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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, 16 Nov 2010 13:47:51 +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/16/t12899151628jygcrhv83qiy3f.htm/, Retrieved Sun, 05 May 2024 01:59:28 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=95745, Retrieved Sun, 05 May 2024 01:59:28 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact131
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] [49c7a512c56172bc46ae7e93e5b58c1c]
-    D      [Central Tendency] [W6] [2010-11-16 13:47:51] [476d588d86fe88306e0383abd6004235] [Current]
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Dataseries X:
72
70
90
81
80
40
49
80
90
86
100
40
100
75
83
100
77
55
97
60
40
100
100
59
65
91
100
85
62
68
75
80
80
34
42
94
85
95
90
80
61
65
73
81
40
90
95
67
90
90
90
85
91
100
60
100
90
85
81
80
45
90
93
75
80
85
70
80
96
62
82
50
75
59
78
95
70
80
75
95
70
90
59
16
60
87
80
70
80
100
100
81
49
75
70
91
75
85
84
100
90
87
86
60
100
78
80
90
81
71
92
50
81
90
90
85
80
95
100
79
80
50
70
81
91
100
57
79
95
90
81
70
90
40
60
100
80
81
100
87
100
88
100
93
60
85
100




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'George Udny Yule' @ 72.249.76.132

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 1 seconds \tabularnewline
R Server & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=95745&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'George Udny Yule' @ 72.249.76.132[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=95745&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=95745&T=0

As an alternative you can also use a QR Code:  

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

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'George Udny Yule' @ 72.249.76.132







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean78.87074829931971.3977521028746956.4268500380789
Geometric Mean76.5219370332731
Harmonic Mean73.162338294083
Quadratic Mean80.6587672525057
Winsorized Mean ( 1 / 49 )78.99319727891161.3650078210635257.8701426174728
Winsorized Mean ( 2 / 49 )79.07482993197281.3476800747077458.6747785442486
Winsorized Mean ( 3 / 49 )79.07482993197281.3476800747077458.6747785442486
Winsorized Mean ( 4 / 49 )79.07482993197281.3476800747077458.6747785442486
Winsorized Mean ( 5 / 49 )79.07482993197281.3476800747077458.6747785442486
Winsorized Mean ( 6 / 49 )79.07482993197281.3476800747077458.6747785442486
Winsorized Mean ( 7 / 49 )79.17006802721091.3290996344119659.5666915988872
Winsorized Mean ( 8 / 49 )79.33333333333331.2986711534582861.0880846333376
Winsorized Mean ( 9 / 49 )79.5782312925171.2560514286873863.3558702096135
Winsorized Mean ( 10 / 49 )79.5782312925171.2560514286873863.3558702096135
Winsorized Mean ( 11 / 49 )79.65306122448981.2437019817630364.045134921773
Winsorized Mean ( 12 / 49 )79.65306122448981.2437019817630364.045134921773
Winsorized Mean ( 13 / 49 )79.65306122448981.2437019817630364.045134921773
Winsorized Mean ( 14 / 49 )80.12925170068031.1696656786126968.506115179612
Winsorized Mean ( 15 / 49 )80.33333333333331.1403402378701770.446811105581
Winsorized Mean ( 16 / 49 )80.55102040816331.1106092725371172.5286762860806
Winsorized Mean ( 17 / 49 )80.55102040816331.1106092725371172.5286762860806
Winsorized Mean ( 18 / 49 )80.55102040816331.1106092725371172.5286762860806
Winsorized Mean ( 19 / 49 )80.29251700680271.048991460845776.5425839997502
Winsorized Mean ( 20 / 49 )80.1564625850341.0344319470182877.4883865643193
Winsorized Mean ( 21 / 49 )80.01360544217691.0197466249348778.4642022691543
Winsorized Mean ( 22 / 49 )80.01360544217691.0197466249348778.4642022691543
Winsorized Mean ( 23 / 49 )80.01360544217691.0197466249348778.4642022691543
Winsorized Mean ( 24 / 49 )80.01360544217691.0197466249348778.4642022691543
Winsorized Mean ( 25 / 49 )80.18367346938780.99710794213462280.4162418942622
Winsorized Mean ( 26 / 49 )80.36054421768710.97403364956393382.502841923032
Winsorized Mean ( 27 / 49 )80.17687074829930.9554760867008783.913006159201
Winsorized Mean ( 28 / 49 )80.55782312925170.86407984651196493.2296054056115
Winsorized Mean ( 29 / 49 )80.55782312925170.86407984651196493.2296054056115
Winsorized Mean ( 30 / 49 )80.76190476190480.794711185498527101.624220516341
Winsorized Mean ( 31 / 49 )80.76190476190480.749822663054741107.708007161166
Winsorized Mean ( 32 / 49 )81.19727891156460.700562193918884115.903027049396
Winsorized Mean ( 33 / 49 )81.19727891156460.700562193918884115.903027049396
Winsorized Mean ( 34 / 49 )81.19727891156460.700562193918884115.903027049396
Winsorized Mean ( 35 / 49 )80.95918367346940.678275422169976119.360338038581
Winsorized Mean ( 36 / 49 )80.95918367346940.678275422169976119.360338038581
Winsorized Mean ( 37 / 49 )80.95918367346940.678275422169976119.360338038581
Winsorized Mean ( 38 / 49 )80.95918367346940.678275422169976119.360338038581
Winsorized Mean ( 39 / 49 )80.95918367346940.678275422169976119.360338038581
Winsorized Mean ( 40 / 49 )81.23129251700680.648508753463287125.258590702439
Winsorized Mean ( 41 / 49 )81.51020408163270.618749038356078131.733867899323
Winsorized Mean ( 42 / 49 )81.7959183673470.58908934643652138.851464318853
Winsorized Mean ( 43 / 49 )82.38095238095240.53122895806165155.076170323139
Winsorized Mean ( 44 / 49 )82.38095238095240.53122895806165155.076170323139
Winsorized Mean ( 45 / 49 )82.38095238095240.53122895806165155.076170323139
Winsorized Mean ( 46 / 49 )82.38095238095240.53122895806165155.076170323139
Winsorized Mean ( 47 / 49 )82.38095238095240.53122895806165155.076170323139
Winsorized Mean ( 48 / 49 )82.38095238095240.53122895806165155.076170323139
Winsorized Mean ( 49 / 49 )82.38095238095240.53122895806165155.076170323139
Trimmed Mean ( 1 / 49 )79.15862068965521.3404864110485659.0521619892705
Trimmed Mean ( 2 / 49 )79.32867132867131.3136494197344760.3880077415985
Trimmed Mean ( 3 / 49 )79.32867132867131.2942283900778661.2941826472366
Trimmed Mean ( 4 / 49 )79.59712230215831.2729682937820162.5287547937849
Trimmed Mean ( 5 / 49 )79.73722627737231.249657319837663.8072734113498
Trimmed Mean ( 6 / 49 )79.73722627737231.2240474168516365.142269147109
Trimmed Mean ( 7 / 49 )80.030075187971.1958451201287066.9234450522799
Trimmed Mean ( 8 / 49 )80.16793893129771.1686425906196468.5991932647182
Trimmed Mean ( 9 / 49 )80.28682170542641.1444376876598670.1539477169758
Trimmed Mean ( 10 / 49 )80.37795275590551.1251479444922671.4376746181385
Trimmed Mean ( 11 / 49 )80.4721.1038686223839672.8999795521038
Trimmed Mean ( 12 / 49 )80.4721.0822589023869274.3555907209627
Trimmed Mean ( 13 / 49 )80.65289256198351.0583337613370976.2074267196084
Trimmed Mean ( 14 / 49 )80.74789915966391.0317712162448078.2614380865862
Trimmed Mean ( 15 / 49 )80.80341880341881.0125384956452179.802811597725
Trimmed Mean ( 16 / 49 )80.84347826086960.99499826971073581.2498681875822
Trimmed Mean ( 17 / 49 )80.86725663716810.9792009262551582.584947040886
Trimmed Mean ( 18 / 49 )80.89189189189190.96161815501831584.1205955500614
Trimmed Mean ( 19 / 49 )80.91743119266050.9420093726891985.8987538114006
Trimmed Mean ( 20 / 49 )80.962616822430.9271588668551387.323348475381
Trimmed Mean ( 21 / 49 )81.01904761904760.91206613975808588.8302329045315
Trimmed Mean ( 22 / 49 )81.08737864077670.89662807179312290.4359133867112
Trimmed Mean ( 23 / 49 )81.15841584158420.87921349565621792.3079732539934
Trimmed Mean ( 24 / 49 )81.15841584158420.85952390339823794.4225233535845
Trimmed Mean ( 25 / 49 )81.30927835051550.83719391297700397.12120106247
Trimmed Mean ( 26 / 49 )81.3789473684210.81464464698811399.8950249894768
Trimmed Mean ( 27 / 49 )81.44086021505380.791856395501503102.848017238625
Trimmed Mean ( 28 / 49 )81.51648351648350.767846303391442106.162500433276
Trimmed Mean ( 29 / 49 )81.57303370786520.751553997899888108.539152124544
Trimmed Mean ( 30 / 49 )81.6321839080460.732838939783032111.391711707097
Trimmed Mean ( 31 / 49 )81.68235294117650.719518155899012113.523685638088
Trimmed Mean ( 32 / 49 )81.73493975903610.709095506725132115.266475367357
Trimmed Mean ( 33 / 49 )81.76543209876540.702568393256607116.380743687827
Trimmed Mean ( 34 / 49 )81.79746835443040.694808435729871117.726648307753
Trimmed Mean ( 35 / 49 )81.83116883116880.68561097214626119.355103922858
Trimmed Mean ( 36 / 49 )81.880.677025822228343120.940734181309
Trimmed Mean ( 37 / 49 )81.9315068493150.666760486298889122.879967443943
Trimmed Mean ( 38 / 49 )81.98591549295770.654497813153818125.265377278945
Trimmed Mean ( 39 / 49 )82.04347826086960.639837862630479128.225419364173
Trimmed Mean ( 40 / 49 )82.10447761194030.622266733801166131.944185912685
Trimmed Mean ( 41 / 49 )82.15384615384620.605753968061692135.622464705802
Trimmed Mean ( 42 / 49 )82.19047619047620.590441503366478139.201725694851
Trimmed Mean ( 43 / 49 )82.21311475409840.576457408934992142.617847354911
Trimmed Mean ( 44 / 49 )82.20338983050850.567881654874744144.754438050371
Trimmed Mean ( 45 / 49 )82.19298245614040.557158133541498147.521821019990
Trimmed Mean ( 46 / 49 )82.18181818181820.543768437725041151.133851250436
Trimmed Mean ( 47 / 49 )82.16981132075470.52701741010052155.914794740998
Trimmed Mean ( 48 / 49 )82.16981132075470.505943148801622162.409178808691
Trimmed Mean ( 49 / 49 )82.14285714285710.479157423749955171.431878274984
Median81
Midrange58
Midmean - Weighted Average at Xnp81.3875
Midmean - Weighted Average at X(n+1)p81.3875
Midmean - Empirical Distribution Function81.3875
Midmean - Empirical Distribution Function - Averaging81.3875
Midmean - Empirical Distribution Function - Interpolation81.3875
Midmean - Closest Observation81.3875
Midmean - True Basic - Statistics Graphics Toolkit81.3875
Midmean - MS Excel (old versions)81.3875
Number of observations147

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 78.8707482993197 & 1.39775210287469 & 56.4268500380789 \tabularnewline
Geometric Mean & 76.5219370332731 &  &  \tabularnewline
Harmonic Mean & 73.162338294083 &  &  \tabularnewline
Quadratic Mean & 80.6587672525057 &  &  \tabularnewline
Winsorized Mean ( 1 / 49 ) & 78.9931972789116 & 1.36500782106352 & 57.8701426174728 \tabularnewline
Winsorized Mean ( 2 / 49 ) & 79.0748299319728 & 1.34768007470774 & 58.6747785442486 \tabularnewline
Winsorized Mean ( 3 / 49 ) & 79.0748299319728 & 1.34768007470774 & 58.6747785442486 \tabularnewline
Winsorized Mean ( 4 / 49 ) & 79.0748299319728 & 1.34768007470774 & 58.6747785442486 \tabularnewline
Winsorized Mean ( 5 / 49 ) & 79.0748299319728 & 1.34768007470774 & 58.6747785442486 \tabularnewline
Winsorized Mean ( 6 / 49 ) & 79.0748299319728 & 1.34768007470774 & 58.6747785442486 \tabularnewline
Winsorized Mean ( 7 / 49 ) & 79.1700680272109 & 1.32909963441196 & 59.5666915988872 \tabularnewline
Winsorized Mean ( 8 / 49 ) & 79.3333333333333 & 1.29867115345828 & 61.0880846333376 \tabularnewline
Winsorized Mean ( 9 / 49 ) & 79.578231292517 & 1.25605142868738 & 63.3558702096135 \tabularnewline
Winsorized Mean ( 10 / 49 ) & 79.578231292517 & 1.25605142868738 & 63.3558702096135 \tabularnewline
Winsorized Mean ( 11 / 49 ) & 79.6530612244898 & 1.24370198176303 & 64.045134921773 \tabularnewline
Winsorized Mean ( 12 / 49 ) & 79.6530612244898 & 1.24370198176303 & 64.045134921773 \tabularnewline
Winsorized Mean ( 13 / 49 ) & 79.6530612244898 & 1.24370198176303 & 64.045134921773 \tabularnewline
Winsorized Mean ( 14 / 49 ) & 80.1292517006803 & 1.16966567861269 & 68.506115179612 \tabularnewline
Winsorized Mean ( 15 / 49 ) & 80.3333333333333 & 1.14034023787017 & 70.446811105581 \tabularnewline
Winsorized Mean ( 16 / 49 ) & 80.5510204081633 & 1.11060927253711 & 72.5286762860806 \tabularnewline
Winsorized Mean ( 17 / 49 ) & 80.5510204081633 & 1.11060927253711 & 72.5286762860806 \tabularnewline
Winsorized Mean ( 18 / 49 ) & 80.5510204081633 & 1.11060927253711 & 72.5286762860806 \tabularnewline
Winsorized Mean ( 19 / 49 ) & 80.2925170068027 & 1.0489914608457 & 76.5425839997502 \tabularnewline
Winsorized Mean ( 20 / 49 ) & 80.156462585034 & 1.03443194701828 & 77.4883865643193 \tabularnewline
Winsorized Mean ( 21 / 49 ) & 80.0136054421769 & 1.01974662493487 & 78.4642022691543 \tabularnewline
Winsorized Mean ( 22 / 49 ) & 80.0136054421769 & 1.01974662493487 & 78.4642022691543 \tabularnewline
Winsorized Mean ( 23 / 49 ) & 80.0136054421769 & 1.01974662493487 & 78.4642022691543 \tabularnewline
Winsorized Mean ( 24 / 49 ) & 80.0136054421769 & 1.01974662493487 & 78.4642022691543 \tabularnewline
Winsorized Mean ( 25 / 49 ) & 80.1836734693878 & 0.997107942134622 & 80.4162418942622 \tabularnewline
Winsorized Mean ( 26 / 49 ) & 80.3605442176871 & 0.974033649563933 & 82.502841923032 \tabularnewline
Winsorized Mean ( 27 / 49 ) & 80.1768707482993 & 0.95547608670087 & 83.913006159201 \tabularnewline
Winsorized Mean ( 28 / 49 ) & 80.5578231292517 & 0.864079846511964 & 93.2296054056115 \tabularnewline
Winsorized Mean ( 29 / 49 ) & 80.5578231292517 & 0.864079846511964 & 93.2296054056115 \tabularnewline
Winsorized Mean ( 30 / 49 ) & 80.7619047619048 & 0.794711185498527 & 101.624220516341 \tabularnewline
Winsorized Mean ( 31 / 49 ) & 80.7619047619048 & 0.749822663054741 & 107.708007161166 \tabularnewline
Winsorized Mean ( 32 / 49 ) & 81.1972789115646 & 0.700562193918884 & 115.903027049396 \tabularnewline
Winsorized Mean ( 33 / 49 ) & 81.1972789115646 & 0.700562193918884 & 115.903027049396 \tabularnewline
Winsorized Mean ( 34 / 49 ) & 81.1972789115646 & 0.700562193918884 & 115.903027049396 \tabularnewline
Winsorized Mean ( 35 / 49 ) & 80.9591836734694 & 0.678275422169976 & 119.360338038581 \tabularnewline
Winsorized Mean ( 36 / 49 ) & 80.9591836734694 & 0.678275422169976 & 119.360338038581 \tabularnewline
Winsorized Mean ( 37 / 49 ) & 80.9591836734694 & 0.678275422169976 & 119.360338038581 \tabularnewline
Winsorized Mean ( 38 / 49 ) & 80.9591836734694 & 0.678275422169976 & 119.360338038581 \tabularnewline
Winsorized Mean ( 39 / 49 ) & 80.9591836734694 & 0.678275422169976 & 119.360338038581 \tabularnewline
Winsorized Mean ( 40 / 49 ) & 81.2312925170068 & 0.648508753463287 & 125.258590702439 \tabularnewline
Winsorized Mean ( 41 / 49 ) & 81.5102040816327 & 0.618749038356078 & 131.733867899323 \tabularnewline
Winsorized Mean ( 42 / 49 ) & 81.795918367347 & 0.58908934643652 & 138.851464318853 \tabularnewline
Winsorized Mean ( 43 / 49 ) & 82.3809523809524 & 0.53122895806165 & 155.076170323139 \tabularnewline
Winsorized Mean ( 44 / 49 ) & 82.3809523809524 & 0.53122895806165 & 155.076170323139 \tabularnewline
Winsorized Mean ( 45 / 49 ) & 82.3809523809524 & 0.53122895806165 & 155.076170323139 \tabularnewline
Winsorized Mean ( 46 / 49 ) & 82.3809523809524 & 0.53122895806165 & 155.076170323139 \tabularnewline
Winsorized Mean ( 47 / 49 ) & 82.3809523809524 & 0.53122895806165 & 155.076170323139 \tabularnewline
Winsorized Mean ( 48 / 49 ) & 82.3809523809524 & 0.53122895806165 & 155.076170323139 \tabularnewline
Winsorized Mean ( 49 / 49 ) & 82.3809523809524 & 0.53122895806165 & 155.076170323139 \tabularnewline
Trimmed Mean ( 1 / 49 ) & 79.1586206896552 & 1.34048641104856 & 59.0521619892705 \tabularnewline
Trimmed Mean ( 2 / 49 ) & 79.3286713286713 & 1.31364941973447 & 60.3880077415985 \tabularnewline
Trimmed Mean ( 3 / 49 ) & 79.3286713286713 & 1.29422839007786 & 61.2941826472366 \tabularnewline
Trimmed Mean ( 4 / 49 ) & 79.5971223021583 & 1.27296829378201 & 62.5287547937849 \tabularnewline
Trimmed Mean ( 5 / 49 ) & 79.7372262773723 & 1.2496573198376 & 63.8072734113498 \tabularnewline
Trimmed Mean ( 6 / 49 ) & 79.7372262773723 & 1.22404741685163 & 65.142269147109 \tabularnewline
Trimmed Mean ( 7 / 49 ) & 80.03007518797 & 1.19584512012870 & 66.9234450522799 \tabularnewline
Trimmed Mean ( 8 / 49 ) & 80.1679389312977 & 1.16864259061964 & 68.5991932647182 \tabularnewline
Trimmed Mean ( 9 / 49 ) & 80.2868217054264 & 1.14443768765986 & 70.1539477169758 \tabularnewline
Trimmed Mean ( 10 / 49 ) & 80.3779527559055 & 1.12514794449226 & 71.4376746181385 \tabularnewline
Trimmed Mean ( 11 / 49 ) & 80.472 & 1.10386862238396 & 72.8999795521038 \tabularnewline
Trimmed Mean ( 12 / 49 ) & 80.472 & 1.08225890238692 & 74.3555907209627 \tabularnewline
Trimmed Mean ( 13 / 49 ) & 80.6528925619835 & 1.05833376133709 & 76.2074267196084 \tabularnewline
Trimmed Mean ( 14 / 49 ) & 80.7478991596639 & 1.03177121624480 & 78.2614380865862 \tabularnewline
Trimmed Mean ( 15 / 49 ) & 80.8034188034188 & 1.01253849564521 & 79.802811597725 \tabularnewline
Trimmed Mean ( 16 / 49 ) & 80.8434782608696 & 0.994998269710735 & 81.2498681875822 \tabularnewline
Trimmed Mean ( 17 / 49 ) & 80.8672566371681 & 0.97920092625515 & 82.584947040886 \tabularnewline
Trimmed Mean ( 18 / 49 ) & 80.8918918918919 & 0.961618155018315 & 84.1205955500614 \tabularnewline
Trimmed Mean ( 19 / 49 ) & 80.9174311926605 & 0.94200937268919 & 85.8987538114006 \tabularnewline
Trimmed Mean ( 20 / 49 ) & 80.96261682243 & 0.92715886685513 & 87.323348475381 \tabularnewline
Trimmed Mean ( 21 / 49 ) & 81.0190476190476 & 0.912066139758085 & 88.8302329045315 \tabularnewline
Trimmed Mean ( 22 / 49 ) & 81.0873786407767 & 0.896628071793122 & 90.4359133867112 \tabularnewline
Trimmed Mean ( 23 / 49 ) & 81.1584158415842 & 0.879213495656217 & 92.3079732539934 \tabularnewline
Trimmed Mean ( 24 / 49 ) & 81.1584158415842 & 0.859523903398237 & 94.4225233535845 \tabularnewline
Trimmed Mean ( 25 / 49 ) & 81.3092783505155 & 0.837193912977003 & 97.12120106247 \tabularnewline
Trimmed Mean ( 26 / 49 ) & 81.378947368421 & 0.814644646988113 & 99.8950249894768 \tabularnewline
Trimmed Mean ( 27 / 49 ) & 81.4408602150538 & 0.791856395501503 & 102.848017238625 \tabularnewline
Trimmed Mean ( 28 / 49 ) & 81.5164835164835 & 0.767846303391442 & 106.162500433276 \tabularnewline
Trimmed Mean ( 29 / 49 ) & 81.5730337078652 & 0.751553997899888 & 108.539152124544 \tabularnewline
Trimmed Mean ( 30 / 49 ) & 81.632183908046 & 0.732838939783032 & 111.391711707097 \tabularnewline
Trimmed Mean ( 31 / 49 ) & 81.6823529411765 & 0.719518155899012 & 113.523685638088 \tabularnewline
Trimmed Mean ( 32 / 49 ) & 81.7349397590361 & 0.709095506725132 & 115.266475367357 \tabularnewline
Trimmed Mean ( 33 / 49 ) & 81.7654320987654 & 0.702568393256607 & 116.380743687827 \tabularnewline
Trimmed Mean ( 34 / 49 ) & 81.7974683544304 & 0.694808435729871 & 117.726648307753 \tabularnewline
Trimmed Mean ( 35 / 49 ) & 81.8311688311688 & 0.68561097214626 & 119.355103922858 \tabularnewline
Trimmed Mean ( 36 / 49 ) & 81.88 & 0.677025822228343 & 120.940734181309 \tabularnewline
Trimmed Mean ( 37 / 49 ) & 81.931506849315 & 0.666760486298889 & 122.879967443943 \tabularnewline
Trimmed Mean ( 38 / 49 ) & 81.9859154929577 & 0.654497813153818 & 125.265377278945 \tabularnewline
Trimmed Mean ( 39 / 49 ) & 82.0434782608696 & 0.639837862630479 & 128.225419364173 \tabularnewline
Trimmed Mean ( 40 / 49 ) & 82.1044776119403 & 0.622266733801166 & 131.944185912685 \tabularnewline
Trimmed Mean ( 41 / 49 ) & 82.1538461538462 & 0.605753968061692 & 135.622464705802 \tabularnewline
Trimmed Mean ( 42 / 49 ) & 82.1904761904762 & 0.590441503366478 & 139.201725694851 \tabularnewline
Trimmed Mean ( 43 / 49 ) & 82.2131147540984 & 0.576457408934992 & 142.617847354911 \tabularnewline
Trimmed Mean ( 44 / 49 ) & 82.2033898305085 & 0.567881654874744 & 144.754438050371 \tabularnewline
Trimmed Mean ( 45 / 49 ) & 82.1929824561404 & 0.557158133541498 & 147.521821019990 \tabularnewline
Trimmed Mean ( 46 / 49 ) & 82.1818181818182 & 0.543768437725041 & 151.133851250436 \tabularnewline
Trimmed Mean ( 47 / 49 ) & 82.1698113207547 & 0.52701741010052 & 155.914794740998 \tabularnewline
Trimmed Mean ( 48 / 49 ) & 82.1698113207547 & 0.505943148801622 & 162.409178808691 \tabularnewline
Trimmed Mean ( 49 / 49 ) & 82.1428571428571 & 0.479157423749955 & 171.431878274984 \tabularnewline
Median & 81 &  &  \tabularnewline
Midrange & 58 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 81.3875 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 81.3875 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 81.3875 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 81.3875 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 81.3875 &  &  \tabularnewline
Midmean - Closest Observation & 81.3875 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 81.3875 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 81.3875 &  &  \tabularnewline
Number of observations & 147 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=95745&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]78.8707482993197[/C][C]1.39775210287469[/C][C]56.4268500380789[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]76.5219370332731[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]73.162338294083[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]80.6587672525057[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 49 )[/C][C]78.9931972789116[/C][C]1.36500782106352[/C][C]57.8701426174728[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 49 )[/C][C]79.0748299319728[/C][C]1.34768007470774[/C][C]58.6747785442486[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 49 )[/C][C]79.0748299319728[/C][C]1.34768007470774[/C][C]58.6747785442486[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 49 )[/C][C]79.0748299319728[/C][C]1.34768007470774[/C][C]58.6747785442486[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 49 )[/C][C]79.0748299319728[/C][C]1.34768007470774[/C][C]58.6747785442486[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 49 )[/C][C]79.0748299319728[/C][C]1.34768007470774[/C][C]58.6747785442486[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 49 )[/C][C]79.1700680272109[/C][C]1.32909963441196[/C][C]59.5666915988872[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 49 )[/C][C]79.3333333333333[/C][C]1.29867115345828[/C][C]61.0880846333376[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 49 )[/C][C]79.578231292517[/C][C]1.25605142868738[/C][C]63.3558702096135[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 49 )[/C][C]79.578231292517[/C][C]1.25605142868738[/C][C]63.3558702096135[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 49 )[/C][C]79.6530612244898[/C][C]1.24370198176303[/C][C]64.045134921773[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 49 )[/C][C]79.6530612244898[/C][C]1.24370198176303[/C][C]64.045134921773[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 49 )[/C][C]79.6530612244898[/C][C]1.24370198176303[/C][C]64.045134921773[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 49 )[/C][C]80.1292517006803[/C][C]1.16966567861269[/C][C]68.506115179612[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 49 )[/C][C]80.3333333333333[/C][C]1.14034023787017[/C][C]70.446811105581[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 49 )[/C][C]80.5510204081633[/C][C]1.11060927253711[/C][C]72.5286762860806[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 49 )[/C][C]80.5510204081633[/C][C]1.11060927253711[/C][C]72.5286762860806[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 49 )[/C][C]80.5510204081633[/C][C]1.11060927253711[/C][C]72.5286762860806[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 49 )[/C][C]80.2925170068027[/C][C]1.0489914608457[/C][C]76.5425839997502[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 49 )[/C][C]80.156462585034[/C][C]1.03443194701828[/C][C]77.4883865643193[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 49 )[/C][C]80.0136054421769[/C][C]1.01974662493487[/C][C]78.4642022691543[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 49 )[/C][C]80.0136054421769[/C][C]1.01974662493487[/C][C]78.4642022691543[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 49 )[/C][C]80.0136054421769[/C][C]1.01974662493487[/C][C]78.4642022691543[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 49 )[/C][C]80.0136054421769[/C][C]1.01974662493487[/C][C]78.4642022691543[/C][/ROW]
[ROW][C]Winsorized Mean ( 25 / 49 )[/C][C]80.1836734693878[/C][C]0.997107942134622[/C][C]80.4162418942622[/C][/ROW]
[ROW][C]Winsorized Mean ( 26 / 49 )[/C][C]80.3605442176871[/C][C]0.974033649563933[/C][C]82.502841923032[/C][/ROW]
[ROW][C]Winsorized Mean ( 27 / 49 )[/C][C]80.1768707482993[/C][C]0.95547608670087[/C][C]83.913006159201[/C][/ROW]
[ROW][C]Winsorized Mean ( 28 / 49 )[/C][C]80.5578231292517[/C][C]0.864079846511964[/C][C]93.2296054056115[/C][/ROW]
[ROW][C]Winsorized Mean ( 29 / 49 )[/C][C]80.5578231292517[/C][C]0.864079846511964[/C][C]93.2296054056115[/C][/ROW]
[ROW][C]Winsorized Mean ( 30 / 49 )[/C][C]80.7619047619048[/C][C]0.794711185498527[/C][C]101.624220516341[/C][/ROW]
[ROW][C]Winsorized Mean ( 31 / 49 )[/C][C]80.7619047619048[/C][C]0.749822663054741[/C][C]107.708007161166[/C][/ROW]
[ROW][C]Winsorized Mean ( 32 / 49 )[/C][C]81.1972789115646[/C][C]0.700562193918884[/C][C]115.903027049396[/C][/ROW]
[ROW][C]Winsorized Mean ( 33 / 49 )[/C][C]81.1972789115646[/C][C]0.700562193918884[/C][C]115.903027049396[/C][/ROW]
[ROW][C]Winsorized Mean ( 34 / 49 )[/C][C]81.1972789115646[/C][C]0.700562193918884[/C][C]115.903027049396[/C][/ROW]
[ROW][C]Winsorized Mean ( 35 / 49 )[/C][C]80.9591836734694[/C][C]0.678275422169976[/C][C]119.360338038581[/C][/ROW]
[ROW][C]Winsorized Mean ( 36 / 49 )[/C][C]80.9591836734694[/C][C]0.678275422169976[/C][C]119.360338038581[/C][/ROW]
[ROW][C]Winsorized Mean ( 37 / 49 )[/C][C]80.9591836734694[/C][C]0.678275422169976[/C][C]119.360338038581[/C][/ROW]
[ROW][C]Winsorized Mean ( 38 / 49 )[/C][C]80.9591836734694[/C][C]0.678275422169976[/C][C]119.360338038581[/C][/ROW]
[ROW][C]Winsorized Mean ( 39 / 49 )[/C][C]80.9591836734694[/C][C]0.678275422169976[/C][C]119.360338038581[/C][/ROW]
[ROW][C]Winsorized Mean ( 40 / 49 )[/C][C]81.2312925170068[/C][C]0.648508753463287[/C][C]125.258590702439[/C][/ROW]
[ROW][C]Winsorized Mean ( 41 / 49 )[/C][C]81.5102040816327[/C][C]0.618749038356078[/C][C]131.733867899323[/C][/ROW]
[ROW][C]Winsorized Mean ( 42 / 49 )[/C][C]81.795918367347[/C][C]0.58908934643652[/C][C]138.851464318853[/C][/ROW]
[ROW][C]Winsorized Mean ( 43 / 49 )[/C][C]82.3809523809524[/C][C]0.53122895806165[/C][C]155.076170323139[/C][/ROW]
[ROW][C]Winsorized Mean ( 44 / 49 )[/C][C]82.3809523809524[/C][C]0.53122895806165[/C][C]155.076170323139[/C][/ROW]
[ROW][C]Winsorized Mean ( 45 / 49 )[/C][C]82.3809523809524[/C][C]0.53122895806165[/C][C]155.076170323139[/C][/ROW]
[ROW][C]Winsorized Mean ( 46 / 49 )[/C][C]82.3809523809524[/C][C]0.53122895806165[/C][C]155.076170323139[/C][/ROW]
[ROW][C]Winsorized Mean ( 47 / 49 )[/C][C]82.3809523809524[/C][C]0.53122895806165[/C][C]155.076170323139[/C][/ROW]
[ROW][C]Winsorized Mean ( 48 / 49 )[/C][C]82.3809523809524[/C][C]0.53122895806165[/C][C]155.076170323139[/C][/ROW]
[ROW][C]Winsorized Mean ( 49 / 49 )[/C][C]82.3809523809524[/C][C]0.53122895806165[/C][C]155.076170323139[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 49 )[/C][C]79.1586206896552[/C][C]1.34048641104856[/C][C]59.0521619892705[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 49 )[/C][C]79.3286713286713[/C][C]1.31364941973447[/C][C]60.3880077415985[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 49 )[/C][C]79.3286713286713[/C][C]1.29422839007786[/C][C]61.2941826472366[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 49 )[/C][C]79.5971223021583[/C][C]1.27296829378201[/C][C]62.5287547937849[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 49 )[/C][C]79.7372262773723[/C][C]1.2496573198376[/C][C]63.8072734113498[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 49 )[/C][C]79.7372262773723[/C][C]1.22404741685163[/C][C]65.142269147109[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 49 )[/C][C]80.03007518797[/C][C]1.19584512012870[/C][C]66.9234450522799[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 49 )[/C][C]80.1679389312977[/C][C]1.16864259061964[/C][C]68.5991932647182[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 49 )[/C][C]80.2868217054264[/C][C]1.14443768765986[/C][C]70.1539477169758[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 49 )[/C][C]80.3779527559055[/C][C]1.12514794449226[/C][C]71.4376746181385[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 49 )[/C][C]80.472[/C][C]1.10386862238396[/C][C]72.8999795521038[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 49 )[/C][C]80.472[/C][C]1.08225890238692[/C][C]74.3555907209627[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 49 )[/C][C]80.6528925619835[/C][C]1.05833376133709[/C][C]76.2074267196084[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 49 )[/C][C]80.7478991596639[/C][C]1.03177121624480[/C][C]78.2614380865862[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 49 )[/C][C]80.8034188034188[/C][C]1.01253849564521[/C][C]79.802811597725[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 49 )[/C][C]80.8434782608696[/C][C]0.994998269710735[/C][C]81.2498681875822[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 49 )[/C][C]80.8672566371681[/C][C]0.97920092625515[/C][C]82.584947040886[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 49 )[/C][C]80.8918918918919[/C][C]0.961618155018315[/C][C]84.1205955500614[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 49 )[/C][C]80.9174311926605[/C][C]0.94200937268919[/C][C]85.8987538114006[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 49 )[/C][C]80.96261682243[/C][C]0.92715886685513[/C][C]87.323348475381[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 49 )[/C][C]81.0190476190476[/C][C]0.912066139758085[/C][C]88.8302329045315[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 49 )[/C][C]81.0873786407767[/C][C]0.896628071793122[/C][C]90.4359133867112[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 49 )[/C][C]81.1584158415842[/C][C]0.879213495656217[/C][C]92.3079732539934[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 49 )[/C][C]81.1584158415842[/C][C]0.859523903398237[/C][C]94.4225233535845[/C][/ROW]
[ROW][C]Trimmed Mean ( 25 / 49 )[/C][C]81.3092783505155[/C][C]0.837193912977003[/C][C]97.12120106247[/C][/ROW]
[ROW][C]Trimmed Mean ( 26 / 49 )[/C][C]81.378947368421[/C][C]0.814644646988113[/C][C]99.8950249894768[/C][/ROW]
[ROW][C]Trimmed Mean ( 27 / 49 )[/C][C]81.4408602150538[/C][C]0.791856395501503[/C][C]102.848017238625[/C][/ROW]
[ROW][C]Trimmed Mean ( 28 / 49 )[/C][C]81.5164835164835[/C][C]0.767846303391442[/C][C]106.162500433276[/C][/ROW]
[ROW][C]Trimmed Mean ( 29 / 49 )[/C][C]81.5730337078652[/C][C]0.751553997899888[/C][C]108.539152124544[/C][/ROW]
[ROW][C]Trimmed Mean ( 30 / 49 )[/C][C]81.632183908046[/C][C]0.732838939783032[/C][C]111.391711707097[/C][/ROW]
[ROW][C]Trimmed Mean ( 31 / 49 )[/C][C]81.6823529411765[/C][C]0.719518155899012[/C][C]113.523685638088[/C][/ROW]
[ROW][C]Trimmed Mean ( 32 / 49 )[/C][C]81.7349397590361[/C][C]0.709095506725132[/C][C]115.266475367357[/C][/ROW]
[ROW][C]Trimmed Mean ( 33 / 49 )[/C][C]81.7654320987654[/C][C]0.702568393256607[/C][C]116.380743687827[/C][/ROW]
[ROW][C]Trimmed Mean ( 34 / 49 )[/C][C]81.7974683544304[/C][C]0.694808435729871[/C][C]117.726648307753[/C][/ROW]
[ROW][C]Trimmed Mean ( 35 / 49 )[/C][C]81.8311688311688[/C][C]0.68561097214626[/C][C]119.355103922858[/C][/ROW]
[ROW][C]Trimmed Mean ( 36 / 49 )[/C][C]81.88[/C][C]0.677025822228343[/C][C]120.940734181309[/C][/ROW]
[ROW][C]Trimmed Mean ( 37 / 49 )[/C][C]81.931506849315[/C][C]0.666760486298889[/C][C]122.879967443943[/C][/ROW]
[ROW][C]Trimmed Mean ( 38 / 49 )[/C][C]81.9859154929577[/C][C]0.654497813153818[/C][C]125.265377278945[/C][/ROW]
[ROW][C]Trimmed Mean ( 39 / 49 )[/C][C]82.0434782608696[/C][C]0.639837862630479[/C][C]128.225419364173[/C][/ROW]
[ROW][C]Trimmed Mean ( 40 / 49 )[/C][C]82.1044776119403[/C][C]0.622266733801166[/C][C]131.944185912685[/C][/ROW]
[ROW][C]Trimmed Mean ( 41 / 49 )[/C][C]82.1538461538462[/C][C]0.605753968061692[/C][C]135.622464705802[/C][/ROW]
[ROW][C]Trimmed Mean ( 42 / 49 )[/C][C]82.1904761904762[/C][C]0.590441503366478[/C][C]139.201725694851[/C][/ROW]
[ROW][C]Trimmed Mean ( 43 / 49 )[/C][C]82.2131147540984[/C][C]0.576457408934992[/C][C]142.617847354911[/C][/ROW]
[ROW][C]Trimmed Mean ( 44 / 49 )[/C][C]82.2033898305085[/C][C]0.567881654874744[/C][C]144.754438050371[/C][/ROW]
[ROW][C]Trimmed Mean ( 45 / 49 )[/C][C]82.1929824561404[/C][C]0.557158133541498[/C][C]147.521821019990[/C][/ROW]
[ROW][C]Trimmed Mean ( 46 / 49 )[/C][C]82.1818181818182[/C][C]0.543768437725041[/C][C]151.133851250436[/C][/ROW]
[ROW][C]Trimmed Mean ( 47 / 49 )[/C][C]82.1698113207547[/C][C]0.52701741010052[/C][C]155.914794740998[/C][/ROW]
[ROW][C]Trimmed Mean ( 48 / 49 )[/C][C]82.1698113207547[/C][C]0.505943148801622[/C][C]162.409178808691[/C][/ROW]
[ROW][C]Trimmed Mean ( 49 / 49 )[/C][C]82.1428571428571[/C][C]0.479157423749955[/C][C]171.431878274984[/C][/ROW]
[ROW][C]Median[/C][C]81[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]58[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]81.3875[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]81.3875[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]81.3875[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]81.3875[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]81.3875[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]81.3875[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]81.3875[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]81.3875[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]147[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=95745&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=95745&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 Mean78.87074829931971.3977521028746956.4268500380789
Geometric Mean76.5219370332731
Harmonic Mean73.162338294083
Quadratic Mean80.6587672525057
Winsorized Mean ( 1 / 49 )78.99319727891161.3650078210635257.8701426174728
Winsorized Mean ( 2 / 49 )79.07482993197281.3476800747077458.6747785442486
Winsorized Mean ( 3 / 49 )79.07482993197281.3476800747077458.6747785442486
Winsorized Mean ( 4 / 49 )79.07482993197281.3476800747077458.6747785442486
Winsorized Mean ( 5 / 49 )79.07482993197281.3476800747077458.6747785442486
Winsorized Mean ( 6 / 49 )79.07482993197281.3476800747077458.6747785442486
Winsorized Mean ( 7 / 49 )79.17006802721091.3290996344119659.5666915988872
Winsorized Mean ( 8 / 49 )79.33333333333331.2986711534582861.0880846333376
Winsorized Mean ( 9 / 49 )79.5782312925171.2560514286873863.3558702096135
Winsorized Mean ( 10 / 49 )79.5782312925171.2560514286873863.3558702096135
Winsorized Mean ( 11 / 49 )79.65306122448981.2437019817630364.045134921773
Winsorized Mean ( 12 / 49 )79.65306122448981.2437019817630364.045134921773
Winsorized Mean ( 13 / 49 )79.65306122448981.2437019817630364.045134921773
Winsorized Mean ( 14 / 49 )80.12925170068031.1696656786126968.506115179612
Winsorized Mean ( 15 / 49 )80.33333333333331.1403402378701770.446811105581
Winsorized Mean ( 16 / 49 )80.55102040816331.1106092725371172.5286762860806
Winsorized Mean ( 17 / 49 )80.55102040816331.1106092725371172.5286762860806
Winsorized Mean ( 18 / 49 )80.55102040816331.1106092725371172.5286762860806
Winsorized Mean ( 19 / 49 )80.29251700680271.048991460845776.5425839997502
Winsorized Mean ( 20 / 49 )80.1564625850341.0344319470182877.4883865643193
Winsorized Mean ( 21 / 49 )80.01360544217691.0197466249348778.4642022691543
Winsorized Mean ( 22 / 49 )80.01360544217691.0197466249348778.4642022691543
Winsorized Mean ( 23 / 49 )80.01360544217691.0197466249348778.4642022691543
Winsorized Mean ( 24 / 49 )80.01360544217691.0197466249348778.4642022691543
Winsorized Mean ( 25 / 49 )80.18367346938780.99710794213462280.4162418942622
Winsorized Mean ( 26 / 49 )80.36054421768710.97403364956393382.502841923032
Winsorized Mean ( 27 / 49 )80.17687074829930.9554760867008783.913006159201
Winsorized Mean ( 28 / 49 )80.55782312925170.86407984651196493.2296054056115
Winsorized Mean ( 29 / 49 )80.55782312925170.86407984651196493.2296054056115
Winsorized Mean ( 30 / 49 )80.76190476190480.794711185498527101.624220516341
Winsorized Mean ( 31 / 49 )80.76190476190480.749822663054741107.708007161166
Winsorized Mean ( 32 / 49 )81.19727891156460.700562193918884115.903027049396
Winsorized Mean ( 33 / 49 )81.19727891156460.700562193918884115.903027049396
Winsorized Mean ( 34 / 49 )81.19727891156460.700562193918884115.903027049396
Winsorized Mean ( 35 / 49 )80.95918367346940.678275422169976119.360338038581
Winsorized Mean ( 36 / 49 )80.95918367346940.678275422169976119.360338038581
Winsorized Mean ( 37 / 49 )80.95918367346940.678275422169976119.360338038581
Winsorized Mean ( 38 / 49 )80.95918367346940.678275422169976119.360338038581
Winsorized Mean ( 39 / 49 )80.95918367346940.678275422169976119.360338038581
Winsorized Mean ( 40 / 49 )81.23129251700680.648508753463287125.258590702439
Winsorized Mean ( 41 / 49 )81.51020408163270.618749038356078131.733867899323
Winsorized Mean ( 42 / 49 )81.7959183673470.58908934643652138.851464318853
Winsorized Mean ( 43 / 49 )82.38095238095240.53122895806165155.076170323139
Winsorized Mean ( 44 / 49 )82.38095238095240.53122895806165155.076170323139
Winsorized Mean ( 45 / 49 )82.38095238095240.53122895806165155.076170323139
Winsorized Mean ( 46 / 49 )82.38095238095240.53122895806165155.076170323139
Winsorized Mean ( 47 / 49 )82.38095238095240.53122895806165155.076170323139
Winsorized Mean ( 48 / 49 )82.38095238095240.53122895806165155.076170323139
Winsorized Mean ( 49 / 49 )82.38095238095240.53122895806165155.076170323139
Trimmed Mean ( 1 / 49 )79.15862068965521.3404864110485659.0521619892705
Trimmed Mean ( 2 / 49 )79.32867132867131.3136494197344760.3880077415985
Trimmed Mean ( 3 / 49 )79.32867132867131.2942283900778661.2941826472366
Trimmed Mean ( 4 / 49 )79.59712230215831.2729682937820162.5287547937849
Trimmed Mean ( 5 / 49 )79.73722627737231.249657319837663.8072734113498
Trimmed Mean ( 6 / 49 )79.73722627737231.2240474168516365.142269147109
Trimmed Mean ( 7 / 49 )80.030075187971.1958451201287066.9234450522799
Trimmed Mean ( 8 / 49 )80.16793893129771.1686425906196468.5991932647182
Trimmed Mean ( 9 / 49 )80.28682170542641.1444376876598670.1539477169758
Trimmed Mean ( 10 / 49 )80.37795275590551.1251479444922671.4376746181385
Trimmed Mean ( 11 / 49 )80.4721.1038686223839672.8999795521038
Trimmed Mean ( 12 / 49 )80.4721.0822589023869274.3555907209627
Trimmed Mean ( 13 / 49 )80.65289256198351.0583337613370976.2074267196084
Trimmed Mean ( 14 / 49 )80.74789915966391.0317712162448078.2614380865862
Trimmed Mean ( 15 / 49 )80.80341880341881.0125384956452179.802811597725
Trimmed Mean ( 16 / 49 )80.84347826086960.99499826971073581.2498681875822
Trimmed Mean ( 17 / 49 )80.86725663716810.9792009262551582.584947040886
Trimmed Mean ( 18 / 49 )80.89189189189190.96161815501831584.1205955500614
Trimmed Mean ( 19 / 49 )80.91743119266050.9420093726891985.8987538114006
Trimmed Mean ( 20 / 49 )80.962616822430.9271588668551387.323348475381
Trimmed Mean ( 21 / 49 )81.01904761904760.91206613975808588.8302329045315
Trimmed Mean ( 22 / 49 )81.08737864077670.89662807179312290.4359133867112
Trimmed Mean ( 23 / 49 )81.15841584158420.87921349565621792.3079732539934
Trimmed Mean ( 24 / 49 )81.15841584158420.85952390339823794.4225233535845
Trimmed Mean ( 25 / 49 )81.30927835051550.83719391297700397.12120106247
Trimmed Mean ( 26 / 49 )81.3789473684210.81464464698811399.8950249894768
Trimmed Mean ( 27 / 49 )81.44086021505380.791856395501503102.848017238625
Trimmed Mean ( 28 / 49 )81.51648351648350.767846303391442106.162500433276
Trimmed Mean ( 29 / 49 )81.57303370786520.751553997899888108.539152124544
Trimmed Mean ( 30 / 49 )81.6321839080460.732838939783032111.391711707097
Trimmed Mean ( 31 / 49 )81.68235294117650.719518155899012113.523685638088
Trimmed Mean ( 32 / 49 )81.73493975903610.709095506725132115.266475367357
Trimmed Mean ( 33 / 49 )81.76543209876540.702568393256607116.380743687827
Trimmed Mean ( 34 / 49 )81.79746835443040.694808435729871117.726648307753
Trimmed Mean ( 35 / 49 )81.83116883116880.68561097214626119.355103922858
Trimmed Mean ( 36 / 49 )81.880.677025822228343120.940734181309
Trimmed Mean ( 37 / 49 )81.9315068493150.666760486298889122.879967443943
Trimmed Mean ( 38 / 49 )81.98591549295770.654497813153818125.265377278945
Trimmed Mean ( 39 / 49 )82.04347826086960.639837862630479128.225419364173
Trimmed Mean ( 40 / 49 )82.10447761194030.622266733801166131.944185912685
Trimmed Mean ( 41 / 49 )82.15384615384620.605753968061692135.622464705802
Trimmed Mean ( 42 / 49 )82.19047619047620.590441503366478139.201725694851
Trimmed Mean ( 43 / 49 )82.21311475409840.576457408934992142.617847354911
Trimmed Mean ( 44 / 49 )82.20338983050850.567881654874744144.754438050371
Trimmed Mean ( 45 / 49 )82.19298245614040.557158133541498147.521821019990
Trimmed Mean ( 46 / 49 )82.18181818181820.543768437725041151.133851250436
Trimmed Mean ( 47 / 49 )82.16981132075470.52701741010052155.914794740998
Trimmed Mean ( 48 / 49 )82.16981132075470.505943148801622162.409178808691
Trimmed Mean ( 49 / 49 )82.14285714285710.479157423749955171.431878274984
Median81
Midrange58
Midmean - Weighted Average at Xnp81.3875
Midmean - Weighted Average at X(n+1)p81.3875
Midmean - Empirical Distribution Function81.3875
Midmean - Empirical Distribution Function - Averaging81.3875
Midmean - Empirical Distribution Function - Interpolation81.3875
Midmean - Closest Observation81.3875
Midmean - True Basic - Statistics Graphics Toolkit81.3875
Midmean - MS Excel (old versions)81.3875
Number of observations147



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')