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of Irreproducible Research!

Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationSat, 17 Dec 2011 08:41:40 -0500
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2011/Dec/17/t1324129638f2ttnayjc8no2pj.htm/, Retrieved Fri, 26 Apr 2024 21:59:36 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=156293, Retrieved Fri, 26 Apr 2024 21:59:36 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact107
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
F     [Histogram] [Frequency Plot (C...] [2010-09-25 09:09:15] [b98453cac15ba1066b407e146608df68]
- R PD  [Histogram] [] [2011-12-17 13:23:24] [18e0b15711387f6270134133fa101957]
-    D    [Histogram] [] [2011-12-17 13:35:44] [18e0b15711387f6270134133fa101957]
- RM          [Central Tendency] [] [2011-12-17 13:41:40] [86c924663d3d275e16f9cde57b3a6185] [Current]
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Dataseries X:
53,23
79,18
93,8
121,91
120,58
95,93
91,19
90,91
81,12
67,68
68,09
141,8
88,37
52,65
80,19
82,79
86,27
93,43
76,92
64,02
80,54
108,55
70,43
65,21
107,64
148
75,53
68,13
82,44
65,68
97,05
86,59
89,32
87,27
93,8
75,1
139,77
107,46
58,87
81,28
135,23
71,63
44,32
49,63
90,43
87,79
84,57
80,7
98,78
111,48
115,75
119,05
61,35
66,36
88,34
97,15
47,43
73,55
65,49
93,63
76,06
99,27
67,09
45,33
50,62
42,85
52,7
77,59
80,33
115,72
143,48
137,41
129,91
98,57
53,31
65,6
56,34
54,51
58,95
100,19
94,09
76,9
122,63
100,04
109,84
58,26
70,22
63,07
70,06
67,4
79,02
59,74
125,43
121,76
84,08
88,51
72,49
54,55
65,05
116,48
115,8
75,02
68,14
91,12
100,36
83,14
100,86
62,63
71,26
55,12
68,27
151,06
87,55
51,17
59,97
48,3
43,22
86,21
59,68
115,2




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'AstonUniversity' @ aston.wessa.net

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 2 seconds \tabularnewline
R Server & 'AstonUniversity' @ aston.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=156293&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]'AstonUniversity' @ aston.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=156293&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=156293&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'AstonUniversity' @ aston.wessa.net







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean84.174252.3169201753436736.3302330808675
Geometric Mean80.5254050205065
Harmonic Mean77.0366780160608
Quadratic Mean87.8869190257193
Winsorized Mean ( 1 / 40 )84.15183333333332.3104054629280836.4229719344084
Winsorized Mean ( 2 / 40 )84.09483333333332.2907479879516236.7106437616172
Winsorized Mean ( 3 / 40 )84.07808333333332.2780546651396736.9078427396642
Winsorized Mean ( 4 / 40 )84.08041666666672.254039064964137.3021115621197
Winsorized Mean ( 5 / 40 )84.01833333333332.2290154410863337.6930243661238
Winsorized Mean ( 6 / 40 )83.97583333333332.1985232011222938.1964735648301
Winsorized Mean ( 7 / 40 )83.723252.1322900826748939.2644746980073
Winsorized Mean ( 8 / 40 )83.461252.0749116634785940.2240015654821
Winsorized Mean ( 9 / 40 )83.362252.0256188958536841.1539654229319
Winsorized Mean ( 10 / 40 )83.30641666666672.0153714401961941.3355151339037
Winsorized Mean ( 11 / 40 )83.341252.0069961652474441.5253658393139
Winsorized Mean ( 12 / 40 )83.231251.9871756365956441.88419406278
Winsorized Mean ( 13 / 40 )83.19551.9449630228783642.7748491983556
Winsorized Mean ( 14 / 40 )82.90033333333331.8988674493241343.6577778837804
Winsorized Mean ( 15 / 40 )82.88658333333331.8773926377260944.1498393398016
Winsorized Mean ( 16 / 40 )83.04258333333331.8564671898831244.7315114352017
Winsorized Mean ( 17 / 40 )83.31033333333331.8236919794858745.682239254471
Winsorized Mean ( 18 / 40 )83.32383333333331.8015691424746146.2506996644496
Winsorized Mean ( 19 / 40 )82.74751.7147967648318848.2549895690483
Winsorized Mean ( 20 / 40 )82.59583333333331.6625865263948749.6791186636361
Winsorized Mean ( 21 / 40 )82.38058333333331.6305966896714350.5217408174265
Winsorized Mean ( 22 / 40 )82.25591666666671.6033247472173851.3033412659689
Winsorized Mean ( 23 / 40 )82.48591666666671.5682912273845152.5960454450995
Winsorized Mean ( 24 / 40 )81.42191666666671.3714966435828559.3672008222807
Winsorized Mean ( 25 / 40 )81.40941666666671.3486278029619760.3646287640432
Winsorized Mean ( 26 / 40 )81.57841666666671.3210141465146361.7543853575705
Winsorized Mean ( 27 / 40 )81.77641666666671.2914530922869463.321244228743
Winsorized Mean ( 28 / 40 )81.63408333333331.2661949797848764.4719688804985
Winsorized Mean ( 29 / 40 )81.58333333333331.2450291545602365.5272473214899
Winsorized Mean ( 30 / 40 )81.55833333333331.2359606733958665.9878061566864
Winsorized Mean ( 31 / 40 )81.21216666666671.1918719016818468.1383347925807
Winsorized Mean ( 32 / 40 )81.36683333333331.1691608412000969.5942170367372
Winsorized Mean ( 33 / 40 )81.25958333333331.1131733816134372.998137285277
Winsorized Mean ( 34 / 40 )80.82608333333331.0470949160639577.1907895772814
Winsorized Mean ( 35 / 40 )80.82316666666671.0293310695529278.5200884898686
Winsorized Mean ( 36 / 40 )80.94616666666671.0161934807125979.6562546434608
Winsorized Mean ( 37 / 40 )80.90608333333331.0093196900072480.1590260591791
Winsorized Mean ( 38 / 40 )80.84591666666671.0022868354427680.6614571875054
Winsorized Mean ( 39 / 40 )80.16016666666670.9227050718547786.8751772497935
Winsorized Mean ( 40 / 40 )80.73350.85676777338261494.2303183058055
Trimmed Mean ( 1 / 40 )83.95762711864412.2592672373205737.1614414318758
Trimmed Mean ( 2 / 40 )83.7567241379312.2023591098668538.0304573230996
Trimmed Mean ( 3 / 40 )83.57877192982462.1505661496131638.8636136325583
Trimmed Mean ( 4 / 40 )83.40044642857142.0980273583695439.7518393150913
Trimmed Mean ( 5 / 40 )83.2152.0471299616943540.6495931167581
Trimmed Mean ( 6 / 40 )83.03648148148151.9970423887431841.5797290781291
Trimmed Mean ( 7 / 40 )82.85924528301891.948204009466142.5310926783927
Trimmed Mean ( 8 / 40 )82.7168269230771.9078042829217943.3570820987973
Trimmed Mean ( 9 / 40 )82.60735294117651.8737012090152844.0877940109729
Trimmed Mean ( 10 / 40 )82.50671.8441154626256344.7405282761025
Trimmed Mean ( 11 / 40 )82.4087755102041.8124085198026445.4692055404694
Trimmed Mean ( 12 / 40 )82.30281251.7778037326742946.2946561464323
Trimmed Mean ( 13 / 40 )82.20404255319151.7416632178941247.1985867925638
Trimmed Mean ( 14 / 40 )82.10456521739131.7069182422259348.1010532234524
Trimmed Mean ( 15 / 40 )82.02877777777781.6741765473822348.9964919805138
Trimmed Mean ( 16 / 40 )81.95079545454551.639772004355949.976945109961
Trimmed Mean ( 17 / 40 )81.85558139534881.6031251081254951.0600083427434
Trimmed Mean ( 18 / 40 )81.73333333333331.5652736204831152.216642677532
Trimmed Mean ( 19 / 40 )81.60402439024391.5245579459093453.5263514313787
Trimmed Mean ( 20 / 40 )81.513751.4900204247920554.7064648535784
Trimmed Mean ( 21 / 40 )81.43051282051281.4571117625492255.8848778202502
Trimmed Mean ( 22 / 40 )81.35907894736841.4232070552179557.1660171645993
Trimmed Mean ( 23 / 40 )81.2929729729731.3873170382416958.5972569586582
Trimmed Mean ( 24 / 40 )81.20652777777781.3498085727567960.1615143189712
Trimmed Mean ( 25 / 40 )81.19114285714291.333018734254760.9077282792559
Trimmed Mean ( 26 / 40 )81.17573529411761.3157032643141161.6976011961448
Trimmed Mean ( 27 / 40 )81.14757575757581.298274290495562.5041844790788
Trimmed Mean ( 28 / 40 )81.103906251.2808384960004463.320946788573
Trimmed Mean ( 29 / 40 )81.06725806451611.2629006460298964.1913188653142
Trimmed Mean ( 30 / 40 )81.03166666666671.243685955206965.154443794604
Trimmed Mean ( 31 / 40 )80.99534482758621.2211220633080566.3286228799827
Trimmed Mean ( 32 / 40 )80.98035714285711.199859379322667.491539874094
Trimmed Mean ( 33 / 40 )80.95351851851851.1766024105547468.8027814598397
Trimmed Mean ( 34 / 40 )80.93211538461541.1562697908799469.9941449849906
Trimmed Mean ( 35 / 40 )80.93961.140956739955170.9401129469509
Trimmed Mean ( 36 / 40 )80.94791666666671.1236016509711172.0432518025445
Trimmed Mean ( 37 / 40 )80.94804347826091.1028409348107473.3995637296076
Trimmed Mean ( 38 / 40 )80.95113636363641.0764929264557275.1989487103852
Trimmed Mean ( 39 / 40 )80.95904761904761.0428312222660277.6338930887852
Trimmed Mean ( 40 / 40 )81.02051.0149000171799279.8310164829144
Median80.91
Midrange96.955
Midmean - Weighted Average at Xnp80.7768852459017
Midmean - Weighted Average at X(n+1)p81.0316666666667
Midmean - Empirical Distribution Function80.7768852459017
Midmean - Empirical Distribution Function - Averaging81.0316666666667
Midmean - Empirical Distribution Function - Interpolation81.0316666666667
Midmean - Closest Observation80.7768852459017
Midmean - True Basic - Statistics Graphics Toolkit81.0316666666667
Midmean - MS Excel (old versions)81.0672580645161
Number of observations120

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 84.17425 & 2.31692017534367 & 36.3302330808675 \tabularnewline
Geometric Mean & 80.5254050205065 &  &  \tabularnewline
Harmonic Mean & 77.0366780160608 &  &  \tabularnewline
Quadratic Mean & 87.8869190257193 &  &  \tabularnewline
Winsorized Mean ( 1 / 40 ) & 84.1518333333333 & 2.31040546292808 & 36.4229719344084 \tabularnewline
Winsorized Mean ( 2 / 40 ) & 84.0948333333333 & 2.29074798795162 & 36.7106437616172 \tabularnewline
Winsorized Mean ( 3 / 40 ) & 84.0780833333333 & 2.27805466513967 & 36.9078427396642 \tabularnewline
Winsorized Mean ( 4 / 40 ) & 84.0804166666667 & 2.2540390649641 & 37.3021115621197 \tabularnewline
Winsorized Mean ( 5 / 40 ) & 84.0183333333333 & 2.22901544108633 & 37.6930243661238 \tabularnewline
Winsorized Mean ( 6 / 40 ) & 83.9758333333333 & 2.19852320112229 & 38.1964735648301 \tabularnewline
Winsorized Mean ( 7 / 40 ) & 83.72325 & 2.13229008267489 & 39.2644746980073 \tabularnewline
Winsorized Mean ( 8 / 40 ) & 83.46125 & 2.07491166347859 & 40.2240015654821 \tabularnewline
Winsorized Mean ( 9 / 40 ) & 83.36225 & 2.02561889585368 & 41.1539654229319 \tabularnewline
Winsorized Mean ( 10 / 40 ) & 83.3064166666667 & 2.01537144019619 & 41.3355151339037 \tabularnewline
Winsorized Mean ( 11 / 40 ) & 83.34125 & 2.00699616524744 & 41.5253658393139 \tabularnewline
Winsorized Mean ( 12 / 40 ) & 83.23125 & 1.98717563659564 & 41.88419406278 \tabularnewline
Winsorized Mean ( 13 / 40 ) & 83.1955 & 1.94496302287836 & 42.7748491983556 \tabularnewline
Winsorized Mean ( 14 / 40 ) & 82.9003333333333 & 1.89886744932413 & 43.6577778837804 \tabularnewline
Winsorized Mean ( 15 / 40 ) & 82.8865833333333 & 1.87739263772609 & 44.1498393398016 \tabularnewline
Winsorized Mean ( 16 / 40 ) & 83.0425833333333 & 1.85646718988312 & 44.7315114352017 \tabularnewline
Winsorized Mean ( 17 / 40 ) & 83.3103333333333 & 1.82369197948587 & 45.682239254471 \tabularnewline
Winsorized Mean ( 18 / 40 ) & 83.3238333333333 & 1.80156914247461 & 46.2506996644496 \tabularnewline
Winsorized Mean ( 19 / 40 ) & 82.7475 & 1.71479676483188 & 48.2549895690483 \tabularnewline
Winsorized Mean ( 20 / 40 ) & 82.5958333333333 & 1.66258652639487 & 49.6791186636361 \tabularnewline
Winsorized Mean ( 21 / 40 ) & 82.3805833333333 & 1.63059668967143 & 50.5217408174265 \tabularnewline
Winsorized Mean ( 22 / 40 ) & 82.2559166666667 & 1.60332474721738 & 51.3033412659689 \tabularnewline
Winsorized Mean ( 23 / 40 ) & 82.4859166666667 & 1.56829122738451 & 52.5960454450995 \tabularnewline
Winsorized Mean ( 24 / 40 ) & 81.4219166666667 & 1.37149664358285 & 59.3672008222807 \tabularnewline
Winsorized Mean ( 25 / 40 ) & 81.4094166666667 & 1.34862780296197 & 60.3646287640432 \tabularnewline
Winsorized Mean ( 26 / 40 ) & 81.5784166666667 & 1.32101414651463 & 61.7543853575705 \tabularnewline
Winsorized Mean ( 27 / 40 ) & 81.7764166666667 & 1.29145309228694 & 63.321244228743 \tabularnewline
Winsorized Mean ( 28 / 40 ) & 81.6340833333333 & 1.26619497978487 & 64.4719688804985 \tabularnewline
Winsorized Mean ( 29 / 40 ) & 81.5833333333333 & 1.24502915456023 & 65.5272473214899 \tabularnewline
Winsorized Mean ( 30 / 40 ) & 81.5583333333333 & 1.23596067339586 & 65.9878061566864 \tabularnewline
Winsorized Mean ( 31 / 40 ) & 81.2121666666667 & 1.19187190168184 & 68.1383347925807 \tabularnewline
Winsorized Mean ( 32 / 40 ) & 81.3668333333333 & 1.16916084120009 & 69.5942170367372 \tabularnewline
Winsorized Mean ( 33 / 40 ) & 81.2595833333333 & 1.11317338161343 & 72.998137285277 \tabularnewline
Winsorized Mean ( 34 / 40 ) & 80.8260833333333 & 1.04709491606395 & 77.1907895772814 \tabularnewline
Winsorized Mean ( 35 / 40 ) & 80.8231666666667 & 1.02933106955292 & 78.5200884898686 \tabularnewline
Winsorized Mean ( 36 / 40 ) & 80.9461666666667 & 1.01619348071259 & 79.6562546434608 \tabularnewline
Winsorized Mean ( 37 / 40 ) & 80.9060833333333 & 1.00931969000724 & 80.1590260591791 \tabularnewline
Winsorized Mean ( 38 / 40 ) & 80.8459166666667 & 1.00228683544276 & 80.6614571875054 \tabularnewline
Winsorized Mean ( 39 / 40 ) & 80.1601666666667 & 0.92270507185477 & 86.8751772497935 \tabularnewline
Winsorized Mean ( 40 / 40 ) & 80.7335 & 0.856767773382614 & 94.2303183058055 \tabularnewline
Trimmed Mean ( 1 / 40 ) & 83.9576271186441 & 2.25926723732057 & 37.1614414318758 \tabularnewline
Trimmed Mean ( 2 / 40 ) & 83.756724137931 & 2.20235910986685 & 38.0304573230996 \tabularnewline
Trimmed Mean ( 3 / 40 ) & 83.5787719298246 & 2.15056614961316 & 38.8636136325583 \tabularnewline
Trimmed Mean ( 4 / 40 ) & 83.4004464285714 & 2.09802735836954 & 39.7518393150913 \tabularnewline
Trimmed Mean ( 5 / 40 ) & 83.215 & 2.04712996169435 & 40.6495931167581 \tabularnewline
Trimmed Mean ( 6 / 40 ) & 83.0364814814815 & 1.99704238874318 & 41.5797290781291 \tabularnewline
Trimmed Mean ( 7 / 40 ) & 82.8592452830189 & 1.9482040094661 & 42.5310926783927 \tabularnewline
Trimmed Mean ( 8 / 40 ) & 82.716826923077 & 1.90780428292179 & 43.3570820987973 \tabularnewline
Trimmed Mean ( 9 / 40 ) & 82.6073529411765 & 1.87370120901528 & 44.0877940109729 \tabularnewline
Trimmed Mean ( 10 / 40 ) & 82.5067 & 1.84411546262563 & 44.7405282761025 \tabularnewline
Trimmed Mean ( 11 / 40 ) & 82.408775510204 & 1.81240851980264 & 45.4692055404694 \tabularnewline
Trimmed Mean ( 12 / 40 ) & 82.3028125 & 1.77780373267429 & 46.2946561464323 \tabularnewline
Trimmed Mean ( 13 / 40 ) & 82.2040425531915 & 1.74166321789412 & 47.1985867925638 \tabularnewline
Trimmed Mean ( 14 / 40 ) & 82.1045652173913 & 1.70691824222593 & 48.1010532234524 \tabularnewline
Trimmed Mean ( 15 / 40 ) & 82.0287777777778 & 1.67417654738223 & 48.9964919805138 \tabularnewline
Trimmed Mean ( 16 / 40 ) & 81.9507954545455 & 1.6397720043559 & 49.976945109961 \tabularnewline
Trimmed Mean ( 17 / 40 ) & 81.8555813953488 & 1.60312510812549 & 51.0600083427434 \tabularnewline
Trimmed Mean ( 18 / 40 ) & 81.7333333333333 & 1.56527362048311 & 52.216642677532 \tabularnewline
Trimmed Mean ( 19 / 40 ) & 81.6040243902439 & 1.52455794590934 & 53.5263514313787 \tabularnewline
Trimmed Mean ( 20 / 40 ) & 81.51375 & 1.49002042479205 & 54.7064648535784 \tabularnewline
Trimmed Mean ( 21 / 40 ) & 81.4305128205128 & 1.45711176254922 & 55.8848778202502 \tabularnewline
Trimmed Mean ( 22 / 40 ) & 81.3590789473684 & 1.42320705521795 & 57.1660171645993 \tabularnewline
Trimmed Mean ( 23 / 40 ) & 81.292972972973 & 1.38731703824169 & 58.5972569586582 \tabularnewline
Trimmed Mean ( 24 / 40 ) & 81.2065277777778 & 1.34980857275679 & 60.1615143189712 \tabularnewline
Trimmed Mean ( 25 / 40 ) & 81.1911428571429 & 1.3330187342547 & 60.9077282792559 \tabularnewline
Trimmed Mean ( 26 / 40 ) & 81.1757352941176 & 1.31570326431411 & 61.6976011961448 \tabularnewline
Trimmed Mean ( 27 / 40 ) & 81.1475757575758 & 1.2982742904955 & 62.5041844790788 \tabularnewline
Trimmed Mean ( 28 / 40 ) & 81.10390625 & 1.28083849600044 & 63.320946788573 \tabularnewline
Trimmed Mean ( 29 / 40 ) & 81.0672580645161 & 1.26290064602989 & 64.1913188653142 \tabularnewline
Trimmed Mean ( 30 / 40 ) & 81.0316666666667 & 1.2436859552069 & 65.154443794604 \tabularnewline
Trimmed Mean ( 31 / 40 ) & 80.9953448275862 & 1.22112206330805 & 66.3286228799827 \tabularnewline
Trimmed Mean ( 32 / 40 ) & 80.9803571428571 & 1.1998593793226 & 67.491539874094 \tabularnewline
Trimmed Mean ( 33 / 40 ) & 80.9535185185185 & 1.17660241055474 & 68.8027814598397 \tabularnewline
Trimmed Mean ( 34 / 40 ) & 80.9321153846154 & 1.15626979087994 & 69.9941449849906 \tabularnewline
Trimmed Mean ( 35 / 40 ) & 80.9396 & 1.1409567399551 & 70.9401129469509 \tabularnewline
Trimmed Mean ( 36 / 40 ) & 80.9479166666667 & 1.12360165097111 & 72.0432518025445 \tabularnewline
Trimmed Mean ( 37 / 40 ) & 80.9480434782609 & 1.10284093481074 & 73.3995637296076 \tabularnewline
Trimmed Mean ( 38 / 40 ) & 80.9511363636364 & 1.07649292645572 & 75.1989487103852 \tabularnewline
Trimmed Mean ( 39 / 40 ) & 80.9590476190476 & 1.04283122226602 & 77.6338930887852 \tabularnewline
Trimmed Mean ( 40 / 40 ) & 81.0205 & 1.01490001717992 & 79.8310164829144 \tabularnewline
Median & 80.91 &  &  \tabularnewline
Midrange & 96.955 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 80.7768852459017 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 81.0316666666667 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 80.7768852459017 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 81.0316666666667 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 81.0316666666667 &  &  \tabularnewline
Midmean - Closest Observation & 80.7768852459017 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 81.0316666666667 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 81.0672580645161 &  &  \tabularnewline
Number of observations & 120 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=156293&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]84.17425[/C][C]2.31692017534367[/C][C]36.3302330808675[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]80.5254050205065[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]77.0366780160608[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]87.8869190257193[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 40 )[/C][C]84.1518333333333[/C][C]2.31040546292808[/C][C]36.4229719344084[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 40 )[/C][C]84.0948333333333[/C][C]2.29074798795162[/C][C]36.7106437616172[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 40 )[/C][C]84.0780833333333[/C][C]2.27805466513967[/C][C]36.9078427396642[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 40 )[/C][C]84.0804166666667[/C][C]2.2540390649641[/C][C]37.3021115621197[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 40 )[/C][C]84.0183333333333[/C][C]2.22901544108633[/C][C]37.6930243661238[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 40 )[/C][C]83.9758333333333[/C][C]2.19852320112229[/C][C]38.1964735648301[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 40 )[/C][C]83.72325[/C][C]2.13229008267489[/C][C]39.2644746980073[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 40 )[/C][C]83.46125[/C][C]2.07491166347859[/C][C]40.2240015654821[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 40 )[/C][C]83.36225[/C][C]2.02561889585368[/C][C]41.1539654229319[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 40 )[/C][C]83.3064166666667[/C][C]2.01537144019619[/C][C]41.3355151339037[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 40 )[/C][C]83.34125[/C][C]2.00699616524744[/C][C]41.5253658393139[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 40 )[/C][C]83.23125[/C][C]1.98717563659564[/C][C]41.88419406278[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 40 )[/C][C]83.1955[/C][C]1.94496302287836[/C][C]42.7748491983556[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 40 )[/C][C]82.9003333333333[/C][C]1.89886744932413[/C][C]43.6577778837804[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 40 )[/C][C]82.8865833333333[/C][C]1.87739263772609[/C][C]44.1498393398016[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 40 )[/C][C]83.0425833333333[/C][C]1.85646718988312[/C][C]44.7315114352017[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 40 )[/C][C]83.3103333333333[/C][C]1.82369197948587[/C][C]45.682239254471[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 40 )[/C][C]83.3238333333333[/C][C]1.80156914247461[/C][C]46.2506996644496[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 40 )[/C][C]82.7475[/C][C]1.71479676483188[/C][C]48.2549895690483[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 40 )[/C][C]82.5958333333333[/C][C]1.66258652639487[/C][C]49.6791186636361[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 40 )[/C][C]82.3805833333333[/C][C]1.63059668967143[/C][C]50.5217408174265[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 40 )[/C][C]82.2559166666667[/C][C]1.60332474721738[/C][C]51.3033412659689[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 40 )[/C][C]82.4859166666667[/C][C]1.56829122738451[/C][C]52.5960454450995[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 40 )[/C][C]81.4219166666667[/C][C]1.37149664358285[/C][C]59.3672008222807[/C][/ROW]
[ROW][C]Winsorized Mean ( 25 / 40 )[/C][C]81.4094166666667[/C][C]1.34862780296197[/C][C]60.3646287640432[/C][/ROW]
[ROW][C]Winsorized Mean ( 26 / 40 )[/C][C]81.5784166666667[/C][C]1.32101414651463[/C][C]61.7543853575705[/C][/ROW]
[ROW][C]Winsorized Mean ( 27 / 40 )[/C][C]81.7764166666667[/C][C]1.29145309228694[/C][C]63.321244228743[/C][/ROW]
[ROW][C]Winsorized Mean ( 28 / 40 )[/C][C]81.6340833333333[/C][C]1.26619497978487[/C][C]64.4719688804985[/C][/ROW]
[ROW][C]Winsorized Mean ( 29 / 40 )[/C][C]81.5833333333333[/C][C]1.24502915456023[/C][C]65.5272473214899[/C][/ROW]
[ROW][C]Winsorized Mean ( 30 / 40 )[/C][C]81.5583333333333[/C][C]1.23596067339586[/C][C]65.9878061566864[/C][/ROW]
[ROW][C]Winsorized Mean ( 31 / 40 )[/C][C]81.2121666666667[/C][C]1.19187190168184[/C][C]68.1383347925807[/C][/ROW]
[ROW][C]Winsorized Mean ( 32 / 40 )[/C][C]81.3668333333333[/C][C]1.16916084120009[/C][C]69.5942170367372[/C][/ROW]
[ROW][C]Winsorized Mean ( 33 / 40 )[/C][C]81.2595833333333[/C][C]1.11317338161343[/C][C]72.998137285277[/C][/ROW]
[ROW][C]Winsorized Mean ( 34 / 40 )[/C][C]80.8260833333333[/C][C]1.04709491606395[/C][C]77.1907895772814[/C][/ROW]
[ROW][C]Winsorized Mean ( 35 / 40 )[/C][C]80.8231666666667[/C][C]1.02933106955292[/C][C]78.5200884898686[/C][/ROW]
[ROW][C]Winsorized Mean ( 36 / 40 )[/C][C]80.9461666666667[/C][C]1.01619348071259[/C][C]79.6562546434608[/C][/ROW]
[ROW][C]Winsorized Mean ( 37 / 40 )[/C][C]80.9060833333333[/C][C]1.00931969000724[/C][C]80.1590260591791[/C][/ROW]
[ROW][C]Winsorized Mean ( 38 / 40 )[/C][C]80.8459166666667[/C][C]1.00228683544276[/C][C]80.6614571875054[/C][/ROW]
[ROW][C]Winsorized Mean ( 39 / 40 )[/C][C]80.1601666666667[/C][C]0.92270507185477[/C][C]86.8751772497935[/C][/ROW]
[ROW][C]Winsorized Mean ( 40 / 40 )[/C][C]80.7335[/C][C]0.856767773382614[/C][C]94.2303183058055[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 40 )[/C][C]83.9576271186441[/C][C]2.25926723732057[/C][C]37.1614414318758[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 40 )[/C][C]83.756724137931[/C][C]2.20235910986685[/C][C]38.0304573230996[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 40 )[/C][C]83.5787719298246[/C][C]2.15056614961316[/C][C]38.8636136325583[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 40 )[/C][C]83.4004464285714[/C][C]2.09802735836954[/C][C]39.7518393150913[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 40 )[/C][C]83.215[/C][C]2.04712996169435[/C][C]40.6495931167581[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 40 )[/C][C]83.0364814814815[/C][C]1.99704238874318[/C][C]41.5797290781291[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 40 )[/C][C]82.8592452830189[/C][C]1.9482040094661[/C][C]42.5310926783927[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 40 )[/C][C]82.716826923077[/C][C]1.90780428292179[/C][C]43.3570820987973[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 40 )[/C][C]82.6073529411765[/C][C]1.87370120901528[/C][C]44.0877940109729[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 40 )[/C][C]82.5067[/C][C]1.84411546262563[/C][C]44.7405282761025[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 40 )[/C][C]82.408775510204[/C][C]1.81240851980264[/C][C]45.4692055404694[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 40 )[/C][C]82.3028125[/C][C]1.77780373267429[/C][C]46.2946561464323[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 40 )[/C][C]82.2040425531915[/C][C]1.74166321789412[/C][C]47.1985867925638[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 40 )[/C][C]82.1045652173913[/C][C]1.70691824222593[/C][C]48.1010532234524[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 40 )[/C][C]82.0287777777778[/C][C]1.67417654738223[/C][C]48.9964919805138[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 40 )[/C][C]81.9507954545455[/C][C]1.6397720043559[/C][C]49.976945109961[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 40 )[/C][C]81.8555813953488[/C][C]1.60312510812549[/C][C]51.0600083427434[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 40 )[/C][C]81.7333333333333[/C][C]1.56527362048311[/C][C]52.216642677532[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 40 )[/C][C]81.6040243902439[/C][C]1.52455794590934[/C][C]53.5263514313787[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 40 )[/C][C]81.51375[/C][C]1.49002042479205[/C][C]54.7064648535784[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 40 )[/C][C]81.4305128205128[/C][C]1.45711176254922[/C][C]55.8848778202502[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 40 )[/C][C]81.3590789473684[/C][C]1.42320705521795[/C][C]57.1660171645993[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 40 )[/C][C]81.292972972973[/C][C]1.38731703824169[/C][C]58.5972569586582[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 40 )[/C][C]81.2065277777778[/C][C]1.34980857275679[/C][C]60.1615143189712[/C][/ROW]
[ROW][C]Trimmed Mean ( 25 / 40 )[/C][C]81.1911428571429[/C][C]1.3330187342547[/C][C]60.9077282792559[/C][/ROW]
[ROW][C]Trimmed Mean ( 26 / 40 )[/C][C]81.1757352941176[/C][C]1.31570326431411[/C][C]61.6976011961448[/C][/ROW]
[ROW][C]Trimmed Mean ( 27 / 40 )[/C][C]81.1475757575758[/C][C]1.2982742904955[/C][C]62.5041844790788[/C][/ROW]
[ROW][C]Trimmed Mean ( 28 / 40 )[/C][C]81.10390625[/C][C]1.28083849600044[/C][C]63.320946788573[/C][/ROW]
[ROW][C]Trimmed Mean ( 29 / 40 )[/C][C]81.0672580645161[/C][C]1.26290064602989[/C][C]64.1913188653142[/C][/ROW]
[ROW][C]Trimmed Mean ( 30 / 40 )[/C][C]81.0316666666667[/C][C]1.2436859552069[/C][C]65.154443794604[/C][/ROW]
[ROW][C]Trimmed Mean ( 31 / 40 )[/C][C]80.9953448275862[/C][C]1.22112206330805[/C][C]66.3286228799827[/C][/ROW]
[ROW][C]Trimmed Mean ( 32 / 40 )[/C][C]80.9803571428571[/C][C]1.1998593793226[/C][C]67.491539874094[/C][/ROW]
[ROW][C]Trimmed Mean ( 33 / 40 )[/C][C]80.9535185185185[/C][C]1.17660241055474[/C][C]68.8027814598397[/C][/ROW]
[ROW][C]Trimmed Mean ( 34 / 40 )[/C][C]80.9321153846154[/C][C]1.15626979087994[/C][C]69.9941449849906[/C][/ROW]
[ROW][C]Trimmed Mean ( 35 / 40 )[/C][C]80.9396[/C][C]1.1409567399551[/C][C]70.9401129469509[/C][/ROW]
[ROW][C]Trimmed Mean ( 36 / 40 )[/C][C]80.9479166666667[/C][C]1.12360165097111[/C][C]72.0432518025445[/C][/ROW]
[ROW][C]Trimmed Mean ( 37 / 40 )[/C][C]80.9480434782609[/C][C]1.10284093481074[/C][C]73.3995637296076[/C][/ROW]
[ROW][C]Trimmed Mean ( 38 / 40 )[/C][C]80.9511363636364[/C][C]1.07649292645572[/C][C]75.1989487103852[/C][/ROW]
[ROW][C]Trimmed Mean ( 39 / 40 )[/C][C]80.9590476190476[/C][C]1.04283122226602[/C][C]77.6338930887852[/C][/ROW]
[ROW][C]Trimmed Mean ( 40 / 40 )[/C][C]81.0205[/C][C]1.01490001717992[/C][C]79.8310164829144[/C][/ROW]
[ROW][C]Median[/C][C]80.91[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]96.955[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]80.7768852459017[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]81.0316666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]80.7768852459017[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]81.0316666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]81.0316666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]80.7768852459017[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]81.0316666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]81.0672580645161[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]120[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=156293&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=156293&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 Mean84.174252.3169201753436736.3302330808675
Geometric Mean80.5254050205065
Harmonic Mean77.0366780160608
Quadratic Mean87.8869190257193
Winsorized Mean ( 1 / 40 )84.15183333333332.3104054629280836.4229719344084
Winsorized Mean ( 2 / 40 )84.09483333333332.2907479879516236.7106437616172
Winsorized Mean ( 3 / 40 )84.07808333333332.2780546651396736.9078427396642
Winsorized Mean ( 4 / 40 )84.08041666666672.254039064964137.3021115621197
Winsorized Mean ( 5 / 40 )84.01833333333332.2290154410863337.6930243661238
Winsorized Mean ( 6 / 40 )83.97583333333332.1985232011222938.1964735648301
Winsorized Mean ( 7 / 40 )83.723252.1322900826748939.2644746980073
Winsorized Mean ( 8 / 40 )83.461252.0749116634785940.2240015654821
Winsorized Mean ( 9 / 40 )83.362252.0256188958536841.1539654229319
Winsorized Mean ( 10 / 40 )83.30641666666672.0153714401961941.3355151339037
Winsorized Mean ( 11 / 40 )83.341252.0069961652474441.5253658393139
Winsorized Mean ( 12 / 40 )83.231251.9871756365956441.88419406278
Winsorized Mean ( 13 / 40 )83.19551.9449630228783642.7748491983556
Winsorized Mean ( 14 / 40 )82.90033333333331.8988674493241343.6577778837804
Winsorized Mean ( 15 / 40 )82.88658333333331.8773926377260944.1498393398016
Winsorized Mean ( 16 / 40 )83.04258333333331.8564671898831244.7315114352017
Winsorized Mean ( 17 / 40 )83.31033333333331.8236919794858745.682239254471
Winsorized Mean ( 18 / 40 )83.32383333333331.8015691424746146.2506996644496
Winsorized Mean ( 19 / 40 )82.74751.7147967648318848.2549895690483
Winsorized Mean ( 20 / 40 )82.59583333333331.6625865263948749.6791186636361
Winsorized Mean ( 21 / 40 )82.38058333333331.6305966896714350.5217408174265
Winsorized Mean ( 22 / 40 )82.25591666666671.6033247472173851.3033412659689
Winsorized Mean ( 23 / 40 )82.48591666666671.5682912273845152.5960454450995
Winsorized Mean ( 24 / 40 )81.42191666666671.3714966435828559.3672008222807
Winsorized Mean ( 25 / 40 )81.40941666666671.3486278029619760.3646287640432
Winsorized Mean ( 26 / 40 )81.57841666666671.3210141465146361.7543853575705
Winsorized Mean ( 27 / 40 )81.77641666666671.2914530922869463.321244228743
Winsorized Mean ( 28 / 40 )81.63408333333331.2661949797848764.4719688804985
Winsorized Mean ( 29 / 40 )81.58333333333331.2450291545602365.5272473214899
Winsorized Mean ( 30 / 40 )81.55833333333331.2359606733958665.9878061566864
Winsorized Mean ( 31 / 40 )81.21216666666671.1918719016818468.1383347925807
Winsorized Mean ( 32 / 40 )81.36683333333331.1691608412000969.5942170367372
Winsorized Mean ( 33 / 40 )81.25958333333331.1131733816134372.998137285277
Winsorized Mean ( 34 / 40 )80.82608333333331.0470949160639577.1907895772814
Winsorized Mean ( 35 / 40 )80.82316666666671.0293310695529278.5200884898686
Winsorized Mean ( 36 / 40 )80.94616666666671.0161934807125979.6562546434608
Winsorized Mean ( 37 / 40 )80.90608333333331.0093196900072480.1590260591791
Winsorized Mean ( 38 / 40 )80.84591666666671.0022868354427680.6614571875054
Winsorized Mean ( 39 / 40 )80.16016666666670.9227050718547786.8751772497935
Winsorized Mean ( 40 / 40 )80.73350.85676777338261494.2303183058055
Trimmed Mean ( 1 / 40 )83.95762711864412.2592672373205737.1614414318758
Trimmed Mean ( 2 / 40 )83.7567241379312.2023591098668538.0304573230996
Trimmed Mean ( 3 / 40 )83.57877192982462.1505661496131638.8636136325583
Trimmed Mean ( 4 / 40 )83.40044642857142.0980273583695439.7518393150913
Trimmed Mean ( 5 / 40 )83.2152.0471299616943540.6495931167581
Trimmed Mean ( 6 / 40 )83.03648148148151.9970423887431841.5797290781291
Trimmed Mean ( 7 / 40 )82.85924528301891.948204009466142.5310926783927
Trimmed Mean ( 8 / 40 )82.7168269230771.9078042829217943.3570820987973
Trimmed Mean ( 9 / 40 )82.60735294117651.8737012090152844.0877940109729
Trimmed Mean ( 10 / 40 )82.50671.8441154626256344.7405282761025
Trimmed Mean ( 11 / 40 )82.4087755102041.8124085198026445.4692055404694
Trimmed Mean ( 12 / 40 )82.30281251.7778037326742946.2946561464323
Trimmed Mean ( 13 / 40 )82.20404255319151.7416632178941247.1985867925638
Trimmed Mean ( 14 / 40 )82.10456521739131.7069182422259348.1010532234524
Trimmed Mean ( 15 / 40 )82.02877777777781.6741765473822348.9964919805138
Trimmed Mean ( 16 / 40 )81.95079545454551.639772004355949.976945109961
Trimmed Mean ( 17 / 40 )81.85558139534881.6031251081254951.0600083427434
Trimmed Mean ( 18 / 40 )81.73333333333331.5652736204831152.216642677532
Trimmed Mean ( 19 / 40 )81.60402439024391.5245579459093453.5263514313787
Trimmed Mean ( 20 / 40 )81.513751.4900204247920554.7064648535784
Trimmed Mean ( 21 / 40 )81.43051282051281.4571117625492255.8848778202502
Trimmed Mean ( 22 / 40 )81.35907894736841.4232070552179557.1660171645993
Trimmed Mean ( 23 / 40 )81.2929729729731.3873170382416958.5972569586582
Trimmed Mean ( 24 / 40 )81.20652777777781.3498085727567960.1615143189712
Trimmed Mean ( 25 / 40 )81.19114285714291.333018734254760.9077282792559
Trimmed Mean ( 26 / 40 )81.17573529411761.3157032643141161.6976011961448
Trimmed Mean ( 27 / 40 )81.14757575757581.298274290495562.5041844790788
Trimmed Mean ( 28 / 40 )81.103906251.2808384960004463.320946788573
Trimmed Mean ( 29 / 40 )81.06725806451611.2629006460298964.1913188653142
Trimmed Mean ( 30 / 40 )81.03166666666671.243685955206965.154443794604
Trimmed Mean ( 31 / 40 )80.99534482758621.2211220633080566.3286228799827
Trimmed Mean ( 32 / 40 )80.98035714285711.199859379322667.491539874094
Trimmed Mean ( 33 / 40 )80.95351851851851.1766024105547468.8027814598397
Trimmed Mean ( 34 / 40 )80.93211538461541.1562697908799469.9941449849906
Trimmed Mean ( 35 / 40 )80.93961.140956739955170.9401129469509
Trimmed Mean ( 36 / 40 )80.94791666666671.1236016509711172.0432518025445
Trimmed Mean ( 37 / 40 )80.94804347826091.1028409348107473.3995637296076
Trimmed Mean ( 38 / 40 )80.95113636363641.0764929264557275.1989487103852
Trimmed Mean ( 39 / 40 )80.95904761904761.0428312222660277.6338930887852
Trimmed Mean ( 40 / 40 )81.02051.0149000171799279.8310164829144
Median80.91
Midrange96.955
Midmean - Weighted Average at Xnp80.7768852459017
Midmean - Weighted Average at X(n+1)p81.0316666666667
Midmean - Empirical Distribution Function80.7768852459017
Midmean - Empirical Distribution Function - Averaging81.0316666666667
Midmean - Empirical Distribution Function - Interpolation81.0316666666667
Midmean - Closest Observation80.7768852459017
Midmean - True Basic - Statistics Graphics Toolkit81.0316666666667
Midmean - MS Excel (old versions)81.0672580645161
Number of observations120



Parameters (Session):
par2 = grey ; par3 = FALSE ; par4 = Unknown ;
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')