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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 computationMon, 20 Oct 2008 13:37:18 -0600
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2008/Oct/20/t1224531483wg060tdzn4lvy0u.htm/, Retrieved Sun, 19 May 2024 14:46:03 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=17978, Retrieved Sun, 19 May 2024 14:46:03 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact107
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
F     [Univariate Data Series] [Tijdsreeks 3] [2008-10-13 19:47:25] [b82ef11dce0545f3fd4676ec3ebed828]
- RMP     [Central Tendency] [Tijdreeks 3: Inve...] [2008-10-20 19:37:18] [4b953869c7238aca4b6e0cfb0c5cddd6] [Current]
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Dataseries X:
65.4
72.2
80.4
77.7
76.5
100.1
73.5
77.3
98.6
112.4
77.3
139.3
75.4
64.2
86.8
79.1
71.7
100
82.1
74.8
92.3
83.3
83.7
148
71.4
71.2
84.6
80.9
80.6
105.5
79.2
78.4
92.6
88.3
98.2
157.4
73.9
80.9
93
84.9
96.2
106.5
81.7
82.9
96
92.6
116.5
155
95.1
86.2
105
89.7
97.1
120.8
92.2
98.8
104.1
106.5
113.4
192.4
103.6
97.6
99.9
106.2
104.9
114.2
94.5




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'Herman Ole Andreas Wold' @ 193.190.124.10:1001

\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 & 3 seconds \tabularnewline
R Server & 'Herman Ole Andreas Wold' @ 193.190.124.10:1001 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=17978&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]3 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Herman Ole Andreas Wold' @ 193.190.124.10:1001[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=17978&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=17978&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 time3 seconds
R Server'Herman Ole Andreas Wold' @ 193.190.124.10:1001







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean94.9656716417912.7996135549684933.9209929432064
Geometric Mean92.7193074811193
Harmonic Mean90.821547261266
Quadratic Mean97.651297841602
Winsorized Mean ( 1 / 22 )94.46119402985072.5597367388026336.9026988588041
Winsorized Mean ( 2 / 22 )94.56268656716422.5061541943515137.7321901343079
Winsorized Mean ( 3 / 22 )94.25820895522392.394222796814439.3690215800459
Winsorized Mean ( 4 / 22 )93.75671641791042.2223335206854942.1884094107489
Winsorized Mean ( 5 / 22 )92.41343283582091.8353184789410350.3528046473673
Winsorized Mean ( 6 / 22 )92.1447761194031.7297778875908953.2697155978421
Winsorized Mean ( 7 / 22 )91.94626865671641.6730812718965354.9562476140147
Winsorized Mean ( 8 / 22 )91.95820895522391.6366549117353256.1866819302319
Winsorized Mean ( 9 / 22 )91.90447761194031.5975535809019557.5282599035286
Winsorized Mean ( 10 / 22 )91.18805970149251.4130914084929164.5308995252799
Winsorized Mean ( 11 / 22 )91.31940298507461.3927304296877665.56861330699
Winsorized Mean ( 12 / 22 )91.2656716417911.3839007008747265.9481360072332
Winsorized Mean ( 13 / 22 )91.20746268656721.3500846974667767.5568450317999
Winsorized Mean ( 14 / 22 )91.24925373134331.3114590345646169.5784247364133
Winsorized Mean ( 15 / 22 )91.38358208955221.2849115631353071.1205227747875
Winsorized Mean ( 16 / 22 )91.21641791044781.2513142742743872.8964895436382
Winsorized Mean ( 17 / 22 )91.39402985074631.1880261206329976.9293101081406
Winsorized Mean ( 18 / 22 )90.50746268656721.0410704781797886.9369217392578
Winsorized Mean ( 19 / 22 )90.56417910447761.0249018474423488.363758276446
Winsorized Mean ( 20 / 22 )90.5343283582091.0207449152426488.6943711462805
Winsorized Mean ( 21 / 22 )90.44029850746270.9378253174784496.4361878719933
Winsorized Mean ( 22 / 22 )90.50597014925370.91050674157038299.4017573040206
Trimmed Mean ( 1 / 22 )93.942.4094443582254838.9882421145368
Trimmed Mean ( 2 / 22 )93.38571428571432.2222572596169942.0229088606103
Trimmed Mean ( 3 / 22 )92.7393442622952.02278588216245.8473361318762
Trimmed Mean ( 4 / 22 )92.1644067796611.8289569046108850.3917870056481
Trimmed Mean ( 5 / 22 )91.69649122807021.6598078762818255.2452440661276
Trimmed Mean ( 6 / 22 )91.52181818181821.5959791457695357.3452469127904
Trimmed Mean ( 7 / 22 )91.39056603773591.5493134022888758.9877851070805
Trimmed Mean ( 8 / 22 )91.2862745098041.5066753937136960.5878843516515
Trimmed Mean ( 9 / 22 )91.17142857142861.4619929785699262.3610577532388
Trimmed Mean ( 10 / 22 )91.05531914893621.4147361378005764.3620507853118
Trimmed Mean ( 11 / 22 )91.03555555555561.3992752653563065.0590758011972
Trimmed Mean ( 12 / 22 )90.99534883720931.3819151230816265.8472776781639
Trimmed Mean ( 13 / 22 )90.95853658536581.3592724722356166.9170739813227
Trimmed Mean ( 14 / 22 )90.9256410256411.3353934049060768.0890295635662
Trimmed Mean ( 15 / 22 )90.88378378378381.3105515052643569.3477390386513
Trimmed Mean ( 16 / 22 )90.821.2808597427791570.9054996161742
Trimmed Mean ( 17 / 22 )90.7696969696971.2465291574256172.8179492866083
Trimmed Mean ( 18 / 22 )90.69032258064521.2130593585163474.7616527946051
Trimmed Mean ( 19 / 22 )90.71379310344831.2045349872116775.3102185212884
Trimmed Mean ( 20 / 22 )90.73333333333331.1908841791732476.1898889246508
Trimmed Mean ( 21 / 22 )90.761.1653611743432477.8814345270676
Trimmed Mean ( 22 / 22 )90.8043478260871.1490411582852879.0261925530977
Median92.3
Midrange128.3
Midmean - Weighted Average at Xnp90.4294117647058
Midmean - Weighted Average at X(n+1)p90.82
Midmean - Empirical Distribution Function90.82
Midmean - Empirical Distribution Function - Averaging90.82
Midmean - Empirical Distribution Function - Interpolation90.769696969697
Midmean - Closest Observation90.4294117647058
Midmean - True Basic - Statistics Graphics Toolkit90.82
Midmean - MS Excel (old versions)90.82
Number of observations67

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 94.965671641791 & 2.79961355496849 & 33.9209929432064 \tabularnewline
Geometric Mean & 92.7193074811193 &  &  \tabularnewline
Harmonic Mean & 90.821547261266 &  &  \tabularnewline
Quadratic Mean & 97.651297841602 &  &  \tabularnewline
Winsorized Mean ( 1 / 22 ) & 94.4611940298507 & 2.55973673880263 & 36.9026988588041 \tabularnewline
Winsorized Mean ( 2 / 22 ) & 94.5626865671642 & 2.50615419435151 & 37.7321901343079 \tabularnewline
Winsorized Mean ( 3 / 22 ) & 94.2582089552239 & 2.3942227968144 & 39.3690215800459 \tabularnewline
Winsorized Mean ( 4 / 22 ) & 93.7567164179104 & 2.22233352068549 & 42.1884094107489 \tabularnewline
Winsorized Mean ( 5 / 22 ) & 92.4134328358209 & 1.83531847894103 & 50.3528046473673 \tabularnewline
Winsorized Mean ( 6 / 22 ) & 92.144776119403 & 1.72977788759089 & 53.2697155978421 \tabularnewline
Winsorized Mean ( 7 / 22 ) & 91.9462686567164 & 1.67308127189653 & 54.9562476140147 \tabularnewline
Winsorized Mean ( 8 / 22 ) & 91.9582089552239 & 1.63665491173532 & 56.1866819302319 \tabularnewline
Winsorized Mean ( 9 / 22 ) & 91.9044776119403 & 1.59755358090195 & 57.5282599035286 \tabularnewline
Winsorized Mean ( 10 / 22 ) & 91.1880597014925 & 1.41309140849291 & 64.5308995252799 \tabularnewline
Winsorized Mean ( 11 / 22 ) & 91.3194029850746 & 1.39273042968776 & 65.56861330699 \tabularnewline
Winsorized Mean ( 12 / 22 ) & 91.265671641791 & 1.38390070087472 & 65.9481360072332 \tabularnewline
Winsorized Mean ( 13 / 22 ) & 91.2074626865672 & 1.35008469746677 & 67.5568450317999 \tabularnewline
Winsorized Mean ( 14 / 22 ) & 91.2492537313433 & 1.31145903456461 & 69.5784247364133 \tabularnewline
Winsorized Mean ( 15 / 22 ) & 91.3835820895522 & 1.28491156313530 & 71.1205227747875 \tabularnewline
Winsorized Mean ( 16 / 22 ) & 91.2164179104478 & 1.25131427427438 & 72.8964895436382 \tabularnewline
Winsorized Mean ( 17 / 22 ) & 91.3940298507463 & 1.18802612063299 & 76.9293101081406 \tabularnewline
Winsorized Mean ( 18 / 22 ) & 90.5074626865672 & 1.04107047817978 & 86.9369217392578 \tabularnewline
Winsorized Mean ( 19 / 22 ) & 90.5641791044776 & 1.02490184744234 & 88.363758276446 \tabularnewline
Winsorized Mean ( 20 / 22 ) & 90.534328358209 & 1.02074491524264 & 88.6943711462805 \tabularnewline
Winsorized Mean ( 21 / 22 ) & 90.4402985074627 & 0.93782531747844 & 96.4361878719933 \tabularnewline
Winsorized Mean ( 22 / 22 ) & 90.5059701492537 & 0.910506741570382 & 99.4017573040206 \tabularnewline
Trimmed Mean ( 1 / 22 ) & 93.94 & 2.40944435822548 & 38.9882421145368 \tabularnewline
Trimmed Mean ( 2 / 22 ) & 93.3857142857143 & 2.22225725961699 & 42.0229088606103 \tabularnewline
Trimmed Mean ( 3 / 22 ) & 92.739344262295 & 2.022785882162 & 45.8473361318762 \tabularnewline
Trimmed Mean ( 4 / 22 ) & 92.164406779661 & 1.82895690461088 & 50.3917870056481 \tabularnewline
Trimmed Mean ( 5 / 22 ) & 91.6964912280702 & 1.65980787628182 & 55.2452440661276 \tabularnewline
Trimmed Mean ( 6 / 22 ) & 91.5218181818182 & 1.59597914576953 & 57.3452469127904 \tabularnewline
Trimmed Mean ( 7 / 22 ) & 91.3905660377359 & 1.54931340228887 & 58.9877851070805 \tabularnewline
Trimmed Mean ( 8 / 22 ) & 91.286274509804 & 1.50667539371369 & 60.5878843516515 \tabularnewline
Trimmed Mean ( 9 / 22 ) & 91.1714285714286 & 1.46199297856992 & 62.3610577532388 \tabularnewline
Trimmed Mean ( 10 / 22 ) & 91.0553191489362 & 1.41473613780057 & 64.3620507853118 \tabularnewline
Trimmed Mean ( 11 / 22 ) & 91.0355555555556 & 1.39927526535630 & 65.0590758011972 \tabularnewline
Trimmed Mean ( 12 / 22 ) & 90.9953488372093 & 1.38191512308162 & 65.8472776781639 \tabularnewline
Trimmed Mean ( 13 / 22 ) & 90.9585365853658 & 1.35927247223561 & 66.9170739813227 \tabularnewline
Trimmed Mean ( 14 / 22 ) & 90.925641025641 & 1.33539340490607 & 68.0890295635662 \tabularnewline
Trimmed Mean ( 15 / 22 ) & 90.8837837837838 & 1.31055150526435 & 69.3477390386513 \tabularnewline
Trimmed Mean ( 16 / 22 ) & 90.82 & 1.28085974277915 & 70.9054996161742 \tabularnewline
Trimmed Mean ( 17 / 22 ) & 90.769696969697 & 1.24652915742561 & 72.8179492866083 \tabularnewline
Trimmed Mean ( 18 / 22 ) & 90.6903225806452 & 1.21305935851634 & 74.7616527946051 \tabularnewline
Trimmed Mean ( 19 / 22 ) & 90.7137931034483 & 1.20453498721167 & 75.3102185212884 \tabularnewline
Trimmed Mean ( 20 / 22 ) & 90.7333333333333 & 1.19088417917324 & 76.1898889246508 \tabularnewline
Trimmed Mean ( 21 / 22 ) & 90.76 & 1.16536117434324 & 77.8814345270676 \tabularnewline
Trimmed Mean ( 22 / 22 ) & 90.804347826087 & 1.14904115828528 & 79.0261925530977 \tabularnewline
Median & 92.3 &  &  \tabularnewline
Midrange & 128.3 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 90.4294117647058 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 90.82 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 90.82 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 90.82 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 90.769696969697 &  &  \tabularnewline
Midmean - Closest Observation & 90.4294117647058 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 90.82 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 90.82 &  &  \tabularnewline
Number of observations & 67 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=17978&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]94.965671641791[/C][C]2.79961355496849[/C][C]33.9209929432064[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]92.7193074811193[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]90.821547261266[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]97.651297841602[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 22 )[/C][C]94.4611940298507[/C][C]2.55973673880263[/C][C]36.9026988588041[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 22 )[/C][C]94.5626865671642[/C][C]2.50615419435151[/C][C]37.7321901343079[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 22 )[/C][C]94.2582089552239[/C][C]2.3942227968144[/C][C]39.3690215800459[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 22 )[/C][C]93.7567164179104[/C][C]2.22233352068549[/C][C]42.1884094107489[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 22 )[/C][C]92.4134328358209[/C][C]1.83531847894103[/C][C]50.3528046473673[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 22 )[/C][C]92.144776119403[/C][C]1.72977788759089[/C][C]53.2697155978421[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 22 )[/C][C]91.9462686567164[/C][C]1.67308127189653[/C][C]54.9562476140147[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 22 )[/C][C]91.9582089552239[/C][C]1.63665491173532[/C][C]56.1866819302319[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 22 )[/C][C]91.9044776119403[/C][C]1.59755358090195[/C][C]57.5282599035286[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 22 )[/C][C]91.1880597014925[/C][C]1.41309140849291[/C][C]64.5308995252799[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 22 )[/C][C]91.3194029850746[/C][C]1.39273042968776[/C][C]65.56861330699[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 22 )[/C][C]91.265671641791[/C][C]1.38390070087472[/C][C]65.9481360072332[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 22 )[/C][C]91.2074626865672[/C][C]1.35008469746677[/C][C]67.5568450317999[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 22 )[/C][C]91.2492537313433[/C][C]1.31145903456461[/C][C]69.5784247364133[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 22 )[/C][C]91.3835820895522[/C][C]1.28491156313530[/C][C]71.1205227747875[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 22 )[/C][C]91.2164179104478[/C][C]1.25131427427438[/C][C]72.8964895436382[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 22 )[/C][C]91.3940298507463[/C][C]1.18802612063299[/C][C]76.9293101081406[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 22 )[/C][C]90.5074626865672[/C][C]1.04107047817978[/C][C]86.9369217392578[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 22 )[/C][C]90.5641791044776[/C][C]1.02490184744234[/C][C]88.363758276446[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 22 )[/C][C]90.534328358209[/C][C]1.02074491524264[/C][C]88.6943711462805[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 22 )[/C][C]90.4402985074627[/C][C]0.93782531747844[/C][C]96.4361878719933[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 22 )[/C][C]90.5059701492537[/C][C]0.910506741570382[/C][C]99.4017573040206[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 22 )[/C][C]93.94[/C][C]2.40944435822548[/C][C]38.9882421145368[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 22 )[/C][C]93.3857142857143[/C][C]2.22225725961699[/C][C]42.0229088606103[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 22 )[/C][C]92.739344262295[/C][C]2.022785882162[/C][C]45.8473361318762[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 22 )[/C][C]92.164406779661[/C][C]1.82895690461088[/C][C]50.3917870056481[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 22 )[/C][C]91.6964912280702[/C][C]1.65980787628182[/C][C]55.2452440661276[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 22 )[/C][C]91.5218181818182[/C][C]1.59597914576953[/C][C]57.3452469127904[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 22 )[/C][C]91.3905660377359[/C][C]1.54931340228887[/C][C]58.9877851070805[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 22 )[/C][C]91.286274509804[/C][C]1.50667539371369[/C][C]60.5878843516515[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 22 )[/C][C]91.1714285714286[/C][C]1.46199297856992[/C][C]62.3610577532388[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 22 )[/C][C]91.0553191489362[/C][C]1.41473613780057[/C][C]64.3620507853118[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 22 )[/C][C]91.0355555555556[/C][C]1.39927526535630[/C][C]65.0590758011972[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 22 )[/C][C]90.9953488372093[/C][C]1.38191512308162[/C][C]65.8472776781639[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 22 )[/C][C]90.9585365853658[/C][C]1.35927247223561[/C][C]66.9170739813227[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 22 )[/C][C]90.925641025641[/C][C]1.33539340490607[/C][C]68.0890295635662[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 22 )[/C][C]90.8837837837838[/C][C]1.31055150526435[/C][C]69.3477390386513[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 22 )[/C][C]90.82[/C][C]1.28085974277915[/C][C]70.9054996161742[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 22 )[/C][C]90.769696969697[/C][C]1.24652915742561[/C][C]72.8179492866083[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 22 )[/C][C]90.6903225806452[/C][C]1.21305935851634[/C][C]74.7616527946051[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 22 )[/C][C]90.7137931034483[/C][C]1.20453498721167[/C][C]75.3102185212884[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 22 )[/C][C]90.7333333333333[/C][C]1.19088417917324[/C][C]76.1898889246508[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 22 )[/C][C]90.76[/C][C]1.16536117434324[/C][C]77.8814345270676[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 22 )[/C][C]90.804347826087[/C][C]1.14904115828528[/C][C]79.0261925530977[/C][/ROW]
[ROW][C]Median[/C][C]92.3[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]128.3[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]90.4294117647058[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]90.82[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]90.82[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]90.82[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]90.769696969697[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]90.4294117647058[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]90.82[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]90.82[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]67[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=17978&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=17978&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 Mean94.9656716417912.7996135549684933.9209929432064
Geometric Mean92.7193074811193
Harmonic Mean90.821547261266
Quadratic Mean97.651297841602
Winsorized Mean ( 1 / 22 )94.46119402985072.5597367388026336.9026988588041
Winsorized Mean ( 2 / 22 )94.56268656716422.5061541943515137.7321901343079
Winsorized Mean ( 3 / 22 )94.25820895522392.394222796814439.3690215800459
Winsorized Mean ( 4 / 22 )93.75671641791042.2223335206854942.1884094107489
Winsorized Mean ( 5 / 22 )92.41343283582091.8353184789410350.3528046473673
Winsorized Mean ( 6 / 22 )92.1447761194031.7297778875908953.2697155978421
Winsorized Mean ( 7 / 22 )91.94626865671641.6730812718965354.9562476140147
Winsorized Mean ( 8 / 22 )91.95820895522391.6366549117353256.1866819302319
Winsorized Mean ( 9 / 22 )91.90447761194031.5975535809019557.5282599035286
Winsorized Mean ( 10 / 22 )91.18805970149251.4130914084929164.5308995252799
Winsorized Mean ( 11 / 22 )91.31940298507461.3927304296877665.56861330699
Winsorized Mean ( 12 / 22 )91.2656716417911.3839007008747265.9481360072332
Winsorized Mean ( 13 / 22 )91.20746268656721.3500846974667767.5568450317999
Winsorized Mean ( 14 / 22 )91.24925373134331.3114590345646169.5784247364133
Winsorized Mean ( 15 / 22 )91.38358208955221.2849115631353071.1205227747875
Winsorized Mean ( 16 / 22 )91.21641791044781.2513142742743872.8964895436382
Winsorized Mean ( 17 / 22 )91.39402985074631.1880261206329976.9293101081406
Winsorized Mean ( 18 / 22 )90.50746268656721.0410704781797886.9369217392578
Winsorized Mean ( 19 / 22 )90.56417910447761.0249018474423488.363758276446
Winsorized Mean ( 20 / 22 )90.5343283582091.0207449152426488.6943711462805
Winsorized Mean ( 21 / 22 )90.44029850746270.9378253174784496.4361878719933
Winsorized Mean ( 22 / 22 )90.50597014925370.91050674157038299.4017573040206
Trimmed Mean ( 1 / 22 )93.942.4094443582254838.9882421145368
Trimmed Mean ( 2 / 22 )93.38571428571432.2222572596169942.0229088606103
Trimmed Mean ( 3 / 22 )92.7393442622952.02278588216245.8473361318762
Trimmed Mean ( 4 / 22 )92.1644067796611.8289569046108850.3917870056481
Trimmed Mean ( 5 / 22 )91.69649122807021.6598078762818255.2452440661276
Trimmed Mean ( 6 / 22 )91.52181818181821.5959791457695357.3452469127904
Trimmed Mean ( 7 / 22 )91.39056603773591.5493134022888758.9877851070805
Trimmed Mean ( 8 / 22 )91.2862745098041.5066753937136960.5878843516515
Trimmed Mean ( 9 / 22 )91.17142857142861.4619929785699262.3610577532388
Trimmed Mean ( 10 / 22 )91.05531914893621.4147361378005764.3620507853118
Trimmed Mean ( 11 / 22 )91.03555555555561.3992752653563065.0590758011972
Trimmed Mean ( 12 / 22 )90.99534883720931.3819151230816265.8472776781639
Trimmed Mean ( 13 / 22 )90.95853658536581.3592724722356166.9170739813227
Trimmed Mean ( 14 / 22 )90.9256410256411.3353934049060768.0890295635662
Trimmed Mean ( 15 / 22 )90.88378378378381.3105515052643569.3477390386513
Trimmed Mean ( 16 / 22 )90.821.2808597427791570.9054996161742
Trimmed Mean ( 17 / 22 )90.7696969696971.2465291574256172.8179492866083
Trimmed Mean ( 18 / 22 )90.69032258064521.2130593585163474.7616527946051
Trimmed Mean ( 19 / 22 )90.71379310344831.2045349872116775.3102185212884
Trimmed Mean ( 20 / 22 )90.73333333333331.1908841791732476.1898889246508
Trimmed Mean ( 21 / 22 )90.761.1653611743432477.8814345270676
Trimmed Mean ( 22 / 22 )90.8043478260871.1490411582852879.0261925530977
Median92.3
Midrange128.3
Midmean - Weighted Average at Xnp90.4294117647058
Midmean - Weighted Average at X(n+1)p90.82
Midmean - Empirical Distribution Function90.82
Midmean - Empirical Distribution Function - Averaging90.82
Midmean - Empirical Distribution Function - Interpolation90.769696969697
Midmean - Closest Observation90.4294117647058
Midmean - True Basic - Statistics Graphics Toolkit90.82
Midmean - MS Excel (old versions)90.82
Number of observations67



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')