Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationFri, 01 Apr 2011 12:39:18 +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/2011/Apr/01/t1301661391mcbypdv78nm11ck.htm/, Retrieved Wed, 08 May 2024 05:45:15 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=119904, Retrieved Wed, 08 May 2024 05:45:15 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsKDGP1W52
Estimated Impact163
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [Centrummaten- Ver...] [2011-04-01 12:39:18] [693533e1fc7e34c5ef37684486948ac1] [Current]
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Dataseries X:
112
118
129
99
116
168
118
129
205
147
150
267
126
129
124
97
102
127
222
214
118
141
154
226
89
77
82
97
127
121
117
117
106
112
134
169
75
108
115
85
101
108
109
124
105
95
135
164
88
85
112
87
91
87
87
142
95
108
139
159
61
82
124
93
108
75
87
103
90
108
123
129
57
65
67
71
76
67
110
118
99
85
107
141
58
65
70
86
93
74
87
73
101
100
96
157
63
115
70
66
67
83
79
77
102
116
100
135
71
60
89
74
73
91
86
74
87
87
109
137
43
69
73
77
69
76
78
70
83
65
110
132
54
55
66
65
60
65
96
55
71
63
74
106
34
47
56
53
53
55
67
52
46
51
58
91
33
40
46
45
41
55
57
54
46
52
48
77
30
35
42
48
44
45
0
0
46
51
63
84
30
39
45
52
28
40
62




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Gwilym Jenkins' @ www.wessa.org

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 2 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ www.wessa.org \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=119904&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ www.wessa.org[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=119904&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=119904&T=0

As an alternative you can also use a QR Code:  

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

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Gwilym Jenkins' @ www.wessa.org







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean89.4278074866312.9297732429793530.5237982840235
Geometric Mean0
Harmonic Mean0
Quadratic Mean97.9483384511835
Winsorized Mean ( 1 / 62 )89.20855614973262.8658347185537831.1282976551945
Winsorized Mean ( 2 / 62 )89.46524064171122.8122008223330331.8132474506177
Winsorized Mean ( 3 / 62 )89.36898395721932.7767213951447732.1850741358082
Winsorized Mean ( 4 / 62 )89.17647058823532.7315392906564832.6469660873167
Winsorized Mean ( 5 / 62 )88.29411764705882.5288106071678534.9152749505208
Winsorized Mean ( 6 / 62 )88.29411764705882.5195847419461535.0431228516091
Winsorized Mean ( 7 / 62 )88.18181818181822.4902767514068635.4104491125337
Winsorized Mean ( 8 / 62 )88.1390374331552.436936087800636.1679725103923
Winsorized Mean ( 9 / 62 )88.09090909090912.4168505412201736.448637426473
Winsorized Mean ( 10 / 62 )87.93048128342252.3926440291913636.7503398794932
Winsorized Mean ( 11 / 62 )87.75401069518722.352122232692637.308439789173
Winsorized Mean ( 12 / 62 )87.62566844919792.3183460085797837.796630927787
Winsorized Mean ( 13 / 62 )87.34759358288772.2645107473024238.5723908296482
Winsorized Mean ( 14 / 62 )87.34759358288772.2470241529741138.8725655072628
Winsorized Mean ( 15 / 62 )87.4278074866312.2387778485124939.0515778708105
Winsorized Mean ( 16 / 62 )87.25668449197862.2170327674622239.3574176135697
Winsorized Mean ( 17 / 62 )87.07486631016042.1945048743882839.678593256455
Winsorized Mean ( 18 / 62 )86.97860962566852.1613639886092940.2424626689714
Winsorized Mean ( 19 / 62 )86.97860962566852.1613639886092940.2424626689714
Winsorized Mean ( 20 / 62 )86.87165775401072.1486698763512840.4304349914981
Winsorized Mean ( 21 / 62 )86.64705882352942.1225242362638640.8226475548041
Winsorized Mean ( 22 / 62 )86.41176470588232.0706520081553541.7316692353645
Winsorized Mean ( 23 / 62 )86.53475935828882.0581682870545742.0445499537495
Winsorized Mean ( 24 / 62 )86.53475935828882.0581682870545742.0445499537495
Winsorized Mean ( 25 / 62 )86.93582887700532.0187809890635743.0635266271906
Winsorized Mean ( 26 / 62 )86.65775401069521.9880334333773143.5896864488235
Winsorized Mean ( 27 / 62 )86.80213903743321.9742293390275243.9676066612357
Winsorized Mean ( 28 / 62 )86.65240641711231.9579443995046844.2568269247246
Winsorized Mean ( 29 / 62 )86.34224598930481.9248734003273644.8560648064547
Winsorized Mean ( 30 / 62 )86.50267379679141.9096126151447945.2985454278813
Winsorized Mean ( 31 / 62 )86.50267379679141.9096126151447945.2985454278813
Winsorized Mean ( 32 / 62 )86.50267379679141.875584731725246.1203763997507
Winsorized Mean ( 33 / 62 )86.14973262032091.8391393796636746.8424163893851
Winsorized Mean ( 34 / 62 )85.78609625668451.7675530218241548.5338177681095
Winsorized Mean ( 35 / 62 )85.78609625668451.7675530218241548.5338177681095
Winsorized Mean ( 36 / 62 )85.78609625668451.7675530218241548.5338177681095
Winsorized Mean ( 37 / 62 )85.78609625668451.7675530218241548.5338177681095
Winsorized Mean ( 38 / 62 )85.78609625668451.7288063263978449.6215770076626
Winsorized Mean ( 39 / 62 )85.99465240641711.7096380454195550.2999173636859
Winsorized Mean ( 40 / 62 )85.78074866310161.6889205799590850.7902797094105
Winsorized Mean ( 41 / 62 )861.6689880906171351.5282286814883
Winsorized Mean ( 42 / 62 )85.77540106951871.6474241384359952.0663738428352
Winsorized Mean ( 43 / 62 )86.2352941176471.6063818073655853.6829374699345
Winsorized Mean ( 44 / 62 )85.52941176470591.5397535197168755.5474695589156
Winsorized Mean ( 45 / 62 )85.77005347593581.5184745073573556.484355226486
Winsorized Mean ( 46 / 62 )86.01604278074871.4970785176742457.4559328487175
Winsorized Mean ( 47 / 62 )85.7647058823531.4290943262698160.0133275360585
Winsorized Mean ( 48 / 62 )85.7647058823531.4290943262698160.0133275360585
Winsorized Mean ( 49 / 62 )85.50267379679141.4053704450146660.839954404975
Winsorized Mean ( 50 / 62 )86.03743315508021.3601051759272563.2579264294204
Winsorized Mean ( 51 / 62 )85.7647058823531.3355199609809664.218213421054
Winsorized Mean ( 52 / 62 )85.7647058823531.3355199609809664.218213421054
Winsorized Mean ( 53 / 62 )85.7647058823531.3355199609809664.218213421054
Winsorized Mean ( 54 / 62 )85.7647058823531.3355199609809664.218213421054
Winsorized Mean ( 55 / 62 )86.05882352941181.3111293721875365.6371715522082
Winsorized Mean ( 56 / 62 )85.759358288771.284342745014466.7729534204741
Winsorized Mean ( 57 / 62 )85.759358288771.23224753697569.5958853359102
Winsorized Mean ( 58 / 62 )85.759358288771.23224753697569.5958853359102
Winsorized Mean ( 59 / 62 )85.44385026737971.204544521190870.9345721675034
Winsorized Mean ( 60 / 62 )84.80213903743321.1492057636446673.7919541653593
Winsorized Mean ( 61 / 62 )85.12834224598931.0677810621036579.724528994995
Winsorized Mean ( 62 / 62 )85.12834224598931.0677810621036579.724528994995
Trimmed Mean ( 1 / 62 )89.4278074866312.7582935625612532.4214248622586
Trimmed Mean ( 2 / 62 )88.95135135135132.6408286649080133.6831209587199
Trimmed Mean ( 3 / 62 )88.28729281767962.5436101815093934.709443081915
Trimmed Mean ( 4 / 62 )88.28729281767962.4520034545901536.006186146437
Trimmed Mean ( 5 / 62 )87.57627118644072.3666355175492837.0045452867742
Trimmed Mean ( 6 / 62 )87.42285714285712.3268879445411337.5707207336523
Trimmed Mean ( 7 / 62 )87.42285714285712.286139531111538.2403855727709
Trimmed Mean ( 8 / 62 )87.26589595375722.2479162927451838.8207942775249
Trimmed Mean ( 9 / 62 )86.982248520712.2158855726333439.2539441544092
Trimmed Mean ( 10 / 62 )86.84431137724552.1845450160614539.7539582561766
Trimmed Mean ( 11 / 62 )86.72121212121212.1543298994131340.2543789346452
Trimmed Mean ( 12 / 62 )86.61349693251532.1272536984601140.716110633731
Trimmed Mean ( 13 / 62 )86.51552795031062.1023335450475441.1521417018317
Trimmed Mean ( 14 / 62 )86.51552795031062.0818493948199641.5570541104355
Trimmed Mean ( 15 / 62 )86.36305732484082.0616647664444141.8899613217839
Trimmed Mean ( 16 / 62 )86.36305732484082.0406948118092542.320417940531
Trimmed Mean ( 17 / 62 )86.2026143790852.0202866783124142.6685060612744
Trimmed Mean ( 18 / 62 )86.13907284768212.0004643993967543.0595380121025
Trimmed Mean ( 19 / 62 )86.08053691275171.9821788269722743.4272305512603
Trimmed Mean ( 20 / 62 )86.02040816326531.9623107402300443.8362826028161
Trimmed Mean ( 21 / 62 )85.96551724137931.9419105661304344.2685254103538
Trimmed Mean ( 22 / 62 )85.92307692307691.9221291863426244.7020301931782
Trimmed Mean ( 23 / 62 )85.89361702127661.9051921305931645.0839658856529
Trimmed Mean ( 24 / 62 )85.85611510791371.8877520146354545.4806110348628
Trimmed Mean ( 25 / 62 )85.81751824817521.8686821131672145.92408609441
Trimmed Mean ( 26 / 62 )85.75555555555561.8510740212768846.3274588535367
Trimmed Mean ( 27 / 62 )85.70676691729321.8343877937015946.7222727994426
Trimmed Mean ( 28 / 62 )85.70676691729321.8171533319564847.1654017358101
Trimmed Mean ( 29 / 62 )85.59689922480621.7995652259375647.5653218850186
Trimmed Mean ( 30 / 62 )85.55905511811021.7829566248573247.9871769875259
Trimmed Mean ( 31 / 62 )85.5121.7658267185655648.4260426580613
Trimmed Mean ( 32 / 62 )85.5121.746888198208348.9510433968847
Trimmed Mean ( 33 / 62 )85.41322314049591.7287342071245649.4079557103028
Trimmed Mean ( 34 / 62 )85.37815126050421.7116602716178649.8803136791887
Trimmed Mean ( 35 / 62 )85.35897435897441.6984789548776650.2561271741648
Trimmed Mean ( 36 / 62 )85.33913043478261.6837214492353150.6848270380713
Trimmed Mean ( 37 / 62 )85.31858407079651.6672111909707151.1744310096196
Trimmed Mean ( 38 / 62 )85.29729729729731.6487453147638451.7346715308271
Trimmed Mean ( 39 / 62 )85.27522935779821.6313210033723252.2737273544045
Trimmed Mean ( 40 / 62 )85.24299065420561.6133393599085652.8363670858664
Trimmed Mean ( 41 / 62 )85.21904761904761.5949198742250353.4315541465402
Trimmed Mean ( 42 / 62 )85.18446601941751.5758473269307254.0562937561543
Trimmed Mean ( 43 / 62 )85.15841584158421.5562542408080854.7201180941784
Trimmed Mean ( 44 / 62 )85.11111111111111.5376058949033155.3530078111876
Trimmed Mean ( 45 / 62 )85.09278350515461.5224608794134155.8916059228663
Trimmed Mean ( 46 / 62 )85.06315789473681.5069685481860356.446538315036
Trimmed Mean ( 47 / 62 )85.02150537634411.4910500091028357.0212299099893
Trimmed Mean ( 48 / 62 )84.9890109890111.4789111350652257.4672872317395
Trimmed Mean ( 49 / 62 )84.95505617977531.4647640549104157.999140472471
Trimmed Mean ( 50 / 62 )84.93103448275861.4505843289292158.5495326186605
Trimmed Mean ( 51 / 62 )84.93103448275861.4381177167201959.0570809992205
Trimmed Mean ( 52 / 62 )84.84337349397591.4258519400124159.5036350641269
Trimmed Mean ( 53 / 62 )84.80246913580251.4113101076972460.0877643214573
Trimmed Mean ( 54 / 62 )84.7594936708861.3941286431911960.797469505303
Trimmed Mean ( 55 / 62 )84.71428571428571.3738671643413561.6611910620186
Trimmed Mean ( 56 / 62 )84.71428571428571.3525409298675562.6334359601094
Trimmed Mean ( 57 / 62 )84.60273972602741.330582168226863.5832508102626
Trimmed Mean ( 58 / 62 )84.54929577464791.3106572502080364.5090818070307
Trimmed Mean ( 59 / 62 )84.49275362318841.2867982015165365.6612307381308
Trimmed Mean ( 60 / 62 )84.44776119402991.2619906278102666.916314062141
Trimmed Mean ( 61 / 62 )84.43076923076921.2397598307211968.1025204548325
Trimmed Mean ( 62 / 62 )84.39682539682541.2234983130924868.9799278786961
Median85
Midrange133.5
Midmean - Weighted Average at Xnp84.7765957446808
Midmean - Weighted Average at X(n+1)p85.6185567010309
Midmean - Empirical Distribution Function85.6185567010309
Midmean - Empirical Distribution Function - Averaging85.6185567010309
Midmean - Empirical Distribution Function - Interpolation85.0215053763441
Midmean - Closest Observation84.7765957446808
Midmean - True Basic - Statistics Graphics Toolkit85.6185567010309
Midmean - MS Excel (old versions)85.6185567010309
Number of observations187

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 89.427807486631 & 2.92977324297935 & 30.5237982840235 \tabularnewline
Geometric Mean & 0 &  &  \tabularnewline
Harmonic Mean & 0 &  &  \tabularnewline
Quadratic Mean & 97.9483384511835 &  &  \tabularnewline
Winsorized Mean ( 1 / 62 ) & 89.2085561497326 & 2.86583471855378 & 31.1282976551945 \tabularnewline
Winsorized Mean ( 2 / 62 ) & 89.4652406417112 & 2.81220082233303 & 31.8132474506177 \tabularnewline
Winsorized Mean ( 3 / 62 ) & 89.3689839572193 & 2.77672139514477 & 32.1850741358082 \tabularnewline
Winsorized Mean ( 4 / 62 ) & 89.1764705882353 & 2.73153929065648 & 32.6469660873167 \tabularnewline
Winsorized Mean ( 5 / 62 ) & 88.2941176470588 & 2.52881060716785 & 34.9152749505208 \tabularnewline
Winsorized Mean ( 6 / 62 ) & 88.2941176470588 & 2.51958474194615 & 35.0431228516091 \tabularnewline
Winsorized Mean ( 7 / 62 ) & 88.1818181818182 & 2.49027675140686 & 35.4104491125337 \tabularnewline
Winsorized Mean ( 8 / 62 ) & 88.139037433155 & 2.4369360878006 & 36.1679725103923 \tabularnewline
Winsorized Mean ( 9 / 62 ) & 88.0909090909091 & 2.41685054122017 & 36.448637426473 \tabularnewline
Winsorized Mean ( 10 / 62 ) & 87.9304812834225 & 2.39264402919136 & 36.7503398794932 \tabularnewline
Winsorized Mean ( 11 / 62 ) & 87.7540106951872 & 2.3521222326926 & 37.308439789173 \tabularnewline
Winsorized Mean ( 12 / 62 ) & 87.6256684491979 & 2.31834600857978 & 37.796630927787 \tabularnewline
Winsorized Mean ( 13 / 62 ) & 87.3475935828877 & 2.26451074730242 & 38.5723908296482 \tabularnewline
Winsorized Mean ( 14 / 62 ) & 87.3475935828877 & 2.24702415297411 & 38.8725655072628 \tabularnewline
Winsorized Mean ( 15 / 62 ) & 87.427807486631 & 2.23877784851249 & 39.0515778708105 \tabularnewline
Winsorized Mean ( 16 / 62 ) & 87.2566844919786 & 2.21703276746222 & 39.3574176135697 \tabularnewline
Winsorized Mean ( 17 / 62 ) & 87.0748663101604 & 2.19450487438828 & 39.678593256455 \tabularnewline
Winsorized Mean ( 18 / 62 ) & 86.9786096256685 & 2.16136398860929 & 40.2424626689714 \tabularnewline
Winsorized Mean ( 19 / 62 ) & 86.9786096256685 & 2.16136398860929 & 40.2424626689714 \tabularnewline
Winsorized Mean ( 20 / 62 ) & 86.8716577540107 & 2.14866987635128 & 40.4304349914981 \tabularnewline
Winsorized Mean ( 21 / 62 ) & 86.6470588235294 & 2.12252423626386 & 40.8226475548041 \tabularnewline
Winsorized Mean ( 22 / 62 ) & 86.4117647058823 & 2.07065200815535 & 41.7316692353645 \tabularnewline
Winsorized Mean ( 23 / 62 ) & 86.5347593582888 & 2.05816828705457 & 42.0445499537495 \tabularnewline
Winsorized Mean ( 24 / 62 ) & 86.5347593582888 & 2.05816828705457 & 42.0445499537495 \tabularnewline
Winsorized Mean ( 25 / 62 ) & 86.9358288770053 & 2.01878098906357 & 43.0635266271906 \tabularnewline
Winsorized Mean ( 26 / 62 ) & 86.6577540106952 & 1.98803343337731 & 43.5896864488235 \tabularnewline
Winsorized Mean ( 27 / 62 ) & 86.8021390374332 & 1.97422933902752 & 43.9676066612357 \tabularnewline
Winsorized Mean ( 28 / 62 ) & 86.6524064171123 & 1.95794439950468 & 44.2568269247246 \tabularnewline
Winsorized Mean ( 29 / 62 ) & 86.3422459893048 & 1.92487340032736 & 44.8560648064547 \tabularnewline
Winsorized Mean ( 30 / 62 ) & 86.5026737967914 & 1.90961261514479 & 45.2985454278813 \tabularnewline
Winsorized Mean ( 31 / 62 ) & 86.5026737967914 & 1.90961261514479 & 45.2985454278813 \tabularnewline
Winsorized Mean ( 32 / 62 ) & 86.5026737967914 & 1.8755847317252 & 46.1203763997507 \tabularnewline
Winsorized Mean ( 33 / 62 ) & 86.1497326203209 & 1.83913937966367 & 46.8424163893851 \tabularnewline
Winsorized Mean ( 34 / 62 ) & 85.7860962566845 & 1.76755302182415 & 48.5338177681095 \tabularnewline
Winsorized Mean ( 35 / 62 ) & 85.7860962566845 & 1.76755302182415 & 48.5338177681095 \tabularnewline
Winsorized Mean ( 36 / 62 ) & 85.7860962566845 & 1.76755302182415 & 48.5338177681095 \tabularnewline
Winsorized Mean ( 37 / 62 ) & 85.7860962566845 & 1.76755302182415 & 48.5338177681095 \tabularnewline
Winsorized Mean ( 38 / 62 ) & 85.7860962566845 & 1.72880632639784 & 49.6215770076626 \tabularnewline
Winsorized Mean ( 39 / 62 ) & 85.9946524064171 & 1.70963804541955 & 50.2999173636859 \tabularnewline
Winsorized Mean ( 40 / 62 ) & 85.7807486631016 & 1.68892057995908 & 50.7902797094105 \tabularnewline
Winsorized Mean ( 41 / 62 ) & 86 & 1.66898809061713 & 51.5282286814883 \tabularnewline
Winsorized Mean ( 42 / 62 ) & 85.7754010695187 & 1.64742413843599 & 52.0663738428352 \tabularnewline
Winsorized Mean ( 43 / 62 ) & 86.235294117647 & 1.60638180736558 & 53.6829374699345 \tabularnewline
Winsorized Mean ( 44 / 62 ) & 85.5294117647059 & 1.53975351971687 & 55.5474695589156 \tabularnewline
Winsorized Mean ( 45 / 62 ) & 85.7700534759358 & 1.51847450735735 & 56.484355226486 \tabularnewline
Winsorized Mean ( 46 / 62 ) & 86.0160427807487 & 1.49707851767424 & 57.4559328487175 \tabularnewline
Winsorized Mean ( 47 / 62 ) & 85.764705882353 & 1.42909432626981 & 60.0133275360585 \tabularnewline
Winsorized Mean ( 48 / 62 ) & 85.764705882353 & 1.42909432626981 & 60.0133275360585 \tabularnewline
Winsorized Mean ( 49 / 62 ) & 85.5026737967914 & 1.40537044501466 & 60.839954404975 \tabularnewline
Winsorized Mean ( 50 / 62 ) & 86.0374331550802 & 1.36010517592725 & 63.2579264294204 \tabularnewline
Winsorized Mean ( 51 / 62 ) & 85.764705882353 & 1.33551996098096 & 64.218213421054 \tabularnewline
Winsorized Mean ( 52 / 62 ) & 85.764705882353 & 1.33551996098096 & 64.218213421054 \tabularnewline
Winsorized Mean ( 53 / 62 ) & 85.764705882353 & 1.33551996098096 & 64.218213421054 \tabularnewline
Winsorized Mean ( 54 / 62 ) & 85.764705882353 & 1.33551996098096 & 64.218213421054 \tabularnewline
Winsorized Mean ( 55 / 62 ) & 86.0588235294118 & 1.31112937218753 & 65.6371715522082 \tabularnewline
Winsorized Mean ( 56 / 62 ) & 85.75935828877 & 1.2843427450144 & 66.7729534204741 \tabularnewline
Winsorized Mean ( 57 / 62 ) & 85.75935828877 & 1.232247536975 & 69.5958853359102 \tabularnewline
Winsorized Mean ( 58 / 62 ) & 85.75935828877 & 1.232247536975 & 69.5958853359102 \tabularnewline
Winsorized Mean ( 59 / 62 ) & 85.4438502673797 & 1.2045445211908 & 70.9345721675034 \tabularnewline
Winsorized Mean ( 60 / 62 ) & 84.8021390374332 & 1.14920576364466 & 73.7919541653593 \tabularnewline
Winsorized Mean ( 61 / 62 ) & 85.1283422459893 & 1.06778106210365 & 79.724528994995 \tabularnewline
Winsorized Mean ( 62 / 62 ) & 85.1283422459893 & 1.06778106210365 & 79.724528994995 \tabularnewline
Trimmed Mean ( 1 / 62 ) & 89.427807486631 & 2.75829356256125 & 32.4214248622586 \tabularnewline
Trimmed Mean ( 2 / 62 ) & 88.9513513513513 & 2.64082866490801 & 33.6831209587199 \tabularnewline
Trimmed Mean ( 3 / 62 ) & 88.2872928176796 & 2.54361018150939 & 34.709443081915 \tabularnewline
Trimmed Mean ( 4 / 62 ) & 88.2872928176796 & 2.45200345459015 & 36.006186146437 \tabularnewline
Trimmed Mean ( 5 / 62 ) & 87.5762711864407 & 2.36663551754928 & 37.0045452867742 \tabularnewline
Trimmed Mean ( 6 / 62 ) & 87.4228571428571 & 2.32688794454113 & 37.5707207336523 \tabularnewline
Trimmed Mean ( 7 / 62 ) & 87.4228571428571 & 2.2861395311115 & 38.2403855727709 \tabularnewline
Trimmed Mean ( 8 / 62 ) & 87.2658959537572 & 2.24791629274518 & 38.8207942775249 \tabularnewline
Trimmed Mean ( 9 / 62 ) & 86.98224852071 & 2.21588557263334 & 39.2539441544092 \tabularnewline
Trimmed Mean ( 10 / 62 ) & 86.8443113772455 & 2.18454501606145 & 39.7539582561766 \tabularnewline
Trimmed Mean ( 11 / 62 ) & 86.7212121212121 & 2.15432989941313 & 40.2543789346452 \tabularnewline
Trimmed Mean ( 12 / 62 ) & 86.6134969325153 & 2.12725369846011 & 40.716110633731 \tabularnewline
Trimmed Mean ( 13 / 62 ) & 86.5155279503106 & 2.10233354504754 & 41.1521417018317 \tabularnewline
Trimmed Mean ( 14 / 62 ) & 86.5155279503106 & 2.08184939481996 & 41.5570541104355 \tabularnewline
Trimmed Mean ( 15 / 62 ) & 86.3630573248408 & 2.06166476644441 & 41.8899613217839 \tabularnewline
Trimmed Mean ( 16 / 62 ) & 86.3630573248408 & 2.04069481180925 & 42.320417940531 \tabularnewline
Trimmed Mean ( 17 / 62 ) & 86.202614379085 & 2.02028667831241 & 42.6685060612744 \tabularnewline
Trimmed Mean ( 18 / 62 ) & 86.1390728476821 & 2.00046439939675 & 43.0595380121025 \tabularnewline
Trimmed Mean ( 19 / 62 ) & 86.0805369127517 & 1.98217882697227 & 43.4272305512603 \tabularnewline
Trimmed Mean ( 20 / 62 ) & 86.0204081632653 & 1.96231074023004 & 43.8362826028161 \tabularnewline
Trimmed Mean ( 21 / 62 ) & 85.9655172413793 & 1.94191056613043 & 44.2685254103538 \tabularnewline
Trimmed Mean ( 22 / 62 ) & 85.9230769230769 & 1.92212918634262 & 44.7020301931782 \tabularnewline
Trimmed Mean ( 23 / 62 ) & 85.8936170212766 & 1.90519213059316 & 45.0839658856529 \tabularnewline
Trimmed Mean ( 24 / 62 ) & 85.8561151079137 & 1.88775201463545 & 45.4806110348628 \tabularnewline
Trimmed Mean ( 25 / 62 ) & 85.8175182481752 & 1.86868211316721 & 45.92408609441 \tabularnewline
Trimmed Mean ( 26 / 62 ) & 85.7555555555556 & 1.85107402127688 & 46.3274588535367 \tabularnewline
Trimmed Mean ( 27 / 62 ) & 85.7067669172932 & 1.83438779370159 & 46.7222727994426 \tabularnewline
Trimmed Mean ( 28 / 62 ) & 85.7067669172932 & 1.81715333195648 & 47.1654017358101 \tabularnewline
Trimmed Mean ( 29 / 62 ) & 85.5968992248062 & 1.79956522593756 & 47.5653218850186 \tabularnewline
Trimmed Mean ( 30 / 62 ) & 85.5590551181102 & 1.78295662485732 & 47.9871769875259 \tabularnewline
Trimmed Mean ( 31 / 62 ) & 85.512 & 1.76582671856556 & 48.4260426580613 \tabularnewline
Trimmed Mean ( 32 / 62 ) & 85.512 & 1.7468881982083 & 48.9510433968847 \tabularnewline
Trimmed Mean ( 33 / 62 ) & 85.4132231404959 & 1.72873420712456 & 49.4079557103028 \tabularnewline
Trimmed Mean ( 34 / 62 ) & 85.3781512605042 & 1.71166027161786 & 49.8803136791887 \tabularnewline
Trimmed Mean ( 35 / 62 ) & 85.3589743589744 & 1.69847895487766 & 50.2561271741648 \tabularnewline
Trimmed Mean ( 36 / 62 ) & 85.3391304347826 & 1.68372144923531 & 50.6848270380713 \tabularnewline
Trimmed Mean ( 37 / 62 ) & 85.3185840707965 & 1.66721119097071 & 51.1744310096196 \tabularnewline
Trimmed Mean ( 38 / 62 ) & 85.2972972972973 & 1.64874531476384 & 51.7346715308271 \tabularnewline
Trimmed Mean ( 39 / 62 ) & 85.2752293577982 & 1.63132100337232 & 52.2737273544045 \tabularnewline
Trimmed Mean ( 40 / 62 ) & 85.2429906542056 & 1.61333935990856 & 52.8363670858664 \tabularnewline
Trimmed Mean ( 41 / 62 ) & 85.2190476190476 & 1.59491987422503 & 53.4315541465402 \tabularnewline
Trimmed Mean ( 42 / 62 ) & 85.1844660194175 & 1.57584732693072 & 54.0562937561543 \tabularnewline
Trimmed Mean ( 43 / 62 ) & 85.1584158415842 & 1.55625424080808 & 54.7201180941784 \tabularnewline
Trimmed Mean ( 44 / 62 ) & 85.1111111111111 & 1.53760589490331 & 55.3530078111876 \tabularnewline
Trimmed Mean ( 45 / 62 ) & 85.0927835051546 & 1.52246087941341 & 55.8916059228663 \tabularnewline
Trimmed Mean ( 46 / 62 ) & 85.0631578947368 & 1.50696854818603 & 56.446538315036 \tabularnewline
Trimmed Mean ( 47 / 62 ) & 85.0215053763441 & 1.49105000910283 & 57.0212299099893 \tabularnewline
Trimmed Mean ( 48 / 62 ) & 84.989010989011 & 1.47891113506522 & 57.4672872317395 \tabularnewline
Trimmed Mean ( 49 / 62 ) & 84.9550561797753 & 1.46476405491041 & 57.999140472471 \tabularnewline
Trimmed Mean ( 50 / 62 ) & 84.9310344827586 & 1.45058432892921 & 58.5495326186605 \tabularnewline
Trimmed Mean ( 51 / 62 ) & 84.9310344827586 & 1.43811771672019 & 59.0570809992205 \tabularnewline
Trimmed Mean ( 52 / 62 ) & 84.8433734939759 & 1.42585194001241 & 59.5036350641269 \tabularnewline
Trimmed Mean ( 53 / 62 ) & 84.8024691358025 & 1.41131010769724 & 60.0877643214573 \tabularnewline
Trimmed Mean ( 54 / 62 ) & 84.759493670886 & 1.39412864319119 & 60.797469505303 \tabularnewline
Trimmed Mean ( 55 / 62 ) & 84.7142857142857 & 1.37386716434135 & 61.6611910620186 \tabularnewline
Trimmed Mean ( 56 / 62 ) & 84.7142857142857 & 1.35254092986755 & 62.6334359601094 \tabularnewline
Trimmed Mean ( 57 / 62 ) & 84.6027397260274 & 1.3305821682268 & 63.5832508102626 \tabularnewline
Trimmed Mean ( 58 / 62 ) & 84.5492957746479 & 1.31065725020803 & 64.5090818070307 \tabularnewline
Trimmed Mean ( 59 / 62 ) & 84.4927536231884 & 1.28679820151653 & 65.6612307381308 \tabularnewline
Trimmed Mean ( 60 / 62 ) & 84.4477611940299 & 1.26199062781026 & 66.916314062141 \tabularnewline
Trimmed Mean ( 61 / 62 ) & 84.4307692307692 & 1.23975983072119 & 68.1025204548325 \tabularnewline
Trimmed Mean ( 62 / 62 ) & 84.3968253968254 & 1.22349831309248 & 68.9799278786961 \tabularnewline
Median & 85 &  &  \tabularnewline
Midrange & 133.5 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 84.7765957446808 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 85.6185567010309 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 85.6185567010309 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 85.6185567010309 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 85.0215053763441 &  &  \tabularnewline
Midmean - Closest Observation & 84.7765957446808 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 85.6185567010309 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 85.6185567010309 &  &  \tabularnewline
Number of observations & 187 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=119904&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]89.427807486631[/C][C]2.92977324297935[/C][C]30.5237982840235[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]0[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]0[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]97.9483384511835[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 62 )[/C][C]89.2085561497326[/C][C]2.86583471855378[/C][C]31.1282976551945[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 62 )[/C][C]89.4652406417112[/C][C]2.81220082233303[/C][C]31.8132474506177[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 62 )[/C][C]89.3689839572193[/C][C]2.77672139514477[/C][C]32.1850741358082[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 62 )[/C][C]89.1764705882353[/C][C]2.73153929065648[/C][C]32.6469660873167[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 62 )[/C][C]88.2941176470588[/C][C]2.52881060716785[/C][C]34.9152749505208[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 62 )[/C][C]88.2941176470588[/C][C]2.51958474194615[/C][C]35.0431228516091[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 62 )[/C][C]88.1818181818182[/C][C]2.49027675140686[/C][C]35.4104491125337[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 62 )[/C][C]88.139037433155[/C][C]2.4369360878006[/C][C]36.1679725103923[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 62 )[/C][C]88.0909090909091[/C][C]2.41685054122017[/C][C]36.448637426473[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 62 )[/C][C]87.9304812834225[/C][C]2.39264402919136[/C][C]36.7503398794932[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 62 )[/C][C]87.7540106951872[/C][C]2.3521222326926[/C][C]37.308439789173[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 62 )[/C][C]87.6256684491979[/C][C]2.31834600857978[/C][C]37.796630927787[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 62 )[/C][C]87.3475935828877[/C][C]2.26451074730242[/C][C]38.5723908296482[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 62 )[/C][C]87.3475935828877[/C][C]2.24702415297411[/C][C]38.8725655072628[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 62 )[/C][C]87.427807486631[/C][C]2.23877784851249[/C][C]39.0515778708105[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 62 )[/C][C]87.2566844919786[/C][C]2.21703276746222[/C][C]39.3574176135697[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 62 )[/C][C]87.0748663101604[/C][C]2.19450487438828[/C][C]39.678593256455[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 62 )[/C][C]86.9786096256685[/C][C]2.16136398860929[/C][C]40.2424626689714[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 62 )[/C][C]86.9786096256685[/C][C]2.16136398860929[/C][C]40.2424626689714[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 62 )[/C][C]86.8716577540107[/C][C]2.14866987635128[/C][C]40.4304349914981[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 62 )[/C][C]86.6470588235294[/C][C]2.12252423626386[/C][C]40.8226475548041[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 62 )[/C][C]86.4117647058823[/C][C]2.07065200815535[/C][C]41.7316692353645[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 62 )[/C][C]86.5347593582888[/C][C]2.05816828705457[/C][C]42.0445499537495[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 62 )[/C][C]86.5347593582888[/C][C]2.05816828705457[/C][C]42.0445499537495[/C][/ROW]
[ROW][C]Winsorized Mean ( 25 / 62 )[/C][C]86.9358288770053[/C][C]2.01878098906357[/C][C]43.0635266271906[/C][/ROW]
[ROW][C]Winsorized Mean ( 26 / 62 )[/C][C]86.6577540106952[/C][C]1.98803343337731[/C][C]43.5896864488235[/C][/ROW]
[ROW][C]Winsorized Mean ( 27 / 62 )[/C][C]86.8021390374332[/C][C]1.97422933902752[/C][C]43.9676066612357[/C][/ROW]
[ROW][C]Winsorized Mean ( 28 / 62 )[/C][C]86.6524064171123[/C][C]1.95794439950468[/C][C]44.2568269247246[/C][/ROW]
[ROW][C]Winsorized Mean ( 29 / 62 )[/C][C]86.3422459893048[/C][C]1.92487340032736[/C][C]44.8560648064547[/C][/ROW]
[ROW][C]Winsorized Mean ( 30 / 62 )[/C][C]86.5026737967914[/C][C]1.90961261514479[/C][C]45.2985454278813[/C][/ROW]
[ROW][C]Winsorized Mean ( 31 / 62 )[/C][C]86.5026737967914[/C][C]1.90961261514479[/C][C]45.2985454278813[/C][/ROW]
[ROW][C]Winsorized Mean ( 32 / 62 )[/C][C]86.5026737967914[/C][C]1.8755847317252[/C][C]46.1203763997507[/C][/ROW]
[ROW][C]Winsorized Mean ( 33 / 62 )[/C][C]86.1497326203209[/C][C]1.83913937966367[/C][C]46.8424163893851[/C][/ROW]
[ROW][C]Winsorized Mean ( 34 / 62 )[/C][C]85.7860962566845[/C][C]1.76755302182415[/C][C]48.5338177681095[/C][/ROW]
[ROW][C]Winsorized Mean ( 35 / 62 )[/C][C]85.7860962566845[/C][C]1.76755302182415[/C][C]48.5338177681095[/C][/ROW]
[ROW][C]Winsorized Mean ( 36 / 62 )[/C][C]85.7860962566845[/C][C]1.76755302182415[/C][C]48.5338177681095[/C][/ROW]
[ROW][C]Winsorized Mean ( 37 / 62 )[/C][C]85.7860962566845[/C][C]1.76755302182415[/C][C]48.5338177681095[/C][/ROW]
[ROW][C]Winsorized Mean ( 38 / 62 )[/C][C]85.7860962566845[/C][C]1.72880632639784[/C][C]49.6215770076626[/C][/ROW]
[ROW][C]Winsorized Mean ( 39 / 62 )[/C][C]85.9946524064171[/C][C]1.70963804541955[/C][C]50.2999173636859[/C][/ROW]
[ROW][C]Winsorized Mean ( 40 / 62 )[/C][C]85.7807486631016[/C][C]1.68892057995908[/C][C]50.7902797094105[/C][/ROW]
[ROW][C]Winsorized Mean ( 41 / 62 )[/C][C]86[/C][C]1.66898809061713[/C][C]51.5282286814883[/C][/ROW]
[ROW][C]Winsorized Mean ( 42 / 62 )[/C][C]85.7754010695187[/C][C]1.64742413843599[/C][C]52.0663738428352[/C][/ROW]
[ROW][C]Winsorized Mean ( 43 / 62 )[/C][C]86.235294117647[/C][C]1.60638180736558[/C][C]53.6829374699345[/C][/ROW]
[ROW][C]Winsorized Mean ( 44 / 62 )[/C][C]85.5294117647059[/C][C]1.53975351971687[/C][C]55.5474695589156[/C][/ROW]
[ROW][C]Winsorized Mean ( 45 / 62 )[/C][C]85.7700534759358[/C][C]1.51847450735735[/C][C]56.484355226486[/C][/ROW]
[ROW][C]Winsorized Mean ( 46 / 62 )[/C][C]86.0160427807487[/C][C]1.49707851767424[/C][C]57.4559328487175[/C][/ROW]
[ROW][C]Winsorized Mean ( 47 / 62 )[/C][C]85.764705882353[/C][C]1.42909432626981[/C][C]60.0133275360585[/C][/ROW]
[ROW][C]Winsorized Mean ( 48 / 62 )[/C][C]85.764705882353[/C][C]1.42909432626981[/C][C]60.0133275360585[/C][/ROW]
[ROW][C]Winsorized Mean ( 49 / 62 )[/C][C]85.5026737967914[/C][C]1.40537044501466[/C][C]60.839954404975[/C][/ROW]
[ROW][C]Winsorized Mean ( 50 / 62 )[/C][C]86.0374331550802[/C][C]1.36010517592725[/C][C]63.2579264294204[/C][/ROW]
[ROW][C]Winsorized Mean ( 51 / 62 )[/C][C]85.764705882353[/C][C]1.33551996098096[/C][C]64.218213421054[/C][/ROW]
[ROW][C]Winsorized Mean ( 52 / 62 )[/C][C]85.764705882353[/C][C]1.33551996098096[/C][C]64.218213421054[/C][/ROW]
[ROW][C]Winsorized Mean ( 53 / 62 )[/C][C]85.764705882353[/C][C]1.33551996098096[/C][C]64.218213421054[/C][/ROW]
[ROW][C]Winsorized Mean ( 54 / 62 )[/C][C]85.764705882353[/C][C]1.33551996098096[/C][C]64.218213421054[/C][/ROW]
[ROW][C]Winsorized Mean ( 55 / 62 )[/C][C]86.0588235294118[/C][C]1.31112937218753[/C][C]65.6371715522082[/C][/ROW]
[ROW][C]Winsorized Mean ( 56 / 62 )[/C][C]85.75935828877[/C][C]1.2843427450144[/C][C]66.7729534204741[/C][/ROW]
[ROW][C]Winsorized Mean ( 57 / 62 )[/C][C]85.75935828877[/C][C]1.232247536975[/C][C]69.5958853359102[/C][/ROW]
[ROW][C]Winsorized Mean ( 58 / 62 )[/C][C]85.75935828877[/C][C]1.232247536975[/C][C]69.5958853359102[/C][/ROW]
[ROW][C]Winsorized Mean ( 59 / 62 )[/C][C]85.4438502673797[/C][C]1.2045445211908[/C][C]70.9345721675034[/C][/ROW]
[ROW][C]Winsorized Mean ( 60 / 62 )[/C][C]84.8021390374332[/C][C]1.14920576364466[/C][C]73.7919541653593[/C][/ROW]
[ROW][C]Winsorized Mean ( 61 / 62 )[/C][C]85.1283422459893[/C][C]1.06778106210365[/C][C]79.724528994995[/C][/ROW]
[ROW][C]Winsorized Mean ( 62 / 62 )[/C][C]85.1283422459893[/C][C]1.06778106210365[/C][C]79.724528994995[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 62 )[/C][C]89.427807486631[/C][C]2.75829356256125[/C][C]32.4214248622586[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 62 )[/C][C]88.9513513513513[/C][C]2.64082866490801[/C][C]33.6831209587199[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 62 )[/C][C]88.2872928176796[/C][C]2.54361018150939[/C][C]34.709443081915[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 62 )[/C][C]88.2872928176796[/C][C]2.45200345459015[/C][C]36.006186146437[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 62 )[/C][C]87.5762711864407[/C][C]2.36663551754928[/C][C]37.0045452867742[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 62 )[/C][C]87.4228571428571[/C][C]2.32688794454113[/C][C]37.5707207336523[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 62 )[/C][C]87.4228571428571[/C][C]2.2861395311115[/C][C]38.2403855727709[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 62 )[/C][C]87.2658959537572[/C][C]2.24791629274518[/C][C]38.8207942775249[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 62 )[/C][C]86.98224852071[/C][C]2.21588557263334[/C][C]39.2539441544092[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 62 )[/C][C]86.8443113772455[/C][C]2.18454501606145[/C][C]39.7539582561766[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 62 )[/C][C]86.7212121212121[/C][C]2.15432989941313[/C][C]40.2543789346452[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 62 )[/C][C]86.6134969325153[/C][C]2.12725369846011[/C][C]40.716110633731[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 62 )[/C][C]86.5155279503106[/C][C]2.10233354504754[/C][C]41.1521417018317[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 62 )[/C][C]86.5155279503106[/C][C]2.08184939481996[/C][C]41.5570541104355[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 62 )[/C][C]86.3630573248408[/C][C]2.06166476644441[/C][C]41.8899613217839[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 62 )[/C][C]86.3630573248408[/C][C]2.04069481180925[/C][C]42.320417940531[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 62 )[/C][C]86.202614379085[/C][C]2.02028667831241[/C][C]42.6685060612744[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 62 )[/C][C]86.1390728476821[/C][C]2.00046439939675[/C][C]43.0595380121025[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 62 )[/C][C]86.0805369127517[/C][C]1.98217882697227[/C][C]43.4272305512603[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 62 )[/C][C]86.0204081632653[/C][C]1.96231074023004[/C][C]43.8362826028161[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 62 )[/C][C]85.9655172413793[/C][C]1.94191056613043[/C][C]44.2685254103538[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 62 )[/C][C]85.9230769230769[/C][C]1.92212918634262[/C][C]44.7020301931782[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 62 )[/C][C]85.8936170212766[/C][C]1.90519213059316[/C][C]45.0839658856529[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 62 )[/C][C]85.8561151079137[/C][C]1.88775201463545[/C][C]45.4806110348628[/C][/ROW]
[ROW][C]Trimmed Mean ( 25 / 62 )[/C][C]85.8175182481752[/C][C]1.86868211316721[/C][C]45.92408609441[/C][/ROW]
[ROW][C]Trimmed Mean ( 26 / 62 )[/C][C]85.7555555555556[/C][C]1.85107402127688[/C][C]46.3274588535367[/C][/ROW]
[ROW][C]Trimmed Mean ( 27 / 62 )[/C][C]85.7067669172932[/C][C]1.83438779370159[/C][C]46.7222727994426[/C][/ROW]
[ROW][C]Trimmed Mean ( 28 / 62 )[/C][C]85.7067669172932[/C][C]1.81715333195648[/C][C]47.1654017358101[/C][/ROW]
[ROW][C]Trimmed Mean ( 29 / 62 )[/C][C]85.5968992248062[/C][C]1.79956522593756[/C][C]47.5653218850186[/C][/ROW]
[ROW][C]Trimmed Mean ( 30 / 62 )[/C][C]85.5590551181102[/C][C]1.78295662485732[/C][C]47.9871769875259[/C][/ROW]
[ROW][C]Trimmed Mean ( 31 / 62 )[/C][C]85.512[/C][C]1.76582671856556[/C][C]48.4260426580613[/C][/ROW]
[ROW][C]Trimmed Mean ( 32 / 62 )[/C][C]85.512[/C][C]1.7468881982083[/C][C]48.9510433968847[/C][/ROW]
[ROW][C]Trimmed Mean ( 33 / 62 )[/C][C]85.4132231404959[/C][C]1.72873420712456[/C][C]49.4079557103028[/C][/ROW]
[ROW][C]Trimmed Mean ( 34 / 62 )[/C][C]85.3781512605042[/C][C]1.71166027161786[/C][C]49.8803136791887[/C][/ROW]
[ROW][C]Trimmed Mean ( 35 / 62 )[/C][C]85.3589743589744[/C][C]1.69847895487766[/C][C]50.2561271741648[/C][/ROW]
[ROW][C]Trimmed Mean ( 36 / 62 )[/C][C]85.3391304347826[/C][C]1.68372144923531[/C][C]50.6848270380713[/C][/ROW]
[ROW][C]Trimmed Mean ( 37 / 62 )[/C][C]85.3185840707965[/C][C]1.66721119097071[/C][C]51.1744310096196[/C][/ROW]
[ROW][C]Trimmed Mean ( 38 / 62 )[/C][C]85.2972972972973[/C][C]1.64874531476384[/C][C]51.7346715308271[/C][/ROW]
[ROW][C]Trimmed Mean ( 39 / 62 )[/C][C]85.2752293577982[/C][C]1.63132100337232[/C][C]52.2737273544045[/C][/ROW]
[ROW][C]Trimmed Mean ( 40 / 62 )[/C][C]85.2429906542056[/C][C]1.61333935990856[/C][C]52.8363670858664[/C][/ROW]
[ROW][C]Trimmed Mean ( 41 / 62 )[/C][C]85.2190476190476[/C][C]1.59491987422503[/C][C]53.4315541465402[/C][/ROW]
[ROW][C]Trimmed Mean ( 42 / 62 )[/C][C]85.1844660194175[/C][C]1.57584732693072[/C][C]54.0562937561543[/C][/ROW]
[ROW][C]Trimmed Mean ( 43 / 62 )[/C][C]85.1584158415842[/C][C]1.55625424080808[/C][C]54.7201180941784[/C][/ROW]
[ROW][C]Trimmed Mean ( 44 / 62 )[/C][C]85.1111111111111[/C][C]1.53760589490331[/C][C]55.3530078111876[/C][/ROW]
[ROW][C]Trimmed Mean ( 45 / 62 )[/C][C]85.0927835051546[/C][C]1.52246087941341[/C][C]55.8916059228663[/C][/ROW]
[ROW][C]Trimmed Mean ( 46 / 62 )[/C][C]85.0631578947368[/C][C]1.50696854818603[/C][C]56.446538315036[/C][/ROW]
[ROW][C]Trimmed Mean ( 47 / 62 )[/C][C]85.0215053763441[/C][C]1.49105000910283[/C][C]57.0212299099893[/C][/ROW]
[ROW][C]Trimmed Mean ( 48 / 62 )[/C][C]84.989010989011[/C][C]1.47891113506522[/C][C]57.4672872317395[/C][/ROW]
[ROW][C]Trimmed Mean ( 49 / 62 )[/C][C]84.9550561797753[/C][C]1.46476405491041[/C][C]57.999140472471[/C][/ROW]
[ROW][C]Trimmed Mean ( 50 / 62 )[/C][C]84.9310344827586[/C][C]1.45058432892921[/C][C]58.5495326186605[/C][/ROW]
[ROW][C]Trimmed Mean ( 51 / 62 )[/C][C]84.9310344827586[/C][C]1.43811771672019[/C][C]59.0570809992205[/C][/ROW]
[ROW][C]Trimmed Mean ( 52 / 62 )[/C][C]84.8433734939759[/C][C]1.42585194001241[/C][C]59.5036350641269[/C][/ROW]
[ROW][C]Trimmed Mean ( 53 / 62 )[/C][C]84.8024691358025[/C][C]1.41131010769724[/C][C]60.0877643214573[/C][/ROW]
[ROW][C]Trimmed Mean ( 54 / 62 )[/C][C]84.759493670886[/C][C]1.39412864319119[/C][C]60.797469505303[/C][/ROW]
[ROW][C]Trimmed Mean ( 55 / 62 )[/C][C]84.7142857142857[/C][C]1.37386716434135[/C][C]61.6611910620186[/C][/ROW]
[ROW][C]Trimmed Mean ( 56 / 62 )[/C][C]84.7142857142857[/C][C]1.35254092986755[/C][C]62.6334359601094[/C][/ROW]
[ROW][C]Trimmed Mean ( 57 / 62 )[/C][C]84.6027397260274[/C][C]1.3305821682268[/C][C]63.5832508102626[/C][/ROW]
[ROW][C]Trimmed Mean ( 58 / 62 )[/C][C]84.5492957746479[/C][C]1.31065725020803[/C][C]64.5090818070307[/C][/ROW]
[ROW][C]Trimmed Mean ( 59 / 62 )[/C][C]84.4927536231884[/C][C]1.28679820151653[/C][C]65.6612307381308[/C][/ROW]
[ROW][C]Trimmed Mean ( 60 / 62 )[/C][C]84.4477611940299[/C][C]1.26199062781026[/C][C]66.916314062141[/C][/ROW]
[ROW][C]Trimmed Mean ( 61 / 62 )[/C][C]84.4307692307692[/C][C]1.23975983072119[/C][C]68.1025204548325[/C][/ROW]
[ROW][C]Trimmed Mean ( 62 / 62 )[/C][C]84.3968253968254[/C][C]1.22349831309248[/C][C]68.9799278786961[/C][/ROW]
[ROW][C]Median[/C][C]85[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]133.5[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]84.7765957446808[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]85.6185567010309[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]85.6185567010309[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]85.6185567010309[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]85.0215053763441[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]84.7765957446808[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]85.6185567010309[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]85.6185567010309[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]187[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=119904&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=119904&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 Mean89.4278074866312.9297732429793530.5237982840235
Geometric Mean0
Harmonic Mean0
Quadratic Mean97.9483384511835
Winsorized Mean ( 1 / 62 )89.20855614973262.8658347185537831.1282976551945
Winsorized Mean ( 2 / 62 )89.46524064171122.8122008223330331.8132474506177
Winsorized Mean ( 3 / 62 )89.36898395721932.7767213951447732.1850741358082
Winsorized Mean ( 4 / 62 )89.17647058823532.7315392906564832.6469660873167
Winsorized Mean ( 5 / 62 )88.29411764705882.5288106071678534.9152749505208
Winsorized Mean ( 6 / 62 )88.29411764705882.5195847419461535.0431228516091
Winsorized Mean ( 7 / 62 )88.18181818181822.4902767514068635.4104491125337
Winsorized Mean ( 8 / 62 )88.1390374331552.436936087800636.1679725103923
Winsorized Mean ( 9 / 62 )88.09090909090912.4168505412201736.448637426473
Winsorized Mean ( 10 / 62 )87.93048128342252.3926440291913636.7503398794932
Winsorized Mean ( 11 / 62 )87.75401069518722.352122232692637.308439789173
Winsorized Mean ( 12 / 62 )87.62566844919792.3183460085797837.796630927787
Winsorized Mean ( 13 / 62 )87.34759358288772.2645107473024238.5723908296482
Winsorized Mean ( 14 / 62 )87.34759358288772.2470241529741138.8725655072628
Winsorized Mean ( 15 / 62 )87.4278074866312.2387778485124939.0515778708105
Winsorized Mean ( 16 / 62 )87.25668449197862.2170327674622239.3574176135697
Winsorized Mean ( 17 / 62 )87.07486631016042.1945048743882839.678593256455
Winsorized Mean ( 18 / 62 )86.97860962566852.1613639886092940.2424626689714
Winsorized Mean ( 19 / 62 )86.97860962566852.1613639886092940.2424626689714
Winsorized Mean ( 20 / 62 )86.87165775401072.1486698763512840.4304349914981
Winsorized Mean ( 21 / 62 )86.64705882352942.1225242362638640.8226475548041
Winsorized Mean ( 22 / 62 )86.41176470588232.0706520081553541.7316692353645
Winsorized Mean ( 23 / 62 )86.53475935828882.0581682870545742.0445499537495
Winsorized Mean ( 24 / 62 )86.53475935828882.0581682870545742.0445499537495
Winsorized Mean ( 25 / 62 )86.93582887700532.0187809890635743.0635266271906
Winsorized Mean ( 26 / 62 )86.65775401069521.9880334333773143.5896864488235
Winsorized Mean ( 27 / 62 )86.80213903743321.9742293390275243.9676066612357
Winsorized Mean ( 28 / 62 )86.65240641711231.9579443995046844.2568269247246
Winsorized Mean ( 29 / 62 )86.34224598930481.9248734003273644.8560648064547
Winsorized Mean ( 30 / 62 )86.50267379679141.9096126151447945.2985454278813
Winsorized Mean ( 31 / 62 )86.50267379679141.9096126151447945.2985454278813
Winsorized Mean ( 32 / 62 )86.50267379679141.875584731725246.1203763997507
Winsorized Mean ( 33 / 62 )86.14973262032091.8391393796636746.8424163893851
Winsorized Mean ( 34 / 62 )85.78609625668451.7675530218241548.5338177681095
Winsorized Mean ( 35 / 62 )85.78609625668451.7675530218241548.5338177681095
Winsorized Mean ( 36 / 62 )85.78609625668451.7675530218241548.5338177681095
Winsorized Mean ( 37 / 62 )85.78609625668451.7675530218241548.5338177681095
Winsorized Mean ( 38 / 62 )85.78609625668451.7288063263978449.6215770076626
Winsorized Mean ( 39 / 62 )85.99465240641711.7096380454195550.2999173636859
Winsorized Mean ( 40 / 62 )85.78074866310161.6889205799590850.7902797094105
Winsorized Mean ( 41 / 62 )861.6689880906171351.5282286814883
Winsorized Mean ( 42 / 62 )85.77540106951871.6474241384359952.0663738428352
Winsorized Mean ( 43 / 62 )86.2352941176471.6063818073655853.6829374699345
Winsorized Mean ( 44 / 62 )85.52941176470591.5397535197168755.5474695589156
Winsorized Mean ( 45 / 62 )85.77005347593581.5184745073573556.484355226486
Winsorized Mean ( 46 / 62 )86.01604278074871.4970785176742457.4559328487175
Winsorized Mean ( 47 / 62 )85.7647058823531.4290943262698160.0133275360585
Winsorized Mean ( 48 / 62 )85.7647058823531.4290943262698160.0133275360585
Winsorized Mean ( 49 / 62 )85.50267379679141.4053704450146660.839954404975
Winsorized Mean ( 50 / 62 )86.03743315508021.3601051759272563.2579264294204
Winsorized Mean ( 51 / 62 )85.7647058823531.3355199609809664.218213421054
Winsorized Mean ( 52 / 62 )85.7647058823531.3355199609809664.218213421054
Winsorized Mean ( 53 / 62 )85.7647058823531.3355199609809664.218213421054
Winsorized Mean ( 54 / 62 )85.7647058823531.3355199609809664.218213421054
Winsorized Mean ( 55 / 62 )86.05882352941181.3111293721875365.6371715522082
Winsorized Mean ( 56 / 62 )85.759358288771.284342745014466.7729534204741
Winsorized Mean ( 57 / 62 )85.759358288771.23224753697569.5958853359102
Winsorized Mean ( 58 / 62 )85.759358288771.23224753697569.5958853359102
Winsorized Mean ( 59 / 62 )85.44385026737971.204544521190870.9345721675034
Winsorized Mean ( 60 / 62 )84.80213903743321.1492057636446673.7919541653593
Winsorized Mean ( 61 / 62 )85.12834224598931.0677810621036579.724528994995
Winsorized Mean ( 62 / 62 )85.12834224598931.0677810621036579.724528994995
Trimmed Mean ( 1 / 62 )89.4278074866312.7582935625612532.4214248622586
Trimmed Mean ( 2 / 62 )88.95135135135132.6408286649080133.6831209587199
Trimmed Mean ( 3 / 62 )88.28729281767962.5436101815093934.709443081915
Trimmed Mean ( 4 / 62 )88.28729281767962.4520034545901536.006186146437
Trimmed Mean ( 5 / 62 )87.57627118644072.3666355175492837.0045452867742
Trimmed Mean ( 6 / 62 )87.42285714285712.3268879445411337.5707207336523
Trimmed Mean ( 7 / 62 )87.42285714285712.286139531111538.2403855727709
Trimmed Mean ( 8 / 62 )87.26589595375722.2479162927451838.8207942775249
Trimmed Mean ( 9 / 62 )86.982248520712.2158855726333439.2539441544092
Trimmed Mean ( 10 / 62 )86.84431137724552.1845450160614539.7539582561766
Trimmed Mean ( 11 / 62 )86.72121212121212.1543298994131340.2543789346452
Trimmed Mean ( 12 / 62 )86.61349693251532.1272536984601140.716110633731
Trimmed Mean ( 13 / 62 )86.51552795031062.1023335450475441.1521417018317
Trimmed Mean ( 14 / 62 )86.51552795031062.0818493948199641.5570541104355
Trimmed Mean ( 15 / 62 )86.36305732484082.0616647664444141.8899613217839
Trimmed Mean ( 16 / 62 )86.36305732484082.0406948118092542.320417940531
Trimmed Mean ( 17 / 62 )86.2026143790852.0202866783124142.6685060612744
Trimmed Mean ( 18 / 62 )86.13907284768212.0004643993967543.0595380121025
Trimmed Mean ( 19 / 62 )86.08053691275171.9821788269722743.4272305512603
Trimmed Mean ( 20 / 62 )86.02040816326531.9623107402300443.8362826028161
Trimmed Mean ( 21 / 62 )85.96551724137931.9419105661304344.2685254103538
Trimmed Mean ( 22 / 62 )85.92307692307691.9221291863426244.7020301931782
Trimmed Mean ( 23 / 62 )85.89361702127661.9051921305931645.0839658856529
Trimmed Mean ( 24 / 62 )85.85611510791371.8877520146354545.4806110348628
Trimmed Mean ( 25 / 62 )85.81751824817521.8686821131672145.92408609441
Trimmed Mean ( 26 / 62 )85.75555555555561.8510740212768846.3274588535367
Trimmed Mean ( 27 / 62 )85.70676691729321.8343877937015946.7222727994426
Trimmed Mean ( 28 / 62 )85.70676691729321.8171533319564847.1654017358101
Trimmed Mean ( 29 / 62 )85.59689922480621.7995652259375647.5653218850186
Trimmed Mean ( 30 / 62 )85.55905511811021.7829566248573247.9871769875259
Trimmed Mean ( 31 / 62 )85.5121.7658267185655648.4260426580613
Trimmed Mean ( 32 / 62 )85.5121.746888198208348.9510433968847
Trimmed Mean ( 33 / 62 )85.41322314049591.7287342071245649.4079557103028
Trimmed Mean ( 34 / 62 )85.37815126050421.7116602716178649.8803136791887
Trimmed Mean ( 35 / 62 )85.35897435897441.6984789548776650.2561271741648
Trimmed Mean ( 36 / 62 )85.33913043478261.6837214492353150.6848270380713
Trimmed Mean ( 37 / 62 )85.31858407079651.6672111909707151.1744310096196
Trimmed Mean ( 38 / 62 )85.29729729729731.6487453147638451.7346715308271
Trimmed Mean ( 39 / 62 )85.27522935779821.6313210033723252.2737273544045
Trimmed Mean ( 40 / 62 )85.24299065420561.6133393599085652.8363670858664
Trimmed Mean ( 41 / 62 )85.21904761904761.5949198742250353.4315541465402
Trimmed Mean ( 42 / 62 )85.18446601941751.5758473269307254.0562937561543
Trimmed Mean ( 43 / 62 )85.15841584158421.5562542408080854.7201180941784
Trimmed Mean ( 44 / 62 )85.11111111111111.5376058949033155.3530078111876
Trimmed Mean ( 45 / 62 )85.09278350515461.5224608794134155.8916059228663
Trimmed Mean ( 46 / 62 )85.06315789473681.5069685481860356.446538315036
Trimmed Mean ( 47 / 62 )85.02150537634411.4910500091028357.0212299099893
Trimmed Mean ( 48 / 62 )84.9890109890111.4789111350652257.4672872317395
Trimmed Mean ( 49 / 62 )84.95505617977531.4647640549104157.999140472471
Trimmed Mean ( 50 / 62 )84.93103448275861.4505843289292158.5495326186605
Trimmed Mean ( 51 / 62 )84.93103448275861.4381177167201959.0570809992205
Trimmed Mean ( 52 / 62 )84.84337349397591.4258519400124159.5036350641269
Trimmed Mean ( 53 / 62 )84.80246913580251.4113101076972460.0877643214573
Trimmed Mean ( 54 / 62 )84.7594936708861.3941286431911960.797469505303
Trimmed Mean ( 55 / 62 )84.71428571428571.3738671643413561.6611910620186
Trimmed Mean ( 56 / 62 )84.71428571428571.3525409298675562.6334359601094
Trimmed Mean ( 57 / 62 )84.60273972602741.330582168226863.5832508102626
Trimmed Mean ( 58 / 62 )84.54929577464791.3106572502080364.5090818070307
Trimmed Mean ( 59 / 62 )84.49275362318841.2867982015165365.6612307381308
Trimmed Mean ( 60 / 62 )84.44776119402991.2619906278102666.916314062141
Trimmed Mean ( 61 / 62 )84.43076923076921.2397598307211968.1025204548325
Trimmed Mean ( 62 / 62 )84.39682539682541.2234983130924868.9799278786961
Median85
Midrange133.5
Midmean - Weighted Average at Xnp84.7765957446808
Midmean - Weighted Average at X(n+1)p85.6185567010309
Midmean - Empirical Distribution Function85.6185567010309
Midmean - Empirical Distribution Function - Averaging85.6185567010309
Midmean - Empirical Distribution Function - Interpolation85.0215053763441
Midmean - Closest Observation84.7765957446808
Midmean - True Basic - Statistics Graphics Toolkit85.6185567010309
Midmean - MS Excel (old versions)85.6185567010309
Number of observations187



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')