Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationMon, 05 Mar 2012 07:37:38 -0500
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2012/Mar/05/t1330951068bn11rbdh1zx3f4i.htm/, Retrieved Thu, 02 May 2024 20:37:30 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=163483, Retrieved Thu, 02 May 2024 20:37:30 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact157
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [] [2012-03-05 12:37:38] [3f9379635061ebc5737ab9ab2503b0b0] [Current]
Feedback Forum

Post a new message
Dataseries X:
65
65,3
62,9
63,5
62,1
59,3
61,6
61,5
60,1
59,5
62,7
65,5
63,8
63,8
62,7
62,3
62,4
64,8
66,4
65,1
67,4
68,8
68,6
71,5
75
84,3
84
79,1
78,8
82,7
85,3
84,5
80,8
70,1
68,2
68,1
72,3
73,1
71,5
74,1
80,3
80,6
81,4
87,4
89,3
93,2
92,8
96,8
100,3
95,6
89
87,4
86,7
92,8
98,6
100,8
105,5
107,8
113,7
120,3




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gertrude Mary Cox' @ cox.wessa.net

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 1 seconds \tabularnewline
R Server & 'Gertrude Mary Cox' @ cox.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=163483&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]'Gertrude Mary Cox' @ cox.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=163483&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=163483&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'Gertrude Mary Cox' @ cox.wessa.net







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean77.81333333333331.9515479393800939.8726220161677
Geometric Mean76.4665785430142
Harmonic Mean75.2202760349977
Quadratic Mean79.2440449918268
Winsorized Mean ( 1 / 20 )77.70666666666671.9131508407231540.6171144546524
Winsorized Mean ( 2 / 20 )77.531.8512666300652741.8794347291111
Winsorized Mean ( 3 / 20 )77.4851.8094023500611442.8235323102027
Winsorized Mean ( 4 / 20 )77.17833333333331.7309366715245944.5876123621296
Winsorized Mean ( 5 / 20 )77.17833333333331.7150745592770844.9999872692792
Winsorized Mean ( 6 / 20 )77.02833333333331.6740965885955546.0118811889788
Winsorized Mean ( 7 / 20 )76.831.6275667256145547.2054379036225
Winsorized Mean ( 8 / 20 )76.711.5888074268293348.2814963630205
Winsorized Mean ( 9 / 20 )76.351.5186291394796950.2756058178619
Winsorized Mean ( 10 / 20 )76.31666666666671.5010921949626550.8407590971224
Winsorized Mean ( 11 / 20 )76.42666666666671.4846424109906951.4781647761685
Winsorized Mean ( 12 / 20 )75.78666666666671.3506442628132856.1114934207837
Winsorized Mean ( 13 / 20 )75.72166666666671.3396729756670456.5225006714522
Winsorized Mean ( 14 / 20 )75.58166666666671.243435853303560.7845322023367
Winsorized Mean ( 15 / 20 )75.63166666666671.2361172390292361.1848652204409
Winsorized Mean ( 16 / 20 )75.47166666666671.2023872010162262.7681886524413
Winsorized Mean ( 17 / 20 )75.13166666666671.1324651668148466.3434680979912
Winsorized Mean ( 18 / 20 )74.95166666666671.0875034688344468.9208529578286
Winsorized Mean ( 19 / 20 )75.17333333333331.0366200690746372.5177290851018
Winsorized Mean ( 20 / 20 )75.40666666666670.97454861829269277.3759925890319
Trimmed Mean ( 1 / 20 )77.41.8507907762028841.8199620374137
Trimmed Mean ( 2 / 20 )77.07142857142861.7728393000138143.4734431771836
Trimmed Mean ( 3 / 20 )76.81666666666671.7177227013770344.7200625602059
Trimmed Mean ( 4 / 20 )76.55961538461541.6685997679600745.8825518585639
Trimmed Mean ( 5 / 20 )76.3741.6376509059613246.6363128564129
Trimmed Mean ( 6 / 20 )76.17291666666671.602374511255247.5375239256631
Trimmed Mean ( 7 / 20 )75.98695652173911.5689456402884848.4318605887249
Trimmed Mean ( 8 / 20 )75.82272727272731.5381885217692949.2935203973001
Trimmed Mean ( 9 / 20 )75.66428571428571.5072639503070350.1997581106303
Trimmed Mean ( 10 / 20 )75.551.484108123782450.9059945089803
Trimmed Mean ( 11 / 20 )75.4289473684211.4553277208842251.829526975953
Trimmed Mean ( 12 / 20 )75.27777777777781.4178572650256153.0926346640529
Trimmed Mean ( 13 / 20 )75.20294117647061.4016954674592753.6514121093538
Trimmed Mean ( 14 / 20 )75.1281251.3780701382540754.5169094914014
Trimmed Mean ( 15 / 20 )75.06333333333331.367306970833754.8986693804131
Trimmed Mean ( 16 / 20 )74.98214285714291.3475634839069755.6427535716153
Trimmed Mean ( 17 / 20 )74.91153846153851.3230190058879856.6216646383393
Trimmed Mean ( 18 / 20 )74.87916666666671.3031591932109657.45972330684
Trimmed Mean ( 19 / 20 )74.86818181818181.2799551257629958.4928176865205
Trimmed Mean ( 20 / 20 )74.821.2525468790470659.7342911883053
Median73.6
Midrange89.8
Midmean - Weighted Average at Xnp75.128125
Midmean - Weighted Average at X(n+1)p75.4612903225806
Midmean - Empirical Distribution Function75.128125
Midmean - Empirical Distribution Function - Averaging75.4612903225806
Midmean - Empirical Distribution Function - Interpolation75.4612903225806
Midmean - Closest Observation75.128125
Midmean - True Basic - Statistics Graphics Toolkit75.4612903225806
Midmean - MS Excel (old versions)75.128125
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 77.8133333333333 & 1.95154793938009 & 39.8726220161677 \tabularnewline
Geometric Mean & 76.4665785430142 &  &  \tabularnewline
Harmonic Mean & 75.2202760349977 &  &  \tabularnewline
Quadratic Mean & 79.2440449918268 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 77.7066666666667 & 1.91315084072315 & 40.6171144546524 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 77.53 & 1.85126663006527 & 41.8794347291111 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 77.485 & 1.80940235006114 & 42.8235323102027 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 77.1783333333333 & 1.73093667152459 & 44.5876123621296 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 77.1783333333333 & 1.71507455927708 & 44.9999872692792 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 77.0283333333333 & 1.67409658859555 & 46.0118811889788 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 76.83 & 1.62756672561455 & 47.2054379036225 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 76.71 & 1.58880742682933 & 48.2814963630205 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 76.35 & 1.51862913947969 & 50.2756058178619 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 76.3166666666667 & 1.50109219496265 & 50.8407590971224 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 76.4266666666667 & 1.48464241099069 & 51.4781647761685 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 75.7866666666667 & 1.35064426281328 & 56.1114934207837 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 75.7216666666667 & 1.33967297566704 & 56.5225006714522 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 75.5816666666667 & 1.2434358533035 & 60.7845322023367 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 75.6316666666667 & 1.23611723902923 & 61.1848652204409 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 75.4716666666667 & 1.20238720101622 & 62.7681886524413 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 75.1316666666667 & 1.13246516681484 & 66.3434680979912 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 74.9516666666667 & 1.08750346883444 & 68.9208529578286 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 75.1733333333333 & 1.03662006907463 & 72.5177290851018 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 75.4066666666667 & 0.974548618292692 & 77.3759925890319 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 77.4 & 1.85079077620288 & 41.8199620374137 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 77.0714285714286 & 1.77283930001381 & 43.4734431771836 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 76.8166666666667 & 1.71772270137703 & 44.7200625602059 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 76.5596153846154 & 1.66859976796007 & 45.8825518585639 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 76.374 & 1.63765090596132 & 46.6363128564129 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 76.1729166666667 & 1.6023745112552 & 47.5375239256631 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 75.9869565217391 & 1.56894564028848 & 48.4318605887249 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 75.8227272727273 & 1.53818852176929 & 49.2935203973001 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 75.6642857142857 & 1.50726395030703 & 50.1997581106303 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 75.55 & 1.4841081237824 & 50.9059945089803 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 75.428947368421 & 1.45532772088422 & 51.829526975953 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 75.2777777777778 & 1.41785726502561 & 53.0926346640529 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 75.2029411764706 & 1.40169546745927 & 53.6514121093538 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 75.128125 & 1.37807013825407 & 54.5169094914014 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 75.0633333333333 & 1.3673069708337 & 54.8986693804131 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 74.9821428571429 & 1.34756348390697 & 55.6427535716153 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 74.9115384615385 & 1.32301900588798 & 56.6216646383393 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 74.8791666666667 & 1.30315919321096 & 57.45972330684 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 74.8681818181818 & 1.27995512576299 & 58.4928176865205 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 74.82 & 1.25254687904706 & 59.7342911883053 \tabularnewline
Median & 73.6 &  &  \tabularnewline
Midrange & 89.8 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 75.128125 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 75.4612903225806 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 75.128125 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 75.4612903225806 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 75.4612903225806 &  &  \tabularnewline
Midmean - Closest Observation & 75.128125 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 75.4612903225806 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 75.128125 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=163483&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]77.8133333333333[/C][C]1.95154793938009[/C][C]39.8726220161677[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]76.4665785430142[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]75.2202760349977[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]79.2440449918268[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]77.7066666666667[/C][C]1.91315084072315[/C][C]40.6171144546524[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]77.53[/C][C]1.85126663006527[/C][C]41.8794347291111[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]77.485[/C][C]1.80940235006114[/C][C]42.8235323102027[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]77.1783333333333[/C][C]1.73093667152459[/C][C]44.5876123621296[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]77.1783333333333[/C][C]1.71507455927708[/C][C]44.9999872692792[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]77.0283333333333[/C][C]1.67409658859555[/C][C]46.0118811889788[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]76.83[/C][C]1.62756672561455[/C][C]47.2054379036225[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]76.71[/C][C]1.58880742682933[/C][C]48.2814963630205[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]76.35[/C][C]1.51862913947969[/C][C]50.2756058178619[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]76.3166666666667[/C][C]1.50109219496265[/C][C]50.8407590971224[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]76.4266666666667[/C][C]1.48464241099069[/C][C]51.4781647761685[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]75.7866666666667[/C][C]1.35064426281328[/C][C]56.1114934207837[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]75.7216666666667[/C][C]1.33967297566704[/C][C]56.5225006714522[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]75.5816666666667[/C][C]1.2434358533035[/C][C]60.7845322023367[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]75.6316666666667[/C][C]1.23611723902923[/C][C]61.1848652204409[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]75.4716666666667[/C][C]1.20238720101622[/C][C]62.7681886524413[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]75.1316666666667[/C][C]1.13246516681484[/C][C]66.3434680979912[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]74.9516666666667[/C][C]1.08750346883444[/C][C]68.9208529578286[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]75.1733333333333[/C][C]1.03662006907463[/C][C]72.5177290851018[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]75.4066666666667[/C][C]0.974548618292692[/C][C]77.3759925890319[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]77.4[/C][C]1.85079077620288[/C][C]41.8199620374137[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]77.0714285714286[/C][C]1.77283930001381[/C][C]43.4734431771836[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]76.8166666666667[/C][C]1.71772270137703[/C][C]44.7200625602059[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]76.5596153846154[/C][C]1.66859976796007[/C][C]45.8825518585639[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]76.374[/C][C]1.63765090596132[/C][C]46.6363128564129[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]76.1729166666667[/C][C]1.6023745112552[/C][C]47.5375239256631[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]75.9869565217391[/C][C]1.56894564028848[/C][C]48.4318605887249[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]75.8227272727273[/C][C]1.53818852176929[/C][C]49.2935203973001[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]75.6642857142857[/C][C]1.50726395030703[/C][C]50.1997581106303[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]75.55[/C][C]1.4841081237824[/C][C]50.9059945089803[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]75.428947368421[/C][C]1.45532772088422[/C][C]51.829526975953[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]75.2777777777778[/C][C]1.41785726502561[/C][C]53.0926346640529[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]75.2029411764706[/C][C]1.40169546745927[/C][C]53.6514121093538[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]75.128125[/C][C]1.37807013825407[/C][C]54.5169094914014[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]75.0633333333333[/C][C]1.3673069708337[/C][C]54.8986693804131[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]74.9821428571429[/C][C]1.34756348390697[/C][C]55.6427535716153[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]74.9115384615385[/C][C]1.32301900588798[/C][C]56.6216646383393[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]74.8791666666667[/C][C]1.30315919321096[/C][C]57.45972330684[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]74.8681818181818[/C][C]1.27995512576299[/C][C]58.4928176865205[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]74.82[/C][C]1.25254687904706[/C][C]59.7342911883053[/C][/ROW]
[ROW][C]Median[/C][C]73.6[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]89.8[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]75.128125[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]75.4612903225806[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]75.128125[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]75.4612903225806[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]75.4612903225806[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]75.128125[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]75.4612903225806[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]75.128125[/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=163483&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=163483&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 Mean77.81333333333331.9515479393800939.8726220161677
Geometric Mean76.4665785430142
Harmonic Mean75.2202760349977
Quadratic Mean79.2440449918268
Winsorized Mean ( 1 / 20 )77.70666666666671.9131508407231540.6171144546524
Winsorized Mean ( 2 / 20 )77.531.8512666300652741.8794347291111
Winsorized Mean ( 3 / 20 )77.4851.8094023500611442.8235323102027
Winsorized Mean ( 4 / 20 )77.17833333333331.7309366715245944.5876123621296
Winsorized Mean ( 5 / 20 )77.17833333333331.7150745592770844.9999872692792
Winsorized Mean ( 6 / 20 )77.02833333333331.6740965885955546.0118811889788
Winsorized Mean ( 7 / 20 )76.831.6275667256145547.2054379036225
Winsorized Mean ( 8 / 20 )76.711.5888074268293348.2814963630205
Winsorized Mean ( 9 / 20 )76.351.5186291394796950.2756058178619
Winsorized Mean ( 10 / 20 )76.31666666666671.5010921949626550.8407590971224
Winsorized Mean ( 11 / 20 )76.42666666666671.4846424109906951.4781647761685
Winsorized Mean ( 12 / 20 )75.78666666666671.3506442628132856.1114934207837
Winsorized Mean ( 13 / 20 )75.72166666666671.3396729756670456.5225006714522
Winsorized Mean ( 14 / 20 )75.58166666666671.243435853303560.7845322023367
Winsorized Mean ( 15 / 20 )75.63166666666671.2361172390292361.1848652204409
Winsorized Mean ( 16 / 20 )75.47166666666671.2023872010162262.7681886524413
Winsorized Mean ( 17 / 20 )75.13166666666671.1324651668148466.3434680979912
Winsorized Mean ( 18 / 20 )74.95166666666671.0875034688344468.9208529578286
Winsorized Mean ( 19 / 20 )75.17333333333331.0366200690746372.5177290851018
Winsorized Mean ( 20 / 20 )75.40666666666670.97454861829269277.3759925890319
Trimmed Mean ( 1 / 20 )77.41.8507907762028841.8199620374137
Trimmed Mean ( 2 / 20 )77.07142857142861.7728393000138143.4734431771836
Trimmed Mean ( 3 / 20 )76.81666666666671.7177227013770344.7200625602059
Trimmed Mean ( 4 / 20 )76.55961538461541.6685997679600745.8825518585639
Trimmed Mean ( 5 / 20 )76.3741.6376509059613246.6363128564129
Trimmed Mean ( 6 / 20 )76.17291666666671.602374511255247.5375239256631
Trimmed Mean ( 7 / 20 )75.98695652173911.5689456402884848.4318605887249
Trimmed Mean ( 8 / 20 )75.82272727272731.5381885217692949.2935203973001
Trimmed Mean ( 9 / 20 )75.66428571428571.5072639503070350.1997581106303
Trimmed Mean ( 10 / 20 )75.551.484108123782450.9059945089803
Trimmed Mean ( 11 / 20 )75.4289473684211.4553277208842251.829526975953
Trimmed Mean ( 12 / 20 )75.27777777777781.4178572650256153.0926346640529
Trimmed Mean ( 13 / 20 )75.20294117647061.4016954674592753.6514121093538
Trimmed Mean ( 14 / 20 )75.1281251.3780701382540754.5169094914014
Trimmed Mean ( 15 / 20 )75.06333333333331.367306970833754.8986693804131
Trimmed Mean ( 16 / 20 )74.98214285714291.3475634839069755.6427535716153
Trimmed Mean ( 17 / 20 )74.91153846153851.3230190058879856.6216646383393
Trimmed Mean ( 18 / 20 )74.87916666666671.3031591932109657.45972330684
Trimmed Mean ( 19 / 20 )74.86818181818181.2799551257629958.4928176865205
Trimmed Mean ( 20 / 20 )74.821.2525468790470659.7342911883053
Median73.6
Midrange89.8
Midmean - Weighted Average at Xnp75.128125
Midmean - Weighted Average at X(n+1)p75.4612903225806
Midmean - Empirical Distribution Function75.128125
Midmean - Empirical Distribution Function - Averaging75.4612903225806
Midmean - Empirical Distribution Function - Interpolation75.4612903225806
Midmean - Closest Observation75.128125
Midmean - True Basic - Statistics Graphics Toolkit75.4612903225806
Midmean - MS Excel (old versions)75.128125
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')