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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 computationSat, 05 Mar 2016 14:05:37 +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/2016/Mar/05/t14571867779mm41ugh0uv2wje.htm/, Retrieved Sat, 27 Apr 2024 07:41:27 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=293472, Retrieved Sat, 27 Apr 2024 07:41:27 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact68
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [] [2016-03-05 14:05:37] [56edb0d8f6220d107203045c2c4d5731] [Current]
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Dataseries X:
37,43
38,39
38,99
39,83
41,21
41,72
42,12
43,18
43,43
43,77
44,19
44,38
44,57
45,13
45,84
46,11
46,35
46,41
46,78
47,09
47,34
47,64
48,17
48,24
48,59
49,29
50,44
52,42
52,9
53,19
53,19
53,38
54,17
54,69
55,39
55,64
55,64
56,57
57,16
57,87
58,89
59,28
59,94
60,35
60,59
61,2
61,62
62,07
62,38
62,62
64,15
64,97
66,12
67,08
68,66
69,04
70,8
73,2
74,19
75,36
75,54
76,81
77,69
79,34
80,36
80,74
81,12
82,95
87,31
88,93
90,8
91,29
91,36
92,72
95,75
97,19
98,73
99,03
99,4
99,66
100,5
101,21
101,26
101,44
101,97
102,23
102,58
101,91
101,63
101,1
100,71
100,75
100,14
97,72
94,91
94,34
97,11
96,51
95,8
95,25
95,09
94,97
95,21
95,46
95,33
95,14
95,6
95,66
95,66
96,33
97,66
98,27
99,53
100,86
101,26
101,29
101,38
101,49
101,29
101,26




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

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 1 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=293472&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' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=293472&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=293472&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' @ jenkins.wessa.net







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean74.46566666666672.0594467239018636.1580932404908
Geometric Mean70.8219695248481
Harmonic Mean67.1056480130336
Quadratic Mean77.7807989694972
Winsorized Mean ( 1 / 40 )74.470752.0579203018247536.1873829292452
Winsorized Mean ( 2 / 40 )74.47641666666672.0559693366164136.2244783228312
Winsorized Mean ( 3 / 40 )74.49591666666672.0527878546338236.2901195554645
Winsorized Mean ( 4 / 40 )74.53258333333332.0453315856994636.4403424141347
Winsorized Mean ( 5 / 40 )74.5482.0417932560080936.5110423303821
Winsorized Mean ( 6 / 40 )74.56552.0388277919937636.5727308077759
Winsorized Mean ( 7 / 40 )74.62383333333332.0302817524088536.7554075904959
Winsorized Mean ( 8 / 40 )74.63452.0274557190175636.8119013894741
Winsorized Mean ( 9 / 40 )74.662.0241716153259636.8842243586037
Winsorized Mean ( 10 / 40 )74.69252.0194297502281336.986926626966
Winsorized Mean ( 11 / 40 )74.70991666666672.0172241254284437.0360019617547
Winsorized Mean ( 12 / 40 )74.72891666666672.0148288491229637.0894613203476
Winsorized Mean ( 13 / 40 )74.78416666666672.0066469153550237.2682239682588
Winsorized Mean ( 14 / 40 )74.85416666666671.995022256439337.5204669647475
Winsorized Mean ( 15 / 40 )74.85791666666671.9876015587949937.6624360830398
Winsorized Mean ( 16 / 40 )74.875251.9821112444737337.775503372355
Winsorized Mean ( 17 / 40 )74.87808333333331.9804625244790737.8083818339501
Winsorized Mean ( 18 / 40 )74.90208333333331.9703363008880238.0148725370259
Winsorized Mean ( 19 / 40 )74.89416666666671.9582655054109838.2451544286118
Winsorized Mean ( 20 / 40 )74.85583333333331.9446817176494138.4925886092115
Winsorized Mean ( 21 / 40 )74.88558333333331.9360201777856538.6801667630266
Winsorized Mean ( 22 / 40 )74.95891666666671.9220360746381838.9997449349526
Winsorized Mean ( 23 / 40 )74.90141666666671.9129171129178739.1555996654847
Winsorized Mean ( 24 / 40 )74.91141666666671.8983968147698239.4603573309038
Winsorized Mean ( 25 / 40 )74.96141666666671.8714275857283740.0557399272766
Winsorized Mean ( 26 / 40 )75.09141666666671.8305386821611941.0214858601139
Winsorized Mean ( 27 / 40 )75.52341666666671.7796105800057142.4381701902584
Winsorized Mean ( 28 / 40 )75.525751.7560208218941443.0095982111042
Winsorized Mean ( 29 / 40 )75.57651.7464483072155143.2743984965105
Winsorized Mean ( 30 / 40 )75.42651.7310005147927843.5739327374083
Winsorized Mean ( 31 / 40 )75.42908333333331.7209563777979343.8297474046666
Winsorized Mean ( 32 / 40 )75.49841666666671.6840321052742144.8319342785767
Winsorized Mean ( 33 / 40 )75.62766666666671.66748402254845.3543576094384
Winsorized Mean ( 34 / 40 )75.80051.6440869255083446.1049223273661
Winsorized Mean ( 35 / 40 )75.87341666666671.6364954805696346.3633524000057
Winsorized Mean ( 36 / 40 )75.85541666666671.6346675361440246.404186165953
Winsorized Mean ( 37 / 40 )76.0991.6006817017646447.5416192464162
Winsorized Mean ( 38 / 40 )76.24466666666671.577421094695648.3350114456152
Winsorized Mean ( 39 / 40 )76.44941666666671.5514335978781449.2766282561011
Winsorized Mean ( 40 / 40 )76.77608333333331.5161092087956150.6402064494573
Trimmed Mean ( 1 / 40 )74.54127118644072.0567659395017236.241980555405
Trimmed Mean ( 2 / 40 )74.6142241379312.0548901857338336.3105652340664
Trimmed Mean ( 3 / 40 )74.68675438596492.0533013336954936.3739862047162
Trimmed Mean ( 4 / 40 )74.75491071428572.0521375560215836.4278264363578
Trimmed Mean ( 5 / 40 )74.81554545454552.0524107495032836.452520760112
Trimmed Mean ( 6 / 40 )74.8752.0528524359822636.4736396477389
Trimmed Mean ( 7 / 40 )74.93339622641512.0532091021163336.4957451967158
Trimmed Mean ( 8 / 40 )74.98442307692312.0544403713632136.4987098784317
Trimmed Mean ( 9 / 40 )75.03588235294122.0554456195369536.5058951887256
Trimmed Mean ( 10 / 40 )75.0862.0562147335098636.5166141338904
Trimmed Mean ( 11 / 40 )75.13418367346942.056878966277836.5282473617953
Trimmed Mean ( 12 / 40 )75.18239583333332.0569980721830436.5495703909651
Trimmed Mean ( 13 / 40 )75.23063829787232.0564983566560636.5819102429043
Trimmed Mean ( 14 / 40 )75.27543478260872.0560231422152136.6121534514953
Trimmed Mean ( 15 / 40 )75.31555555555562.0559247662480736.6334200511634
Trimmed Mean ( 16 / 40 )75.35715909090912.0556280896527136.6589459787155
Trimmed Mean ( 17 / 40 )75.39918604651162.0548192475126536.6938289768221
Trimmed Mean ( 18 / 40 )75.44297619047622.0529323288570436.7488860348742
Trimmed Mean ( 19 / 40 )75.48695121951222.0507756604920236.8089755860479
Trimmed Mean ( 20 / 40 )75.533752.0484556190602536.8735106082757
Trimmed Mean ( 21 / 40 )75.58589743589742.0460329087935136.9426596762162
Trimmed Mean ( 22 / 40 )75.63855263157892.0428788399032537.0254716795446
Trimmed Mean ( 23 / 40 )75.68864864864872.0394482444914937.11231645769
Trimmed Mean ( 24 / 40 )75.74569444444442.0350182911897637.2211369167401
Trimmed Mean ( 25 / 40 )75.80528571428572.0300212721241537.3421139744834
Trimmed Mean ( 26 / 40 )75.86485294117652.0257559693267237.4501440893649
Trimmed Mean ( 27 / 40 )75.91893939393942.0238747154438637.511679361679
Trimmed Mean ( 28 / 40 )75.946406252.0258261391322437.4891037206833
Trimmed Mean ( 29 / 40 )75.97548387096772.0286638278328537.4509974637491
Trimmed Mean ( 30 / 40 )76.0032.030755214227737.4259780142453
Trimmed Mean ( 31 / 40 )76.04275862068972.0325378447465337.412714758171
Trimmed Mean ( 32 / 40 )76.08517857142862.0332070341153337.4212646792922
Trimmed Mean ( 33 / 40 )76.12592592592592.0359683328351137.3905255294024
Trimmed Mean ( 34 / 40 )76.16076923076922.0383578262697337.3637877752534
Trimmed Mean ( 35 / 40 )76.18622.0411205983828737.325672995687
Trimmed Mean ( 36 / 40 )76.20854166666672.0418630023469137.3230435044236
Trimmed Mean ( 37 / 40 )76.23413043478262.0390631688069937.3868409772638
Trimmed Mean ( 38 / 40 )76.24409090909092.0369583695758237.4303628625303
Trimmed Mean ( 39 / 40 )76.24404761904762.0336613868621137.4910238801802
Trimmed Mean ( 40 / 40 )76.228252.0291101020126437.567330587133
Median75.45
Midrange70.005
Midmean - Weighted Average at Xnp75.6290163934426
Midmean - Weighted Average at X(n+1)p75.6290163934426
Midmean - Empirical Distribution Function75.6290163934426
Midmean - Empirical Distribution Function - Averaging75.6290163934426
Midmean - Empirical Distribution Function - Interpolation75.6290163934426
Midmean - Closest Observation75.6290163934426
Midmean - True Basic - Statistics Graphics Toolkit75.6290163934426
Midmean - MS Excel (old versions)75.9754838709677
Number of observations120

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 74.4656666666667 & 2.05944672390186 & 36.1580932404908 \tabularnewline
Geometric Mean & 70.8219695248481 &  &  \tabularnewline
Harmonic Mean & 67.1056480130336 &  &  \tabularnewline
Quadratic Mean & 77.7807989694972 &  &  \tabularnewline
Winsorized Mean ( 1 / 40 ) & 74.47075 & 2.05792030182475 & 36.1873829292452 \tabularnewline
Winsorized Mean ( 2 / 40 ) & 74.4764166666667 & 2.05596933661641 & 36.2244783228312 \tabularnewline
Winsorized Mean ( 3 / 40 ) & 74.4959166666667 & 2.05278785463382 & 36.2901195554645 \tabularnewline
Winsorized Mean ( 4 / 40 ) & 74.5325833333333 & 2.04533158569946 & 36.4403424141347 \tabularnewline
Winsorized Mean ( 5 / 40 ) & 74.548 & 2.04179325600809 & 36.5110423303821 \tabularnewline
Winsorized Mean ( 6 / 40 ) & 74.5655 & 2.03882779199376 & 36.5727308077759 \tabularnewline
Winsorized Mean ( 7 / 40 ) & 74.6238333333333 & 2.03028175240885 & 36.7554075904959 \tabularnewline
Winsorized Mean ( 8 / 40 ) & 74.6345 & 2.02745571901756 & 36.8119013894741 \tabularnewline
Winsorized Mean ( 9 / 40 ) & 74.66 & 2.02417161532596 & 36.8842243586037 \tabularnewline
Winsorized Mean ( 10 / 40 ) & 74.6925 & 2.01942975022813 & 36.986926626966 \tabularnewline
Winsorized Mean ( 11 / 40 ) & 74.7099166666667 & 2.01722412542844 & 37.0360019617547 \tabularnewline
Winsorized Mean ( 12 / 40 ) & 74.7289166666667 & 2.01482884912296 & 37.0894613203476 \tabularnewline
Winsorized Mean ( 13 / 40 ) & 74.7841666666667 & 2.00664691535502 & 37.2682239682588 \tabularnewline
Winsorized Mean ( 14 / 40 ) & 74.8541666666667 & 1.9950222564393 & 37.5204669647475 \tabularnewline
Winsorized Mean ( 15 / 40 ) & 74.8579166666667 & 1.98760155879499 & 37.6624360830398 \tabularnewline
Winsorized Mean ( 16 / 40 ) & 74.87525 & 1.98211124447373 & 37.775503372355 \tabularnewline
Winsorized Mean ( 17 / 40 ) & 74.8780833333333 & 1.98046252447907 & 37.8083818339501 \tabularnewline
Winsorized Mean ( 18 / 40 ) & 74.9020833333333 & 1.97033630088802 & 38.0148725370259 \tabularnewline
Winsorized Mean ( 19 / 40 ) & 74.8941666666667 & 1.95826550541098 & 38.2451544286118 \tabularnewline
Winsorized Mean ( 20 / 40 ) & 74.8558333333333 & 1.94468171764941 & 38.4925886092115 \tabularnewline
Winsorized Mean ( 21 / 40 ) & 74.8855833333333 & 1.93602017778565 & 38.6801667630266 \tabularnewline
Winsorized Mean ( 22 / 40 ) & 74.9589166666667 & 1.92203607463818 & 38.9997449349526 \tabularnewline
Winsorized Mean ( 23 / 40 ) & 74.9014166666667 & 1.91291711291787 & 39.1555996654847 \tabularnewline
Winsorized Mean ( 24 / 40 ) & 74.9114166666667 & 1.89839681476982 & 39.4603573309038 \tabularnewline
Winsorized Mean ( 25 / 40 ) & 74.9614166666667 & 1.87142758572837 & 40.0557399272766 \tabularnewline
Winsorized Mean ( 26 / 40 ) & 75.0914166666667 & 1.83053868216119 & 41.0214858601139 \tabularnewline
Winsorized Mean ( 27 / 40 ) & 75.5234166666667 & 1.77961058000571 & 42.4381701902584 \tabularnewline
Winsorized Mean ( 28 / 40 ) & 75.52575 & 1.75602082189414 & 43.0095982111042 \tabularnewline
Winsorized Mean ( 29 / 40 ) & 75.5765 & 1.74644830721551 & 43.2743984965105 \tabularnewline
Winsorized Mean ( 30 / 40 ) & 75.4265 & 1.73100051479278 & 43.5739327374083 \tabularnewline
Winsorized Mean ( 31 / 40 ) & 75.4290833333333 & 1.72095637779793 & 43.8297474046666 \tabularnewline
Winsorized Mean ( 32 / 40 ) & 75.4984166666667 & 1.68403210527421 & 44.8319342785767 \tabularnewline
Winsorized Mean ( 33 / 40 ) & 75.6276666666667 & 1.667484022548 & 45.3543576094384 \tabularnewline
Winsorized Mean ( 34 / 40 ) & 75.8005 & 1.64408692550834 & 46.1049223273661 \tabularnewline
Winsorized Mean ( 35 / 40 ) & 75.8734166666667 & 1.63649548056963 & 46.3633524000057 \tabularnewline
Winsorized Mean ( 36 / 40 ) & 75.8554166666667 & 1.63466753614402 & 46.404186165953 \tabularnewline
Winsorized Mean ( 37 / 40 ) & 76.099 & 1.60068170176464 & 47.5416192464162 \tabularnewline
Winsorized Mean ( 38 / 40 ) & 76.2446666666667 & 1.5774210946956 & 48.3350114456152 \tabularnewline
Winsorized Mean ( 39 / 40 ) & 76.4494166666667 & 1.55143359787814 & 49.2766282561011 \tabularnewline
Winsorized Mean ( 40 / 40 ) & 76.7760833333333 & 1.51610920879561 & 50.6402064494573 \tabularnewline
Trimmed Mean ( 1 / 40 ) & 74.5412711864407 & 2.05676593950172 & 36.241980555405 \tabularnewline
Trimmed Mean ( 2 / 40 ) & 74.614224137931 & 2.05489018573383 & 36.3105652340664 \tabularnewline
Trimmed Mean ( 3 / 40 ) & 74.6867543859649 & 2.05330133369549 & 36.3739862047162 \tabularnewline
Trimmed Mean ( 4 / 40 ) & 74.7549107142857 & 2.05213755602158 & 36.4278264363578 \tabularnewline
Trimmed Mean ( 5 / 40 ) & 74.8155454545455 & 2.05241074950328 & 36.452520760112 \tabularnewline
Trimmed Mean ( 6 / 40 ) & 74.875 & 2.05285243598226 & 36.4736396477389 \tabularnewline
Trimmed Mean ( 7 / 40 ) & 74.9333962264151 & 2.05320910211633 & 36.4957451967158 \tabularnewline
Trimmed Mean ( 8 / 40 ) & 74.9844230769231 & 2.05444037136321 & 36.4987098784317 \tabularnewline
Trimmed Mean ( 9 / 40 ) & 75.0358823529412 & 2.05544561953695 & 36.5058951887256 \tabularnewline
Trimmed Mean ( 10 / 40 ) & 75.086 & 2.05621473350986 & 36.5166141338904 \tabularnewline
Trimmed Mean ( 11 / 40 ) & 75.1341836734694 & 2.0568789662778 & 36.5282473617953 \tabularnewline
Trimmed Mean ( 12 / 40 ) & 75.1823958333333 & 2.05699807218304 & 36.5495703909651 \tabularnewline
Trimmed Mean ( 13 / 40 ) & 75.2306382978723 & 2.05649835665606 & 36.5819102429043 \tabularnewline
Trimmed Mean ( 14 / 40 ) & 75.2754347826087 & 2.05602314221521 & 36.6121534514953 \tabularnewline
Trimmed Mean ( 15 / 40 ) & 75.3155555555556 & 2.05592476624807 & 36.6334200511634 \tabularnewline
Trimmed Mean ( 16 / 40 ) & 75.3571590909091 & 2.05562808965271 & 36.6589459787155 \tabularnewline
Trimmed Mean ( 17 / 40 ) & 75.3991860465116 & 2.05481924751265 & 36.6938289768221 \tabularnewline
Trimmed Mean ( 18 / 40 ) & 75.4429761904762 & 2.05293232885704 & 36.7488860348742 \tabularnewline
Trimmed Mean ( 19 / 40 ) & 75.4869512195122 & 2.05077566049202 & 36.8089755860479 \tabularnewline
Trimmed Mean ( 20 / 40 ) & 75.53375 & 2.04845561906025 & 36.8735106082757 \tabularnewline
Trimmed Mean ( 21 / 40 ) & 75.5858974358974 & 2.04603290879351 & 36.9426596762162 \tabularnewline
Trimmed Mean ( 22 / 40 ) & 75.6385526315789 & 2.04287883990325 & 37.0254716795446 \tabularnewline
Trimmed Mean ( 23 / 40 ) & 75.6886486486487 & 2.03944824449149 & 37.11231645769 \tabularnewline
Trimmed Mean ( 24 / 40 ) & 75.7456944444444 & 2.03501829118976 & 37.2211369167401 \tabularnewline
Trimmed Mean ( 25 / 40 ) & 75.8052857142857 & 2.03002127212415 & 37.3421139744834 \tabularnewline
Trimmed Mean ( 26 / 40 ) & 75.8648529411765 & 2.02575596932672 & 37.4501440893649 \tabularnewline
Trimmed Mean ( 27 / 40 ) & 75.9189393939394 & 2.02387471544386 & 37.511679361679 \tabularnewline
Trimmed Mean ( 28 / 40 ) & 75.94640625 & 2.02582613913224 & 37.4891037206833 \tabularnewline
Trimmed Mean ( 29 / 40 ) & 75.9754838709677 & 2.02866382783285 & 37.4509974637491 \tabularnewline
Trimmed Mean ( 30 / 40 ) & 76.003 & 2.0307552142277 & 37.4259780142453 \tabularnewline
Trimmed Mean ( 31 / 40 ) & 76.0427586206897 & 2.03253784474653 & 37.412714758171 \tabularnewline
Trimmed Mean ( 32 / 40 ) & 76.0851785714286 & 2.03320703411533 & 37.4212646792922 \tabularnewline
Trimmed Mean ( 33 / 40 ) & 76.1259259259259 & 2.03596833283511 & 37.3905255294024 \tabularnewline
Trimmed Mean ( 34 / 40 ) & 76.1607692307692 & 2.03835782626973 & 37.3637877752534 \tabularnewline
Trimmed Mean ( 35 / 40 ) & 76.1862 & 2.04112059838287 & 37.325672995687 \tabularnewline
Trimmed Mean ( 36 / 40 ) & 76.2085416666667 & 2.04186300234691 & 37.3230435044236 \tabularnewline
Trimmed Mean ( 37 / 40 ) & 76.2341304347826 & 2.03906316880699 & 37.3868409772638 \tabularnewline
Trimmed Mean ( 38 / 40 ) & 76.2440909090909 & 2.03695836957582 & 37.4303628625303 \tabularnewline
Trimmed Mean ( 39 / 40 ) & 76.2440476190476 & 2.03366138686211 & 37.4910238801802 \tabularnewline
Trimmed Mean ( 40 / 40 ) & 76.22825 & 2.02911010201264 & 37.567330587133 \tabularnewline
Median & 75.45 &  &  \tabularnewline
Midrange & 70.005 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 75.6290163934426 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 75.6290163934426 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 75.6290163934426 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 75.6290163934426 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 75.6290163934426 &  &  \tabularnewline
Midmean - Closest Observation & 75.6290163934426 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 75.6290163934426 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 75.9754838709677 &  &  \tabularnewline
Number of observations & 120 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=293472&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]74.4656666666667[/C][C]2.05944672390186[/C][C]36.1580932404908[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]70.8219695248481[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]67.1056480130336[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]77.7807989694972[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 40 )[/C][C]74.47075[/C][C]2.05792030182475[/C][C]36.1873829292452[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 40 )[/C][C]74.4764166666667[/C][C]2.05596933661641[/C][C]36.2244783228312[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 40 )[/C][C]74.4959166666667[/C][C]2.05278785463382[/C][C]36.2901195554645[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 40 )[/C][C]74.5325833333333[/C][C]2.04533158569946[/C][C]36.4403424141347[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 40 )[/C][C]74.548[/C][C]2.04179325600809[/C][C]36.5110423303821[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 40 )[/C][C]74.5655[/C][C]2.03882779199376[/C][C]36.5727308077759[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 40 )[/C][C]74.6238333333333[/C][C]2.03028175240885[/C][C]36.7554075904959[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 40 )[/C][C]74.6345[/C][C]2.02745571901756[/C][C]36.8119013894741[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 40 )[/C][C]74.66[/C][C]2.02417161532596[/C][C]36.8842243586037[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 40 )[/C][C]74.6925[/C][C]2.01942975022813[/C][C]36.986926626966[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 40 )[/C][C]74.7099166666667[/C][C]2.01722412542844[/C][C]37.0360019617547[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 40 )[/C][C]74.7289166666667[/C][C]2.01482884912296[/C][C]37.0894613203476[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 40 )[/C][C]74.7841666666667[/C][C]2.00664691535502[/C][C]37.2682239682588[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 40 )[/C][C]74.8541666666667[/C][C]1.9950222564393[/C][C]37.5204669647475[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 40 )[/C][C]74.8579166666667[/C][C]1.98760155879499[/C][C]37.6624360830398[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 40 )[/C][C]74.87525[/C][C]1.98211124447373[/C][C]37.775503372355[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 40 )[/C][C]74.8780833333333[/C][C]1.98046252447907[/C][C]37.8083818339501[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 40 )[/C][C]74.9020833333333[/C][C]1.97033630088802[/C][C]38.0148725370259[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 40 )[/C][C]74.8941666666667[/C][C]1.95826550541098[/C][C]38.2451544286118[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 40 )[/C][C]74.8558333333333[/C][C]1.94468171764941[/C][C]38.4925886092115[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 40 )[/C][C]74.8855833333333[/C][C]1.93602017778565[/C][C]38.6801667630266[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 40 )[/C][C]74.9589166666667[/C][C]1.92203607463818[/C][C]38.9997449349526[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 40 )[/C][C]74.9014166666667[/C][C]1.91291711291787[/C][C]39.1555996654847[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 40 )[/C][C]74.9114166666667[/C][C]1.89839681476982[/C][C]39.4603573309038[/C][/ROW]
[ROW][C]Winsorized Mean ( 25 / 40 )[/C][C]74.9614166666667[/C][C]1.87142758572837[/C][C]40.0557399272766[/C][/ROW]
[ROW][C]Winsorized Mean ( 26 / 40 )[/C][C]75.0914166666667[/C][C]1.83053868216119[/C][C]41.0214858601139[/C][/ROW]
[ROW][C]Winsorized Mean ( 27 / 40 )[/C][C]75.5234166666667[/C][C]1.77961058000571[/C][C]42.4381701902584[/C][/ROW]
[ROW][C]Winsorized Mean ( 28 / 40 )[/C][C]75.52575[/C][C]1.75602082189414[/C][C]43.0095982111042[/C][/ROW]
[ROW][C]Winsorized Mean ( 29 / 40 )[/C][C]75.5765[/C][C]1.74644830721551[/C][C]43.2743984965105[/C][/ROW]
[ROW][C]Winsorized Mean ( 30 / 40 )[/C][C]75.4265[/C][C]1.73100051479278[/C][C]43.5739327374083[/C][/ROW]
[ROW][C]Winsorized Mean ( 31 / 40 )[/C][C]75.4290833333333[/C][C]1.72095637779793[/C][C]43.8297474046666[/C][/ROW]
[ROW][C]Winsorized Mean ( 32 / 40 )[/C][C]75.4984166666667[/C][C]1.68403210527421[/C][C]44.8319342785767[/C][/ROW]
[ROW][C]Winsorized Mean ( 33 / 40 )[/C][C]75.6276666666667[/C][C]1.667484022548[/C][C]45.3543576094384[/C][/ROW]
[ROW][C]Winsorized Mean ( 34 / 40 )[/C][C]75.8005[/C][C]1.64408692550834[/C][C]46.1049223273661[/C][/ROW]
[ROW][C]Winsorized Mean ( 35 / 40 )[/C][C]75.8734166666667[/C][C]1.63649548056963[/C][C]46.3633524000057[/C][/ROW]
[ROW][C]Winsorized Mean ( 36 / 40 )[/C][C]75.8554166666667[/C][C]1.63466753614402[/C][C]46.404186165953[/C][/ROW]
[ROW][C]Winsorized Mean ( 37 / 40 )[/C][C]76.099[/C][C]1.60068170176464[/C][C]47.5416192464162[/C][/ROW]
[ROW][C]Winsorized Mean ( 38 / 40 )[/C][C]76.2446666666667[/C][C]1.5774210946956[/C][C]48.3350114456152[/C][/ROW]
[ROW][C]Winsorized Mean ( 39 / 40 )[/C][C]76.4494166666667[/C][C]1.55143359787814[/C][C]49.2766282561011[/C][/ROW]
[ROW][C]Winsorized Mean ( 40 / 40 )[/C][C]76.7760833333333[/C][C]1.51610920879561[/C][C]50.6402064494573[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 40 )[/C][C]74.5412711864407[/C][C]2.05676593950172[/C][C]36.241980555405[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 40 )[/C][C]74.614224137931[/C][C]2.05489018573383[/C][C]36.3105652340664[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 40 )[/C][C]74.6867543859649[/C][C]2.05330133369549[/C][C]36.3739862047162[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 40 )[/C][C]74.7549107142857[/C][C]2.05213755602158[/C][C]36.4278264363578[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 40 )[/C][C]74.8155454545455[/C][C]2.05241074950328[/C][C]36.452520760112[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 40 )[/C][C]74.875[/C][C]2.05285243598226[/C][C]36.4736396477389[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 40 )[/C][C]74.9333962264151[/C][C]2.05320910211633[/C][C]36.4957451967158[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 40 )[/C][C]74.9844230769231[/C][C]2.05444037136321[/C][C]36.4987098784317[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 40 )[/C][C]75.0358823529412[/C][C]2.05544561953695[/C][C]36.5058951887256[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 40 )[/C][C]75.086[/C][C]2.05621473350986[/C][C]36.5166141338904[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 40 )[/C][C]75.1341836734694[/C][C]2.0568789662778[/C][C]36.5282473617953[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 40 )[/C][C]75.1823958333333[/C][C]2.05699807218304[/C][C]36.5495703909651[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 40 )[/C][C]75.2306382978723[/C][C]2.05649835665606[/C][C]36.5819102429043[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 40 )[/C][C]75.2754347826087[/C][C]2.05602314221521[/C][C]36.6121534514953[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 40 )[/C][C]75.3155555555556[/C][C]2.05592476624807[/C][C]36.6334200511634[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 40 )[/C][C]75.3571590909091[/C][C]2.05562808965271[/C][C]36.6589459787155[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 40 )[/C][C]75.3991860465116[/C][C]2.05481924751265[/C][C]36.6938289768221[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 40 )[/C][C]75.4429761904762[/C][C]2.05293232885704[/C][C]36.7488860348742[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 40 )[/C][C]75.4869512195122[/C][C]2.05077566049202[/C][C]36.8089755860479[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 40 )[/C][C]75.53375[/C][C]2.04845561906025[/C][C]36.8735106082757[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 40 )[/C][C]75.5858974358974[/C][C]2.04603290879351[/C][C]36.9426596762162[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 40 )[/C][C]75.6385526315789[/C][C]2.04287883990325[/C][C]37.0254716795446[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 40 )[/C][C]75.6886486486487[/C][C]2.03944824449149[/C][C]37.11231645769[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 40 )[/C][C]75.7456944444444[/C][C]2.03501829118976[/C][C]37.2211369167401[/C][/ROW]
[ROW][C]Trimmed Mean ( 25 / 40 )[/C][C]75.8052857142857[/C][C]2.03002127212415[/C][C]37.3421139744834[/C][/ROW]
[ROW][C]Trimmed Mean ( 26 / 40 )[/C][C]75.8648529411765[/C][C]2.02575596932672[/C][C]37.4501440893649[/C][/ROW]
[ROW][C]Trimmed Mean ( 27 / 40 )[/C][C]75.9189393939394[/C][C]2.02387471544386[/C][C]37.511679361679[/C][/ROW]
[ROW][C]Trimmed Mean ( 28 / 40 )[/C][C]75.94640625[/C][C]2.02582613913224[/C][C]37.4891037206833[/C][/ROW]
[ROW][C]Trimmed Mean ( 29 / 40 )[/C][C]75.9754838709677[/C][C]2.02866382783285[/C][C]37.4509974637491[/C][/ROW]
[ROW][C]Trimmed Mean ( 30 / 40 )[/C][C]76.003[/C][C]2.0307552142277[/C][C]37.4259780142453[/C][/ROW]
[ROW][C]Trimmed Mean ( 31 / 40 )[/C][C]76.0427586206897[/C][C]2.03253784474653[/C][C]37.412714758171[/C][/ROW]
[ROW][C]Trimmed Mean ( 32 / 40 )[/C][C]76.0851785714286[/C][C]2.03320703411533[/C][C]37.4212646792922[/C][/ROW]
[ROW][C]Trimmed Mean ( 33 / 40 )[/C][C]76.1259259259259[/C][C]2.03596833283511[/C][C]37.3905255294024[/C][/ROW]
[ROW][C]Trimmed Mean ( 34 / 40 )[/C][C]76.1607692307692[/C][C]2.03835782626973[/C][C]37.3637877752534[/C][/ROW]
[ROW][C]Trimmed Mean ( 35 / 40 )[/C][C]76.1862[/C][C]2.04112059838287[/C][C]37.325672995687[/C][/ROW]
[ROW][C]Trimmed Mean ( 36 / 40 )[/C][C]76.2085416666667[/C][C]2.04186300234691[/C][C]37.3230435044236[/C][/ROW]
[ROW][C]Trimmed Mean ( 37 / 40 )[/C][C]76.2341304347826[/C][C]2.03906316880699[/C][C]37.3868409772638[/C][/ROW]
[ROW][C]Trimmed Mean ( 38 / 40 )[/C][C]76.2440909090909[/C][C]2.03695836957582[/C][C]37.4303628625303[/C][/ROW]
[ROW][C]Trimmed Mean ( 39 / 40 )[/C][C]76.2440476190476[/C][C]2.03366138686211[/C][C]37.4910238801802[/C][/ROW]
[ROW][C]Trimmed Mean ( 40 / 40 )[/C][C]76.22825[/C][C]2.02911010201264[/C][C]37.567330587133[/C][/ROW]
[ROW][C]Median[/C][C]75.45[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]70.005[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]75.6290163934426[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]75.6290163934426[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]75.6290163934426[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]75.6290163934426[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]75.6290163934426[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]75.6290163934426[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]75.6290163934426[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]75.9754838709677[/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=293472&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=293472&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 Mean74.46566666666672.0594467239018636.1580932404908
Geometric Mean70.8219695248481
Harmonic Mean67.1056480130336
Quadratic Mean77.7807989694972
Winsorized Mean ( 1 / 40 )74.470752.0579203018247536.1873829292452
Winsorized Mean ( 2 / 40 )74.47641666666672.0559693366164136.2244783228312
Winsorized Mean ( 3 / 40 )74.49591666666672.0527878546338236.2901195554645
Winsorized Mean ( 4 / 40 )74.53258333333332.0453315856994636.4403424141347
Winsorized Mean ( 5 / 40 )74.5482.0417932560080936.5110423303821
Winsorized Mean ( 6 / 40 )74.56552.0388277919937636.5727308077759
Winsorized Mean ( 7 / 40 )74.62383333333332.0302817524088536.7554075904959
Winsorized Mean ( 8 / 40 )74.63452.0274557190175636.8119013894741
Winsorized Mean ( 9 / 40 )74.662.0241716153259636.8842243586037
Winsorized Mean ( 10 / 40 )74.69252.0194297502281336.986926626966
Winsorized Mean ( 11 / 40 )74.70991666666672.0172241254284437.0360019617547
Winsorized Mean ( 12 / 40 )74.72891666666672.0148288491229637.0894613203476
Winsorized Mean ( 13 / 40 )74.78416666666672.0066469153550237.2682239682588
Winsorized Mean ( 14 / 40 )74.85416666666671.995022256439337.5204669647475
Winsorized Mean ( 15 / 40 )74.85791666666671.9876015587949937.6624360830398
Winsorized Mean ( 16 / 40 )74.875251.9821112444737337.775503372355
Winsorized Mean ( 17 / 40 )74.87808333333331.9804625244790737.8083818339501
Winsorized Mean ( 18 / 40 )74.90208333333331.9703363008880238.0148725370259
Winsorized Mean ( 19 / 40 )74.89416666666671.9582655054109838.2451544286118
Winsorized Mean ( 20 / 40 )74.85583333333331.9446817176494138.4925886092115
Winsorized Mean ( 21 / 40 )74.88558333333331.9360201777856538.6801667630266
Winsorized Mean ( 22 / 40 )74.95891666666671.9220360746381838.9997449349526
Winsorized Mean ( 23 / 40 )74.90141666666671.9129171129178739.1555996654847
Winsorized Mean ( 24 / 40 )74.91141666666671.8983968147698239.4603573309038
Winsorized Mean ( 25 / 40 )74.96141666666671.8714275857283740.0557399272766
Winsorized Mean ( 26 / 40 )75.09141666666671.8305386821611941.0214858601139
Winsorized Mean ( 27 / 40 )75.52341666666671.7796105800057142.4381701902584
Winsorized Mean ( 28 / 40 )75.525751.7560208218941443.0095982111042
Winsorized Mean ( 29 / 40 )75.57651.7464483072155143.2743984965105
Winsorized Mean ( 30 / 40 )75.42651.7310005147927843.5739327374083
Winsorized Mean ( 31 / 40 )75.42908333333331.7209563777979343.8297474046666
Winsorized Mean ( 32 / 40 )75.49841666666671.6840321052742144.8319342785767
Winsorized Mean ( 33 / 40 )75.62766666666671.66748402254845.3543576094384
Winsorized Mean ( 34 / 40 )75.80051.6440869255083446.1049223273661
Winsorized Mean ( 35 / 40 )75.87341666666671.6364954805696346.3633524000057
Winsorized Mean ( 36 / 40 )75.85541666666671.6346675361440246.404186165953
Winsorized Mean ( 37 / 40 )76.0991.6006817017646447.5416192464162
Winsorized Mean ( 38 / 40 )76.24466666666671.577421094695648.3350114456152
Winsorized Mean ( 39 / 40 )76.44941666666671.5514335978781449.2766282561011
Winsorized Mean ( 40 / 40 )76.77608333333331.5161092087956150.6402064494573
Trimmed Mean ( 1 / 40 )74.54127118644072.0567659395017236.241980555405
Trimmed Mean ( 2 / 40 )74.6142241379312.0548901857338336.3105652340664
Trimmed Mean ( 3 / 40 )74.68675438596492.0533013336954936.3739862047162
Trimmed Mean ( 4 / 40 )74.75491071428572.0521375560215836.4278264363578
Trimmed Mean ( 5 / 40 )74.81554545454552.0524107495032836.452520760112
Trimmed Mean ( 6 / 40 )74.8752.0528524359822636.4736396477389
Trimmed Mean ( 7 / 40 )74.93339622641512.0532091021163336.4957451967158
Trimmed Mean ( 8 / 40 )74.98442307692312.0544403713632136.4987098784317
Trimmed Mean ( 9 / 40 )75.03588235294122.0554456195369536.5058951887256
Trimmed Mean ( 10 / 40 )75.0862.0562147335098636.5166141338904
Trimmed Mean ( 11 / 40 )75.13418367346942.056878966277836.5282473617953
Trimmed Mean ( 12 / 40 )75.18239583333332.0569980721830436.5495703909651
Trimmed Mean ( 13 / 40 )75.23063829787232.0564983566560636.5819102429043
Trimmed Mean ( 14 / 40 )75.27543478260872.0560231422152136.6121534514953
Trimmed Mean ( 15 / 40 )75.31555555555562.0559247662480736.6334200511634
Trimmed Mean ( 16 / 40 )75.35715909090912.0556280896527136.6589459787155
Trimmed Mean ( 17 / 40 )75.39918604651162.0548192475126536.6938289768221
Trimmed Mean ( 18 / 40 )75.44297619047622.0529323288570436.7488860348742
Trimmed Mean ( 19 / 40 )75.48695121951222.0507756604920236.8089755860479
Trimmed Mean ( 20 / 40 )75.533752.0484556190602536.8735106082757
Trimmed Mean ( 21 / 40 )75.58589743589742.0460329087935136.9426596762162
Trimmed Mean ( 22 / 40 )75.63855263157892.0428788399032537.0254716795446
Trimmed Mean ( 23 / 40 )75.68864864864872.0394482444914937.11231645769
Trimmed Mean ( 24 / 40 )75.74569444444442.0350182911897637.2211369167401
Trimmed Mean ( 25 / 40 )75.80528571428572.0300212721241537.3421139744834
Trimmed Mean ( 26 / 40 )75.86485294117652.0257559693267237.4501440893649
Trimmed Mean ( 27 / 40 )75.91893939393942.0238747154438637.511679361679
Trimmed Mean ( 28 / 40 )75.946406252.0258261391322437.4891037206833
Trimmed Mean ( 29 / 40 )75.97548387096772.0286638278328537.4509974637491
Trimmed Mean ( 30 / 40 )76.0032.030755214227737.4259780142453
Trimmed Mean ( 31 / 40 )76.04275862068972.0325378447465337.412714758171
Trimmed Mean ( 32 / 40 )76.08517857142862.0332070341153337.4212646792922
Trimmed Mean ( 33 / 40 )76.12592592592592.0359683328351137.3905255294024
Trimmed Mean ( 34 / 40 )76.16076923076922.0383578262697337.3637877752534
Trimmed Mean ( 35 / 40 )76.18622.0411205983828737.325672995687
Trimmed Mean ( 36 / 40 )76.20854166666672.0418630023469137.3230435044236
Trimmed Mean ( 37 / 40 )76.23413043478262.0390631688069937.3868409772638
Trimmed Mean ( 38 / 40 )76.24409090909092.0369583695758237.4303628625303
Trimmed Mean ( 39 / 40 )76.24404761904762.0336613868621137.4910238801802
Trimmed Mean ( 40 / 40 )76.228252.0291101020126437.567330587133
Median75.45
Midrange70.005
Midmean - Weighted Average at Xnp75.6290163934426
Midmean - Weighted Average at X(n+1)p75.6290163934426
Midmean - Empirical Distribution Function75.6290163934426
Midmean - Empirical Distribution Function - Averaging75.6290163934426
Midmean - Empirical Distribution Function - Interpolation75.6290163934426
Midmean - Closest Observation75.6290163934426
Midmean - True Basic - Statistics Graphics Toolkit75.6290163934426
Midmean - MS Excel (old versions)75.9754838709677
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')