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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 computationFri, 11 Oct 2013 08:34:29 -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/2013/Oct/11/t1381494875e6enig2gwcbx6cz.htm/, Retrieved Sun, 28 Apr 2024 11:10:23 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=214768, Retrieved Sun, 28 Apr 2024 11:10:23 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact70
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [] [2013-10-11 12:34:29] [a1de13929df8f72ca0bba4a56316571d] [Current]
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Dataseries X:
3.875
3.863
3.876
3.878
3.881
3.883
3.884
3.885
3.895
3.903
3.911
3.929
3.946
3.965
3.992
4.010
4.015
4.020
4.037
4.059
4.083
4.102
4.126
4.145
4.162
4.169
4.178
4.174
4.168
4.170
4.159
4.159
4.143
4.159
4.167
4.176
4.185
4.195
4.210
4.226
4.250
4.259
4.270
4.277
4.286
4.303
4.320
4.336
4.352
4.371
4.392
4.415
4.442
4.457
4.472
4.474
4.461
4.453
4.446
4.450
4.459
4.474
4.492
4.509
4.526
4.541
4.550
4.562
4.555
4.554
4.551
4.553




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=214768&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=214768&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=214768&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 Mean4.219097222222220.0262842530057991160.51805700133
Geometric Mean4.21326477647987
Harmonic Mean4.20741850734634
Quadratic Mean4.22490622019524
Winsorized Mean ( 1 / 24 )4.219166666666670.0262352574295425160.820479006073
Winsorized Mean ( 2 / 24 )4.219166666666670.026225129808827160.882584659183
Winsorized Mean ( 3 / 24 )4.219208333333330.0262023241504298161.02420186509
Winsorized Mean ( 4 / 24 )4.219263888888890.0261519649576948161.33640037046
Winsorized Mean ( 5 / 24 )4.219333333333330.0261143207163976161.571628806869
Winsorized Mean ( 6 / 24 )4.218666666666670.0259667537530105162.464153463063
Winsorized Mean ( 7 / 24 )4.217305555555560.0256982051132792164.108953795233
Winsorized Mean ( 8 / 24 )4.216527777777780.025182774531558167.436982469656
Winsorized Mean ( 9 / 24 )4.215402777777780.0246619448890983170.927426718936
Winsorized Mean ( 10 / 24 )4.214013888888890.0240766860805125175.024663892581
Winsorized Mean ( 11 / 24 )4.216763888888890.0235967068623541178.701371911191
Winsorized Mean ( 12 / 24 )4.219263888888890.0230656000684192182.924522942102
Winsorized Mean ( 13 / 24 )4.220708333333330.0221962053664187190.15449999931
Winsorized Mean ( 14 / 24 )4.225569444444440.0213048778311675198.338121341524
Winsorized Mean ( 15 / 24 )4.228902777777780.0206710218010949204.581216084528
Winsorized Mean ( 16 / 24 )4.2291250.0203680141542286207.635607869116
Winsorized Mean ( 17 / 24 )4.229597222222220.0200842772431469210.592453540515
Winsorized Mean ( 18 / 24 )4.232847222222220.0193132652415074219.167870854128
Winsorized Mean ( 19 / 24 )4.237597222222220.0183351221888926231.119115464055
Winsorized Mean ( 20 / 24 )4.236763888888890.0162649773647516260.483847833107
Winsorized Mean ( 21 / 24 )4.235597222222220.0145087079205947291.93483288818
Winsorized Mean ( 22 / 24 )4.236513888888890.0126095201051857335.977408620541
Winsorized Mean ( 23 / 24 )4.2358750.0110462631056559383.466785055224
Winsorized Mean ( 24 / 24 )4.231208333333330.0101854659081862415.416277613049
Trimmed Mean ( 1 / 24 )4.219285714285710.0260883047566418161.730927081857
Trimmed Mean ( 2 / 24 )4.219411764705880.0258993563949826162.915699539286
Trimmed Mean ( 3 / 24 )4.219545454545450.025666756108749164.397301967861
Trimmed Mean ( 4 / 24 )4.2196718750.0253855689410356166.223254038594
Trimmed Mean ( 5 / 24 )4.219790322580650.0250533659615968168.432071325225
Trimmed Mean ( 6 / 24 )4.21990.0246523018945608171.176712748722
Trimmed Mean ( 7 / 24 )4.220155172413790.0241957609257916174.417129734296
Trimmed Mean ( 8 / 24 )4.220678571428570.0236969654907414178.110508414152
Trimmed Mean ( 9 / 24 )4.221370370370370.0231992297321512181.961660758076
Trimmed Mean ( 10 / 24 )4.222288461538460.022692919150951186.061935595514
Trimmed Mean ( 11 / 24 )4.223480.0221807646028568190.411830954467
Trimmed Mean ( 12 / 24 )4.224395833333330.0216337121093587195.269115719898
Trimmed Mean ( 13 / 24 )4.22506521739130.0210476203153938200.738380590283
Trimmed Mean ( 14 / 24 )4.225613636363640.0204818079417692206.310578068951
Trimmed Mean ( 15 / 24 )4.225619047619050.0199397743735598211.919100409794
Trimmed Mean ( 16 / 24 )4.2252250.019358675504995218.260025016164
Trimmed Mean ( 17 / 24 )4.224763157894740.0186404718150764226.644647185258
Trimmed Mean ( 18 / 24 )4.224194444444440.0177251421936421238.316533559862
Trimmed Mean ( 19 / 24 )4.223176470588240.0166646952802844253.420563626181
Trimmed Mean ( 20 / 24 )4.221468750.0154457286333184273.309783579503
Trimmed Mean ( 21 / 24 )4.219633333333330.0143812204598813293.412742340239
Trimmed Mean ( 22 / 24 )4.217678571428570.0134261702091572314.138619258076
Trimmed Mean ( 23 / 24 )4.215307692307690.0126624544018642332.8981537487
Trimmed Mean ( 24 / 24 )4.2126250.0120486352134691349.635035451214
Median4.1815
Midrange4.2125
Midmean - Weighted Average at Xnp4.21867567567568
Midmean - Weighted Average at X(n+1)p4.22419444444444
Midmean - Empirical Distribution Function4.21867567567568
Midmean - Empirical Distribution Function - Averaging4.22419444444444
Midmean - Empirical Distribution Function - Interpolation4.22419444444444
Midmean - Closest Observation4.21867567567568
Midmean - True Basic - Statistics Graphics Toolkit4.22419444444444
Midmean - MS Excel (old versions)4.22476315789474
Number of observations72

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 4.21909722222222 & 0.0262842530057991 & 160.51805700133 \tabularnewline
Geometric Mean & 4.21326477647987 &  &  \tabularnewline
Harmonic Mean & 4.20741850734634 &  &  \tabularnewline
Quadratic Mean & 4.22490622019524 &  &  \tabularnewline
Winsorized Mean ( 1 / 24 ) & 4.21916666666667 & 0.0262352574295425 & 160.820479006073 \tabularnewline
Winsorized Mean ( 2 / 24 ) & 4.21916666666667 & 0.026225129808827 & 160.882584659183 \tabularnewline
Winsorized Mean ( 3 / 24 ) & 4.21920833333333 & 0.0262023241504298 & 161.02420186509 \tabularnewline
Winsorized Mean ( 4 / 24 ) & 4.21926388888889 & 0.0261519649576948 & 161.33640037046 \tabularnewline
Winsorized Mean ( 5 / 24 ) & 4.21933333333333 & 0.0261143207163976 & 161.571628806869 \tabularnewline
Winsorized Mean ( 6 / 24 ) & 4.21866666666667 & 0.0259667537530105 & 162.464153463063 \tabularnewline
Winsorized Mean ( 7 / 24 ) & 4.21730555555556 & 0.0256982051132792 & 164.108953795233 \tabularnewline
Winsorized Mean ( 8 / 24 ) & 4.21652777777778 & 0.025182774531558 & 167.436982469656 \tabularnewline
Winsorized Mean ( 9 / 24 ) & 4.21540277777778 & 0.0246619448890983 & 170.927426718936 \tabularnewline
Winsorized Mean ( 10 / 24 ) & 4.21401388888889 & 0.0240766860805125 & 175.024663892581 \tabularnewline
Winsorized Mean ( 11 / 24 ) & 4.21676388888889 & 0.0235967068623541 & 178.701371911191 \tabularnewline
Winsorized Mean ( 12 / 24 ) & 4.21926388888889 & 0.0230656000684192 & 182.924522942102 \tabularnewline
Winsorized Mean ( 13 / 24 ) & 4.22070833333333 & 0.0221962053664187 & 190.15449999931 \tabularnewline
Winsorized Mean ( 14 / 24 ) & 4.22556944444444 & 0.0213048778311675 & 198.338121341524 \tabularnewline
Winsorized Mean ( 15 / 24 ) & 4.22890277777778 & 0.0206710218010949 & 204.581216084528 \tabularnewline
Winsorized Mean ( 16 / 24 ) & 4.229125 & 0.0203680141542286 & 207.635607869116 \tabularnewline
Winsorized Mean ( 17 / 24 ) & 4.22959722222222 & 0.0200842772431469 & 210.592453540515 \tabularnewline
Winsorized Mean ( 18 / 24 ) & 4.23284722222222 & 0.0193132652415074 & 219.167870854128 \tabularnewline
Winsorized Mean ( 19 / 24 ) & 4.23759722222222 & 0.0183351221888926 & 231.119115464055 \tabularnewline
Winsorized Mean ( 20 / 24 ) & 4.23676388888889 & 0.0162649773647516 & 260.483847833107 \tabularnewline
Winsorized Mean ( 21 / 24 ) & 4.23559722222222 & 0.0145087079205947 & 291.93483288818 \tabularnewline
Winsorized Mean ( 22 / 24 ) & 4.23651388888889 & 0.0126095201051857 & 335.977408620541 \tabularnewline
Winsorized Mean ( 23 / 24 ) & 4.235875 & 0.0110462631056559 & 383.466785055224 \tabularnewline
Winsorized Mean ( 24 / 24 ) & 4.23120833333333 & 0.0101854659081862 & 415.416277613049 \tabularnewline
Trimmed Mean ( 1 / 24 ) & 4.21928571428571 & 0.0260883047566418 & 161.730927081857 \tabularnewline
Trimmed Mean ( 2 / 24 ) & 4.21941176470588 & 0.0258993563949826 & 162.915699539286 \tabularnewline
Trimmed Mean ( 3 / 24 ) & 4.21954545454545 & 0.025666756108749 & 164.397301967861 \tabularnewline
Trimmed Mean ( 4 / 24 ) & 4.219671875 & 0.0253855689410356 & 166.223254038594 \tabularnewline
Trimmed Mean ( 5 / 24 ) & 4.21979032258065 & 0.0250533659615968 & 168.432071325225 \tabularnewline
Trimmed Mean ( 6 / 24 ) & 4.2199 & 0.0246523018945608 & 171.176712748722 \tabularnewline
Trimmed Mean ( 7 / 24 ) & 4.22015517241379 & 0.0241957609257916 & 174.417129734296 \tabularnewline
Trimmed Mean ( 8 / 24 ) & 4.22067857142857 & 0.0236969654907414 & 178.110508414152 \tabularnewline
Trimmed Mean ( 9 / 24 ) & 4.22137037037037 & 0.0231992297321512 & 181.961660758076 \tabularnewline
Trimmed Mean ( 10 / 24 ) & 4.22228846153846 & 0.022692919150951 & 186.061935595514 \tabularnewline
Trimmed Mean ( 11 / 24 ) & 4.22348 & 0.0221807646028568 & 190.411830954467 \tabularnewline
Trimmed Mean ( 12 / 24 ) & 4.22439583333333 & 0.0216337121093587 & 195.269115719898 \tabularnewline
Trimmed Mean ( 13 / 24 ) & 4.2250652173913 & 0.0210476203153938 & 200.738380590283 \tabularnewline
Trimmed Mean ( 14 / 24 ) & 4.22561363636364 & 0.0204818079417692 & 206.310578068951 \tabularnewline
Trimmed Mean ( 15 / 24 ) & 4.22561904761905 & 0.0199397743735598 & 211.919100409794 \tabularnewline
Trimmed Mean ( 16 / 24 ) & 4.225225 & 0.019358675504995 & 218.260025016164 \tabularnewline
Trimmed Mean ( 17 / 24 ) & 4.22476315789474 & 0.0186404718150764 & 226.644647185258 \tabularnewline
Trimmed Mean ( 18 / 24 ) & 4.22419444444444 & 0.0177251421936421 & 238.316533559862 \tabularnewline
Trimmed Mean ( 19 / 24 ) & 4.22317647058824 & 0.0166646952802844 & 253.420563626181 \tabularnewline
Trimmed Mean ( 20 / 24 ) & 4.22146875 & 0.0154457286333184 & 273.309783579503 \tabularnewline
Trimmed Mean ( 21 / 24 ) & 4.21963333333333 & 0.0143812204598813 & 293.412742340239 \tabularnewline
Trimmed Mean ( 22 / 24 ) & 4.21767857142857 & 0.0134261702091572 & 314.138619258076 \tabularnewline
Trimmed Mean ( 23 / 24 ) & 4.21530769230769 & 0.0126624544018642 & 332.8981537487 \tabularnewline
Trimmed Mean ( 24 / 24 ) & 4.212625 & 0.0120486352134691 & 349.635035451214 \tabularnewline
Median & 4.1815 &  &  \tabularnewline
Midrange & 4.2125 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 4.21867567567568 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 4.22419444444444 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 4.21867567567568 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 4.22419444444444 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 4.22419444444444 &  &  \tabularnewline
Midmean - Closest Observation & 4.21867567567568 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 4.22419444444444 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 4.22476315789474 &  &  \tabularnewline
Number of observations & 72 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=214768&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]4.21909722222222[/C][C]0.0262842530057991[/C][C]160.51805700133[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]4.21326477647987[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]4.20741850734634[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]4.22490622019524[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 24 )[/C][C]4.21916666666667[/C][C]0.0262352574295425[/C][C]160.820479006073[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 24 )[/C][C]4.21916666666667[/C][C]0.026225129808827[/C][C]160.882584659183[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 24 )[/C][C]4.21920833333333[/C][C]0.0262023241504298[/C][C]161.02420186509[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 24 )[/C][C]4.21926388888889[/C][C]0.0261519649576948[/C][C]161.33640037046[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 24 )[/C][C]4.21933333333333[/C][C]0.0261143207163976[/C][C]161.571628806869[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 24 )[/C][C]4.21866666666667[/C][C]0.0259667537530105[/C][C]162.464153463063[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 24 )[/C][C]4.21730555555556[/C][C]0.0256982051132792[/C][C]164.108953795233[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 24 )[/C][C]4.21652777777778[/C][C]0.025182774531558[/C][C]167.436982469656[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 24 )[/C][C]4.21540277777778[/C][C]0.0246619448890983[/C][C]170.927426718936[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 24 )[/C][C]4.21401388888889[/C][C]0.0240766860805125[/C][C]175.024663892581[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 24 )[/C][C]4.21676388888889[/C][C]0.0235967068623541[/C][C]178.701371911191[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 24 )[/C][C]4.21926388888889[/C][C]0.0230656000684192[/C][C]182.924522942102[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 24 )[/C][C]4.22070833333333[/C][C]0.0221962053664187[/C][C]190.15449999931[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 24 )[/C][C]4.22556944444444[/C][C]0.0213048778311675[/C][C]198.338121341524[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 24 )[/C][C]4.22890277777778[/C][C]0.0206710218010949[/C][C]204.581216084528[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 24 )[/C][C]4.229125[/C][C]0.0203680141542286[/C][C]207.635607869116[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 24 )[/C][C]4.22959722222222[/C][C]0.0200842772431469[/C][C]210.592453540515[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 24 )[/C][C]4.23284722222222[/C][C]0.0193132652415074[/C][C]219.167870854128[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 24 )[/C][C]4.23759722222222[/C][C]0.0183351221888926[/C][C]231.119115464055[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 24 )[/C][C]4.23676388888889[/C][C]0.0162649773647516[/C][C]260.483847833107[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 24 )[/C][C]4.23559722222222[/C][C]0.0145087079205947[/C][C]291.93483288818[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 24 )[/C][C]4.23651388888889[/C][C]0.0126095201051857[/C][C]335.977408620541[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 24 )[/C][C]4.235875[/C][C]0.0110462631056559[/C][C]383.466785055224[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 24 )[/C][C]4.23120833333333[/C][C]0.0101854659081862[/C][C]415.416277613049[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 24 )[/C][C]4.21928571428571[/C][C]0.0260883047566418[/C][C]161.730927081857[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 24 )[/C][C]4.21941176470588[/C][C]0.0258993563949826[/C][C]162.915699539286[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 24 )[/C][C]4.21954545454545[/C][C]0.025666756108749[/C][C]164.397301967861[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 24 )[/C][C]4.219671875[/C][C]0.0253855689410356[/C][C]166.223254038594[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 24 )[/C][C]4.21979032258065[/C][C]0.0250533659615968[/C][C]168.432071325225[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 24 )[/C][C]4.2199[/C][C]0.0246523018945608[/C][C]171.176712748722[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 24 )[/C][C]4.22015517241379[/C][C]0.0241957609257916[/C][C]174.417129734296[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 24 )[/C][C]4.22067857142857[/C][C]0.0236969654907414[/C][C]178.110508414152[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 24 )[/C][C]4.22137037037037[/C][C]0.0231992297321512[/C][C]181.961660758076[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 24 )[/C][C]4.22228846153846[/C][C]0.022692919150951[/C][C]186.061935595514[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 24 )[/C][C]4.22348[/C][C]0.0221807646028568[/C][C]190.411830954467[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 24 )[/C][C]4.22439583333333[/C][C]0.0216337121093587[/C][C]195.269115719898[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 24 )[/C][C]4.2250652173913[/C][C]0.0210476203153938[/C][C]200.738380590283[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 24 )[/C][C]4.22561363636364[/C][C]0.0204818079417692[/C][C]206.310578068951[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 24 )[/C][C]4.22561904761905[/C][C]0.0199397743735598[/C][C]211.919100409794[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 24 )[/C][C]4.225225[/C][C]0.019358675504995[/C][C]218.260025016164[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 24 )[/C][C]4.22476315789474[/C][C]0.0186404718150764[/C][C]226.644647185258[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 24 )[/C][C]4.22419444444444[/C][C]0.0177251421936421[/C][C]238.316533559862[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 24 )[/C][C]4.22317647058824[/C][C]0.0166646952802844[/C][C]253.420563626181[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 24 )[/C][C]4.22146875[/C][C]0.0154457286333184[/C][C]273.309783579503[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 24 )[/C][C]4.21963333333333[/C][C]0.0143812204598813[/C][C]293.412742340239[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 24 )[/C][C]4.21767857142857[/C][C]0.0134261702091572[/C][C]314.138619258076[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 24 )[/C][C]4.21530769230769[/C][C]0.0126624544018642[/C][C]332.8981537487[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 24 )[/C][C]4.212625[/C][C]0.0120486352134691[/C][C]349.635035451214[/C][/ROW]
[ROW][C]Median[/C][C]4.1815[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]4.2125[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]4.21867567567568[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]4.22419444444444[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]4.21867567567568[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]4.22419444444444[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]4.22419444444444[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]4.21867567567568[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]4.22419444444444[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]4.22476315789474[/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=214768&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=214768&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 Mean4.219097222222220.0262842530057991160.51805700133
Geometric Mean4.21326477647987
Harmonic Mean4.20741850734634
Quadratic Mean4.22490622019524
Winsorized Mean ( 1 / 24 )4.219166666666670.0262352574295425160.820479006073
Winsorized Mean ( 2 / 24 )4.219166666666670.026225129808827160.882584659183
Winsorized Mean ( 3 / 24 )4.219208333333330.0262023241504298161.02420186509
Winsorized Mean ( 4 / 24 )4.219263888888890.0261519649576948161.33640037046
Winsorized Mean ( 5 / 24 )4.219333333333330.0261143207163976161.571628806869
Winsorized Mean ( 6 / 24 )4.218666666666670.0259667537530105162.464153463063
Winsorized Mean ( 7 / 24 )4.217305555555560.0256982051132792164.108953795233
Winsorized Mean ( 8 / 24 )4.216527777777780.025182774531558167.436982469656
Winsorized Mean ( 9 / 24 )4.215402777777780.0246619448890983170.927426718936
Winsorized Mean ( 10 / 24 )4.214013888888890.0240766860805125175.024663892581
Winsorized Mean ( 11 / 24 )4.216763888888890.0235967068623541178.701371911191
Winsorized Mean ( 12 / 24 )4.219263888888890.0230656000684192182.924522942102
Winsorized Mean ( 13 / 24 )4.220708333333330.0221962053664187190.15449999931
Winsorized Mean ( 14 / 24 )4.225569444444440.0213048778311675198.338121341524
Winsorized Mean ( 15 / 24 )4.228902777777780.0206710218010949204.581216084528
Winsorized Mean ( 16 / 24 )4.2291250.0203680141542286207.635607869116
Winsorized Mean ( 17 / 24 )4.229597222222220.0200842772431469210.592453540515
Winsorized Mean ( 18 / 24 )4.232847222222220.0193132652415074219.167870854128
Winsorized Mean ( 19 / 24 )4.237597222222220.0183351221888926231.119115464055
Winsorized Mean ( 20 / 24 )4.236763888888890.0162649773647516260.483847833107
Winsorized Mean ( 21 / 24 )4.235597222222220.0145087079205947291.93483288818
Winsorized Mean ( 22 / 24 )4.236513888888890.0126095201051857335.977408620541
Winsorized Mean ( 23 / 24 )4.2358750.0110462631056559383.466785055224
Winsorized Mean ( 24 / 24 )4.231208333333330.0101854659081862415.416277613049
Trimmed Mean ( 1 / 24 )4.219285714285710.0260883047566418161.730927081857
Trimmed Mean ( 2 / 24 )4.219411764705880.0258993563949826162.915699539286
Trimmed Mean ( 3 / 24 )4.219545454545450.025666756108749164.397301967861
Trimmed Mean ( 4 / 24 )4.2196718750.0253855689410356166.223254038594
Trimmed Mean ( 5 / 24 )4.219790322580650.0250533659615968168.432071325225
Trimmed Mean ( 6 / 24 )4.21990.0246523018945608171.176712748722
Trimmed Mean ( 7 / 24 )4.220155172413790.0241957609257916174.417129734296
Trimmed Mean ( 8 / 24 )4.220678571428570.0236969654907414178.110508414152
Trimmed Mean ( 9 / 24 )4.221370370370370.0231992297321512181.961660758076
Trimmed Mean ( 10 / 24 )4.222288461538460.022692919150951186.061935595514
Trimmed Mean ( 11 / 24 )4.223480.0221807646028568190.411830954467
Trimmed Mean ( 12 / 24 )4.224395833333330.0216337121093587195.269115719898
Trimmed Mean ( 13 / 24 )4.22506521739130.0210476203153938200.738380590283
Trimmed Mean ( 14 / 24 )4.225613636363640.0204818079417692206.310578068951
Trimmed Mean ( 15 / 24 )4.225619047619050.0199397743735598211.919100409794
Trimmed Mean ( 16 / 24 )4.2252250.019358675504995218.260025016164
Trimmed Mean ( 17 / 24 )4.224763157894740.0186404718150764226.644647185258
Trimmed Mean ( 18 / 24 )4.224194444444440.0177251421936421238.316533559862
Trimmed Mean ( 19 / 24 )4.223176470588240.0166646952802844253.420563626181
Trimmed Mean ( 20 / 24 )4.221468750.0154457286333184273.309783579503
Trimmed Mean ( 21 / 24 )4.219633333333330.0143812204598813293.412742340239
Trimmed Mean ( 22 / 24 )4.217678571428570.0134261702091572314.138619258076
Trimmed Mean ( 23 / 24 )4.215307692307690.0126624544018642332.8981537487
Trimmed Mean ( 24 / 24 )4.2126250.0120486352134691349.635035451214
Median4.1815
Midrange4.2125
Midmean - Weighted Average at Xnp4.21867567567568
Midmean - Weighted Average at X(n+1)p4.22419444444444
Midmean - Empirical Distribution Function4.21867567567568
Midmean - Empirical Distribution Function - Averaging4.22419444444444
Midmean - Empirical Distribution Function - Interpolation4.22419444444444
Midmean - Closest Observation4.21867567567568
Midmean - True Basic - Statistics Graphics Toolkit4.22419444444444
Midmean - MS Excel (old versions)4.22476315789474
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')