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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 computationTue, 13 Dec 2011 09:58:14 -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/13/t1323788332lmay3l32o1pacpq.htm/, Retrieved Fri, 03 May 2024 00:44:19 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=154408, Retrieved Fri, 03 May 2024 00:44:19 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact104
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Recursive Partitioning (Regression Trees)] [] [2010-12-05 20:30:15] [b98453cac15ba1066b407e146608df68]
- RMPD  [Kernel Density Estimation] [] [2011-12-13 14:43:33] [c4580079d5d2b3f0ba412f27cdc441be]
- RMPD      [Central Tendency] [] [2011-12-13 14:58:14] [885a9dbaf162325773a0a0afdf9f947e] [Current]
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Dataseries X:
28
32
0
47
65
123
26
48
37
60
39
64
26
64
25
26
76
2
36
23
14
78
14
24
39
50
57
61
49
40
21
29
35
13
56
14
43
20
72
87
21
56
59
82
43
25
38
25
38
12
29
47
45
40
30
41
25
23
14
16
26
21
27
9
33
42
68
32
6
67
33
77
46
30
0
36
46
18
48
29
28
34
33
34
33
80
32
30
41
41
51
18
34
31
39
54
14
24
24
8
26
19
11
14
1
39
5
37
32
38
47
47
37
51
45
21
1
42
26
21
4
10
43
34
31
19
34
6
11
24
16
72
21




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=154408&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=154408&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=154408&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 Mean34.84210526315791.7762721191563619.6152970524055
Geometric Mean0
Harmonic Mean0
Quadratic Mean40.3788450530664
Winsorized Mean ( 1 / 44 )34.57142857142861.6931800569356420.418046166925
Winsorized Mean ( 2 / 44 )34.51127819548871.6739740651539620.6163756738457
Winsorized Mean ( 3 / 44 )34.46616541353381.6644510976261120.7072262217199
Winsorized Mean ( 4 / 44 )34.43609022556391.6476594480680120.9000047102831
Winsorized Mean ( 5 / 44 )34.47368421052631.6292418896648121.1593406904231
Winsorized Mean ( 6 / 44 )34.47368421052631.614067901634821.3582614310153
Winsorized Mean ( 7 / 44 )34.31578947368421.5671121715862121.8974685385478
Winsorized Mean ( 8 / 44 )34.31578947368421.5671121715862121.8974685385478
Winsorized Mean ( 9 / 44 )34.18045112781961.5011135301204122.7700639838199
Winsorized Mean ( 10 / 44 )34.18045112781961.4785561680384223.117451921469
Winsorized Mean ( 11 / 44 )34.09774436090231.4406250012948123.6687162379215
Winsorized Mean ( 12 / 44 )34.09774436090231.4147718821172224.1012312952352
Winsorized Mean ( 13 / 44 )34.09774436090231.4147718821172224.1012312952352
Winsorized Mean ( 14 / 44 )33.88721804511281.3525186472645325.0548989573266
Winsorized Mean ( 15 / 44 )33.88721804511281.3218484978545325.6362344853548
Winsorized Mean ( 16 / 44 )33.88721804511281.2897431809075326.2743921012771
Winsorized Mean ( 17 / 44 )33.63157894736841.2528151796075226.8448048002616
Winsorized Mean ( 18 / 44 )33.49624060150381.2339017641089727.1466024085736
Winsorized Mean ( 19 / 44 )33.49624060150381.2339017641089727.1466024085736
Winsorized Mean ( 20 / 44 )33.19548872180451.1932472456007627.8194555606048
Winsorized Mean ( 21 / 44 )32.72180451127821.132956328110528.8817880260665
Winsorized Mean ( 22 / 44 )33.05263157894741.0926709479884630.2493917677552
Winsorized Mean ( 23 / 44 )32.87969924812031.0714419620785130.6873357697663
Winsorized Mean ( 24 / 44 )33.06015037593981.0077032643825232.8074260989893
Winsorized Mean ( 25 / 44 )32.87218045112780.98550751144727533.3555858979229
Winsorized Mean ( 26 / 44 )33.06766917293230.96351743966653734.3197412019617
Winsorized Mean ( 27 / 44 )32.86466165413530.94003279144721234.9611864108901
Winsorized Mean ( 28 / 44 )33.07518796992480.91689442230446536.0730605022067
Winsorized Mean ( 29 / 44 )33.29323308270680.89375073701465737.2511391642755
Winsorized Mean ( 30 / 44 )33.29323308270680.89375073701465737.2511391642755
Winsorized Mean ( 31 / 44 )33.06015037593980.86702847039620638.1304092134741
Winsorized Mean ( 32 / 44 )33.06015037593980.86702847039620638.1304092134741
Winsorized Mean ( 33 / 44 )32.8120300751880.83934833350919839.0922680908956
Winsorized Mean ( 34 / 44 )32.8120300751880.83934833350919839.0922680908956
Winsorized Mean ( 35 / 44 )32.8120300751880.72736993921486745.1105115927745
Winsorized Mean ( 36 / 44 )32.8120300751880.72736993921486745.1105115927745
Winsorized Mean ( 37 / 44 )33.09022556390980.69944959699400947.3089493597824
Winsorized Mean ( 38 / 44 )32.80451127819550.66923565003400349.0178777483368
Winsorized Mean ( 39 / 44 )32.80451127819550.66923565003400349.0178777483368
Winsorized Mean ( 40 / 44 )32.50375939849620.63840982638075150.9136264126217
Winsorized Mean ( 41 / 44 )32.8120300751880.60783507148982753.9817980472309
Winsorized Mean ( 42 / 44 )32.8120300751880.60783507148982753.9817980472309
Winsorized Mean ( 43 / 44 )32.48872180451130.57533575062386956.4691517418862
Winsorized Mean ( 44 / 44 )32.48872180451130.57533575062386956.4691517418862
Trimmed Mean ( 1 / 44 )34.43511450381681.6503562574395620.8652612722789
Trimmed Mean ( 2 / 44 )34.29457364341081.6030646484316421.3931320093441
Trimmed Mean ( 3 / 44 )34.18110236220471.562089033981621.8816607879774
Trimmed Mean ( 4 / 44 )34.081.520721390783722.4104166657622
Trimmed Mean ( 5 / 44 )33.98373983739841.4803787432575922.9561117330128
Trimmed Mean ( 6 / 44 )33.87603305785121.4406328120532523.5146893604136
Trimmed Mean ( 7 / 44 )33.76470588235291.400078633433424.1162925253362
Trimmed Mean ( 8 / 44 )33.67521367521371.3651071011309224.6685506560734
Trimmed Mean ( 9 / 44 )33.58260869565221.3261428506058125.3235227866371
Trimmed Mean ( 10 / 44 )33.50442477876111.2947504075527425.8771301274113
Trimmed Mean ( 11 / 44 )33.42342342342341.263521433416426.4525971142815
Trimmed Mean ( 12 / 44 )33.3486238532111.2347180800235827.0090998040413
Trimmed Mean ( 13 / 44 )33.27102803738321.2063993604683527.5787845448348
Trimmed Mean ( 14 / 44 )33.19047619047621.174601112099328.2568063733199
Trimmed Mean ( 15 / 44 )33.1262135922331.1478946878033628.8582340733924
Trimmed Mean ( 16 / 44 )33.05940594059411.1220403782094129.4636508477095
Trimmed Mean ( 17 / 44 )32.9898989898991.0971651548110530.0683072600683
Trimmed Mean ( 18 / 44 )32.93814432989691.0740230149483230.6680060589594
Trimmed Mean ( 19 / 44 )32.89473684210531.0502997688881231.3193793015195
Trimmed Mean ( 20 / 44 )32.84946236559141.0233307182414132.1005338548256
Trimmed Mean ( 21 / 44 )32.82417582417580.99799474241281232.8901290049065
Trimmed Mean ( 22 / 44 )32.83146067415730.97677785776284733.6120033979399
Trimmed Mean ( 23 / 44 )32.8160919540230.95746601766775834.2738972960712
Trimmed Mean ( 24 / 44 )32.81176470588240.93791802895177934.9836165774027
Trimmed Mean ( 25 / 44 )32.79518072289160.92310261376543435.5271236738422
Trimmed Mean ( 26 / 44 )32.79012345679010.90858661935514436.0891551320252
Trimmed Mean ( 27 / 44 )32.77215189873420.89427283874826736.6467038679225
Trimmed Mean ( 28 / 44 )32.76623376623380.88038861267556837.2179209209155
Trimmed Mean ( 29 / 44 )32.74666666666670.8668246564242337.7777286605473
Trimmed Mean ( 30 / 44 )32.71232876712330.85351797999936138.3264670852602
Trimmed Mean ( 31 / 44 )32.67605633802820.83768740007018639.0074583135551
Trimmed Mean ( 32 / 44 )32.65217391304350.8224332535246939.7019135268504
Trimmed Mean ( 33 / 44 )32.62686567164180.80417156973278840.5720208219785
Trimmed Mean ( 34 / 44 )32.61538461538460.78620690773812741.4844798415944
Trimmed Mean ( 35 / 44 )32.60317460317460.76452974162341842.6447433345685
Trimmed Mean ( 36 / 44 )32.59016393442620.75435966012231343.2024214141329
Trimmed Mean ( 37 / 44 )32.57627118644070.74168028774453743.9222556197438
Trimmed Mean ( 38 / 44 )32.54385964912280.72981190947198244.5921191840624
Trimmed Mean ( 39 / 44 )32.52727272727270.71954650208048445.2052405691974
Trimmed Mean ( 40 / 44 )32.50943396226420.70639965001166346.0213053074523
Trimmed Mean ( 41 / 44 )32.50980392156860.69472666314599446.7951003555147
Trimmed Mean ( 42 / 44 )32.48979591836730.6845739830346747.4598753729178
Trimmed Mean ( 43 / 44 )32.4680851063830.67109687219390648.3806235011057
Trimmed Mean ( 44 / 44 )32.46666666666670.65950700902226649.2286908592514
Median33
Midrange61.5
Midmean - Weighted Average at Xnp31.9718309859155
Midmean - Weighted Average at X(n+1)p31.9718309859155
Midmean - Empirical Distribution Function31.9718309859155
Midmean - Empirical Distribution Function - Averaging31.9718309859155
Midmean - Empirical Distribution Function - Interpolation31.9718309859155
Midmean - Closest Observation31.9718309859155
Midmean - True Basic - Statistics Graphics Toolkit31.9718309859155
Midmean - MS Excel (old versions)31.9718309859155
Number of observations133

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 34.8421052631579 & 1.77627211915636 & 19.6152970524055 \tabularnewline
Geometric Mean & 0 &  &  \tabularnewline
Harmonic Mean & 0 &  &  \tabularnewline
Quadratic Mean & 40.3788450530664 &  &  \tabularnewline
Winsorized Mean ( 1 / 44 ) & 34.5714285714286 & 1.69318005693564 & 20.418046166925 \tabularnewline
Winsorized Mean ( 2 / 44 ) & 34.5112781954887 & 1.67397406515396 & 20.6163756738457 \tabularnewline
Winsorized Mean ( 3 / 44 ) & 34.4661654135338 & 1.66445109762611 & 20.7072262217199 \tabularnewline
Winsorized Mean ( 4 / 44 ) & 34.4360902255639 & 1.64765944806801 & 20.9000047102831 \tabularnewline
Winsorized Mean ( 5 / 44 ) & 34.4736842105263 & 1.62924188966481 & 21.1593406904231 \tabularnewline
Winsorized Mean ( 6 / 44 ) & 34.4736842105263 & 1.6140679016348 & 21.3582614310153 \tabularnewline
Winsorized Mean ( 7 / 44 ) & 34.3157894736842 & 1.56711217158621 & 21.8974685385478 \tabularnewline
Winsorized Mean ( 8 / 44 ) & 34.3157894736842 & 1.56711217158621 & 21.8974685385478 \tabularnewline
Winsorized Mean ( 9 / 44 ) & 34.1804511278196 & 1.50111353012041 & 22.7700639838199 \tabularnewline
Winsorized Mean ( 10 / 44 ) & 34.1804511278196 & 1.47855616803842 & 23.117451921469 \tabularnewline
Winsorized Mean ( 11 / 44 ) & 34.0977443609023 & 1.44062500129481 & 23.6687162379215 \tabularnewline
Winsorized Mean ( 12 / 44 ) & 34.0977443609023 & 1.41477188211722 & 24.1012312952352 \tabularnewline
Winsorized Mean ( 13 / 44 ) & 34.0977443609023 & 1.41477188211722 & 24.1012312952352 \tabularnewline
Winsorized Mean ( 14 / 44 ) & 33.8872180451128 & 1.35251864726453 & 25.0548989573266 \tabularnewline
Winsorized Mean ( 15 / 44 ) & 33.8872180451128 & 1.32184849785453 & 25.6362344853548 \tabularnewline
Winsorized Mean ( 16 / 44 ) & 33.8872180451128 & 1.28974318090753 & 26.2743921012771 \tabularnewline
Winsorized Mean ( 17 / 44 ) & 33.6315789473684 & 1.25281517960752 & 26.8448048002616 \tabularnewline
Winsorized Mean ( 18 / 44 ) & 33.4962406015038 & 1.23390176410897 & 27.1466024085736 \tabularnewline
Winsorized Mean ( 19 / 44 ) & 33.4962406015038 & 1.23390176410897 & 27.1466024085736 \tabularnewline
Winsorized Mean ( 20 / 44 ) & 33.1954887218045 & 1.19324724560076 & 27.8194555606048 \tabularnewline
Winsorized Mean ( 21 / 44 ) & 32.7218045112782 & 1.1329563281105 & 28.8817880260665 \tabularnewline
Winsorized Mean ( 22 / 44 ) & 33.0526315789474 & 1.09267094798846 & 30.2493917677552 \tabularnewline
Winsorized Mean ( 23 / 44 ) & 32.8796992481203 & 1.07144196207851 & 30.6873357697663 \tabularnewline
Winsorized Mean ( 24 / 44 ) & 33.0601503759398 & 1.00770326438252 & 32.8074260989893 \tabularnewline
Winsorized Mean ( 25 / 44 ) & 32.8721804511278 & 0.985507511447275 & 33.3555858979229 \tabularnewline
Winsorized Mean ( 26 / 44 ) & 33.0676691729323 & 0.963517439666537 & 34.3197412019617 \tabularnewline
Winsorized Mean ( 27 / 44 ) & 32.8646616541353 & 0.940032791447212 & 34.9611864108901 \tabularnewline
Winsorized Mean ( 28 / 44 ) & 33.0751879699248 & 0.916894422304465 & 36.0730605022067 \tabularnewline
Winsorized Mean ( 29 / 44 ) & 33.2932330827068 & 0.893750737014657 & 37.2511391642755 \tabularnewline
Winsorized Mean ( 30 / 44 ) & 33.2932330827068 & 0.893750737014657 & 37.2511391642755 \tabularnewline
Winsorized Mean ( 31 / 44 ) & 33.0601503759398 & 0.867028470396206 & 38.1304092134741 \tabularnewline
Winsorized Mean ( 32 / 44 ) & 33.0601503759398 & 0.867028470396206 & 38.1304092134741 \tabularnewline
Winsorized Mean ( 33 / 44 ) & 32.812030075188 & 0.839348333509198 & 39.0922680908956 \tabularnewline
Winsorized Mean ( 34 / 44 ) & 32.812030075188 & 0.839348333509198 & 39.0922680908956 \tabularnewline
Winsorized Mean ( 35 / 44 ) & 32.812030075188 & 0.727369939214867 & 45.1105115927745 \tabularnewline
Winsorized Mean ( 36 / 44 ) & 32.812030075188 & 0.727369939214867 & 45.1105115927745 \tabularnewline
Winsorized Mean ( 37 / 44 ) & 33.0902255639098 & 0.699449596994009 & 47.3089493597824 \tabularnewline
Winsorized Mean ( 38 / 44 ) & 32.8045112781955 & 0.669235650034003 & 49.0178777483368 \tabularnewline
Winsorized Mean ( 39 / 44 ) & 32.8045112781955 & 0.669235650034003 & 49.0178777483368 \tabularnewline
Winsorized Mean ( 40 / 44 ) & 32.5037593984962 & 0.638409826380751 & 50.9136264126217 \tabularnewline
Winsorized Mean ( 41 / 44 ) & 32.812030075188 & 0.607835071489827 & 53.9817980472309 \tabularnewline
Winsorized Mean ( 42 / 44 ) & 32.812030075188 & 0.607835071489827 & 53.9817980472309 \tabularnewline
Winsorized Mean ( 43 / 44 ) & 32.4887218045113 & 0.575335750623869 & 56.4691517418862 \tabularnewline
Winsorized Mean ( 44 / 44 ) & 32.4887218045113 & 0.575335750623869 & 56.4691517418862 \tabularnewline
Trimmed Mean ( 1 / 44 ) & 34.4351145038168 & 1.65035625743956 & 20.8652612722789 \tabularnewline
Trimmed Mean ( 2 / 44 ) & 34.2945736434108 & 1.60306464843164 & 21.3931320093441 \tabularnewline
Trimmed Mean ( 3 / 44 ) & 34.1811023622047 & 1.5620890339816 & 21.8816607879774 \tabularnewline
Trimmed Mean ( 4 / 44 ) & 34.08 & 1.5207213907837 & 22.4104166657622 \tabularnewline
Trimmed Mean ( 5 / 44 ) & 33.9837398373984 & 1.48037874325759 & 22.9561117330128 \tabularnewline
Trimmed Mean ( 6 / 44 ) & 33.8760330578512 & 1.44063281205325 & 23.5146893604136 \tabularnewline
Trimmed Mean ( 7 / 44 ) & 33.7647058823529 & 1.4000786334334 & 24.1162925253362 \tabularnewline
Trimmed Mean ( 8 / 44 ) & 33.6752136752137 & 1.36510710113092 & 24.6685506560734 \tabularnewline
Trimmed Mean ( 9 / 44 ) & 33.5826086956522 & 1.32614285060581 & 25.3235227866371 \tabularnewline
Trimmed Mean ( 10 / 44 ) & 33.5044247787611 & 1.29475040755274 & 25.8771301274113 \tabularnewline
Trimmed Mean ( 11 / 44 ) & 33.4234234234234 & 1.2635214334164 & 26.4525971142815 \tabularnewline
Trimmed Mean ( 12 / 44 ) & 33.348623853211 & 1.23471808002358 & 27.0090998040413 \tabularnewline
Trimmed Mean ( 13 / 44 ) & 33.2710280373832 & 1.20639936046835 & 27.5787845448348 \tabularnewline
Trimmed Mean ( 14 / 44 ) & 33.1904761904762 & 1.1746011120993 & 28.2568063733199 \tabularnewline
Trimmed Mean ( 15 / 44 ) & 33.126213592233 & 1.14789468780336 & 28.8582340733924 \tabularnewline
Trimmed Mean ( 16 / 44 ) & 33.0594059405941 & 1.12204037820941 & 29.4636508477095 \tabularnewline
Trimmed Mean ( 17 / 44 ) & 32.989898989899 & 1.09716515481105 & 30.0683072600683 \tabularnewline
Trimmed Mean ( 18 / 44 ) & 32.9381443298969 & 1.07402301494832 & 30.6680060589594 \tabularnewline
Trimmed Mean ( 19 / 44 ) & 32.8947368421053 & 1.05029976888812 & 31.3193793015195 \tabularnewline
Trimmed Mean ( 20 / 44 ) & 32.8494623655914 & 1.02333071824141 & 32.1005338548256 \tabularnewline
Trimmed Mean ( 21 / 44 ) & 32.8241758241758 & 0.997994742412812 & 32.8901290049065 \tabularnewline
Trimmed Mean ( 22 / 44 ) & 32.8314606741573 & 0.976777857762847 & 33.6120033979399 \tabularnewline
Trimmed Mean ( 23 / 44 ) & 32.816091954023 & 0.957466017667758 & 34.2738972960712 \tabularnewline
Trimmed Mean ( 24 / 44 ) & 32.8117647058824 & 0.937918028951779 & 34.9836165774027 \tabularnewline
Trimmed Mean ( 25 / 44 ) & 32.7951807228916 & 0.923102613765434 & 35.5271236738422 \tabularnewline
Trimmed Mean ( 26 / 44 ) & 32.7901234567901 & 0.908586619355144 & 36.0891551320252 \tabularnewline
Trimmed Mean ( 27 / 44 ) & 32.7721518987342 & 0.894272838748267 & 36.6467038679225 \tabularnewline
Trimmed Mean ( 28 / 44 ) & 32.7662337662338 & 0.880388612675568 & 37.2179209209155 \tabularnewline
Trimmed Mean ( 29 / 44 ) & 32.7466666666667 & 0.86682465642423 & 37.7777286605473 \tabularnewline
Trimmed Mean ( 30 / 44 ) & 32.7123287671233 & 0.853517979999361 & 38.3264670852602 \tabularnewline
Trimmed Mean ( 31 / 44 ) & 32.6760563380282 & 0.837687400070186 & 39.0074583135551 \tabularnewline
Trimmed Mean ( 32 / 44 ) & 32.6521739130435 & 0.82243325352469 & 39.7019135268504 \tabularnewline
Trimmed Mean ( 33 / 44 ) & 32.6268656716418 & 0.804171569732788 & 40.5720208219785 \tabularnewline
Trimmed Mean ( 34 / 44 ) & 32.6153846153846 & 0.786206907738127 & 41.4844798415944 \tabularnewline
Trimmed Mean ( 35 / 44 ) & 32.6031746031746 & 0.764529741623418 & 42.6447433345685 \tabularnewline
Trimmed Mean ( 36 / 44 ) & 32.5901639344262 & 0.754359660122313 & 43.2024214141329 \tabularnewline
Trimmed Mean ( 37 / 44 ) & 32.5762711864407 & 0.741680287744537 & 43.9222556197438 \tabularnewline
Trimmed Mean ( 38 / 44 ) & 32.5438596491228 & 0.729811909471982 & 44.5921191840624 \tabularnewline
Trimmed Mean ( 39 / 44 ) & 32.5272727272727 & 0.719546502080484 & 45.2052405691974 \tabularnewline
Trimmed Mean ( 40 / 44 ) & 32.5094339622642 & 0.706399650011663 & 46.0213053074523 \tabularnewline
Trimmed Mean ( 41 / 44 ) & 32.5098039215686 & 0.694726663145994 & 46.7951003555147 \tabularnewline
Trimmed Mean ( 42 / 44 ) & 32.4897959183673 & 0.68457398303467 & 47.4598753729178 \tabularnewline
Trimmed Mean ( 43 / 44 ) & 32.468085106383 & 0.671096872193906 & 48.3806235011057 \tabularnewline
Trimmed Mean ( 44 / 44 ) & 32.4666666666667 & 0.659507009022266 & 49.2286908592514 \tabularnewline
Median & 33 &  &  \tabularnewline
Midrange & 61.5 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 31.9718309859155 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 31.9718309859155 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 31.9718309859155 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 31.9718309859155 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 31.9718309859155 &  &  \tabularnewline
Midmean - Closest Observation & 31.9718309859155 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 31.9718309859155 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 31.9718309859155 &  &  \tabularnewline
Number of observations & 133 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=154408&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]34.8421052631579[/C][C]1.77627211915636[/C][C]19.6152970524055[/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]40.3788450530664[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 44 )[/C][C]34.5714285714286[/C][C]1.69318005693564[/C][C]20.418046166925[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 44 )[/C][C]34.5112781954887[/C][C]1.67397406515396[/C][C]20.6163756738457[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 44 )[/C][C]34.4661654135338[/C][C]1.66445109762611[/C][C]20.7072262217199[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 44 )[/C][C]34.4360902255639[/C][C]1.64765944806801[/C][C]20.9000047102831[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 44 )[/C][C]34.4736842105263[/C][C]1.62924188966481[/C][C]21.1593406904231[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 44 )[/C][C]34.4736842105263[/C][C]1.6140679016348[/C][C]21.3582614310153[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 44 )[/C][C]34.3157894736842[/C][C]1.56711217158621[/C][C]21.8974685385478[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 44 )[/C][C]34.3157894736842[/C][C]1.56711217158621[/C][C]21.8974685385478[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 44 )[/C][C]34.1804511278196[/C][C]1.50111353012041[/C][C]22.7700639838199[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 44 )[/C][C]34.1804511278196[/C][C]1.47855616803842[/C][C]23.117451921469[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 44 )[/C][C]34.0977443609023[/C][C]1.44062500129481[/C][C]23.6687162379215[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 44 )[/C][C]34.0977443609023[/C][C]1.41477188211722[/C][C]24.1012312952352[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 44 )[/C][C]34.0977443609023[/C][C]1.41477188211722[/C][C]24.1012312952352[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 44 )[/C][C]33.8872180451128[/C][C]1.35251864726453[/C][C]25.0548989573266[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 44 )[/C][C]33.8872180451128[/C][C]1.32184849785453[/C][C]25.6362344853548[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 44 )[/C][C]33.8872180451128[/C][C]1.28974318090753[/C][C]26.2743921012771[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 44 )[/C][C]33.6315789473684[/C][C]1.25281517960752[/C][C]26.8448048002616[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 44 )[/C][C]33.4962406015038[/C][C]1.23390176410897[/C][C]27.1466024085736[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 44 )[/C][C]33.4962406015038[/C][C]1.23390176410897[/C][C]27.1466024085736[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 44 )[/C][C]33.1954887218045[/C][C]1.19324724560076[/C][C]27.8194555606048[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 44 )[/C][C]32.7218045112782[/C][C]1.1329563281105[/C][C]28.8817880260665[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 44 )[/C][C]33.0526315789474[/C][C]1.09267094798846[/C][C]30.2493917677552[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 44 )[/C][C]32.8796992481203[/C][C]1.07144196207851[/C][C]30.6873357697663[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 44 )[/C][C]33.0601503759398[/C][C]1.00770326438252[/C][C]32.8074260989893[/C][/ROW]
[ROW][C]Winsorized Mean ( 25 / 44 )[/C][C]32.8721804511278[/C][C]0.985507511447275[/C][C]33.3555858979229[/C][/ROW]
[ROW][C]Winsorized Mean ( 26 / 44 )[/C][C]33.0676691729323[/C][C]0.963517439666537[/C][C]34.3197412019617[/C][/ROW]
[ROW][C]Winsorized Mean ( 27 / 44 )[/C][C]32.8646616541353[/C][C]0.940032791447212[/C][C]34.9611864108901[/C][/ROW]
[ROW][C]Winsorized Mean ( 28 / 44 )[/C][C]33.0751879699248[/C][C]0.916894422304465[/C][C]36.0730605022067[/C][/ROW]
[ROW][C]Winsorized Mean ( 29 / 44 )[/C][C]33.2932330827068[/C][C]0.893750737014657[/C][C]37.2511391642755[/C][/ROW]
[ROW][C]Winsorized Mean ( 30 / 44 )[/C][C]33.2932330827068[/C][C]0.893750737014657[/C][C]37.2511391642755[/C][/ROW]
[ROW][C]Winsorized Mean ( 31 / 44 )[/C][C]33.0601503759398[/C][C]0.867028470396206[/C][C]38.1304092134741[/C][/ROW]
[ROW][C]Winsorized Mean ( 32 / 44 )[/C][C]33.0601503759398[/C][C]0.867028470396206[/C][C]38.1304092134741[/C][/ROW]
[ROW][C]Winsorized Mean ( 33 / 44 )[/C][C]32.812030075188[/C][C]0.839348333509198[/C][C]39.0922680908956[/C][/ROW]
[ROW][C]Winsorized Mean ( 34 / 44 )[/C][C]32.812030075188[/C][C]0.839348333509198[/C][C]39.0922680908956[/C][/ROW]
[ROW][C]Winsorized Mean ( 35 / 44 )[/C][C]32.812030075188[/C][C]0.727369939214867[/C][C]45.1105115927745[/C][/ROW]
[ROW][C]Winsorized Mean ( 36 / 44 )[/C][C]32.812030075188[/C][C]0.727369939214867[/C][C]45.1105115927745[/C][/ROW]
[ROW][C]Winsorized Mean ( 37 / 44 )[/C][C]33.0902255639098[/C][C]0.699449596994009[/C][C]47.3089493597824[/C][/ROW]
[ROW][C]Winsorized Mean ( 38 / 44 )[/C][C]32.8045112781955[/C][C]0.669235650034003[/C][C]49.0178777483368[/C][/ROW]
[ROW][C]Winsorized Mean ( 39 / 44 )[/C][C]32.8045112781955[/C][C]0.669235650034003[/C][C]49.0178777483368[/C][/ROW]
[ROW][C]Winsorized Mean ( 40 / 44 )[/C][C]32.5037593984962[/C][C]0.638409826380751[/C][C]50.9136264126217[/C][/ROW]
[ROW][C]Winsorized Mean ( 41 / 44 )[/C][C]32.812030075188[/C][C]0.607835071489827[/C][C]53.9817980472309[/C][/ROW]
[ROW][C]Winsorized Mean ( 42 / 44 )[/C][C]32.812030075188[/C][C]0.607835071489827[/C][C]53.9817980472309[/C][/ROW]
[ROW][C]Winsorized Mean ( 43 / 44 )[/C][C]32.4887218045113[/C][C]0.575335750623869[/C][C]56.4691517418862[/C][/ROW]
[ROW][C]Winsorized Mean ( 44 / 44 )[/C][C]32.4887218045113[/C][C]0.575335750623869[/C][C]56.4691517418862[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 44 )[/C][C]34.4351145038168[/C][C]1.65035625743956[/C][C]20.8652612722789[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 44 )[/C][C]34.2945736434108[/C][C]1.60306464843164[/C][C]21.3931320093441[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 44 )[/C][C]34.1811023622047[/C][C]1.5620890339816[/C][C]21.8816607879774[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 44 )[/C][C]34.08[/C][C]1.5207213907837[/C][C]22.4104166657622[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 44 )[/C][C]33.9837398373984[/C][C]1.48037874325759[/C][C]22.9561117330128[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 44 )[/C][C]33.8760330578512[/C][C]1.44063281205325[/C][C]23.5146893604136[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 44 )[/C][C]33.7647058823529[/C][C]1.4000786334334[/C][C]24.1162925253362[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 44 )[/C][C]33.6752136752137[/C][C]1.36510710113092[/C][C]24.6685506560734[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 44 )[/C][C]33.5826086956522[/C][C]1.32614285060581[/C][C]25.3235227866371[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 44 )[/C][C]33.5044247787611[/C][C]1.29475040755274[/C][C]25.8771301274113[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 44 )[/C][C]33.4234234234234[/C][C]1.2635214334164[/C][C]26.4525971142815[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 44 )[/C][C]33.348623853211[/C][C]1.23471808002358[/C][C]27.0090998040413[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 44 )[/C][C]33.2710280373832[/C][C]1.20639936046835[/C][C]27.5787845448348[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 44 )[/C][C]33.1904761904762[/C][C]1.1746011120993[/C][C]28.2568063733199[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 44 )[/C][C]33.126213592233[/C][C]1.14789468780336[/C][C]28.8582340733924[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 44 )[/C][C]33.0594059405941[/C][C]1.12204037820941[/C][C]29.4636508477095[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 44 )[/C][C]32.989898989899[/C][C]1.09716515481105[/C][C]30.0683072600683[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 44 )[/C][C]32.9381443298969[/C][C]1.07402301494832[/C][C]30.6680060589594[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 44 )[/C][C]32.8947368421053[/C][C]1.05029976888812[/C][C]31.3193793015195[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 44 )[/C][C]32.8494623655914[/C][C]1.02333071824141[/C][C]32.1005338548256[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 44 )[/C][C]32.8241758241758[/C][C]0.997994742412812[/C][C]32.8901290049065[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 44 )[/C][C]32.8314606741573[/C][C]0.976777857762847[/C][C]33.6120033979399[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 44 )[/C][C]32.816091954023[/C][C]0.957466017667758[/C][C]34.2738972960712[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 44 )[/C][C]32.8117647058824[/C][C]0.937918028951779[/C][C]34.9836165774027[/C][/ROW]
[ROW][C]Trimmed Mean ( 25 / 44 )[/C][C]32.7951807228916[/C][C]0.923102613765434[/C][C]35.5271236738422[/C][/ROW]
[ROW][C]Trimmed Mean ( 26 / 44 )[/C][C]32.7901234567901[/C][C]0.908586619355144[/C][C]36.0891551320252[/C][/ROW]
[ROW][C]Trimmed Mean ( 27 / 44 )[/C][C]32.7721518987342[/C][C]0.894272838748267[/C][C]36.6467038679225[/C][/ROW]
[ROW][C]Trimmed Mean ( 28 / 44 )[/C][C]32.7662337662338[/C][C]0.880388612675568[/C][C]37.2179209209155[/C][/ROW]
[ROW][C]Trimmed Mean ( 29 / 44 )[/C][C]32.7466666666667[/C][C]0.86682465642423[/C][C]37.7777286605473[/C][/ROW]
[ROW][C]Trimmed Mean ( 30 / 44 )[/C][C]32.7123287671233[/C][C]0.853517979999361[/C][C]38.3264670852602[/C][/ROW]
[ROW][C]Trimmed Mean ( 31 / 44 )[/C][C]32.6760563380282[/C][C]0.837687400070186[/C][C]39.0074583135551[/C][/ROW]
[ROW][C]Trimmed Mean ( 32 / 44 )[/C][C]32.6521739130435[/C][C]0.82243325352469[/C][C]39.7019135268504[/C][/ROW]
[ROW][C]Trimmed Mean ( 33 / 44 )[/C][C]32.6268656716418[/C][C]0.804171569732788[/C][C]40.5720208219785[/C][/ROW]
[ROW][C]Trimmed Mean ( 34 / 44 )[/C][C]32.6153846153846[/C][C]0.786206907738127[/C][C]41.4844798415944[/C][/ROW]
[ROW][C]Trimmed Mean ( 35 / 44 )[/C][C]32.6031746031746[/C][C]0.764529741623418[/C][C]42.6447433345685[/C][/ROW]
[ROW][C]Trimmed Mean ( 36 / 44 )[/C][C]32.5901639344262[/C][C]0.754359660122313[/C][C]43.2024214141329[/C][/ROW]
[ROW][C]Trimmed Mean ( 37 / 44 )[/C][C]32.5762711864407[/C][C]0.741680287744537[/C][C]43.9222556197438[/C][/ROW]
[ROW][C]Trimmed Mean ( 38 / 44 )[/C][C]32.5438596491228[/C][C]0.729811909471982[/C][C]44.5921191840624[/C][/ROW]
[ROW][C]Trimmed Mean ( 39 / 44 )[/C][C]32.5272727272727[/C][C]0.719546502080484[/C][C]45.2052405691974[/C][/ROW]
[ROW][C]Trimmed Mean ( 40 / 44 )[/C][C]32.5094339622642[/C][C]0.706399650011663[/C][C]46.0213053074523[/C][/ROW]
[ROW][C]Trimmed Mean ( 41 / 44 )[/C][C]32.5098039215686[/C][C]0.694726663145994[/C][C]46.7951003555147[/C][/ROW]
[ROW][C]Trimmed Mean ( 42 / 44 )[/C][C]32.4897959183673[/C][C]0.68457398303467[/C][C]47.4598753729178[/C][/ROW]
[ROW][C]Trimmed Mean ( 43 / 44 )[/C][C]32.468085106383[/C][C]0.671096872193906[/C][C]48.3806235011057[/C][/ROW]
[ROW][C]Trimmed Mean ( 44 / 44 )[/C][C]32.4666666666667[/C][C]0.659507009022266[/C][C]49.2286908592514[/C][/ROW]
[ROW][C]Median[/C][C]33[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]61.5[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]31.9718309859155[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]31.9718309859155[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]31.9718309859155[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]31.9718309859155[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]31.9718309859155[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]31.9718309859155[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]31.9718309859155[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]31.9718309859155[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]133[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=154408&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=154408&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 Mean34.84210526315791.7762721191563619.6152970524055
Geometric Mean0
Harmonic Mean0
Quadratic Mean40.3788450530664
Winsorized Mean ( 1 / 44 )34.57142857142861.6931800569356420.418046166925
Winsorized Mean ( 2 / 44 )34.51127819548871.6739740651539620.6163756738457
Winsorized Mean ( 3 / 44 )34.46616541353381.6644510976261120.7072262217199
Winsorized Mean ( 4 / 44 )34.43609022556391.6476594480680120.9000047102831
Winsorized Mean ( 5 / 44 )34.47368421052631.6292418896648121.1593406904231
Winsorized Mean ( 6 / 44 )34.47368421052631.614067901634821.3582614310153
Winsorized Mean ( 7 / 44 )34.31578947368421.5671121715862121.8974685385478
Winsorized Mean ( 8 / 44 )34.31578947368421.5671121715862121.8974685385478
Winsorized Mean ( 9 / 44 )34.18045112781961.5011135301204122.7700639838199
Winsorized Mean ( 10 / 44 )34.18045112781961.4785561680384223.117451921469
Winsorized Mean ( 11 / 44 )34.09774436090231.4406250012948123.6687162379215
Winsorized Mean ( 12 / 44 )34.09774436090231.4147718821172224.1012312952352
Winsorized Mean ( 13 / 44 )34.09774436090231.4147718821172224.1012312952352
Winsorized Mean ( 14 / 44 )33.88721804511281.3525186472645325.0548989573266
Winsorized Mean ( 15 / 44 )33.88721804511281.3218484978545325.6362344853548
Winsorized Mean ( 16 / 44 )33.88721804511281.2897431809075326.2743921012771
Winsorized Mean ( 17 / 44 )33.63157894736841.2528151796075226.8448048002616
Winsorized Mean ( 18 / 44 )33.49624060150381.2339017641089727.1466024085736
Winsorized Mean ( 19 / 44 )33.49624060150381.2339017641089727.1466024085736
Winsorized Mean ( 20 / 44 )33.19548872180451.1932472456007627.8194555606048
Winsorized Mean ( 21 / 44 )32.72180451127821.132956328110528.8817880260665
Winsorized Mean ( 22 / 44 )33.05263157894741.0926709479884630.2493917677552
Winsorized Mean ( 23 / 44 )32.87969924812031.0714419620785130.6873357697663
Winsorized Mean ( 24 / 44 )33.06015037593981.0077032643825232.8074260989893
Winsorized Mean ( 25 / 44 )32.87218045112780.98550751144727533.3555858979229
Winsorized Mean ( 26 / 44 )33.06766917293230.96351743966653734.3197412019617
Winsorized Mean ( 27 / 44 )32.86466165413530.94003279144721234.9611864108901
Winsorized Mean ( 28 / 44 )33.07518796992480.91689442230446536.0730605022067
Winsorized Mean ( 29 / 44 )33.29323308270680.89375073701465737.2511391642755
Winsorized Mean ( 30 / 44 )33.29323308270680.89375073701465737.2511391642755
Winsorized Mean ( 31 / 44 )33.06015037593980.86702847039620638.1304092134741
Winsorized Mean ( 32 / 44 )33.06015037593980.86702847039620638.1304092134741
Winsorized Mean ( 33 / 44 )32.8120300751880.83934833350919839.0922680908956
Winsorized Mean ( 34 / 44 )32.8120300751880.83934833350919839.0922680908956
Winsorized Mean ( 35 / 44 )32.8120300751880.72736993921486745.1105115927745
Winsorized Mean ( 36 / 44 )32.8120300751880.72736993921486745.1105115927745
Winsorized Mean ( 37 / 44 )33.09022556390980.69944959699400947.3089493597824
Winsorized Mean ( 38 / 44 )32.80451127819550.66923565003400349.0178777483368
Winsorized Mean ( 39 / 44 )32.80451127819550.66923565003400349.0178777483368
Winsorized Mean ( 40 / 44 )32.50375939849620.63840982638075150.9136264126217
Winsorized Mean ( 41 / 44 )32.8120300751880.60783507148982753.9817980472309
Winsorized Mean ( 42 / 44 )32.8120300751880.60783507148982753.9817980472309
Winsorized Mean ( 43 / 44 )32.48872180451130.57533575062386956.4691517418862
Winsorized Mean ( 44 / 44 )32.48872180451130.57533575062386956.4691517418862
Trimmed Mean ( 1 / 44 )34.43511450381681.6503562574395620.8652612722789
Trimmed Mean ( 2 / 44 )34.29457364341081.6030646484316421.3931320093441
Trimmed Mean ( 3 / 44 )34.18110236220471.562089033981621.8816607879774
Trimmed Mean ( 4 / 44 )34.081.520721390783722.4104166657622
Trimmed Mean ( 5 / 44 )33.98373983739841.4803787432575922.9561117330128
Trimmed Mean ( 6 / 44 )33.87603305785121.4406328120532523.5146893604136
Trimmed Mean ( 7 / 44 )33.76470588235291.400078633433424.1162925253362
Trimmed Mean ( 8 / 44 )33.67521367521371.3651071011309224.6685506560734
Trimmed Mean ( 9 / 44 )33.58260869565221.3261428506058125.3235227866371
Trimmed Mean ( 10 / 44 )33.50442477876111.2947504075527425.8771301274113
Trimmed Mean ( 11 / 44 )33.42342342342341.263521433416426.4525971142815
Trimmed Mean ( 12 / 44 )33.3486238532111.2347180800235827.0090998040413
Trimmed Mean ( 13 / 44 )33.27102803738321.2063993604683527.5787845448348
Trimmed Mean ( 14 / 44 )33.19047619047621.174601112099328.2568063733199
Trimmed Mean ( 15 / 44 )33.1262135922331.1478946878033628.8582340733924
Trimmed Mean ( 16 / 44 )33.05940594059411.1220403782094129.4636508477095
Trimmed Mean ( 17 / 44 )32.9898989898991.0971651548110530.0683072600683
Trimmed Mean ( 18 / 44 )32.93814432989691.0740230149483230.6680060589594
Trimmed Mean ( 19 / 44 )32.89473684210531.0502997688881231.3193793015195
Trimmed Mean ( 20 / 44 )32.84946236559141.0233307182414132.1005338548256
Trimmed Mean ( 21 / 44 )32.82417582417580.99799474241281232.8901290049065
Trimmed Mean ( 22 / 44 )32.83146067415730.97677785776284733.6120033979399
Trimmed Mean ( 23 / 44 )32.8160919540230.95746601766775834.2738972960712
Trimmed Mean ( 24 / 44 )32.81176470588240.93791802895177934.9836165774027
Trimmed Mean ( 25 / 44 )32.79518072289160.92310261376543435.5271236738422
Trimmed Mean ( 26 / 44 )32.79012345679010.90858661935514436.0891551320252
Trimmed Mean ( 27 / 44 )32.77215189873420.89427283874826736.6467038679225
Trimmed Mean ( 28 / 44 )32.76623376623380.88038861267556837.2179209209155
Trimmed Mean ( 29 / 44 )32.74666666666670.8668246564242337.7777286605473
Trimmed Mean ( 30 / 44 )32.71232876712330.85351797999936138.3264670852602
Trimmed Mean ( 31 / 44 )32.67605633802820.83768740007018639.0074583135551
Trimmed Mean ( 32 / 44 )32.65217391304350.8224332535246939.7019135268504
Trimmed Mean ( 33 / 44 )32.62686567164180.80417156973278840.5720208219785
Trimmed Mean ( 34 / 44 )32.61538461538460.78620690773812741.4844798415944
Trimmed Mean ( 35 / 44 )32.60317460317460.76452974162341842.6447433345685
Trimmed Mean ( 36 / 44 )32.59016393442620.75435966012231343.2024214141329
Trimmed Mean ( 37 / 44 )32.57627118644070.74168028774453743.9222556197438
Trimmed Mean ( 38 / 44 )32.54385964912280.72981190947198244.5921191840624
Trimmed Mean ( 39 / 44 )32.52727272727270.71954650208048445.2052405691974
Trimmed Mean ( 40 / 44 )32.50943396226420.70639965001166346.0213053074523
Trimmed Mean ( 41 / 44 )32.50980392156860.69472666314599446.7951003555147
Trimmed Mean ( 42 / 44 )32.48979591836730.6845739830346747.4598753729178
Trimmed Mean ( 43 / 44 )32.4680851063830.67109687219390648.3806235011057
Trimmed Mean ( 44 / 44 )32.46666666666670.65950700902226649.2286908592514
Median33
Midrange61.5
Midmean - Weighted Average at Xnp31.9718309859155
Midmean - Weighted Average at X(n+1)p31.9718309859155
Midmean - Empirical Distribution Function31.9718309859155
Midmean - Empirical Distribution Function - Averaging31.9718309859155
Midmean - Empirical Distribution Function - Interpolation31.9718309859155
Midmean - Closest Observation31.9718309859155
Midmean - True Basic - Statistics Graphics Toolkit31.9718309859155
Midmean - MS Excel (old versions)31.9718309859155
Number of observations133



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')