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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, 15 Nov 2010 15:51:43 +0000
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2010/Nov/15/t1289836235hd07d5mdtijkw78.htm/, Retrieved Sun, 28 Apr 2024 15:27:23 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=94888, Retrieved Sun, 28 Apr 2024 15:27:23 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact134
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Central Tendency] [Arabica Price in ...] [2008-01-06 21:28:17] [74be16979710d4c4e7c6647856088456]
-  M D    [Central Tendency] [Mini tutorial Uni...] [2010-11-15 15:51:43] [628a2d48b4bd249e4129ba023c5511b0] [Current]
-    D      [Central Tendency] [W6] [2010-11-16 13:47:51] [5ddc7dfb25e070b079c4c8fcccc4d42e]
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Dataseries X:
43
30
30
54
30
16
42
0
30
44
70
30
5
30
62
91
41
73
60
20
4
60
62
60
76
65
60
88
16
65
35
70
21
60
100
65
80
65
60
31
55
74
32
10
20
40
55
70
80
50
55
29
70
50
60
60
27
38
70
15
40
37
10
75
60
55
91
29
50
10
57
45
70
38
70
40
61
15
25
54
36
50
68
14
68
100
74
59
50
60
60
70
45
60
21
0
65
33
70
20
60
65
60
53
71
32
70
60
60
50
25
20
80
53
39
53
39
70
60
77
80
50
69
70
36
30
57
80
91
8
60
63
60
18
39
41
50
65
80
68
58
30
60
100




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

\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 & 'RServer@AstonUniversity' @ vre.aston.ac.uk \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=94888&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]'RServer@AstonUniversity' @ vre.aston.ac.uk[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=94888&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=94888&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'RServer@AstonUniversity' @ vre.aston.ac.uk







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean50.82638888888891.862799072036727.2849550184269
Geometric Mean0
Harmonic Mean0
Quadratic Mean55.4935556819188
Winsorized Mean ( 1 / 48 )50.82638888888891.862799072036727.2849550184269
Winsorized Mean ( 2 / 48 )50.88194444444441.8525821593983627.465418570677
Winsorized Mean ( 3 / 48 )50.71527777777781.8169607767111827.9121478172886
Winsorized Mean ( 4 / 48 )50.79861111111111.8027104436862228.1790185933783
Winsorized Mean ( 5 / 48 )50.86805555555561.79140567101528.3956093131792
Winsorized Mean ( 6 / 48 )50.74305555555561.7724239470276528.6291863978997
Winsorized Mean ( 7 / 48 )50.35416666666671.7203326311757629.2700177594447
Winsorized Mean ( 8 / 48 )50.57638888888891.6852282216378230.0115961977751
Winsorized Mean ( 9 / 48 )50.63888888888891.6758375630108730.2170628028586
Winsorized Mean ( 10 / 48 )50.63888888888891.6758375630108730.2170628028586
Winsorized Mean ( 11 / 48 )50.71527777777781.6645867906509430.4671874501332
Winsorized Mean ( 12 / 48 )50.71527777777781.6645867906509430.4671874501332
Winsorized Mean ( 13 / 48 )50.6251.6063646658783431.5152599377669
Winsorized Mean ( 14 / 48 )50.72222222222221.5681688368349132.3448732246182
Winsorized Mean ( 15 / 48 )50.61805555555561.5565922589875232.5185065409999
Winsorized Mean ( 16 / 48 )50.50694444444441.5445972123958332.6991037139728
Winsorized Mean ( 17 / 48 )50.50694444444441.5445972123958332.6991037139728
Winsorized Mean ( 18 / 48 )50.50694444444441.5143061797019933.3531917926824
Winsorized Mean ( 19 / 48 )50.24305555555561.4877199525855233.7718503191663
Winsorized Mean ( 20 / 48 )50.65972222222221.4003816216764336.1756548629768
Winsorized Mean ( 21 / 48 )50.65972222222221.4003816216764336.1756548629768
Winsorized Mean ( 22 / 48 )50.96527777777781.3619957274319137.4195577499164
Winsorized Mean ( 23 / 48 )51.28472222222221.3235239096729438.7486178733977
Winsorized Mean ( 24 / 48 )51.28472222222221.3235239096729438.7486178733977
Winsorized Mean ( 25 / 48 )51.45833333333331.3033068261095239.4829001908481
Winsorized Mean ( 26 / 48 )51.45833333333331.3033068261095239.4829001908481
Winsorized Mean ( 27 / 48 )51.45833333333331.3033068261095239.4829001908481
Winsorized Mean ( 28 / 48 )51.45833333333331.3033068261095239.4829001908481
Winsorized Mean ( 29 / 48 )51.45833333333331.3033068261095239.4829001908481
Winsorized Mean ( 30 / 48 )51.45833333333331.3033068261095239.4829001908481
Winsorized Mean ( 31 / 48 )51.45833333333331.3033068261095239.4829001908481
Winsorized Mean ( 32 / 48 )51.23611111111111.2814795328960439.9819972117085
Winsorized Mean ( 33 / 48 )51.23611111111111.2330429519836641.5525761115497
Winsorized Mean ( 34 / 48 )51.47222222222221.2061639333018142.6743171480178
Winsorized Mean ( 35 / 48 )51.47222222222221.2061639333018142.6743171480178
Winsorized Mean ( 36 / 48 )50.97222222222221.1086535564726145.9766912076661
Winsorized Mean ( 37 / 48 )51.48611111111111.0513240491513248.9726370786184
Winsorized Mean ( 38 / 48 )51.751.0226409356633850.6042719348311
Winsorized Mean ( 39 / 48 )51.751.0226409356633850.6042719348311
Winsorized Mean ( 40 / 48 )52.02777777777780.99297965244775152.395613192603
Winsorized Mean ( 41 / 48 )52.31250.96311484514254854.315952312268
Winsorized Mean ( 42 / 48 )52.31250.96311484514254854.315952312268
Winsorized Mean ( 43 / 48 )52.01388888888890.87844040645863659.211630642742
Winsorized Mean ( 44 / 48 )51.70833333333330.8521691208716860.6784874819697
Winsorized Mean ( 45 / 48 )51.70833333333330.8521691208716860.6784874819697
Winsorized Mean ( 46 / 48 )51.70833333333330.79240243076142365.2551422433757
Winsorized Mean ( 47 / 48 )51.38194444444440.76617475146611767.0629570422704
Winsorized Mean ( 48 / 48 )51.38194444444440.76617475146611767.0629570422704
Trimmed Mean ( 1 / 48 )50.83802816901411.8218158025152427.9051417266367
Trimmed Mean ( 2 / 48 )50.851.7770353326493228.6150753818663
Trimmed Mean ( 3 / 48 )50.83333333333331.733930415759429.3168242919771
Trimmed Mean ( 4 / 48 )50.8751.7010645615912229.9077419803574
Trimmed Mean ( 5 / 48 )50.89552238805971.6695759514871930.4841012729754
Trimmed Mean ( 6 / 48 )50.90151515151511.6380445344638831.0745612103733
Trimmed Mean ( 7 / 48 )50.93076923076921.6077550751956431.6781890578524
Trimmed Mean ( 8 / 48 )51.02343751.5847709990897332.1960949116984
Trimmed Mean ( 9 / 48 )51.08730158730161.5658263132722832.626416579077
Trimmed Mean ( 10 / 48 )51.14516129032261.5464947950487633.0716672659153
Trimmed Mean ( 11 / 48 )51.20491803278691.5251554821154433.5735724214584
Trimmed Mean ( 12 / 48 )51.25833333333331.5032409354427134.0985480935148
Trimmed Mean ( 13 / 48 )51.31355932203391.4789899079086234.6950030204022
Trimmed Mean ( 14 / 48 )51.37931034482761.4598399602378735.1951664184173
Trimmed Mean ( 15 / 48 )51.43859649122811.443391005493635.6373264731807
Trimmed Mean ( 16 / 48 )51.50892857142861.4263896527230836.1114008876146
Trimmed Mean ( 17 / 48 )51.59090909090911.4087357296719236.6221343040145
Trimmed Mean ( 18 / 48 )51.67592592592591.3889509043498637.2050054210622
Trimmed Mean ( 19 / 48 )51.76415094339621.3702362967231537.7775359382811
Trimmed Mean ( 20 / 48 )51.8751.351960895747238.3701926314442
Trimmed Mean ( 21 / 48 )51.96078431372551.3410706560393838.7457469744231
Trimmed Mean ( 22 / 48 )52.051.3285805442750839.1771505493484
Trimmed Mean ( 23 / 48 )52.12244897959181.3184560609383139.5329435115932
Trimmed Mean ( 24 / 48 )52.17708333333331.3108015151835939.8054798754374
Trimmed Mean ( 25 / 48 )52.23404255319151.3017969324132940.1245703170918
Trimmed Mean ( 26 / 48 )52.28260869565221.2933663383505640.4236658596887
Trimmed Mean ( 27 / 48 )52.33333333333331.283429394721840.7761685594535
Trimmed Mean ( 28 / 48 )52.38636363636361.271772947928241.1916008448713
Trimmed Mean ( 29 / 48 )52.44186046511631.2581449714273741.6818901287827
Trimmed Mean ( 30 / 48 )52.51.2422450204219242.2621939608732
Trimmed Mean ( 31 / 48 )52.56097560975611.2237115293027242.9520964305255
Trimmed Mean ( 32 / 48 )52.6251.2021045627343943.7773897807156
Trimmed Mean ( 33 / 48 )52.70512820512821.179256409398444.6935270269302
Trimmed Mean ( 34 / 48 )52.78947368421051.158237588794345.5774136454709
Trimmed Mean ( 35 / 48 )52.86486486486491.1369275881667546.4980051632904
Trimmed Mean ( 36 / 48 )52.94444444444441.1116978106738447.6248526677885
Trimmed Mean ( 37 / 48 )53.05714285714291.0933424949659848.5274679265017
Trimmed Mean ( 38 / 48 )53.14705882352941.0790251644329449.2546981992399
Trimmed Mean ( 39 / 48 )53.22727272727271.065412021713649.9593318288846
Trimmed Mean ( 40 / 48 )53.31251.0486373906094250.8397854944094
Trimmed Mean ( 41 / 48 )53.38709677419361.0323572136412951.7137828541816
Trimmed Mean ( 42 / 48 )53.451.0166481428339352.5747284119428
Trimmed Mean ( 43 / 48 )53.51724137931030.99704383966582753.6759159930695
Trimmed Mean ( 44 / 48 )53.60714285714290.98451602304327354.4502492620038
Trimmed Mean ( 45 / 48 )53.72222222222220.97143574058705255.3018794529396
Trimmed Mean ( 46 / 48 )53.84615384615380.95422558502041556.4291659031568
Trimmed Mean ( 47 / 48 )53.980.94133643598571457.3440036276459
Trimmed Mean ( 48 / 48 )54.14583333333330.92684050330028258.4197962222535
Median55
Midrange50
Midmean - Weighted Average at Xnp52.3783783783784
Midmean - Weighted Average at X(n+1)p52.9444444444444
Midmean - Empirical Distribution Function52.3783783783784
Midmean - Empirical Distribution Function - Averaging52.9444444444444
Midmean - Empirical Distribution Function - Interpolation52.9444444444444
Midmean - Closest Observation52.3783783783784
Midmean - True Basic - Statistics Graphics Toolkit52.9444444444444
Midmean - MS Excel (old versions)52.987012987013
Number of observations144

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 50.8263888888889 & 1.8627990720367 & 27.2849550184269 \tabularnewline
Geometric Mean & 0 &  &  \tabularnewline
Harmonic Mean & 0 &  &  \tabularnewline
Quadratic Mean & 55.4935556819188 &  &  \tabularnewline
Winsorized Mean ( 1 / 48 ) & 50.8263888888889 & 1.8627990720367 & 27.2849550184269 \tabularnewline
Winsorized Mean ( 2 / 48 ) & 50.8819444444444 & 1.85258215939836 & 27.465418570677 \tabularnewline
Winsorized Mean ( 3 / 48 ) & 50.7152777777778 & 1.81696077671118 & 27.9121478172886 \tabularnewline
Winsorized Mean ( 4 / 48 ) & 50.7986111111111 & 1.80271044368622 & 28.1790185933783 \tabularnewline
Winsorized Mean ( 5 / 48 ) & 50.8680555555556 & 1.791405671015 & 28.3956093131792 \tabularnewline
Winsorized Mean ( 6 / 48 ) & 50.7430555555556 & 1.77242394702765 & 28.6291863978997 \tabularnewline
Winsorized Mean ( 7 / 48 ) & 50.3541666666667 & 1.72033263117576 & 29.2700177594447 \tabularnewline
Winsorized Mean ( 8 / 48 ) & 50.5763888888889 & 1.68522822163782 & 30.0115961977751 \tabularnewline
Winsorized Mean ( 9 / 48 ) & 50.6388888888889 & 1.67583756301087 & 30.2170628028586 \tabularnewline
Winsorized Mean ( 10 / 48 ) & 50.6388888888889 & 1.67583756301087 & 30.2170628028586 \tabularnewline
Winsorized Mean ( 11 / 48 ) & 50.7152777777778 & 1.66458679065094 & 30.4671874501332 \tabularnewline
Winsorized Mean ( 12 / 48 ) & 50.7152777777778 & 1.66458679065094 & 30.4671874501332 \tabularnewline
Winsorized Mean ( 13 / 48 ) & 50.625 & 1.60636466587834 & 31.5152599377669 \tabularnewline
Winsorized Mean ( 14 / 48 ) & 50.7222222222222 & 1.56816883683491 & 32.3448732246182 \tabularnewline
Winsorized Mean ( 15 / 48 ) & 50.6180555555556 & 1.55659225898752 & 32.5185065409999 \tabularnewline
Winsorized Mean ( 16 / 48 ) & 50.5069444444444 & 1.54459721239583 & 32.6991037139728 \tabularnewline
Winsorized Mean ( 17 / 48 ) & 50.5069444444444 & 1.54459721239583 & 32.6991037139728 \tabularnewline
Winsorized Mean ( 18 / 48 ) & 50.5069444444444 & 1.51430617970199 & 33.3531917926824 \tabularnewline
Winsorized Mean ( 19 / 48 ) & 50.2430555555556 & 1.48771995258552 & 33.7718503191663 \tabularnewline
Winsorized Mean ( 20 / 48 ) & 50.6597222222222 & 1.40038162167643 & 36.1756548629768 \tabularnewline
Winsorized Mean ( 21 / 48 ) & 50.6597222222222 & 1.40038162167643 & 36.1756548629768 \tabularnewline
Winsorized Mean ( 22 / 48 ) & 50.9652777777778 & 1.36199572743191 & 37.4195577499164 \tabularnewline
Winsorized Mean ( 23 / 48 ) & 51.2847222222222 & 1.32352390967294 & 38.7486178733977 \tabularnewline
Winsorized Mean ( 24 / 48 ) & 51.2847222222222 & 1.32352390967294 & 38.7486178733977 \tabularnewline
Winsorized Mean ( 25 / 48 ) & 51.4583333333333 & 1.30330682610952 & 39.4829001908481 \tabularnewline
Winsorized Mean ( 26 / 48 ) & 51.4583333333333 & 1.30330682610952 & 39.4829001908481 \tabularnewline
Winsorized Mean ( 27 / 48 ) & 51.4583333333333 & 1.30330682610952 & 39.4829001908481 \tabularnewline
Winsorized Mean ( 28 / 48 ) & 51.4583333333333 & 1.30330682610952 & 39.4829001908481 \tabularnewline
Winsorized Mean ( 29 / 48 ) & 51.4583333333333 & 1.30330682610952 & 39.4829001908481 \tabularnewline
Winsorized Mean ( 30 / 48 ) & 51.4583333333333 & 1.30330682610952 & 39.4829001908481 \tabularnewline
Winsorized Mean ( 31 / 48 ) & 51.4583333333333 & 1.30330682610952 & 39.4829001908481 \tabularnewline
Winsorized Mean ( 32 / 48 ) & 51.2361111111111 & 1.28147953289604 & 39.9819972117085 \tabularnewline
Winsorized Mean ( 33 / 48 ) & 51.2361111111111 & 1.23304295198366 & 41.5525761115497 \tabularnewline
Winsorized Mean ( 34 / 48 ) & 51.4722222222222 & 1.20616393330181 & 42.6743171480178 \tabularnewline
Winsorized Mean ( 35 / 48 ) & 51.4722222222222 & 1.20616393330181 & 42.6743171480178 \tabularnewline
Winsorized Mean ( 36 / 48 ) & 50.9722222222222 & 1.10865355647261 & 45.9766912076661 \tabularnewline
Winsorized Mean ( 37 / 48 ) & 51.4861111111111 & 1.05132404915132 & 48.9726370786184 \tabularnewline
Winsorized Mean ( 38 / 48 ) & 51.75 & 1.02264093566338 & 50.6042719348311 \tabularnewline
Winsorized Mean ( 39 / 48 ) & 51.75 & 1.02264093566338 & 50.6042719348311 \tabularnewline
Winsorized Mean ( 40 / 48 ) & 52.0277777777778 & 0.992979652447751 & 52.395613192603 \tabularnewline
Winsorized Mean ( 41 / 48 ) & 52.3125 & 0.963114845142548 & 54.315952312268 \tabularnewline
Winsorized Mean ( 42 / 48 ) & 52.3125 & 0.963114845142548 & 54.315952312268 \tabularnewline
Winsorized Mean ( 43 / 48 ) & 52.0138888888889 & 0.878440406458636 & 59.211630642742 \tabularnewline
Winsorized Mean ( 44 / 48 ) & 51.7083333333333 & 0.85216912087168 & 60.6784874819697 \tabularnewline
Winsorized Mean ( 45 / 48 ) & 51.7083333333333 & 0.85216912087168 & 60.6784874819697 \tabularnewline
Winsorized Mean ( 46 / 48 ) & 51.7083333333333 & 0.792402430761423 & 65.2551422433757 \tabularnewline
Winsorized Mean ( 47 / 48 ) & 51.3819444444444 & 0.766174751466117 & 67.0629570422704 \tabularnewline
Winsorized Mean ( 48 / 48 ) & 51.3819444444444 & 0.766174751466117 & 67.0629570422704 \tabularnewline
Trimmed Mean ( 1 / 48 ) & 50.8380281690141 & 1.82181580251524 & 27.9051417266367 \tabularnewline
Trimmed Mean ( 2 / 48 ) & 50.85 & 1.77703533264932 & 28.6150753818663 \tabularnewline
Trimmed Mean ( 3 / 48 ) & 50.8333333333333 & 1.7339304157594 & 29.3168242919771 \tabularnewline
Trimmed Mean ( 4 / 48 ) & 50.875 & 1.70106456159122 & 29.9077419803574 \tabularnewline
Trimmed Mean ( 5 / 48 ) & 50.8955223880597 & 1.66957595148719 & 30.4841012729754 \tabularnewline
Trimmed Mean ( 6 / 48 ) & 50.9015151515151 & 1.63804453446388 & 31.0745612103733 \tabularnewline
Trimmed Mean ( 7 / 48 ) & 50.9307692307692 & 1.60775507519564 & 31.6781890578524 \tabularnewline
Trimmed Mean ( 8 / 48 ) & 51.0234375 & 1.58477099908973 & 32.1960949116984 \tabularnewline
Trimmed Mean ( 9 / 48 ) & 51.0873015873016 & 1.56582631327228 & 32.626416579077 \tabularnewline
Trimmed Mean ( 10 / 48 ) & 51.1451612903226 & 1.54649479504876 & 33.0716672659153 \tabularnewline
Trimmed Mean ( 11 / 48 ) & 51.2049180327869 & 1.52515548211544 & 33.5735724214584 \tabularnewline
Trimmed Mean ( 12 / 48 ) & 51.2583333333333 & 1.50324093544271 & 34.0985480935148 \tabularnewline
Trimmed Mean ( 13 / 48 ) & 51.3135593220339 & 1.47898990790862 & 34.6950030204022 \tabularnewline
Trimmed Mean ( 14 / 48 ) & 51.3793103448276 & 1.45983996023787 & 35.1951664184173 \tabularnewline
Trimmed Mean ( 15 / 48 ) & 51.4385964912281 & 1.4433910054936 & 35.6373264731807 \tabularnewline
Trimmed Mean ( 16 / 48 ) & 51.5089285714286 & 1.42638965272308 & 36.1114008876146 \tabularnewline
Trimmed Mean ( 17 / 48 ) & 51.5909090909091 & 1.40873572967192 & 36.6221343040145 \tabularnewline
Trimmed Mean ( 18 / 48 ) & 51.6759259259259 & 1.38895090434986 & 37.2050054210622 \tabularnewline
Trimmed Mean ( 19 / 48 ) & 51.7641509433962 & 1.37023629672315 & 37.7775359382811 \tabularnewline
Trimmed Mean ( 20 / 48 ) & 51.875 & 1.3519608957472 & 38.3701926314442 \tabularnewline
Trimmed Mean ( 21 / 48 ) & 51.9607843137255 & 1.34107065603938 & 38.7457469744231 \tabularnewline
Trimmed Mean ( 22 / 48 ) & 52.05 & 1.32858054427508 & 39.1771505493484 \tabularnewline
Trimmed Mean ( 23 / 48 ) & 52.1224489795918 & 1.31845606093831 & 39.5329435115932 \tabularnewline
Trimmed Mean ( 24 / 48 ) & 52.1770833333333 & 1.31080151518359 & 39.8054798754374 \tabularnewline
Trimmed Mean ( 25 / 48 ) & 52.2340425531915 & 1.30179693241329 & 40.1245703170918 \tabularnewline
Trimmed Mean ( 26 / 48 ) & 52.2826086956522 & 1.29336633835056 & 40.4236658596887 \tabularnewline
Trimmed Mean ( 27 / 48 ) & 52.3333333333333 & 1.2834293947218 & 40.7761685594535 \tabularnewline
Trimmed Mean ( 28 / 48 ) & 52.3863636363636 & 1.2717729479282 & 41.1916008448713 \tabularnewline
Trimmed Mean ( 29 / 48 ) & 52.4418604651163 & 1.25814497142737 & 41.6818901287827 \tabularnewline
Trimmed Mean ( 30 / 48 ) & 52.5 & 1.24224502042192 & 42.2621939608732 \tabularnewline
Trimmed Mean ( 31 / 48 ) & 52.5609756097561 & 1.22371152930272 & 42.9520964305255 \tabularnewline
Trimmed Mean ( 32 / 48 ) & 52.625 & 1.20210456273439 & 43.7773897807156 \tabularnewline
Trimmed Mean ( 33 / 48 ) & 52.7051282051282 & 1.1792564093984 & 44.6935270269302 \tabularnewline
Trimmed Mean ( 34 / 48 ) & 52.7894736842105 & 1.1582375887943 & 45.5774136454709 \tabularnewline
Trimmed Mean ( 35 / 48 ) & 52.8648648648649 & 1.13692758816675 & 46.4980051632904 \tabularnewline
Trimmed Mean ( 36 / 48 ) & 52.9444444444444 & 1.11169781067384 & 47.6248526677885 \tabularnewline
Trimmed Mean ( 37 / 48 ) & 53.0571428571429 & 1.09334249496598 & 48.5274679265017 \tabularnewline
Trimmed Mean ( 38 / 48 ) & 53.1470588235294 & 1.07902516443294 & 49.2546981992399 \tabularnewline
Trimmed Mean ( 39 / 48 ) & 53.2272727272727 & 1.0654120217136 & 49.9593318288846 \tabularnewline
Trimmed Mean ( 40 / 48 ) & 53.3125 & 1.04863739060942 & 50.8397854944094 \tabularnewline
Trimmed Mean ( 41 / 48 ) & 53.3870967741936 & 1.03235721364129 & 51.7137828541816 \tabularnewline
Trimmed Mean ( 42 / 48 ) & 53.45 & 1.01664814283393 & 52.5747284119428 \tabularnewline
Trimmed Mean ( 43 / 48 ) & 53.5172413793103 & 0.997043839665827 & 53.6759159930695 \tabularnewline
Trimmed Mean ( 44 / 48 ) & 53.6071428571429 & 0.984516023043273 & 54.4502492620038 \tabularnewline
Trimmed Mean ( 45 / 48 ) & 53.7222222222222 & 0.971435740587052 & 55.3018794529396 \tabularnewline
Trimmed Mean ( 46 / 48 ) & 53.8461538461538 & 0.954225585020415 & 56.4291659031568 \tabularnewline
Trimmed Mean ( 47 / 48 ) & 53.98 & 0.941336435985714 & 57.3440036276459 \tabularnewline
Trimmed Mean ( 48 / 48 ) & 54.1458333333333 & 0.926840503300282 & 58.4197962222535 \tabularnewline
Median & 55 &  &  \tabularnewline
Midrange & 50 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 52.3783783783784 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 52.9444444444444 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 52.3783783783784 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 52.9444444444444 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 52.9444444444444 &  &  \tabularnewline
Midmean - Closest Observation & 52.3783783783784 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 52.9444444444444 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 52.987012987013 &  &  \tabularnewline
Number of observations & 144 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=94888&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]50.8263888888889[/C][C]1.8627990720367[/C][C]27.2849550184269[/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]55.4935556819188[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 48 )[/C][C]50.8263888888889[/C][C]1.8627990720367[/C][C]27.2849550184269[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 48 )[/C][C]50.8819444444444[/C][C]1.85258215939836[/C][C]27.465418570677[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 48 )[/C][C]50.7152777777778[/C][C]1.81696077671118[/C][C]27.9121478172886[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 48 )[/C][C]50.7986111111111[/C][C]1.80271044368622[/C][C]28.1790185933783[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 48 )[/C][C]50.8680555555556[/C][C]1.791405671015[/C][C]28.3956093131792[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 48 )[/C][C]50.7430555555556[/C][C]1.77242394702765[/C][C]28.6291863978997[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 48 )[/C][C]50.3541666666667[/C][C]1.72033263117576[/C][C]29.2700177594447[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 48 )[/C][C]50.5763888888889[/C][C]1.68522822163782[/C][C]30.0115961977751[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 48 )[/C][C]50.6388888888889[/C][C]1.67583756301087[/C][C]30.2170628028586[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 48 )[/C][C]50.6388888888889[/C][C]1.67583756301087[/C][C]30.2170628028586[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 48 )[/C][C]50.7152777777778[/C][C]1.66458679065094[/C][C]30.4671874501332[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 48 )[/C][C]50.7152777777778[/C][C]1.66458679065094[/C][C]30.4671874501332[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 48 )[/C][C]50.625[/C][C]1.60636466587834[/C][C]31.5152599377669[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 48 )[/C][C]50.7222222222222[/C][C]1.56816883683491[/C][C]32.3448732246182[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 48 )[/C][C]50.6180555555556[/C][C]1.55659225898752[/C][C]32.5185065409999[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 48 )[/C][C]50.5069444444444[/C][C]1.54459721239583[/C][C]32.6991037139728[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 48 )[/C][C]50.5069444444444[/C][C]1.54459721239583[/C][C]32.6991037139728[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 48 )[/C][C]50.5069444444444[/C][C]1.51430617970199[/C][C]33.3531917926824[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 48 )[/C][C]50.2430555555556[/C][C]1.48771995258552[/C][C]33.7718503191663[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 48 )[/C][C]50.6597222222222[/C][C]1.40038162167643[/C][C]36.1756548629768[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 48 )[/C][C]50.6597222222222[/C][C]1.40038162167643[/C][C]36.1756548629768[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 48 )[/C][C]50.9652777777778[/C][C]1.36199572743191[/C][C]37.4195577499164[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 48 )[/C][C]51.2847222222222[/C][C]1.32352390967294[/C][C]38.7486178733977[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 48 )[/C][C]51.2847222222222[/C][C]1.32352390967294[/C][C]38.7486178733977[/C][/ROW]
[ROW][C]Winsorized Mean ( 25 / 48 )[/C][C]51.4583333333333[/C][C]1.30330682610952[/C][C]39.4829001908481[/C][/ROW]
[ROW][C]Winsorized Mean ( 26 / 48 )[/C][C]51.4583333333333[/C][C]1.30330682610952[/C][C]39.4829001908481[/C][/ROW]
[ROW][C]Winsorized Mean ( 27 / 48 )[/C][C]51.4583333333333[/C][C]1.30330682610952[/C][C]39.4829001908481[/C][/ROW]
[ROW][C]Winsorized Mean ( 28 / 48 )[/C][C]51.4583333333333[/C][C]1.30330682610952[/C][C]39.4829001908481[/C][/ROW]
[ROW][C]Winsorized Mean ( 29 / 48 )[/C][C]51.4583333333333[/C][C]1.30330682610952[/C][C]39.4829001908481[/C][/ROW]
[ROW][C]Winsorized Mean ( 30 / 48 )[/C][C]51.4583333333333[/C][C]1.30330682610952[/C][C]39.4829001908481[/C][/ROW]
[ROW][C]Winsorized Mean ( 31 / 48 )[/C][C]51.4583333333333[/C][C]1.30330682610952[/C][C]39.4829001908481[/C][/ROW]
[ROW][C]Winsorized Mean ( 32 / 48 )[/C][C]51.2361111111111[/C][C]1.28147953289604[/C][C]39.9819972117085[/C][/ROW]
[ROW][C]Winsorized Mean ( 33 / 48 )[/C][C]51.2361111111111[/C][C]1.23304295198366[/C][C]41.5525761115497[/C][/ROW]
[ROW][C]Winsorized Mean ( 34 / 48 )[/C][C]51.4722222222222[/C][C]1.20616393330181[/C][C]42.6743171480178[/C][/ROW]
[ROW][C]Winsorized Mean ( 35 / 48 )[/C][C]51.4722222222222[/C][C]1.20616393330181[/C][C]42.6743171480178[/C][/ROW]
[ROW][C]Winsorized Mean ( 36 / 48 )[/C][C]50.9722222222222[/C][C]1.10865355647261[/C][C]45.9766912076661[/C][/ROW]
[ROW][C]Winsorized Mean ( 37 / 48 )[/C][C]51.4861111111111[/C][C]1.05132404915132[/C][C]48.9726370786184[/C][/ROW]
[ROW][C]Winsorized Mean ( 38 / 48 )[/C][C]51.75[/C][C]1.02264093566338[/C][C]50.6042719348311[/C][/ROW]
[ROW][C]Winsorized Mean ( 39 / 48 )[/C][C]51.75[/C][C]1.02264093566338[/C][C]50.6042719348311[/C][/ROW]
[ROW][C]Winsorized Mean ( 40 / 48 )[/C][C]52.0277777777778[/C][C]0.992979652447751[/C][C]52.395613192603[/C][/ROW]
[ROW][C]Winsorized Mean ( 41 / 48 )[/C][C]52.3125[/C][C]0.963114845142548[/C][C]54.315952312268[/C][/ROW]
[ROW][C]Winsorized Mean ( 42 / 48 )[/C][C]52.3125[/C][C]0.963114845142548[/C][C]54.315952312268[/C][/ROW]
[ROW][C]Winsorized Mean ( 43 / 48 )[/C][C]52.0138888888889[/C][C]0.878440406458636[/C][C]59.211630642742[/C][/ROW]
[ROW][C]Winsorized Mean ( 44 / 48 )[/C][C]51.7083333333333[/C][C]0.85216912087168[/C][C]60.6784874819697[/C][/ROW]
[ROW][C]Winsorized Mean ( 45 / 48 )[/C][C]51.7083333333333[/C][C]0.85216912087168[/C][C]60.6784874819697[/C][/ROW]
[ROW][C]Winsorized Mean ( 46 / 48 )[/C][C]51.7083333333333[/C][C]0.792402430761423[/C][C]65.2551422433757[/C][/ROW]
[ROW][C]Winsorized Mean ( 47 / 48 )[/C][C]51.3819444444444[/C][C]0.766174751466117[/C][C]67.0629570422704[/C][/ROW]
[ROW][C]Winsorized Mean ( 48 / 48 )[/C][C]51.3819444444444[/C][C]0.766174751466117[/C][C]67.0629570422704[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 48 )[/C][C]50.8380281690141[/C][C]1.82181580251524[/C][C]27.9051417266367[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 48 )[/C][C]50.85[/C][C]1.77703533264932[/C][C]28.6150753818663[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 48 )[/C][C]50.8333333333333[/C][C]1.7339304157594[/C][C]29.3168242919771[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 48 )[/C][C]50.875[/C][C]1.70106456159122[/C][C]29.9077419803574[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 48 )[/C][C]50.8955223880597[/C][C]1.66957595148719[/C][C]30.4841012729754[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 48 )[/C][C]50.9015151515151[/C][C]1.63804453446388[/C][C]31.0745612103733[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 48 )[/C][C]50.9307692307692[/C][C]1.60775507519564[/C][C]31.6781890578524[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 48 )[/C][C]51.0234375[/C][C]1.58477099908973[/C][C]32.1960949116984[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 48 )[/C][C]51.0873015873016[/C][C]1.56582631327228[/C][C]32.626416579077[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 48 )[/C][C]51.1451612903226[/C][C]1.54649479504876[/C][C]33.0716672659153[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 48 )[/C][C]51.2049180327869[/C][C]1.52515548211544[/C][C]33.5735724214584[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 48 )[/C][C]51.2583333333333[/C][C]1.50324093544271[/C][C]34.0985480935148[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 48 )[/C][C]51.3135593220339[/C][C]1.47898990790862[/C][C]34.6950030204022[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 48 )[/C][C]51.3793103448276[/C][C]1.45983996023787[/C][C]35.1951664184173[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 48 )[/C][C]51.4385964912281[/C][C]1.4433910054936[/C][C]35.6373264731807[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 48 )[/C][C]51.5089285714286[/C][C]1.42638965272308[/C][C]36.1114008876146[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 48 )[/C][C]51.5909090909091[/C][C]1.40873572967192[/C][C]36.6221343040145[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 48 )[/C][C]51.6759259259259[/C][C]1.38895090434986[/C][C]37.2050054210622[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 48 )[/C][C]51.7641509433962[/C][C]1.37023629672315[/C][C]37.7775359382811[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 48 )[/C][C]51.875[/C][C]1.3519608957472[/C][C]38.3701926314442[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 48 )[/C][C]51.9607843137255[/C][C]1.34107065603938[/C][C]38.7457469744231[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 48 )[/C][C]52.05[/C][C]1.32858054427508[/C][C]39.1771505493484[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 48 )[/C][C]52.1224489795918[/C][C]1.31845606093831[/C][C]39.5329435115932[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 48 )[/C][C]52.1770833333333[/C][C]1.31080151518359[/C][C]39.8054798754374[/C][/ROW]
[ROW][C]Trimmed Mean ( 25 / 48 )[/C][C]52.2340425531915[/C][C]1.30179693241329[/C][C]40.1245703170918[/C][/ROW]
[ROW][C]Trimmed Mean ( 26 / 48 )[/C][C]52.2826086956522[/C][C]1.29336633835056[/C][C]40.4236658596887[/C][/ROW]
[ROW][C]Trimmed Mean ( 27 / 48 )[/C][C]52.3333333333333[/C][C]1.2834293947218[/C][C]40.7761685594535[/C][/ROW]
[ROW][C]Trimmed Mean ( 28 / 48 )[/C][C]52.3863636363636[/C][C]1.2717729479282[/C][C]41.1916008448713[/C][/ROW]
[ROW][C]Trimmed Mean ( 29 / 48 )[/C][C]52.4418604651163[/C][C]1.25814497142737[/C][C]41.6818901287827[/C][/ROW]
[ROW][C]Trimmed Mean ( 30 / 48 )[/C][C]52.5[/C][C]1.24224502042192[/C][C]42.2621939608732[/C][/ROW]
[ROW][C]Trimmed Mean ( 31 / 48 )[/C][C]52.5609756097561[/C][C]1.22371152930272[/C][C]42.9520964305255[/C][/ROW]
[ROW][C]Trimmed Mean ( 32 / 48 )[/C][C]52.625[/C][C]1.20210456273439[/C][C]43.7773897807156[/C][/ROW]
[ROW][C]Trimmed Mean ( 33 / 48 )[/C][C]52.7051282051282[/C][C]1.1792564093984[/C][C]44.6935270269302[/C][/ROW]
[ROW][C]Trimmed Mean ( 34 / 48 )[/C][C]52.7894736842105[/C][C]1.1582375887943[/C][C]45.5774136454709[/C][/ROW]
[ROW][C]Trimmed Mean ( 35 / 48 )[/C][C]52.8648648648649[/C][C]1.13692758816675[/C][C]46.4980051632904[/C][/ROW]
[ROW][C]Trimmed Mean ( 36 / 48 )[/C][C]52.9444444444444[/C][C]1.11169781067384[/C][C]47.6248526677885[/C][/ROW]
[ROW][C]Trimmed Mean ( 37 / 48 )[/C][C]53.0571428571429[/C][C]1.09334249496598[/C][C]48.5274679265017[/C][/ROW]
[ROW][C]Trimmed Mean ( 38 / 48 )[/C][C]53.1470588235294[/C][C]1.07902516443294[/C][C]49.2546981992399[/C][/ROW]
[ROW][C]Trimmed Mean ( 39 / 48 )[/C][C]53.2272727272727[/C][C]1.0654120217136[/C][C]49.9593318288846[/C][/ROW]
[ROW][C]Trimmed Mean ( 40 / 48 )[/C][C]53.3125[/C][C]1.04863739060942[/C][C]50.8397854944094[/C][/ROW]
[ROW][C]Trimmed Mean ( 41 / 48 )[/C][C]53.3870967741936[/C][C]1.03235721364129[/C][C]51.7137828541816[/C][/ROW]
[ROW][C]Trimmed Mean ( 42 / 48 )[/C][C]53.45[/C][C]1.01664814283393[/C][C]52.5747284119428[/C][/ROW]
[ROW][C]Trimmed Mean ( 43 / 48 )[/C][C]53.5172413793103[/C][C]0.997043839665827[/C][C]53.6759159930695[/C][/ROW]
[ROW][C]Trimmed Mean ( 44 / 48 )[/C][C]53.6071428571429[/C][C]0.984516023043273[/C][C]54.4502492620038[/C][/ROW]
[ROW][C]Trimmed Mean ( 45 / 48 )[/C][C]53.7222222222222[/C][C]0.971435740587052[/C][C]55.3018794529396[/C][/ROW]
[ROW][C]Trimmed Mean ( 46 / 48 )[/C][C]53.8461538461538[/C][C]0.954225585020415[/C][C]56.4291659031568[/C][/ROW]
[ROW][C]Trimmed Mean ( 47 / 48 )[/C][C]53.98[/C][C]0.941336435985714[/C][C]57.3440036276459[/C][/ROW]
[ROW][C]Trimmed Mean ( 48 / 48 )[/C][C]54.1458333333333[/C][C]0.926840503300282[/C][C]58.4197962222535[/C][/ROW]
[ROW][C]Median[/C][C]55[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]50[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]52.3783783783784[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]52.9444444444444[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]52.3783783783784[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]52.9444444444444[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]52.9444444444444[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]52.3783783783784[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]52.9444444444444[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]52.987012987013[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]144[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=94888&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=94888&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 Mean50.82638888888891.862799072036727.2849550184269
Geometric Mean0
Harmonic Mean0
Quadratic Mean55.4935556819188
Winsorized Mean ( 1 / 48 )50.82638888888891.862799072036727.2849550184269
Winsorized Mean ( 2 / 48 )50.88194444444441.8525821593983627.465418570677
Winsorized Mean ( 3 / 48 )50.71527777777781.8169607767111827.9121478172886
Winsorized Mean ( 4 / 48 )50.79861111111111.8027104436862228.1790185933783
Winsorized Mean ( 5 / 48 )50.86805555555561.79140567101528.3956093131792
Winsorized Mean ( 6 / 48 )50.74305555555561.7724239470276528.6291863978997
Winsorized Mean ( 7 / 48 )50.35416666666671.7203326311757629.2700177594447
Winsorized Mean ( 8 / 48 )50.57638888888891.6852282216378230.0115961977751
Winsorized Mean ( 9 / 48 )50.63888888888891.6758375630108730.2170628028586
Winsorized Mean ( 10 / 48 )50.63888888888891.6758375630108730.2170628028586
Winsorized Mean ( 11 / 48 )50.71527777777781.6645867906509430.4671874501332
Winsorized Mean ( 12 / 48 )50.71527777777781.6645867906509430.4671874501332
Winsorized Mean ( 13 / 48 )50.6251.6063646658783431.5152599377669
Winsorized Mean ( 14 / 48 )50.72222222222221.5681688368349132.3448732246182
Winsorized Mean ( 15 / 48 )50.61805555555561.5565922589875232.5185065409999
Winsorized Mean ( 16 / 48 )50.50694444444441.5445972123958332.6991037139728
Winsorized Mean ( 17 / 48 )50.50694444444441.5445972123958332.6991037139728
Winsorized Mean ( 18 / 48 )50.50694444444441.5143061797019933.3531917926824
Winsorized Mean ( 19 / 48 )50.24305555555561.4877199525855233.7718503191663
Winsorized Mean ( 20 / 48 )50.65972222222221.4003816216764336.1756548629768
Winsorized Mean ( 21 / 48 )50.65972222222221.4003816216764336.1756548629768
Winsorized Mean ( 22 / 48 )50.96527777777781.3619957274319137.4195577499164
Winsorized Mean ( 23 / 48 )51.28472222222221.3235239096729438.7486178733977
Winsorized Mean ( 24 / 48 )51.28472222222221.3235239096729438.7486178733977
Winsorized Mean ( 25 / 48 )51.45833333333331.3033068261095239.4829001908481
Winsorized Mean ( 26 / 48 )51.45833333333331.3033068261095239.4829001908481
Winsorized Mean ( 27 / 48 )51.45833333333331.3033068261095239.4829001908481
Winsorized Mean ( 28 / 48 )51.45833333333331.3033068261095239.4829001908481
Winsorized Mean ( 29 / 48 )51.45833333333331.3033068261095239.4829001908481
Winsorized Mean ( 30 / 48 )51.45833333333331.3033068261095239.4829001908481
Winsorized Mean ( 31 / 48 )51.45833333333331.3033068261095239.4829001908481
Winsorized Mean ( 32 / 48 )51.23611111111111.2814795328960439.9819972117085
Winsorized Mean ( 33 / 48 )51.23611111111111.2330429519836641.5525761115497
Winsorized Mean ( 34 / 48 )51.47222222222221.2061639333018142.6743171480178
Winsorized Mean ( 35 / 48 )51.47222222222221.2061639333018142.6743171480178
Winsorized Mean ( 36 / 48 )50.97222222222221.1086535564726145.9766912076661
Winsorized Mean ( 37 / 48 )51.48611111111111.0513240491513248.9726370786184
Winsorized Mean ( 38 / 48 )51.751.0226409356633850.6042719348311
Winsorized Mean ( 39 / 48 )51.751.0226409356633850.6042719348311
Winsorized Mean ( 40 / 48 )52.02777777777780.99297965244775152.395613192603
Winsorized Mean ( 41 / 48 )52.31250.96311484514254854.315952312268
Winsorized Mean ( 42 / 48 )52.31250.96311484514254854.315952312268
Winsorized Mean ( 43 / 48 )52.01388888888890.87844040645863659.211630642742
Winsorized Mean ( 44 / 48 )51.70833333333330.8521691208716860.6784874819697
Winsorized Mean ( 45 / 48 )51.70833333333330.8521691208716860.6784874819697
Winsorized Mean ( 46 / 48 )51.70833333333330.79240243076142365.2551422433757
Winsorized Mean ( 47 / 48 )51.38194444444440.76617475146611767.0629570422704
Winsorized Mean ( 48 / 48 )51.38194444444440.76617475146611767.0629570422704
Trimmed Mean ( 1 / 48 )50.83802816901411.8218158025152427.9051417266367
Trimmed Mean ( 2 / 48 )50.851.7770353326493228.6150753818663
Trimmed Mean ( 3 / 48 )50.83333333333331.733930415759429.3168242919771
Trimmed Mean ( 4 / 48 )50.8751.7010645615912229.9077419803574
Trimmed Mean ( 5 / 48 )50.89552238805971.6695759514871930.4841012729754
Trimmed Mean ( 6 / 48 )50.90151515151511.6380445344638831.0745612103733
Trimmed Mean ( 7 / 48 )50.93076923076921.6077550751956431.6781890578524
Trimmed Mean ( 8 / 48 )51.02343751.5847709990897332.1960949116984
Trimmed Mean ( 9 / 48 )51.08730158730161.5658263132722832.626416579077
Trimmed Mean ( 10 / 48 )51.14516129032261.5464947950487633.0716672659153
Trimmed Mean ( 11 / 48 )51.20491803278691.5251554821154433.5735724214584
Trimmed Mean ( 12 / 48 )51.25833333333331.5032409354427134.0985480935148
Trimmed Mean ( 13 / 48 )51.31355932203391.4789899079086234.6950030204022
Trimmed Mean ( 14 / 48 )51.37931034482761.4598399602378735.1951664184173
Trimmed Mean ( 15 / 48 )51.43859649122811.443391005493635.6373264731807
Trimmed Mean ( 16 / 48 )51.50892857142861.4263896527230836.1114008876146
Trimmed Mean ( 17 / 48 )51.59090909090911.4087357296719236.6221343040145
Trimmed Mean ( 18 / 48 )51.67592592592591.3889509043498637.2050054210622
Trimmed Mean ( 19 / 48 )51.76415094339621.3702362967231537.7775359382811
Trimmed Mean ( 20 / 48 )51.8751.351960895747238.3701926314442
Trimmed Mean ( 21 / 48 )51.96078431372551.3410706560393838.7457469744231
Trimmed Mean ( 22 / 48 )52.051.3285805442750839.1771505493484
Trimmed Mean ( 23 / 48 )52.12244897959181.3184560609383139.5329435115932
Trimmed Mean ( 24 / 48 )52.17708333333331.3108015151835939.8054798754374
Trimmed Mean ( 25 / 48 )52.23404255319151.3017969324132940.1245703170918
Trimmed Mean ( 26 / 48 )52.28260869565221.2933663383505640.4236658596887
Trimmed Mean ( 27 / 48 )52.33333333333331.283429394721840.7761685594535
Trimmed Mean ( 28 / 48 )52.38636363636361.271772947928241.1916008448713
Trimmed Mean ( 29 / 48 )52.44186046511631.2581449714273741.6818901287827
Trimmed Mean ( 30 / 48 )52.51.2422450204219242.2621939608732
Trimmed Mean ( 31 / 48 )52.56097560975611.2237115293027242.9520964305255
Trimmed Mean ( 32 / 48 )52.6251.2021045627343943.7773897807156
Trimmed Mean ( 33 / 48 )52.70512820512821.179256409398444.6935270269302
Trimmed Mean ( 34 / 48 )52.78947368421051.158237588794345.5774136454709
Trimmed Mean ( 35 / 48 )52.86486486486491.1369275881667546.4980051632904
Trimmed Mean ( 36 / 48 )52.94444444444441.1116978106738447.6248526677885
Trimmed Mean ( 37 / 48 )53.05714285714291.0933424949659848.5274679265017
Trimmed Mean ( 38 / 48 )53.14705882352941.0790251644329449.2546981992399
Trimmed Mean ( 39 / 48 )53.22727272727271.065412021713649.9593318288846
Trimmed Mean ( 40 / 48 )53.31251.0486373906094250.8397854944094
Trimmed Mean ( 41 / 48 )53.38709677419361.0323572136412951.7137828541816
Trimmed Mean ( 42 / 48 )53.451.0166481428339352.5747284119428
Trimmed Mean ( 43 / 48 )53.51724137931030.99704383966582753.6759159930695
Trimmed Mean ( 44 / 48 )53.60714285714290.98451602304327354.4502492620038
Trimmed Mean ( 45 / 48 )53.72222222222220.97143574058705255.3018794529396
Trimmed Mean ( 46 / 48 )53.84615384615380.95422558502041556.4291659031568
Trimmed Mean ( 47 / 48 )53.980.94133643598571457.3440036276459
Trimmed Mean ( 48 / 48 )54.14583333333330.92684050330028258.4197962222535
Median55
Midrange50
Midmean - Weighted Average at Xnp52.3783783783784
Midmean - Weighted Average at X(n+1)p52.9444444444444
Midmean - Empirical Distribution Function52.3783783783784
Midmean - Empirical Distribution Function - Averaging52.9444444444444
Midmean - Empirical Distribution Function - Interpolation52.9444444444444
Midmean - Closest Observation52.3783783783784
Midmean - True Basic - Statistics Graphics Toolkit52.9444444444444
Midmean - MS Excel (old versions)52.987012987013
Number of observations144



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')