Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationMon, 17 Oct 2011 14:52:09 -0400
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/Oct/17/t131887759057qavctcnb8a9vz.htm/, Retrieved Wed, 15 May 2024 01:32:32 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=130998, Retrieved Wed, 15 May 2024 01:32:32 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsKDG2011W52a
Estimated Impact42
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [Prijsindex graan ...] [2011-10-17 18:52:09] [1dca9aa876cba4edc5cb0d742d3acdc5] [Current]
Feedback Forum

Post a new message
Dataseries X:
48,6
48,9
50
49,3
51
47,7
43,4
42,6
44,1
46,8
47,9
48,5
49,7
48
48,2
47,3
46,6
45,6
47,7
48,1
47,6
46,3
46,1
46,7
47,1
46,7
46,3
45,9
46,6
49
54,1
59,2
63,8
62,5
59,5
56,9
54,4
54,7
53,3
52,9
54,8
52,6
49,1
52,6
53,6
52,7
55,8
57,9
60,6
61,9
65,5
67,5
65,5
62,2
55,5
52,3
52,5
50,8
50,9
51,5
51,1
51,1
54,3
51,9
52,4
53,4
56
53,4
53,8
53,8
51,6
54,2
55,7
59,2
59,8
61,6
65,8
64,2
67
62,8
65,5
75,2
80,9
83,2
83,7
86,4
85,9
80,4
81,8
87,5
83,7
87
99,7
101,4
101,9
115,7
123,2
136,9
146,8
149,6
146,5
157
147,9
133,6
128,7
100,8
91,8
89,3
96,7
91,6
93,3
93,3
101
100,4
86,9
83,9
80,3
87,7
92,7
95,5
92
87,4
86,8
83,7
85
81,7
90,9
101,5
113,8
120,1
122,1
132,5




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 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 & 2 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=130998&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' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=130998&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=130998&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' @ jenkins.wessa.net







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean71.97954545454552.4164619562733729.7871627019327
Geometric Mean67.565839451332
Harmonic Mean64.011336943805
Quadratic Mean77.1103218928844
Winsorized Mean ( 1 / 44 )71.92954545454552.4014551304862229.9524836177064
Winsorized Mean ( 2 / 44 )71.91439393939392.3942039882164430.0368699965982
Winsorized Mean ( 3 / 44 )71.92348484848482.3852324066797330.1536590929532
Winsorized Mean ( 4 / 44 )71.92348484848482.3822950006453930.1908390140599
Winsorized Mean ( 5 / 44 )71.56742424242422.298692035794431.1339766823925
Winsorized Mean ( 6 / 44 )71.42651515151512.2659379381591231.52183206286
Winsorized Mean ( 7 / 44 )71.36818181818182.2537896525709531.6658574311807
Winsorized Mean ( 8 / 44 )71.15606060606062.2054577271467932.2636247932602
Winsorized Mean ( 9 / 44 )70.78106060606062.132900502381733.1853551194831
Winsorized Mean ( 10 / 44 )70.7053030303032.1167046833757833.4034802235805
Winsorized Mean ( 11 / 44 )70.53863636363642.0861437849358333.8129312432825
Winsorized Mean ( 12 / 44 )70.14772727272732.014521783817534.8210318876761
Winsorized Mean ( 13 / 44 )69.99015151515151.9799556103905235.3493538682651
Winsorized Mean ( 14 / 44 )68.74924242424241.780889276743938.6038836451081
Winsorized Mean ( 15 / 44 )68.73787878787881.7713309635020838.805779498134
Winsorized Mean ( 16 / 44 )68.73787878787881.768518400588838.8674942624253
Winsorized Mean ( 17 / 44 )68.68636363636361.761279623853638.997989135922
Winsorized Mean ( 18 / 44 )68.68636363636361.7549918140329839.1377116902454
Winsorized Mean ( 19 / 44 )68.64318181818181.7456724832194939.3219131755949
Winsorized Mean ( 20 / 44 )68.55227272727271.7296503512627339.6336014832282
Winsorized Mean ( 21 / 44 )68.09090909090911.6640549005888640.918667447098
Winsorized Mean ( 22 / 44 )67.94090909090911.6334973579681241.5922981200407
Winsorized Mean ( 23 / 44 )67.5751.5834404221306242.6760609717627
Winsorized Mean ( 24 / 44 )67.62954545454551.5784752913724942.8448553006751
Winsorized Mean ( 25 / 44 )67.53484848484851.5627217343842543.2161702233308
Winsorized Mean ( 26 / 44 )67.41666666666671.5440846833789943.6612495366094
Winsorized Mean ( 27 / 44 )67.41666666666671.5354245437567143.9075087999562
Winsorized Mean ( 28 / 44 )67.45909090909091.522687533359644.3026487254755
Winsorized Mean ( 29 / 44 )67.37121212121211.4983125408044244.964725507164
Winsorized Mean ( 30 / 44 )67.18939393939391.439234227841546.6841273224593
Winsorized Mean ( 31 / 44 )66.83712121212121.3936770259551747.9573961307955
Winsorized Mean ( 32 / 44 )66.81287878787881.3860309858410748.2044625772456
Winsorized Mean ( 33 / 44 )66.81287878787881.3810100520780448.3797193853469
Winsorized Mean ( 34 / 44 )66.70984848484851.3693206937906548.7174763277531
Winsorized Mean ( 35 / 44 )66.78939393939391.3571459323257149.2131261263396
Winsorized Mean ( 36 / 44 )66.78939393939391.3517199988633149.4106723253028
Winsorized Mean ( 37 / 44 )66.76136363636361.3318864957030450.1254152300144
Winsorized Mean ( 38 / 44 )66.73257575757581.3059604174161151.0984673560083
Winsorized Mean ( 39 / 44 )66.49621212121211.2738256330255852.2019736431827
Winsorized Mean ( 40 / 44 )66.19318181818181.2345300849428453.6181196598757
Winsorized Mean ( 41 / 44 )66.16212121212121.2251077035852954.005146664654
Winsorized Mean ( 42 / 44 )66.16212121212121.2251077035852954.005146664654
Winsorized Mean ( 43 / 44 )66.1946969696971.2223586498948954.1532527915509
Winsorized Mean ( 44 / 44 )66.0946969696971.1985593144478755.1451197892063
Trimmed Mean ( 1 / 44 )71.55153846153852.3531088647355130.4072367980225
Trimmed Mean ( 2 / 44 )71.161718752.2994618403623630.9471188001041
Trimmed Mean ( 3 / 44 )70.76746031746032.2440512767151931.5355807827389
Trimmed Mean ( 4 / 44 )70.35725806451612.1859243749310732.1865014505522
Trimmed Mean ( 5 / 44 )69.9336065573772.1218205605248332.9592463464861
Trimmed Mean ( 6 / 44 )69.57416666666672.0734463981866333.5548421832915
Trimmed Mean ( 7 / 44 )69.2288135593222.027216346554934.1496918555195
Trimmed Mean ( 8 / 44 )68.88103448275861.9780318666939734.8230155654088
Trimmed Mean ( 9 / 44 )68.55175438596491.9324708976616435.4736283319532
Trimmed Mean ( 10 / 44 )68.25982142857141.8946949153113136.0268140675069
Trimmed Mean ( 11 / 44 )67.96636363636361.8549616881510836.6403058728985
Trimmed Mean ( 12 / 44 )67.68055555555561.8152175183321837.2850938645305
Trimmed Mean ( 13 / 44 )67.42452830188681.7816166232191337.8445774602508
Trimmed Mean ( 14 / 44 )67.17403846153851.7487347368799838.412937677093
Trimmed Mean ( 15 / 44 )67.0284313725491.7390154339679338.5438967724452
Trimmed Mean ( 16 / 44 )66.8781.7287536118559738.6856747782587
Trimmed Mean ( 17 / 44 )66.72142857142861.7170162654676638.8589379805648
Trimmed Mean ( 18 / 44 )66.56251.7041552995803339.0589402364866
Trimmed Mean ( 19 / 44 )66.39680851063831.6898207172869239.2922206666049
Trimmed Mean ( 20 / 44 )66.22717391304351.6741700764741539.5582114647036
Trimmed Mean ( 21 / 44 )66.05666666666671.6577959059901239.8460790185232
Trimmed Mean ( 22 / 44 )65.91136363636361.6464572268158140.0322356164902
Trimmed Mean ( 23 / 44 )65.76976744186051.6363551550987240.1928439782331
Trimmed Mean ( 24 / 44 )65.64642857142861.6298144149095540.2784684997842
Trimmed Mean ( 25 / 44 )65.51341463414631.6219416936370840.3919665492027
Trimmed Mean ( 26 / 44 )65.381.6138173159047240.5126400340718
Trimmed Mean ( 27 / 44 )65.24743589743591.6056849598659140.6352662747024
Trimmed Mean ( 28 / 44 )65.10789473684211.5962662170332840.7876167785143
Trimmed Mean ( 29 / 44 )64.95810810810811.5857029769085140.9648648290681
Trimmed Mean ( 30 / 44 )64.80555555555561.5752311712616341.1403460887914
Trimmed Mean ( 31 / 44 )64.65571428571431.5687800850784241.2140075595632
Trimmed Mean ( 32 / 44 )64.51911764705881.5654750971713541.2137617287161
Trimmed Mean ( 33 / 44 )64.37575757575761.5609752205557641.2407299795815
Trimmed Mean ( 34 / 44 )64.22343751.5546712480206641.309979573988
Trimmed Mean ( 35 / 44 )64.06774193548391.5471486101061241.410205533578
Trimmed Mean ( 36 / 44 )63.89666666666671.5378317090463441.5498433871486
Trimmed Mean ( 37 / 44 )63.71379310344831.525556533233441.7642950067589
Trimmed Mean ( 38 / 44 )63.51964285714291.5116203992560842.0208955160984
Trimmed Mean ( 39 / 44 )63.3129629629631.4964109083212942.3098779960037
Trimmed Mean ( 40 / 44 )63.10576923076921.4810349950533542.6092357314594
Trimmed Mean ( 41 / 44 )62.9021.4666510234168842.8881847117633
Trimmed Mean ( 42 / 44 )62.68333333333331.447841182531643.294343391814
Trimmed Mean ( 43 / 44 )62.4456521739131.4215651254892143.9273945697166
Trimmed Mean ( 44 / 44 )62.18409090909091.3857891836572544.8726917791207
Median59.65
Midrange99.8
Midmean - Weighted Average at Xnp64.1761194029851
Midmean - Weighted Average at X(n+1)p64.3757575757576
Midmean - Empirical Distribution Function64.1761194029851
Midmean - Empirical Distribution Function - Averaging64.3757575757576
Midmean - Empirical Distribution Function - Interpolation64.3757575757576
Midmean - Closest Observation64.1761194029851
Midmean - True Basic - Statistics Graphics Toolkit64.3757575757576
Midmean - MS Excel (old versions)64.5191176470588
Number of observations132

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 71.9795454545455 & 2.41646195627337 & 29.7871627019327 \tabularnewline
Geometric Mean & 67.565839451332 &  &  \tabularnewline
Harmonic Mean & 64.011336943805 &  &  \tabularnewline
Quadratic Mean & 77.1103218928844 &  &  \tabularnewline
Winsorized Mean ( 1 / 44 ) & 71.9295454545455 & 2.40145513048622 & 29.9524836177064 \tabularnewline
Winsorized Mean ( 2 / 44 ) & 71.9143939393939 & 2.39420398821644 & 30.0368699965982 \tabularnewline
Winsorized Mean ( 3 / 44 ) & 71.9234848484848 & 2.38523240667973 & 30.1536590929532 \tabularnewline
Winsorized Mean ( 4 / 44 ) & 71.9234848484848 & 2.38229500064539 & 30.1908390140599 \tabularnewline
Winsorized Mean ( 5 / 44 ) & 71.5674242424242 & 2.2986920357944 & 31.1339766823925 \tabularnewline
Winsorized Mean ( 6 / 44 ) & 71.4265151515151 & 2.26593793815912 & 31.52183206286 \tabularnewline
Winsorized Mean ( 7 / 44 ) & 71.3681818181818 & 2.25378965257095 & 31.6658574311807 \tabularnewline
Winsorized Mean ( 8 / 44 ) & 71.1560606060606 & 2.20545772714679 & 32.2636247932602 \tabularnewline
Winsorized Mean ( 9 / 44 ) & 70.7810606060606 & 2.1329005023817 & 33.1853551194831 \tabularnewline
Winsorized Mean ( 10 / 44 ) & 70.705303030303 & 2.11670468337578 & 33.4034802235805 \tabularnewline
Winsorized Mean ( 11 / 44 ) & 70.5386363636364 & 2.08614378493583 & 33.8129312432825 \tabularnewline
Winsorized Mean ( 12 / 44 ) & 70.1477272727273 & 2.0145217838175 & 34.8210318876761 \tabularnewline
Winsorized Mean ( 13 / 44 ) & 69.9901515151515 & 1.97995561039052 & 35.3493538682651 \tabularnewline
Winsorized Mean ( 14 / 44 ) & 68.7492424242424 & 1.7808892767439 & 38.6038836451081 \tabularnewline
Winsorized Mean ( 15 / 44 ) & 68.7378787878788 & 1.77133096350208 & 38.805779498134 \tabularnewline
Winsorized Mean ( 16 / 44 ) & 68.7378787878788 & 1.7685184005888 & 38.8674942624253 \tabularnewline
Winsorized Mean ( 17 / 44 ) & 68.6863636363636 & 1.7612796238536 & 38.997989135922 \tabularnewline
Winsorized Mean ( 18 / 44 ) & 68.6863636363636 & 1.75499181403298 & 39.1377116902454 \tabularnewline
Winsorized Mean ( 19 / 44 ) & 68.6431818181818 & 1.74567248321949 & 39.3219131755949 \tabularnewline
Winsorized Mean ( 20 / 44 ) & 68.5522727272727 & 1.72965035126273 & 39.6336014832282 \tabularnewline
Winsorized Mean ( 21 / 44 ) & 68.0909090909091 & 1.66405490058886 & 40.918667447098 \tabularnewline
Winsorized Mean ( 22 / 44 ) & 67.9409090909091 & 1.63349735796812 & 41.5922981200407 \tabularnewline
Winsorized Mean ( 23 / 44 ) & 67.575 & 1.58344042213062 & 42.6760609717627 \tabularnewline
Winsorized Mean ( 24 / 44 ) & 67.6295454545455 & 1.57847529137249 & 42.8448553006751 \tabularnewline
Winsorized Mean ( 25 / 44 ) & 67.5348484848485 & 1.56272173438425 & 43.2161702233308 \tabularnewline
Winsorized Mean ( 26 / 44 ) & 67.4166666666667 & 1.54408468337899 & 43.6612495366094 \tabularnewline
Winsorized Mean ( 27 / 44 ) & 67.4166666666667 & 1.53542454375671 & 43.9075087999562 \tabularnewline
Winsorized Mean ( 28 / 44 ) & 67.4590909090909 & 1.5226875333596 & 44.3026487254755 \tabularnewline
Winsorized Mean ( 29 / 44 ) & 67.3712121212121 & 1.49831254080442 & 44.964725507164 \tabularnewline
Winsorized Mean ( 30 / 44 ) & 67.1893939393939 & 1.4392342278415 & 46.6841273224593 \tabularnewline
Winsorized Mean ( 31 / 44 ) & 66.8371212121212 & 1.39367702595517 & 47.9573961307955 \tabularnewline
Winsorized Mean ( 32 / 44 ) & 66.8128787878788 & 1.38603098584107 & 48.2044625772456 \tabularnewline
Winsorized Mean ( 33 / 44 ) & 66.8128787878788 & 1.38101005207804 & 48.3797193853469 \tabularnewline
Winsorized Mean ( 34 / 44 ) & 66.7098484848485 & 1.36932069379065 & 48.7174763277531 \tabularnewline
Winsorized Mean ( 35 / 44 ) & 66.7893939393939 & 1.35714593232571 & 49.2131261263396 \tabularnewline
Winsorized Mean ( 36 / 44 ) & 66.7893939393939 & 1.35171999886331 & 49.4106723253028 \tabularnewline
Winsorized Mean ( 37 / 44 ) & 66.7613636363636 & 1.33188649570304 & 50.1254152300144 \tabularnewline
Winsorized Mean ( 38 / 44 ) & 66.7325757575758 & 1.30596041741611 & 51.0984673560083 \tabularnewline
Winsorized Mean ( 39 / 44 ) & 66.4962121212121 & 1.27382563302558 & 52.2019736431827 \tabularnewline
Winsorized Mean ( 40 / 44 ) & 66.1931818181818 & 1.23453008494284 & 53.6181196598757 \tabularnewline
Winsorized Mean ( 41 / 44 ) & 66.1621212121212 & 1.22510770358529 & 54.005146664654 \tabularnewline
Winsorized Mean ( 42 / 44 ) & 66.1621212121212 & 1.22510770358529 & 54.005146664654 \tabularnewline
Winsorized Mean ( 43 / 44 ) & 66.194696969697 & 1.22235864989489 & 54.1532527915509 \tabularnewline
Winsorized Mean ( 44 / 44 ) & 66.094696969697 & 1.19855931444787 & 55.1451197892063 \tabularnewline
Trimmed Mean ( 1 / 44 ) & 71.5515384615385 & 2.35310886473551 & 30.4072367980225 \tabularnewline
Trimmed Mean ( 2 / 44 ) & 71.16171875 & 2.29946184036236 & 30.9471188001041 \tabularnewline
Trimmed Mean ( 3 / 44 ) & 70.7674603174603 & 2.24405127671519 & 31.5355807827389 \tabularnewline
Trimmed Mean ( 4 / 44 ) & 70.3572580645161 & 2.18592437493107 & 32.1865014505522 \tabularnewline
Trimmed Mean ( 5 / 44 ) & 69.933606557377 & 2.12182056052483 & 32.9592463464861 \tabularnewline
Trimmed Mean ( 6 / 44 ) & 69.5741666666667 & 2.07344639818663 & 33.5548421832915 \tabularnewline
Trimmed Mean ( 7 / 44 ) & 69.228813559322 & 2.0272163465549 & 34.1496918555195 \tabularnewline
Trimmed Mean ( 8 / 44 ) & 68.8810344827586 & 1.97803186669397 & 34.8230155654088 \tabularnewline
Trimmed Mean ( 9 / 44 ) & 68.5517543859649 & 1.93247089766164 & 35.4736283319532 \tabularnewline
Trimmed Mean ( 10 / 44 ) & 68.2598214285714 & 1.89469491531131 & 36.0268140675069 \tabularnewline
Trimmed Mean ( 11 / 44 ) & 67.9663636363636 & 1.85496168815108 & 36.6403058728985 \tabularnewline
Trimmed Mean ( 12 / 44 ) & 67.6805555555556 & 1.81521751833218 & 37.2850938645305 \tabularnewline
Trimmed Mean ( 13 / 44 ) & 67.4245283018868 & 1.78161662321913 & 37.8445774602508 \tabularnewline
Trimmed Mean ( 14 / 44 ) & 67.1740384615385 & 1.74873473687998 & 38.412937677093 \tabularnewline
Trimmed Mean ( 15 / 44 ) & 67.028431372549 & 1.73901543396793 & 38.5438967724452 \tabularnewline
Trimmed Mean ( 16 / 44 ) & 66.878 & 1.72875361185597 & 38.6856747782587 \tabularnewline
Trimmed Mean ( 17 / 44 ) & 66.7214285714286 & 1.71701626546766 & 38.8589379805648 \tabularnewline
Trimmed Mean ( 18 / 44 ) & 66.5625 & 1.70415529958033 & 39.0589402364866 \tabularnewline
Trimmed Mean ( 19 / 44 ) & 66.3968085106383 & 1.68982071728692 & 39.2922206666049 \tabularnewline
Trimmed Mean ( 20 / 44 ) & 66.2271739130435 & 1.67417007647415 & 39.5582114647036 \tabularnewline
Trimmed Mean ( 21 / 44 ) & 66.0566666666667 & 1.65779590599012 & 39.8460790185232 \tabularnewline
Trimmed Mean ( 22 / 44 ) & 65.9113636363636 & 1.64645722681581 & 40.0322356164902 \tabularnewline
Trimmed Mean ( 23 / 44 ) & 65.7697674418605 & 1.63635515509872 & 40.1928439782331 \tabularnewline
Trimmed Mean ( 24 / 44 ) & 65.6464285714286 & 1.62981441490955 & 40.2784684997842 \tabularnewline
Trimmed Mean ( 25 / 44 ) & 65.5134146341463 & 1.62194169363708 & 40.3919665492027 \tabularnewline
Trimmed Mean ( 26 / 44 ) & 65.38 & 1.61381731590472 & 40.5126400340718 \tabularnewline
Trimmed Mean ( 27 / 44 ) & 65.2474358974359 & 1.60568495986591 & 40.6352662747024 \tabularnewline
Trimmed Mean ( 28 / 44 ) & 65.1078947368421 & 1.59626621703328 & 40.7876167785143 \tabularnewline
Trimmed Mean ( 29 / 44 ) & 64.9581081081081 & 1.58570297690851 & 40.9648648290681 \tabularnewline
Trimmed Mean ( 30 / 44 ) & 64.8055555555556 & 1.57523117126163 & 41.1403460887914 \tabularnewline
Trimmed Mean ( 31 / 44 ) & 64.6557142857143 & 1.56878008507842 & 41.2140075595632 \tabularnewline
Trimmed Mean ( 32 / 44 ) & 64.5191176470588 & 1.56547509717135 & 41.2137617287161 \tabularnewline
Trimmed Mean ( 33 / 44 ) & 64.3757575757576 & 1.56097522055576 & 41.2407299795815 \tabularnewline
Trimmed Mean ( 34 / 44 ) & 64.2234375 & 1.55467124802066 & 41.309979573988 \tabularnewline
Trimmed Mean ( 35 / 44 ) & 64.0677419354839 & 1.54714861010612 & 41.410205533578 \tabularnewline
Trimmed Mean ( 36 / 44 ) & 63.8966666666667 & 1.53783170904634 & 41.5498433871486 \tabularnewline
Trimmed Mean ( 37 / 44 ) & 63.7137931034483 & 1.5255565332334 & 41.7642950067589 \tabularnewline
Trimmed Mean ( 38 / 44 ) & 63.5196428571429 & 1.51162039925608 & 42.0208955160984 \tabularnewline
Trimmed Mean ( 39 / 44 ) & 63.312962962963 & 1.49641090832129 & 42.3098779960037 \tabularnewline
Trimmed Mean ( 40 / 44 ) & 63.1057692307692 & 1.48103499505335 & 42.6092357314594 \tabularnewline
Trimmed Mean ( 41 / 44 ) & 62.902 & 1.46665102341688 & 42.8881847117633 \tabularnewline
Trimmed Mean ( 42 / 44 ) & 62.6833333333333 & 1.4478411825316 & 43.294343391814 \tabularnewline
Trimmed Mean ( 43 / 44 ) & 62.445652173913 & 1.42156512548921 & 43.9273945697166 \tabularnewline
Trimmed Mean ( 44 / 44 ) & 62.1840909090909 & 1.38578918365725 & 44.8726917791207 \tabularnewline
Median & 59.65 &  &  \tabularnewline
Midrange & 99.8 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 64.1761194029851 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 64.3757575757576 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 64.1761194029851 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 64.3757575757576 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 64.3757575757576 &  &  \tabularnewline
Midmean - Closest Observation & 64.1761194029851 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 64.3757575757576 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 64.5191176470588 &  &  \tabularnewline
Number of observations & 132 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=130998&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]71.9795454545455[/C][C]2.41646195627337[/C][C]29.7871627019327[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]67.565839451332[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]64.011336943805[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]77.1103218928844[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 44 )[/C][C]71.9295454545455[/C][C]2.40145513048622[/C][C]29.9524836177064[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 44 )[/C][C]71.9143939393939[/C][C]2.39420398821644[/C][C]30.0368699965982[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 44 )[/C][C]71.9234848484848[/C][C]2.38523240667973[/C][C]30.1536590929532[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 44 )[/C][C]71.9234848484848[/C][C]2.38229500064539[/C][C]30.1908390140599[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 44 )[/C][C]71.5674242424242[/C][C]2.2986920357944[/C][C]31.1339766823925[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 44 )[/C][C]71.4265151515151[/C][C]2.26593793815912[/C][C]31.52183206286[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 44 )[/C][C]71.3681818181818[/C][C]2.25378965257095[/C][C]31.6658574311807[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 44 )[/C][C]71.1560606060606[/C][C]2.20545772714679[/C][C]32.2636247932602[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 44 )[/C][C]70.7810606060606[/C][C]2.1329005023817[/C][C]33.1853551194831[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 44 )[/C][C]70.705303030303[/C][C]2.11670468337578[/C][C]33.4034802235805[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 44 )[/C][C]70.5386363636364[/C][C]2.08614378493583[/C][C]33.8129312432825[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 44 )[/C][C]70.1477272727273[/C][C]2.0145217838175[/C][C]34.8210318876761[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 44 )[/C][C]69.9901515151515[/C][C]1.97995561039052[/C][C]35.3493538682651[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 44 )[/C][C]68.7492424242424[/C][C]1.7808892767439[/C][C]38.6038836451081[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 44 )[/C][C]68.7378787878788[/C][C]1.77133096350208[/C][C]38.805779498134[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 44 )[/C][C]68.7378787878788[/C][C]1.7685184005888[/C][C]38.8674942624253[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 44 )[/C][C]68.6863636363636[/C][C]1.7612796238536[/C][C]38.997989135922[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 44 )[/C][C]68.6863636363636[/C][C]1.75499181403298[/C][C]39.1377116902454[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 44 )[/C][C]68.6431818181818[/C][C]1.74567248321949[/C][C]39.3219131755949[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 44 )[/C][C]68.5522727272727[/C][C]1.72965035126273[/C][C]39.6336014832282[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 44 )[/C][C]68.0909090909091[/C][C]1.66405490058886[/C][C]40.918667447098[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 44 )[/C][C]67.9409090909091[/C][C]1.63349735796812[/C][C]41.5922981200407[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 44 )[/C][C]67.575[/C][C]1.58344042213062[/C][C]42.6760609717627[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 44 )[/C][C]67.6295454545455[/C][C]1.57847529137249[/C][C]42.8448553006751[/C][/ROW]
[ROW][C]Winsorized Mean ( 25 / 44 )[/C][C]67.5348484848485[/C][C]1.56272173438425[/C][C]43.2161702233308[/C][/ROW]
[ROW][C]Winsorized Mean ( 26 / 44 )[/C][C]67.4166666666667[/C][C]1.54408468337899[/C][C]43.6612495366094[/C][/ROW]
[ROW][C]Winsorized Mean ( 27 / 44 )[/C][C]67.4166666666667[/C][C]1.53542454375671[/C][C]43.9075087999562[/C][/ROW]
[ROW][C]Winsorized Mean ( 28 / 44 )[/C][C]67.4590909090909[/C][C]1.5226875333596[/C][C]44.3026487254755[/C][/ROW]
[ROW][C]Winsorized Mean ( 29 / 44 )[/C][C]67.3712121212121[/C][C]1.49831254080442[/C][C]44.964725507164[/C][/ROW]
[ROW][C]Winsorized Mean ( 30 / 44 )[/C][C]67.1893939393939[/C][C]1.4392342278415[/C][C]46.6841273224593[/C][/ROW]
[ROW][C]Winsorized Mean ( 31 / 44 )[/C][C]66.8371212121212[/C][C]1.39367702595517[/C][C]47.9573961307955[/C][/ROW]
[ROW][C]Winsorized Mean ( 32 / 44 )[/C][C]66.8128787878788[/C][C]1.38603098584107[/C][C]48.2044625772456[/C][/ROW]
[ROW][C]Winsorized Mean ( 33 / 44 )[/C][C]66.8128787878788[/C][C]1.38101005207804[/C][C]48.3797193853469[/C][/ROW]
[ROW][C]Winsorized Mean ( 34 / 44 )[/C][C]66.7098484848485[/C][C]1.36932069379065[/C][C]48.7174763277531[/C][/ROW]
[ROW][C]Winsorized Mean ( 35 / 44 )[/C][C]66.7893939393939[/C][C]1.35714593232571[/C][C]49.2131261263396[/C][/ROW]
[ROW][C]Winsorized Mean ( 36 / 44 )[/C][C]66.7893939393939[/C][C]1.35171999886331[/C][C]49.4106723253028[/C][/ROW]
[ROW][C]Winsorized Mean ( 37 / 44 )[/C][C]66.7613636363636[/C][C]1.33188649570304[/C][C]50.1254152300144[/C][/ROW]
[ROW][C]Winsorized Mean ( 38 / 44 )[/C][C]66.7325757575758[/C][C]1.30596041741611[/C][C]51.0984673560083[/C][/ROW]
[ROW][C]Winsorized Mean ( 39 / 44 )[/C][C]66.4962121212121[/C][C]1.27382563302558[/C][C]52.2019736431827[/C][/ROW]
[ROW][C]Winsorized Mean ( 40 / 44 )[/C][C]66.1931818181818[/C][C]1.23453008494284[/C][C]53.6181196598757[/C][/ROW]
[ROW][C]Winsorized Mean ( 41 / 44 )[/C][C]66.1621212121212[/C][C]1.22510770358529[/C][C]54.005146664654[/C][/ROW]
[ROW][C]Winsorized Mean ( 42 / 44 )[/C][C]66.1621212121212[/C][C]1.22510770358529[/C][C]54.005146664654[/C][/ROW]
[ROW][C]Winsorized Mean ( 43 / 44 )[/C][C]66.194696969697[/C][C]1.22235864989489[/C][C]54.1532527915509[/C][/ROW]
[ROW][C]Winsorized Mean ( 44 / 44 )[/C][C]66.094696969697[/C][C]1.19855931444787[/C][C]55.1451197892063[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 44 )[/C][C]71.5515384615385[/C][C]2.35310886473551[/C][C]30.4072367980225[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 44 )[/C][C]71.16171875[/C][C]2.29946184036236[/C][C]30.9471188001041[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 44 )[/C][C]70.7674603174603[/C][C]2.24405127671519[/C][C]31.5355807827389[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 44 )[/C][C]70.3572580645161[/C][C]2.18592437493107[/C][C]32.1865014505522[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 44 )[/C][C]69.933606557377[/C][C]2.12182056052483[/C][C]32.9592463464861[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 44 )[/C][C]69.5741666666667[/C][C]2.07344639818663[/C][C]33.5548421832915[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 44 )[/C][C]69.228813559322[/C][C]2.0272163465549[/C][C]34.1496918555195[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 44 )[/C][C]68.8810344827586[/C][C]1.97803186669397[/C][C]34.8230155654088[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 44 )[/C][C]68.5517543859649[/C][C]1.93247089766164[/C][C]35.4736283319532[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 44 )[/C][C]68.2598214285714[/C][C]1.89469491531131[/C][C]36.0268140675069[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 44 )[/C][C]67.9663636363636[/C][C]1.85496168815108[/C][C]36.6403058728985[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 44 )[/C][C]67.6805555555556[/C][C]1.81521751833218[/C][C]37.2850938645305[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 44 )[/C][C]67.4245283018868[/C][C]1.78161662321913[/C][C]37.8445774602508[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 44 )[/C][C]67.1740384615385[/C][C]1.74873473687998[/C][C]38.412937677093[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 44 )[/C][C]67.028431372549[/C][C]1.73901543396793[/C][C]38.5438967724452[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 44 )[/C][C]66.878[/C][C]1.72875361185597[/C][C]38.6856747782587[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 44 )[/C][C]66.7214285714286[/C][C]1.71701626546766[/C][C]38.8589379805648[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 44 )[/C][C]66.5625[/C][C]1.70415529958033[/C][C]39.0589402364866[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 44 )[/C][C]66.3968085106383[/C][C]1.68982071728692[/C][C]39.2922206666049[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 44 )[/C][C]66.2271739130435[/C][C]1.67417007647415[/C][C]39.5582114647036[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 44 )[/C][C]66.0566666666667[/C][C]1.65779590599012[/C][C]39.8460790185232[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 44 )[/C][C]65.9113636363636[/C][C]1.64645722681581[/C][C]40.0322356164902[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 44 )[/C][C]65.7697674418605[/C][C]1.63635515509872[/C][C]40.1928439782331[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 44 )[/C][C]65.6464285714286[/C][C]1.62981441490955[/C][C]40.2784684997842[/C][/ROW]
[ROW][C]Trimmed Mean ( 25 / 44 )[/C][C]65.5134146341463[/C][C]1.62194169363708[/C][C]40.3919665492027[/C][/ROW]
[ROW][C]Trimmed Mean ( 26 / 44 )[/C][C]65.38[/C][C]1.61381731590472[/C][C]40.5126400340718[/C][/ROW]
[ROW][C]Trimmed Mean ( 27 / 44 )[/C][C]65.2474358974359[/C][C]1.60568495986591[/C][C]40.6352662747024[/C][/ROW]
[ROW][C]Trimmed Mean ( 28 / 44 )[/C][C]65.1078947368421[/C][C]1.59626621703328[/C][C]40.7876167785143[/C][/ROW]
[ROW][C]Trimmed Mean ( 29 / 44 )[/C][C]64.9581081081081[/C][C]1.58570297690851[/C][C]40.9648648290681[/C][/ROW]
[ROW][C]Trimmed Mean ( 30 / 44 )[/C][C]64.8055555555556[/C][C]1.57523117126163[/C][C]41.1403460887914[/C][/ROW]
[ROW][C]Trimmed Mean ( 31 / 44 )[/C][C]64.6557142857143[/C][C]1.56878008507842[/C][C]41.2140075595632[/C][/ROW]
[ROW][C]Trimmed Mean ( 32 / 44 )[/C][C]64.5191176470588[/C][C]1.56547509717135[/C][C]41.2137617287161[/C][/ROW]
[ROW][C]Trimmed Mean ( 33 / 44 )[/C][C]64.3757575757576[/C][C]1.56097522055576[/C][C]41.2407299795815[/C][/ROW]
[ROW][C]Trimmed Mean ( 34 / 44 )[/C][C]64.2234375[/C][C]1.55467124802066[/C][C]41.309979573988[/C][/ROW]
[ROW][C]Trimmed Mean ( 35 / 44 )[/C][C]64.0677419354839[/C][C]1.54714861010612[/C][C]41.410205533578[/C][/ROW]
[ROW][C]Trimmed Mean ( 36 / 44 )[/C][C]63.8966666666667[/C][C]1.53783170904634[/C][C]41.5498433871486[/C][/ROW]
[ROW][C]Trimmed Mean ( 37 / 44 )[/C][C]63.7137931034483[/C][C]1.5255565332334[/C][C]41.7642950067589[/C][/ROW]
[ROW][C]Trimmed Mean ( 38 / 44 )[/C][C]63.5196428571429[/C][C]1.51162039925608[/C][C]42.0208955160984[/C][/ROW]
[ROW][C]Trimmed Mean ( 39 / 44 )[/C][C]63.312962962963[/C][C]1.49641090832129[/C][C]42.3098779960037[/C][/ROW]
[ROW][C]Trimmed Mean ( 40 / 44 )[/C][C]63.1057692307692[/C][C]1.48103499505335[/C][C]42.6092357314594[/C][/ROW]
[ROW][C]Trimmed Mean ( 41 / 44 )[/C][C]62.902[/C][C]1.46665102341688[/C][C]42.8881847117633[/C][/ROW]
[ROW][C]Trimmed Mean ( 42 / 44 )[/C][C]62.6833333333333[/C][C]1.4478411825316[/C][C]43.294343391814[/C][/ROW]
[ROW][C]Trimmed Mean ( 43 / 44 )[/C][C]62.445652173913[/C][C]1.42156512548921[/C][C]43.9273945697166[/C][/ROW]
[ROW][C]Trimmed Mean ( 44 / 44 )[/C][C]62.1840909090909[/C][C]1.38578918365725[/C][C]44.8726917791207[/C][/ROW]
[ROW][C]Median[/C][C]59.65[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]99.8[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]64.1761194029851[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]64.3757575757576[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]64.1761194029851[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]64.3757575757576[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]64.3757575757576[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]64.1761194029851[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]64.3757575757576[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]64.5191176470588[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]132[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=130998&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=130998&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 Mean71.97954545454552.4164619562733729.7871627019327
Geometric Mean67.565839451332
Harmonic Mean64.011336943805
Quadratic Mean77.1103218928844
Winsorized Mean ( 1 / 44 )71.92954545454552.4014551304862229.9524836177064
Winsorized Mean ( 2 / 44 )71.91439393939392.3942039882164430.0368699965982
Winsorized Mean ( 3 / 44 )71.92348484848482.3852324066797330.1536590929532
Winsorized Mean ( 4 / 44 )71.92348484848482.3822950006453930.1908390140599
Winsorized Mean ( 5 / 44 )71.56742424242422.298692035794431.1339766823925
Winsorized Mean ( 6 / 44 )71.42651515151512.2659379381591231.52183206286
Winsorized Mean ( 7 / 44 )71.36818181818182.2537896525709531.6658574311807
Winsorized Mean ( 8 / 44 )71.15606060606062.2054577271467932.2636247932602
Winsorized Mean ( 9 / 44 )70.78106060606062.132900502381733.1853551194831
Winsorized Mean ( 10 / 44 )70.7053030303032.1167046833757833.4034802235805
Winsorized Mean ( 11 / 44 )70.53863636363642.0861437849358333.8129312432825
Winsorized Mean ( 12 / 44 )70.14772727272732.014521783817534.8210318876761
Winsorized Mean ( 13 / 44 )69.99015151515151.9799556103905235.3493538682651
Winsorized Mean ( 14 / 44 )68.74924242424241.780889276743938.6038836451081
Winsorized Mean ( 15 / 44 )68.73787878787881.7713309635020838.805779498134
Winsorized Mean ( 16 / 44 )68.73787878787881.768518400588838.8674942624253
Winsorized Mean ( 17 / 44 )68.68636363636361.761279623853638.997989135922
Winsorized Mean ( 18 / 44 )68.68636363636361.7549918140329839.1377116902454
Winsorized Mean ( 19 / 44 )68.64318181818181.7456724832194939.3219131755949
Winsorized Mean ( 20 / 44 )68.55227272727271.7296503512627339.6336014832282
Winsorized Mean ( 21 / 44 )68.09090909090911.6640549005888640.918667447098
Winsorized Mean ( 22 / 44 )67.94090909090911.6334973579681241.5922981200407
Winsorized Mean ( 23 / 44 )67.5751.5834404221306242.6760609717627
Winsorized Mean ( 24 / 44 )67.62954545454551.5784752913724942.8448553006751
Winsorized Mean ( 25 / 44 )67.53484848484851.5627217343842543.2161702233308
Winsorized Mean ( 26 / 44 )67.41666666666671.5440846833789943.6612495366094
Winsorized Mean ( 27 / 44 )67.41666666666671.5354245437567143.9075087999562
Winsorized Mean ( 28 / 44 )67.45909090909091.522687533359644.3026487254755
Winsorized Mean ( 29 / 44 )67.37121212121211.4983125408044244.964725507164
Winsorized Mean ( 30 / 44 )67.18939393939391.439234227841546.6841273224593
Winsorized Mean ( 31 / 44 )66.83712121212121.3936770259551747.9573961307955
Winsorized Mean ( 32 / 44 )66.81287878787881.3860309858410748.2044625772456
Winsorized Mean ( 33 / 44 )66.81287878787881.3810100520780448.3797193853469
Winsorized Mean ( 34 / 44 )66.70984848484851.3693206937906548.7174763277531
Winsorized Mean ( 35 / 44 )66.78939393939391.3571459323257149.2131261263396
Winsorized Mean ( 36 / 44 )66.78939393939391.3517199988633149.4106723253028
Winsorized Mean ( 37 / 44 )66.76136363636361.3318864957030450.1254152300144
Winsorized Mean ( 38 / 44 )66.73257575757581.3059604174161151.0984673560083
Winsorized Mean ( 39 / 44 )66.49621212121211.2738256330255852.2019736431827
Winsorized Mean ( 40 / 44 )66.19318181818181.2345300849428453.6181196598757
Winsorized Mean ( 41 / 44 )66.16212121212121.2251077035852954.005146664654
Winsorized Mean ( 42 / 44 )66.16212121212121.2251077035852954.005146664654
Winsorized Mean ( 43 / 44 )66.1946969696971.2223586498948954.1532527915509
Winsorized Mean ( 44 / 44 )66.0946969696971.1985593144478755.1451197892063
Trimmed Mean ( 1 / 44 )71.55153846153852.3531088647355130.4072367980225
Trimmed Mean ( 2 / 44 )71.161718752.2994618403623630.9471188001041
Trimmed Mean ( 3 / 44 )70.76746031746032.2440512767151931.5355807827389
Trimmed Mean ( 4 / 44 )70.35725806451612.1859243749310732.1865014505522
Trimmed Mean ( 5 / 44 )69.9336065573772.1218205605248332.9592463464861
Trimmed Mean ( 6 / 44 )69.57416666666672.0734463981866333.5548421832915
Trimmed Mean ( 7 / 44 )69.2288135593222.027216346554934.1496918555195
Trimmed Mean ( 8 / 44 )68.88103448275861.9780318666939734.8230155654088
Trimmed Mean ( 9 / 44 )68.55175438596491.9324708976616435.4736283319532
Trimmed Mean ( 10 / 44 )68.25982142857141.8946949153113136.0268140675069
Trimmed Mean ( 11 / 44 )67.96636363636361.8549616881510836.6403058728985
Trimmed Mean ( 12 / 44 )67.68055555555561.8152175183321837.2850938645305
Trimmed Mean ( 13 / 44 )67.42452830188681.7816166232191337.8445774602508
Trimmed Mean ( 14 / 44 )67.17403846153851.7487347368799838.412937677093
Trimmed Mean ( 15 / 44 )67.0284313725491.7390154339679338.5438967724452
Trimmed Mean ( 16 / 44 )66.8781.7287536118559738.6856747782587
Trimmed Mean ( 17 / 44 )66.72142857142861.7170162654676638.8589379805648
Trimmed Mean ( 18 / 44 )66.56251.7041552995803339.0589402364866
Trimmed Mean ( 19 / 44 )66.39680851063831.6898207172869239.2922206666049
Trimmed Mean ( 20 / 44 )66.22717391304351.6741700764741539.5582114647036
Trimmed Mean ( 21 / 44 )66.05666666666671.6577959059901239.8460790185232
Trimmed Mean ( 22 / 44 )65.91136363636361.6464572268158140.0322356164902
Trimmed Mean ( 23 / 44 )65.76976744186051.6363551550987240.1928439782331
Trimmed Mean ( 24 / 44 )65.64642857142861.6298144149095540.2784684997842
Trimmed Mean ( 25 / 44 )65.51341463414631.6219416936370840.3919665492027
Trimmed Mean ( 26 / 44 )65.381.6138173159047240.5126400340718
Trimmed Mean ( 27 / 44 )65.24743589743591.6056849598659140.6352662747024
Trimmed Mean ( 28 / 44 )65.10789473684211.5962662170332840.7876167785143
Trimmed Mean ( 29 / 44 )64.95810810810811.5857029769085140.9648648290681
Trimmed Mean ( 30 / 44 )64.80555555555561.5752311712616341.1403460887914
Trimmed Mean ( 31 / 44 )64.65571428571431.5687800850784241.2140075595632
Trimmed Mean ( 32 / 44 )64.51911764705881.5654750971713541.2137617287161
Trimmed Mean ( 33 / 44 )64.37575757575761.5609752205557641.2407299795815
Trimmed Mean ( 34 / 44 )64.22343751.5546712480206641.309979573988
Trimmed Mean ( 35 / 44 )64.06774193548391.5471486101061241.410205533578
Trimmed Mean ( 36 / 44 )63.89666666666671.5378317090463441.5498433871486
Trimmed Mean ( 37 / 44 )63.71379310344831.525556533233441.7642950067589
Trimmed Mean ( 38 / 44 )63.51964285714291.5116203992560842.0208955160984
Trimmed Mean ( 39 / 44 )63.3129629629631.4964109083212942.3098779960037
Trimmed Mean ( 40 / 44 )63.10576923076921.4810349950533542.6092357314594
Trimmed Mean ( 41 / 44 )62.9021.4666510234168842.8881847117633
Trimmed Mean ( 42 / 44 )62.68333333333331.447841182531643.294343391814
Trimmed Mean ( 43 / 44 )62.4456521739131.4215651254892143.9273945697166
Trimmed Mean ( 44 / 44 )62.18409090909091.3857891836572544.8726917791207
Median59.65
Midrange99.8
Midmean - Weighted Average at Xnp64.1761194029851
Midmean - Weighted Average at X(n+1)p64.3757575757576
Midmean - Empirical Distribution Function64.1761194029851
Midmean - Empirical Distribution Function - Averaging64.3757575757576
Midmean - Empirical Distribution Function - Interpolation64.3757575757576
Midmean - Closest Observation64.1761194029851
Midmean - True Basic - Statistics Graphics Toolkit64.3757575757576
Midmean - MS Excel (old versions)64.5191176470588
Number of observations132



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')