Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationSat, 02 Apr 2011 10:16:07 +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/2011/Apr/02/t1301739197fpgl5hlc5lbbo8a.htm/, Retrieved Thu, 09 May 2024 09:57:09 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=119936, Retrieved Thu, 09 May 2024 09:57:09 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsKDGP1W52
Estimated Impact171
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [Opgave 5 oef2 - S...] [2011-04-02 10:16:07] [439e035dc5bc96f212031d0688fc7c62] [Current]
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Dataseries X:
112
118
129
99
116
168
118
129
205
147
150
267
126
129
124
97
102
127
222
214
118
141
154
226
89
77
82
97
127
121
117
117
106
112
134
169
75
108
115
85
101
108
109
124
105
95
135
164
88
85
112
87
91
87
87
142
95
108
139
159
61
82
124
93
108
75
87
103
90
108
123
129
57
65
67
71
76
67
110
118
99
85
107
141
58
65
70
86
93
74
87
73
101
100
96
157
63
115
70
66
67
83
79
77
102
116
100
135
71
60
89
74
73
91
86
74
87
87
109
137
43
69
73
77
69
76
78
70
83
65
110
132
54
55
66
65
60
65
96
55
71
63
74
106
34
47
56
53
53
55
67
52
46
51
58
91
33
40
46
45
41
55
57
54
46
52
48
77
77
35
42
48
44
45
0
0
46
51
63
84
30
39
45
52
28
40
62




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'George Udny Yule' @ 216.218.223.82

\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 & 'George Udny Yule' @ 216.218.223.82 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=119936&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]'George Udny Yule' @ 216.218.223.82[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=119936&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=119936&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'George Udny Yule' @ 216.218.223.82







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean89.67914438502672.913097154477930.7848106772462
Geometric Mean0
Harmonic Mean0
Quadratic Mean98.0855241790344
Winsorized Mean ( 1 / 62 )89.45989304812832.8488883704569931.4016842414145
Winsorized Mean ( 2 / 62 )89.7165775401072.7948051947153832.101191778858
Winsorized Mean ( 3 / 62 )89.6203208556152.7591492268042532.4811430947563
Winsorized Mean ( 4 / 62 )89.49197860962572.7063918593439533.0668961705047
Winsorized Mean ( 5 / 62 )88.55614973262032.5088891498993935.2969559201815
Winsorized Mean ( 6 / 62 )88.55614973262032.4996587682009235.4272954609549
Winsorized Mean ( 7 / 62 )88.55614973262032.4577632763968836.0311957555347
Winsorized Mean ( 8 / 62 )88.38502673796792.4186985904516236.5423898152868
Winsorized Mean ( 9 / 62 )88.2887700534762.403747137179236.7296412704552
Winsorized Mean ( 10 / 62 )88.18181818181822.3737140469734137.1493012371284
Winsorized Mean ( 11 / 62 )88.00534759358292.3331012312114537.7203296694874
Winsorized Mean ( 12 / 62 )87.87700534759362.2992710662547438.2195064502488
Winsorized Mean ( 13 / 62 )87.59893048128342.2453122653265239.0141415223349
Winsorized Mean ( 14 / 62 )87.59893048128342.2278556511395239.3198412278091
Winsorized Mean ( 15 / 62 )87.59893048128342.2278556511395239.3198412278091
Winsorized Mean ( 16 / 62 )87.4278074866312.2060742759811439.6304913386237
Winsorized Mean ( 17 / 62 )87.3368983957222.1741351758565140.1708685667695
Winsorized Mean ( 18 / 62 )87.1443850267382.1507975555361340.5172419888749
Winsorized Mean ( 19 / 62 )87.1443850267382.1507975555361340.5172419888749
Winsorized Mean ( 20 / 62 )87.03743315508022.1380852920849740.7081202407061
Winsorized Mean ( 21 / 62 )86.92513368983962.100330822900941.3864010098094
Winsorized Mean ( 22 / 62 )86.68983957219252.048377097811742.3212306292645
Winsorized Mean ( 23 / 62 )86.68983957219252.048377097811742.3212306292645
Winsorized Mean ( 24 / 62 )87.07486631016042.0102445336983643.3155593016158
Winsorized Mean ( 25 / 62 )87.07486631016042.0102445336983643.3155593016158
Winsorized Mean ( 26 / 62 )86.93582887700531.9660685404911344.2181068902555
Winsorized Mean ( 27 / 62 )86.93582887700531.9660685404911344.2181068902555
Winsorized Mean ( 28 / 62 )86.78609625668451.9497706374833244.5109258434131
Winsorized Mean ( 29 / 62 )86.63101604278071.9018037682900945.552026706031
Winsorized Mean ( 30 / 62 )86.63101604278071.9018037682900945.552026706031
Winsorized Mean ( 31 / 62 )86.79679144385031.8861741047887446.0173804865018
Winsorized Mean ( 32 / 62 )86.62566844919791.8681435255509946.3699214029332
Winsorized Mean ( 33 / 62 )86.44919786096261.8150992651668647.6278072059136
Winsorized Mean ( 34 / 62 )85.9037433155081.76043728150348.7968212319195
Winsorized Mean ( 35 / 62 )85.9037433155081.76043728150348.7968212319195
Winsorized Mean ( 36 / 62 )85.9037433155081.76043728150348.7968212319195
Winsorized Mean ( 37 / 62 )86.10160427807491.7419081054781449.4294756464439
Winsorized Mean ( 38 / 62 )86.10160427807491.7032194560308850.5522667517684
Winsorized Mean ( 39 / 62 )86.10160427807491.7032194560308850.5522667517684
Winsorized Mean ( 40 / 62 )86.10160427807491.6629053312232151.7778148048512
Winsorized Mean ( 41 / 62 )86.10160427807491.6629053312232151.7778148048512
Winsorized Mean ( 42 / 62 )86.32620320855621.6009626869635953.9214335921118
Winsorized Mean ( 43 / 62 )86.32620320855621.6009626869635953.9214335921118
Winsorized Mean ( 44 / 62 )85.8556149732621.5133726412606256.7313116627676
Winsorized Mean ( 45 / 62 )86.0962566844921.4923016313864257.693602200585
Winsorized Mean ( 46 / 62 )86.34224598930481.4711307356344658.691076121163
Winsorized Mean ( 47 / 62 )85.83957219251341.4246366725712660.2536589470113
Winsorized Mean ( 48 / 62 )85.83957219251341.4246366725712660.2536589470113
Winsorized Mean ( 49 / 62 )86.10160427807491.3562772355613963.4837789948128
Winsorized Mean ( 50 / 62 )86.10160427807491.3562772355613963.4837789948128
Winsorized Mean ( 51 / 62 )85.82887700534761.3316920069625564.4509965942608
Winsorized Mean ( 52 / 62 )85.82887700534761.3316920069625564.4509965942608
Winsorized Mean ( 53 / 62 )85.82887700534761.3316920069625564.4509965942608
Winsorized Mean ( 54 / 62 )86.11764705882351.3076058314006565.8590264671567
Winsorized Mean ( 55 / 62 )86.11764705882351.3076058314006565.8590264671567
Winsorized Mean ( 56 / 62 )86.11764705882351.2561093503045668.5590367096171
Winsorized Mean ( 57 / 62 )85.8128342245991.2290267890930469.8217768612875
Winsorized Mean ( 58 / 62 )85.8128342245991.2290267890930469.8217768612875
Winsorized Mean ( 59 / 62 )85.49732620320861.2013250100390571.1691885948746
Winsorized Mean ( 60 / 62 )85.49732620320861.0930587507857278.218417941168
Winsorized Mean ( 61 / 62 )85.17112299465241.0651607492650179.9608162931489
Winsorized Mean ( 62 / 62 )85.50267379679141.0383197440828482.3471520059716
Trimmed Mean ( 1 / 62 )89.67914438502672.7404261003276632.7245257131014
Trimmed Mean ( 2 / 62 )89.20540540540542.6218887339081434.0233375473708
Trimmed Mean ( 3 / 62 )88.54696132596682.5237293165574235.0857600872793
Trimmed Mean ( 4 / 62 )88.54696132596682.4311344349484336.4220752472888
Trimmed Mean ( 5 / 62 )87.82485875706212.3470383881829537.4194385567997
Trimmed Mean ( 6 / 62 )87.66857142857142.3073579538483937.9952192863491
Trimmed Mean ( 7 / 62 )87.66857142857142.2666779454217138.6771184700705
Trimmed Mean ( 8 / 62 )87.50867052023122.2308516568929639.2265753080641
Trimmed Mean ( 9 / 62 )87.20118343195272.1990062159249539.6548144341074
Trimmed Mean ( 10 / 62 )87.0658682634732.1670902257407440.1763928558687
Trimmed Mean ( 11 / 62 )86.9393939393942.1370745725707740.6814975271599
Trimmed Mean ( 12 / 62 )86.82822085889572.1102246747302141.1464342629756
Trimmed Mean ( 13 / 62 )86.72670807453422.0855534510104841.584505078263
Trimmed Mean ( 14 / 62 )86.72670807453422.0653509574029941.9912692144032
Trimmed Mean ( 15 / 62 )86.56687898089172.0454630644217542.3214090181403
Trimmed Mean ( 16 / 62 )86.56687898089172.0239528128344842.771194284741
Trimmed Mean ( 17 / 62 )86.41176470588232.0029761441675543.1416844167137
Trimmed Mean ( 18 / 62 )86.34437086092721.9834646779581943.5320940274123
Trimmed Mean ( 19 / 62 )86.28859060402691.9645944500959643.9218336383939
Trimmed Mean ( 20 / 62 )86.23129251700681.9440996954075244.3553860538675
Trimmed Mean ( 21 / 62 )86.17931034482761.9230321325718844.8142851516322
Trimmed Mean ( 22 / 62 )86.13286713286711.903571106363545.2480429257049
Trimmed Mean ( 23 / 62 )86.09929078014181.8869869778467545.6279199543762
Trimmed Mean ( 24 / 62 )86.06474820143881.8688689391664746.0517837274477
Trimmed Mean ( 25 / 62 )86.0072992700731.852246623929246.4340429395003
Trimmed Mean ( 26 / 62 )85.94814814814811.8340287696086446.8630315796455
Trimmed Mean ( 27 / 62 )85.89473684210531.8177770531934747.2526246776002
Trimmed Mean ( 28 / 62 )85.89473684210531.7999092034871647.7217054480815
Trimmed Mean ( 29 / 62 )85.79069767441861.7816447583312348.1525271933415
Trimmed Mean ( 30 / 62 )85.7480314960631.7654975050427348.5687639043069
Trimmed Mean ( 31 / 62 )85.7041.7476629187058249.0392049191416
Trimmed Mean ( 32 / 62 )85.7041.7292007145693549.5627831274314
Trimmed Mean ( 33 / 62 )85.6033057851241.7103025741538950.0515564197598
Trimmed Mean ( 34 / 62 )85.5630252100841.6937445612794550.5170774661853
Trimmed Mean ( 35 / 62 )85.54700854700851.6798109326940850.9265697002034
Trimmed Mean ( 36 / 62 )85.53043478260871.6642387382980751.3931281698661
Trimmed Mean ( 37 / 62 )85.51327433628321.6468428902284751.9255812704878
Trimmed Mean ( 38 / 62 )85.48648648648651.6289188801906652.4805056446277
Trimmed Mean ( 39 / 62 )85.45871559633031.6120791553796653.0114884936924
Trimmed Mean ( 40 / 62 )85.4299065420561.5931718251293453.6225316030307
Trimmed Mean ( 41 / 62 )85.41.5753713440947454.2094410439296
Trimmed Mean ( 42 / 62 )85.3689320388351.5553124506673554.8886058246401
Trimmed Mean ( 43 / 62 )85.32673267326731.5380397007127455.4775878891333
Trimmed Mean ( 44 / 62 )85.28282828282831.5184592493266656.1640546630711
Trimmed Mean ( 45 / 62 )85.25773195876291.5040950938114156.6837378231971
Trimmed Mean ( 46 / 62 )85.2210526315791.4894311462394757.2171817722127
Trimmed Mean ( 47 / 62 )85.17204301075271.4743897285007957.7676589604014
Trimmed Mean ( 48 / 62 )85.14285714285711.4613934030670358.2614215748941
Trimmed Mean ( 49 / 62 )85.11235955056181.4463011716878158.8482960649454
Trimmed Mean ( 50 / 62 )85.06896551724141.4350216432744959.2806149760416
Trimmed Mean ( 51 / 62 )85.06896551724141.4217179483056859.8353320492447
Trimmed Mean ( 52 / 62 )84.98795180722891.4085392962690760.3376505237335
Trimmed Mean ( 53 / 62 )84.95061728395061.3929829918586160.9846766115957
Trimmed Mean ( 54 / 62 )84.91139240506331.3746664489849461.7687239459161
Trimmed Mean ( 55 / 62 )84.85714285714291.3555680325782862.5989554325394
Trimmed Mean ( 56 / 62 )84.85714285714291.3330179807252963.6579131595601
Trimmed Mean ( 57 / 62 )84.73972602739731.3123386176438364.5715403693133
Trimmed Mean ( 58 / 62 )84.69014084507041.2911385877725665.5933775406525
Trimmed Mean ( 59 / 62 )84.63768115942031.2658157192074466.8641413399528
Trimmed Mean ( 60 / 62 )84.59701492537311.2393480474687568.2592876941667
Trimmed Mean ( 61 / 62 )84.55384615384621.2218032797622869.2041407601207
Trimmed Mean ( 62 / 62 )84.52380952380951.2041609765213870.1931146847031
Median85
Midrange133.5
Midmean - Weighted Average at Xnp84.936170212766
Midmean - Weighted Average at X(n+1)p85.7731958762887
Midmean - Empirical Distribution Function85.7731958762887
Midmean - Empirical Distribution Function - Averaging85.7731958762887
Midmean - Empirical Distribution Function - Interpolation84.936170212766
Midmean - Closest Observation84.936170212766
Midmean - True Basic - Statistics Graphics Toolkit85.7731958762887
Midmean - MS Excel (old versions)85.7731958762887
Number of observations187

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 89.6791443850267 & 2.9130971544779 & 30.7848106772462 \tabularnewline
Geometric Mean & 0 &  &  \tabularnewline
Harmonic Mean & 0 &  &  \tabularnewline
Quadratic Mean & 98.0855241790344 &  &  \tabularnewline
Winsorized Mean ( 1 / 62 ) & 89.4598930481283 & 2.84888837045699 & 31.4016842414145 \tabularnewline
Winsorized Mean ( 2 / 62 ) & 89.716577540107 & 2.79480519471538 & 32.101191778858 \tabularnewline
Winsorized Mean ( 3 / 62 ) & 89.620320855615 & 2.75914922680425 & 32.4811430947563 \tabularnewline
Winsorized Mean ( 4 / 62 ) & 89.4919786096257 & 2.70639185934395 & 33.0668961705047 \tabularnewline
Winsorized Mean ( 5 / 62 ) & 88.5561497326203 & 2.50888914989939 & 35.2969559201815 \tabularnewline
Winsorized Mean ( 6 / 62 ) & 88.5561497326203 & 2.49965876820092 & 35.4272954609549 \tabularnewline
Winsorized Mean ( 7 / 62 ) & 88.5561497326203 & 2.45776327639688 & 36.0311957555347 \tabularnewline
Winsorized Mean ( 8 / 62 ) & 88.3850267379679 & 2.41869859045162 & 36.5423898152868 \tabularnewline
Winsorized Mean ( 9 / 62 ) & 88.288770053476 & 2.4037471371792 & 36.7296412704552 \tabularnewline
Winsorized Mean ( 10 / 62 ) & 88.1818181818182 & 2.37371404697341 & 37.1493012371284 \tabularnewline
Winsorized Mean ( 11 / 62 ) & 88.0053475935829 & 2.33310123121145 & 37.7203296694874 \tabularnewline
Winsorized Mean ( 12 / 62 ) & 87.8770053475936 & 2.29927106625474 & 38.2195064502488 \tabularnewline
Winsorized Mean ( 13 / 62 ) & 87.5989304812834 & 2.24531226532652 & 39.0141415223349 \tabularnewline
Winsorized Mean ( 14 / 62 ) & 87.5989304812834 & 2.22785565113952 & 39.3198412278091 \tabularnewline
Winsorized Mean ( 15 / 62 ) & 87.5989304812834 & 2.22785565113952 & 39.3198412278091 \tabularnewline
Winsorized Mean ( 16 / 62 ) & 87.427807486631 & 2.20607427598114 & 39.6304913386237 \tabularnewline
Winsorized Mean ( 17 / 62 ) & 87.336898395722 & 2.17413517585651 & 40.1708685667695 \tabularnewline
Winsorized Mean ( 18 / 62 ) & 87.144385026738 & 2.15079755553613 & 40.5172419888749 \tabularnewline
Winsorized Mean ( 19 / 62 ) & 87.144385026738 & 2.15079755553613 & 40.5172419888749 \tabularnewline
Winsorized Mean ( 20 / 62 ) & 87.0374331550802 & 2.13808529208497 & 40.7081202407061 \tabularnewline
Winsorized Mean ( 21 / 62 ) & 86.9251336898396 & 2.1003308229009 & 41.3864010098094 \tabularnewline
Winsorized Mean ( 22 / 62 ) & 86.6898395721925 & 2.0483770978117 & 42.3212306292645 \tabularnewline
Winsorized Mean ( 23 / 62 ) & 86.6898395721925 & 2.0483770978117 & 42.3212306292645 \tabularnewline
Winsorized Mean ( 24 / 62 ) & 87.0748663101604 & 2.01024453369836 & 43.3155593016158 \tabularnewline
Winsorized Mean ( 25 / 62 ) & 87.0748663101604 & 2.01024453369836 & 43.3155593016158 \tabularnewline
Winsorized Mean ( 26 / 62 ) & 86.9358288770053 & 1.96606854049113 & 44.2181068902555 \tabularnewline
Winsorized Mean ( 27 / 62 ) & 86.9358288770053 & 1.96606854049113 & 44.2181068902555 \tabularnewline
Winsorized Mean ( 28 / 62 ) & 86.7860962566845 & 1.94977063748332 & 44.5109258434131 \tabularnewline
Winsorized Mean ( 29 / 62 ) & 86.6310160427807 & 1.90180376829009 & 45.552026706031 \tabularnewline
Winsorized Mean ( 30 / 62 ) & 86.6310160427807 & 1.90180376829009 & 45.552026706031 \tabularnewline
Winsorized Mean ( 31 / 62 ) & 86.7967914438503 & 1.88617410478874 & 46.0173804865018 \tabularnewline
Winsorized Mean ( 32 / 62 ) & 86.6256684491979 & 1.86814352555099 & 46.3699214029332 \tabularnewline
Winsorized Mean ( 33 / 62 ) & 86.4491978609626 & 1.81509926516686 & 47.6278072059136 \tabularnewline
Winsorized Mean ( 34 / 62 ) & 85.903743315508 & 1.760437281503 & 48.7968212319195 \tabularnewline
Winsorized Mean ( 35 / 62 ) & 85.903743315508 & 1.760437281503 & 48.7968212319195 \tabularnewline
Winsorized Mean ( 36 / 62 ) & 85.903743315508 & 1.760437281503 & 48.7968212319195 \tabularnewline
Winsorized Mean ( 37 / 62 ) & 86.1016042780749 & 1.74190810547814 & 49.4294756464439 \tabularnewline
Winsorized Mean ( 38 / 62 ) & 86.1016042780749 & 1.70321945603088 & 50.5522667517684 \tabularnewline
Winsorized Mean ( 39 / 62 ) & 86.1016042780749 & 1.70321945603088 & 50.5522667517684 \tabularnewline
Winsorized Mean ( 40 / 62 ) & 86.1016042780749 & 1.66290533122321 & 51.7778148048512 \tabularnewline
Winsorized Mean ( 41 / 62 ) & 86.1016042780749 & 1.66290533122321 & 51.7778148048512 \tabularnewline
Winsorized Mean ( 42 / 62 ) & 86.3262032085562 & 1.60096268696359 & 53.9214335921118 \tabularnewline
Winsorized Mean ( 43 / 62 ) & 86.3262032085562 & 1.60096268696359 & 53.9214335921118 \tabularnewline
Winsorized Mean ( 44 / 62 ) & 85.855614973262 & 1.51337264126062 & 56.7313116627676 \tabularnewline
Winsorized Mean ( 45 / 62 ) & 86.096256684492 & 1.49230163138642 & 57.693602200585 \tabularnewline
Winsorized Mean ( 46 / 62 ) & 86.3422459893048 & 1.47113073563446 & 58.691076121163 \tabularnewline
Winsorized Mean ( 47 / 62 ) & 85.8395721925134 & 1.42463667257126 & 60.2536589470113 \tabularnewline
Winsorized Mean ( 48 / 62 ) & 85.8395721925134 & 1.42463667257126 & 60.2536589470113 \tabularnewline
Winsorized Mean ( 49 / 62 ) & 86.1016042780749 & 1.35627723556139 & 63.4837789948128 \tabularnewline
Winsorized Mean ( 50 / 62 ) & 86.1016042780749 & 1.35627723556139 & 63.4837789948128 \tabularnewline
Winsorized Mean ( 51 / 62 ) & 85.8288770053476 & 1.33169200696255 & 64.4509965942608 \tabularnewline
Winsorized Mean ( 52 / 62 ) & 85.8288770053476 & 1.33169200696255 & 64.4509965942608 \tabularnewline
Winsorized Mean ( 53 / 62 ) & 85.8288770053476 & 1.33169200696255 & 64.4509965942608 \tabularnewline
Winsorized Mean ( 54 / 62 ) & 86.1176470588235 & 1.30760583140065 & 65.8590264671567 \tabularnewline
Winsorized Mean ( 55 / 62 ) & 86.1176470588235 & 1.30760583140065 & 65.8590264671567 \tabularnewline
Winsorized Mean ( 56 / 62 ) & 86.1176470588235 & 1.25610935030456 & 68.5590367096171 \tabularnewline
Winsorized Mean ( 57 / 62 ) & 85.812834224599 & 1.22902678909304 & 69.8217768612875 \tabularnewline
Winsorized Mean ( 58 / 62 ) & 85.812834224599 & 1.22902678909304 & 69.8217768612875 \tabularnewline
Winsorized Mean ( 59 / 62 ) & 85.4973262032086 & 1.20132501003905 & 71.1691885948746 \tabularnewline
Winsorized Mean ( 60 / 62 ) & 85.4973262032086 & 1.09305875078572 & 78.218417941168 \tabularnewline
Winsorized Mean ( 61 / 62 ) & 85.1711229946524 & 1.06516074926501 & 79.9608162931489 \tabularnewline
Winsorized Mean ( 62 / 62 ) & 85.5026737967914 & 1.03831974408284 & 82.3471520059716 \tabularnewline
Trimmed Mean ( 1 / 62 ) & 89.6791443850267 & 2.74042610032766 & 32.7245257131014 \tabularnewline
Trimmed Mean ( 2 / 62 ) & 89.2054054054054 & 2.62188873390814 & 34.0233375473708 \tabularnewline
Trimmed Mean ( 3 / 62 ) & 88.5469613259668 & 2.52372931655742 & 35.0857600872793 \tabularnewline
Trimmed Mean ( 4 / 62 ) & 88.5469613259668 & 2.43113443494843 & 36.4220752472888 \tabularnewline
Trimmed Mean ( 5 / 62 ) & 87.8248587570621 & 2.34703838818295 & 37.4194385567997 \tabularnewline
Trimmed Mean ( 6 / 62 ) & 87.6685714285714 & 2.30735795384839 & 37.9952192863491 \tabularnewline
Trimmed Mean ( 7 / 62 ) & 87.6685714285714 & 2.26667794542171 & 38.6771184700705 \tabularnewline
Trimmed Mean ( 8 / 62 ) & 87.5086705202312 & 2.23085165689296 & 39.2265753080641 \tabularnewline
Trimmed Mean ( 9 / 62 ) & 87.2011834319527 & 2.19900621592495 & 39.6548144341074 \tabularnewline
Trimmed Mean ( 10 / 62 ) & 87.065868263473 & 2.16709022574074 & 40.1763928558687 \tabularnewline
Trimmed Mean ( 11 / 62 ) & 86.939393939394 & 2.13707457257077 & 40.6814975271599 \tabularnewline
Trimmed Mean ( 12 / 62 ) & 86.8282208588957 & 2.11022467473021 & 41.1464342629756 \tabularnewline
Trimmed Mean ( 13 / 62 ) & 86.7267080745342 & 2.08555345101048 & 41.584505078263 \tabularnewline
Trimmed Mean ( 14 / 62 ) & 86.7267080745342 & 2.06535095740299 & 41.9912692144032 \tabularnewline
Trimmed Mean ( 15 / 62 ) & 86.5668789808917 & 2.04546306442175 & 42.3214090181403 \tabularnewline
Trimmed Mean ( 16 / 62 ) & 86.5668789808917 & 2.02395281283448 & 42.771194284741 \tabularnewline
Trimmed Mean ( 17 / 62 ) & 86.4117647058823 & 2.00297614416755 & 43.1416844167137 \tabularnewline
Trimmed Mean ( 18 / 62 ) & 86.3443708609272 & 1.98346467795819 & 43.5320940274123 \tabularnewline
Trimmed Mean ( 19 / 62 ) & 86.2885906040269 & 1.96459445009596 & 43.9218336383939 \tabularnewline
Trimmed Mean ( 20 / 62 ) & 86.2312925170068 & 1.94409969540752 & 44.3553860538675 \tabularnewline
Trimmed Mean ( 21 / 62 ) & 86.1793103448276 & 1.92303213257188 & 44.8142851516322 \tabularnewline
Trimmed Mean ( 22 / 62 ) & 86.1328671328671 & 1.9035711063635 & 45.2480429257049 \tabularnewline
Trimmed Mean ( 23 / 62 ) & 86.0992907801418 & 1.88698697784675 & 45.6279199543762 \tabularnewline
Trimmed Mean ( 24 / 62 ) & 86.0647482014388 & 1.86886893916647 & 46.0517837274477 \tabularnewline
Trimmed Mean ( 25 / 62 ) & 86.007299270073 & 1.8522466239292 & 46.4340429395003 \tabularnewline
Trimmed Mean ( 26 / 62 ) & 85.9481481481481 & 1.83402876960864 & 46.8630315796455 \tabularnewline
Trimmed Mean ( 27 / 62 ) & 85.8947368421053 & 1.81777705319347 & 47.2526246776002 \tabularnewline
Trimmed Mean ( 28 / 62 ) & 85.8947368421053 & 1.79990920348716 & 47.7217054480815 \tabularnewline
Trimmed Mean ( 29 / 62 ) & 85.7906976744186 & 1.78164475833123 & 48.1525271933415 \tabularnewline
Trimmed Mean ( 30 / 62 ) & 85.748031496063 & 1.76549750504273 & 48.5687639043069 \tabularnewline
Trimmed Mean ( 31 / 62 ) & 85.704 & 1.74766291870582 & 49.0392049191416 \tabularnewline
Trimmed Mean ( 32 / 62 ) & 85.704 & 1.72920071456935 & 49.5627831274314 \tabularnewline
Trimmed Mean ( 33 / 62 ) & 85.603305785124 & 1.71030257415389 & 50.0515564197598 \tabularnewline
Trimmed Mean ( 34 / 62 ) & 85.563025210084 & 1.69374456127945 & 50.5170774661853 \tabularnewline
Trimmed Mean ( 35 / 62 ) & 85.5470085470085 & 1.67981093269408 & 50.9265697002034 \tabularnewline
Trimmed Mean ( 36 / 62 ) & 85.5304347826087 & 1.66423873829807 & 51.3931281698661 \tabularnewline
Trimmed Mean ( 37 / 62 ) & 85.5132743362832 & 1.64684289022847 & 51.9255812704878 \tabularnewline
Trimmed Mean ( 38 / 62 ) & 85.4864864864865 & 1.62891888019066 & 52.4805056446277 \tabularnewline
Trimmed Mean ( 39 / 62 ) & 85.4587155963303 & 1.61207915537966 & 53.0114884936924 \tabularnewline
Trimmed Mean ( 40 / 62 ) & 85.429906542056 & 1.59317182512934 & 53.6225316030307 \tabularnewline
Trimmed Mean ( 41 / 62 ) & 85.4 & 1.57537134409474 & 54.2094410439296 \tabularnewline
Trimmed Mean ( 42 / 62 ) & 85.368932038835 & 1.55531245066735 & 54.8886058246401 \tabularnewline
Trimmed Mean ( 43 / 62 ) & 85.3267326732673 & 1.53803970071274 & 55.4775878891333 \tabularnewline
Trimmed Mean ( 44 / 62 ) & 85.2828282828283 & 1.51845924932666 & 56.1640546630711 \tabularnewline
Trimmed Mean ( 45 / 62 ) & 85.2577319587629 & 1.50409509381141 & 56.6837378231971 \tabularnewline
Trimmed Mean ( 46 / 62 ) & 85.221052631579 & 1.48943114623947 & 57.2171817722127 \tabularnewline
Trimmed Mean ( 47 / 62 ) & 85.1720430107527 & 1.47438972850079 & 57.7676589604014 \tabularnewline
Trimmed Mean ( 48 / 62 ) & 85.1428571428571 & 1.46139340306703 & 58.2614215748941 \tabularnewline
Trimmed Mean ( 49 / 62 ) & 85.1123595505618 & 1.44630117168781 & 58.8482960649454 \tabularnewline
Trimmed Mean ( 50 / 62 ) & 85.0689655172414 & 1.43502164327449 & 59.2806149760416 \tabularnewline
Trimmed Mean ( 51 / 62 ) & 85.0689655172414 & 1.42171794830568 & 59.8353320492447 \tabularnewline
Trimmed Mean ( 52 / 62 ) & 84.9879518072289 & 1.40853929626907 & 60.3376505237335 \tabularnewline
Trimmed Mean ( 53 / 62 ) & 84.9506172839506 & 1.39298299185861 & 60.9846766115957 \tabularnewline
Trimmed Mean ( 54 / 62 ) & 84.9113924050633 & 1.37466644898494 & 61.7687239459161 \tabularnewline
Trimmed Mean ( 55 / 62 ) & 84.8571428571429 & 1.35556803257828 & 62.5989554325394 \tabularnewline
Trimmed Mean ( 56 / 62 ) & 84.8571428571429 & 1.33301798072529 & 63.6579131595601 \tabularnewline
Trimmed Mean ( 57 / 62 ) & 84.7397260273973 & 1.31233861764383 & 64.5715403693133 \tabularnewline
Trimmed Mean ( 58 / 62 ) & 84.6901408450704 & 1.29113858777256 & 65.5933775406525 \tabularnewline
Trimmed Mean ( 59 / 62 ) & 84.6376811594203 & 1.26581571920744 & 66.8641413399528 \tabularnewline
Trimmed Mean ( 60 / 62 ) & 84.5970149253731 & 1.23934804746875 & 68.2592876941667 \tabularnewline
Trimmed Mean ( 61 / 62 ) & 84.5538461538462 & 1.22180327976228 & 69.2041407601207 \tabularnewline
Trimmed Mean ( 62 / 62 ) & 84.5238095238095 & 1.20416097652138 & 70.1931146847031 \tabularnewline
Median & 85 &  &  \tabularnewline
Midrange & 133.5 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 84.936170212766 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 85.7731958762887 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 85.7731958762887 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 85.7731958762887 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 84.936170212766 &  &  \tabularnewline
Midmean - Closest Observation & 84.936170212766 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 85.7731958762887 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 85.7731958762887 &  &  \tabularnewline
Number of observations & 187 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=119936&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]89.6791443850267[/C][C]2.9130971544779[/C][C]30.7848106772462[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]0[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]0[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]98.0855241790344[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 62 )[/C][C]89.4598930481283[/C][C]2.84888837045699[/C][C]31.4016842414145[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 62 )[/C][C]89.716577540107[/C][C]2.79480519471538[/C][C]32.101191778858[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 62 )[/C][C]89.620320855615[/C][C]2.75914922680425[/C][C]32.4811430947563[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 62 )[/C][C]89.4919786096257[/C][C]2.70639185934395[/C][C]33.0668961705047[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 62 )[/C][C]88.5561497326203[/C][C]2.50888914989939[/C][C]35.2969559201815[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 62 )[/C][C]88.5561497326203[/C][C]2.49965876820092[/C][C]35.4272954609549[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 62 )[/C][C]88.5561497326203[/C][C]2.45776327639688[/C][C]36.0311957555347[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 62 )[/C][C]88.3850267379679[/C][C]2.41869859045162[/C][C]36.5423898152868[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 62 )[/C][C]88.288770053476[/C][C]2.4037471371792[/C][C]36.7296412704552[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 62 )[/C][C]88.1818181818182[/C][C]2.37371404697341[/C][C]37.1493012371284[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 62 )[/C][C]88.0053475935829[/C][C]2.33310123121145[/C][C]37.7203296694874[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 62 )[/C][C]87.8770053475936[/C][C]2.29927106625474[/C][C]38.2195064502488[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 62 )[/C][C]87.5989304812834[/C][C]2.24531226532652[/C][C]39.0141415223349[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 62 )[/C][C]87.5989304812834[/C][C]2.22785565113952[/C][C]39.3198412278091[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 62 )[/C][C]87.5989304812834[/C][C]2.22785565113952[/C][C]39.3198412278091[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 62 )[/C][C]87.427807486631[/C][C]2.20607427598114[/C][C]39.6304913386237[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 62 )[/C][C]87.336898395722[/C][C]2.17413517585651[/C][C]40.1708685667695[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 62 )[/C][C]87.144385026738[/C][C]2.15079755553613[/C][C]40.5172419888749[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 62 )[/C][C]87.144385026738[/C][C]2.15079755553613[/C][C]40.5172419888749[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 62 )[/C][C]87.0374331550802[/C][C]2.13808529208497[/C][C]40.7081202407061[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 62 )[/C][C]86.9251336898396[/C][C]2.1003308229009[/C][C]41.3864010098094[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 62 )[/C][C]86.6898395721925[/C][C]2.0483770978117[/C][C]42.3212306292645[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 62 )[/C][C]86.6898395721925[/C][C]2.0483770978117[/C][C]42.3212306292645[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 62 )[/C][C]87.0748663101604[/C][C]2.01024453369836[/C][C]43.3155593016158[/C][/ROW]
[ROW][C]Winsorized Mean ( 25 / 62 )[/C][C]87.0748663101604[/C][C]2.01024453369836[/C][C]43.3155593016158[/C][/ROW]
[ROW][C]Winsorized Mean ( 26 / 62 )[/C][C]86.9358288770053[/C][C]1.96606854049113[/C][C]44.2181068902555[/C][/ROW]
[ROW][C]Winsorized Mean ( 27 / 62 )[/C][C]86.9358288770053[/C][C]1.96606854049113[/C][C]44.2181068902555[/C][/ROW]
[ROW][C]Winsorized Mean ( 28 / 62 )[/C][C]86.7860962566845[/C][C]1.94977063748332[/C][C]44.5109258434131[/C][/ROW]
[ROW][C]Winsorized Mean ( 29 / 62 )[/C][C]86.6310160427807[/C][C]1.90180376829009[/C][C]45.552026706031[/C][/ROW]
[ROW][C]Winsorized Mean ( 30 / 62 )[/C][C]86.6310160427807[/C][C]1.90180376829009[/C][C]45.552026706031[/C][/ROW]
[ROW][C]Winsorized Mean ( 31 / 62 )[/C][C]86.7967914438503[/C][C]1.88617410478874[/C][C]46.0173804865018[/C][/ROW]
[ROW][C]Winsorized Mean ( 32 / 62 )[/C][C]86.6256684491979[/C][C]1.86814352555099[/C][C]46.3699214029332[/C][/ROW]
[ROW][C]Winsorized Mean ( 33 / 62 )[/C][C]86.4491978609626[/C][C]1.81509926516686[/C][C]47.6278072059136[/C][/ROW]
[ROW][C]Winsorized Mean ( 34 / 62 )[/C][C]85.903743315508[/C][C]1.760437281503[/C][C]48.7968212319195[/C][/ROW]
[ROW][C]Winsorized Mean ( 35 / 62 )[/C][C]85.903743315508[/C][C]1.760437281503[/C][C]48.7968212319195[/C][/ROW]
[ROW][C]Winsorized Mean ( 36 / 62 )[/C][C]85.903743315508[/C][C]1.760437281503[/C][C]48.7968212319195[/C][/ROW]
[ROW][C]Winsorized Mean ( 37 / 62 )[/C][C]86.1016042780749[/C][C]1.74190810547814[/C][C]49.4294756464439[/C][/ROW]
[ROW][C]Winsorized Mean ( 38 / 62 )[/C][C]86.1016042780749[/C][C]1.70321945603088[/C][C]50.5522667517684[/C][/ROW]
[ROW][C]Winsorized Mean ( 39 / 62 )[/C][C]86.1016042780749[/C][C]1.70321945603088[/C][C]50.5522667517684[/C][/ROW]
[ROW][C]Winsorized Mean ( 40 / 62 )[/C][C]86.1016042780749[/C][C]1.66290533122321[/C][C]51.7778148048512[/C][/ROW]
[ROW][C]Winsorized Mean ( 41 / 62 )[/C][C]86.1016042780749[/C][C]1.66290533122321[/C][C]51.7778148048512[/C][/ROW]
[ROW][C]Winsorized Mean ( 42 / 62 )[/C][C]86.3262032085562[/C][C]1.60096268696359[/C][C]53.9214335921118[/C][/ROW]
[ROW][C]Winsorized Mean ( 43 / 62 )[/C][C]86.3262032085562[/C][C]1.60096268696359[/C][C]53.9214335921118[/C][/ROW]
[ROW][C]Winsorized Mean ( 44 / 62 )[/C][C]85.855614973262[/C][C]1.51337264126062[/C][C]56.7313116627676[/C][/ROW]
[ROW][C]Winsorized Mean ( 45 / 62 )[/C][C]86.096256684492[/C][C]1.49230163138642[/C][C]57.693602200585[/C][/ROW]
[ROW][C]Winsorized Mean ( 46 / 62 )[/C][C]86.3422459893048[/C][C]1.47113073563446[/C][C]58.691076121163[/C][/ROW]
[ROW][C]Winsorized Mean ( 47 / 62 )[/C][C]85.8395721925134[/C][C]1.42463667257126[/C][C]60.2536589470113[/C][/ROW]
[ROW][C]Winsorized Mean ( 48 / 62 )[/C][C]85.8395721925134[/C][C]1.42463667257126[/C][C]60.2536589470113[/C][/ROW]
[ROW][C]Winsorized Mean ( 49 / 62 )[/C][C]86.1016042780749[/C][C]1.35627723556139[/C][C]63.4837789948128[/C][/ROW]
[ROW][C]Winsorized Mean ( 50 / 62 )[/C][C]86.1016042780749[/C][C]1.35627723556139[/C][C]63.4837789948128[/C][/ROW]
[ROW][C]Winsorized Mean ( 51 / 62 )[/C][C]85.8288770053476[/C][C]1.33169200696255[/C][C]64.4509965942608[/C][/ROW]
[ROW][C]Winsorized Mean ( 52 / 62 )[/C][C]85.8288770053476[/C][C]1.33169200696255[/C][C]64.4509965942608[/C][/ROW]
[ROW][C]Winsorized Mean ( 53 / 62 )[/C][C]85.8288770053476[/C][C]1.33169200696255[/C][C]64.4509965942608[/C][/ROW]
[ROW][C]Winsorized Mean ( 54 / 62 )[/C][C]86.1176470588235[/C][C]1.30760583140065[/C][C]65.8590264671567[/C][/ROW]
[ROW][C]Winsorized Mean ( 55 / 62 )[/C][C]86.1176470588235[/C][C]1.30760583140065[/C][C]65.8590264671567[/C][/ROW]
[ROW][C]Winsorized Mean ( 56 / 62 )[/C][C]86.1176470588235[/C][C]1.25610935030456[/C][C]68.5590367096171[/C][/ROW]
[ROW][C]Winsorized Mean ( 57 / 62 )[/C][C]85.812834224599[/C][C]1.22902678909304[/C][C]69.8217768612875[/C][/ROW]
[ROW][C]Winsorized Mean ( 58 / 62 )[/C][C]85.812834224599[/C][C]1.22902678909304[/C][C]69.8217768612875[/C][/ROW]
[ROW][C]Winsorized Mean ( 59 / 62 )[/C][C]85.4973262032086[/C][C]1.20132501003905[/C][C]71.1691885948746[/C][/ROW]
[ROW][C]Winsorized Mean ( 60 / 62 )[/C][C]85.4973262032086[/C][C]1.09305875078572[/C][C]78.218417941168[/C][/ROW]
[ROW][C]Winsorized Mean ( 61 / 62 )[/C][C]85.1711229946524[/C][C]1.06516074926501[/C][C]79.9608162931489[/C][/ROW]
[ROW][C]Winsorized Mean ( 62 / 62 )[/C][C]85.5026737967914[/C][C]1.03831974408284[/C][C]82.3471520059716[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 62 )[/C][C]89.6791443850267[/C][C]2.74042610032766[/C][C]32.7245257131014[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 62 )[/C][C]89.2054054054054[/C][C]2.62188873390814[/C][C]34.0233375473708[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 62 )[/C][C]88.5469613259668[/C][C]2.52372931655742[/C][C]35.0857600872793[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 62 )[/C][C]88.5469613259668[/C][C]2.43113443494843[/C][C]36.4220752472888[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 62 )[/C][C]87.8248587570621[/C][C]2.34703838818295[/C][C]37.4194385567997[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 62 )[/C][C]87.6685714285714[/C][C]2.30735795384839[/C][C]37.9952192863491[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 62 )[/C][C]87.6685714285714[/C][C]2.26667794542171[/C][C]38.6771184700705[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 62 )[/C][C]87.5086705202312[/C][C]2.23085165689296[/C][C]39.2265753080641[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 62 )[/C][C]87.2011834319527[/C][C]2.19900621592495[/C][C]39.6548144341074[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 62 )[/C][C]87.065868263473[/C][C]2.16709022574074[/C][C]40.1763928558687[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 62 )[/C][C]86.939393939394[/C][C]2.13707457257077[/C][C]40.6814975271599[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 62 )[/C][C]86.8282208588957[/C][C]2.11022467473021[/C][C]41.1464342629756[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 62 )[/C][C]86.7267080745342[/C][C]2.08555345101048[/C][C]41.584505078263[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 62 )[/C][C]86.7267080745342[/C][C]2.06535095740299[/C][C]41.9912692144032[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 62 )[/C][C]86.5668789808917[/C][C]2.04546306442175[/C][C]42.3214090181403[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 62 )[/C][C]86.5668789808917[/C][C]2.02395281283448[/C][C]42.771194284741[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 62 )[/C][C]86.4117647058823[/C][C]2.00297614416755[/C][C]43.1416844167137[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 62 )[/C][C]86.3443708609272[/C][C]1.98346467795819[/C][C]43.5320940274123[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 62 )[/C][C]86.2885906040269[/C][C]1.96459445009596[/C][C]43.9218336383939[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 62 )[/C][C]86.2312925170068[/C][C]1.94409969540752[/C][C]44.3553860538675[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 62 )[/C][C]86.1793103448276[/C][C]1.92303213257188[/C][C]44.8142851516322[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 62 )[/C][C]86.1328671328671[/C][C]1.9035711063635[/C][C]45.2480429257049[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 62 )[/C][C]86.0992907801418[/C][C]1.88698697784675[/C][C]45.6279199543762[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 62 )[/C][C]86.0647482014388[/C][C]1.86886893916647[/C][C]46.0517837274477[/C][/ROW]
[ROW][C]Trimmed Mean ( 25 / 62 )[/C][C]86.007299270073[/C][C]1.8522466239292[/C][C]46.4340429395003[/C][/ROW]
[ROW][C]Trimmed Mean ( 26 / 62 )[/C][C]85.9481481481481[/C][C]1.83402876960864[/C][C]46.8630315796455[/C][/ROW]
[ROW][C]Trimmed Mean ( 27 / 62 )[/C][C]85.8947368421053[/C][C]1.81777705319347[/C][C]47.2526246776002[/C][/ROW]
[ROW][C]Trimmed Mean ( 28 / 62 )[/C][C]85.8947368421053[/C][C]1.79990920348716[/C][C]47.7217054480815[/C][/ROW]
[ROW][C]Trimmed Mean ( 29 / 62 )[/C][C]85.7906976744186[/C][C]1.78164475833123[/C][C]48.1525271933415[/C][/ROW]
[ROW][C]Trimmed Mean ( 30 / 62 )[/C][C]85.748031496063[/C][C]1.76549750504273[/C][C]48.5687639043069[/C][/ROW]
[ROW][C]Trimmed Mean ( 31 / 62 )[/C][C]85.704[/C][C]1.74766291870582[/C][C]49.0392049191416[/C][/ROW]
[ROW][C]Trimmed Mean ( 32 / 62 )[/C][C]85.704[/C][C]1.72920071456935[/C][C]49.5627831274314[/C][/ROW]
[ROW][C]Trimmed Mean ( 33 / 62 )[/C][C]85.603305785124[/C][C]1.71030257415389[/C][C]50.0515564197598[/C][/ROW]
[ROW][C]Trimmed Mean ( 34 / 62 )[/C][C]85.563025210084[/C][C]1.69374456127945[/C][C]50.5170774661853[/C][/ROW]
[ROW][C]Trimmed Mean ( 35 / 62 )[/C][C]85.5470085470085[/C][C]1.67981093269408[/C][C]50.9265697002034[/C][/ROW]
[ROW][C]Trimmed Mean ( 36 / 62 )[/C][C]85.5304347826087[/C][C]1.66423873829807[/C][C]51.3931281698661[/C][/ROW]
[ROW][C]Trimmed Mean ( 37 / 62 )[/C][C]85.5132743362832[/C][C]1.64684289022847[/C][C]51.9255812704878[/C][/ROW]
[ROW][C]Trimmed Mean ( 38 / 62 )[/C][C]85.4864864864865[/C][C]1.62891888019066[/C][C]52.4805056446277[/C][/ROW]
[ROW][C]Trimmed Mean ( 39 / 62 )[/C][C]85.4587155963303[/C][C]1.61207915537966[/C][C]53.0114884936924[/C][/ROW]
[ROW][C]Trimmed Mean ( 40 / 62 )[/C][C]85.429906542056[/C][C]1.59317182512934[/C][C]53.6225316030307[/C][/ROW]
[ROW][C]Trimmed Mean ( 41 / 62 )[/C][C]85.4[/C][C]1.57537134409474[/C][C]54.2094410439296[/C][/ROW]
[ROW][C]Trimmed Mean ( 42 / 62 )[/C][C]85.368932038835[/C][C]1.55531245066735[/C][C]54.8886058246401[/C][/ROW]
[ROW][C]Trimmed Mean ( 43 / 62 )[/C][C]85.3267326732673[/C][C]1.53803970071274[/C][C]55.4775878891333[/C][/ROW]
[ROW][C]Trimmed Mean ( 44 / 62 )[/C][C]85.2828282828283[/C][C]1.51845924932666[/C][C]56.1640546630711[/C][/ROW]
[ROW][C]Trimmed Mean ( 45 / 62 )[/C][C]85.2577319587629[/C][C]1.50409509381141[/C][C]56.6837378231971[/C][/ROW]
[ROW][C]Trimmed Mean ( 46 / 62 )[/C][C]85.221052631579[/C][C]1.48943114623947[/C][C]57.2171817722127[/C][/ROW]
[ROW][C]Trimmed Mean ( 47 / 62 )[/C][C]85.1720430107527[/C][C]1.47438972850079[/C][C]57.7676589604014[/C][/ROW]
[ROW][C]Trimmed Mean ( 48 / 62 )[/C][C]85.1428571428571[/C][C]1.46139340306703[/C][C]58.2614215748941[/C][/ROW]
[ROW][C]Trimmed Mean ( 49 / 62 )[/C][C]85.1123595505618[/C][C]1.44630117168781[/C][C]58.8482960649454[/C][/ROW]
[ROW][C]Trimmed Mean ( 50 / 62 )[/C][C]85.0689655172414[/C][C]1.43502164327449[/C][C]59.2806149760416[/C][/ROW]
[ROW][C]Trimmed Mean ( 51 / 62 )[/C][C]85.0689655172414[/C][C]1.42171794830568[/C][C]59.8353320492447[/C][/ROW]
[ROW][C]Trimmed Mean ( 52 / 62 )[/C][C]84.9879518072289[/C][C]1.40853929626907[/C][C]60.3376505237335[/C][/ROW]
[ROW][C]Trimmed Mean ( 53 / 62 )[/C][C]84.9506172839506[/C][C]1.39298299185861[/C][C]60.9846766115957[/C][/ROW]
[ROW][C]Trimmed Mean ( 54 / 62 )[/C][C]84.9113924050633[/C][C]1.37466644898494[/C][C]61.7687239459161[/C][/ROW]
[ROW][C]Trimmed Mean ( 55 / 62 )[/C][C]84.8571428571429[/C][C]1.35556803257828[/C][C]62.5989554325394[/C][/ROW]
[ROW][C]Trimmed Mean ( 56 / 62 )[/C][C]84.8571428571429[/C][C]1.33301798072529[/C][C]63.6579131595601[/C][/ROW]
[ROW][C]Trimmed Mean ( 57 / 62 )[/C][C]84.7397260273973[/C][C]1.31233861764383[/C][C]64.5715403693133[/C][/ROW]
[ROW][C]Trimmed Mean ( 58 / 62 )[/C][C]84.6901408450704[/C][C]1.29113858777256[/C][C]65.5933775406525[/C][/ROW]
[ROW][C]Trimmed Mean ( 59 / 62 )[/C][C]84.6376811594203[/C][C]1.26581571920744[/C][C]66.8641413399528[/C][/ROW]
[ROW][C]Trimmed Mean ( 60 / 62 )[/C][C]84.5970149253731[/C][C]1.23934804746875[/C][C]68.2592876941667[/C][/ROW]
[ROW][C]Trimmed Mean ( 61 / 62 )[/C][C]84.5538461538462[/C][C]1.22180327976228[/C][C]69.2041407601207[/C][/ROW]
[ROW][C]Trimmed Mean ( 62 / 62 )[/C][C]84.5238095238095[/C][C]1.20416097652138[/C][C]70.1931146847031[/C][/ROW]
[ROW][C]Median[/C][C]85[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]133.5[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]84.936170212766[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]85.7731958762887[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]85.7731958762887[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]85.7731958762887[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]84.936170212766[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]84.936170212766[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]85.7731958762887[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]85.7731958762887[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]187[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=119936&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=119936&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 Mean89.67914438502672.913097154477930.7848106772462
Geometric Mean0
Harmonic Mean0
Quadratic Mean98.0855241790344
Winsorized Mean ( 1 / 62 )89.45989304812832.8488883704569931.4016842414145
Winsorized Mean ( 2 / 62 )89.7165775401072.7948051947153832.101191778858
Winsorized Mean ( 3 / 62 )89.6203208556152.7591492268042532.4811430947563
Winsorized Mean ( 4 / 62 )89.49197860962572.7063918593439533.0668961705047
Winsorized Mean ( 5 / 62 )88.55614973262032.5088891498993935.2969559201815
Winsorized Mean ( 6 / 62 )88.55614973262032.4996587682009235.4272954609549
Winsorized Mean ( 7 / 62 )88.55614973262032.4577632763968836.0311957555347
Winsorized Mean ( 8 / 62 )88.38502673796792.4186985904516236.5423898152868
Winsorized Mean ( 9 / 62 )88.2887700534762.403747137179236.7296412704552
Winsorized Mean ( 10 / 62 )88.18181818181822.3737140469734137.1493012371284
Winsorized Mean ( 11 / 62 )88.00534759358292.3331012312114537.7203296694874
Winsorized Mean ( 12 / 62 )87.87700534759362.2992710662547438.2195064502488
Winsorized Mean ( 13 / 62 )87.59893048128342.2453122653265239.0141415223349
Winsorized Mean ( 14 / 62 )87.59893048128342.2278556511395239.3198412278091
Winsorized Mean ( 15 / 62 )87.59893048128342.2278556511395239.3198412278091
Winsorized Mean ( 16 / 62 )87.4278074866312.2060742759811439.6304913386237
Winsorized Mean ( 17 / 62 )87.3368983957222.1741351758565140.1708685667695
Winsorized Mean ( 18 / 62 )87.1443850267382.1507975555361340.5172419888749
Winsorized Mean ( 19 / 62 )87.1443850267382.1507975555361340.5172419888749
Winsorized Mean ( 20 / 62 )87.03743315508022.1380852920849740.7081202407061
Winsorized Mean ( 21 / 62 )86.92513368983962.100330822900941.3864010098094
Winsorized Mean ( 22 / 62 )86.68983957219252.048377097811742.3212306292645
Winsorized Mean ( 23 / 62 )86.68983957219252.048377097811742.3212306292645
Winsorized Mean ( 24 / 62 )87.07486631016042.0102445336983643.3155593016158
Winsorized Mean ( 25 / 62 )87.07486631016042.0102445336983643.3155593016158
Winsorized Mean ( 26 / 62 )86.93582887700531.9660685404911344.2181068902555
Winsorized Mean ( 27 / 62 )86.93582887700531.9660685404911344.2181068902555
Winsorized Mean ( 28 / 62 )86.78609625668451.9497706374833244.5109258434131
Winsorized Mean ( 29 / 62 )86.63101604278071.9018037682900945.552026706031
Winsorized Mean ( 30 / 62 )86.63101604278071.9018037682900945.552026706031
Winsorized Mean ( 31 / 62 )86.79679144385031.8861741047887446.0173804865018
Winsorized Mean ( 32 / 62 )86.62566844919791.8681435255509946.3699214029332
Winsorized Mean ( 33 / 62 )86.44919786096261.8150992651668647.6278072059136
Winsorized Mean ( 34 / 62 )85.9037433155081.76043728150348.7968212319195
Winsorized Mean ( 35 / 62 )85.9037433155081.76043728150348.7968212319195
Winsorized Mean ( 36 / 62 )85.9037433155081.76043728150348.7968212319195
Winsorized Mean ( 37 / 62 )86.10160427807491.7419081054781449.4294756464439
Winsorized Mean ( 38 / 62 )86.10160427807491.7032194560308850.5522667517684
Winsorized Mean ( 39 / 62 )86.10160427807491.7032194560308850.5522667517684
Winsorized Mean ( 40 / 62 )86.10160427807491.6629053312232151.7778148048512
Winsorized Mean ( 41 / 62 )86.10160427807491.6629053312232151.7778148048512
Winsorized Mean ( 42 / 62 )86.32620320855621.6009626869635953.9214335921118
Winsorized Mean ( 43 / 62 )86.32620320855621.6009626869635953.9214335921118
Winsorized Mean ( 44 / 62 )85.8556149732621.5133726412606256.7313116627676
Winsorized Mean ( 45 / 62 )86.0962566844921.4923016313864257.693602200585
Winsorized Mean ( 46 / 62 )86.34224598930481.4711307356344658.691076121163
Winsorized Mean ( 47 / 62 )85.83957219251341.4246366725712660.2536589470113
Winsorized Mean ( 48 / 62 )85.83957219251341.4246366725712660.2536589470113
Winsorized Mean ( 49 / 62 )86.10160427807491.3562772355613963.4837789948128
Winsorized Mean ( 50 / 62 )86.10160427807491.3562772355613963.4837789948128
Winsorized Mean ( 51 / 62 )85.82887700534761.3316920069625564.4509965942608
Winsorized Mean ( 52 / 62 )85.82887700534761.3316920069625564.4509965942608
Winsorized Mean ( 53 / 62 )85.82887700534761.3316920069625564.4509965942608
Winsorized Mean ( 54 / 62 )86.11764705882351.3076058314006565.8590264671567
Winsorized Mean ( 55 / 62 )86.11764705882351.3076058314006565.8590264671567
Winsorized Mean ( 56 / 62 )86.11764705882351.2561093503045668.5590367096171
Winsorized Mean ( 57 / 62 )85.8128342245991.2290267890930469.8217768612875
Winsorized Mean ( 58 / 62 )85.8128342245991.2290267890930469.8217768612875
Winsorized Mean ( 59 / 62 )85.49732620320861.2013250100390571.1691885948746
Winsorized Mean ( 60 / 62 )85.49732620320861.0930587507857278.218417941168
Winsorized Mean ( 61 / 62 )85.17112299465241.0651607492650179.9608162931489
Winsorized Mean ( 62 / 62 )85.50267379679141.0383197440828482.3471520059716
Trimmed Mean ( 1 / 62 )89.67914438502672.7404261003276632.7245257131014
Trimmed Mean ( 2 / 62 )89.20540540540542.6218887339081434.0233375473708
Trimmed Mean ( 3 / 62 )88.54696132596682.5237293165574235.0857600872793
Trimmed Mean ( 4 / 62 )88.54696132596682.4311344349484336.4220752472888
Trimmed Mean ( 5 / 62 )87.82485875706212.3470383881829537.4194385567997
Trimmed Mean ( 6 / 62 )87.66857142857142.3073579538483937.9952192863491
Trimmed Mean ( 7 / 62 )87.66857142857142.2666779454217138.6771184700705
Trimmed Mean ( 8 / 62 )87.50867052023122.2308516568929639.2265753080641
Trimmed Mean ( 9 / 62 )87.20118343195272.1990062159249539.6548144341074
Trimmed Mean ( 10 / 62 )87.0658682634732.1670902257407440.1763928558687
Trimmed Mean ( 11 / 62 )86.9393939393942.1370745725707740.6814975271599
Trimmed Mean ( 12 / 62 )86.82822085889572.1102246747302141.1464342629756
Trimmed Mean ( 13 / 62 )86.72670807453422.0855534510104841.584505078263
Trimmed Mean ( 14 / 62 )86.72670807453422.0653509574029941.9912692144032
Trimmed Mean ( 15 / 62 )86.56687898089172.0454630644217542.3214090181403
Trimmed Mean ( 16 / 62 )86.56687898089172.0239528128344842.771194284741
Trimmed Mean ( 17 / 62 )86.41176470588232.0029761441675543.1416844167137
Trimmed Mean ( 18 / 62 )86.34437086092721.9834646779581943.5320940274123
Trimmed Mean ( 19 / 62 )86.28859060402691.9645944500959643.9218336383939
Trimmed Mean ( 20 / 62 )86.23129251700681.9440996954075244.3553860538675
Trimmed Mean ( 21 / 62 )86.17931034482761.9230321325718844.8142851516322
Trimmed Mean ( 22 / 62 )86.13286713286711.903571106363545.2480429257049
Trimmed Mean ( 23 / 62 )86.09929078014181.8869869778467545.6279199543762
Trimmed Mean ( 24 / 62 )86.06474820143881.8688689391664746.0517837274477
Trimmed Mean ( 25 / 62 )86.0072992700731.852246623929246.4340429395003
Trimmed Mean ( 26 / 62 )85.94814814814811.8340287696086446.8630315796455
Trimmed Mean ( 27 / 62 )85.89473684210531.8177770531934747.2526246776002
Trimmed Mean ( 28 / 62 )85.89473684210531.7999092034871647.7217054480815
Trimmed Mean ( 29 / 62 )85.79069767441861.7816447583312348.1525271933415
Trimmed Mean ( 30 / 62 )85.7480314960631.7654975050427348.5687639043069
Trimmed Mean ( 31 / 62 )85.7041.7476629187058249.0392049191416
Trimmed Mean ( 32 / 62 )85.7041.7292007145693549.5627831274314
Trimmed Mean ( 33 / 62 )85.6033057851241.7103025741538950.0515564197598
Trimmed Mean ( 34 / 62 )85.5630252100841.6937445612794550.5170774661853
Trimmed Mean ( 35 / 62 )85.54700854700851.6798109326940850.9265697002034
Trimmed Mean ( 36 / 62 )85.53043478260871.6642387382980751.3931281698661
Trimmed Mean ( 37 / 62 )85.51327433628321.6468428902284751.9255812704878
Trimmed Mean ( 38 / 62 )85.48648648648651.6289188801906652.4805056446277
Trimmed Mean ( 39 / 62 )85.45871559633031.6120791553796653.0114884936924
Trimmed Mean ( 40 / 62 )85.4299065420561.5931718251293453.6225316030307
Trimmed Mean ( 41 / 62 )85.41.5753713440947454.2094410439296
Trimmed Mean ( 42 / 62 )85.3689320388351.5553124506673554.8886058246401
Trimmed Mean ( 43 / 62 )85.32673267326731.5380397007127455.4775878891333
Trimmed Mean ( 44 / 62 )85.28282828282831.5184592493266656.1640546630711
Trimmed Mean ( 45 / 62 )85.25773195876291.5040950938114156.6837378231971
Trimmed Mean ( 46 / 62 )85.2210526315791.4894311462394757.2171817722127
Trimmed Mean ( 47 / 62 )85.17204301075271.4743897285007957.7676589604014
Trimmed Mean ( 48 / 62 )85.14285714285711.4613934030670358.2614215748941
Trimmed Mean ( 49 / 62 )85.11235955056181.4463011716878158.8482960649454
Trimmed Mean ( 50 / 62 )85.06896551724141.4350216432744959.2806149760416
Trimmed Mean ( 51 / 62 )85.06896551724141.4217179483056859.8353320492447
Trimmed Mean ( 52 / 62 )84.98795180722891.4085392962690760.3376505237335
Trimmed Mean ( 53 / 62 )84.95061728395061.3929829918586160.9846766115957
Trimmed Mean ( 54 / 62 )84.91139240506331.3746664489849461.7687239459161
Trimmed Mean ( 55 / 62 )84.85714285714291.3555680325782862.5989554325394
Trimmed Mean ( 56 / 62 )84.85714285714291.3330179807252963.6579131595601
Trimmed Mean ( 57 / 62 )84.73972602739731.3123386176438364.5715403693133
Trimmed Mean ( 58 / 62 )84.69014084507041.2911385877725665.5933775406525
Trimmed Mean ( 59 / 62 )84.63768115942031.2658157192074466.8641413399528
Trimmed Mean ( 60 / 62 )84.59701492537311.2393480474687568.2592876941667
Trimmed Mean ( 61 / 62 )84.55384615384621.2218032797622869.2041407601207
Trimmed Mean ( 62 / 62 )84.52380952380951.2041609765213870.1931146847031
Median85
Midrange133.5
Midmean - Weighted Average at Xnp84.936170212766
Midmean - Weighted Average at X(n+1)p85.7731958762887
Midmean - Empirical Distribution Function85.7731958762887
Midmean - Empirical Distribution Function - Averaging85.7731958762887
Midmean - Empirical Distribution Function - Interpolation84.936170212766
Midmean - Closest Observation84.936170212766
Midmean - True Basic - Statistics Graphics Toolkit85.7731958762887
Midmean - MS Excel (old versions)85.7731958762887
Number of observations187



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')