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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 computationWed, 22 Apr 2009 14:19:58 -0600
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2009/Apr/22/t1240431641dnaorjwz14aqcgj.htm/, Retrieved Fri, 03 May 2024 06:54:38 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=39302, Retrieved Fri, 03 May 2024 06:54:38 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact179
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Central Tendency] [Anke Winckelmans] [2009-03-10 10:44:37] [74be16979710d4c4e7c6647856088456]
-    D    [Central Tendency] [Anke Winckelmans ...] [2009-04-22 20:19:58] [d41d8cd98f00b204e9800998ecf8427e] [Current]
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Dataseries X:
3779,7
3795,5
3813,1
3826,9
3833,3
3844,8
3851,3
3851,8
3854,1
3858,4
3861,6
3856,3
3855,8
3860,4
3855,1
3839,5
3833
3833,6
3826,8
3818,2
3811,4
3806,8
3810,3
3818,2
3858,9
3867,8
3872,3
3873,3
3876,7
3882,6
3883,5
3882,2
3888,1
3893,7
3901,9
3914,3
3930,3
3948,3
3971,5
3990,1
3993
3998
4015,8
4041,2
4060,7
4076,7
4103
4125,3
4139,7
4146,7
4158
4155,1
4144,8
4148,2
4142,5
4142,1
4145,4
4146,3
4143,5
4149,2
4158,9
4166,1
4179,1
4194,4
4211,7
4226,3
4235,8
4243,6
4258,7
4278,2
4298
4315,1
4334,3
4356
4374
4395,5




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Sir Ronald Aylmer Fisher' @ 193.190.124.24

\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 Ronald Aylmer Fisher' @ 193.190.124.24 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=39302&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 Ronald Aylmer Fisher' @ 193.190.124.24[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=39302&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=39302&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 Ronald Aylmer Fisher' @ 193.190.124.24







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean4010.9513157894720.2782208373366197.796017114304
Geometric Mean4007.15380695152
Harmonic Mean4003.40575394724
Quadratic Mean4014.79400787362
Winsorized Mean ( 1 / 25 )4010.8763157894720.1779100050005198.775607324817
Winsorized Mean ( 2 / 25 )4010.720.0252691245030200.281952520303
Winsorized Mean ( 3 / 25 )4009.9815789473719.8146465153472202.374621007823
Winsorized Mean ( 4 / 25 )4009.0289473684219.5913208330941204.632907680032
Winsorized Mean ( 5 / 25 )4008.0157894736819.3466702382472207.16824859867
Winsorized Mean ( 6 / 25 )4006.8552631578918.9877645178426211.023012182013
Winsorized Mean ( 7 / 25 )4005.0592105263218.6537711889751214.705067943228
Winsorized Mean ( 8 / 25 )4004.37518.2515505830110219.399167308413
Winsorized Mean ( 9 / 25 )4003.4631578947418.0902052437714221.305568618309
Winsorized Mean ( 10 / 25 )4003.0157894736817.7750622722162225.204037441304
Winsorized Mean ( 11 / 25 )4000.9460526315817.4220588588135229.648291574194
Winsorized Mean ( 12 / 25 )3998.2618421052616.9852529397839235.39607306879
Winsorized Mean ( 13 / 25 )3996.6539473684216.4607965359900242.798332306101
Winsorized Mean ( 14 / 25 )3995.2355263157915.9897661025373249.862036798763
Winsorized Mean ( 15 / 25 )3995.0973684210515.6300552775043255.603534183980
Winsorized Mean ( 16 / 25 )3995.0131578947415.5907098228181256.243186057363
Winsorized Mean ( 17 / 25 )3994.8789473684215.4378328080656258.772004920358
Winsorized Mean ( 18 / 25 )3993.7184210526315.2171723991814262.448128751402
Winsorized Mean ( 19 / 25 )3993.6434210526315.1619193266721263.399595724481
Winsorized Mean ( 20 / 25 )3993.3802631579015.0924177570548264.595131637622
Winsorized Mean ( 21 / 25 )3993.8515.0073962466933266.125444703974
Winsorized Mean ( 22 / 25 )3993.7342105263214.9547296458733267.054925438145
Winsorized Mean ( 23 / 25 )3994.0065789473714.8757149715275268.491738823445
Winsorized Mean ( 24 / 25 )3993.97514.7749497728241270.320715901601
Winsorized Mean ( 25 / 25 )3995.6855263157914.4886902903485275.779621638919
Trimmed Mean ( 1 / 25 )4008.8797297297319.9137493203705201.312151982796
Trimmed Mean ( 2 / 25 )4006.7722222222219.5960757886732204.468091746113
Trimmed Mean ( 3 / 25 )4004.6419.3088253028394207.399463053359
Trimmed Mean ( 4 / 25 )4002.6519.053891790438210.069944976212
Trimmed Mean ( 5 / 25 )4000.8136363636418.8209281775784212.572599959754
Trimmed Mean ( 6 / 25 )3999.10312518.6065403312641214.929968376787
Trimmed Mean ( 7 / 25 )3997.5193548387118.4336057353318216.860413108253
Trimmed Mean ( 8 / 25 )3996.15518.2932245530421218.450005269052
Trimmed Mean ( 9 / 25 )3994.8086206896618.1961619648473219.541276254143
Trimmed Mean ( 10 / 25 )3993.5035714285718.0929427592685220.721616409404
Trimmed Mean ( 11 / 25 )3992.1648148148118.0088469518551221.677980022123
Trimmed Mean ( 12 / 25 )3990.9980769230817.9522496962986222.311863105710
Trimmed Mean ( 13 / 25 )3990.07817.9398815298798222.413843333041
Trimmed Mean ( 14 / 25 )3989.2770833333317.9892669536093221.758735006872
Trimmed Mean ( 15 / 25 )3988.5739130434818.0967588404471220.402667030564
Trimmed Mean ( 16 / 25 )3987.8227272727318.2481995009883218.532394226442
Trimmed Mean ( 17 / 25 )3987.0095238095218.3927290870531216.770959053381
Trimmed Mean ( 18 / 25 )3986.1318.5463619350438214.927866390233
Trimmed Mean ( 19 / 25 )3985.2868421052618.7216198384344212.870834708635
Trimmed Mean ( 20 / 25 )3984.3583333333318.8869461827769210.958314529783
Trimmed Mean ( 21 / 25 )3983.3519.0382569389303209.228713152551
Trimmed Mean ( 22 / 25 )3982.162519.1677767180890207.752967835959
Trimmed Mean ( 23 / 25 )3980.8319.2554229710257206.738122864925
Trimmed Mean ( 24 / 25 )3979.27519.2832476744198206.359170777997
Trimmed Mean ( 25 / 25 )3977.4846153846219.2239111463644206.9029858233
Median3959.9
Midrange4087.6
Midmean - Weighted Average at Xnp3981.94871794872
Midmean - Weighted Average at X(n+1)p3985.28684210526
Midmean - Empirical Distribution Function3981.94871794872
Midmean - Empirical Distribution Function - Averaging3985.28684210526
Midmean - Empirical Distribution Function - Interpolation3985.28684210526
Midmean - Closest Observation3981.94871794872
Midmean - True Basic - Statistics Graphics Toolkit3985.28684210526
Midmean - MS Excel (old versions)3986.13
Number of observations76

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 4010.95131578947 & 20.2782208373366 & 197.796017114304 \tabularnewline
Geometric Mean & 4007.15380695152 &  &  \tabularnewline
Harmonic Mean & 4003.40575394724 &  &  \tabularnewline
Quadratic Mean & 4014.79400787362 &  &  \tabularnewline
Winsorized Mean ( 1 / 25 ) & 4010.87631578947 & 20.1779100050005 & 198.775607324817 \tabularnewline
Winsorized Mean ( 2 / 25 ) & 4010.7 & 20.0252691245030 & 200.281952520303 \tabularnewline
Winsorized Mean ( 3 / 25 ) & 4009.98157894737 & 19.8146465153472 & 202.374621007823 \tabularnewline
Winsorized Mean ( 4 / 25 ) & 4009.02894736842 & 19.5913208330941 & 204.632907680032 \tabularnewline
Winsorized Mean ( 5 / 25 ) & 4008.01578947368 & 19.3466702382472 & 207.16824859867 \tabularnewline
Winsorized Mean ( 6 / 25 ) & 4006.85526315789 & 18.9877645178426 & 211.023012182013 \tabularnewline
Winsorized Mean ( 7 / 25 ) & 4005.05921052632 & 18.6537711889751 & 214.705067943228 \tabularnewline
Winsorized Mean ( 8 / 25 ) & 4004.375 & 18.2515505830110 & 219.399167308413 \tabularnewline
Winsorized Mean ( 9 / 25 ) & 4003.46315789474 & 18.0902052437714 & 221.305568618309 \tabularnewline
Winsorized Mean ( 10 / 25 ) & 4003.01578947368 & 17.7750622722162 & 225.204037441304 \tabularnewline
Winsorized Mean ( 11 / 25 ) & 4000.94605263158 & 17.4220588588135 & 229.648291574194 \tabularnewline
Winsorized Mean ( 12 / 25 ) & 3998.26184210526 & 16.9852529397839 & 235.39607306879 \tabularnewline
Winsorized Mean ( 13 / 25 ) & 3996.65394736842 & 16.4607965359900 & 242.798332306101 \tabularnewline
Winsorized Mean ( 14 / 25 ) & 3995.23552631579 & 15.9897661025373 & 249.862036798763 \tabularnewline
Winsorized Mean ( 15 / 25 ) & 3995.09736842105 & 15.6300552775043 & 255.603534183980 \tabularnewline
Winsorized Mean ( 16 / 25 ) & 3995.01315789474 & 15.5907098228181 & 256.243186057363 \tabularnewline
Winsorized Mean ( 17 / 25 ) & 3994.87894736842 & 15.4378328080656 & 258.772004920358 \tabularnewline
Winsorized Mean ( 18 / 25 ) & 3993.71842105263 & 15.2171723991814 & 262.448128751402 \tabularnewline
Winsorized Mean ( 19 / 25 ) & 3993.64342105263 & 15.1619193266721 & 263.399595724481 \tabularnewline
Winsorized Mean ( 20 / 25 ) & 3993.38026315790 & 15.0924177570548 & 264.595131637622 \tabularnewline
Winsorized Mean ( 21 / 25 ) & 3993.85 & 15.0073962466933 & 266.125444703974 \tabularnewline
Winsorized Mean ( 22 / 25 ) & 3993.73421052632 & 14.9547296458733 & 267.054925438145 \tabularnewline
Winsorized Mean ( 23 / 25 ) & 3994.00657894737 & 14.8757149715275 & 268.491738823445 \tabularnewline
Winsorized Mean ( 24 / 25 ) & 3993.975 & 14.7749497728241 & 270.320715901601 \tabularnewline
Winsorized Mean ( 25 / 25 ) & 3995.68552631579 & 14.4886902903485 & 275.779621638919 \tabularnewline
Trimmed Mean ( 1 / 25 ) & 4008.87972972973 & 19.9137493203705 & 201.312151982796 \tabularnewline
Trimmed Mean ( 2 / 25 ) & 4006.77222222222 & 19.5960757886732 & 204.468091746113 \tabularnewline
Trimmed Mean ( 3 / 25 ) & 4004.64 & 19.3088253028394 & 207.399463053359 \tabularnewline
Trimmed Mean ( 4 / 25 ) & 4002.65 & 19.053891790438 & 210.069944976212 \tabularnewline
Trimmed Mean ( 5 / 25 ) & 4000.81363636364 & 18.8209281775784 & 212.572599959754 \tabularnewline
Trimmed Mean ( 6 / 25 ) & 3999.103125 & 18.6065403312641 & 214.929968376787 \tabularnewline
Trimmed Mean ( 7 / 25 ) & 3997.51935483871 & 18.4336057353318 & 216.860413108253 \tabularnewline
Trimmed Mean ( 8 / 25 ) & 3996.155 & 18.2932245530421 & 218.450005269052 \tabularnewline
Trimmed Mean ( 9 / 25 ) & 3994.80862068966 & 18.1961619648473 & 219.541276254143 \tabularnewline
Trimmed Mean ( 10 / 25 ) & 3993.50357142857 & 18.0929427592685 & 220.721616409404 \tabularnewline
Trimmed Mean ( 11 / 25 ) & 3992.16481481481 & 18.0088469518551 & 221.677980022123 \tabularnewline
Trimmed Mean ( 12 / 25 ) & 3990.99807692308 & 17.9522496962986 & 222.311863105710 \tabularnewline
Trimmed Mean ( 13 / 25 ) & 3990.078 & 17.9398815298798 & 222.413843333041 \tabularnewline
Trimmed Mean ( 14 / 25 ) & 3989.27708333333 & 17.9892669536093 & 221.758735006872 \tabularnewline
Trimmed Mean ( 15 / 25 ) & 3988.57391304348 & 18.0967588404471 & 220.402667030564 \tabularnewline
Trimmed Mean ( 16 / 25 ) & 3987.82272727273 & 18.2481995009883 & 218.532394226442 \tabularnewline
Trimmed Mean ( 17 / 25 ) & 3987.00952380952 & 18.3927290870531 & 216.770959053381 \tabularnewline
Trimmed Mean ( 18 / 25 ) & 3986.13 & 18.5463619350438 & 214.927866390233 \tabularnewline
Trimmed Mean ( 19 / 25 ) & 3985.28684210526 & 18.7216198384344 & 212.870834708635 \tabularnewline
Trimmed Mean ( 20 / 25 ) & 3984.35833333333 & 18.8869461827769 & 210.958314529783 \tabularnewline
Trimmed Mean ( 21 / 25 ) & 3983.35 & 19.0382569389303 & 209.228713152551 \tabularnewline
Trimmed Mean ( 22 / 25 ) & 3982.1625 & 19.1677767180890 & 207.752967835959 \tabularnewline
Trimmed Mean ( 23 / 25 ) & 3980.83 & 19.2554229710257 & 206.738122864925 \tabularnewline
Trimmed Mean ( 24 / 25 ) & 3979.275 & 19.2832476744198 & 206.359170777997 \tabularnewline
Trimmed Mean ( 25 / 25 ) & 3977.48461538462 & 19.2239111463644 & 206.9029858233 \tabularnewline
Median & 3959.9 &  &  \tabularnewline
Midrange & 4087.6 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 3981.94871794872 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 3985.28684210526 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 3981.94871794872 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 3985.28684210526 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 3985.28684210526 &  &  \tabularnewline
Midmean - Closest Observation & 3981.94871794872 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 3985.28684210526 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 3986.13 &  &  \tabularnewline
Number of observations & 76 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=39302&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]4010.95131578947[/C][C]20.2782208373366[/C][C]197.796017114304[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]4007.15380695152[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]4003.40575394724[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]4014.79400787362[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 25 )[/C][C]4010.87631578947[/C][C]20.1779100050005[/C][C]198.775607324817[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 25 )[/C][C]4010.7[/C][C]20.0252691245030[/C][C]200.281952520303[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 25 )[/C][C]4009.98157894737[/C][C]19.8146465153472[/C][C]202.374621007823[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 25 )[/C][C]4009.02894736842[/C][C]19.5913208330941[/C][C]204.632907680032[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 25 )[/C][C]4008.01578947368[/C][C]19.3466702382472[/C][C]207.16824859867[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 25 )[/C][C]4006.85526315789[/C][C]18.9877645178426[/C][C]211.023012182013[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 25 )[/C][C]4005.05921052632[/C][C]18.6537711889751[/C][C]214.705067943228[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 25 )[/C][C]4004.375[/C][C]18.2515505830110[/C][C]219.399167308413[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 25 )[/C][C]4003.46315789474[/C][C]18.0902052437714[/C][C]221.305568618309[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 25 )[/C][C]4003.01578947368[/C][C]17.7750622722162[/C][C]225.204037441304[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 25 )[/C][C]4000.94605263158[/C][C]17.4220588588135[/C][C]229.648291574194[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 25 )[/C][C]3998.26184210526[/C][C]16.9852529397839[/C][C]235.39607306879[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 25 )[/C][C]3996.65394736842[/C][C]16.4607965359900[/C][C]242.798332306101[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 25 )[/C][C]3995.23552631579[/C][C]15.9897661025373[/C][C]249.862036798763[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 25 )[/C][C]3995.09736842105[/C][C]15.6300552775043[/C][C]255.603534183980[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 25 )[/C][C]3995.01315789474[/C][C]15.5907098228181[/C][C]256.243186057363[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 25 )[/C][C]3994.87894736842[/C][C]15.4378328080656[/C][C]258.772004920358[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 25 )[/C][C]3993.71842105263[/C][C]15.2171723991814[/C][C]262.448128751402[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 25 )[/C][C]3993.64342105263[/C][C]15.1619193266721[/C][C]263.399595724481[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 25 )[/C][C]3993.38026315790[/C][C]15.0924177570548[/C][C]264.595131637622[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 25 )[/C][C]3993.85[/C][C]15.0073962466933[/C][C]266.125444703974[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 25 )[/C][C]3993.73421052632[/C][C]14.9547296458733[/C][C]267.054925438145[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 25 )[/C][C]3994.00657894737[/C][C]14.8757149715275[/C][C]268.491738823445[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 25 )[/C][C]3993.975[/C][C]14.7749497728241[/C][C]270.320715901601[/C][/ROW]
[ROW][C]Winsorized Mean ( 25 / 25 )[/C][C]3995.68552631579[/C][C]14.4886902903485[/C][C]275.779621638919[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 25 )[/C][C]4008.87972972973[/C][C]19.9137493203705[/C][C]201.312151982796[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 25 )[/C][C]4006.77222222222[/C][C]19.5960757886732[/C][C]204.468091746113[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 25 )[/C][C]4004.64[/C][C]19.3088253028394[/C][C]207.399463053359[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 25 )[/C][C]4002.65[/C][C]19.053891790438[/C][C]210.069944976212[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 25 )[/C][C]4000.81363636364[/C][C]18.8209281775784[/C][C]212.572599959754[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 25 )[/C][C]3999.103125[/C][C]18.6065403312641[/C][C]214.929968376787[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 25 )[/C][C]3997.51935483871[/C][C]18.4336057353318[/C][C]216.860413108253[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 25 )[/C][C]3996.155[/C][C]18.2932245530421[/C][C]218.450005269052[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 25 )[/C][C]3994.80862068966[/C][C]18.1961619648473[/C][C]219.541276254143[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 25 )[/C][C]3993.50357142857[/C][C]18.0929427592685[/C][C]220.721616409404[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 25 )[/C][C]3992.16481481481[/C][C]18.0088469518551[/C][C]221.677980022123[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 25 )[/C][C]3990.99807692308[/C][C]17.9522496962986[/C][C]222.311863105710[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 25 )[/C][C]3990.078[/C][C]17.9398815298798[/C][C]222.413843333041[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 25 )[/C][C]3989.27708333333[/C][C]17.9892669536093[/C][C]221.758735006872[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 25 )[/C][C]3988.57391304348[/C][C]18.0967588404471[/C][C]220.402667030564[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 25 )[/C][C]3987.82272727273[/C][C]18.2481995009883[/C][C]218.532394226442[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 25 )[/C][C]3987.00952380952[/C][C]18.3927290870531[/C][C]216.770959053381[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 25 )[/C][C]3986.13[/C][C]18.5463619350438[/C][C]214.927866390233[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 25 )[/C][C]3985.28684210526[/C][C]18.7216198384344[/C][C]212.870834708635[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 25 )[/C][C]3984.35833333333[/C][C]18.8869461827769[/C][C]210.958314529783[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 25 )[/C][C]3983.35[/C][C]19.0382569389303[/C][C]209.228713152551[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 25 )[/C][C]3982.1625[/C][C]19.1677767180890[/C][C]207.752967835959[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 25 )[/C][C]3980.83[/C][C]19.2554229710257[/C][C]206.738122864925[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 25 )[/C][C]3979.275[/C][C]19.2832476744198[/C][C]206.359170777997[/C][/ROW]
[ROW][C]Trimmed Mean ( 25 / 25 )[/C][C]3977.48461538462[/C][C]19.2239111463644[/C][C]206.9029858233[/C][/ROW]
[ROW][C]Median[/C][C]3959.9[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]4087.6[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]3981.94871794872[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]3985.28684210526[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]3981.94871794872[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]3985.28684210526[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]3985.28684210526[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]3981.94871794872[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]3985.28684210526[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]3986.13[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]76[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=39302&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=39302&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 Mean4010.9513157894720.2782208373366197.796017114304
Geometric Mean4007.15380695152
Harmonic Mean4003.40575394724
Quadratic Mean4014.79400787362
Winsorized Mean ( 1 / 25 )4010.8763157894720.1779100050005198.775607324817
Winsorized Mean ( 2 / 25 )4010.720.0252691245030200.281952520303
Winsorized Mean ( 3 / 25 )4009.9815789473719.8146465153472202.374621007823
Winsorized Mean ( 4 / 25 )4009.0289473684219.5913208330941204.632907680032
Winsorized Mean ( 5 / 25 )4008.0157894736819.3466702382472207.16824859867
Winsorized Mean ( 6 / 25 )4006.8552631578918.9877645178426211.023012182013
Winsorized Mean ( 7 / 25 )4005.0592105263218.6537711889751214.705067943228
Winsorized Mean ( 8 / 25 )4004.37518.2515505830110219.399167308413
Winsorized Mean ( 9 / 25 )4003.4631578947418.0902052437714221.305568618309
Winsorized Mean ( 10 / 25 )4003.0157894736817.7750622722162225.204037441304
Winsorized Mean ( 11 / 25 )4000.9460526315817.4220588588135229.648291574194
Winsorized Mean ( 12 / 25 )3998.2618421052616.9852529397839235.39607306879
Winsorized Mean ( 13 / 25 )3996.6539473684216.4607965359900242.798332306101
Winsorized Mean ( 14 / 25 )3995.2355263157915.9897661025373249.862036798763
Winsorized Mean ( 15 / 25 )3995.0973684210515.6300552775043255.603534183980
Winsorized Mean ( 16 / 25 )3995.0131578947415.5907098228181256.243186057363
Winsorized Mean ( 17 / 25 )3994.8789473684215.4378328080656258.772004920358
Winsorized Mean ( 18 / 25 )3993.7184210526315.2171723991814262.448128751402
Winsorized Mean ( 19 / 25 )3993.6434210526315.1619193266721263.399595724481
Winsorized Mean ( 20 / 25 )3993.3802631579015.0924177570548264.595131637622
Winsorized Mean ( 21 / 25 )3993.8515.0073962466933266.125444703974
Winsorized Mean ( 22 / 25 )3993.7342105263214.9547296458733267.054925438145
Winsorized Mean ( 23 / 25 )3994.0065789473714.8757149715275268.491738823445
Winsorized Mean ( 24 / 25 )3993.97514.7749497728241270.320715901601
Winsorized Mean ( 25 / 25 )3995.6855263157914.4886902903485275.779621638919
Trimmed Mean ( 1 / 25 )4008.8797297297319.9137493203705201.312151982796
Trimmed Mean ( 2 / 25 )4006.7722222222219.5960757886732204.468091746113
Trimmed Mean ( 3 / 25 )4004.6419.3088253028394207.399463053359
Trimmed Mean ( 4 / 25 )4002.6519.053891790438210.069944976212
Trimmed Mean ( 5 / 25 )4000.8136363636418.8209281775784212.572599959754
Trimmed Mean ( 6 / 25 )3999.10312518.6065403312641214.929968376787
Trimmed Mean ( 7 / 25 )3997.5193548387118.4336057353318216.860413108253
Trimmed Mean ( 8 / 25 )3996.15518.2932245530421218.450005269052
Trimmed Mean ( 9 / 25 )3994.8086206896618.1961619648473219.541276254143
Trimmed Mean ( 10 / 25 )3993.5035714285718.0929427592685220.721616409404
Trimmed Mean ( 11 / 25 )3992.1648148148118.0088469518551221.677980022123
Trimmed Mean ( 12 / 25 )3990.9980769230817.9522496962986222.311863105710
Trimmed Mean ( 13 / 25 )3990.07817.9398815298798222.413843333041
Trimmed Mean ( 14 / 25 )3989.2770833333317.9892669536093221.758735006872
Trimmed Mean ( 15 / 25 )3988.5739130434818.0967588404471220.402667030564
Trimmed Mean ( 16 / 25 )3987.8227272727318.2481995009883218.532394226442
Trimmed Mean ( 17 / 25 )3987.0095238095218.3927290870531216.770959053381
Trimmed Mean ( 18 / 25 )3986.1318.5463619350438214.927866390233
Trimmed Mean ( 19 / 25 )3985.2868421052618.7216198384344212.870834708635
Trimmed Mean ( 20 / 25 )3984.3583333333318.8869461827769210.958314529783
Trimmed Mean ( 21 / 25 )3983.3519.0382569389303209.228713152551
Trimmed Mean ( 22 / 25 )3982.162519.1677767180890207.752967835959
Trimmed Mean ( 23 / 25 )3980.8319.2554229710257206.738122864925
Trimmed Mean ( 24 / 25 )3979.27519.2832476744198206.359170777997
Trimmed Mean ( 25 / 25 )3977.4846153846219.2239111463644206.9029858233
Median3959.9
Midrange4087.6
Midmean - Weighted Average at Xnp3981.94871794872
Midmean - Weighted Average at X(n+1)p3985.28684210526
Midmean - Empirical Distribution Function3981.94871794872
Midmean - Empirical Distribution Function - Averaging3985.28684210526
Midmean - Empirical Distribution Function - Interpolation3985.28684210526
Midmean - Closest Observation3981.94871794872
Midmean - True Basic - Statistics Graphics Toolkit3985.28684210526
Midmean - MS Excel (old versions)3986.13
Number of observations76



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')