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of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationFri, 06 Aug 2010 11:26:13 +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/Aug/06/t1281093933ou4a6lcy6o8khqi.htm/, Retrieved Tue, 07 May 2024 03:23:36 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=78462, Retrieved Tue, 07 May 2024 03:23:36 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact154
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [] [2010-08-06 11:26:13] [d41d8cd98f00b204e9800998ecf8427e] [Current]
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Dataseries X:
94
93
92
90
88
87
88
90
91
91
92
94
88
90
82
83
88
83
85
81
79
71
70
85
88
84
81
93
99
96
90
95
93
86
77
89
90
84
76
96
104
101
95
101
95
90
88
99
81
79
70
95
100
105
107
106
99
86
81
95
82
78
68
96
98
107
102
98
93
69
65
90
87
80
67
85
85
92
87
85
79
58
47
67




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=78462&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=78462&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=78462&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 Mean87.30952380952381.2133291317248671.9586479271337
Geometric Mean86.5291602282555
Harmonic Mean85.6424491577599
Quadratic Mean88.0064932669338
Winsorized Mean ( 1 / 28 )87.44047619047621.1670990745032474.9212111471294
Winsorized Mean ( 2 / 28 )87.58333333333331.1165844584873878.4386104137445
Winsorized Mean ( 3 / 28 )87.61904761904761.0927845500534780.1796178530897
Winsorized Mean ( 4 / 28 )87.57142857142861.0838730348503880.7949139388982
Winsorized Mean ( 5 / 28 )87.51190476190481.0496145848416483.3752751016774
Winsorized Mean ( 6 / 28 )87.51190476190481.0221996642772985.611361283098
Winsorized Mean ( 7 / 28 )87.59523809523811.0043107099825387.2192611555062
Winsorized Mean ( 8 / 28 )87.50.98940166901547388.4372876458445
Winsorized Mean ( 9 / 28 )87.50.95081267893854592.0265389158273
Winsorized Mean ( 10 / 28 )88.09523809523810.836045908904219105.371292601266
Winsorized Mean ( 11 / 28 )88.22619047619050.813742970509016108.420218267450
Winsorized Mean ( 12 / 28 )88.22619047619050.768041968531884114.871574850051
Winsorized Mean ( 13 / 28 )88.38095238095240.743860848618161118.813824581753
Winsorized Mean ( 14 / 28 )88.0476190476190.694810028623864126.721859818295
Winsorized Mean ( 15 / 28 )88.0476190476190.694810028623864126.721859818295
Winsorized Mean ( 16 / 28 )88.23809523809520.665651632820247132.558970619881
Winsorized Mean ( 17 / 28 )88.23809523809520.608228866835356145.073836592469
Winsorized Mean ( 18 / 28 )88.23809523809520.608228866835356145.073836592469
Winsorized Mean ( 19 / 28 )88.23809523809520.608228866835356145.073836592469
Winsorized Mean ( 20 / 28 )88.23809523809520.608228866835356145.073836592469
Winsorized Mean ( 21 / 28 )88.48809523809520.57323503664237154.366166723513
Winsorized Mean ( 22 / 28 )88.22619047619050.538359631733103163.879654557624
Winsorized Mean ( 23 / 28 )88.50.501146133309017176.595196725641
Winsorized Mean ( 24 / 28 )88.21428571428570.464478754167184189.921034972751
Winsorized Mean ( 25 / 28 )88.51190476190480.425281806479273208.125302830744
Winsorized Mean ( 26 / 28 )88.51190476190480.425281806479273208.125302830744
Winsorized Mean ( 27 / 28 )88.83333333333330.385417393511588230.486051820239
Winsorized Mean ( 28 / 28 )88.50.343157021275563257.899429453703
Trimmed Mean ( 1 / 28 )87.56097560975611.1142364663902878.5838358830791
Trimmed Mean ( 2 / 28 )87.68751.0519111224308283.3601795153247
Trimmed Mean ( 3 / 28 )87.74358974358971.0113303993430386.7605579745145
Trimmed Mean ( 4 / 28 )87.78947368421050.9746462767217790.0731637527936
Trimmed Mean ( 5 / 28 )87.85135135135140.93468330931920193.9904997504877
Trimmed Mean ( 6 / 28 )87.93055555555560.89825216930391597.8907244094894
Trimmed Mean ( 7 / 28 )88.01428571428570.862730236235314102.018315827613
Trimmed Mean ( 8 / 28 )88.08823529411770.825072240995373106.764269741820
Trimmed Mean ( 9 / 28 )88.18181818181820.783248001375841112.584798208127
Trimmed Mean ( 10 / 28 )88.281250.741843461405544119.002531656391
Trimmed Mean ( 11 / 28 )88.30645161290320.7186378463032122.880324306836
Trimmed Mean ( 12 / 28 )88.31666666666670.695218401105296127.034420444361
Trimmed Mean ( 13 / 28 )88.32758620689660.676002954561749130.661538697207
Trimmed Mean ( 14 / 28 )88.32142857142860.657181675872084134.394234979582
Trimmed Mean ( 15 / 28 )88.35185185185180.643278099869546137.346276625567
Trimmed Mean ( 16 / 28 )88.38461538461540.625714581636535141.253884724004
Trimmed Mean ( 17 / 28 )88.40.609449400220044145.048957252370
Trimmed Mean ( 18 / 28 )88.41666666666670.599817742215974147.40588756181
Trimmed Mean ( 19 / 28 )88.43478260869570.587019141408312150.650594453415
Trimmed Mean ( 20 / 28 )88.45454545454550.57009192672782155.158389914854
Trimmed Mean ( 21 / 28 )88.47619047619050.547656919359036161.554044783623
Trimmed Mean ( 22 / 28 )88.4750.526219584662193168.133232929361
Trimmed Mean ( 23 / 28 )88.50.505657888721953175.019518085010
Trimmed Mean ( 24 / 28 )88.50.487136107573220181.674071423043
Trimmed Mean ( 25 / 28 )88.52941176470590.470588235294118188.125
Trimmed Mean ( 26 / 28 )88.531250.457871070650581193.354102660837
Trimmed Mean ( 27 / 28 )88.53333333333330.438737303469786201.791214544925
Trimmed Mean ( 28 / 28 )88.50.422577127364258209.429224321726
Median88
Midrange77
Midmean - Weighted Average at Xnp88.4
Midmean - Weighted Average at X(n+1)p89.0434782608696
Midmean - Empirical Distribution Function88.4
Midmean - Empirical Distribution Function - Averaging89.0434782608696
Midmean - Empirical Distribution Function - Interpolation89.0434782608696
Midmean - Closest Observation88.4
Midmean - True Basic - Statistics Graphics Toolkit89.0434782608696
Midmean - MS Excel (old versions)88.4
Number of observations84

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 87.3095238095238 & 1.21332913172486 & 71.9586479271337 \tabularnewline
Geometric Mean & 86.5291602282555 &  &  \tabularnewline
Harmonic Mean & 85.6424491577599 &  &  \tabularnewline
Quadratic Mean & 88.0064932669338 &  &  \tabularnewline
Winsorized Mean ( 1 / 28 ) & 87.4404761904762 & 1.16709907450324 & 74.9212111471294 \tabularnewline
Winsorized Mean ( 2 / 28 ) & 87.5833333333333 & 1.11658445848738 & 78.4386104137445 \tabularnewline
Winsorized Mean ( 3 / 28 ) & 87.6190476190476 & 1.09278455005347 & 80.1796178530897 \tabularnewline
Winsorized Mean ( 4 / 28 ) & 87.5714285714286 & 1.08387303485038 & 80.7949139388982 \tabularnewline
Winsorized Mean ( 5 / 28 ) & 87.5119047619048 & 1.04961458484164 & 83.3752751016774 \tabularnewline
Winsorized Mean ( 6 / 28 ) & 87.5119047619048 & 1.02219966427729 & 85.611361283098 \tabularnewline
Winsorized Mean ( 7 / 28 ) & 87.5952380952381 & 1.00431070998253 & 87.2192611555062 \tabularnewline
Winsorized Mean ( 8 / 28 ) & 87.5 & 0.989401669015473 & 88.4372876458445 \tabularnewline
Winsorized Mean ( 9 / 28 ) & 87.5 & 0.950812678938545 & 92.0265389158273 \tabularnewline
Winsorized Mean ( 10 / 28 ) & 88.0952380952381 & 0.836045908904219 & 105.371292601266 \tabularnewline
Winsorized Mean ( 11 / 28 ) & 88.2261904761905 & 0.813742970509016 & 108.420218267450 \tabularnewline
Winsorized Mean ( 12 / 28 ) & 88.2261904761905 & 0.768041968531884 & 114.871574850051 \tabularnewline
Winsorized Mean ( 13 / 28 ) & 88.3809523809524 & 0.743860848618161 & 118.813824581753 \tabularnewline
Winsorized Mean ( 14 / 28 ) & 88.047619047619 & 0.694810028623864 & 126.721859818295 \tabularnewline
Winsorized Mean ( 15 / 28 ) & 88.047619047619 & 0.694810028623864 & 126.721859818295 \tabularnewline
Winsorized Mean ( 16 / 28 ) & 88.2380952380952 & 0.665651632820247 & 132.558970619881 \tabularnewline
Winsorized Mean ( 17 / 28 ) & 88.2380952380952 & 0.608228866835356 & 145.073836592469 \tabularnewline
Winsorized Mean ( 18 / 28 ) & 88.2380952380952 & 0.608228866835356 & 145.073836592469 \tabularnewline
Winsorized Mean ( 19 / 28 ) & 88.2380952380952 & 0.608228866835356 & 145.073836592469 \tabularnewline
Winsorized Mean ( 20 / 28 ) & 88.2380952380952 & 0.608228866835356 & 145.073836592469 \tabularnewline
Winsorized Mean ( 21 / 28 ) & 88.4880952380952 & 0.57323503664237 & 154.366166723513 \tabularnewline
Winsorized Mean ( 22 / 28 ) & 88.2261904761905 & 0.538359631733103 & 163.879654557624 \tabularnewline
Winsorized Mean ( 23 / 28 ) & 88.5 & 0.501146133309017 & 176.595196725641 \tabularnewline
Winsorized Mean ( 24 / 28 ) & 88.2142857142857 & 0.464478754167184 & 189.921034972751 \tabularnewline
Winsorized Mean ( 25 / 28 ) & 88.5119047619048 & 0.425281806479273 & 208.125302830744 \tabularnewline
Winsorized Mean ( 26 / 28 ) & 88.5119047619048 & 0.425281806479273 & 208.125302830744 \tabularnewline
Winsorized Mean ( 27 / 28 ) & 88.8333333333333 & 0.385417393511588 & 230.486051820239 \tabularnewline
Winsorized Mean ( 28 / 28 ) & 88.5 & 0.343157021275563 & 257.899429453703 \tabularnewline
Trimmed Mean ( 1 / 28 ) & 87.5609756097561 & 1.11423646639028 & 78.5838358830791 \tabularnewline
Trimmed Mean ( 2 / 28 ) & 87.6875 & 1.05191112243082 & 83.3601795153247 \tabularnewline
Trimmed Mean ( 3 / 28 ) & 87.7435897435897 & 1.01133039934303 & 86.7605579745145 \tabularnewline
Trimmed Mean ( 4 / 28 ) & 87.7894736842105 & 0.97464627672177 & 90.0731637527936 \tabularnewline
Trimmed Mean ( 5 / 28 ) & 87.8513513513514 & 0.934683309319201 & 93.9904997504877 \tabularnewline
Trimmed Mean ( 6 / 28 ) & 87.9305555555556 & 0.898252169303915 & 97.8907244094894 \tabularnewline
Trimmed Mean ( 7 / 28 ) & 88.0142857142857 & 0.862730236235314 & 102.018315827613 \tabularnewline
Trimmed Mean ( 8 / 28 ) & 88.0882352941177 & 0.825072240995373 & 106.764269741820 \tabularnewline
Trimmed Mean ( 9 / 28 ) & 88.1818181818182 & 0.783248001375841 & 112.584798208127 \tabularnewline
Trimmed Mean ( 10 / 28 ) & 88.28125 & 0.741843461405544 & 119.002531656391 \tabularnewline
Trimmed Mean ( 11 / 28 ) & 88.3064516129032 & 0.7186378463032 & 122.880324306836 \tabularnewline
Trimmed Mean ( 12 / 28 ) & 88.3166666666667 & 0.695218401105296 & 127.034420444361 \tabularnewline
Trimmed Mean ( 13 / 28 ) & 88.3275862068966 & 0.676002954561749 & 130.661538697207 \tabularnewline
Trimmed Mean ( 14 / 28 ) & 88.3214285714286 & 0.657181675872084 & 134.394234979582 \tabularnewline
Trimmed Mean ( 15 / 28 ) & 88.3518518518518 & 0.643278099869546 & 137.346276625567 \tabularnewline
Trimmed Mean ( 16 / 28 ) & 88.3846153846154 & 0.625714581636535 & 141.253884724004 \tabularnewline
Trimmed Mean ( 17 / 28 ) & 88.4 & 0.609449400220044 & 145.048957252370 \tabularnewline
Trimmed Mean ( 18 / 28 ) & 88.4166666666667 & 0.599817742215974 & 147.40588756181 \tabularnewline
Trimmed Mean ( 19 / 28 ) & 88.4347826086957 & 0.587019141408312 & 150.650594453415 \tabularnewline
Trimmed Mean ( 20 / 28 ) & 88.4545454545455 & 0.57009192672782 & 155.158389914854 \tabularnewline
Trimmed Mean ( 21 / 28 ) & 88.4761904761905 & 0.547656919359036 & 161.554044783623 \tabularnewline
Trimmed Mean ( 22 / 28 ) & 88.475 & 0.526219584662193 & 168.133232929361 \tabularnewline
Trimmed Mean ( 23 / 28 ) & 88.5 & 0.505657888721953 & 175.019518085010 \tabularnewline
Trimmed Mean ( 24 / 28 ) & 88.5 & 0.487136107573220 & 181.674071423043 \tabularnewline
Trimmed Mean ( 25 / 28 ) & 88.5294117647059 & 0.470588235294118 & 188.125 \tabularnewline
Trimmed Mean ( 26 / 28 ) & 88.53125 & 0.457871070650581 & 193.354102660837 \tabularnewline
Trimmed Mean ( 27 / 28 ) & 88.5333333333333 & 0.438737303469786 & 201.791214544925 \tabularnewline
Trimmed Mean ( 28 / 28 ) & 88.5 & 0.422577127364258 & 209.429224321726 \tabularnewline
Median & 88 &  &  \tabularnewline
Midrange & 77 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 88.4 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 89.0434782608696 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 88.4 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 89.0434782608696 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 89.0434782608696 &  &  \tabularnewline
Midmean - Closest Observation & 88.4 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 89.0434782608696 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 88.4 &  &  \tabularnewline
Number of observations & 84 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=78462&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]87.3095238095238[/C][C]1.21332913172486[/C][C]71.9586479271337[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]86.5291602282555[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]85.6424491577599[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]88.0064932669338[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 28 )[/C][C]87.4404761904762[/C][C]1.16709907450324[/C][C]74.9212111471294[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 28 )[/C][C]87.5833333333333[/C][C]1.11658445848738[/C][C]78.4386104137445[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 28 )[/C][C]87.6190476190476[/C][C]1.09278455005347[/C][C]80.1796178530897[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 28 )[/C][C]87.5714285714286[/C][C]1.08387303485038[/C][C]80.7949139388982[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 28 )[/C][C]87.5119047619048[/C][C]1.04961458484164[/C][C]83.3752751016774[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 28 )[/C][C]87.5119047619048[/C][C]1.02219966427729[/C][C]85.611361283098[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 28 )[/C][C]87.5952380952381[/C][C]1.00431070998253[/C][C]87.2192611555062[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 28 )[/C][C]87.5[/C][C]0.989401669015473[/C][C]88.4372876458445[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 28 )[/C][C]87.5[/C][C]0.950812678938545[/C][C]92.0265389158273[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 28 )[/C][C]88.0952380952381[/C][C]0.836045908904219[/C][C]105.371292601266[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 28 )[/C][C]88.2261904761905[/C][C]0.813742970509016[/C][C]108.420218267450[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 28 )[/C][C]88.2261904761905[/C][C]0.768041968531884[/C][C]114.871574850051[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 28 )[/C][C]88.3809523809524[/C][C]0.743860848618161[/C][C]118.813824581753[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 28 )[/C][C]88.047619047619[/C][C]0.694810028623864[/C][C]126.721859818295[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 28 )[/C][C]88.047619047619[/C][C]0.694810028623864[/C][C]126.721859818295[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 28 )[/C][C]88.2380952380952[/C][C]0.665651632820247[/C][C]132.558970619881[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 28 )[/C][C]88.2380952380952[/C][C]0.608228866835356[/C][C]145.073836592469[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 28 )[/C][C]88.2380952380952[/C][C]0.608228866835356[/C][C]145.073836592469[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 28 )[/C][C]88.2380952380952[/C][C]0.608228866835356[/C][C]145.073836592469[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 28 )[/C][C]88.2380952380952[/C][C]0.608228866835356[/C][C]145.073836592469[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 28 )[/C][C]88.4880952380952[/C][C]0.57323503664237[/C][C]154.366166723513[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 28 )[/C][C]88.2261904761905[/C][C]0.538359631733103[/C][C]163.879654557624[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 28 )[/C][C]88.5[/C][C]0.501146133309017[/C][C]176.595196725641[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 28 )[/C][C]88.2142857142857[/C][C]0.464478754167184[/C][C]189.921034972751[/C][/ROW]
[ROW][C]Winsorized Mean ( 25 / 28 )[/C][C]88.5119047619048[/C][C]0.425281806479273[/C][C]208.125302830744[/C][/ROW]
[ROW][C]Winsorized Mean ( 26 / 28 )[/C][C]88.5119047619048[/C][C]0.425281806479273[/C][C]208.125302830744[/C][/ROW]
[ROW][C]Winsorized Mean ( 27 / 28 )[/C][C]88.8333333333333[/C][C]0.385417393511588[/C][C]230.486051820239[/C][/ROW]
[ROW][C]Winsorized Mean ( 28 / 28 )[/C][C]88.5[/C][C]0.343157021275563[/C][C]257.899429453703[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 28 )[/C][C]87.5609756097561[/C][C]1.11423646639028[/C][C]78.5838358830791[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 28 )[/C][C]87.6875[/C][C]1.05191112243082[/C][C]83.3601795153247[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 28 )[/C][C]87.7435897435897[/C][C]1.01133039934303[/C][C]86.7605579745145[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 28 )[/C][C]87.7894736842105[/C][C]0.97464627672177[/C][C]90.0731637527936[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 28 )[/C][C]87.8513513513514[/C][C]0.934683309319201[/C][C]93.9904997504877[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 28 )[/C][C]87.9305555555556[/C][C]0.898252169303915[/C][C]97.8907244094894[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 28 )[/C][C]88.0142857142857[/C][C]0.862730236235314[/C][C]102.018315827613[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 28 )[/C][C]88.0882352941177[/C][C]0.825072240995373[/C][C]106.764269741820[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 28 )[/C][C]88.1818181818182[/C][C]0.783248001375841[/C][C]112.584798208127[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 28 )[/C][C]88.28125[/C][C]0.741843461405544[/C][C]119.002531656391[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 28 )[/C][C]88.3064516129032[/C][C]0.7186378463032[/C][C]122.880324306836[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 28 )[/C][C]88.3166666666667[/C][C]0.695218401105296[/C][C]127.034420444361[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 28 )[/C][C]88.3275862068966[/C][C]0.676002954561749[/C][C]130.661538697207[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 28 )[/C][C]88.3214285714286[/C][C]0.657181675872084[/C][C]134.394234979582[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 28 )[/C][C]88.3518518518518[/C][C]0.643278099869546[/C][C]137.346276625567[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 28 )[/C][C]88.3846153846154[/C][C]0.625714581636535[/C][C]141.253884724004[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 28 )[/C][C]88.4[/C][C]0.609449400220044[/C][C]145.048957252370[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 28 )[/C][C]88.4166666666667[/C][C]0.599817742215974[/C][C]147.40588756181[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 28 )[/C][C]88.4347826086957[/C][C]0.587019141408312[/C][C]150.650594453415[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 28 )[/C][C]88.4545454545455[/C][C]0.57009192672782[/C][C]155.158389914854[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 28 )[/C][C]88.4761904761905[/C][C]0.547656919359036[/C][C]161.554044783623[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 28 )[/C][C]88.475[/C][C]0.526219584662193[/C][C]168.133232929361[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 28 )[/C][C]88.5[/C][C]0.505657888721953[/C][C]175.019518085010[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 28 )[/C][C]88.5[/C][C]0.487136107573220[/C][C]181.674071423043[/C][/ROW]
[ROW][C]Trimmed Mean ( 25 / 28 )[/C][C]88.5294117647059[/C][C]0.470588235294118[/C][C]188.125[/C][/ROW]
[ROW][C]Trimmed Mean ( 26 / 28 )[/C][C]88.53125[/C][C]0.457871070650581[/C][C]193.354102660837[/C][/ROW]
[ROW][C]Trimmed Mean ( 27 / 28 )[/C][C]88.5333333333333[/C][C]0.438737303469786[/C][C]201.791214544925[/C][/ROW]
[ROW][C]Trimmed Mean ( 28 / 28 )[/C][C]88.5[/C][C]0.422577127364258[/C][C]209.429224321726[/C][/ROW]
[ROW][C]Median[/C][C]88[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]77[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]88.4[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]89.0434782608696[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]88.4[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]89.0434782608696[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]89.0434782608696[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]88.4[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]89.0434782608696[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]88.4[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]84[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=78462&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=78462&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 Mean87.30952380952381.2133291317248671.9586479271337
Geometric Mean86.5291602282555
Harmonic Mean85.6424491577599
Quadratic Mean88.0064932669338
Winsorized Mean ( 1 / 28 )87.44047619047621.1670990745032474.9212111471294
Winsorized Mean ( 2 / 28 )87.58333333333331.1165844584873878.4386104137445
Winsorized Mean ( 3 / 28 )87.61904761904761.0927845500534780.1796178530897
Winsorized Mean ( 4 / 28 )87.57142857142861.0838730348503880.7949139388982
Winsorized Mean ( 5 / 28 )87.51190476190481.0496145848416483.3752751016774
Winsorized Mean ( 6 / 28 )87.51190476190481.0221996642772985.611361283098
Winsorized Mean ( 7 / 28 )87.59523809523811.0043107099825387.2192611555062
Winsorized Mean ( 8 / 28 )87.50.98940166901547388.4372876458445
Winsorized Mean ( 9 / 28 )87.50.95081267893854592.0265389158273
Winsorized Mean ( 10 / 28 )88.09523809523810.836045908904219105.371292601266
Winsorized Mean ( 11 / 28 )88.22619047619050.813742970509016108.420218267450
Winsorized Mean ( 12 / 28 )88.22619047619050.768041968531884114.871574850051
Winsorized Mean ( 13 / 28 )88.38095238095240.743860848618161118.813824581753
Winsorized Mean ( 14 / 28 )88.0476190476190.694810028623864126.721859818295
Winsorized Mean ( 15 / 28 )88.0476190476190.694810028623864126.721859818295
Winsorized Mean ( 16 / 28 )88.23809523809520.665651632820247132.558970619881
Winsorized Mean ( 17 / 28 )88.23809523809520.608228866835356145.073836592469
Winsorized Mean ( 18 / 28 )88.23809523809520.608228866835356145.073836592469
Winsorized Mean ( 19 / 28 )88.23809523809520.608228866835356145.073836592469
Winsorized Mean ( 20 / 28 )88.23809523809520.608228866835356145.073836592469
Winsorized Mean ( 21 / 28 )88.48809523809520.57323503664237154.366166723513
Winsorized Mean ( 22 / 28 )88.22619047619050.538359631733103163.879654557624
Winsorized Mean ( 23 / 28 )88.50.501146133309017176.595196725641
Winsorized Mean ( 24 / 28 )88.21428571428570.464478754167184189.921034972751
Winsorized Mean ( 25 / 28 )88.51190476190480.425281806479273208.125302830744
Winsorized Mean ( 26 / 28 )88.51190476190480.425281806479273208.125302830744
Winsorized Mean ( 27 / 28 )88.83333333333330.385417393511588230.486051820239
Winsorized Mean ( 28 / 28 )88.50.343157021275563257.899429453703
Trimmed Mean ( 1 / 28 )87.56097560975611.1142364663902878.5838358830791
Trimmed Mean ( 2 / 28 )87.68751.0519111224308283.3601795153247
Trimmed Mean ( 3 / 28 )87.74358974358971.0113303993430386.7605579745145
Trimmed Mean ( 4 / 28 )87.78947368421050.9746462767217790.0731637527936
Trimmed Mean ( 5 / 28 )87.85135135135140.93468330931920193.9904997504877
Trimmed Mean ( 6 / 28 )87.93055555555560.89825216930391597.8907244094894
Trimmed Mean ( 7 / 28 )88.01428571428570.862730236235314102.018315827613
Trimmed Mean ( 8 / 28 )88.08823529411770.825072240995373106.764269741820
Trimmed Mean ( 9 / 28 )88.18181818181820.783248001375841112.584798208127
Trimmed Mean ( 10 / 28 )88.281250.741843461405544119.002531656391
Trimmed Mean ( 11 / 28 )88.30645161290320.7186378463032122.880324306836
Trimmed Mean ( 12 / 28 )88.31666666666670.695218401105296127.034420444361
Trimmed Mean ( 13 / 28 )88.32758620689660.676002954561749130.661538697207
Trimmed Mean ( 14 / 28 )88.32142857142860.657181675872084134.394234979582
Trimmed Mean ( 15 / 28 )88.35185185185180.643278099869546137.346276625567
Trimmed Mean ( 16 / 28 )88.38461538461540.625714581636535141.253884724004
Trimmed Mean ( 17 / 28 )88.40.609449400220044145.048957252370
Trimmed Mean ( 18 / 28 )88.41666666666670.599817742215974147.40588756181
Trimmed Mean ( 19 / 28 )88.43478260869570.587019141408312150.650594453415
Trimmed Mean ( 20 / 28 )88.45454545454550.57009192672782155.158389914854
Trimmed Mean ( 21 / 28 )88.47619047619050.547656919359036161.554044783623
Trimmed Mean ( 22 / 28 )88.4750.526219584662193168.133232929361
Trimmed Mean ( 23 / 28 )88.50.505657888721953175.019518085010
Trimmed Mean ( 24 / 28 )88.50.487136107573220181.674071423043
Trimmed Mean ( 25 / 28 )88.52941176470590.470588235294118188.125
Trimmed Mean ( 26 / 28 )88.531250.457871070650581193.354102660837
Trimmed Mean ( 27 / 28 )88.53333333333330.438737303469786201.791214544925
Trimmed Mean ( 28 / 28 )88.50.422577127364258209.429224321726
Median88
Midrange77
Midmean - Weighted Average at Xnp88.4
Midmean - Weighted Average at X(n+1)p89.0434782608696
Midmean - Empirical Distribution Function88.4
Midmean - Empirical Distribution Function - Averaging89.0434782608696
Midmean - Empirical Distribution Function - Interpolation89.0434782608696
Midmean - Closest Observation88.4
Midmean - True Basic - Statistics Graphics Toolkit89.0434782608696
Midmean - MS Excel (old versions)88.4
Number of observations84



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')