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of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationFri, 06 Aug 2010 10:34:52 +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/Aug/06/t1281090875l56jy22nkmxa23g.htm/, Retrieved Mon, 06 May 2024 13:22:28 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=78448, Retrieved Mon, 06 May 2024 13:22:28 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsGosselin Claudia
Estimated Impact155
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [Tijdreeks A - sta...] [2010-08-06 10:34:52] [f0cd0ad4d4cb2a25864ed1f6cd7bfd87] [Current]
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Dataseries X:
155
154
153
151
171
170
155
145
146
146
147
149
146
155
149
140
155
152
137
127
134
125
132
141
133
143
141
132
144
140
130
122
124
119
128
131
121
123
116
109
116
109
103
98
95
83
92
94
76
75
77
68
80
66
69
67
68
64
72
70
55
55
54
55
67
54
57
53
49
47
64
58
38
41
38
41
60
49
53
55
56
52
68
68
41
46
41
47
62
48
53
61
59
46
69
69
42
42
42
50
64
47
51
66
64
49
71
68
39
30
22
33
46
24
27
45
38
18
36
31




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135

\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 & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=78448&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]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=78448&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=78448&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'Gwilym Jenkins' @ 72.249.127.135







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean85.05833333333333.9035159012386721.7901849218399
Geometric Mean74.403696749972
Harmonic Mean64.5469574728297
Quadratic Mean95.1218954815346
Winsorized Mean ( 1 / 40 )85.08333333333333.8973089784588721.8313030359164
Winsorized Mean ( 2 / 40 )84.86666666666673.8507872041315522.0387838038966
Winsorized Mean ( 3 / 40 )84.94166666666673.8410523154238122.1141655180228
Winsorized Mean ( 4 / 40 )85.04166666666673.8286732574393922.2117848529969
Winsorized Mean ( 5 / 40 )85.08333333333333.8236801485765122.2516868637687
Winsorized Mean ( 6 / 40 )85.13333333333333.8043343505279522.3779840280124
Winsorized Mean ( 7 / 40 )85.253.7758307376130722.5778129169772
Winsorized Mean ( 8 / 40 )85.31666666666673.7514513220186222.7423094006078
Winsorized Mean ( 9 / 40 )85.24166666666673.7403095303490322.7900033339519
Winsorized Mean ( 10 / 40 )85.0753.7159502236205722.8945477953977
Winsorized Mean ( 11 / 40 )85.16666666666673.7062732294269922.9790577743870
Winsorized Mean ( 12 / 40 )85.16666666666673.656970883269823.2888555542769
Winsorized Mean ( 13 / 40 )85.05833333333333.6416570518240623.3570410730271
Winsorized Mean ( 14 / 40 )85.05833333333333.6416570518240623.3570410730271
Winsorized Mean ( 15 / 40 )85.05833333333333.6416570518240623.3570410730271
Winsorized Mean ( 16 / 40 )85.05833333333333.6095169845578223.5650181720237
Winsorized Mean ( 17 / 40 )84.91666666666673.5898351540481623.6547537763422
Winsorized Mean ( 18 / 40 )84.76666666666673.5691789366714923.749626502536
Winsorized Mean ( 19 / 40 )84.9253.4791931052854124.4093953483025
Winsorized Mean ( 20 / 40 )85.09166666666673.463252382297924.5698716910165
Winsorized Mean ( 21 / 40 )84.91666666666673.4396066670880224.6879003576759
Winsorized Mean ( 22 / 40 )84.91666666666673.4396066670880224.6879003576759
Winsorized Mean ( 23 / 40 )84.53333333333333.3448596235159225.2726101684581
Winsorized Mean ( 24 / 40 )83.93333333333333.2666666666666725.6938775510204
Winsorized Mean ( 25 / 40 )83.7253.2399372875799625.8415495636144
Winsorized Mean ( 26 / 40 )83.7253.1918129359232826.2311738440841
Winsorized Mean ( 27 / 40 )83.953.1708107190821926.4758787065978
Winsorized Mean ( 28 / 40 )83.71666666666673.1411960320348326.6512073149526
Winsorized Mean ( 29 / 40 )83.4753.1107242552429626.8345867877255
Winsorized Mean ( 30 / 40 )83.2253.0250231496671927.512186149437
Winsorized Mean ( 31 / 40 )83.2252.9692509712943128.0289543742144
Winsorized Mean ( 32 / 40 )82.95833333333332.8792796872262328.8121830266693
Winsorized Mean ( 33 / 40 )82.95833333333332.8209002832482229.4084600671557
Winsorized Mean ( 34 / 40 )82.6752.7863503457569229.6714302729010
Winsorized Mean ( 35 / 40 )82.38333333333332.7509657925505729.9470584317776
Winsorized Mean ( 36 / 40 )82.38333333333332.6879277611063630.6493851975487
Winsorized Mean ( 37 / 40 )81.76666666666672.6137894759977531.2828050680915
Winsorized Mean ( 38 / 40 )81.13333333333332.4724230659402732.8153116070684
Winsorized Mean ( 39 / 40 )81.13333333333332.4724230659402732.8153116070684
Winsorized Mean ( 40 / 40 )78.82.1993314492202935.8290697966131
Trimmed Mean ( 1 / 40 )84.89830508474583.8600084635052821.994331330468
Trimmed Mean ( 2 / 40 )84.70689655172413.8184240734895322.1837320636608
Trimmed Mean ( 3 / 40 )84.62280701754393.7985564706622422.2776224787283
Trimmed Mean ( 4 / 40 )84.50892857142863.7796446350843122.3589614184836
Trimmed Mean ( 5 / 40 )84.36363636363643.7616369848945222.4273731629109
Trimmed Mean ( 6 / 40 )84.20370370370373.7420449662539922.5020555506570
Trimmed Mean ( 7 / 40 )84.02830188679243.7236153573148322.5663216587942
Trimmed Mean ( 8 / 40 )83.82692307692313.7076320149483122.6092888234195
Trimmed Mean ( 9 / 40 )83.6078431372553.6929878109203822.6396206589206
Trimmed Mean ( 10 / 40 )83.393.6773094852765722.6769055837921
Trimmed Mean ( 11 / 40 )83.18367346938783.6623865590580122.7129692969338
Trimmed Mean ( 12 / 40 )82.95833333333333.6457111508348622.7550483022595
Trimmed Mean ( 13 / 40 )82.72340425531923.6324626324118022.7733668936312
Trimmed Mean ( 14 / 40 )82.48913043478263.6181674678519522.7985938096323
Trimmed Mean ( 15 / 40 )82.24444444444443.6005031938212322.8424861795937
Trimmed Mean ( 16 / 40 )81.98863636363643.5789897729273222.9083181471559
Trimmed Mean ( 17 / 40 )81.72093023255813.5570646517132722.9742605868007
Trimmed Mean ( 18 / 40 )81.4523809523813.5330748003700623.0542475194268
Trimmed Mean ( 19 / 40 )81.18292682926833.5067418205449923.1505286056820
Trimmed Mean ( 20 / 40 )80.88753.4855939394541523.2062315361574
Trimmed Mean ( 21 / 40 )80.56410256410263.4610524936065023.2773419972469
Trimmed Mean ( 22 / 40 )80.23684210526323.4338290438115523.3665803048251
Trimmed Mean ( 23 / 40 )79.89189189189193.4002726314223523.495731240372
Trimmed Mean ( 24 / 40 )79.55555555555563.3714306975977723.5969719360510
Trimmed Mean ( 25 / 40 )79.24285714285713.3459864845168823.6829579287134
Trimmed Mean ( 26 / 40 )78.92647058823533.3173735986216123.7918546831836
Trimmed Mean ( 27 / 40 )78.59090909090913.2872556959560523.9077566091348
Trimmed Mean ( 28 / 40 )78.218753.2512565298385024.0580062760798
Trimmed Mean ( 29 / 40 )77.83870967741943.2100939383059124.2481096109287
Trimmed Mean ( 30 / 40 )77.453.1627622376257524.4880880006146
Trimmed Mean ( 31 / 40 )77.0517241379313.1156788306559124.7303166744276
Trimmed Mean ( 32 / 40 )76.6253.0636709264303425.0108454334814
Trimmed Mean ( 33 / 40 )76.18518518518523.011284863600825.2998931140926
Trimmed Mean ( 34 / 40 )75.71153846153852.9524048201538225.6440234566457
Trimmed Mean ( 35 / 40 )75.222.8822171171173226.0979644986746
Trimmed Mean ( 36 / 40 )74.70833333333332.7976938218897726.7035415915777
Trimmed Mean ( 37 / 40 )74.15217391304352.6983565209778627.4804953817487
Trimmed Mean ( 38 / 40 )73.59090909090912.5847818948186828.4708389665007
Trimmed Mean ( 39 / 40 )73.02380952380952.4673214033362829.5963912221033
Trimmed Mean ( 40 / 40 )72.42.3060122089209131.3961911042437
Median68
Midrange94.5
Midmean - Weighted Average at Xnp76.0952380952381
Midmean - Weighted Average at X(n+1)p77.45
Midmean - Empirical Distribution Function76.0952380952381
Midmean - Empirical Distribution Function - Averaging77.45
Midmean - Empirical Distribution Function - Interpolation77.45
Midmean - Closest Observation76.0952380952381
Midmean - True Basic - Statistics Graphics Toolkit77.45
Midmean - MS Excel (old versions)76.9375
Number of observations120

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 85.0583333333333 & 3.90351590123867 & 21.7901849218399 \tabularnewline
Geometric Mean & 74.403696749972 &  &  \tabularnewline
Harmonic Mean & 64.5469574728297 &  &  \tabularnewline
Quadratic Mean & 95.1218954815346 &  &  \tabularnewline
Winsorized Mean ( 1 / 40 ) & 85.0833333333333 & 3.89730897845887 & 21.8313030359164 \tabularnewline
Winsorized Mean ( 2 / 40 ) & 84.8666666666667 & 3.85078720413155 & 22.0387838038966 \tabularnewline
Winsorized Mean ( 3 / 40 ) & 84.9416666666667 & 3.84105231542381 & 22.1141655180228 \tabularnewline
Winsorized Mean ( 4 / 40 ) & 85.0416666666667 & 3.82867325743939 & 22.2117848529969 \tabularnewline
Winsorized Mean ( 5 / 40 ) & 85.0833333333333 & 3.82368014857651 & 22.2516868637687 \tabularnewline
Winsorized Mean ( 6 / 40 ) & 85.1333333333333 & 3.80433435052795 & 22.3779840280124 \tabularnewline
Winsorized Mean ( 7 / 40 ) & 85.25 & 3.77583073761307 & 22.5778129169772 \tabularnewline
Winsorized Mean ( 8 / 40 ) & 85.3166666666667 & 3.75145132201862 & 22.7423094006078 \tabularnewline
Winsorized Mean ( 9 / 40 ) & 85.2416666666667 & 3.74030953034903 & 22.7900033339519 \tabularnewline
Winsorized Mean ( 10 / 40 ) & 85.075 & 3.71595022362057 & 22.8945477953977 \tabularnewline
Winsorized Mean ( 11 / 40 ) & 85.1666666666667 & 3.70627322942699 & 22.9790577743870 \tabularnewline
Winsorized Mean ( 12 / 40 ) & 85.1666666666667 & 3.6569708832698 & 23.2888555542769 \tabularnewline
Winsorized Mean ( 13 / 40 ) & 85.0583333333333 & 3.64165705182406 & 23.3570410730271 \tabularnewline
Winsorized Mean ( 14 / 40 ) & 85.0583333333333 & 3.64165705182406 & 23.3570410730271 \tabularnewline
Winsorized Mean ( 15 / 40 ) & 85.0583333333333 & 3.64165705182406 & 23.3570410730271 \tabularnewline
Winsorized Mean ( 16 / 40 ) & 85.0583333333333 & 3.60951698455782 & 23.5650181720237 \tabularnewline
Winsorized Mean ( 17 / 40 ) & 84.9166666666667 & 3.58983515404816 & 23.6547537763422 \tabularnewline
Winsorized Mean ( 18 / 40 ) & 84.7666666666667 & 3.56917893667149 & 23.749626502536 \tabularnewline
Winsorized Mean ( 19 / 40 ) & 84.925 & 3.47919310528541 & 24.4093953483025 \tabularnewline
Winsorized Mean ( 20 / 40 ) & 85.0916666666667 & 3.4632523822979 & 24.5698716910165 \tabularnewline
Winsorized Mean ( 21 / 40 ) & 84.9166666666667 & 3.43960666708802 & 24.6879003576759 \tabularnewline
Winsorized Mean ( 22 / 40 ) & 84.9166666666667 & 3.43960666708802 & 24.6879003576759 \tabularnewline
Winsorized Mean ( 23 / 40 ) & 84.5333333333333 & 3.34485962351592 & 25.2726101684581 \tabularnewline
Winsorized Mean ( 24 / 40 ) & 83.9333333333333 & 3.26666666666667 & 25.6938775510204 \tabularnewline
Winsorized Mean ( 25 / 40 ) & 83.725 & 3.23993728757996 & 25.8415495636144 \tabularnewline
Winsorized Mean ( 26 / 40 ) & 83.725 & 3.19181293592328 & 26.2311738440841 \tabularnewline
Winsorized Mean ( 27 / 40 ) & 83.95 & 3.17081071908219 & 26.4758787065978 \tabularnewline
Winsorized Mean ( 28 / 40 ) & 83.7166666666667 & 3.14119603203483 & 26.6512073149526 \tabularnewline
Winsorized Mean ( 29 / 40 ) & 83.475 & 3.11072425524296 & 26.8345867877255 \tabularnewline
Winsorized Mean ( 30 / 40 ) & 83.225 & 3.02502314966719 & 27.512186149437 \tabularnewline
Winsorized Mean ( 31 / 40 ) & 83.225 & 2.96925097129431 & 28.0289543742144 \tabularnewline
Winsorized Mean ( 32 / 40 ) & 82.9583333333333 & 2.87927968722623 & 28.8121830266693 \tabularnewline
Winsorized Mean ( 33 / 40 ) & 82.9583333333333 & 2.82090028324822 & 29.4084600671557 \tabularnewline
Winsorized Mean ( 34 / 40 ) & 82.675 & 2.78635034575692 & 29.6714302729010 \tabularnewline
Winsorized Mean ( 35 / 40 ) & 82.3833333333333 & 2.75096579255057 & 29.9470584317776 \tabularnewline
Winsorized Mean ( 36 / 40 ) & 82.3833333333333 & 2.68792776110636 & 30.6493851975487 \tabularnewline
Winsorized Mean ( 37 / 40 ) & 81.7666666666667 & 2.61378947599775 & 31.2828050680915 \tabularnewline
Winsorized Mean ( 38 / 40 ) & 81.1333333333333 & 2.47242306594027 & 32.8153116070684 \tabularnewline
Winsorized Mean ( 39 / 40 ) & 81.1333333333333 & 2.47242306594027 & 32.8153116070684 \tabularnewline
Winsorized Mean ( 40 / 40 ) & 78.8 & 2.19933144922029 & 35.8290697966131 \tabularnewline
Trimmed Mean ( 1 / 40 ) & 84.8983050847458 & 3.86000846350528 & 21.994331330468 \tabularnewline
Trimmed Mean ( 2 / 40 ) & 84.7068965517241 & 3.81842407348953 & 22.1837320636608 \tabularnewline
Trimmed Mean ( 3 / 40 ) & 84.6228070175439 & 3.79855647066224 & 22.2776224787283 \tabularnewline
Trimmed Mean ( 4 / 40 ) & 84.5089285714286 & 3.77964463508431 & 22.3589614184836 \tabularnewline
Trimmed Mean ( 5 / 40 ) & 84.3636363636364 & 3.76163698489452 & 22.4273731629109 \tabularnewline
Trimmed Mean ( 6 / 40 ) & 84.2037037037037 & 3.74204496625399 & 22.5020555506570 \tabularnewline
Trimmed Mean ( 7 / 40 ) & 84.0283018867924 & 3.72361535731483 & 22.5663216587942 \tabularnewline
Trimmed Mean ( 8 / 40 ) & 83.8269230769231 & 3.70763201494831 & 22.6092888234195 \tabularnewline
Trimmed Mean ( 9 / 40 ) & 83.607843137255 & 3.69298781092038 & 22.6396206589206 \tabularnewline
Trimmed Mean ( 10 / 40 ) & 83.39 & 3.67730948527657 & 22.6769055837921 \tabularnewline
Trimmed Mean ( 11 / 40 ) & 83.1836734693878 & 3.66238655905801 & 22.7129692969338 \tabularnewline
Trimmed Mean ( 12 / 40 ) & 82.9583333333333 & 3.64571115083486 & 22.7550483022595 \tabularnewline
Trimmed Mean ( 13 / 40 ) & 82.7234042553192 & 3.63246263241180 & 22.7733668936312 \tabularnewline
Trimmed Mean ( 14 / 40 ) & 82.4891304347826 & 3.61816746785195 & 22.7985938096323 \tabularnewline
Trimmed Mean ( 15 / 40 ) & 82.2444444444444 & 3.60050319382123 & 22.8424861795937 \tabularnewline
Trimmed Mean ( 16 / 40 ) & 81.9886363636364 & 3.57898977292732 & 22.9083181471559 \tabularnewline
Trimmed Mean ( 17 / 40 ) & 81.7209302325581 & 3.55706465171327 & 22.9742605868007 \tabularnewline
Trimmed Mean ( 18 / 40 ) & 81.452380952381 & 3.53307480037006 & 23.0542475194268 \tabularnewline
Trimmed Mean ( 19 / 40 ) & 81.1829268292683 & 3.50674182054499 & 23.1505286056820 \tabularnewline
Trimmed Mean ( 20 / 40 ) & 80.8875 & 3.48559393945415 & 23.2062315361574 \tabularnewline
Trimmed Mean ( 21 / 40 ) & 80.5641025641026 & 3.46105249360650 & 23.2773419972469 \tabularnewline
Trimmed Mean ( 22 / 40 ) & 80.2368421052632 & 3.43382904381155 & 23.3665803048251 \tabularnewline
Trimmed Mean ( 23 / 40 ) & 79.8918918918919 & 3.40027263142235 & 23.495731240372 \tabularnewline
Trimmed Mean ( 24 / 40 ) & 79.5555555555556 & 3.37143069759777 & 23.5969719360510 \tabularnewline
Trimmed Mean ( 25 / 40 ) & 79.2428571428571 & 3.34598648451688 & 23.6829579287134 \tabularnewline
Trimmed Mean ( 26 / 40 ) & 78.9264705882353 & 3.31737359862161 & 23.7918546831836 \tabularnewline
Trimmed Mean ( 27 / 40 ) & 78.5909090909091 & 3.28725569595605 & 23.9077566091348 \tabularnewline
Trimmed Mean ( 28 / 40 ) & 78.21875 & 3.25125652983850 & 24.0580062760798 \tabularnewline
Trimmed Mean ( 29 / 40 ) & 77.8387096774194 & 3.21009393830591 & 24.2481096109287 \tabularnewline
Trimmed Mean ( 30 / 40 ) & 77.45 & 3.16276223762575 & 24.4880880006146 \tabularnewline
Trimmed Mean ( 31 / 40 ) & 77.051724137931 & 3.11567883065591 & 24.7303166744276 \tabularnewline
Trimmed Mean ( 32 / 40 ) & 76.625 & 3.06367092643034 & 25.0108454334814 \tabularnewline
Trimmed Mean ( 33 / 40 ) & 76.1851851851852 & 3.0112848636008 & 25.2998931140926 \tabularnewline
Trimmed Mean ( 34 / 40 ) & 75.7115384615385 & 2.95240482015382 & 25.6440234566457 \tabularnewline
Trimmed Mean ( 35 / 40 ) & 75.22 & 2.88221711711732 & 26.0979644986746 \tabularnewline
Trimmed Mean ( 36 / 40 ) & 74.7083333333333 & 2.79769382188977 & 26.7035415915777 \tabularnewline
Trimmed Mean ( 37 / 40 ) & 74.1521739130435 & 2.69835652097786 & 27.4804953817487 \tabularnewline
Trimmed Mean ( 38 / 40 ) & 73.5909090909091 & 2.58478189481868 & 28.4708389665007 \tabularnewline
Trimmed Mean ( 39 / 40 ) & 73.0238095238095 & 2.46732140333628 & 29.5963912221033 \tabularnewline
Trimmed Mean ( 40 / 40 ) & 72.4 & 2.30601220892091 & 31.3961911042437 \tabularnewline
Median & 68 &  &  \tabularnewline
Midrange & 94.5 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 76.0952380952381 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 77.45 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 76.0952380952381 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 77.45 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 77.45 &  &  \tabularnewline
Midmean - Closest Observation & 76.0952380952381 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 77.45 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 76.9375 &  &  \tabularnewline
Number of observations & 120 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=78448&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]85.0583333333333[/C][C]3.90351590123867[/C][C]21.7901849218399[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]74.403696749972[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]64.5469574728297[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]95.1218954815346[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 40 )[/C][C]85.0833333333333[/C][C]3.89730897845887[/C][C]21.8313030359164[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 40 )[/C][C]84.8666666666667[/C][C]3.85078720413155[/C][C]22.0387838038966[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 40 )[/C][C]84.9416666666667[/C][C]3.84105231542381[/C][C]22.1141655180228[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 40 )[/C][C]85.0416666666667[/C][C]3.82867325743939[/C][C]22.2117848529969[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 40 )[/C][C]85.0833333333333[/C][C]3.82368014857651[/C][C]22.2516868637687[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 40 )[/C][C]85.1333333333333[/C][C]3.80433435052795[/C][C]22.3779840280124[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 40 )[/C][C]85.25[/C][C]3.77583073761307[/C][C]22.5778129169772[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 40 )[/C][C]85.3166666666667[/C][C]3.75145132201862[/C][C]22.7423094006078[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 40 )[/C][C]85.2416666666667[/C][C]3.74030953034903[/C][C]22.7900033339519[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 40 )[/C][C]85.075[/C][C]3.71595022362057[/C][C]22.8945477953977[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 40 )[/C][C]85.1666666666667[/C][C]3.70627322942699[/C][C]22.9790577743870[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 40 )[/C][C]85.1666666666667[/C][C]3.6569708832698[/C][C]23.2888555542769[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 40 )[/C][C]85.0583333333333[/C][C]3.64165705182406[/C][C]23.3570410730271[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 40 )[/C][C]85.0583333333333[/C][C]3.64165705182406[/C][C]23.3570410730271[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 40 )[/C][C]85.0583333333333[/C][C]3.64165705182406[/C][C]23.3570410730271[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 40 )[/C][C]85.0583333333333[/C][C]3.60951698455782[/C][C]23.5650181720237[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 40 )[/C][C]84.9166666666667[/C][C]3.58983515404816[/C][C]23.6547537763422[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 40 )[/C][C]84.7666666666667[/C][C]3.56917893667149[/C][C]23.749626502536[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 40 )[/C][C]84.925[/C][C]3.47919310528541[/C][C]24.4093953483025[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 40 )[/C][C]85.0916666666667[/C][C]3.4632523822979[/C][C]24.5698716910165[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 40 )[/C][C]84.9166666666667[/C][C]3.43960666708802[/C][C]24.6879003576759[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 40 )[/C][C]84.9166666666667[/C][C]3.43960666708802[/C][C]24.6879003576759[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 40 )[/C][C]84.5333333333333[/C][C]3.34485962351592[/C][C]25.2726101684581[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 40 )[/C][C]83.9333333333333[/C][C]3.26666666666667[/C][C]25.6938775510204[/C][/ROW]
[ROW][C]Winsorized Mean ( 25 / 40 )[/C][C]83.725[/C][C]3.23993728757996[/C][C]25.8415495636144[/C][/ROW]
[ROW][C]Winsorized Mean ( 26 / 40 )[/C][C]83.725[/C][C]3.19181293592328[/C][C]26.2311738440841[/C][/ROW]
[ROW][C]Winsorized Mean ( 27 / 40 )[/C][C]83.95[/C][C]3.17081071908219[/C][C]26.4758787065978[/C][/ROW]
[ROW][C]Winsorized Mean ( 28 / 40 )[/C][C]83.7166666666667[/C][C]3.14119603203483[/C][C]26.6512073149526[/C][/ROW]
[ROW][C]Winsorized Mean ( 29 / 40 )[/C][C]83.475[/C][C]3.11072425524296[/C][C]26.8345867877255[/C][/ROW]
[ROW][C]Winsorized Mean ( 30 / 40 )[/C][C]83.225[/C][C]3.02502314966719[/C][C]27.512186149437[/C][/ROW]
[ROW][C]Winsorized Mean ( 31 / 40 )[/C][C]83.225[/C][C]2.96925097129431[/C][C]28.0289543742144[/C][/ROW]
[ROW][C]Winsorized Mean ( 32 / 40 )[/C][C]82.9583333333333[/C][C]2.87927968722623[/C][C]28.8121830266693[/C][/ROW]
[ROW][C]Winsorized Mean ( 33 / 40 )[/C][C]82.9583333333333[/C][C]2.82090028324822[/C][C]29.4084600671557[/C][/ROW]
[ROW][C]Winsorized Mean ( 34 / 40 )[/C][C]82.675[/C][C]2.78635034575692[/C][C]29.6714302729010[/C][/ROW]
[ROW][C]Winsorized Mean ( 35 / 40 )[/C][C]82.3833333333333[/C][C]2.75096579255057[/C][C]29.9470584317776[/C][/ROW]
[ROW][C]Winsorized Mean ( 36 / 40 )[/C][C]82.3833333333333[/C][C]2.68792776110636[/C][C]30.6493851975487[/C][/ROW]
[ROW][C]Winsorized Mean ( 37 / 40 )[/C][C]81.7666666666667[/C][C]2.61378947599775[/C][C]31.2828050680915[/C][/ROW]
[ROW][C]Winsorized Mean ( 38 / 40 )[/C][C]81.1333333333333[/C][C]2.47242306594027[/C][C]32.8153116070684[/C][/ROW]
[ROW][C]Winsorized Mean ( 39 / 40 )[/C][C]81.1333333333333[/C][C]2.47242306594027[/C][C]32.8153116070684[/C][/ROW]
[ROW][C]Winsorized Mean ( 40 / 40 )[/C][C]78.8[/C][C]2.19933144922029[/C][C]35.8290697966131[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 40 )[/C][C]84.8983050847458[/C][C]3.86000846350528[/C][C]21.994331330468[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 40 )[/C][C]84.7068965517241[/C][C]3.81842407348953[/C][C]22.1837320636608[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 40 )[/C][C]84.6228070175439[/C][C]3.79855647066224[/C][C]22.2776224787283[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 40 )[/C][C]84.5089285714286[/C][C]3.77964463508431[/C][C]22.3589614184836[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 40 )[/C][C]84.3636363636364[/C][C]3.76163698489452[/C][C]22.4273731629109[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 40 )[/C][C]84.2037037037037[/C][C]3.74204496625399[/C][C]22.5020555506570[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 40 )[/C][C]84.0283018867924[/C][C]3.72361535731483[/C][C]22.5663216587942[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 40 )[/C][C]83.8269230769231[/C][C]3.70763201494831[/C][C]22.6092888234195[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 40 )[/C][C]83.607843137255[/C][C]3.69298781092038[/C][C]22.6396206589206[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 40 )[/C][C]83.39[/C][C]3.67730948527657[/C][C]22.6769055837921[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 40 )[/C][C]83.1836734693878[/C][C]3.66238655905801[/C][C]22.7129692969338[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 40 )[/C][C]82.9583333333333[/C][C]3.64571115083486[/C][C]22.7550483022595[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 40 )[/C][C]82.7234042553192[/C][C]3.63246263241180[/C][C]22.7733668936312[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 40 )[/C][C]82.4891304347826[/C][C]3.61816746785195[/C][C]22.7985938096323[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 40 )[/C][C]82.2444444444444[/C][C]3.60050319382123[/C][C]22.8424861795937[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 40 )[/C][C]81.9886363636364[/C][C]3.57898977292732[/C][C]22.9083181471559[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 40 )[/C][C]81.7209302325581[/C][C]3.55706465171327[/C][C]22.9742605868007[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 40 )[/C][C]81.452380952381[/C][C]3.53307480037006[/C][C]23.0542475194268[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 40 )[/C][C]81.1829268292683[/C][C]3.50674182054499[/C][C]23.1505286056820[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 40 )[/C][C]80.8875[/C][C]3.48559393945415[/C][C]23.2062315361574[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 40 )[/C][C]80.5641025641026[/C][C]3.46105249360650[/C][C]23.2773419972469[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 40 )[/C][C]80.2368421052632[/C][C]3.43382904381155[/C][C]23.3665803048251[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 40 )[/C][C]79.8918918918919[/C][C]3.40027263142235[/C][C]23.495731240372[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 40 )[/C][C]79.5555555555556[/C][C]3.37143069759777[/C][C]23.5969719360510[/C][/ROW]
[ROW][C]Trimmed Mean ( 25 / 40 )[/C][C]79.2428571428571[/C][C]3.34598648451688[/C][C]23.6829579287134[/C][/ROW]
[ROW][C]Trimmed Mean ( 26 / 40 )[/C][C]78.9264705882353[/C][C]3.31737359862161[/C][C]23.7918546831836[/C][/ROW]
[ROW][C]Trimmed Mean ( 27 / 40 )[/C][C]78.5909090909091[/C][C]3.28725569595605[/C][C]23.9077566091348[/C][/ROW]
[ROW][C]Trimmed Mean ( 28 / 40 )[/C][C]78.21875[/C][C]3.25125652983850[/C][C]24.0580062760798[/C][/ROW]
[ROW][C]Trimmed Mean ( 29 / 40 )[/C][C]77.8387096774194[/C][C]3.21009393830591[/C][C]24.2481096109287[/C][/ROW]
[ROW][C]Trimmed Mean ( 30 / 40 )[/C][C]77.45[/C][C]3.16276223762575[/C][C]24.4880880006146[/C][/ROW]
[ROW][C]Trimmed Mean ( 31 / 40 )[/C][C]77.051724137931[/C][C]3.11567883065591[/C][C]24.7303166744276[/C][/ROW]
[ROW][C]Trimmed Mean ( 32 / 40 )[/C][C]76.625[/C][C]3.06367092643034[/C][C]25.0108454334814[/C][/ROW]
[ROW][C]Trimmed Mean ( 33 / 40 )[/C][C]76.1851851851852[/C][C]3.0112848636008[/C][C]25.2998931140926[/C][/ROW]
[ROW][C]Trimmed Mean ( 34 / 40 )[/C][C]75.7115384615385[/C][C]2.95240482015382[/C][C]25.6440234566457[/C][/ROW]
[ROW][C]Trimmed Mean ( 35 / 40 )[/C][C]75.22[/C][C]2.88221711711732[/C][C]26.0979644986746[/C][/ROW]
[ROW][C]Trimmed Mean ( 36 / 40 )[/C][C]74.7083333333333[/C][C]2.79769382188977[/C][C]26.7035415915777[/C][/ROW]
[ROW][C]Trimmed Mean ( 37 / 40 )[/C][C]74.1521739130435[/C][C]2.69835652097786[/C][C]27.4804953817487[/C][/ROW]
[ROW][C]Trimmed Mean ( 38 / 40 )[/C][C]73.5909090909091[/C][C]2.58478189481868[/C][C]28.4708389665007[/C][/ROW]
[ROW][C]Trimmed Mean ( 39 / 40 )[/C][C]73.0238095238095[/C][C]2.46732140333628[/C][C]29.5963912221033[/C][/ROW]
[ROW][C]Trimmed Mean ( 40 / 40 )[/C][C]72.4[/C][C]2.30601220892091[/C][C]31.3961911042437[/C][/ROW]
[ROW][C]Median[/C][C]68[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]94.5[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]76.0952380952381[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]77.45[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]76.0952380952381[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]77.45[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]77.45[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]76.0952380952381[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]77.45[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]76.9375[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]120[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=78448&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=78448&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 Mean85.05833333333333.9035159012386721.7901849218399
Geometric Mean74.403696749972
Harmonic Mean64.5469574728297
Quadratic Mean95.1218954815346
Winsorized Mean ( 1 / 40 )85.08333333333333.8973089784588721.8313030359164
Winsorized Mean ( 2 / 40 )84.86666666666673.8507872041315522.0387838038966
Winsorized Mean ( 3 / 40 )84.94166666666673.8410523154238122.1141655180228
Winsorized Mean ( 4 / 40 )85.04166666666673.8286732574393922.2117848529969
Winsorized Mean ( 5 / 40 )85.08333333333333.8236801485765122.2516868637687
Winsorized Mean ( 6 / 40 )85.13333333333333.8043343505279522.3779840280124
Winsorized Mean ( 7 / 40 )85.253.7758307376130722.5778129169772
Winsorized Mean ( 8 / 40 )85.31666666666673.7514513220186222.7423094006078
Winsorized Mean ( 9 / 40 )85.24166666666673.7403095303490322.7900033339519
Winsorized Mean ( 10 / 40 )85.0753.7159502236205722.8945477953977
Winsorized Mean ( 11 / 40 )85.16666666666673.7062732294269922.9790577743870
Winsorized Mean ( 12 / 40 )85.16666666666673.656970883269823.2888555542769
Winsorized Mean ( 13 / 40 )85.05833333333333.6416570518240623.3570410730271
Winsorized Mean ( 14 / 40 )85.05833333333333.6416570518240623.3570410730271
Winsorized Mean ( 15 / 40 )85.05833333333333.6416570518240623.3570410730271
Winsorized Mean ( 16 / 40 )85.05833333333333.6095169845578223.5650181720237
Winsorized Mean ( 17 / 40 )84.91666666666673.5898351540481623.6547537763422
Winsorized Mean ( 18 / 40 )84.76666666666673.5691789366714923.749626502536
Winsorized Mean ( 19 / 40 )84.9253.4791931052854124.4093953483025
Winsorized Mean ( 20 / 40 )85.09166666666673.463252382297924.5698716910165
Winsorized Mean ( 21 / 40 )84.91666666666673.4396066670880224.6879003576759
Winsorized Mean ( 22 / 40 )84.91666666666673.4396066670880224.6879003576759
Winsorized Mean ( 23 / 40 )84.53333333333333.3448596235159225.2726101684581
Winsorized Mean ( 24 / 40 )83.93333333333333.2666666666666725.6938775510204
Winsorized Mean ( 25 / 40 )83.7253.2399372875799625.8415495636144
Winsorized Mean ( 26 / 40 )83.7253.1918129359232826.2311738440841
Winsorized Mean ( 27 / 40 )83.953.1708107190821926.4758787065978
Winsorized Mean ( 28 / 40 )83.71666666666673.1411960320348326.6512073149526
Winsorized Mean ( 29 / 40 )83.4753.1107242552429626.8345867877255
Winsorized Mean ( 30 / 40 )83.2253.0250231496671927.512186149437
Winsorized Mean ( 31 / 40 )83.2252.9692509712943128.0289543742144
Winsorized Mean ( 32 / 40 )82.95833333333332.8792796872262328.8121830266693
Winsorized Mean ( 33 / 40 )82.95833333333332.8209002832482229.4084600671557
Winsorized Mean ( 34 / 40 )82.6752.7863503457569229.6714302729010
Winsorized Mean ( 35 / 40 )82.38333333333332.7509657925505729.9470584317776
Winsorized Mean ( 36 / 40 )82.38333333333332.6879277611063630.6493851975487
Winsorized Mean ( 37 / 40 )81.76666666666672.6137894759977531.2828050680915
Winsorized Mean ( 38 / 40 )81.13333333333332.4724230659402732.8153116070684
Winsorized Mean ( 39 / 40 )81.13333333333332.4724230659402732.8153116070684
Winsorized Mean ( 40 / 40 )78.82.1993314492202935.8290697966131
Trimmed Mean ( 1 / 40 )84.89830508474583.8600084635052821.994331330468
Trimmed Mean ( 2 / 40 )84.70689655172413.8184240734895322.1837320636608
Trimmed Mean ( 3 / 40 )84.62280701754393.7985564706622422.2776224787283
Trimmed Mean ( 4 / 40 )84.50892857142863.7796446350843122.3589614184836
Trimmed Mean ( 5 / 40 )84.36363636363643.7616369848945222.4273731629109
Trimmed Mean ( 6 / 40 )84.20370370370373.7420449662539922.5020555506570
Trimmed Mean ( 7 / 40 )84.02830188679243.7236153573148322.5663216587942
Trimmed Mean ( 8 / 40 )83.82692307692313.7076320149483122.6092888234195
Trimmed Mean ( 9 / 40 )83.6078431372553.6929878109203822.6396206589206
Trimmed Mean ( 10 / 40 )83.393.6773094852765722.6769055837921
Trimmed Mean ( 11 / 40 )83.18367346938783.6623865590580122.7129692969338
Trimmed Mean ( 12 / 40 )82.95833333333333.6457111508348622.7550483022595
Trimmed Mean ( 13 / 40 )82.72340425531923.6324626324118022.7733668936312
Trimmed Mean ( 14 / 40 )82.48913043478263.6181674678519522.7985938096323
Trimmed Mean ( 15 / 40 )82.24444444444443.6005031938212322.8424861795937
Trimmed Mean ( 16 / 40 )81.98863636363643.5789897729273222.9083181471559
Trimmed Mean ( 17 / 40 )81.72093023255813.5570646517132722.9742605868007
Trimmed Mean ( 18 / 40 )81.4523809523813.5330748003700623.0542475194268
Trimmed Mean ( 19 / 40 )81.18292682926833.5067418205449923.1505286056820
Trimmed Mean ( 20 / 40 )80.88753.4855939394541523.2062315361574
Trimmed Mean ( 21 / 40 )80.56410256410263.4610524936065023.2773419972469
Trimmed Mean ( 22 / 40 )80.23684210526323.4338290438115523.3665803048251
Trimmed Mean ( 23 / 40 )79.89189189189193.4002726314223523.495731240372
Trimmed Mean ( 24 / 40 )79.55555555555563.3714306975977723.5969719360510
Trimmed Mean ( 25 / 40 )79.24285714285713.3459864845168823.6829579287134
Trimmed Mean ( 26 / 40 )78.92647058823533.3173735986216123.7918546831836
Trimmed Mean ( 27 / 40 )78.59090909090913.2872556959560523.9077566091348
Trimmed Mean ( 28 / 40 )78.218753.2512565298385024.0580062760798
Trimmed Mean ( 29 / 40 )77.83870967741943.2100939383059124.2481096109287
Trimmed Mean ( 30 / 40 )77.453.1627622376257524.4880880006146
Trimmed Mean ( 31 / 40 )77.0517241379313.1156788306559124.7303166744276
Trimmed Mean ( 32 / 40 )76.6253.0636709264303425.0108454334814
Trimmed Mean ( 33 / 40 )76.18518518518523.011284863600825.2998931140926
Trimmed Mean ( 34 / 40 )75.71153846153852.9524048201538225.6440234566457
Trimmed Mean ( 35 / 40 )75.222.8822171171173226.0979644986746
Trimmed Mean ( 36 / 40 )74.70833333333332.7976938218897726.7035415915777
Trimmed Mean ( 37 / 40 )74.15217391304352.6983565209778627.4804953817487
Trimmed Mean ( 38 / 40 )73.59090909090912.5847818948186828.4708389665007
Trimmed Mean ( 39 / 40 )73.02380952380952.4673214033362829.5963912221033
Trimmed Mean ( 40 / 40 )72.42.3060122089209131.3961911042437
Median68
Midrange94.5
Midmean - Weighted Average at Xnp76.0952380952381
Midmean - Weighted Average at X(n+1)p77.45
Midmean - Empirical Distribution Function76.0952380952381
Midmean - Empirical Distribution Function - Averaging77.45
Midmean - Empirical Distribution Function - Interpolation77.45
Midmean - Closest Observation76.0952380952381
Midmean - True Basic - Statistics Graphics Toolkit77.45
Midmean - MS Excel (old versions)76.9375
Number of observations120



Parameters (Session):
Parameters (R input):
R code (references can be found in the software module):
geomean <- function(x) {
return(exp(mean(log(x))))
}
harmean <- function(x) {
return(1/mean(1/x))
}
quamean <- function(x) {
return(sqrt(mean(x*x)))
}
winmean <- function(x) {
x <-sort(x[!is.na(x)])
n<-length(x)
denom <- 3
nodenom <- n/denom
if (nodenom>40) denom <- n/40
sqrtn = sqrt(n)
roundnodenom = floor(nodenom)
win <- array(NA,dim=c(roundnodenom,2))
for (j in 1:roundnodenom) {
win[j,1] <- (j*x[j+1]+sum(x[(j+1):(n-j)])+j*x[n-j])/n
win[j,2] <- sd(c(rep(x[j+1],j),x[(j+1):(n-j)],rep(x[n-j],j)))/sqrtn
}
return(win)
}
trimean <- function(x) {
x <-sort(x[!is.na(x)])
n<-length(x)
denom <- 3
nodenom <- n/denom
if (nodenom>40) denom <- n/40
sqrtn = sqrt(n)
roundnodenom = floor(nodenom)
tri <- array(NA,dim=c(roundnodenom,2))
for (j in 1:roundnodenom) {
tri[j,1] <- mean(x,trim=j/n)
tri[j,2] <- sd(x[(j+1):(n-j)]) / sqrt(n-j*2)
}
return(tri)
}
midrange <- function(x) {
return((max(x)+min(x))/2)
}
q1 <- function(data,n,p,i,f) {
np <- n*p;
i <<- floor(np)
f <<- np - i
qvalue <- (1-f)*data[i] + f*data[i+1]
}
q2 <- function(data,n,p,i,f) {
np <- (n+1)*p
i <<- floor(np)
f <<- np - i
qvalue <- (1-f)*data[i] + f*data[i+1]
}
q3 <- function(data,n,p,i,f) {
np <- n*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- data[i]
} else {
qvalue <- data[i+1]
}
}
q4 <- function(data,n,p,i,f) {
np <- n*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- (data[i]+data[i+1])/2
} else {
qvalue <- data[i+1]
}
}
q5 <- function(data,n,p,i,f) {
np <- (n-1)*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- data[i+1]
} else {
qvalue <- data[i+1] + f*(data[i+2]-data[i+1])
}
}
q6 <- function(data,n,p,i,f) {
np <- n*p+0.5
i <<- floor(np)
f <<- np - i
qvalue <- data[i]
}
q7 <- function(data,n,p,i,f) {
np <- (n+1)*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- data[i]
} else {
qvalue <- f*data[i] + (1-f)*data[i+1]
}
}
q8 <- function(data,n,p,i,f) {
np <- (n+1)*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- data[i]
} else {
if (f == 0.5) {
qvalue <- (data[i]+data[i+1])/2
} else {
if (f < 0.5) {
qvalue <- data[i]
} else {
qvalue <- data[i+1]
}
}
}
}
midmean <- function(x,def) {
x <-sort(x[!is.na(x)])
n<-length(x)
if (def==1) {
qvalue1 <- q1(x,n,0.25,i,f)
qvalue3 <- q1(x,n,0.75,i,f)
}
if (def==2) {
qvalue1 <- q2(x,n,0.25,i,f)
qvalue3 <- q2(x,n,0.75,i,f)
}
if (def==3) {
qvalue1 <- q3(x,n,0.25,i,f)
qvalue3 <- q3(x,n,0.75,i,f)
}
if (def==4) {
qvalue1 <- q4(x,n,0.25,i,f)
qvalue3 <- q4(x,n,0.75,i,f)
}
if (def==5) {
qvalue1 <- q5(x,n,0.25,i,f)
qvalue3 <- q5(x,n,0.75,i,f)
}
if (def==6) {
qvalue1 <- q6(x,n,0.25,i,f)
qvalue3 <- q6(x,n,0.75,i,f)
}
if (def==7) {
qvalue1 <- q7(x,n,0.25,i,f)
qvalue3 <- q7(x,n,0.75,i,f)
}
if (def==8) {
qvalue1 <- q8(x,n,0.25,i,f)
qvalue3 <- q8(x,n,0.75,i,f)
}
midm <- 0
myn <- 0
roundno4 <- round(n/4)
round3no4 <- round(3*n/4)
for (i in 1:n) {
if ((x[i]>=qvalue1) & (x[i]<=qvalue3)){
midm = midm + x[i]
myn = myn + 1
}
}
midm = midm / myn
return(midm)
}
(arm <- mean(x))
sqrtn <- sqrt(length(x))
(armse <- sd(x) / sqrtn)
(armose <- arm / armse)
(geo <- geomean(x))
(har <- harmean(x))
(qua <- quamean(x))
(win <- winmean(x))
(tri <- trimean(x))
(midr <- midrange(x))
midm <- array(NA,dim=8)
for (j in 1:8) midm[j] <- midmean(x,j)
midm
bitmap(file='test1.png')
lb <- win[,1] - 2*win[,2]
ub <- win[,1] + 2*win[,2]
if ((ylimmin == '') | (ylimmax == '')) plot(win[,1],type='b',main=main, xlab='j', pch=19, ylab='Winsorized Mean(j/n)', ylim=c(min(lb),max(ub))) else plot(win[,1],type='l',main=main, xlab='j', pch=19, ylab='Winsorized Mean(j/n)', ylim=c(ylimmin,ylimmax))
lines(ub,lty=3)
lines(lb,lty=3)
grid()
dev.off()
bitmap(file='test2.png')
lb <- tri[,1] - 2*tri[,2]
ub <- tri[,1] + 2*tri[,2]
if ((ylimmin == '') | (ylimmax == '')) plot(tri[,1],type='b',main=main, xlab='j', pch=19, ylab='Trimmed Mean(j/n)', ylim=c(min(lb),max(ub))) else plot(tri[,1],type='l',main=main, xlab='j', pch=19, ylab='Trimmed Mean(j/n)', ylim=c(ylimmin,ylimmax))
lines(ub,lty=3)
lines(lb,lty=3)
grid()
dev.off()
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Central Tendency - Ungrouped Data',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Measure',header=TRUE)
a<-table.element(a,'Value',header=TRUE)
a<-table.element(a,'S.E.',header=TRUE)
a<-table.element(a,'Value/S.E.',header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('arithmetic_mean.htm', 'Arithmetic Mean', 'click to view the definition of the Arithmetic Mean'),header=TRUE)
a<-table.element(a,arm)
a<-table.element(a,hyperlink('arithmetic_mean_standard_error.htm', armse, 'click to view the definition of the Standard Error of the Arithmetic Mean'))
a<-table.element(a,armose)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('geometric_mean.htm', 'Geometric Mean', 'click to view the definition of the Geometric Mean'),header=TRUE)
a<-table.element(a,geo)
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('harmonic_mean.htm', 'Harmonic Mean', 'click to view the definition of the Harmonic Mean'),header=TRUE)
a<-table.element(a,har)
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('quadratic_mean.htm', 'Quadratic Mean', 'click to view the definition of the Quadratic Mean'),header=TRUE)
a<-table.element(a,qua)
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
for (j in 1:length(win[,1])) {
a<-table.row.start(a)
mylabel <- paste('Winsorized Mean (',j)
mylabel <- paste(mylabel,'/')
mylabel <- paste(mylabel,length(win[,1]))
mylabel <- paste(mylabel,')')
a<-table.element(a,hyperlink('winsorized_mean.htm', mylabel, 'click to view the definition of the Winsorized Mean'),header=TRUE)
a<-table.element(a,win[j,1])
a<-table.element(a,win[j,2])
a<-table.element(a,win[j,1]/win[j,2])
a<-table.row.end(a)
}
for (j in 1:length(tri[,1])) {
a<-table.row.start(a)
mylabel <- paste('Trimmed Mean (',j)
mylabel <- paste(mylabel,'/')
mylabel <- paste(mylabel,length(tri[,1]))
mylabel <- paste(mylabel,')')
a<-table.element(a,hyperlink('arithmetic_mean.htm', mylabel, 'click to view the definition of the Trimmed Mean'),header=TRUE)
a<-table.element(a,tri[j,1])
a<-table.element(a,tri[j,2])
a<-table.element(a,tri[j,1]/tri[j,2])
a<-table.row.end(a)
}
a<-table.row.start(a)
a<-table.element(a,hyperlink('median_1.htm', 'Median', 'click to view the definition of the Median'),header=TRUE)
a<-table.element(a,median(x))
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('midrange.htm', 'Midrange', 'click to view the definition of the Midrange'),header=TRUE)
a<-table.element(a,midr)
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_1.htm','Weighted Average at Xnp',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[1])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_2.htm','Weighted Average at X(n+1)p',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[2])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_3.htm','Empirical Distribution Function',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[3])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_4.htm','Empirical Distribution Function - Averaging',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[4])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_5.htm','Empirical Distribution Function - Interpolation',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[5])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_6.htm','Closest Observation',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[6])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_7.htm','True Basic - Statistics Graphics Toolkit',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[7])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_8.htm','MS Excel (old versions)',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[8])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Number of observations',header=TRUE)
a<-table.element(a,length(x))
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable.tab')