Mean ( 1 / 24 )3.974722222222220.0185296491067177214.506070748055
Winsorized Mean ( 2 / 24 )3.975555555555560.0183385490754967216.786810079078
Winsorized Mean ( 3 / 24 )3.975972222222220.0182484802486631217.879635347361
Winsorized Mean ( 4 / 24 )3.975416666666670.0181714335607453218.772869701074
Winsorized Mean ( 5 / 24 )3.976111111111110.0180251037294756220.587419123096
Winsorized Mean ( 6 / 24 )3.976111111111110.0180251037294756220.587419123096
Winsorized Mean ( 7 / 24 )3.976111111111110.0180251037294756220.587419123096
Winsorized Mean ( 8 / 24 )3.973888888888890.0173707563191699228.768904236104
Winsorized Mean ( 9 / 24 )3.973888888888890.0173707563191699228.768904236104
Winsorized Mean ( 10 / 24 )3.975277777777780.0170873804002993232.644073266383
Winsorized Mean ( 11 / 24 )3.976805555555560.0167810935664733236.981311128659
Winsorized Mean ( 12 / 24 )3.983472222222220.0155004666018696256.99047161211
Winsorized Mean ( 13 / 24 )3.981666666666670.0152816540821568260.552074092278
Winsorized Mean ( 14 / 24 )3.983611111111110.0149232590352444266.939755029581
Winsorized Mean ( 15 / 24 )3.981527777777780.0146805574987821271.210938556529
Winsorized Mean ( 16 / 24 )3.983750.0142749075350077279.073611526398
Winsorized Mean ( 17 / 24 )3.983750.0135825268345499293.299623002882
Winsorized Mean ( 18 / 24 )3.988750.0126913175932809314.289668561423
Winsorized Mean ( 19 / 24 )3.991388888888890.0122287559005252326.39370033688
Winsorized Mean ( 20 / 24 )4.00250.0103286184912312387.515523339163
Winsorized Mean ( 21 / 24 )4.008333333333330.00853969833040575469.376455496278
Winsorized Mean ( 22 / 24 )4.023611111111110.00617083844282631652.036372105741
Winsorized Mean ( 23 / 24 )4.023611111111110.00617083844282631652.036372105741
Winsorized Mean ( 24 / 24 )4.023611111111110.00526788464089814763.800156114488
Trimmed Mean ( 1 / 24 )3.976571428571430.0183229434676943217.026889570589
Trimmed Mean ( 2 / 24 )3.978529411764710.0180688186757044220.187577459853
Trimmed Mean ( 3 / 24 )3.980151515151510.0178774544167104222.635248977684
Trimmed Mean ( 4 / 24 )3.981718750.0176784477333535225.230111266374
Trimmed Mean ( 5 / 24 )3.983548387096770.0174544762179208228.225031640124
Trimmed Mean ( 6 / 24 )3.985333333333330.017218218354827231.460262101745
Trimmed Mean ( 7 / 24 )3.987241379310340.0169190684197348235.665539047027
Trimmed Mean ( 8 / 24 )3.989285714285710.016541677278877241.165732291239
Trimmed Mean ( 9 / 24 )3.991851851851850.016218446921646246.130339799929
Trimmed Mean ( 10 / 24 )3.994615384615380.0158005611582517252.814779463022
Trimmed Mean ( 11 / 24 )3.99740.0153325317743758260.713628957258
Trimmed Mean ( 12 / 24 )4.000208333333330.0148021514134169270.245062464871
Trimmed Mean ( 13 / 24 )4.002391304347830.0144335384482152277.297997210293
Trimmed Mean ( 14 / 24 )4.0050.0139823960599451286.431594615819
Trimmed Mean ( 15 / 24 )4.007619047619050.013468289956654297.55960560079
Trimmed Mean ( 16 / 24 )4.010750.0128121912095372313.041690871304
Trimmed Mean ( 17 / 24 )4.013947368421050.0120249827287988333.8006763875
Trimmed Mean ( 18 / 24 )4.01750.011108233754421361.668658476068
Trimmed Mean ( 19 / 24 )4.020882352941180.0101096276720876397.728035429309
Trimmed Mean ( 20 / 24 )4.0243750.00879811082177634457.413538147213
Trimmed Mean ( 21 / 24 )4.0270.00768862422860784523.760803007687
Trimmed Mean ( 22 / 24 )4.029285714285710.00678327720090209594.002809401608
Trimmed Mean ( 23 / 24 )4.030.00649259933723359620.706714010344
Trimmed Mean ( 24 / 24 )4.030833333333330.00601678409295662669.931523395017
Median4.035
Midrange3.925
Midmean - Weighted Average at Xnp4.01394736842105
Midmean - Weighted Average at X(n+1)p4.01945945945946
Midmean - Empirical Distribution Function4.01394736842105
Midmean - Empirical Distribution Function - Averaging4.01945945945946
Midmean - Empirical Distribution Function - Interpolation4.01945945945946
Midmean - Closest Observation4.01394736842105
Midmean - True Basic - Statistics Graphics Toolkit4.01945945945946
Midmean - MS Excel (old versions)4.01394736842105
Number of observations72

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 3.97513888888889 & 0.0186496328379525 & 213.148372594198 \tabularnewline
Geometric Mean & 3.97197043338947 &  &  \tabularnewline
Harmonic Mean & 3.96874063240233 &  &  \tabularnewline
Quadratic Mean & 3.97824378477628 &  &  \tabularnewline
Winsorized Mean ( 1 / 24 ) & 3.97472222222222 & 0.0185296491067177 & 214.506070748055 \tabularnewline
Winsorized Mean ( 2 / 24 ) & 3.97555555555556 & 0.0183385490754967 & 216.786810079078 \tabularnewline
Winsorized Mean ( 3 / 24 ) & 3.97597222222222 & 0.0182484802486631 & 217.879635347361 \tabularnewline
Winsorized Mean ( 4 / 24 ) & 3.97541666666667 & 0.0181714335607453 & 218.772869701074 \tabularnewline
Winsorized Mean ( 5 / 24 ) & 3.97611111111111 & 0.0180251037294756 & 220.587419123096 \tabularnewline
Winsorized Mean ( 6 / 24 ) & 3.97611111111111 & 0.0180251037294756 & 220.587419123096 \tabularnewline
Winsorized Mean ( 7 / 24 ) & 3.97611111111111 & 0.0180251037294756 & 220.587419123096 \tabularnewline
Winsorized Mean ( 8 / 24 ) & 3.97388888888889 & 0.0173707563191699 & 228.768904236104 \tabularnewline
Winsorized Mean ( 9 / 24 ) & 3.97388888888889 & 0.0173707563191699 & 228.768904236104 \tabularnewline
Winsorized Mean ( 10 / 24 ) & 3.97527777777778 & 0.0170873804002993 & 232.644073266383 \tabularnewline
Winsorized Mean ( 11 / 24 ) & 3.97680555555556 & 0.0167810935664733 & 236.981311128659 \tabularnewline
Winsorized Mean ( 12 / 24 ) & 3.98347222222222 & 0.0155004666018696 & 256.99047161211 \tabularnewline
Winsorized Mean ( 13 / 24 ) & 3.98166666666667 & 0.0152816540821568 & 260.552074092278 \tabularnewline
Winsorized Mean ( 14 / 24 ) & 3.98361111111111 & 0.0149232590352444 & 266.939755029581 \tabularnewline
Winsorized Mean ( 15 / 24 ) & 3.98152777777778 & 0.0146805574987821 & 271.210938556529 \tabularnewline
Winsorized Mean ( 16 / 24 ) & 3.98375 & 0.0142749075350077 & 279.073611526398 \tabularnewline
Winsorized Mean ( 17 / 24 ) & 3.98375 & 0.0135825268345499 & 293.299623002882 \tabularnewline
Winsorized Mean ( 18 / 24 ) & 3.98875 & 0.0126913175932809 & 314.289668561423 \tabularnewline
Winsorized Mean ( 19 / 24 ) & 3.99138888888889 & 0.0122287559005252 & 326.39370033688 \tabularnewline
Winsorized Mean ( 20 / 24 ) & 4.0025 & 0.0103286184912312 & 387.515523339163 \tabularnewline
Winsorized Mean ( 21 / 24 ) & 4.00833333333333 & 0.00853969833040575 & 469.376455496278 \tabularnewline
Winsorized Mean ( 22 / 24 ) & 4.02361111111111 & 0.00617083844282631 & 652.036372105741 \tabularnewline
Winsorized Mean ( 23 / 24 ) & 4.02361111111111 & 0.00617083844282631 & 652.036372105741 \tabularnewline
Winsorized Mean ( 24 / 24 ) & 4.02361111111111 & 0.00526788464089814 & 763.800156114488 \tabularnewline
Trimmed Mean ( 1 / 24 ) & 3.97657142857143 & 0.0183229434676943 & 217.026889570589 \tabularnewline
Trimmed Mean ( 2 / 24 ) & 3.97852941176471 & 0.0180688186757044 & 220.187577459853 \tabularnewline
Trimmed Mean ( 3 / 24 ) & 3.98015151515151 & 0.0178774544167104 & 222.635248977684 \tabularnewline
Trimmed Mean ( 4 / 24 ) & 3.98171875 & 0.0176784477333535 & 225.230111266374 \tabularnewline
Trimmed Mean ( 5 / 24 ) & 3.98354838709677 & 0.0174544762179208 & 228.225031640124 \tabularnewline
Trimmed Mean ( 6 / 24 ) & 3.98533333333333 & 0.017218218354827 & 231.460262101745 \tabularnewline
Trimmed Mean ( 7 / 24 ) & 3.98724137931034 & 0.0169190684197348 & 235.665539047027 \tabularnewline
Trimmed Mean ( 8 / 24 ) & 3.98928571428571 & 0.016541677278877 & 241.165732291239 \tabularnewline
Trimmed Mean ( 9 / 24 ) & 3.99185185185185 & 0.016218446921646 & 246.130339799929 \tabularnewline
Trimmed Mean ( 10 / 24 ) & 3.99461538461538 & 0.0158005611582517 & 252.814779463022 \tabularnewline
Trimmed Mean ( 11 / 24 ) & 3.9974 & 0.0153325317743758 & 260.713628957258 \tabularnewline
Trimmed Mean ( 12 / 24 ) & 4.00020833333333 & 0.0148021514134169 & 270.245062464871 \tabularnewline
Trimmed Mean ( 13 / 24 ) & 4.00239130434783 & 0.0144335384482152 & 277.297997210293 \tabularnewline
Trimmed Mean ( 14 / 24 ) & 4.005 & 0.0139823960599451 & 286.431594615819 \tabularnewline
Trimmed Mean ( 15 / 24 ) & 4.00761904761905 & 0.013468289956654 & 297.55960560079 \tabularnewline
Trimmed Mean ( 16 / 24 ) & 4.01075 & 0.0128121912095372 & 313.041690871304 \tabularnewline
Trimmed Mean ( 17 / 24 ) & 4.01394736842105 & 0.0120249827287988 & 333.8006763875 \tabularnewline
Trimmed Mean ( 18 / 24 ) & 4.0175 & 0.011108233754421 & 361.668658476068 \tabularnewline
Trimmed Mean ( 19 / 24 ) & 4.02088235294118 & 0.0101096276720876 & 397.728035429309 \tabularnewline
Trimmed Mean ( 20 / 24 ) & 4.024375 & 0.00879811082177634 & 457.413538147213 \tabularnewline
Trimmed Mean ( 21 / 24 ) & 4.027 & 0.00768862422860784 & 523.760803007687 \tabularnewline
Trimmed Mean ( 22 / 24 ) & 4.02928571428571 & 0.00678327720090209 & 594.002809401608 \tabularnewline
Trimmed Mean ( 23 / 24 ) & 4.03 & 0.00649259933723359 & 620.706714010344 \tabularnewline
Trimmed Mean ( 24 / 24 ) & 4.03083333333333 & 0.00601678409295662 & 669.931523395017 \tabularnewline
Median & 4.035 &  &  \tabularnewline
Midrange & 3.925 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 4.01394736842105 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 4.01945945945946 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 4.01394736842105 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 4.01945945945946 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 4.01945945945946 &  &  \tabularnewline
Midmean - Closest Observation & 4.01394736842105 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 4.01945945945946 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 4.01394736842105 &  &  \tabularnewline
Number of observations & 72 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=175482&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]3.97513888888889[/C][C]0.0186496328379525[/C][C]213.148372594198[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]3.97197043338947[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]3.96874063240233[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]3.97824378477628[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 24 )[/C][C]3.97472222222222[/C][C]0.0185296491067177[/C][C]214.506070748055[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 24 )[/C][C]3.97555555555556[/C][C]0.0183385490754967[/C][C]216.786810079078[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 24 )[/C][C]3.97597222222222[/C][C]0.0182484802486631[/C][C]217.879635347361[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 24 )[/C][C]3.97541666666667[/C][C]0.0181714335607453[/C][C]218.772869701074[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 24 )[/C][C]3.97611111111111[/C][C]0.0180251037294756[/C][C]220.587419123096[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 24 )[/C][C]3.97611111111111[/C][C]0.0180251037294756[/C][C]220.587419123096[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 24 )[/C][C]3.97611111111111[/C][C]0.0180251037294756[/C][C]220.587419123096[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 24 )[/C][C]3.97388888888889[/C][C]0.0173707563191699[/C][C]228.768904236104[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 24 )[/C][C]3.97388888888889[/C][C]0.0173707563191699[/C][C]228.768904236104[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 24 )[/C][C]3.97527777777778[/C][C]0.0170873804002993[/C][C]232.644073266383[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 24 )[/C][C]3.97680555555556[/C][C]0.0167810935664733[/C][C]236.981311128659[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 24 )[/C][C]3.98347222222222[/C][C]0.0155004666018696[/C][C]256.99047161211[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 24 )[/C][C]3.98166666666667[/C][C]0.0152816540821568[/C][C]260.552074092278[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 24 )[/C][C]3.98361111111111[/C][C]0.0149232590352444[/C][C]266.939755029581[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 24 )[/C][C]3.98152777777778[/C][C]0.0146805574987821[/C][C]271.210938556529[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 24 )[/C][C]3.98375[/C][C]0.0142749075350077[/C][C]279.073611526398[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 24 )[/C][C]3.98375[/C][C]0.0135825268345499[/C][C]293.299623002882[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 24 )[/C][C]3.98875[/C][C]0.0126913175932809[/C][C]314.289668561423[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 24 )[/C][C]3.99138888888889[/C][C]0.0122287559005252[/C][C]326.39370033688[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 24 )[/C][C]4.0025[/C][C]0.0103286184912312[/C][C]387.515523339163[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 24 )[/C][C]4.00833333333333[/C][C]0.00853969833040575[/C][C]469.376455496278[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 24 )[/C][C]4.02361111111111[/C][C]0.00617083844282631[/C][C]652.036372105741[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 24 )[/C][C]4.02361111111111[/C][C]0.00617083844282631[/C][C]652.036372105741[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 24 )[/C][C]4.02361111111111[/C][C]0.00526788464089814[/C][C]763.800156114488[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 24 )[/C][C]3.97657142857143[/C][C]0.0183229434676943[/C][C]217.026889570589[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 24 )[/C][C]3.97852941176471[/C][C]0.0180688186757044[/C][C]220.187577459853[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 24 )[/C][C]3.98015151515151[/C][C]0.0178774544167104[/C][C]222.635248977684[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 24 )[/C][C]3.98171875[/C][C]0.0176784477333535[/C][C]225.230111266374[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 24 )[/C][C]3.98354838709677[/C][C]0.0174544762179208[/C][C]228.225031640124[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 24 )[/C][C]3.98533333333333[/C][C]0.017218218354827[/C][C]231.460262101745[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 24 )[/C][C]3.98724137931034[/C][C]0.0169190684197348[/C][C]235.665539047027[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 24 )[/C][C]3.98928571428571[/C][C]0.016541677278877[/C][C]241.165732291239[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 24 )[/C][C]3.99185185185185[/C][C]0.016218446921646[/C][C]246.130339799929[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 24 )[/C][C]3.99461538461538[/C][C]0.0158005611582517[/C][C]252.814779463022[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 24 )[/C][C]3.9974[/C][C]0.0153325317743758[/C][C]260.713628957258[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 24 )[/C][C]4.00020833333333[/C][C]0.0148021514134169[/C][C]270.245062464871[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 24 )[/C][C]4.00239130434783[/C][C]0.0144335384482152[/C][C]277.297997210293[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 24 )[/C][C]4.005[/C][C]0.0139823960599451[/C][C]286.431594615819[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 24 )[/C][C]4.00761904761905[/C][C]0.013468289956654[/C][C]297.55960560079[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 24 )[/C][C]4.01075[/C][C]0.0128121912095372[/C][C]313.041690871304[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 24 )[/C][C]4.01394736842105[/C][C]0.0120249827287988[/C][C]333.8006763875[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 24 )[/C][C]4.0175[/C][C]0.011108233754421[/C][C]361.668658476068[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 24 )[/C][C]4.02088235294118[/C][C]0.0101096276720876[/C][C]397.728035429309[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 24 )[/C][C]4.024375[/C][C]0.00879811082177634[/C][C]457.413538147213[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 24 )[/C][C]4.027[/C][C]0.00768862422860784[/C][C]523.760803007687[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 24 )[/C][C]4.02928571428571[/C][C]0.00678327720090209[/C][C]594.002809401608[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 24 )[/C][C]4.03[/C][C]0.00649259933723359[/C][C]620.706714010344[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 24 )[/C][C]4.03083333333333[/C][C]0.00601678409295662[/C][C]669.931523395017[/C][/ROW]
[ROW][C]Median[/C][C]4.035[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]3.925[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]4.01394736842105[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]4.01945945945946[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]4.01394736842105[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]4.01945945945946[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]4.01945945945946[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]4.01394736842105[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]4.01945945945946[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]4.01394736842105[/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=175482&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=175482&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 Mean3.975138888888890.0186496328379525213.148372594198
Geometric Mean3.97197043338947
Harmonic Mean3.96874063240233
Quadratic Mean3.97824378477628
Winsorized Mean ( 1 / 24 )3.974722222222220.0185296491067177214.506070748055
Winsorized Mean ( 2 / 24 )3.975555555555560.0183385490754967216.786810079078
Winsorized Mean ( 3 / 24 )3.975972222222220.0182484802486631217.879635347361
Winsorized Mean ( 4 / 24 )3.975416666666670.0181714335607453218.772869701074
Winsorized Mean ( 5 / 24 )3.976111111111110.0180251037294756220.587419123096
Winsorized Mean ( 6 / 24 )3.976111111111110.0180251037294756220.587419123096
Winsorized Mean ( 7 / 24 )3.976111111111110.0180251037294756220.587419123096
Winsorized Mean ( 8 / 24 )3.973888888888890.0173707563191699228.768904236104
Winsorized Mean ( 9 / 24 )3.973888888888890.0173707563191699228.768904236104
Winsorized Mean ( 10 / 24 )3.975277777777780.0170873804002993232.644073266383
Winsorized Mean ( 11 / 24 )3.976805555555560.0167810935664733236.981311128659
Winsorized Mean ( 12 / 24 )3.983472222222220.0155004666018696256.99047161211
Winsorized Mean ( 13 / 24 )3.981666666666670.0152816540821568260.552074092278
Winsorized Mean ( 14 / 24 )3.983611111111110.0149232590352444266.939755029581
Winsorized Mean ( 15 / 24 )3.981527777777780.0146805574987821271.210938556529
Winsorized Mean ( 16 / 24 )3.983750.0142749075350077279.073611526398
Winsorized Mean ( 17 / 24 )3.983750.0135825268345499293.299623002882
Winsorized Mean ( 18 / 24 )3.988750.0126913175932809314.289668561423
Winsorized Mean ( 19 / 24 )3.991388888888890.0122287559005252326.39370033688
Winsorized Mean ( 20 / 24 )4.00250.0103286184912312387.515523339163
Winsorized Mean ( 21 / 24 )4.008333333333330.00853969833040575469.376455496278
Winsorized Mean ( 22 / 24 )4.023611111111110.00617083844282631652.036372105741
Winsorized Mean ( 23 / 24 )4.023611111111110.00617083844282631652.036372105741
Winsorized Mean ( 24 / 24 )4.023611111111110.00526788464089814763.800156114488
Trimmed Mean ( 1 / 24 )3.976571428571430.0183229434676943217.026889570589
Trimmed Mean ( 2 / 24 )3.978529411764710.0180688186757044220.187577459853
Trimmed Mean ( 3 / 24 )3.980151515151510.0178774544167104222.635248977684
Trimmed Mean ( 4 / 24 )3.981718750.0176784477333535225.230111266374
Trimmed Mean ( 5 / 24 )3.983548387096770.0174544762179208228.225031640124
Trimmed Mean ( 6 / 24 )3.985333333333330.017218218354827231.460262101745
Trimmed Mean ( 7 / 24 )3.987241379310340.0169190684197348235.665539047027
Trimmed Mean ( 8 / 24 )3.989285714285710.016541677278877241.165732291239
Trimmed Mean ( 9 / 24 )3.991851851851850.016218446921646246.130339799929
Trimmed Mean ( 10 / 24 )3.994615384615380.0158005611582517252.814779463022
Trimmed Mean ( 11 / 24 )3.99740.0153325317743758260.713628957258
Trimmed Mean ( 12 / 24 )4.000208333333330.0148021514134169270.245062464871
Trimmed Mean ( 13 / 24 )4.002391304347830.0144335384482152277.297997210293
Trimmed Mean ( 14 / 24 )4.0050.0139823960599451286.431594615819
Trimmed Mean ( 15 / 24 )4.007619047619050.013468289956654297.55960560079
Trimmed Mean ( 16 / 24 )4.010750.0128121912095372313.041690871304
Trimmed Mean ( 17 / 24 )4.013947368421050.0120249827287988333.8006763875
Trimmed Mean ( 18 / 24 )4.01750.011108233754421361.668658476068
Trimmed Mean ( 19 / 24 )4.020882352941180.0101096276720876397.728035429309
Trimmed Mean ( 20 / 24 )4.0243750.00879811082177634457.413538147213
Trimmed Mean ( 21 / 24 )4.0270.00768862422860784523.760803007687
Trimmed Mean ( 22 / 24 )4.029285714285710.00678327720090209594.002809401608
Trimmed Mean ( 23 / 24 )4.030.00649259933723359620.706714010344
Trimmed Mean ( 24 / 24 )4.030833333333330.00601678409295662669.931523395017
Median4.035
Midrange3.925
Midmean - Weighted Average at Xnp4.01394736842105
Midmean - Weighted Average at X(n+1)p4.01945945945946
Midmean - Empirical Distribution Function4.01394736842105
Midmean - Empirical Distribution Function - Averaging4.01945945945946
Midmean - Empirical Distribution Function - Interpolation4.01945945945946
Midmean - Closest Observation4.01394736842105
Midmean - True Basic - Statistics Graphics Toolkit4.01945945945946
Midmean - MS Excel (old versions)4.01394736842105
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')