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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 computationWed, 10 Dec 2008 05:50:14 -0700
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/Dec/10/t1228913451oy4bkl8ypti5bk5.htm/, Retrieved Fri, 17 May 2024 03:04:27 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=31931, Retrieved Fri, 17 May 2024 03:04:27 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact161
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [Central Tendency ...] [2008-12-10 12:50:14] [28deb8481dba3cc87d2d53a86e0e0d0b] [Current]
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Dataseries X:
85,0
95,9
108,9
96,2
100,1
105,7
64,5
66,8
110,3
96,1
102,5
97,6
83,6
86,5
96,0
91,1
87,2
84,5
59,2
61,5
98,8
97,9
92,7
84,2
74,5
79,7
86,8
79,8
87,0
91,4
58,7
62,8
87,9
90,4
80,6
73,5
71,4
70,6
78,3
76,0
77,4
80,9
63,4
58,1
88,2
81,2
84,9
76,4
71,5
76,1
82,9
78,0
82,0
84,7
55,7
59,5
83,2
87,6
76,2
76,4
68,3
70,0
76,3
70,9
72,4
80,1
57,4
62,7
82,6
88,9
80,4
72,0
69,4
69,2
77,3
79,4
78,6
76,1
61,8
59,4
78,1




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135

\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 & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=31931&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]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=31931&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=31931&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'Gwilym Jenkins' @ 72.249.127.135







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean79.7259259259261.4076628666792756.6370881928584
Geometric Mean78.724280702201
Harmonic Mean77.7148889543859
Quadratic Mean80.7139668486467
Winsorized Mean ( 1 / 27 )79.72962962962961.3987300726682657.0014409410208
Winsorized Mean ( 2 / 27 )79.66790123456791.3756601413755657.9124878583062
Winsorized Mean ( 3 / 27 )79.57160493827161.3446627859525359.1758809491443
Winsorized Mean ( 4 / 27 )79.47777777777781.3156360241906460.4101562411013
Winsorized Mean ( 5 / 27 )79.40987654320991.2979002569419561.1833429560386
Winsorized Mean ( 6 / 27 )79.35061728395061.2842266292833561.7886403182838
Winsorized Mean ( 7 / 27 )79.49753086419751.247232708825863.7391324823737
Winsorized Mean ( 8 / 27 )79.38888888888891.2174008439354865.2117905818508
Winsorized Mean ( 9 / 27 )79.47777777777781.1976906791667766.35918535583
Winsorized Mean ( 10 / 27 )79.47777777777781.193392301460566.598198832447
Winsorized Mean ( 11 / 27 )79.54567901234571.1769337245240167.5872203802439
Winsorized Mean ( 12 / 27 )79.23456790123461.0703079637780174.0296910634485
Winsorized Mean ( 13 / 27 )79.3950617283950.97623125997183681.3281288807384
Winsorized Mean ( 14 / 27 )79.60246913580250.92754983112725785.8201537690553
Winsorized Mean ( 15 / 27 )79.63950617283950.88260221142842890.2326157147836
Winsorized Mean ( 16 / 27 )79.38271604938270.83294581753493595.3035772294436
Winsorized Mean ( 17 / 27 )79.36172839506170.7934989865592100.014908322937
Winsorized Mean ( 18 / 27 )79.42839506172840.764786814820413103.856909562935
Winsorized Mean ( 19 / 27 )79.42839506172840.744977492757831106.618516443621
Winsorized Mean ( 20 / 27 )79.4530864197530.713967973180613111.283824211053
Winsorized Mean ( 21 / 27 )79.42716049382720.70330790796961112.933694607710
Winsorized Mean ( 22 / 27 )79.50864197530860.677012768473023117.440387652714
Winsorized Mean ( 23 / 27 )79.5370370370370.649903707123013122.382802506437
Winsorized Mean ( 24 / 27 )79.41851851851850.547260605284194145.120108686201
Winsorized Mean ( 25 / 27 )79.69629629629630.502446006080318158.616638070273
Winsorized Mean ( 26 / 27 )80.11358024691360.434239625939254184.491638858681
Winsorized Mean ( 27 / 27 )80.08024691358030.421528742459399189.975768784719
Trimmed Mean ( 1 / 27 )79.64303797468361.3558421602337858.7406412859675
Trimmed Mean ( 2 / 27 )79.5519480519481.3056669825319760.9282068982704
Trimmed Mean ( 3 / 27 )79.48933333333331.2614942852949663.0120439386276
Trimmed Mean ( 4 / 27 )79.4589041095891.223683145238564.9342147260697
Trimmed Mean ( 5 / 27 )79.45352112676061.1896482258851966.7874077378136
Trimmed Mean ( 6 / 27 )79.4637681159421.1548315256247168.809836199229
Trimmed Mean ( 7 / 27 )79.48656716417911.1171677366435771.1500740282647
Trimmed Mean ( 8 / 27 )79.48461538461541.0816792295414173.4826122327537
Trimmed Mean ( 9 / 27 )79.51.046188801653275.9901079751315
Trimmed Mean ( 10 / 27 )79.50327868852461.0078055129757178.8875211188101
Trimmed Mean ( 11 / 27 )79.5067796610170.96190095374147882.6558902470798
Trimmed Mean ( 12 / 27 )79.50175438596490.90909664610278287.4513779440085
Trimmed Mean ( 13 / 27 )79.53454545454550.86820848937472791.6076569486498
Trimmed Mean ( 14 / 27 )79.55094339622640.83808399322004194.9200128385462
Trimmed Mean ( 15 / 27 )79.54509803921570.81066573332065598.1231779877786
Trimmed Mean ( 16 / 27 )79.5346938775510.785430419611496101.262558581436
Trimmed Mean ( 17 / 27 )79.55106382978720.763566006725963104.183611016012
Trimmed Mean ( 18 / 27 )79.57111111111110.743480908181594107.025089999589
Trimmed Mean ( 19 / 27 )79.5860465116280.723215575397663110.044707579572
Trimmed Mean ( 20 / 27 )79.60243902439030.7005789226695113.623799472972
Trimmed Mean ( 21 / 27 )79.61794871794870.677335732807255117.545767721375
Trimmed Mean ( 22 / 27 )79.63783783783780.648112891856705122.876490868269
Trimmed Mean ( 23 / 27 )79.65142857142860.614849457950787129.546228823062
Trimmed Mean ( 24 / 27 )79.66363636363640.576017186287069138.300797719488
Trimmed Mean ( 25 / 27 )79.69032258064520.552498816983304144.236186813507
Trimmed Mean ( 26 / 27 )79.68965517241380.531990055732882149.795384920553
Trimmed Mean ( 27 / 27 )79.64074074074070.521647053487264152.671696712047
Median79.7
Midrange83
Midmean - Weighted Average at Xnp79.4125
Midmean - Weighted Average at X(n+1)p79.6024390243902
Midmean - Empirical Distribution Function79.6024390243902
Midmean - Empirical Distribution Function - Averaging79.6024390243902
Midmean - Empirical Distribution Function - Interpolation79.6024390243902
Midmean - Closest Observation79.395238095238
Midmean - True Basic - Statistics Graphics Toolkit79.6024390243902
Midmean - MS Excel (old versions)79.6024390243902
Number of observations81

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 79.725925925926 & 1.40766286667927 & 56.6370881928584 \tabularnewline
Geometric Mean & 78.724280702201 &  &  \tabularnewline
Harmonic Mean & 77.7148889543859 &  &  \tabularnewline
Quadratic Mean & 80.7139668486467 &  &  \tabularnewline
Winsorized Mean ( 1 / 27 ) & 79.7296296296296 & 1.39873007266826 & 57.0014409410208 \tabularnewline
Winsorized Mean ( 2 / 27 ) & 79.6679012345679 & 1.37566014137556 & 57.9124878583062 \tabularnewline
Winsorized Mean ( 3 / 27 ) & 79.5716049382716 & 1.34466278595253 & 59.1758809491443 \tabularnewline
Winsorized Mean ( 4 / 27 ) & 79.4777777777778 & 1.31563602419064 & 60.4101562411013 \tabularnewline
Winsorized Mean ( 5 / 27 ) & 79.4098765432099 & 1.29790025694195 & 61.1833429560386 \tabularnewline
Winsorized Mean ( 6 / 27 ) & 79.3506172839506 & 1.28422662928335 & 61.7886403182838 \tabularnewline
Winsorized Mean ( 7 / 27 ) & 79.4975308641975 & 1.2472327088258 & 63.7391324823737 \tabularnewline
Winsorized Mean ( 8 / 27 ) & 79.3888888888889 & 1.21740084393548 & 65.2117905818508 \tabularnewline
Winsorized Mean ( 9 / 27 ) & 79.4777777777778 & 1.19769067916677 & 66.35918535583 \tabularnewline
Winsorized Mean ( 10 / 27 ) & 79.4777777777778 & 1.1933923014605 & 66.598198832447 \tabularnewline
Winsorized Mean ( 11 / 27 ) & 79.5456790123457 & 1.17693372452401 & 67.5872203802439 \tabularnewline
Winsorized Mean ( 12 / 27 ) & 79.2345679012346 & 1.07030796377801 & 74.0296910634485 \tabularnewline
Winsorized Mean ( 13 / 27 ) & 79.395061728395 & 0.976231259971836 & 81.3281288807384 \tabularnewline
Winsorized Mean ( 14 / 27 ) & 79.6024691358025 & 0.927549831127257 & 85.8201537690553 \tabularnewline
Winsorized Mean ( 15 / 27 ) & 79.6395061728395 & 0.882602211428428 & 90.2326157147836 \tabularnewline
Winsorized Mean ( 16 / 27 ) & 79.3827160493827 & 0.832945817534935 & 95.3035772294436 \tabularnewline
Winsorized Mean ( 17 / 27 ) & 79.3617283950617 & 0.7934989865592 & 100.014908322937 \tabularnewline
Winsorized Mean ( 18 / 27 ) & 79.4283950617284 & 0.764786814820413 & 103.856909562935 \tabularnewline
Winsorized Mean ( 19 / 27 ) & 79.4283950617284 & 0.744977492757831 & 106.618516443621 \tabularnewline
Winsorized Mean ( 20 / 27 ) & 79.453086419753 & 0.713967973180613 & 111.283824211053 \tabularnewline
Winsorized Mean ( 21 / 27 ) & 79.4271604938272 & 0.70330790796961 & 112.933694607710 \tabularnewline
Winsorized Mean ( 22 / 27 ) & 79.5086419753086 & 0.677012768473023 & 117.440387652714 \tabularnewline
Winsorized Mean ( 23 / 27 ) & 79.537037037037 & 0.649903707123013 & 122.382802506437 \tabularnewline
Winsorized Mean ( 24 / 27 ) & 79.4185185185185 & 0.547260605284194 & 145.120108686201 \tabularnewline
Winsorized Mean ( 25 / 27 ) & 79.6962962962963 & 0.502446006080318 & 158.616638070273 \tabularnewline
Winsorized Mean ( 26 / 27 ) & 80.1135802469136 & 0.434239625939254 & 184.491638858681 \tabularnewline
Winsorized Mean ( 27 / 27 ) & 80.0802469135803 & 0.421528742459399 & 189.975768784719 \tabularnewline
Trimmed Mean ( 1 / 27 ) & 79.6430379746836 & 1.35584216023378 & 58.7406412859675 \tabularnewline
Trimmed Mean ( 2 / 27 ) & 79.551948051948 & 1.30566698253197 & 60.9282068982704 \tabularnewline
Trimmed Mean ( 3 / 27 ) & 79.4893333333333 & 1.26149428529496 & 63.0120439386276 \tabularnewline
Trimmed Mean ( 4 / 27 ) & 79.458904109589 & 1.2236831452385 & 64.9342147260697 \tabularnewline
Trimmed Mean ( 5 / 27 ) & 79.4535211267606 & 1.18964822588519 & 66.7874077378136 \tabularnewline
Trimmed Mean ( 6 / 27 ) & 79.463768115942 & 1.15483152562471 & 68.809836199229 \tabularnewline
Trimmed Mean ( 7 / 27 ) & 79.4865671641791 & 1.11716773664357 & 71.1500740282647 \tabularnewline
Trimmed Mean ( 8 / 27 ) & 79.4846153846154 & 1.08167922954141 & 73.4826122327537 \tabularnewline
Trimmed Mean ( 9 / 27 ) & 79.5 & 1.0461888016532 & 75.9901079751315 \tabularnewline
Trimmed Mean ( 10 / 27 ) & 79.5032786885246 & 1.00780551297571 & 78.8875211188101 \tabularnewline
Trimmed Mean ( 11 / 27 ) & 79.506779661017 & 0.961900953741478 & 82.6558902470798 \tabularnewline
Trimmed Mean ( 12 / 27 ) & 79.5017543859649 & 0.909096646102782 & 87.4513779440085 \tabularnewline
Trimmed Mean ( 13 / 27 ) & 79.5345454545455 & 0.868208489374727 & 91.6076569486498 \tabularnewline
Trimmed Mean ( 14 / 27 ) & 79.5509433962264 & 0.838083993220041 & 94.9200128385462 \tabularnewline
Trimmed Mean ( 15 / 27 ) & 79.5450980392157 & 0.810665733320655 & 98.1231779877786 \tabularnewline
Trimmed Mean ( 16 / 27 ) & 79.534693877551 & 0.785430419611496 & 101.262558581436 \tabularnewline
Trimmed Mean ( 17 / 27 ) & 79.5510638297872 & 0.763566006725963 & 104.183611016012 \tabularnewline
Trimmed Mean ( 18 / 27 ) & 79.5711111111111 & 0.743480908181594 & 107.025089999589 \tabularnewline
Trimmed Mean ( 19 / 27 ) & 79.586046511628 & 0.723215575397663 & 110.044707579572 \tabularnewline
Trimmed Mean ( 20 / 27 ) & 79.6024390243903 & 0.7005789226695 & 113.623799472972 \tabularnewline
Trimmed Mean ( 21 / 27 ) & 79.6179487179487 & 0.677335732807255 & 117.545767721375 \tabularnewline
Trimmed Mean ( 22 / 27 ) & 79.6378378378378 & 0.648112891856705 & 122.876490868269 \tabularnewline
Trimmed Mean ( 23 / 27 ) & 79.6514285714286 & 0.614849457950787 & 129.546228823062 \tabularnewline
Trimmed Mean ( 24 / 27 ) & 79.6636363636364 & 0.576017186287069 & 138.300797719488 \tabularnewline
Trimmed Mean ( 25 / 27 ) & 79.6903225806452 & 0.552498816983304 & 144.236186813507 \tabularnewline
Trimmed Mean ( 26 / 27 ) & 79.6896551724138 & 0.531990055732882 & 149.795384920553 \tabularnewline
Trimmed Mean ( 27 / 27 ) & 79.6407407407407 & 0.521647053487264 & 152.671696712047 \tabularnewline
Median & 79.7 &  &  \tabularnewline
Midrange & 83 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 79.4125 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 79.6024390243902 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 79.6024390243902 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 79.6024390243902 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 79.6024390243902 &  &  \tabularnewline
Midmean - Closest Observation & 79.395238095238 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 79.6024390243902 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 79.6024390243902 &  &  \tabularnewline
Number of observations & 81 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=31931&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]79.725925925926[/C][C]1.40766286667927[/C][C]56.6370881928584[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]78.724280702201[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]77.7148889543859[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]80.7139668486467[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 27 )[/C][C]79.7296296296296[/C][C]1.39873007266826[/C][C]57.0014409410208[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 27 )[/C][C]79.6679012345679[/C][C]1.37566014137556[/C][C]57.9124878583062[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 27 )[/C][C]79.5716049382716[/C][C]1.34466278595253[/C][C]59.1758809491443[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 27 )[/C][C]79.4777777777778[/C][C]1.31563602419064[/C][C]60.4101562411013[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 27 )[/C][C]79.4098765432099[/C][C]1.29790025694195[/C][C]61.1833429560386[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 27 )[/C][C]79.3506172839506[/C][C]1.28422662928335[/C][C]61.7886403182838[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 27 )[/C][C]79.4975308641975[/C][C]1.2472327088258[/C][C]63.7391324823737[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 27 )[/C][C]79.3888888888889[/C][C]1.21740084393548[/C][C]65.2117905818508[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 27 )[/C][C]79.4777777777778[/C][C]1.19769067916677[/C][C]66.35918535583[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 27 )[/C][C]79.4777777777778[/C][C]1.1933923014605[/C][C]66.598198832447[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 27 )[/C][C]79.5456790123457[/C][C]1.17693372452401[/C][C]67.5872203802439[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 27 )[/C][C]79.2345679012346[/C][C]1.07030796377801[/C][C]74.0296910634485[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 27 )[/C][C]79.395061728395[/C][C]0.976231259971836[/C][C]81.3281288807384[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 27 )[/C][C]79.6024691358025[/C][C]0.927549831127257[/C][C]85.8201537690553[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 27 )[/C][C]79.6395061728395[/C][C]0.882602211428428[/C][C]90.2326157147836[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 27 )[/C][C]79.3827160493827[/C][C]0.832945817534935[/C][C]95.3035772294436[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 27 )[/C][C]79.3617283950617[/C][C]0.7934989865592[/C][C]100.014908322937[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 27 )[/C][C]79.4283950617284[/C][C]0.764786814820413[/C][C]103.856909562935[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 27 )[/C][C]79.4283950617284[/C][C]0.744977492757831[/C][C]106.618516443621[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 27 )[/C][C]79.453086419753[/C][C]0.713967973180613[/C][C]111.283824211053[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 27 )[/C][C]79.4271604938272[/C][C]0.70330790796961[/C][C]112.933694607710[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 27 )[/C][C]79.5086419753086[/C][C]0.677012768473023[/C][C]117.440387652714[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 27 )[/C][C]79.537037037037[/C][C]0.649903707123013[/C][C]122.382802506437[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 27 )[/C][C]79.4185185185185[/C][C]0.547260605284194[/C][C]145.120108686201[/C][/ROW]
[ROW][C]Winsorized Mean ( 25 / 27 )[/C][C]79.6962962962963[/C][C]0.502446006080318[/C][C]158.616638070273[/C][/ROW]
[ROW][C]Winsorized Mean ( 26 / 27 )[/C][C]80.1135802469136[/C][C]0.434239625939254[/C][C]184.491638858681[/C][/ROW]
[ROW][C]Winsorized Mean ( 27 / 27 )[/C][C]80.0802469135803[/C][C]0.421528742459399[/C][C]189.975768784719[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 27 )[/C][C]79.6430379746836[/C][C]1.35584216023378[/C][C]58.7406412859675[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 27 )[/C][C]79.551948051948[/C][C]1.30566698253197[/C][C]60.9282068982704[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 27 )[/C][C]79.4893333333333[/C][C]1.26149428529496[/C][C]63.0120439386276[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 27 )[/C][C]79.458904109589[/C][C]1.2236831452385[/C][C]64.9342147260697[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 27 )[/C][C]79.4535211267606[/C][C]1.18964822588519[/C][C]66.7874077378136[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 27 )[/C][C]79.463768115942[/C][C]1.15483152562471[/C][C]68.809836199229[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 27 )[/C][C]79.4865671641791[/C][C]1.11716773664357[/C][C]71.1500740282647[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 27 )[/C][C]79.4846153846154[/C][C]1.08167922954141[/C][C]73.4826122327537[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 27 )[/C][C]79.5[/C][C]1.0461888016532[/C][C]75.9901079751315[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 27 )[/C][C]79.5032786885246[/C][C]1.00780551297571[/C][C]78.8875211188101[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 27 )[/C][C]79.506779661017[/C][C]0.961900953741478[/C][C]82.6558902470798[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 27 )[/C][C]79.5017543859649[/C][C]0.909096646102782[/C][C]87.4513779440085[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 27 )[/C][C]79.5345454545455[/C][C]0.868208489374727[/C][C]91.6076569486498[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 27 )[/C][C]79.5509433962264[/C][C]0.838083993220041[/C][C]94.9200128385462[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 27 )[/C][C]79.5450980392157[/C][C]0.810665733320655[/C][C]98.1231779877786[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 27 )[/C][C]79.534693877551[/C][C]0.785430419611496[/C][C]101.262558581436[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 27 )[/C][C]79.5510638297872[/C][C]0.763566006725963[/C][C]104.183611016012[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 27 )[/C][C]79.5711111111111[/C][C]0.743480908181594[/C][C]107.025089999589[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 27 )[/C][C]79.586046511628[/C][C]0.723215575397663[/C][C]110.044707579572[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 27 )[/C][C]79.6024390243903[/C][C]0.7005789226695[/C][C]113.623799472972[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 27 )[/C][C]79.6179487179487[/C][C]0.677335732807255[/C][C]117.545767721375[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 27 )[/C][C]79.6378378378378[/C][C]0.648112891856705[/C][C]122.876490868269[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 27 )[/C][C]79.6514285714286[/C][C]0.614849457950787[/C][C]129.546228823062[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 27 )[/C][C]79.6636363636364[/C][C]0.576017186287069[/C][C]138.300797719488[/C][/ROW]
[ROW][C]Trimmed Mean ( 25 / 27 )[/C][C]79.6903225806452[/C][C]0.552498816983304[/C][C]144.236186813507[/C][/ROW]
[ROW][C]Trimmed Mean ( 26 / 27 )[/C][C]79.6896551724138[/C][C]0.531990055732882[/C][C]149.795384920553[/C][/ROW]
[ROW][C]Trimmed Mean ( 27 / 27 )[/C][C]79.6407407407407[/C][C]0.521647053487264[/C][C]152.671696712047[/C][/ROW]
[ROW][C]Median[/C][C]79.7[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]83[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]79.4125[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]79.6024390243902[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]79.6024390243902[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]79.6024390243902[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]79.6024390243902[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]79.395238095238[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]79.6024390243902[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]79.6024390243902[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]81[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=31931&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=31931&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 Mean79.7259259259261.4076628666792756.6370881928584
Geometric Mean78.724280702201
Harmonic Mean77.7148889543859
Quadratic Mean80.7139668486467
Winsorized Mean ( 1 / 27 )79.72962962962961.3987300726682657.0014409410208
Winsorized Mean ( 2 / 27 )79.66790123456791.3756601413755657.9124878583062
Winsorized Mean ( 3 / 27 )79.57160493827161.3446627859525359.1758809491443
Winsorized Mean ( 4 / 27 )79.47777777777781.3156360241906460.4101562411013
Winsorized Mean ( 5 / 27 )79.40987654320991.2979002569419561.1833429560386
Winsorized Mean ( 6 / 27 )79.35061728395061.2842266292833561.7886403182838
Winsorized Mean ( 7 / 27 )79.49753086419751.247232708825863.7391324823737
Winsorized Mean ( 8 / 27 )79.38888888888891.2174008439354865.2117905818508
Winsorized Mean ( 9 / 27 )79.47777777777781.1976906791667766.35918535583
Winsorized Mean ( 10 / 27 )79.47777777777781.193392301460566.598198832447
Winsorized Mean ( 11 / 27 )79.54567901234571.1769337245240167.5872203802439
Winsorized Mean ( 12 / 27 )79.23456790123461.0703079637780174.0296910634485
Winsorized Mean ( 13 / 27 )79.3950617283950.97623125997183681.3281288807384
Winsorized Mean ( 14 / 27 )79.60246913580250.92754983112725785.8201537690553
Winsorized Mean ( 15 / 27 )79.63950617283950.88260221142842890.2326157147836
Winsorized Mean ( 16 / 27 )79.38271604938270.83294581753493595.3035772294436
Winsorized Mean ( 17 / 27 )79.36172839506170.7934989865592100.014908322937
Winsorized Mean ( 18 / 27 )79.42839506172840.764786814820413103.856909562935
Winsorized Mean ( 19 / 27 )79.42839506172840.744977492757831106.618516443621
Winsorized Mean ( 20 / 27 )79.4530864197530.713967973180613111.283824211053
Winsorized Mean ( 21 / 27 )79.42716049382720.70330790796961112.933694607710
Winsorized Mean ( 22 / 27 )79.50864197530860.677012768473023117.440387652714
Winsorized Mean ( 23 / 27 )79.5370370370370.649903707123013122.382802506437
Winsorized Mean ( 24 / 27 )79.41851851851850.547260605284194145.120108686201
Winsorized Mean ( 25 / 27 )79.69629629629630.502446006080318158.616638070273
Winsorized Mean ( 26 / 27 )80.11358024691360.434239625939254184.491638858681
Winsorized Mean ( 27 / 27 )80.08024691358030.421528742459399189.975768784719
Trimmed Mean ( 1 / 27 )79.64303797468361.3558421602337858.7406412859675
Trimmed Mean ( 2 / 27 )79.5519480519481.3056669825319760.9282068982704
Trimmed Mean ( 3 / 27 )79.48933333333331.2614942852949663.0120439386276
Trimmed Mean ( 4 / 27 )79.4589041095891.223683145238564.9342147260697
Trimmed Mean ( 5 / 27 )79.45352112676061.1896482258851966.7874077378136
Trimmed Mean ( 6 / 27 )79.4637681159421.1548315256247168.809836199229
Trimmed Mean ( 7 / 27 )79.48656716417911.1171677366435771.1500740282647
Trimmed Mean ( 8 / 27 )79.48461538461541.0816792295414173.4826122327537
Trimmed Mean ( 9 / 27 )79.51.046188801653275.9901079751315
Trimmed Mean ( 10 / 27 )79.50327868852461.0078055129757178.8875211188101
Trimmed Mean ( 11 / 27 )79.5067796610170.96190095374147882.6558902470798
Trimmed Mean ( 12 / 27 )79.50175438596490.90909664610278287.4513779440085
Trimmed Mean ( 13 / 27 )79.53454545454550.86820848937472791.6076569486498
Trimmed Mean ( 14 / 27 )79.55094339622640.83808399322004194.9200128385462
Trimmed Mean ( 15 / 27 )79.54509803921570.81066573332065598.1231779877786
Trimmed Mean ( 16 / 27 )79.5346938775510.785430419611496101.262558581436
Trimmed Mean ( 17 / 27 )79.55106382978720.763566006725963104.183611016012
Trimmed Mean ( 18 / 27 )79.57111111111110.743480908181594107.025089999589
Trimmed Mean ( 19 / 27 )79.5860465116280.723215575397663110.044707579572
Trimmed Mean ( 20 / 27 )79.60243902439030.7005789226695113.623799472972
Trimmed Mean ( 21 / 27 )79.61794871794870.677335732807255117.545767721375
Trimmed Mean ( 22 / 27 )79.63783783783780.648112891856705122.876490868269
Trimmed Mean ( 23 / 27 )79.65142857142860.614849457950787129.546228823062
Trimmed Mean ( 24 / 27 )79.66363636363640.576017186287069138.300797719488
Trimmed Mean ( 25 / 27 )79.69032258064520.552498816983304144.236186813507
Trimmed Mean ( 26 / 27 )79.68965517241380.531990055732882149.795384920553
Trimmed Mean ( 27 / 27 )79.64074074074070.521647053487264152.671696712047
Median79.7
Midrange83
Midmean - Weighted Average at Xnp79.4125
Midmean - Weighted Average at X(n+1)p79.6024390243902
Midmean - Empirical Distribution Function79.6024390243902
Midmean - Empirical Distribution Function - Averaging79.6024390243902
Midmean - Empirical Distribution Function - Interpolation79.6024390243902
Midmean - Closest Observation79.395238095238
Midmean - True Basic - Statistics Graphics Toolkit79.6024390243902
Midmean - MS Excel (old versions)79.6024390243902
Number of observations81



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')