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Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationFri, 26 Nov 2010 14:22:51 +0000
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2010/Nov/26/t1290782181jay8qtutgkvefel.htm/, Retrieved Sat, 04 May 2024 00:55:32 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=101939, Retrieved Sat, 04 May 2024 00:55:32 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact104
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
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Dataseries X:
4946
4490
4851
4591
4279
4191
4285
4516
4197
4404
4373
5307
5320
4356
4484
4210
4018
3912
3972
3886
3892
4242
4134
4743
5116
4823
5489
4263
4221
4076
3715
3715
3784
4141
3968
4767
5019
4343
4853
4154
4035
3996
4734
3778
3887
3953
3987
4436
4803
4672
4560
4289
3961
3943
3932
3816
3834
4130
4467
4447




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'RServer@AstonUniversity' @ vre.aston.ac.uk

\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 & 'RServer@AstonUniversity' @ vre.aston.ac.uk \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=101939&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]'RServer@AstonUniversity' @ vre.aston.ac.uk[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=101939&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=101939&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'RServer@AstonUniversity' @ vre.aston.ac.uk







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean4328.4333333333355.337022714115478.2194834676068
Geometric Mean4308.38124318079
Harmonic Mean4289.1309213628
Quadratic Mean4349.25328073682
Winsorized Mean ( 1 / 20 )4325.6166666666754.399526894683179.5157037861931
Winsorized Mean ( 2 / 20 )4327.2833333333353.884366105078680.306843081253
Winsorized Mean ( 3 / 20 )4318.0333333333351.09082953450284.5167982723267
Winsorized Mean ( 4 / 20 )4313.749.073439143578887.9029486272401
Winsorized Mean ( 5 / 20 )4309.1166666666747.382284060073990.9436248620546
Winsorized Mean ( 6 / 20 )4305.0166666666744.491670595225596.7600588845646
Winsorized Mean ( 7 / 20 )4304.944.42439587830796.9039626738545
Winsorized Mean ( 8 / 20 )4301.8333333333343.550439402238698.778184385258
Winsorized Mean ( 9 / 20 )4301.8333333333342.4734823664301101.282802672507
Winsorized Mean ( 10 / 20 )4299.1666666666740.7760465208212105.433631592298
Winsorized Mean ( 11 / 20 )4296.7833333333339.6216719479033108.445280627808
Winsorized Mean ( 12 / 20 )4296.9833333333338.9779127058867110.241494093253
Winsorized Mean ( 13 / 20 )4285.2833333333336.2228436497131118.303338489199
Winsorized Mean ( 14 / 20 )4268.0166666666732.6721126412793130.631793343975
Winsorized Mean ( 15 / 20 )4261.2666666666731.2380044020215136.412896669894
Winsorized Mean ( 16 / 20 )4253.5333333333328.7493597734332147.952280219609
Winsorized Mean ( 17 / 20 )4248.7166666666727.2247300720373156.060928994501
Winsorized Mean ( 18 / 20 )4253.5166666666725.926378727774164.061348919124
Winsorized Mean ( 19 / 20 )4253.5166666666724.2948750921646175.078762518046
Winsorized Mean ( 20 / 20 )4260.5166666666721.2529757526505200.46682950435
Trimmed Mean ( 1 / 20 )431952.498846240887282.2684746286152
Trimmed Mean ( 2 / 20 )4311.9107142857150.136600913499986.0032518304344
Trimmed Mean ( 3 / 20 )4303.3703703703747.520375535685990.5584251357338
Trimmed Mean ( 4 / 20 )4297.7307692307745.668993307956394.1060982065054
Trimmed Mean ( 5 / 20 )4292.9444.159824848070397.2137007963607
Trimmed Mean ( 6 / 20 )4288.8958333333342.8372232371109100.120771357975
Trimmed Mean ( 7 / 20 )4285.3913043478342.0416112969672101.932137521498
Trimmed Mean ( 8 / 20 )4281.5909090909140.9935708642301104.445424461105
Trimmed Mean ( 9 / 20 )4277.9761904761939.845819114728107.363238741777
Trimmed Mean ( 10 / 20 )427438.5953697236153110.738672296871
Trimmed Mean ( 11 / 20 )4270.0263157894737.3668044548444114.273253442091
Trimmed Mean ( 12 / 20 )4265.9722222222235.988589155213118.536800757145
Trimmed Mean ( 13 / 20 )4261.4117647058834.2244900287929124.513521198439
Trimmed Mean ( 14 / 20 )4257.9687532.6115790704119130.566163043089
Trimmed Mean ( 15 / 20 )4256.5333333333331.4396606301086135.38738167094
Trimmed Mean ( 16 / 20 )4255.8571428571430.1427254943337141.190190105973
Trimmed Mean ( 17 / 20 )4256.1923076923129.0073740879675146.727942170326
Trimmed Mean ( 18 / 20 )4257.2916666666727.7323177223982153.513734743787
Trimmed Mean ( 19 / 20 )4257.8636363636426.1476241505988162.839407964572
Trimmed Mean ( 20 / 20 )4258.5524.1950924776079176.008833359129
Median4252.5
Midrange4602
Midmean - Weighted Average at Xnp4247.22580645161
Midmean - Weighted Average at X(n+1)p4256.53333333333
Midmean - Empirical Distribution Function4247.22580645161
Midmean - Empirical Distribution Function - Averaging4256.53333333333
Midmean - Empirical Distribution Function - Interpolation4256.53333333333
Midmean - Closest Observation4247.22580645161
Midmean - True Basic - Statistics Graphics Toolkit4256.53333333333
Midmean - MS Excel (old versions)4257.96875
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 4328.43333333333 & 55.3370227141154 & 78.2194834676068 \tabularnewline
Geometric Mean & 4308.38124318079 &  &  \tabularnewline
Harmonic Mean & 4289.1309213628 &  &  \tabularnewline
Quadratic Mean & 4349.25328073682 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 4325.61666666667 & 54.3995268946831 & 79.5157037861931 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 4327.28333333333 & 53.8843661050786 & 80.306843081253 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 4318.03333333333 & 51.090829534502 & 84.5167982723267 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 4313.7 & 49.0734391435788 & 87.9029486272401 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 4309.11666666667 & 47.3822840600739 & 90.9436248620546 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 4305.01666666667 & 44.4916705952255 & 96.7600588845646 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 4304.9 & 44.424395878307 & 96.9039626738545 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 4301.83333333333 & 43.5504394022386 & 98.778184385258 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 4301.83333333333 & 42.4734823664301 & 101.282802672507 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 4299.16666666667 & 40.7760465208212 & 105.433631592298 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 4296.78333333333 & 39.6216719479033 & 108.445280627808 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 4296.98333333333 & 38.9779127058867 & 110.241494093253 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 4285.28333333333 & 36.2228436497131 & 118.303338489199 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 4268.01666666667 & 32.6721126412793 & 130.631793343975 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 4261.26666666667 & 31.2380044020215 & 136.412896669894 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 4253.53333333333 & 28.7493597734332 & 147.952280219609 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 4248.71666666667 & 27.2247300720373 & 156.060928994501 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 4253.51666666667 & 25.926378727774 & 164.061348919124 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 4253.51666666667 & 24.2948750921646 & 175.078762518046 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 4260.51666666667 & 21.2529757526505 & 200.46682950435 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 4319 & 52.4988462408872 & 82.2684746286152 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 4311.91071428571 & 50.1366009134999 & 86.0032518304344 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 4303.37037037037 & 47.5203755356859 & 90.5584251357338 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 4297.73076923077 & 45.6689933079563 & 94.1060982065054 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 4292.94 & 44.1598248480703 & 97.2137007963607 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 4288.89583333333 & 42.8372232371109 & 100.120771357975 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 4285.39130434783 & 42.0416112969672 & 101.932137521498 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 4281.59090909091 & 40.9935708642301 & 104.445424461105 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 4277.97619047619 & 39.845819114728 & 107.363238741777 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 4274 & 38.5953697236153 & 110.738672296871 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 4270.02631578947 & 37.3668044548444 & 114.273253442091 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 4265.97222222222 & 35.988589155213 & 118.536800757145 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 4261.41176470588 & 34.2244900287929 & 124.513521198439 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 4257.96875 & 32.6115790704119 & 130.566163043089 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 4256.53333333333 & 31.4396606301086 & 135.38738167094 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 4255.85714285714 & 30.1427254943337 & 141.190190105973 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 4256.19230769231 & 29.0073740879675 & 146.727942170326 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 4257.29166666667 & 27.7323177223982 & 153.513734743787 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 4257.86363636364 & 26.1476241505988 & 162.839407964572 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 4258.55 & 24.1950924776079 & 176.008833359129 \tabularnewline
Median & 4252.5 &  &  \tabularnewline
Midrange & 4602 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 4247.22580645161 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 4256.53333333333 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 4247.22580645161 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 4256.53333333333 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 4256.53333333333 &  &  \tabularnewline
Midmean - Closest Observation & 4247.22580645161 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 4256.53333333333 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 4257.96875 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=101939&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]4328.43333333333[/C][C]55.3370227141154[/C][C]78.2194834676068[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]4308.38124318079[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]4289.1309213628[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]4349.25328073682[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]4325.61666666667[/C][C]54.3995268946831[/C][C]79.5157037861931[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]4327.28333333333[/C][C]53.8843661050786[/C][C]80.306843081253[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]4318.03333333333[/C][C]51.090829534502[/C][C]84.5167982723267[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]4313.7[/C][C]49.0734391435788[/C][C]87.9029486272401[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]4309.11666666667[/C][C]47.3822840600739[/C][C]90.9436248620546[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]4305.01666666667[/C][C]44.4916705952255[/C][C]96.7600588845646[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]4304.9[/C][C]44.424395878307[/C][C]96.9039626738545[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]4301.83333333333[/C][C]43.5504394022386[/C][C]98.778184385258[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]4301.83333333333[/C][C]42.4734823664301[/C][C]101.282802672507[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]4299.16666666667[/C][C]40.7760465208212[/C][C]105.433631592298[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]4296.78333333333[/C][C]39.6216719479033[/C][C]108.445280627808[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]4296.98333333333[/C][C]38.9779127058867[/C][C]110.241494093253[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]4285.28333333333[/C][C]36.2228436497131[/C][C]118.303338489199[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]4268.01666666667[/C][C]32.6721126412793[/C][C]130.631793343975[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]4261.26666666667[/C][C]31.2380044020215[/C][C]136.412896669894[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]4253.53333333333[/C][C]28.7493597734332[/C][C]147.952280219609[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]4248.71666666667[/C][C]27.2247300720373[/C][C]156.060928994501[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]4253.51666666667[/C][C]25.926378727774[/C][C]164.061348919124[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]4253.51666666667[/C][C]24.2948750921646[/C][C]175.078762518046[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]4260.51666666667[/C][C]21.2529757526505[/C][C]200.46682950435[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]4319[/C][C]52.4988462408872[/C][C]82.2684746286152[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]4311.91071428571[/C][C]50.1366009134999[/C][C]86.0032518304344[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]4303.37037037037[/C][C]47.5203755356859[/C][C]90.5584251357338[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]4297.73076923077[/C][C]45.6689933079563[/C][C]94.1060982065054[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]4292.94[/C][C]44.1598248480703[/C][C]97.2137007963607[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]4288.89583333333[/C][C]42.8372232371109[/C][C]100.120771357975[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]4285.39130434783[/C][C]42.0416112969672[/C][C]101.932137521498[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]4281.59090909091[/C][C]40.9935708642301[/C][C]104.445424461105[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]4277.97619047619[/C][C]39.845819114728[/C][C]107.363238741777[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]4274[/C][C]38.5953697236153[/C][C]110.738672296871[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]4270.02631578947[/C][C]37.3668044548444[/C][C]114.273253442091[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]4265.97222222222[/C][C]35.988589155213[/C][C]118.536800757145[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]4261.41176470588[/C][C]34.2244900287929[/C][C]124.513521198439[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]4257.96875[/C][C]32.6115790704119[/C][C]130.566163043089[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]4256.53333333333[/C][C]31.4396606301086[/C][C]135.38738167094[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]4255.85714285714[/C][C]30.1427254943337[/C][C]141.190190105973[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]4256.19230769231[/C][C]29.0073740879675[/C][C]146.727942170326[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]4257.29166666667[/C][C]27.7323177223982[/C][C]153.513734743787[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]4257.86363636364[/C][C]26.1476241505988[/C][C]162.839407964572[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]4258.55[/C][C]24.1950924776079[/C][C]176.008833359129[/C][/ROW]
[ROW][C]Median[/C][C]4252.5[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]4602[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]4247.22580645161[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]4256.53333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]4247.22580645161[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]4256.53333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]4256.53333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]4247.22580645161[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]4256.53333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]4257.96875[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]60[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=101939&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=101939&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 Mean4328.4333333333355.337022714115478.2194834676068
Geometric Mean4308.38124318079
Harmonic Mean4289.1309213628
Quadratic Mean4349.25328073682
Winsorized Mean ( 1 / 20 )4325.6166666666754.399526894683179.5157037861931
Winsorized Mean ( 2 / 20 )4327.2833333333353.884366105078680.306843081253
Winsorized Mean ( 3 / 20 )4318.0333333333351.09082953450284.5167982723267
Winsorized Mean ( 4 / 20 )4313.749.073439143578887.9029486272401
Winsorized Mean ( 5 / 20 )4309.1166666666747.382284060073990.9436248620546
Winsorized Mean ( 6 / 20 )4305.0166666666744.491670595225596.7600588845646
Winsorized Mean ( 7 / 20 )4304.944.42439587830796.9039626738545
Winsorized Mean ( 8 / 20 )4301.8333333333343.550439402238698.778184385258
Winsorized Mean ( 9 / 20 )4301.8333333333342.4734823664301101.282802672507
Winsorized Mean ( 10 / 20 )4299.1666666666740.7760465208212105.433631592298
Winsorized Mean ( 11 / 20 )4296.7833333333339.6216719479033108.445280627808
Winsorized Mean ( 12 / 20 )4296.9833333333338.9779127058867110.241494093253
Winsorized Mean ( 13 / 20 )4285.2833333333336.2228436497131118.303338489199
Winsorized Mean ( 14 / 20 )4268.0166666666732.6721126412793130.631793343975
Winsorized Mean ( 15 / 20 )4261.2666666666731.2380044020215136.412896669894
Winsorized Mean ( 16 / 20 )4253.5333333333328.7493597734332147.952280219609
Winsorized Mean ( 17 / 20 )4248.7166666666727.2247300720373156.060928994501
Winsorized Mean ( 18 / 20 )4253.5166666666725.926378727774164.061348919124
Winsorized Mean ( 19 / 20 )4253.5166666666724.2948750921646175.078762518046
Winsorized Mean ( 20 / 20 )4260.5166666666721.2529757526505200.46682950435
Trimmed Mean ( 1 / 20 )431952.498846240887282.2684746286152
Trimmed Mean ( 2 / 20 )4311.9107142857150.136600913499986.0032518304344
Trimmed Mean ( 3 / 20 )4303.3703703703747.520375535685990.5584251357338
Trimmed Mean ( 4 / 20 )4297.7307692307745.668993307956394.1060982065054
Trimmed Mean ( 5 / 20 )4292.9444.159824848070397.2137007963607
Trimmed Mean ( 6 / 20 )4288.8958333333342.8372232371109100.120771357975
Trimmed Mean ( 7 / 20 )4285.3913043478342.0416112969672101.932137521498
Trimmed Mean ( 8 / 20 )4281.5909090909140.9935708642301104.445424461105
Trimmed Mean ( 9 / 20 )4277.9761904761939.845819114728107.363238741777
Trimmed Mean ( 10 / 20 )427438.5953697236153110.738672296871
Trimmed Mean ( 11 / 20 )4270.0263157894737.3668044548444114.273253442091
Trimmed Mean ( 12 / 20 )4265.9722222222235.988589155213118.536800757145
Trimmed Mean ( 13 / 20 )4261.4117647058834.2244900287929124.513521198439
Trimmed Mean ( 14 / 20 )4257.9687532.6115790704119130.566163043089
Trimmed Mean ( 15 / 20 )4256.5333333333331.4396606301086135.38738167094
Trimmed Mean ( 16 / 20 )4255.8571428571430.1427254943337141.190190105973
Trimmed Mean ( 17 / 20 )4256.1923076923129.0073740879675146.727942170326
Trimmed Mean ( 18 / 20 )4257.2916666666727.7323177223982153.513734743787
Trimmed Mean ( 19 / 20 )4257.8636363636426.1476241505988162.839407964572
Trimmed Mean ( 20 / 20 )4258.5524.1950924776079176.008833359129
Median4252.5
Midrange4602
Midmean - Weighted Average at Xnp4247.22580645161
Midmean - Weighted Average at X(n+1)p4256.53333333333
Midmean - Empirical Distribution Function4247.22580645161
Midmean - Empirical Distribution Function - Averaging4256.53333333333
Midmean - Empirical Distribution Function - Interpolation4256.53333333333
Midmean - Closest Observation4247.22580645161
Midmean - True Basic - Statistics Graphics Toolkit4256.53333333333
Midmean - MS Excel (old versions)4257.96875
Number of observations60



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')