Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationFri, 05 Dec 2008 07:51:06 -0700
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2008/Dec/05/t1228488801vbv3pl2xfxjoqp9.htm/, Retrieved Thu, 16 May 2024 15:32:25 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=29289, Retrieved Thu, 16 May 2024 15:32:25 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordspaper131
Estimated Impact170
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [paper ct invester...] [2008-12-05 14:51:06] [d8c5724db236abb5950452133b88474d] [Current]
Feedback Forum

Post a new message
Dataseries X:
107.4
103.8
103.5
106.6
111
110.1
109.1
108.3
99.5
115.6
90.6
92.9
102
102.7
97.9
102.6
106.7
101.9
103.4
91.2
94.6
91.7
98.8
104.4
100.3
104.2
105.7
108.7
100.2
104.2
101.4
105.4
105.4
111.5
104
103.6
108.4
107.1
108.2
109.2
102.6
108.1
112.8
108.1
110.4
102.7
108.2
109.3
111.2
113.5
114.3
108.6
121.3
116.1
113.1
113
117.4
121.2
121
122
123.1
120.7
123.5
125.8
124.3
130.5
129.2
124.6
128.9
127.8
128.6
132.7




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 1 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=29289&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=29289&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=29289&T=0

As an alternative you can also use a QR Code:  

The GUIDs for individual cells are displayed in the table below:

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean109.9777777777781.1845117821527992.8465038801885
Geometric Mean109.532222368921
Harmonic Mean109.093838417736
Quadratic Mean110.429748910538
Winsorized Mean ( 1 / 24 )109.9555555555561.1747221708776693.6013282812271
Winsorized Mean ( 2 / 24 )109.9333333333331.1629652887815794.5284733721587
Winsorized Mean ( 3 / 24 )109.9708333333331.1493048138611195.6846538942828
Winsorized Mean ( 4 / 24 )110.0486111111111.1264305685331797.6967548514025
Winsorized Mean ( 5 / 24 )110.2222222222221.07281864103406102.740778363044
Winsorized Mean ( 6 / 24 )110.1305555555561.02367445280435107.583573326318
Winsorized Mean ( 7 / 24 )110.0819444444440.98858573044294111.352957112907
Winsorized Mean ( 8 / 24 )110.1263888888890.970239860828907113.504292428065
Winsorized Mean ( 9 / 24 )110.0388888888890.948146110456861116.056890046057
Winsorized Mean ( 10 / 24 )110.1361111111110.915723598443496120.272221113790
Winsorized Mean ( 11 / 24 )110.0444444444440.872584725762576126.113191298729
Winsorized Mean ( 12 / 24 )109.9444444444440.84812895628103129.631754263574
Winsorized Mean ( 13 / 24 )110.0347222222220.83074047263423132.453787731454
Winsorized Mean ( 14 / 24 )109.9958333333330.823399565629705133.587431818977
Winsorized Mean ( 15 / 24 )109.9541666666670.809037705548039135.907345124519
Winsorized Mean ( 16 / 24 )109.2208333333330.677548909991272161.199924791762
Winsorized Mean ( 17 / 24 )109.0791666666670.604119716485594180.558858931511
Winsorized Mean ( 18 / 24 )108.9791666666670.580529605151162187.723702115571
Winsorized Mean ( 19 / 24 )108.66250.523323156729498207.639388019985
Winsorized Mean ( 20 / 24 )108.4958333333330.482622261059423224.804867258236
Winsorized Mean ( 21 / 24 )108.43750.457751177446693236.891799175389
Winsorized Mean ( 22 / 24 )108.4680555555560.445068730906132243.710797958602
Winsorized Mean ( 23 / 24 )108.4041666666670.435950194837342248.661814928454
Winsorized Mean ( 24 / 24 )108.03750.367052920222863294.3376664444
Trimmed Mean ( 1 / 24 )109.931.1403140572089496.4032665431372
Trimmed Mean ( 2 / 24 )109.9029411764711.0993792058373499.9681825824265
Trimmed Mean ( 3 / 24 )109.8863636363641.05807999213696103.854495362332
Trimmed Mean ( 4 / 24 )109.85468751.01485477127677108.246707419815
Trimmed Mean ( 5 / 24 )109.7983870967740.971349195351395113.036987750892
Trimmed Mean ( 6 / 24 )109.6966666666670.936114600964732117.182945927365
Trimmed Mean ( 7 / 24 )109.6068965517240.907656689433818120.758099210501
Trimmed Mean ( 8 / 24 )109.5196428571430.88204462752948124.165648130409
Trimmed Mean ( 9 / 24 )109.4185185185190.854629658021233128.030331608033
Trimmed Mean ( 10 / 24 )109.3230769230770.825789148531691132.38618734269
Trimmed Mean ( 11 / 24 )109.2060.79673010307309137.067746754865
Trimmed Mean ( 12 / 24 )109.0916666666670.769981079562453141.680970561846
Trimmed Mean ( 13 / 24 )108.9804347826090.741330697818909147.006504793668
Trimmed Mean ( 14 / 24 )108.8477272727270.707409356928666153.868090952751
Trimmed Mean ( 15 / 24 )108.7071428571430.664019653735893163.710730918184
Trimmed Mean ( 16 / 24 )108.55750.608938625807232178.273302758701
Trimmed Mean ( 17 / 24 )108.4789473684210.575534359839743188.483876789957
Trimmed Mean ( 18 / 24 )108.4083333333330.550373249972883196.972387990649
Trimmed Mean ( 19 / 24 )108.3411764705880.521978917336372207.558529420014
Trimmed Mean ( 20 / 24 )108.3031250.499666912742395216.750643755025
Trimmed Mean ( 21 / 24 )108.280.479904205000343225.628362643588
Trimmed Mean ( 22 / 24 )108.2607142857140.458325087536627236.209444408959
Trimmed Mean ( 23 / 24 )108.2346153846150.429380315828872252.071674910575
Trimmed Mean ( 24 / 24 )108.21250.387079013953841279.561784801137
Median108.25
Midrange111.65
Midmean - Weighted Average at Xnp108.272972972973
Midmean - Weighted Average at X(n+1)p108.408333333333
Midmean - Empirical Distribution Function108.272972972973
Midmean - Empirical Distribution Function - Averaging108.408333333333
Midmean - Empirical Distribution Function - Interpolation108.408333333333
Midmean - Closest Observation108.272972972973
Midmean - True Basic - Statistics Graphics Toolkit108.408333333333
Midmean - MS Excel (old versions)108.478947368421
Number of observations72

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 109.977777777778 & 1.18451178215279 & 92.8465038801885 \tabularnewline
Geometric Mean & 109.532222368921 &  &  \tabularnewline
Harmonic Mean & 109.093838417736 &  &  \tabularnewline
Quadratic Mean & 110.429748910538 &  &  \tabularnewline
Winsorized Mean ( 1 / 24 ) & 109.955555555556 & 1.17472217087766 & 93.6013282812271 \tabularnewline
Winsorized Mean ( 2 / 24 ) & 109.933333333333 & 1.16296528878157 & 94.5284733721587 \tabularnewline
Winsorized Mean ( 3 / 24 ) & 109.970833333333 & 1.14930481386111 & 95.6846538942828 \tabularnewline
Winsorized Mean ( 4 / 24 ) & 110.048611111111 & 1.12643056853317 & 97.6967548514025 \tabularnewline
Winsorized Mean ( 5 / 24 ) & 110.222222222222 & 1.07281864103406 & 102.740778363044 \tabularnewline
Winsorized Mean ( 6 / 24 ) & 110.130555555556 & 1.02367445280435 & 107.583573326318 \tabularnewline
Winsorized Mean ( 7 / 24 ) & 110.081944444444 & 0.98858573044294 & 111.352957112907 \tabularnewline
Winsorized Mean ( 8 / 24 ) & 110.126388888889 & 0.970239860828907 & 113.504292428065 \tabularnewline
Winsorized Mean ( 9 / 24 ) & 110.038888888889 & 0.948146110456861 & 116.056890046057 \tabularnewline
Winsorized Mean ( 10 / 24 ) & 110.136111111111 & 0.915723598443496 & 120.272221113790 \tabularnewline
Winsorized Mean ( 11 / 24 ) & 110.044444444444 & 0.872584725762576 & 126.113191298729 \tabularnewline
Winsorized Mean ( 12 / 24 ) & 109.944444444444 & 0.84812895628103 & 129.631754263574 \tabularnewline
Winsorized Mean ( 13 / 24 ) & 110.034722222222 & 0.83074047263423 & 132.453787731454 \tabularnewline
Winsorized Mean ( 14 / 24 ) & 109.995833333333 & 0.823399565629705 & 133.587431818977 \tabularnewline
Winsorized Mean ( 15 / 24 ) & 109.954166666667 & 0.809037705548039 & 135.907345124519 \tabularnewline
Winsorized Mean ( 16 / 24 ) & 109.220833333333 & 0.677548909991272 & 161.199924791762 \tabularnewline
Winsorized Mean ( 17 / 24 ) & 109.079166666667 & 0.604119716485594 & 180.558858931511 \tabularnewline
Winsorized Mean ( 18 / 24 ) & 108.979166666667 & 0.580529605151162 & 187.723702115571 \tabularnewline
Winsorized Mean ( 19 / 24 ) & 108.6625 & 0.523323156729498 & 207.639388019985 \tabularnewline
Winsorized Mean ( 20 / 24 ) & 108.495833333333 & 0.482622261059423 & 224.804867258236 \tabularnewline
Winsorized Mean ( 21 / 24 ) & 108.4375 & 0.457751177446693 & 236.891799175389 \tabularnewline
Winsorized Mean ( 22 / 24 ) & 108.468055555556 & 0.445068730906132 & 243.710797958602 \tabularnewline
Winsorized Mean ( 23 / 24 ) & 108.404166666667 & 0.435950194837342 & 248.661814928454 \tabularnewline
Winsorized Mean ( 24 / 24 ) & 108.0375 & 0.367052920222863 & 294.3376664444 \tabularnewline
Trimmed Mean ( 1 / 24 ) & 109.93 & 1.14031405720894 & 96.4032665431372 \tabularnewline
Trimmed Mean ( 2 / 24 ) & 109.902941176471 & 1.09937920583734 & 99.9681825824265 \tabularnewline
Trimmed Mean ( 3 / 24 ) & 109.886363636364 & 1.05807999213696 & 103.854495362332 \tabularnewline
Trimmed Mean ( 4 / 24 ) & 109.8546875 & 1.01485477127677 & 108.246707419815 \tabularnewline
Trimmed Mean ( 5 / 24 ) & 109.798387096774 & 0.971349195351395 & 113.036987750892 \tabularnewline
Trimmed Mean ( 6 / 24 ) & 109.696666666667 & 0.936114600964732 & 117.182945927365 \tabularnewline
Trimmed Mean ( 7 / 24 ) & 109.606896551724 & 0.907656689433818 & 120.758099210501 \tabularnewline
Trimmed Mean ( 8 / 24 ) & 109.519642857143 & 0.88204462752948 & 124.165648130409 \tabularnewline
Trimmed Mean ( 9 / 24 ) & 109.418518518519 & 0.854629658021233 & 128.030331608033 \tabularnewline
Trimmed Mean ( 10 / 24 ) & 109.323076923077 & 0.825789148531691 & 132.38618734269 \tabularnewline
Trimmed Mean ( 11 / 24 ) & 109.206 & 0.79673010307309 & 137.067746754865 \tabularnewline
Trimmed Mean ( 12 / 24 ) & 109.091666666667 & 0.769981079562453 & 141.680970561846 \tabularnewline
Trimmed Mean ( 13 / 24 ) & 108.980434782609 & 0.741330697818909 & 147.006504793668 \tabularnewline
Trimmed Mean ( 14 / 24 ) & 108.847727272727 & 0.707409356928666 & 153.868090952751 \tabularnewline
Trimmed Mean ( 15 / 24 ) & 108.707142857143 & 0.664019653735893 & 163.710730918184 \tabularnewline
Trimmed Mean ( 16 / 24 ) & 108.5575 & 0.608938625807232 & 178.273302758701 \tabularnewline
Trimmed Mean ( 17 / 24 ) & 108.478947368421 & 0.575534359839743 & 188.483876789957 \tabularnewline
Trimmed Mean ( 18 / 24 ) & 108.408333333333 & 0.550373249972883 & 196.972387990649 \tabularnewline
Trimmed Mean ( 19 / 24 ) & 108.341176470588 & 0.521978917336372 & 207.558529420014 \tabularnewline
Trimmed Mean ( 20 / 24 ) & 108.303125 & 0.499666912742395 & 216.750643755025 \tabularnewline
Trimmed Mean ( 21 / 24 ) & 108.28 & 0.479904205000343 & 225.628362643588 \tabularnewline
Trimmed Mean ( 22 / 24 ) & 108.260714285714 & 0.458325087536627 & 236.209444408959 \tabularnewline
Trimmed Mean ( 23 / 24 ) & 108.234615384615 & 0.429380315828872 & 252.071674910575 \tabularnewline
Trimmed Mean ( 24 / 24 ) & 108.2125 & 0.387079013953841 & 279.561784801137 \tabularnewline
Median & 108.25 &  &  \tabularnewline
Midrange & 111.65 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 108.272972972973 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 108.408333333333 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 108.272972972973 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 108.408333333333 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 108.408333333333 &  &  \tabularnewline
Midmean - Closest Observation & 108.272972972973 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 108.408333333333 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 108.478947368421 &  &  \tabularnewline
Number of observations & 72 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=29289&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]109.977777777778[/C][C]1.18451178215279[/C][C]92.8465038801885[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]109.532222368921[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]109.093838417736[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]110.429748910538[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 24 )[/C][C]109.955555555556[/C][C]1.17472217087766[/C][C]93.6013282812271[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 24 )[/C][C]109.933333333333[/C][C]1.16296528878157[/C][C]94.5284733721587[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 24 )[/C][C]109.970833333333[/C][C]1.14930481386111[/C][C]95.6846538942828[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 24 )[/C][C]110.048611111111[/C][C]1.12643056853317[/C][C]97.6967548514025[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 24 )[/C][C]110.222222222222[/C][C]1.07281864103406[/C][C]102.740778363044[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 24 )[/C][C]110.130555555556[/C][C]1.02367445280435[/C][C]107.583573326318[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 24 )[/C][C]110.081944444444[/C][C]0.98858573044294[/C][C]111.352957112907[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 24 )[/C][C]110.126388888889[/C][C]0.970239860828907[/C][C]113.504292428065[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 24 )[/C][C]110.038888888889[/C][C]0.948146110456861[/C][C]116.056890046057[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 24 )[/C][C]110.136111111111[/C][C]0.915723598443496[/C][C]120.272221113790[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 24 )[/C][C]110.044444444444[/C][C]0.872584725762576[/C][C]126.113191298729[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 24 )[/C][C]109.944444444444[/C][C]0.84812895628103[/C][C]129.631754263574[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 24 )[/C][C]110.034722222222[/C][C]0.83074047263423[/C][C]132.453787731454[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 24 )[/C][C]109.995833333333[/C][C]0.823399565629705[/C][C]133.587431818977[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 24 )[/C][C]109.954166666667[/C][C]0.809037705548039[/C][C]135.907345124519[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 24 )[/C][C]109.220833333333[/C][C]0.677548909991272[/C][C]161.199924791762[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 24 )[/C][C]109.079166666667[/C][C]0.604119716485594[/C][C]180.558858931511[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 24 )[/C][C]108.979166666667[/C][C]0.580529605151162[/C][C]187.723702115571[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 24 )[/C][C]108.6625[/C][C]0.523323156729498[/C][C]207.639388019985[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 24 )[/C][C]108.495833333333[/C][C]0.482622261059423[/C][C]224.804867258236[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 24 )[/C][C]108.4375[/C][C]0.457751177446693[/C][C]236.891799175389[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 24 )[/C][C]108.468055555556[/C][C]0.445068730906132[/C][C]243.710797958602[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 24 )[/C][C]108.404166666667[/C][C]0.435950194837342[/C][C]248.661814928454[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 24 )[/C][C]108.0375[/C][C]0.367052920222863[/C][C]294.3376664444[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 24 )[/C][C]109.93[/C][C]1.14031405720894[/C][C]96.4032665431372[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 24 )[/C][C]109.902941176471[/C][C]1.09937920583734[/C][C]99.9681825824265[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 24 )[/C][C]109.886363636364[/C][C]1.05807999213696[/C][C]103.854495362332[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 24 )[/C][C]109.8546875[/C][C]1.01485477127677[/C][C]108.246707419815[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 24 )[/C][C]109.798387096774[/C][C]0.971349195351395[/C][C]113.036987750892[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 24 )[/C][C]109.696666666667[/C][C]0.936114600964732[/C][C]117.182945927365[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 24 )[/C][C]109.606896551724[/C][C]0.907656689433818[/C][C]120.758099210501[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 24 )[/C][C]109.519642857143[/C][C]0.88204462752948[/C][C]124.165648130409[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 24 )[/C][C]109.418518518519[/C][C]0.854629658021233[/C][C]128.030331608033[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 24 )[/C][C]109.323076923077[/C][C]0.825789148531691[/C][C]132.38618734269[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 24 )[/C][C]109.206[/C][C]0.79673010307309[/C][C]137.067746754865[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 24 )[/C][C]109.091666666667[/C][C]0.769981079562453[/C][C]141.680970561846[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 24 )[/C][C]108.980434782609[/C][C]0.741330697818909[/C][C]147.006504793668[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 24 )[/C][C]108.847727272727[/C][C]0.707409356928666[/C][C]153.868090952751[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 24 )[/C][C]108.707142857143[/C][C]0.664019653735893[/C][C]163.710730918184[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 24 )[/C][C]108.5575[/C][C]0.608938625807232[/C][C]178.273302758701[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 24 )[/C][C]108.478947368421[/C][C]0.575534359839743[/C][C]188.483876789957[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 24 )[/C][C]108.408333333333[/C][C]0.550373249972883[/C][C]196.972387990649[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 24 )[/C][C]108.341176470588[/C][C]0.521978917336372[/C][C]207.558529420014[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 24 )[/C][C]108.303125[/C][C]0.499666912742395[/C][C]216.750643755025[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 24 )[/C][C]108.28[/C][C]0.479904205000343[/C][C]225.628362643588[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 24 )[/C][C]108.260714285714[/C][C]0.458325087536627[/C][C]236.209444408959[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 24 )[/C][C]108.234615384615[/C][C]0.429380315828872[/C][C]252.071674910575[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 24 )[/C][C]108.2125[/C][C]0.387079013953841[/C][C]279.561784801137[/C][/ROW]
[ROW][C]Median[/C][C]108.25[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]111.65[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]108.272972972973[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]108.408333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]108.272972972973[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]108.408333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]108.408333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]108.272972972973[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]108.408333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]108.478947368421[/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=29289&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=29289&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 Mean109.9777777777781.1845117821527992.8465038801885
Geometric Mean109.532222368921
Harmonic Mean109.093838417736
Quadratic Mean110.429748910538
Winsorized Mean ( 1 / 24 )109.9555555555561.1747221708776693.6013282812271
Winsorized Mean ( 2 / 24 )109.9333333333331.1629652887815794.5284733721587
Winsorized Mean ( 3 / 24 )109.9708333333331.1493048138611195.6846538942828
Winsorized Mean ( 4 / 24 )110.0486111111111.1264305685331797.6967548514025
Winsorized Mean ( 5 / 24 )110.2222222222221.07281864103406102.740778363044
Winsorized Mean ( 6 / 24 )110.1305555555561.02367445280435107.583573326318
Winsorized Mean ( 7 / 24 )110.0819444444440.98858573044294111.352957112907
Winsorized Mean ( 8 / 24 )110.1263888888890.970239860828907113.504292428065
Winsorized Mean ( 9 / 24 )110.0388888888890.948146110456861116.056890046057
Winsorized Mean ( 10 / 24 )110.1361111111110.915723598443496120.272221113790
Winsorized Mean ( 11 / 24 )110.0444444444440.872584725762576126.113191298729
Winsorized Mean ( 12 / 24 )109.9444444444440.84812895628103129.631754263574
Winsorized Mean ( 13 / 24 )110.0347222222220.83074047263423132.453787731454
Winsorized Mean ( 14 / 24 )109.9958333333330.823399565629705133.587431818977
Winsorized Mean ( 15 / 24 )109.9541666666670.809037705548039135.907345124519
Winsorized Mean ( 16 / 24 )109.2208333333330.677548909991272161.199924791762
Winsorized Mean ( 17 / 24 )109.0791666666670.604119716485594180.558858931511
Winsorized Mean ( 18 / 24 )108.9791666666670.580529605151162187.723702115571
Winsorized Mean ( 19 / 24 )108.66250.523323156729498207.639388019985
Winsorized Mean ( 20 / 24 )108.4958333333330.482622261059423224.804867258236
Winsorized Mean ( 21 / 24 )108.43750.457751177446693236.891799175389
Winsorized Mean ( 22 / 24 )108.4680555555560.445068730906132243.710797958602
Winsorized Mean ( 23 / 24 )108.4041666666670.435950194837342248.661814928454
Winsorized Mean ( 24 / 24 )108.03750.367052920222863294.3376664444
Trimmed Mean ( 1 / 24 )109.931.1403140572089496.4032665431372
Trimmed Mean ( 2 / 24 )109.9029411764711.0993792058373499.9681825824265
Trimmed Mean ( 3 / 24 )109.8863636363641.05807999213696103.854495362332
Trimmed Mean ( 4 / 24 )109.85468751.01485477127677108.246707419815
Trimmed Mean ( 5 / 24 )109.7983870967740.971349195351395113.036987750892
Trimmed Mean ( 6 / 24 )109.6966666666670.936114600964732117.182945927365
Trimmed Mean ( 7 / 24 )109.6068965517240.907656689433818120.758099210501
Trimmed Mean ( 8 / 24 )109.5196428571430.88204462752948124.165648130409
Trimmed Mean ( 9 / 24 )109.4185185185190.854629658021233128.030331608033
Trimmed Mean ( 10 / 24 )109.3230769230770.825789148531691132.38618734269
Trimmed Mean ( 11 / 24 )109.2060.79673010307309137.067746754865
Trimmed Mean ( 12 / 24 )109.0916666666670.769981079562453141.680970561846
Trimmed Mean ( 13 / 24 )108.9804347826090.741330697818909147.006504793668
Trimmed Mean ( 14 / 24 )108.8477272727270.707409356928666153.868090952751
Trimmed Mean ( 15 / 24 )108.7071428571430.664019653735893163.710730918184
Trimmed Mean ( 16 / 24 )108.55750.608938625807232178.273302758701
Trimmed Mean ( 17 / 24 )108.4789473684210.575534359839743188.483876789957
Trimmed Mean ( 18 / 24 )108.4083333333330.550373249972883196.972387990649
Trimmed Mean ( 19 / 24 )108.3411764705880.521978917336372207.558529420014
Trimmed Mean ( 20 / 24 )108.3031250.499666912742395216.750643755025
Trimmed Mean ( 21 / 24 )108.280.479904205000343225.628362643588
Trimmed Mean ( 22 / 24 )108.2607142857140.458325087536627236.209444408959
Trimmed Mean ( 23 / 24 )108.2346153846150.429380315828872252.071674910575
Trimmed Mean ( 24 / 24 )108.21250.387079013953841279.561784801137
Median108.25
Midrange111.65
Midmean - Weighted Average at Xnp108.272972972973
Midmean - Weighted Average at X(n+1)p108.408333333333
Midmean - Empirical Distribution Function108.272972972973
Midmean - Empirical Distribution Function - Averaging108.408333333333
Midmean - Empirical Distribution Function - Interpolation108.408333333333
Midmean - Closest Observation108.272972972973
Midmean - True Basic - Statistics Graphics Toolkit108.408333333333
Midmean - MS Excel (old versions)108.478947368421
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')