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Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationMon, 13 Dec 2010 20:37:20 +0000
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2010/Dec/13/t1292272517ls8bnow6lmt7pqb.htm/, Retrieved Mon, 06 May 2024 19:36:05 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=109178, Retrieved Mon, 06 May 2024 19:36:05 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact145
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
F     [Central Tendency] [Time needed to su...] [2010-09-25 09:42:08] [b98453cac15ba1066b407e146608df68]
-    D  [Central Tendency] [Paper - Central t...] [2010-12-11 10:56:18] [1f5baf2b24e732d76900bb8178fc04e7]
-    D      [Central Tendency] [Paper - Central t...] [2010-12-13 20:37:20] [ee4a783fb13f41eb2e9bc8a0c4f26279] [Current]
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Dataseries X:
10.81
9.12
11.03
12.74
9.98
11.62
9.40
9.27
7.76
8.78
10.65
10.95
12.36
10.85
11.84
12.14
11.65
8.86
7.63
7.38
7.25
8.03
7.75
7.16
7.18
7.51
7.07
7.11
8.98
9.53
10.54
11.31
10.36
11.44
10.45
10.69
11.28
11.96
13.52
12.89
14.03
16.27
16.17
17.25
19.38
26.20
33.53
32.20
38.45
44.86
41.67
36.06
39.76
36.81
42.65
46.89
53.61
57.59
67.82
71.89
75.51
68.49
62.72
70.39
59.77
57.27
67.96
67.85
76.98
81.08
91.66
84.84
85.73
84.61
92.91
99.80
121.19
122.04
131.76
138.48
153.47
189.95
182.22
198.08
135.36
125.02
143.50
173.95
188.75
167.44
158.95
169.53
113.66
107.59
92.67
85.35
90.13
89.31
105.12
125.83
135.81
142.43
163.39
168.21
185.35
188.50
199.91
210.73
192.06
204.62
235.00
261.09
256.88
251.53
257.25
243.10
283.75




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

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 2 seconds \tabularnewline
R Server & 'RServer@AstonUniversity' @ vre.aston.ac.uk \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=109178&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'RServer@AstonUniversity' @ vre.aston.ac.uk[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=109178&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=109178&T=0

As an alternative you can also use a QR Code:  

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

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







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean79.20042735042737.0239936400011711.2756974749217
Geometric Mean42.5388678083587
Harmonic Mean21.9260816943321
Quadratic Mean109.52506628368
Winsorized Mean ( 1 / 39 )79.0070940170946.9778603601473111.3225387066109
Winsorized Mean ( 2 / 39 )78.94230769230776.9631560375952711.3371447180107
Winsorized Mean ( 3 / 39 )78.93333333333336.961017944401611.3393377181013
Winsorized Mean ( 4 / 39 )78.75282051282056.920968321188211.3788731371191
Winsorized Mean ( 5 / 39 )78.39811965811976.844332108107111.4544587287425
Winsorized Mean ( 6 / 39 )77.98940170940176.7590479471985311.5385187852864
Winsorized Mean ( 7 / 39 )76.54452991452996.4831320790655211.8067207302004
Winsorized Mean ( 8 / 39 )76.13495726495736.4089994090380911.8793827875207
Winsorized Mean ( 9 / 39 )75.77341880341886.3470737473402811.9383233628208
Winsorized Mean ( 10 / 39 )75.64008547008556.3186936475795211.9708423431892
Winsorized Mean ( 11 / 39 )75.14461538461546.2190511181509712.0829711730939
Winsorized Mean ( 12 / 39 )74.93641025641036.1834085048392112.1189486668662
Winsorized Mean ( 13 / 39 )74.81641025641036.1608620068123612.1438217856011
Winsorized Mean ( 14 / 39 )74.80324786324796.1545531977385612.1541313333247
Winsorized Mean ( 15 / 39 )74.41863247863256.0889085905068612.2219986344774
Winsorized Mean ( 16 / 39 )74.00837606837616.0204896007935712.2927504199361
Winsorized Mean ( 17 / 39 )72.8256410256415.8358369168155512.4790397784762
Winsorized Mean ( 18 / 39 )72.21487179487185.7287701838410212.6056499872462
Winsorized Mean ( 19 / 39 )72.06222222222225.6916932158965812.6609463104857
Winsorized Mean ( 20 / 39 )71.94598290598295.6711179259654612.6863845621293
Winsorized Mean ( 21 / 39 )71.23521367521375.5649480325290912.8006970161839
Winsorized Mean ( 22 / 39 )70.42102564102565.4448833429289512.9334314815906
Winsorized Mean ( 23 / 39 )69.35162393162395.2948456799509813.0979499920508
Winsorized Mean ( 24 / 39 )67.33111111111115.0184676669676713.41666731347
Winsorized Mean ( 25 / 39 )67.11102564102564.9877980945283213.4550405547986
Winsorized Mean ( 26 / 39 )66.25547008547014.8724006294773213.5981162313776
Winsorized Mean ( 27 / 39 )65.65777777777784.7923411198131313.7005643246735
Winsorized Mean ( 28 / 39 )65.60991452991454.7728873614450213.7463781483523
Winsorized Mean ( 29 / 39 )64.72504273504274.6606173840585213.8876542314828
Winsorized Mean ( 30 / 39 )63.23786324786324.4712398527965114.1432500446854
Winsorized Mean ( 31 / 39 )63.07094017094024.4406213885977214.2031789363733
Winsorized Mean ( 32 / 39 )62.26410256410264.3424222799945714.3385646418939
Winsorized Mean ( 33 / 39 )62.07794871794874.308634041017814.4078025952013
Winsorized Mean ( 34 / 39 )59.92461538461544.0504407264727114.7945913621109
Winsorized Mean ( 35 / 39 )58.16264957264963.8402576553293515.1455070968829
Winsorized Mean ( 36 / 39 )57.47034188034193.7494500961020715.3276721672034
Winsorized Mean ( 37 / 39 )55.90811965811973.5551738094471715.7258470766056
Winsorized Mean ( 38 / 39 )53.71905982905983.3168082846192316.1960099045118
Winsorized Mean ( 39 / 39 )53.84905982905983.2864101566894416.385374089552
Trimmed Mean ( 1 / 39 )78.04895652173916.8902200994359711.3274983085269
Trimmed Mean ( 2 / 39 )77.05690265486736.7915005969521611.346079052021
Trimmed Mean ( 3 / 39 )76.06324324324326.6888657666499411.3716205253344
Trimmed Mean ( 4 / 39 )75.03633027522946.5738450866225311.4143745838984
Trimmed Mean ( 5 / 39 )74.02037383177576.4569755119454111.4636293253456
Trimmed Mean ( 6 / 39 )73.04476190476196.3458612324856311.5106144349379
Trimmed Mean ( 7 / 39 )72.1086407766996.2404188187249311.5550963599319
Trimmed Mean ( 8 / 39 )71.37455445544556.1796979748120511.5498451132017
Trimmed Mean ( 9 / 39 )70.67131313131316.1239696235904811.5401149050571
Trimmed Mean ( 10 / 39 )69.98752577319596.0704299821503611.5292534431645
Trimmed Mean ( 11 / 39 )69.29136842105266.0128256137508211.523927828971
Trimmed Mean ( 12 / 39 )68.6219354838715.9615452088912811.5107632466706
Trimmed Mean ( 13 / 39 )67.94538461538465.9067518046512411.5030031500361
Trimmed Mean ( 14 / 39 )67.25056179775285.8456607431489411.5043559235917
Trimmed Mean ( 15 / 39 )67.25056179775285.7747382926789411.6456466751076
Trimmed Mean ( 16 / 39 )65.8007058823535.7010571278509911.5418429260954
Trimmed Mean ( 17 / 39 )65.07759036144585.6242250508473611.5709435118783
Trimmed Mean ( 18 / 39 )64.41925925925935.5598999701727111.5864061592565
Trimmed Mean ( 19 / 39 )63.77784810126585.498052503072911.6000798583899
Trimmed Mean ( 20 / 39 )63.11532467532475.4288912689041411.6258222073519
Trimmed Mean ( 21 / 39 )62.42653333333335.3487781260023511.6711764561434
Trimmed Mean ( 22 / 39 )61.75424657534255.2679983321578911.7225258402932
Trimmed Mean ( 23 / 39 )61.10507042253525.1881096562971911.7779064959368
Trimmed Mean ( 24 / 39 )60.49710144927545.1133038374329611.831313642345
Trimmed Mean ( 25 / 39 )59.99985074626875.0618426794287311.8533614231251
Trimmed Mean ( 26 / 39 )59.48784615384625.0017813725380511.8933319397885
Trimmed Mean ( 27 / 39 )59.00444444444444.9437106407045911.9352544541391
Trimmed Mean ( 28 / 39 )58.53180327868854.8824836436492611.9881207087753
Trimmed Mean ( 29 / 39 )58.03050847457634.807799621033512.0700763444259
Trimmed Mean ( 30 / 39 )58.03050847457634.7317673178961512.2640241110541
Trimmed Mean ( 31 / 39 )57.15381818181824.6663330507800212.2481223607184
Trimmed Mean ( 32 / 39 )56.73245283018874.5867779931997312.368693866217
Trimmed Mean ( 33 / 39 )56.33588235294124.5017064840727712.5143392960558
Trimmed Mean ( 34 / 39 )55.92040816326534.3974652945688412.7165092655378
Trimmed Mean ( 35 / 39 )55.62723404255324.3126996134432412.8984717296693
Trimmed Mean ( 36 / 39 )55.43888888888894.2413899858826613.0709246434343
Trimmed Mean ( 37 / 39 )55.28534883720934.1626651706854613.2812384783054
Trimmed Mean ( 38 / 39 )55.23731707317074.0950756868491713.4887170096901
Trimmed Mean ( 39 / 39 )55.35717948717954.0483857423157513.6738895477668
Median57.59
Midrange145.41
Midmean - Weighted Average at Xnp56.7593103448276
Midmean - Weighted Average at X(n+1)p58.0305084745763
Midmean - Empirical Distribution Function58.0305084745763
Midmean - Empirical Distribution Function - Averaging58.0305084745763
Midmean - Empirical Distribution Function - Interpolation58.0305084745763
Midmean - Closest Observation57.2513333333333
Midmean - True Basic - Statistics Graphics Toolkit58.0305084745763
Midmean - MS Excel (old versions)58.0305084745763
Number of observations117

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 79.2004273504273 & 7.02399364000117 & 11.2756974749217 \tabularnewline
Geometric Mean & 42.5388678083587 &  &  \tabularnewline
Harmonic Mean & 21.9260816943321 &  &  \tabularnewline
Quadratic Mean & 109.52506628368 &  &  \tabularnewline
Winsorized Mean ( 1 / 39 ) & 79.007094017094 & 6.97786036014731 & 11.3225387066109 \tabularnewline
Winsorized Mean ( 2 / 39 ) & 78.9423076923077 & 6.96315603759527 & 11.3371447180107 \tabularnewline
Winsorized Mean ( 3 / 39 ) & 78.9333333333333 & 6.9610179444016 & 11.3393377181013 \tabularnewline
Winsorized Mean ( 4 / 39 ) & 78.7528205128205 & 6.9209683211882 & 11.3788731371191 \tabularnewline
Winsorized Mean ( 5 / 39 ) & 78.3981196581197 & 6.8443321081071 & 11.4544587287425 \tabularnewline
Winsorized Mean ( 6 / 39 ) & 77.9894017094017 & 6.75904794719853 & 11.5385187852864 \tabularnewline
Winsorized Mean ( 7 / 39 ) & 76.5445299145299 & 6.48313207906552 & 11.8067207302004 \tabularnewline
Winsorized Mean ( 8 / 39 ) & 76.1349572649573 & 6.40899940903809 & 11.8793827875207 \tabularnewline
Winsorized Mean ( 9 / 39 ) & 75.7734188034188 & 6.34707374734028 & 11.9383233628208 \tabularnewline
Winsorized Mean ( 10 / 39 ) & 75.6400854700855 & 6.31869364757952 & 11.9708423431892 \tabularnewline
Winsorized Mean ( 11 / 39 ) & 75.1446153846154 & 6.21905111815097 & 12.0829711730939 \tabularnewline
Winsorized Mean ( 12 / 39 ) & 74.9364102564103 & 6.18340850483921 & 12.1189486668662 \tabularnewline
Winsorized Mean ( 13 / 39 ) & 74.8164102564103 & 6.16086200681236 & 12.1438217856011 \tabularnewline
Winsorized Mean ( 14 / 39 ) & 74.8032478632479 & 6.15455319773856 & 12.1541313333247 \tabularnewline
Winsorized Mean ( 15 / 39 ) & 74.4186324786325 & 6.08890859050686 & 12.2219986344774 \tabularnewline
Winsorized Mean ( 16 / 39 ) & 74.0083760683761 & 6.02048960079357 & 12.2927504199361 \tabularnewline
Winsorized Mean ( 17 / 39 ) & 72.825641025641 & 5.83583691681555 & 12.4790397784762 \tabularnewline
Winsorized Mean ( 18 / 39 ) & 72.2148717948718 & 5.72877018384102 & 12.6056499872462 \tabularnewline
Winsorized Mean ( 19 / 39 ) & 72.0622222222222 & 5.69169321589658 & 12.6609463104857 \tabularnewline
Winsorized Mean ( 20 / 39 ) & 71.9459829059829 & 5.67111792596546 & 12.6863845621293 \tabularnewline
Winsorized Mean ( 21 / 39 ) & 71.2352136752137 & 5.56494803252909 & 12.8006970161839 \tabularnewline
Winsorized Mean ( 22 / 39 ) & 70.4210256410256 & 5.44488334292895 & 12.9334314815906 \tabularnewline
Winsorized Mean ( 23 / 39 ) & 69.3516239316239 & 5.29484567995098 & 13.0979499920508 \tabularnewline
Winsorized Mean ( 24 / 39 ) & 67.3311111111111 & 5.01846766696767 & 13.41666731347 \tabularnewline
Winsorized Mean ( 25 / 39 ) & 67.1110256410256 & 4.98779809452832 & 13.4550405547986 \tabularnewline
Winsorized Mean ( 26 / 39 ) & 66.2554700854701 & 4.87240062947732 & 13.5981162313776 \tabularnewline
Winsorized Mean ( 27 / 39 ) & 65.6577777777778 & 4.79234111981313 & 13.7005643246735 \tabularnewline
Winsorized Mean ( 28 / 39 ) & 65.6099145299145 & 4.77288736144502 & 13.7463781483523 \tabularnewline
Winsorized Mean ( 29 / 39 ) & 64.7250427350427 & 4.66061738405852 & 13.8876542314828 \tabularnewline
Winsorized Mean ( 30 / 39 ) & 63.2378632478632 & 4.47123985279651 & 14.1432500446854 \tabularnewline
Winsorized Mean ( 31 / 39 ) & 63.0709401709402 & 4.44062138859772 & 14.2031789363733 \tabularnewline
Winsorized Mean ( 32 / 39 ) & 62.2641025641026 & 4.34242227999457 & 14.3385646418939 \tabularnewline
Winsorized Mean ( 33 / 39 ) & 62.0779487179487 & 4.3086340410178 & 14.4078025952013 \tabularnewline
Winsorized Mean ( 34 / 39 ) & 59.9246153846154 & 4.05044072647271 & 14.7945913621109 \tabularnewline
Winsorized Mean ( 35 / 39 ) & 58.1626495726496 & 3.84025765532935 & 15.1455070968829 \tabularnewline
Winsorized Mean ( 36 / 39 ) & 57.4703418803419 & 3.74945009610207 & 15.3276721672034 \tabularnewline
Winsorized Mean ( 37 / 39 ) & 55.9081196581197 & 3.55517380944717 & 15.7258470766056 \tabularnewline
Winsorized Mean ( 38 / 39 ) & 53.7190598290598 & 3.31680828461923 & 16.1960099045118 \tabularnewline
Winsorized Mean ( 39 / 39 ) & 53.8490598290598 & 3.28641015668944 & 16.385374089552 \tabularnewline
Trimmed Mean ( 1 / 39 ) & 78.0489565217391 & 6.89022009943597 & 11.3274983085269 \tabularnewline
Trimmed Mean ( 2 / 39 ) & 77.0569026548673 & 6.79150059695216 & 11.346079052021 \tabularnewline
Trimmed Mean ( 3 / 39 ) & 76.0632432432432 & 6.68886576664994 & 11.3716205253344 \tabularnewline
Trimmed Mean ( 4 / 39 ) & 75.0363302752294 & 6.57384508662253 & 11.4143745838984 \tabularnewline
Trimmed Mean ( 5 / 39 ) & 74.0203738317757 & 6.45697551194541 & 11.4636293253456 \tabularnewline
Trimmed Mean ( 6 / 39 ) & 73.0447619047619 & 6.34586123248563 & 11.5106144349379 \tabularnewline
Trimmed Mean ( 7 / 39 ) & 72.108640776699 & 6.24041881872493 & 11.5550963599319 \tabularnewline
Trimmed Mean ( 8 / 39 ) & 71.3745544554455 & 6.17969797481205 & 11.5498451132017 \tabularnewline
Trimmed Mean ( 9 / 39 ) & 70.6713131313131 & 6.12396962359048 & 11.5401149050571 \tabularnewline
Trimmed Mean ( 10 / 39 ) & 69.9875257731959 & 6.07042998215036 & 11.5292534431645 \tabularnewline
Trimmed Mean ( 11 / 39 ) & 69.2913684210526 & 6.01282561375082 & 11.523927828971 \tabularnewline
Trimmed Mean ( 12 / 39 ) & 68.621935483871 & 5.96154520889128 & 11.5107632466706 \tabularnewline
Trimmed Mean ( 13 / 39 ) & 67.9453846153846 & 5.90675180465124 & 11.5030031500361 \tabularnewline
Trimmed Mean ( 14 / 39 ) & 67.2505617977528 & 5.84566074314894 & 11.5043559235917 \tabularnewline
Trimmed Mean ( 15 / 39 ) & 67.2505617977528 & 5.77473829267894 & 11.6456466751076 \tabularnewline
Trimmed Mean ( 16 / 39 ) & 65.800705882353 & 5.70105712785099 & 11.5418429260954 \tabularnewline
Trimmed Mean ( 17 / 39 ) & 65.0775903614458 & 5.62422505084736 & 11.5709435118783 \tabularnewline
Trimmed Mean ( 18 / 39 ) & 64.4192592592593 & 5.55989997017271 & 11.5864061592565 \tabularnewline
Trimmed Mean ( 19 / 39 ) & 63.7778481012658 & 5.4980525030729 & 11.6000798583899 \tabularnewline
Trimmed Mean ( 20 / 39 ) & 63.1153246753247 & 5.42889126890414 & 11.6258222073519 \tabularnewline
Trimmed Mean ( 21 / 39 ) & 62.4265333333333 & 5.34877812600235 & 11.6711764561434 \tabularnewline
Trimmed Mean ( 22 / 39 ) & 61.7542465753425 & 5.26799833215789 & 11.7225258402932 \tabularnewline
Trimmed Mean ( 23 / 39 ) & 61.1050704225352 & 5.18810965629719 & 11.7779064959368 \tabularnewline
Trimmed Mean ( 24 / 39 ) & 60.4971014492754 & 5.11330383743296 & 11.831313642345 \tabularnewline
Trimmed Mean ( 25 / 39 ) & 59.9998507462687 & 5.06184267942873 & 11.8533614231251 \tabularnewline
Trimmed Mean ( 26 / 39 ) & 59.4878461538462 & 5.00178137253805 & 11.8933319397885 \tabularnewline
Trimmed Mean ( 27 / 39 ) & 59.0044444444444 & 4.94371064070459 & 11.9352544541391 \tabularnewline
Trimmed Mean ( 28 / 39 ) & 58.5318032786885 & 4.88248364364926 & 11.9881207087753 \tabularnewline
Trimmed Mean ( 29 / 39 ) & 58.0305084745763 & 4.8077996210335 & 12.0700763444259 \tabularnewline
Trimmed Mean ( 30 / 39 ) & 58.0305084745763 & 4.73176731789615 & 12.2640241110541 \tabularnewline
Trimmed Mean ( 31 / 39 ) & 57.1538181818182 & 4.66633305078002 & 12.2481223607184 \tabularnewline
Trimmed Mean ( 32 / 39 ) & 56.7324528301887 & 4.58677799319973 & 12.368693866217 \tabularnewline
Trimmed Mean ( 33 / 39 ) & 56.3358823529412 & 4.50170648407277 & 12.5143392960558 \tabularnewline
Trimmed Mean ( 34 / 39 ) & 55.9204081632653 & 4.39746529456884 & 12.7165092655378 \tabularnewline
Trimmed Mean ( 35 / 39 ) & 55.6272340425532 & 4.31269961344324 & 12.8984717296693 \tabularnewline
Trimmed Mean ( 36 / 39 ) & 55.4388888888889 & 4.24138998588266 & 13.0709246434343 \tabularnewline
Trimmed Mean ( 37 / 39 ) & 55.2853488372093 & 4.16266517068546 & 13.2812384783054 \tabularnewline
Trimmed Mean ( 38 / 39 ) & 55.2373170731707 & 4.09507568684917 & 13.4887170096901 \tabularnewline
Trimmed Mean ( 39 / 39 ) & 55.3571794871795 & 4.04838574231575 & 13.6738895477668 \tabularnewline
Median & 57.59 &  &  \tabularnewline
Midrange & 145.41 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 56.7593103448276 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 58.0305084745763 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 58.0305084745763 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 58.0305084745763 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 58.0305084745763 &  &  \tabularnewline
Midmean - Closest Observation & 57.2513333333333 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 58.0305084745763 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 58.0305084745763 &  &  \tabularnewline
Number of observations & 117 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=109178&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]79.2004273504273[/C][C]7.02399364000117[/C][C]11.2756974749217[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]42.5388678083587[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]21.9260816943321[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]109.52506628368[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 39 )[/C][C]79.007094017094[/C][C]6.97786036014731[/C][C]11.3225387066109[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 39 )[/C][C]78.9423076923077[/C][C]6.96315603759527[/C][C]11.3371447180107[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 39 )[/C][C]78.9333333333333[/C][C]6.9610179444016[/C][C]11.3393377181013[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 39 )[/C][C]78.7528205128205[/C][C]6.9209683211882[/C][C]11.3788731371191[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 39 )[/C][C]78.3981196581197[/C][C]6.8443321081071[/C][C]11.4544587287425[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 39 )[/C][C]77.9894017094017[/C][C]6.75904794719853[/C][C]11.5385187852864[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 39 )[/C][C]76.5445299145299[/C][C]6.48313207906552[/C][C]11.8067207302004[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 39 )[/C][C]76.1349572649573[/C][C]6.40899940903809[/C][C]11.8793827875207[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 39 )[/C][C]75.7734188034188[/C][C]6.34707374734028[/C][C]11.9383233628208[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 39 )[/C][C]75.6400854700855[/C][C]6.31869364757952[/C][C]11.9708423431892[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 39 )[/C][C]75.1446153846154[/C][C]6.21905111815097[/C][C]12.0829711730939[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 39 )[/C][C]74.9364102564103[/C][C]6.18340850483921[/C][C]12.1189486668662[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 39 )[/C][C]74.8164102564103[/C][C]6.16086200681236[/C][C]12.1438217856011[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 39 )[/C][C]74.8032478632479[/C][C]6.15455319773856[/C][C]12.1541313333247[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 39 )[/C][C]74.4186324786325[/C][C]6.08890859050686[/C][C]12.2219986344774[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 39 )[/C][C]74.0083760683761[/C][C]6.02048960079357[/C][C]12.2927504199361[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 39 )[/C][C]72.825641025641[/C][C]5.83583691681555[/C][C]12.4790397784762[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 39 )[/C][C]72.2148717948718[/C][C]5.72877018384102[/C][C]12.6056499872462[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 39 )[/C][C]72.0622222222222[/C][C]5.69169321589658[/C][C]12.6609463104857[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 39 )[/C][C]71.9459829059829[/C][C]5.67111792596546[/C][C]12.6863845621293[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 39 )[/C][C]71.2352136752137[/C][C]5.56494803252909[/C][C]12.8006970161839[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 39 )[/C][C]70.4210256410256[/C][C]5.44488334292895[/C][C]12.9334314815906[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 39 )[/C][C]69.3516239316239[/C][C]5.29484567995098[/C][C]13.0979499920508[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 39 )[/C][C]67.3311111111111[/C][C]5.01846766696767[/C][C]13.41666731347[/C][/ROW]
[ROW][C]Winsorized Mean ( 25 / 39 )[/C][C]67.1110256410256[/C][C]4.98779809452832[/C][C]13.4550405547986[/C][/ROW]
[ROW][C]Winsorized Mean ( 26 / 39 )[/C][C]66.2554700854701[/C][C]4.87240062947732[/C][C]13.5981162313776[/C][/ROW]
[ROW][C]Winsorized Mean ( 27 / 39 )[/C][C]65.6577777777778[/C][C]4.79234111981313[/C][C]13.7005643246735[/C][/ROW]
[ROW][C]Winsorized Mean ( 28 / 39 )[/C][C]65.6099145299145[/C][C]4.77288736144502[/C][C]13.7463781483523[/C][/ROW]
[ROW][C]Winsorized Mean ( 29 / 39 )[/C][C]64.7250427350427[/C][C]4.66061738405852[/C][C]13.8876542314828[/C][/ROW]
[ROW][C]Winsorized Mean ( 30 / 39 )[/C][C]63.2378632478632[/C][C]4.47123985279651[/C][C]14.1432500446854[/C][/ROW]
[ROW][C]Winsorized Mean ( 31 / 39 )[/C][C]63.0709401709402[/C][C]4.44062138859772[/C][C]14.2031789363733[/C][/ROW]
[ROW][C]Winsorized Mean ( 32 / 39 )[/C][C]62.2641025641026[/C][C]4.34242227999457[/C][C]14.3385646418939[/C][/ROW]
[ROW][C]Winsorized Mean ( 33 / 39 )[/C][C]62.0779487179487[/C][C]4.3086340410178[/C][C]14.4078025952013[/C][/ROW]
[ROW][C]Winsorized Mean ( 34 / 39 )[/C][C]59.9246153846154[/C][C]4.05044072647271[/C][C]14.7945913621109[/C][/ROW]
[ROW][C]Winsorized Mean ( 35 / 39 )[/C][C]58.1626495726496[/C][C]3.84025765532935[/C][C]15.1455070968829[/C][/ROW]
[ROW][C]Winsorized Mean ( 36 / 39 )[/C][C]57.4703418803419[/C][C]3.74945009610207[/C][C]15.3276721672034[/C][/ROW]
[ROW][C]Winsorized Mean ( 37 / 39 )[/C][C]55.9081196581197[/C][C]3.55517380944717[/C][C]15.7258470766056[/C][/ROW]
[ROW][C]Winsorized Mean ( 38 / 39 )[/C][C]53.7190598290598[/C][C]3.31680828461923[/C][C]16.1960099045118[/C][/ROW]
[ROW][C]Winsorized Mean ( 39 / 39 )[/C][C]53.8490598290598[/C][C]3.28641015668944[/C][C]16.385374089552[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 39 )[/C][C]78.0489565217391[/C][C]6.89022009943597[/C][C]11.3274983085269[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 39 )[/C][C]77.0569026548673[/C][C]6.79150059695216[/C][C]11.346079052021[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 39 )[/C][C]76.0632432432432[/C][C]6.68886576664994[/C][C]11.3716205253344[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 39 )[/C][C]75.0363302752294[/C][C]6.57384508662253[/C][C]11.4143745838984[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 39 )[/C][C]74.0203738317757[/C][C]6.45697551194541[/C][C]11.4636293253456[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 39 )[/C][C]73.0447619047619[/C][C]6.34586123248563[/C][C]11.5106144349379[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 39 )[/C][C]72.108640776699[/C][C]6.24041881872493[/C][C]11.5550963599319[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 39 )[/C][C]71.3745544554455[/C][C]6.17969797481205[/C][C]11.5498451132017[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 39 )[/C][C]70.6713131313131[/C][C]6.12396962359048[/C][C]11.5401149050571[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 39 )[/C][C]69.9875257731959[/C][C]6.07042998215036[/C][C]11.5292534431645[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 39 )[/C][C]69.2913684210526[/C][C]6.01282561375082[/C][C]11.523927828971[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 39 )[/C][C]68.621935483871[/C][C]5.96154520889128[/C][C]11.5107632466706[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 39 )[/C][C]67.9453846153846[/C][C]5.90675180465124[/C][C]11.5030031500361[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 39 )[/C][C]67.2505617977528[/C][C]5.84566074314894[/C][C]11.5043559235917[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 39 )[/C][C]67.2505617977528[/C][C]5.77473829267894[/C][C]11.6456466751076[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 39 )[/C][C]65.800705882353[/C][C]5.70105712785099[/C][C]11.5418429260954[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 39 )[/C][C]65.0775903614458[/C][C]5.62422505084736[/C][C]11.5709435118783[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 39 )[/C][C]64.4192592592593[/C][C]5.55989997017271[/C][C]11.5864061592565[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 39 )[/C][C]63.7778481012658[/C][C]5.4980525030729[/C][C]11.6000798583899[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 39 )[/C][C]63.1153246753247[/C][C]5.42889126890414[/C][C]11.6258222073519[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 39 )[/C][C]62.4265333333333[/C][C]5.34877812600235[/C][C]11.6711764561434[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 39 )[/C][C]61.7542465753425[/C][C]5.26799833215789[/C][C]11.7225258402932[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 39 )[/C][C]61.1050704225352[/C][C]5.18810965629719[/C][C]11.7779064959368[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 39 )[/C][C]60.4971014492754[/C][C]5.11330383743296[/C][C]11.831313642345[/C][/ROW]
[ROW][C]Trimmed Mean ( 25 / 39 )[/C][C]59.9998507462687[/C][C]5.06184267942873[/C][C]11.8533614231251[/C][/ROW]
[ROW][C]Trimmed Mean ( 26 / 39 )[/C][C]59.4878461538462[/C][C]5.00178137253805[/C][C]11.8933319397885[/C][/ROW]
[ROW][C]Trimmed Mean ( 27 / 39 )[/C][C]59.0044444444444[/C][C]4.94371064070459[/C][C]11.9352544541391[/C][/ROW]
[ROW][C]Trimmed Mean ( 28 / 39 )[/C][C]58.5318032786885[/C][C]4.88248364364926[/C][C]11.9881207087753[/C][/ROW]
[ROW][C]Trimmed Mean ( 29 / 39 )[/C][C]58.0305084745763[/C][C]4.8077996210335[/C][C]12.0700763444259[/C][/ROW]
[ROW][C]Trimmed Mean ( 30 / 39 )[/C][C]58.0305084745763[/C][C]4.73176731789615[/C][C]12.2640241110541[/C][/ROW]
[ROW][C]Trimmed Mean ( 31 / 39 )[/C][C]57.1538181818182[/C][C]4.66633305078002[/C][C]12.2481223607184[/C][/ROW]
[ROW][C]Trimmed Mean ( 32 / 39 )[/C][C]56.7324528301887[/C][C]4.58677799319973[/C][C]12.368693866217[/C][/ROW]
[ROW][C]Trimmed Mean ( 33 / 39 )[/C][C]56.3358823529412[/C][C]4.50170648407277[/C][C]12.5143392960558[/C][/ROW]
[ROW][C]Trimmed Mean ( 34 / 39 )[/C][C]55.9204081632653[/C][C]4.39746529456884[/C][C]12.7165092655378[/C][/ROW]
[ROW][C]Trimmed Mean ( 35 / 39 )[/C][C]55.6272340425532[/C][C]4.31269961344324[/C][C]12.8984717296693[/C][/ROW]
[ROW][C]Trimmed Mean ( 36 / 39 )[/C][C]55.4388888888889[/C][C]4.24138998588266[/C][C]13.0709246434343[/C][/ROW]
[ROW][C]Trimmed Mean ( 37 / 39 )[/C][C]55.2853488372093[/C][C]4.16266517068546[/C][C]13.2812384783054[/C][/ROW]
[ROW][C]Trimmed Mean ( 38 / 39 )[/C][C]55.2373170731707[/C][C]4.09507568684917[/C][C]13.4887170096901[/C][/ROW]
[ROW][C]Trimmed Mean ( 39 / 39 )[/C][C]55.3571794871795[/C][C]4.04838574231575[/C][C]13.6738895477668[/C][/ROW]
[ROW][C]Median[/C][C]57.59[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]145.41[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]56.7593103448276[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]58.0305084745763[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]58.0305084745763[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]58.0305084745763[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]58.0305084745763[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]57.2513333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]58.0305084745763[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]58.0305084745763[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]117[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=109178&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=109178&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 Mean79.20042735042737.0239936400011711.2756974749217
Geometric Mean42.5388678083587
Harmonic Mean21.9260816943321
Quadratic Mean109.52506628368
Winsorized Mean ( 1 / 39 )79.0070940170946.9778603601473111.3225387066109
Winsorized Mean ( 2 / 39 )78.94230769230776.9631560375952711.3371447180107
Winsorized Mean ( 3 / 39 )78.93333333333336.961017944401611.3393377181013
Winsorized Mean ( 4 / 39 )78.75282051282056.920968321188211.3788731371191
Winsorized Mean ( 5 / 39 )78.39811965811976.844332108107111.4544587287425
Winsorized Mean ( 6 / 39 )77.98940170940176.7590479471985311.5385187852864
Winsorized Mean ( 7 / 39 )76.54452991452996.4831320790655211.8067207302004
Winsorized Mean ( 8 / 39 )76.13495726495736.4089994090380911.8793827875207
Winsorized Mean ( 9 / 39 )75.77341880341886.3470737473402811.9383233628208
Winsorized Mean ( 10 / 39 )75.64008547008556.3186936475795211.9708423431892
Winsorized Mean ( 11 / 39 )75.14461538461546.2190511181509712.0829711730939
Winsorized Mean ( 12 / 39 )74.93641025641036.1834085048392112.1189486668662
Winsorized Mean ( 13 / 39 )74.81641025641036.1608620068123612.1438217856011
Winsorized Mean ( 14 / 39 )74.80324786324796.1545531977385612.1541313333247
Winsorized Mean ( 15 / 39 )74.41863247863256.0889085905068612.2219986344774
Winsorized Mean ( 16 / 39 )74.00837606837616.0204896007935712.2927504199361
Winsorized Mean ( 17 / 39 )72.8256410256415.8358369168155512.4790397784762
Winsorized Mean ( 18 / 39 )72.21487179487185.7287701838410212.6056499872462
Winsorized Mean ( 19 / 39 )72.06222222222225.6916932158965812.6609463104857
Winsorized Mean ( 20 / 39 )71.94598290598295.6711179259654612.6863845621293
Winsorized Mean ( 21 / 39 )71.23521367521375.5649480325290912.8006970161839
Winsorized Mean ( 22 / 39 )70.42102564102565.4448833429289512.9334314815906
Winsorized Mean ( 23 / 39 )69.35162393162395.2948456799509813.0979499920508
Winsorized Mean ( 24 / 39 )67.33111111111115.0184676669676713.41666731347
Winsorized Mean ( 25 / 39 )67.11102564102564.9877980945283213.4550405547986
Winsorized Mean ( 26 / 39 )66.25547008547014.8724006294773213.5981162313776
Winsorized Mean ( 27 / 39 )65.65777777777784.7923411198131313.7005643246735
Winsorized Mean ( 28 / 39 )65.60991452991454.7728873614450213.7463781483523
Winsorized Mean ( 29 / 39 )64.72504273504274.6606173840585213.8876542314828
Winsorized Mean ( 30 / 39 )63.23786324786324.4712398527965114.1432500446854
Winsorized Mean ( 31 / 39 )63.07094017094024.4406213885977214.2031789363733
Winsorized Mean ( 32 / 39 )62.26410256410264.3424222799945714.3385646418939
Winsorized Mean ( 33 / 39 )62.07794871794874.308634041017814.4078025952013
Winsorized Mean ( 34 / 39 )59.92461538461544.0504407264727114.7945913621109
Winsorized Mean ( 35 / 39 )58.16264957264963.8402576553293515.1455070968829
Winsorized Mean ( 36 / 39 )57.47034188034193.7494500961020715.3276721672034
Winsorized Mean ( 37 / 39 )55.90811965811973.5551738094471715.7258470766056
Winsorized Mean ( 38 / 39 )53.71905982905983.3168082846192316.1960099045118
Winsorized Mean ( 39 / 39 )53.84905982905983.2864101566894416.385374089552
Trimmed Mean ( 1 / 39 )78.04895652173916.8902200994359711.3274983085269
Trimmed Mean ( 2 / 39 )77.05690265486736.7915005969521611.346079052021
Trimmed Mean ( 3 / 39 )76.06324324324326.6888657666499411.3716205253344
Trimmed Mean ( 4 / 39 )75.03633027522946.5738450866225311.4143745838984
Trimmed Mean ( 5 / 39 )74.02037383177576.4569755119454111.4636293253456
Trimmed Mean ( 6 / 39 )73.04476190476196.3458612324856311.5106144349379
Trimmed Mean ( 7 / 39 )72.1086407766996.2404188187249311.5550963599319
Trimmed Mean ( 8 / 39 )71.37455445544556.1796979748120511.5498451132017
Trimmed Mean ( 9 / 39 )70.67131313131316.1239696235904811.5401149050571
Trimmed Mean ( 10 / 39 )69.98752577319596.0704299821503611.5292534431645
Trimmed Mean ( 11 / 39 )69.29136842105266.0128256137508211.523927828971
Trimmed Mean ( 12 / 39 )68.6219354838715.9615452088912811.5107632466706
Trimmed Mean ( 13 / 39 )67.94538461538465.9067518046512411.5030031500361
Trimmed Mean ( 14 / 39 )67.25056179775285.8456607431489411.5043559235917
Trimmed Mean ( 15 / 39 )67.25056179775285.7747382926789411.6456466751076
Trimmed Mean ( 16 / 39 )65.8007058823535.7010571278509911.5418429260954
Trimmed Mean ( 17 / 39 )65.07759036144585.6242250508473611.5709435118783
Trimmed Mean ( 18 / 39 )64.41925925925935.5598999701727111.5864061592565
Trimmed Mean ( 19 / 39 )63.77784810126585.498052503072911.6000798583899
Trimmed Mean ( 20 / 39 )63.11532467532475.4288912689041411.6258222073519
Trimmed Mean ( 21 / 39 )62.42653333333335.3487781260023511.6711764561434
Trimmed Mean ( 22 / 39 )61.75424657534255.2679983321578911.7225258402932
Trimmed Mean ( 23 / 39 )61.10507042253525.1881096562971911.7779064959368
Trimmed Mean ( 24 / 39 )60.49710144927545.1133038374329611.831313642345
Trimmed Mean ( 25 / 39 )59.99985074626875.0618426794287311.8533614231251
Trimmed Mean ( 26 / 39 )59.48784615384625.0017813725380511.8933319397885
Trimmed Mean ( 27 / 39 )59.00444444444444.9437106407045911.9352544541391
Trimmed Mean ( 28 / 39 )58.53180327868854.8824836436492611.9881207087753
Trimmed Mean ( 29 / 39 )58.03050847457634.807799621033512.0700763444259
Trimmed Mean ( 30 / 39 )58.03050847457634.7317673178961512.2640241110541
Trimmed Mean ( 31 / 39 )57.15381818181824.6663330507800212.2481223607184
Trimmed Mean ( 32 / 39 )56.73245283018874.5867779931997312.368693866217
Trimmed Mean ( 33 / 39 )56.33588235294124.5017064840727712.5143392960558
Trimmed Mean ( 34 / 39 )55.92040816326534.3974652945688412.7165092655378
Trimmed Mean ( 35 / 39 )55.62723404255324.3126996134432412.8984717296693
Trimmed Mean ( 36 / 39 )55.43888888888894.2413899858826613.0709246434343
Trimmed Mean ( 37 / 39 )55.28534883720934.1626651706854613.2812384783054
Trimmed Mean ( 38 / 39 )55.23731707317074.0950756868491713.4887170096901
Trimmed Mean ( 39 / 39 )55.35717948717954.0483857423157513.6738895477668
Median57.59
Midrange145.41
Midmean - Weighted Average at Xnp56.7593103448276
Midmean - Weighted Average at X(n+1)p58.0305084745763
Midmean - Empirical Distribution Function58.0305084745763
Midmean - Empirical Distribution Function - Averaging58.0305084745763
Midmean - Empirical Distribution Function - Interpolation58.0305084745763
Midmean - Closest Observation57.2513333333333
Midmean - True Basic - Statistics Graphics Toolkit58.0305084745763
Midmean - MS Excel (old versions)58.0305084745763
Number of observations117



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')