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Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationMon, 14 Nov 2011 13:39:50 -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/Nov/14/t1321296002d8zpop03v32f86t.htm/, Retrieved Thu, 25 Apr 2024 04:05:35 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=142226, Retrieved Thu, 25 Apr 2024 04:05:35 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact71
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
F     [Percentiles] [Percentiles of ti...] [2010-09-25 09:52:29] [b98453cac15ba1066b407e146608df68]
- RM D    [Central Tendency] [] [2011-11-14 18:39:50] [87b6e955a128bfb8d1e350b3ce0d281e] [Current]
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Post a new message
Dataseries X:
27.01
33.56
47.24
71.23
59.14
40.99
17.54
28.45
39.09
24.69
21.47
39.81
35.66
31.21
30.63
26.11
29.63
44.55
43.9
33.47
55.10
48.13
33.25
25.33
26.98
88.74
36.54
11.78
29.11
32.47
55.17
42.33
22.87
41.36
27.69
20.47
60.03
50.14
30.63
36.99
27.55
18.55
14.33
8.78
40.55
22.63
45.77
41.36
39.44
41.66
66.47
69.48
17.66
19.64
44.47
50.17
21.63
36.12
23.69
54.12
45.16
69.41
41.96
13.25
16.17
9.66
20.45
24.21
33.64
25.44
60.74
71.33
55.21
66.23
19.65
21.33
14.47
16.22
23.56
66.87
54.22
43.98
71.33
55.21
66.23
19.65
21.33
16.66
19.87
14.55
19.41
20.63
60.03
50.14
30.63
36.99
27.55
18.55
14.33
66.47
69.48
17.66
19.64
44.47
50.17
21.63
36.12
23.69
33.25
25.33
26.98
88.74
36.54
11.78
18.55
14.33
8.78
40.55
22.63
45.77




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Herman Ole Andreas Wold' @ wold.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 & 1 seconds \tabularnewline
R Server & 'Herman Ole Andreas Wold' @ wold.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=142226&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Herman Ole Andreas Wold' @ wold.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=142226&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=142226&T=0

As an alternative you can also use a QR Code:  

The GUIDs for individual cells are displayed in the table below:

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Herman Ole Andreas Wold' @ wold.wessa.net







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean35.86141666666671.6483552760822421.7558782302691
Geometric Mean31.5061177601291
Harmonic Mean27.4224191612729
Quadratic Mean40.1169932094451
Winsorized Mean ( 1 / 40 )35.86141666666671.6483552760822421.7558782302691
Winsorized Mean ( 2 / 40 )35.58591666666671.5793817377730822.5315487798679
Winsorized Mean ( 3 / 40 )35.63891666666671.5723465256044222.6660701609442
Winsorized Mean ( 4 / 40 )35.63558333333331.5717114251233322.6731082841986
Winsorized Mean ( 5 / 40 )35.62391666666671.5504601751878722.9763506581845
Winsorized Mean ( 6 / 40 )35.67791666666671.5440487670989323.1067291570724
Winsorized Mean ( 7 / 40 )35.67383333333331.5432981261600623.1153221329276
Winsorized Mean ( 8 / 40 )35.50451.5129875876808123.4664846487097
Winsorized Mean ( 9 / 40 )35.4851.5065491110779123.5538289054587
Winsorized Mean ( 10 / 40 )35.49166666666671.5057688104589323.5704620922847
Winsorized Mean ( 11 / 40 )35.61816666666671.4851097111352823.9835255265005
Winsorized Mean ( 12 / 40 )35.62316666666671.4845600173602723.9957740004402
Winsorized Mean ( 13 / 40 )35.07608333333331.3811350490633325.3965630349628
Winsorized Mean ( 14 / 40 )35.09591666666671.3569374269338725.8640641565686
Winsorized Mean ( 15 / 40 )35.11091666666671.3553105011632925.9061791645016
Winsorized Mean ( 16 / 40 )34.992251.3371376755369426.1695191454003
Winsorized Mean ( 17 / 40 )34.56158333333331.242186182722527.8231909306742
Winsorized Mean ( 18 / 40 )34.56158333333331.242186182722527.8231909306742
Winsorized Mean ( 19 / 40 )34.555251.2413019107567927.8379092955174
Winsorized Mean ( 20 / 40 )34.68691666666671.2243893567245728.3299723867736
Winsorized Mean ( 21 / 40 )34.57316666666671.1987781009598128.8403388742132
Winsorized Mean ( 22 / 40 )34.55483333333331.1962557715284128.8858237140908
Winsorized Mean ( 23 / 40 )33.79966666666671.0963286385295830.8298675039625
Winsorized Mean ( 24 / 40 )33.79966666666671.0963286385295830.8298675039625
Winsorized Mean ( 25 / 40 )33.839251.090591789101331.0283374019211
Winsorized Mean ( 26 / 40 )33.96491666666671.0772031166699731.5306520572135
Winsorized Mean ( 27 / 40 )33.51716666666671.0209579259701732.8291360633857
Winsorized Mean ( 28 / 40 )33.34683333333330.99223308671199533.6078626886311
Winsorized Mean ( 29 / 40 )33.160750.93301281633275435.541580372218
Winsorized Mean ( 30 / 40 )33.160750.93301281633275435.541580372218
Winsorized Mean ( 31 / 40 )33.03933333333330.91140168722734936.2511215376889
Winsorized Mean ( 32 / 40 )32.91933333333330.88881404265888937.0373686208367
Winsorized Mean ( 33 / 40 )32.89733333333330.88639760296995837.1135179327062
Winsorized Mean ( 34 / 40 )33.18066666666670.85659388948513338.7355864593084
Winsorized Mean ( 35 / 40 )33.037750.84086467153361439.2902105635428
Winsorized Mean ( 36 / 40 )33.085750.83077520801568339.8251532794602
Winsorized Mean ( 37 / 40 )32.81441666666670.75675498438016343.3620092949161
Winsorized Mean ( 38 / 40 )32.73841666666670.74020129365174444.2290724799377
Winsorized Mean ( 39 / 40 )32.64091666666670.73003621217724744.7113665352558
Winsorized Mean ( 40 / 40 )32.714250.70191422603284146.6071904325093
Trimmed Mean ( 1 / 40 )35.64279661016951.598217290057222.3015961796371
Trimmed Mean ( 2 / 40 )35.41663793103451.5419615321000222.9685612732505
Trimmed Mean ( 3 / 40 )35.32754385964911.5200290465840823.24136103783
Trimmed Mean ( 4 / 40 )35.21633928571431.4983813016134123.5029222853985
Trimmed Mean ( 5 / 40 )35.1021.4743845002957223.8079008514804
Trimmed Mean ( 6 / 40 )34.98601851851851.4531797587400424.0754925934647
Trimmed Mean ( 7 / 40 )34.85547169811321.4307888934847224.3610163992969
Trimmed Mean ( 8 / 40 )34.72057692307691.4057272749455424.6993691748792
Trimmed Mean ( 9 / 40 )34.60529411764711.3834355909410225.0140261998814
Trimmed Mean ( 10 / 40 )34.4881.3593956990761325.3700964505322
Trimmed Mean ( 11 / 40 )34.36510204081631.3322821257646525.7941627949807
Trimmed Mean ( 12 / 40 )34.22270833333331.3047038169568326.2302507960438
Trimmed Mean ( 13 / 40 )34.07372340425531.2733245053425326.7596541661541
Trimmed Mean ( 14 / 40 )33.9731521739131.2536916050020627.0984921956602
Trimmed Mean ( 15 / 40 )33.86622222222221.234572336227327.4315414564636
Trimmed Mean ( 16 / 40 )33.75306818181821.2127566071736427.8316918515748
Trimmed Mean ( 17 / 40 )33.6451.1902357736979828.2675086260157
Trimmed Mean ( 18 / 40 )33.56797619047621.1772359589940528.5142293981234
Trimmed Mean ( 19 / 40 )33.48719512195121.1619750066681128.8192043114366
Trimmed Mean ( 20 / 40 )33.4028751.1441998917179129.1932163617396
Trimmed Mean ( 21 / 40 )33.30410256410261.1254018771731129.5930753623397
Trimmed Mean ( 22 / 40 )33.20868421052631.1067497116712530.0055955382897
Trimmed Mean ( 23 / 40 )33.10945945945951.0850350375220930.5146454395352
Trimmed Mean ( 24 / 40 )33.05944444444441.073162893053530.8056164245295
Trimmed Mean ( 25 / 40 )33.00657142857141.0587895914648931.1738722165801
Trimmed Mean ( 26 / 40 )32.94779411764711.042158116694731.6149666637383
Trimmed Mean ( 27 / 40 )32.87666666666671.0237439249791132.1141506821031
Trimmed Mean ( 28 / 40 )32.83218751.0095556952555532.5214226954454
Trimmed Mean ( 29 / 40 )32.79661290322580.99614120486455132.9236585567056
Trimmed Mean ( 30 / 40 )32.77150.98764093823684533.1815933617578
Trimmed Mean ( 31 / 40 )32.74465517241380.97660594826788333.5290351553664
Trimmed Mean ( 32 / 40 )32.72428571428570.96561768997419233.8894844761599
Trimmed Mean ( 33 / 40 )32.71074074074070.95476029209614334.2606840811587
Trimmed Mean ( 34 / 40 )32.69769230769230.94090741219560634.7512325696237
Trimmed Mean ( 35 / 40 )32.66360.9275444325129235.2151324023446
Trimmed Mean ( 36 / 40 )32.6368750.91264303048124635.7608329981879
Trimmed Mean ( 37 / 40 )32.6043478260870.89463320161249936.4443749318943
Trimmed Mean ( 38 / 40 )32.58886363636360.88455261060076236.8421993737945
Trimmed Mean ( 39 / 40 )32.5776190476190.87332070875456937.3031564705222
Trimmed Mean ( 40 / 40 )32.572750.85928943420175337.9066106291169
Median32.86
Midrange48.76
Midmean - Weighted Average at Xnp32.7966129032258
Midmean - Weighted Average at X(n+1)p32.7966129032258
Midmean - Empirical Distribution Function32.7966129032258
Midmean - Empirical Distribution Function - Averaging32.7966129032258
Midmean - Empirical Distribution Function - Interpolation32.7966129032258
Midmean - Closest Observation32.7966129032258
Midmean - True Basic - Statistics Graphics Toolkit32.7966129032258
Midmean - MS Excel (old versions)32.7966129032258
Number of observations120

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 35.8614166666667 & 1.64835527608224 & 21.7558782302691 \tabularnewline
Geometric Mean & 31.5061177601291 &  &  \tabularnewline
Harmonic Mean & 27.4224191612729 &  &  \tabularnewline
Quadratic Mean & 40.1169932094451 &  &  \tabularnewline
Winsorized Mean ( 1 / 40 ) & 35.8614166666667 & 1.64835527608224 & 21.7558782302691 \tabularnewline
Winsorized Mean ( 2 / 40 ) & 35.5859166666667 & 1.57938173777308 & 22.5315487798679 \tabularnewline
Winsorized Mean ( 3 / 40 ) & 35.6389166666667 & 1.57234652560442 & 22.6660701609442 \tabularnewline
Winsorized Mean ( 4 / 40 ) & 35.6355833333333 & 1.57171142512333 & 22.6731082841986 \tabularnewline
Winsorized Mean ( 5 / 40 ) & 35.6239166666667 & 1.55046017518787 & 22.9763506581845 \tabularnewline
Winsorized Mean ( 6 / 40 ) & 35.6779166666667 & 1.54404876709893 & 23.1067291570724 \tabularnewline
Winsorized Mean ( 7 / 40 ) & 35.6738333333333 & 1.54329812616006 & 23.1153221329276 \tabularnewline
Winsorized Mean ( 8 / 40 ) & 35.5045 & 1.51298758768081 & 23.4664846487097 \tabularnewline
Winsorized Mean ( 9 / 40 ) & 35.485 & 1.50654911107791 & 23.5538289054587 \tabularnewline
Winsorized Mean ( 10 / 40 ) & 35.4916666666667 & 1.50576881045893 & 23.5704620922847 \tabularnewline
Winsorized Mean ( 11 / 40 ) & 35.6181666666667 & 1.48510971113528 & 23.9835255265005 \tabularnewline
Winsorized Mean ( 12 / 40 ) & 35.6231666666667 & 1.48456001736027 & 23.9957740004402 \tabularnewline
Winsorized Mean ( 13 / 40 ) & 35.0760833333333 & 1.38113504906333 & 25.3965630349628 \tabularnewline
Winsorized Mean ( 14 / 40 ) & 35.0959166666667 & 1.35693742693387 & 25.8640641565686 \tabularnewline
Winsorized Mean ( 15 / 40 ) & 35.1109166666667 & 1.35531050116329 & 25.9061791645016 \tabularnewline
Winsorized Mean ( 16 / 40 ) & 34.99225 & 1.33713767553694 & 26.1695191454003 \tabularnewline
Winsorized Mean ( 17 / 40 ) & 34.5615833333333 & 1.2421861827225 & 27.8231909306742 \tabularnewline
Winsorized Mean ( 18 / 40 ) & 34.5615833333333 & 1.2421861827225 & 27.8231909306742 \tabularnewline
Winsorized Mean ( 19 / 40 ) & 34.55525 & 1.24130191075679 & 27.8379092955174 \tabularnewline
Winsorized Mean ( 20 / 40 ) & 34.6869166666667 & 1.22438935672457 & 28.3299723867736 \tabularnewline
Winsorized Mean ( 21 / 40 ) & 34.5731666666667 & 1.19877810095981 & 28.8403388742132 \tabularnewline
Winsorized Mean ( 22 / 40 ) & 34.5548333333333 & 1.19625577152841 & 28.8858237140908 \tabularnewline
Winsorized Mean ( 23 / 40 ) & 33.7996666666667 & 1.09632863852958 & 30.8298675039625 \tabularnewline
Winsorized Mean ( 24 / 40 ) & 33.7996666666667 & 1.09632863852958 & 30.8298675039625 \tabularnewline
Winsorized Mean ( 25 / 40 ) & 33.83925 & 1.0905917891013 & 31.0283374019211 \tabularnewline
Winsorized Mean ( 26 / 40 ) & 33.9649166666667 & 1.07720311666997 & 31.5306520572135 \tabularnewline
Winsorized Mean ( 27 / 40 ) & 33.5171666666667 & 1.02095792597017 & 32.8291360633857 \tabularnewline
Winsorized Mean ( 28 / 40 ) & 33.3468333333333 & 0.992233086711995 & 33.6078626886311 \tabularnewline
Winsorized Mean ( 29 / 40 ) & 33.16075 & 0.933012816332754 & 35.541580372218 \tabularnewline
Winsorized Mean ( 30 / 40 ) & 33.16075 & 0.933012816332754 & 35.541580372218 \tabularnewline
Winsorized Mean ( 31 / 40 ) & 33.0393333333333 & 0.911401687227349 & 36.2511215376889 \tabularnewline
Winsorized Mean ( 32 / 40 ) & 32.9193333333333 & 0.888814042658889 & 37.0373686208367 \tabularnewline
Winsorized Mean ( 33 / 40 ) & 32.8973333333333 & 0.886397602969958 & 37.1135179327062 \tabularnewline
Winsorized Mean ( 34 / 40 ) & 33.1806666666667 & 0.856593889485133 & 38.7355864593084 \tabularnewline
Winsorized Mean ( 35 / 40 ) & 33.03775 & 0.840864671533614 & 39.2902105635428 \tabularnewline
Winsorized Mean ( 36 / 40 ) & 33.08575 & 0.830775208015683 & 39.8251532794602 \tabularnewline
Winsorized Mean ( 37 / 40 ) & 32.8144166666667 & 0.756754984380163 & 43.3620092949161 \tabularnewline
Winsorized Mean ( 38 / 40 ) & 32.7384166666667 & 0.740201293651744 & 44.2290724799377 \tabularnewline
Winsorized Mean ( 39 / 40 ) & 32.6409166666667 & 0.730036212177247 & 44.7113665352558 \tabularnewline
Winsorized Mean ( 40 / 40 ) & 32.71425 & 0.701914226032841 & 46.6071904325093 \tabularnewline
Trimmed Mean ( 1 / 40 ) & 35.6427966101695 & 1.5982172900572 & 22.3015961796371 \tabularnewline
Trimmed Mean ( 2 / 40 ) & 35.4166379310345 & 1.54196153210002 & 22.9685612732505 \tabularnewline
Trimmed Mean ( 3 / 40 ) & 35.3275438596491 & 1.52002904658408 & 23.24136103783 \tabularnewline
Trimmed Mean ( 4 / 40 ) & 35.2163392857143 & 1.49838130161341 & 23.5029222853985 \tabularnewline
Trimmed Mean ( 5 / 40 ) & 35.102 & 1.47438450029572 & 23.8079008514804 \tabularnewline
Trimmed Mean ( 6 / 40 ) & 34.9860185185185 & 1.45317975874004 & 24.0754925934647 \tabularnewline
Trimmed Mean ( 7 / 40 ) & 34.8554716981132 & 1.43078889348472 & 24.3610163992969 \tabularnewline
Trimmed Mean ( 8 / 40 ) & 34.7205769230769 & 1.40572727494554 & 24.6993691748792 \tabularnewline
Trimmed Mean ( 9 / 40 ) & 34.6052941176471 & 1.38343559094102 & 25.0140261998814 \tabularnewline
Trimmed Mean ( 10 / 40 ) & 34.488 & 1.35939569907613 & 25.3700964505322 \tabularnewline
Trimmed Mean ( 11 / 40 ) & 34.3651020408163 & 1.33228212576465 & 25.7941627949807 \tabularnewline
Trimmed Mean ( 12 / 40 ) & 34.2227083333333 & 1.30470381695683 & 26.2302507960438 \tabularnewline
Trimmed Mean ( 13 / 40 ) & 34.0737234042553 & 1.27332450534253 & 26.7596541661541 \tabularnewline
Trimmed Mean ( 14 / 40 ) & 33.973152173913 & 1.25369160500206 & 27.0984921956602 \tabularnewline
Trimmed Mean ( 15 / 40 ) & 33.8662222222222 & 1.2345723362273 & 27.4315414564636 \tabularnewline
Trimmed Mean ( 16 / 40 ) & 33.7530681818182 & 1.21275660717364 & 27.8316918515748 \tabularnewline
Trimmed Mean ( 17 / 40 ) & 33.645 & 1.19023577369798 & 28.2675086260157 \tabularnewline
Trimmed Mean ( 18 / 40 ) & 33.5679761904762 & 1.17723595899405 & 28.5142293981234 \tabularnewline
Trimmed Mean ( 19 / 40 ) & 33.4871951219512 & 1.16197500666811 & 28.8192043114366 \tabularnewline
Trimmed Mean ( 20 / 40 ) & 33.402875 & 1.14419989171791 & 29.1932163617396 \tabularnewline
Trimmed Mean ( 21 / 40 ) & 33.3041025641026 & 1.12540187717311 & 29.5930753623397 \tabularnewline
Trimmed Mean ( 22 / 40 ) & 33.2086842105263 & 1.10674971167125 & 30.0055955382897 \tabularnewline
Trimmed Mean ( 23 / 40 ) & 33.1094594594595 & 1.08503503752209 & 30.5146454395352 \tabularnewline
Trimmed Mean ( 24 / 40 ) & 33.0594444444444 & 1.0731628930535 & 30.8056164245295 \tabularnewline
Trimmed Mean ( 25 / 40 ) & 33.0065714285714 & 1.05878959146489 & 31.1738722165801 \tabularnewline
Trimmed Mean ( 26 / 40 ) & 32.9477941176471 & 1.0421581166947 & 31.6149666637383 \tabularnewline
Trimmed Mean ( 27 / 40 ) & 32.8766666666667 & 1.02374392497911 & 32.1141506821031 \tabularnewline
Trimmed Mean ( 28 / 40 ) & 32.8321875 & 1.00955569525555 & 32.5214226954454 \tabularnewline
Trimmed Mean ( 29 / 40 ) & 32.7966129032258 & 0.996141204864551 & 32.9236585567056 \tabularnewline
Trimmed Mean ( 30 / 40 ) & 32.7715 & 0.987640938236845 & 33.1815933617578 \tabularnewline
Trimmed Mean ( 31 / 40 ) & 32.7446551724138 & 0.976605948267883 & 33.5290351553664 \tabularnewline
Trimmed Mean ( 32 / 40 ) & 32.7242857142857 & 0.965617689974192 & 33.8894844761599 \tabularnewline
Trimmed Mean ( 33 / 40 ) & 32.7107407407407 & 0.954760292096143 & 34.2606840811587 \tabularnewline
Trimmed Mean ( 34 / 40 ) & 32.6976923076923 & 0.940907412195606 & 34.7512325696237 \tabularnewline
Trimmed Mean ( 35 / 40 ) & 32.6636 & 0.92754443251292 & 35.2151324023446 \tabularnewline
Trimmed Mean ( 36 / 40 ) & 32.636875 & 0.912643030481246 & 35.7608329981879 \tabularnewline
Trimmed Mean ( 37 / 40 ) & 32.604347826087 & 0.894633201612499 & 36.4443749318943 \tabularnewline
Trimmed Mean ( 38 / 40 ) & 32.5888636363636 & 0.884552610600762 & 36.8421993737945 \tabularnewline
Trimmed Mean ( 39 / 40 ) & 32.577619047619 & 0.873320708754569 & 37.3031564705222 \tabularnewline
Trimmed Mean ( 40 / 40 ) & 32.57275 & 0.859289434201753 & 37.9066106291169 \tabularnewline
Median & 32.86 &  &  \tabularnewline
Midrange & 48.76 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 32.7966129032258 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 32.7966129032258 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 32.7966129032258 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 32.7966129032258 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 32.7966129032258 &  &  \tabularnewline
Midmean - Closest Observation & 32.7966129032258 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 32.7966129032258 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 32.7966129032258 &  &  \tabularnewline
Number of observations & 120 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=142226&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]35.8614166666667[/C][C]1.64835527608224[/C][C]21.7558782302691[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]31.5061177601291[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]27.4224191612729[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]40.1169932094451[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 40 )[/C][C]35.8614166666667[/C][C]1.64835527608224[/C][C]21.7558782302691[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 40 )[/C][C]35.5859166666667[/C][C]1.57938173777308[/C][C]22.5315487798679[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 40 )[/C][C]35.6389166666667[/C][C]1.57234652560442[/C][C]22.6660701609442[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 40 )[/C][C]35.6355833333333[/C][C]1.57171142512333[/C][C]22.6731082841986[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 40 )[/C][C]35.6239166666667[/C][C]1.55046017518787[/C][C]22.9763506581845[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 40 )[/C][C]35.6779166666667[/C][C]1.54404876709893[/C][C]23.1067291570724[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 40 )[/C][C]35.6738333333333[/C][C]1.54329812616006[/C][C]23.1153221329276[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 40 )[/C][C]35.5045[/C][C]1.51298758768081[/C][C]23.4664846487097[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 40 )[/C][C]35.485[/C][C]1.50654911107791[/C][C]23.5538289054587[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 40 )[/C][C]35.4916666666667[/C][C]1.50576881045893[/C][C]23.5704620922847[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 40 )[/C][C]35.6181666666667[/C][C]1.48510971113528[/C][C]23.9835255265005[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 40 )[/C][C]35.6231666666667[/C][C]1.48456001736027[/C][C]23.9957740004402[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 40 )[/C][C]35.0760833333333[/C][C]1.38113504906333[/C][C]25.3965630349628[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 40 )[/C][C]35.0959166666667[/C][C]1.35693742693387[/C][C]25.8640641565686[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 40 )[/C][C]35.1109166666667[/C][C]1.35531050116329[/C][C]25.9061791645016[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 40 )[/C][C]34.99225[/C][C]1.33713767553694[/C][C]26.1695191454003[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 40 )[/C][C]34.5615833333333[/C][C]1.2421861827225[/C][C]27.8231909306742[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 40 )[/C][C]34.5615833333333[/C][C]1.2421861827225[/C][C]27.8231909306742[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 40 )[/C][C]34.55525[/C][C]1.24130191075679[/C][C]27.8379092955174[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 40 )[/C][C]34.6869166666667[/C][C]1.22438935672457[/C][C]28.3299723867736[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 40 )[/C][C]34.5731666666667[/C][C]1.19877810095981[/C][C]28.8403388742132[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 40 )[/C][C]34.5548333333333[/C][C]1.19625577152841[/C][C]28.8858237140908[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 40 )[/C][C]33.7996666666667[/C][C]1.09632863852958[/C][C]30.8298675039625[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 40 )[/C][C]33.7996666666667[/C][C]1.09632863852958[/C][C]30.8298675039625[/C][/ROW]
[ROW][C]Winsorized Mean ( 25 / 40 )[/C][C]33.83925[/C][C]1.0905917891013[/C][C]31.0283374019211[/C][/ROW]
[ROW][C]Winsorized Mean ( 26 / 40 )[/C][C]33.9649166666667[/C][C]1.07720311666997[/C][C]31.5306520572135[/C][/ROW]
[ROW][C]Winsorized Mean ( 27 / 40 )[/C][C]33.5171666666667[/C][C]1.02095792597017[/C][C]32.8291360633857[/C][/ROW]
[ROW][C]Winsorized Mean ( 28 / 40 )[/C][C]33.3468333333333[/C][C]0.992233086711995[/C][C]33.6078626886311[/C][/ROW]
[ROW][C]Winsorized Mean ( 29 / 40 )[/C][C]33.16075[/C][C]0.933012816332754[/C][C]35.541580372218[/C][/ROW]
[ROW][C]Winsorized Mean ( 30 / 40 )[/C][C]33.16075[/C][C]0.933012816332754[/C][C]35.541580372218[/C][/ROW]
[ROW][C]Winsorized Mean ( 31 / 40 )[/C][C]33.0393333333333[/C][C]0.911401687227349[/C][C]36.2511215376889[/C][/ROW]
[ROW][C]Winsorized Mean ( 32 / 40 )[/C][C]32.9193333333333[/C][C]0.888814042658889[/C][C]37.0373686208367[/C][/ROW]
[ROW][C]Winsorized Mean ( 33 / 40 )[/C][C]32.8973333333333[/C][C]0.886397602969958[/C][C]37.1135179327062[/C][/ROW]
[ROW][C]Winsorized Mean ( 34 / 40 )[/C][C]33.1806666666667[/C][C]0.856593889485133[/C][C]38.7355864593084[/C][/ROW]
[ROW][C]Winsorized Mean ( 35 / 40 )[/C][C]33.03775[/C][C]0.840864671533614[/C][C]39.2902105635428[/C][/ROW]
[ROW][C]Winsorized Mean ( 36 / 40 )[/C][C]33.08575[/C][C]0.830775208015683[/C][C]39.8251532794602[/C][/ROW]
[ROW][C]Winsorized Mean ( 37 / 40 )[/C][C]32.8144166666667[/C][C]0.756754984380163[/C][C]43.3620092949161[/C][/ROW]
[ROW][C]Winsorized Mean ( 38 / 40 )[/C][C]32.7384166666667[/C][C]0.740201293651744[/C][C]44.2290724799377[/C][/ROW]
[ROW][C]Winsorized Mean ( 39 / 40 )[/C][C]32.6409166666667[/C][C]0.730036212177247[/C][C]44.7113665352558[/C][/ROW]
[ROW][C]Winsorized Mean ( 40 / 40 )[/C][C]32.71425[/C][C]0.701914226032841[/C][C]46.6071904325093[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 40 )[/C][C]35.6427966101695[/C][C]1.5982172900572[/C][C]22.3015961796371[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 40 )[/C][C]35.4166379310345[/C][C]1.54196153210002[/C][C]22.9685612732505[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 40 )[/C][C]35.3275438596491[/C][C]1.52002904658408[/C][C]23.24136103783[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 40 )[/C][C]35.2163392857143[/C][C]1.49838130161341[/C][C]23.5029222853985[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 40 )[/C][C]35.102[/C][C]1.47438450029572[/C][C]23.8079008514804[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 40 )[/C][C]34.9860185185185[/C][C]1.45317975874004[/C][C]24.0754925934647[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 40 )[/C][C]34.8554716981132[/C][C]1.43078889348472[/C][C]24.3610163992969[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 40 )[/C][C]34.7205769230769[/C][C]1.40572727494554[/C][C]24.6993691748792[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 40 )[/C][C]34.6052941176471[/C][C]1.38343559094102[/C][C]25.0140261998814[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 40 )[/C][C]34.488[/C][C]1.35939569907613[/C][C]25.3700964505322[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 40 )[/C][C]34.3651020408163[/C][C]1.33228212576465[/C][C]25.7941627949807[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 40 )[/C][C]34.2227083333333[/C][C]1.30470381695683[/C][C]26.2302507960438[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 40 )[/C][C]34.0737234042553[/C][C]1.27332450534253[/C][C]26.7596541661541[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 40 )[/C][C]33.973152173913[/C][C]1.25369160500206[/C][C]27.0984921956602[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 40 )[/C][C]33.8662222222222[/C][C]1.2345723362273[/C][C]27.4315414564636[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 40 )[/C][C]33.7530681818182[/C][C]1.21275660717364[/C][C]27.8316918515748[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 40 )[/C][C]33.645[/C][C]1.19023577369798[/C][C]28.2675086260157[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 40 )[/C][C]33.5679761904762[/C][C]1.17723595899405[/C][C]28.5142293981234[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 40 )[/C][C]33.4871951219512[/C][C]1.16197500666811[/C][C]28.8192043114366[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 40 )[/C][C]33.402875[/C][C]1.14419989171791[/C][C]29.1932163617396[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 40 )[/C][C]33.3041025641026[/C][C]1.12540187717311[/C][C]29.5930753623397[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 40 )[/C][C]33.2086842105263[/C][C]1.10674971167125[/C][C]30.0055955382897[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 40 )[/C][C]33.1094594594595[/C][C]1.08503503752209[/C][C]30.5146454395352[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 40 )[/C][C]33.0594444444444[/C][C]1.0731628930535[/C][C]30.8056164245295[/C][/ROW]
[ROW][C]Trimmed Mean ( 25 / 40 )[/C][C]33.0065714285714[/C][C]1.05878959146489[/C][C]31.1738722165801[/C][/ROW]
[ROW][C]Trimmed Mean ( 26 / 40 )[/C][C]32.9477941176471[/C][C]1.0421581166947[/C][C]31.6149666637383[/C][/ROW]
[ROW][C]Trimmed Mean ( 27 / 40 )[/C][C]32.8766666666667[/C][C]1.02374392497911[/C][C]32.1141506821031[/C][/ROW]
[ROW][C]Trimmed Mean ( 28 / 40 )[/C][C]32.8321875[/C][C]1.00955569525555[/C][C]32.5214226954454[/C][/ROW]
[ROW][C]Trimmed Mean ( 29 / 40 )[/C][C]32.7966129032258[/C][C]0.996141204864551[/C][C]32.9236585567056[/C][/ROW]
[ROW][C]Trimmed Mean ( 30 / 40 )[/C][C]32.7715[/C][C]0.987640938236845[/C][C]33.1815933617578[/C][/ROW]
[ROW][C]Trimmed Mean ( 31 / 40 )[/C][C]32.7446551724138[/C][C]0.976605948267883[/C][C]33.5290351553664[/C][/ROW]
[ROW][C]Trimmed Mean ( 32 / 40 )[/C][C]32.7242857142857[/C][C]0.965617689974192[/C][C]33.8894844761599[/C][/ROW]
[ROW][C]Trimmed Mean ( 33 / 40 )[/C][C]32.7107407407407[/C][C]0.954760292096143[/C][C]34.2606840811587[/C][/ROW]
[ROW][C]Trimmed Mean ( 34 / 40 )[/C][C]32.6976923076923[/C][C]0.940907412195606[/C][C]34.7512325696237[/C][/ROW]
[ROW][C]Trimmed Mean ( 35 / 40 )[/C][C]32.6636[/C][C]0.92754443251292[/C][C]35.2151324023446[/C][/ROW]
[ROW][C]Trimmed Mean ( 36 / 40 )[/C][C]32.636875[/C][C]0.912643030481246[/C][C]35.7608329981879[/C][/ROW]
[ROW][C]Trimmed Mean ( 37 / 40 )[/C][C]32.604347826087[/C][C]0.894633201612499[/C][C]36.4443749318943[/C][/ROW]
[ROW][C]Trimmed Mean ( 38 / 40 )[/C][C]32.5888636363636[/C][C]0.884552610600762[/C][C]36.8421993737945[/C][/ROW]
[ROW][C]Trimmed Mean ( 39 / 40 )[/C][C]32.577619047619[/C][C]0.873320708754569[/C][C]37.3031564705222[/C][/ROW]
[ROW][C]Trimmed Mean ( 40 / 40 )[/C][C]32.57275[/C][C]0.859289434201753[/C][C]37.9066106291169[/C][/ROW]
[ROW][C]Median[/C][C]32.86[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]48.76[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]32.7966129032258[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]32.7966129032258[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]32.7966129032258[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]32.7966129032258[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]32.7966129032258[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]32.7966129032258[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]32.7966129032258[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]32.7966129032258[/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=142226&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=142226&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 Mean35.86141666666671.6483552760822421.7558782302691
Geometric Mean31.5061177601291
Harmonic Mean27.4224191612729
Quadratic Mean40.1169932094451
Winsorized Mean ( 1 / 40 )35.86141666666671.6483552760822421.7558782302691
Winsorized Mean ( 2 / 40 )35.58591666666671.5793817377730822.5315487798679
Winsorized Mean ( 3 / 40 )35.63891666666671.5723465256044222.6660701609442
Winsorized Mean ( 4 / 40 )35.63558333333331.5717114251233322.6731082841986
Winsorized Mean ( 5 / 40 )35.62391666666671.5504601751878722.9763506581845
Winsorized Mean ( 6 / 40 )35.67791666666671.5440487670989323.1067291570724
Winsorized Mean ( 7 / 40 )35.67383333333331.5432981261600623.1153221329276
Winsorized Mean ( 8 / 40 )35.50451.5129875876808123.4664846487097
Winsorized Mean ( 9 / 40 )35.4851.5065491110779123.5538289054587
Winsorized Mean ( 10 / 40 )35.49166666666671.5057688104589323.5704620922847
Winsorized Mean ( 11 / 40 )35.61816666666671.4851097111352823.9835255265005
Winsorized Mean ( 12 / 40 )35.62316666666671.4845600173602723.9957740004402
Winsorized Mean ( 13 / 40 )35.07608333333331.3811350490633325.3965630349628
Winsorized Mean ( 14 / 40 )35.09591666666671.3569374269338725.8640641565686
Winsorized Mean ( 15 / 40 )35.11091666666671.3553105011632925.9061791645016
Winsorized Mean ( 16 / 40 )34.992251.3371376755369426.1695191454003
Winsorized Mean ( 17 / 40 )34.56158333333331.242186182722527.8231909306742
Winsorized Mean ( 18 / 40 )34.56158333333331.242186182722527.8231909306742
Winsorized Mean ( 19 / 40 )34.555251.2413019107567927.8379092955174
Winsorized Mean ( 20 / 40 )34.68691666666671.2243893567245728.3299723867736
Winsorized Mean ( 21 / 40 )34.57316666666671.1987781009598128.8403388742132
Winsorized Mean ( 22 / 40 )34.55483333333331.1962557715284128.8858237140908
Winsorized Mean ( 23 / 40 )33.79966666666671.0963286385295830.8298675039625
Winsorized Mean ( 24 / 40 )33.79966666666671.0963286385295830.8298675039625
Winsorized Mean ( 25 / 40 )33.839251.090591789101331.0283374019211
Winsorized Mean ( 26 / 40 )33.96491666666671.0772031166699731.5306520572135
Winsorized Mean ( 27 / 40 )33.51716666666671.0209579259701732.8291360633857
Winsorized Mean ( 28 / 40 )33.34683333333330.99223308671199533.6078626886311
Winsorized Mean ( 29 / 40 )33.160750.93301281633275435.541580372218
Winsorized Mean ( 30 / 40 )33.160750.93301281633275435.541580372218
Winsorized Mean ( 31 / 40 )33.03933333333330.91140168722734936.2511215376889
Winsorized Mean ( 32 / 40 )32.91933333333330.88881404265888937.0373686208367
Winsorized Mean ( 33 / 40 )32.89733333333330.88639760296995837.1135179327062
Winsorized Mean ( 34 / 40 )33.18066666666670.85659388948513338.7355864593084
Winsorized Mean ( 35 / 40 )33.037750.84086467153361439.2902105635428
Winsorized Mean ( 36 / 40 )33.085750.83077520801568339.8251532794602
Winsorized Mean ( 37 / 40 )32.81441666666670.75675498438016343.3620092949161
Winsorized Mean ( 38 / 40 )32.73841666666670.74020129365174444.2290724799377
Winsorized Mean ( 39 / 40 )32.64091666666670.73003621217724744.7113665352558
Winsorized Mean ( 40 / 40 )32.714250.70191422603284146.6071904325093
Trimmed Mean ( 1 / 40 )35.64279661016951.598217290057222.3015961796371
Trimmed Mean ( 2 / 40 )35.41663793103451.5419615321000222.9685612732505
Trimmed Mean ( 3 / 40 )35.32754385964911.5200290465840823.24136103783
Trimmed Mean ( 4 / 40 )35.21633928571431.4983813016134123.5029222853985
Trimmed Mean ( 5 / 40 )35.1021.4743845002957223.8079008514804
Trimmed Mean ( 6 / 40 )34.98601851851851.4531797587400424.0754925934647
Trimmed Mean ( 7 / 40 )34.85547169811321.4307888934847224.3610163992969
Trimmed Mean ( 8 / 40 )34.72057692307691.4057272749455424.6993691748792
Trimmed Mean ( 9 / 40 )34.60529411764711.3834355909410225.0140261998814
Trimmed Mean ( 10 / 40 )34.4881.3593956990761325.3700964505322
Trimmed Mean ( 11 / 40 )34.36510204081631.3322821257646525.7941627949807
Trimmed Mean ( 12 / 40 )34.22270833333331.3047038169568326.2302507960438
Trimmed Mean ( 13 / 40 )34.07372340425531.2733245053425326.7596541661541
Trimmed Mean ( 14 / 40 )33.9731521739131.2536916050020627.0984921956602
Trimmed Mean ( 15 / 40 )33.86622222222221.234572336227327.4315414564636
Trimmed Mean ( 16 / 40 )33.75306818181821.2127566071736427.8316918515748
Trimmed Mean ( 17 / 40 )33.6451.1902357736979828.2675086260157
Trimmed Mean ( 18 / 40 )33.56797619047621.1772359589940528.5142293981234
Trimmed Mean ( 19 / 40 )33.48719512195121.1619750066681128.8192043114366
Trimmed Mean ( 20 / 40 )33.4028751.1441998917179129.1932163617396
Trimmed Mean ( 21 / 40 )33.30410256410261.1254018771731129.5930753623397
Trimmed Mean ( 22 / 40 )33.20868421052631.1067497116712530.0055955382897
Trimmed Mean ( 23 / 40 )33.10945945945951.0850350375220930.5146454395352
Trimmed Mean ( 24 / 40 )33.05944444444441.073162893053530.8056164245295
Trimmed Mean ( 25 / 40 )33.00657142857141.0587895914648931.1738722165801
Trimmed Mean ( 26 / 40 )32.94779411764711.042158116694731.6149666637383
Trimmed Mean ( 27 / 40 )32.87666666666671.0237439249791132.1141506821031
Trimmed Mean ( 28 / 40 )32.83218751.0095556952555532.5214226954454
Trimmed Mean ( 29 / 40 )32.79661290322580.99614120486455132.9236585567056
Trimmed Mean ( 30 / 40 )32.77150.98764093823684533.1815933617578
Trimmed Mean ( 31 / 40 )32.74465517241380.97660594826788333.5290351553664
Trimmed Mean ( 32 / 40 )32.72428571428570.96561768997419233.8894844761599
Trimmed Mean ( 33 / 40 )32.71074074074070.95476029209614334.2606840811587
Trimmed Mean ( 34 / 40 )32.69769230769230.94090741219560634.7512325696237
Trimmed Mean ( 35 / 40 )32.66360.9275444325129235.2151324023446
Trimmed Mean ( 36 / 40 )32.6368750.91264303048124635.7608329981879
Trimmed Mean ( 37 / 40 )32.6043478260870.89463320161249936.4443749318943
Trimmed Mean ( 38 / 40 )32.58886363636360.88455261060076236.8421993737945
Trimmed Mean ( 39 / 40 )32.5776190476190.87332070875456937.3031564705222
Trimmed Mean ( 40 / 40 )32.572750.85928943420175337.9066106291169
Median32.86
Midrange48.76
Midmean - Weighted Average at Xnp32.7966129032258
Midmean - Weighted Average at X(n+1)p32.7966129032258
Midmean - Empirical Distribution Function32.7966129032258
Midmean - Empirical Distribution Function - Averaging32.7966129032258
Midmean - Empirical Distribution Function - Interpolation32.7966129032258
Midmean - Closest Observation32.7966129032258
Midmean - True Basic - Statistics Graphics Toolkit32.7966129032258
Midmean - MS Excel (old versions)32.7966129032258
Number of observations120



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')