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of Irreproducible Research!

Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationFri, 05 Dec 2008 04:26:04 -0700
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2008/Dec/05/t12284764073n17lfe03o7tr2t.htm/, Retrieved Thu, 16 May 2024 15:24:58 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=29180, Retrieved Thu, 16 May 2024 15:24:58 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact199
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Univariate Data Series] [Werkloosheidsgraa...] [2008-12-05 10:45:42] [e5d91604aae608e98a8ea24759233f66]
-   PD  [Univariate Data Series] [Inflatie op jaarb...] [2008-12-05 10:52:23] [e5d91604aae608e98a8ea24759233f66]
-   PD    [Univariate Data Series] [Investeringen vol...] [2008-12-05 10:58:14] [e5d91604aae608e98a8ea24759233f66]
-   P       [Univariate Data Series] [Investeringen vol...] [2008-12-05 11:13:01] [e5d91604aae608e98a8ea24759233f66]
- RMP           [Central Tendency] [Central tendency ...] [2008-12-05 11:26:04] [55ca0ca4a201c9689dcf5fae352c92eb] [Current]
- RMP             [Histogram] [Histogram: invest...] [2008-12-05 11:31:13] [e5d91604aae608e98a8ea24759233f66]
- RMP             [Tukey lambda PPCC Plot] [PPCC plot investe...] [2008-12-05 12:51:45] [e5d91604aae608e98a8ea24759233f66]
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Dataseries X:
24.1
26.2
22.7
22.9
12.6
12.2
10.1
17.3
22.9
21.7
21
18.8
19.7
21.4
24.3
26
23.5
23.8
25
31.8
26.6
26.5
21
17.9
17.1
17.7
26.2
22.3
26.6
19.6
21
14.5
16.8
18.7
23.3
23.3
27
22.8
20.3
16
14.7
17.4
17.7
20.7
18.5
15.6
20.2
17.9
16
9.5
7.9
7.1
6.2
8
9.5
7.7
7.5
11.5
17.2
18.1
19.1
19.2
21
20.5
20.1
20.5
16
16.5
16.2
16.7
6.4
3.8
2.3
11.9
14
15.3
12.1
12.8
18.2
20.9
28.3
22.3
21.9
23.3
26.8
24.2
20.8
23.8
29.6
43.1
34.7
31.5
9.7
12.6
16.9
16.6
14.9
13.1
18.4
18.3
18.3
5.2
10.4
8.9
25.6
23.8
25.7
26.7
28.5
29.6
29
26.1
24.2
28
29.4
31.5
26.7
27.5
25.6
27.4




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'Sir Ronald Aylmer Fisher' @ 193.190.124.24

\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 & 3 seconds \tabularnewline
R Server & 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=29180&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]3 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Sir Ronald Aylmer Fisher' @ 193.190.124.24[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=29180&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=29180&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 time3 seconds
R Server'Sir Ronald Aylmer Fisher' @ 193.190.124.24







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean19.62083333333330.64833539906636330.2633997180909
Geometric Mean17.9919193482532
Harmonic Mean15.6543697921414
Quadratic Mean20.8565916838458
Winsorized Mean ( 1 / 40 )19.56333333333330.62781236529163131.1611150319503
Winsorized Mean ( 2 / 40 )19.53833333333330.614099262194831.8162462262258
Winsorized Mean ( 3 / 40 )19.55583333333330.60809063786265432.1594053841531
Winsorized Mean ( 4 / 40 )19.56250.60686786283438732.2351885773503
Winsorized Mean ( 5 / 40 )19.51250.58937910939720133.1068741475360
Winsorized Mean ( 6 / 40 )19.53250.58588337681870933.3385461558231
Winsorized Mean ( 7 / 40 )19.53250.58220719128625933.5490531417986
Winsorized Mean ( 8 / 40 )19.51916666666670.5761959865294333.8759157005507
Winsorized Mean ( 9 / 40 )19.48916666666670.56984050527076934.2010904567166
Winsorized Mean ( 10 / 40 )19.54750.55522847456122535.2062275182259
Winsorized Mean ( 11 / 40 )19.5750.54289174112066836.0569124879155
Winsorized Mean ( 12 / 40 )19.5250.5365078622671936.3927565152367
Winsorized Mean ( 13 / 40 )19.53583333333330.53177309749323936.7371599379973
Winsorized Mean ( 14 / 40 )19.53583333333330.51885836195109537.6515726948517
Winsorized Mean ( 15 / 40 )19.54833333333330.51016280058419338.317833662016
Winsorized Mean ( 16 / 40 )19.68166666666670.48714279211195340.4022536828247
Winsorized Mean ( 17 / 40 )19.73833333333330.47924892120698441.1859734261321
Winsorized Mean ( 18 / 40 )19.75333333333330.47332179336546141.7334118357009
Winsorized Mean ( 19 / 40 )19.76916666666670.47117737362232541.9569524629015
Winsorized Mean ( 20 / 40 )19.81916666666670.46025096039583143.0616519509737
Winsorized Mean ( 21 / 40 )19.76666666666670.4539221131213843.5463840497698
Winsorized Mean ( 22 / 40 )19.80333333333330.44908704984446244.0968701729255
Winsorized Mean ( 23 / 40 )19.84166666666670.43931698855523445.1648062414322
Winsorized Mean ( 24 / 40 )20.00166666666670.41432335464410948.2754989369293
Winsorized Mean ( 25 / 40 )20.04333333333330.39425448799879250.8385673301321
Winsorized Mean ( 26 / 40 )20.0650.38655747395732651.9068996250091
Winsorized Mean ( 27 / 40 )20.110.38134988015264552.7337257637276
Winsorized Mean ( 28 / 40 )20.06333333333330.35403226152929656.6709182001287
Winsorized Mean ( 29 / 40 )19.96666666666670.3264942665179561.1547237248925
Winsorized Mean ( 30 / 40 )20.04166666666670.31264791084081864.1029924452965
Winsorized Mean ( 31 / 40 )20.04166666666670.31264791084081864.1029924452965
Winsorized Mean ( 32 / 40 )20.0150.30967962572348164.6313103525635
Winsorized Mean ( 33 / 40 )19.98750.29465253358187667.834135878713
Winsorized Mean ( 34 / 40 )20.07250.28559231903024970.2837529670186
Winsorized Mean ( 35 / 40 )20.10166666666670.28254045428927671.1461539807881
Winsorized Mean ( 36 / 40 )20.04166666666670.26961322887414274.334878708872
Winsorized Mean ( 37 / 40 )20.01083333333330.25980168000195777.0234947409985
Winsorized Mean ( 38 / 40 )20.04250.25652728899670778.1300893109165
Winsorized Mean ( 39 / 40 )20.10750.24989399012885680.4641199639563
Winsorized Mean ( 40 / 40 )20.00750.2323794904698786.0983900065576
Trimmed Mean ( 1 / 40 )19.56864406779660.61080817592286532.0372988430132
Trimmed Mean ( 2 / 40 )19.57413793103450.59187542842484733.0713812248077
Trimmed Mean ( 3 / 40 )19.59298245614040.5789007664033733.8451485871557
Trimmed Mean ( 4 / 40 )19.606250.56694143338049234.5824962608468
Trimmed Mean ( 5 / 40 )19.61818181818180.55400909266840535.4112993411176
Trimmed Mean ( 6 / 40 )19.64166666666670.54430263639463936.0859296893535
Trimmed Mean ( 7 / 40 )19.66226415094340.53427105260002736.8020390684786
Trimmed Mean ( 8 / 40 )19.68365384615380.52380257587485737.5783830640354
Trimmed Mean ( 9 / 40 )19.70784313725490.51320494655690138.4015065900574
Trimmed Mean ( 10 / 40 )19.7370.50240563715231639.2849891411873
Trimmed Mean ( 11 / 40 )19.76020408163270.49274718586430340.1021145295275
Trimmed Mean ( 12 / 40 )19.781250.48382230068523240.8853621918296
Trimmed Mean ( 13 / 40 )19.80851063829790.47464820281622241.7330362166514
Trimmed Mean ( 14 / 40 )19.83586956521740.4649198398963442.6651389401667
Trimmed Mean ( 15 / 40 )19.86444444444440.45570680476912643.5904055777888
Trimmed Mean ( 16 / 40 )19.89318181818180.44640616317982944.5629640874114
Trimmed Mean ( 17 / 40 )19.91162790697670.439012131323445.3555300327425
Trimmed Mean ( 18 / 40 )19.92619047619050.43157478597694746.1708865384339
Trimmed Mean ( 19 / 40 )19.94024390243900.42377001908567547.0543998026619
Trimmed Mean ( 20 / 40 )19.953750.41500702964154648.0805108704657
Trimmed Mean ( 21 / 40 )19.96410256410260.40631861846364449.1341072176068
Trimmed Mean ( 22 / 40 )19.97894736842110.39701215585028450.323263592854
Trimmed Mean ( 23 / 40 )19.99189189189190.38679019143571951.6866568350256
Trimmed Mean ( 24 / 40 )20.00277777777780.37616783320891353.175141550896
Trimmed Mean ( 25 / 40 )20.00285714285710.36722884493044754.4697330261344
Trimmed Mean ( 26 / 40 )200.35943937422063755.6422068210126
Trimmed Mean ( 27 / 40 )19.99545454545450.35121123627483256.9328440557282
Trimmed Mean ( 28 / 40 )19.98750.34206930398701258.4311417804356
Trimmed Mean ( 29 / 40 )19.98225806451610.33510082930972259.6305837430418
Trimmed Mean ( 30 / 40 )19.98333333333330.33057189502100460.4507934108059
Trimmed Mean ( 31 / 40 )19.97931034482760.32685561859400761.125797472199
Trimmed Mean ( 32 / 40 )19.9750.32209994818903162.0149121796109
Trimmed Mean ( 33 / 40 )19.97222222222220.31651951415645163.0994972788637
Trimmed Mean ( 34 / 40 )19.97115384615380.31181288306565064.0485205415616
Trimmed Mean ( 35 / 40 )19.9640.30714963447672264.9976355466347
Trimmed Mean ( 36 / 40 )19.95416666666670.30151741439265766.1791515652923
Trimmed Mean ( 37 / 40 )19.94782608695650.29646449927077767.2857159492042
Trimmed Mean ( 38 / 40 )19.94318181818180.29151854599006268.4113655632108
Trimmed Mean ( 39 / 40 )19.93571428571430.28539398422523969.8533094165733
Trimmed Mean ( 40 / 40 )19.92250.2783764169019771.5667664011053
Median20.15
Midrange22.7
Midmean - Weighted Average at Xnp19.9114754098361
Midmean - Weighted Average at X(n+1)p19.9833333333333
Midmean - Empirical Distribution Function19.9114754098361
Midmean - Empirical Distribution Function - Averaging19.9833333333333
Midmean - Empirical Distribution Function - Interpolation19.9833333333333
Midmean - Closest Observation19.9114754098361
Midmean - True Basic - Statistics Graphics Toolkit19.9833333333333
Midmean - MS Excel (old versions)19.9822580645161
Number of observations120

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 19.6208333333333 & 0.648335399066363 & 30.2633997180909 \tabularnewline
Geometric Mean & 17.9919193482532 &  &  \tabularnewline
Harmonic Mean & 15.6543697921414 &  &  \tabularnewline
Quadratic Mean & 20.8565916838458 &  &  \tabularnewline
Winsorized Mean ( 1 / 40 ) & 19.5633333333333 & 0.627812365291631 & 31.1611150319503 \tabularnewline
Winsorized Mean ( 2 / 40 ) & 19.5383333333333 & 0.6140992621948 & 31.8162462262258 \tabularnewline
Winsorized Mean ( 3 / 40 ) & 19.5558333333333 & 0.608090637862654 & 32.1594053841531 \tabularnewline
Winsorized Mean ( 4 / 40 ) & 19.5625 & 0.606867862834387 & 32.2351885773503 \tabularnewline
Winsorized Mean ( 5 / 40 ) & 19.5125 & 0.589379109397201 & 33.1068741475360 \tabularnewline
Winsorized Mean ( 6 / 40 ) & 19.5325 & 0.585883376818709 & 33.3385461558231 \tabularnewline
Winsorized Mean ( 7 / 40 ) & 19.5325 & 0.582207191286259 & 33.5490531417986 \tabularnewline
Winsorized Mean ( 8 / 40 ) & 19.5191666666667 & 0.57619598652943 & 33.8759157005507 \tabularnewline
Winsorized Mean ( 9 / 40 ) & 19.4891666666667 & 0.569840505270769 & 34.2010904567166 \tabularnewline
Winsorized Mean ( 10 / 40 ) & 19.5475 & 0.555228474561225 & 35.2062275182259 \tabularnewline
Winsorized Mean ( 11 / 40 ) & 19.575 & 0.542891741120668 & 36.0569124879155 \tabularnewline
Winsorized Mean ( 12 / 40 ) & 19.525 & 0.53650786226719 & 36.3927565152367 \tabularnewline
Winsorized Mean ( 13 / 40 ) & 19.5358333333333 & 0.531773097493239 & 36.7371599379973 \tabularnewline
Winsorized Mean ( 14 / 40 ) & 19.5358333333333 & 0.518858361951095 & 37.6515726948517 \tabularnewline
Winsorized Mean ( 15 / 40 ) & 19.5483333333333 & 0.510162800584193 & 38.317833662016 \tabularnewline
Winsorized Mean ( 16 / 40 ) & 19.6816666666667 & 0.487142792111953 & 40.4022536828247 \tabularnewline
Winsorized Mean ( 17 / 40 ) & 19.7383333333333 & 0.479248921206984 & 41.1859734261321 \tabularnewline
Winsorized Mean ( 18 / 40 ) & 19.7533333333333 & 0.473321793365461 & 41.7334118357009 \tabularnewline
Winsorized Mean ( 19 / 40 ) & 19.7691666666667 & 0.471177373622325 & 41.9569524629015 \tabularnewline
Winsorized Mean ( 20 / 40 ) & 19.8191666666667 & 0.460250960395831 & 43.0616519509737 \tabularnewline
Winsorized Mean ( 21 / 40 ) & 19.7666666666667 & 0.45392211312138 & 43.5463840497698 \tabularnewline
Winsorized Mean ( 22 / 40 ) & 19.8033333333333 & 0.449087049844462 & 44.0968701729255 \tabularnewline
Winsorized Mean ( 23 / 40 ) & 19.8416666666667 & 0.439316988555234 & 45.1648062414322 \tabularnewline
Winsorized Mean ( 24 / 40 ) & 20.0016666666667 & 0.414323354644109 & 48.2754989369293 \tabularnewline
Winsorized Mean ( 25 / 40 ) & 20.0433333333333 & 0.394254487998792 & 50.8385673301321 \tabularnewline
Winsorized Mean ( 26 / 40 ) & 20.065 & 0.386557473957326 & 51.9068996250091 \tabularnewline
Winsorized Mean ( 27 / 40 ) & 20.11 & 0.381349880152645 & 52.7337257637276 \tabularnewline
Winsorized Mean ( 28 / 40 ) & 20.0633333333333 & 0.354032261529296 & 56.6709182001287 \tabularnewline
Winsorized Mean ( 29 / 40 ) & 19.9666666666667 & 0.32649426651795 & 61.1547237248925 \tabularnewline
Winsorized Mean ( 30 / 40 ) & 20.0416666666667 & 0.312647910840818 & 64.1029924452965 \tabularnewline
Winsorized Mean ( 31 / 40 ) & 20.0416666666667 & 0.312647910840818 & 64.1029924452965 \tabularnewline
Winsorized Mean ( 32 / 40 ) & 20.015 & 0.309679625723481 & 64.6313103525635 \tabularnewline
Winsorized Mean ( 33 / 40 ) & 19.9875 & 0.294652533581876 & 67.834135878713 \tabularnewline
Winsorized Mean ( 34 / 40 ) & 20.0725 & 0.285592319030249 & 70.2837529670186 \tabularnewline
Winsorized Mean ( 35 / 40 ) & 20.1016666666667 & 0.282540454289276 & 71.1461539807881 \tabularnewline
Winsorized Mean ( 36 / 40 ) & 20.0416666666667 & 0.269613228874142 & 74.334878708872 \tabularnewline
Winsorized Mean ( 37 / 40 ) & 20.0108333333333 & 0.259801680001957 & 77.0234947409985 \tabularnewline
Winsorized Mean ( 38 / 40 ) & 20.0425 & 0.256527288996707 & 78.1300893109165 \tabularnewline
Winsorized Mean ( 39 / 40 ) & 20.1075 & 0.249893990128856 & 80.4641199639563 \tabularnewline
Winsorized Mean ( 40 / 40 ) & 20.0075 & 0.23237949046987 & 86.0983900065576 \tabularnewline
Trimmed Mean ( 1 / 40 ) & 19.5686440677966 & 0.610808175922865 & 32.0372988430132 \tabularnewline
Trimmed Mean ( 2 / 40 ) & 19.5741379310345 & 0.591875428424847 & 33.0713812248077 \tabularnewline
Trimmed Mean ( 3 / 40 ) & 19.5929824561404 & 0.57890076640337 & 33.8451485871557 \tabularnewline
Trimmed Mean ( 4 / 40 ) & 19.60625 & 0.566941433380492 & 34.5824962608468 \tabularnewline
Trimmed Mean ( 5 / 40 ) & 19.6181818181818 & 0.554009092668405 & 35.4112993411176 \tabularnewline
Trimmed Mean ( 6 / 40 ) & 19.6416666666667 & 0.544302636394639 & 36.0859296893535 \tabularnewline
Trimmed Mean ( 7 / 40 ) & 19.6622641509434 & 0.534271052600027 & 36.8020390684786 \tabularnewline
Trimmed Mean ( 8 / 40 ) & 19.6836538461538 & 0.523802575874857 & 37.5783830640354 \tabularnewline
Trimmed Mean ( 9 / 40 ) & 19.7078431372549 & 0.513204946556901 & 38.4015065900574 \tabularnewline
Trimmed Mean ( 10 / 40 ) & 19.737 & 0.502405637152316 & 39.2849891411873 \tabularnewline
Trimmed Mean ( 11 / 40 ) & 19.7602040816327 & 0.492747185864303 & 40.1021145295275 \tabularnewline
Trimmed Mean ( 12 / 40 ) & 19.78125 & 0.483822300685232 & 40.8853621918296 \tabularnewline
Trimmed Mean ( 13 / 40 ) & 19.8085106382979 & 0.474648202816222 & 41.7330362166514 \tabularnewline
Trimmed Mean ( 14 / 40 ) & 19.8358695652174 & 0.46491983989634 & 42.6651389401667 \tabularnewline
Trimmed Mean ( 15 / 40 ) & 19.8644444444444 & 0.455706804769126 & 43.5904055777888 \tabularnewline
Trimmed Mean ( 16 / 40 ) & 19.8931818181818 & 0.446406163179829 & 44.5629640874114 \tabularnewline
Trimmed Mean ( 17 / 40 ) & 19.9116279069767 & 0.4390121313234 & 45.3555300327425 \tabularnewline
Trimmed Mean ( 18 / 40 ) & 19.9261904761905 & 0.431574785976947 & 46.1708865384339 \tabularnewline
Trimmed Mean ( 19 / 40 ) & 19.9402439024390 & 0.423770019085675 & 47.0543998026619 \tabularnewline
Trimmed Mean ( 20 / 40 ) & 19.95375 & 0.415007029641546 & 48.0805108704657 \tabularnewline
Trimmed Mean ( 21 / 40 ) & 19.9641025641026 & 0.406318618463644 & 49.1341072176068 \tabularnewline
Trimmed Mean ( 22 / 40 ) & 19.9789473684211 & 0.397012155850284 & 50.323263592854 \tabularnewline
Trimmed Mean ( 23 / 40 ) & 19.9918918918919 & 0.386790191435719 & 51.6866568350256 \tabularnewline
Trimmed Mean ( 24 / 40 ) & 20.0027777777778 & 0.376167833208913 & 53.175141550896 \tabularnewline
Trimmed Mean ( 25 / 40 ) & 20.0028571428571 & 0.367228844930447 & 54.4697330261344 \tabularnewline
Trimmed Mean ( 26 / 40 ) & 20 & 0.359439374220637 & 55.6422068210126 \tabularnewline
Trimmed Mean ( 27 / 40 ) & 19.9954545454545 & 0.351211236274832 & 56.9328440557282 \tabularnewline
Trimmed Mean ( 28 / 40 ) & 19.9875 & 0.342069303987012 & 58.4311417804356 \tabularnewline
Trimmed Mean ( 29 / 40 ) & 19.9822580645161 & 0.335100829309722 & 59.6305837430418 \tabularnewline
Trimmed Mean ( 30 / 40 ) & 19.9833333333333 & 0.330571895021004 & 60.4507934108059 \tabularnewline
Trimmed Mean ( 31 / 40 ) & 19.9793103448276 & 0.326855618594007 & 61.125797472199 \tabularnewline
Trimmed Mean ( 32 / 40 ) & 19.975 & 0.322099948189031 & 62.0149121796109 \tabularnewline
Trimmed Mean ( 33 / 40 ) & 19.9722222222222 & 0.316519514156451 & 63.0994972788637 \tabularnewline
Trimmed Mean ( 34 / 40 ) & 19.9711538461538 & 0.311812883065650 & 64.0485205415616 \tabularnewline
Trimmed Mean ( 35 / 40 ) & 19.964 & 0.307149634476722 & 64.9976355466347 \tabularnewline
Trimmed Mean ( 36 / 40 ) & 19.9541666666667 & 0.301517414392657 & 66.1791515652923 \tabularnewline
Trimmed Mean ( 37 / 40 ) & 19.9478260869565 & 0.296464499270777 & 67.2857159492042 \tabularnewline
Trimmed Mean ( 38 / 40 ) & 19.9431818181818 & 0.291518545990062 & 68.4113655632108 \tabularnewline
Trimmed Mean ( 39 / 40 ) & 19.9357142857143 & 0.285393984225239 & 69.8533094165733 \tabularnewline
Trimmed Mean ( 40 / 40 ) & 19.9225 & 0.27837641690197 & 71.5667664011053 \tabularnewline
Median & 20.15 &  &  \tabularnewline
Midrange & 22.7 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 19.9114754098361 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 19.9833333333333 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 19.9114754098361 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 19.9833333333333 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 19.9833333333333 &  &  \tabularnewline
Midmean - Closest Observation & 19.9114754098361 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 19.9833333333333 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 19.9822580645161 &  &  \tabularnewline
Number of observations & 120 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=29180&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]19.6208333333333[/C][C]0.648335399066363[/C][C]30.2633997180909[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]17.9919193482532[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]15.6543697921414[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]20.8565916838458[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 40 )[/C][C]19.5633333333333[/C][C]0.627812365291631[/C][C]31.1611150319503[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 40 )[/C][C]19.5383333333333[/C][C]0.6140992621948[/C][C]31.8162462262258[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 40 )[/C][C]19.5558333333333[/C][C]0.608090637862654[/C][C]32.1594053841531[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 40 )[/C][C]19.5625[/C][C]0.606867862834387[/C][C]32.2351885773503[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 40 )[/C][C]19.5125[/C][C]0.589379109397201[/C][C]33.1068741475360[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 40 )[/C][C]19.5325[/C][C]0.585883376818709[/C][C]33.3385461558231[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 40 )[/C][C]19.5325[/C][C]0.582207191286259[/C][C]33.5490531417986[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 40 )[/C][C]19.5191666666667[/C][C]0.57619598652943[/C][C]33.8759157005507[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 40 )[/C][C]19.4891666666667[/C][C]0.569840505270769[/C][C]34.2010904567166[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 40 )[/C][C]19.5475[/C][C]0.555228474561225[/C][C]35.2062275182259[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 40 )[/C][C]19.575[/C][C]0.542891741120668[/C][C]36.0569124879155[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 40 )[/C][C]19.525[/C][C]0.53650786226719[/C][C]36.3927565152367[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 40 )[/C][C]19.5358333333333[/C][C]0.531773097493239[/C][C]36.7371599379973[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 40 )[/C][C]19.5358333333333[/C][C]0.518858361951095[/C][C]37.6515726948517[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 40 )[/C][C]19.5483333333333[/C][C]0.510162800584193[/C][C]38.317833662016[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 40 )[/C][C]19.6816666666667[/C][C]0.487142792111953[/C][C]40.4022536828247[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 40 )[/C][C]19.7383333333333[/C][C]0.479248921206984[/C][C]41.1859734261321[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 40 )[/C][C]19.7533333333333[/C][C]0.473321793365461[/C][C]41.7334118357009[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 40 )[/C][C]19.7691666666667[/C][C]0.471177373622325[/C][C]41.9569524629015[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 40 )[/C][C]19.8191666666667[/C][C]0.460250960395831[/C][C]43.0616519509737[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 40 )[/C][C]19.7666666666667[/C][C]0.45392211312138[/C][C]43.5463840497698[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 40 )[/C][C]19.8033333333333[/C][C]0.449087049844462[/C][C]44.0968701729255[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 40 )[/C][C]19.8416666666667[/C][C]0.439316988555234[/C][C]45.1648062414322[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 40 )[/C][C]20.0016666666667[/C][C]0.414323354644109[/C][C]48.2754989369293[/C][/ROW]
[ROW][C]Winsorized Mean ( 25 / 40 )[/C][C]20.0433333333333[/C][C]0.394254487998792[/C][C]50.8385673301321[/C][/ROW]
[ROW][C]Winsorized Mean ( 26 / 40 )[/C][C]20.065[/C][C]0.386557473957326[/C][C]51.9068996250091[/C][/ROW]
[ROW][C]Winsorized Mean ( 27 / 40 )[/C][C]20.11[/C][C]0.381349880152645[/C][C]52.7337257637276[/C][/ROW]
[ROW][C]Winsorized Mean ( 28 / 40 )[/C][C]20.0633333333333[/C][C]0.354032261529296[/C][C]56.6709182001287[/C][/ROW]
[ROW][C]Winsorized Mean ( 29 / 40 )[/C][C]19.9666666666667[/C][C]0.32649426651795[/C][C]61.1547237248925[/C][/ROW]
[ROW][C]Winsorized Mean ( 30 / 40 )[/C][C]20.0416666666667[/C][C]0.312647910840818[/C][C]64.1029924452965[/C][/ROW]
[ROW][C]Winsorized Mean ( 31 / 40 )[/C][C]20.0416666666667[/C][C]0.312647910840818[/C][C]64.1029924452965[/C][/ROW]
[ROW][C]Winsorized Mean ( 32 / 40 )[/C][C]20.015[/C][C]0.309679625723481[/C][C]64.6313103525635[/C][/ROW]
[ROW][C]Winsorized Mean ( 33 / 40 )[/C][C]19.9875[/C][C]0.294652533581876[/C][C]67.834135878713[/C][/ROW]
[ROW][C]Winsorized Mean ( 34 / 40 )[/C][C]20.0725[/C][C]0.285592319030249[/C][C]70.2837529670186[/C][/ROW]
[ROW][C]Winsorized Mean ( 35 / 40 )[/C][C]20.1016666666667[/C][C]0.282540454289276[/C][C]71.1461539807881[/C][/ROW]
[ROW][C]Winsorized Mean ( 36 / 40 )[/C][C]20.0416666666667[/C][C]0.269613228874142[/C][C]74.334878708872[/C][/ROW]
[ROW][C]Winsorized Mean ( 37 / 40 )[/C][C]20.0108333333333[/C][C]0.259801680001957[/C][C]77.0234947409985[/C][/ROW]
[ROW][C]Winsorized Mean ( 38 / 40 )[/C][C]20.0425[/C][C]0.256527288996707[/C][C]78.1300893109165[/C][/ROW]
[ROW][C]Winsorized Mean ( 39 / 40 )[/C][C]20.1075[/C][C]0.249893990128856[/C][C]80.4641199639563[/C][/ROW]
[ROW][C]Winsorized Mean ( 40 / 40 )[/C][C]20.0075[/C][C]0.23237949046987[/C][C]86.0983900065576[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 40 )[/C][C]19.5686440677966[/C][C]0.610808175922865[/C][C]32.0372988430132[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 40 )[/C][C]19.5741379310345[/C][C]0.591875428424847[/C][C]33.0713812248077[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 40 )[/C][C]19.5929824561404[/C][C]0.57890076640337[/C][C]33.8451485871557[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 40 )[/C][C]19.60625[/C][C]0.566941433380492[/C][C]34.5824962608468[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 40 )[/C][C]19.6181818181818[/C][C]0.554009092668405[/C][C]35.4112993411176[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 40 )[/C][C]19.6416666666667[/C][C]0.544302636394639[/C][C]36.0859296893535[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 40 )[/C][C]19.6622641509434[/C][C]0.534271052600027[/C][C]36.8020390684786[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 40 )[/C][C]19.6836538461538[/C][C]0.523802575874857[/C][C]37.5783830640354[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 40 )[/C][C]19.7078431372549[/C][C]0.513204946556901[/C][C]38.4015065900574[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 40 )[/C][C]19.737[/C][C]0.502405637152316[/C][C]39.2849891411873[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 40 )[/C][C]19.7602040816327[/C][C]0.492747185864303[/C][C]40.1021145295275[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 40 )[/C][C]19.78125[/C][C]0.483822300685232[/C][C]40.8853621918296[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 40 )[/C][C]19.8085106382979[/C][C]0.474648202816222[/C][C]41.7330362166514[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 40 )[/C][C]19.8358695652174[/C][C]0.46491983989634[/C][C]42.6651389401667[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 40 )[/C][C]19.8644444444444[/C][C]0.455706804769126[/C][C]43.5904055777888[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 40 )[/C][C]19.8931818181818[/C][C]0.446406163179829[/C][C]44.5629640874114[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 40 )[/C][C]19.9116279069767[/C][C]0.4390121313234[/C][C]45.3555300327425[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 40 )[/C][C]19.9261904761905[/C][C]0.431574785976947[/C][C]46.1708865384339[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 40 )[/C][C]19.9402439024390[/C][C]0.423770019085675[/C][C]47.0543998026619[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 40 )[/C][C]19.95375[/C][C]0.415007029641546[/C][C]48.0805108704657[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 40 )[/C][C]19.9641025641026[/C][C]0.406318618463644[/C][C]49.1341072176068[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 40 )[/C][C]19.9789473684211[/C][C]0.397012155850284[/C][C]50.323263592854[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 40 )[/C][C]19.9918918918919[/C][C]0.386790191435719[/C][C]51.6866568350256[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 40 )[/C][C]20.0027777777778[/C][C]0.376167833208913[/C][C]53.175141550896[/C][/ROW]
[ROW][C]Trimmed Mean ( 25 / 40 )[/C][C]20.0028571428571[/C][C]0.367228844930447[/C][C]54.4697330261344[/C][/ROW]
[ROW][C]Trimmed Mean ( 26 / 40 )[/C][C]20[/C][C]0.359439374220637[/C][C]55.6422068210126[/C][/ROW]
[ROW][C]Trimmed Mean ( 27 / 40 )[/C][C]19.9954545454545[/C][C]0.351211236274832[/C][C]56.9328440557282[/C][/ROW]
[ROW][C]Trimmed Mean ( 28 / 40 )[/C][C]19.9875[/C][C]0.342069303987012[/C][C]58.4311417804356[/C][/ROW]
[ROW][C]Trimmed Mean ( 29 / 40 )[/C][C]19.9822580645161[/C][C]0.335100829309722[/C][C]59.6305837430418[/C][/ROW]
[ROW][C]Trimmed Mean ( 30 / 40 )[/C][C]19.9833333333333[/C][C]0.330571895021004[/C][C]60.4507934108059[/C][/ROW]
[ROW][C]Trimmed Mean ( 31 / 40 )[/C][C]19.9793103448276[/C][C]0.326855618594007[/C][C]61.125797472199[/C][/ROW]
[ROW][C]Trimmed Mean ( 32 / 40 )[/C][C]19.975[/C][C]0.322099948189031[/C][C]62.0149121796109[/C][/ROW]
[ROW][C]Trimmed Mean ( 33 / 40 )[/C][C]19.9722222222222[/C][C]0.316519514156451[/C][C]63.0994972788637[/C][/ROW]
[ROW][C]Trimmed Mean ( 34 / 40 )[/C][C]19.9711538461538[/C][C]0.311812883065650[/C][C]64.0485205415616[/C][/ROW]
[ROW][C]Trimmed Mean ( 35 / 40 )[/C][C]19.964[/C][C]0.307149634476722[/C][C]64.9976355466347[/C][/ROW]
[ROW][C]Trimmed Mean ( 36 / 40 )[/C][C]19.9541666666667[/C][C]0.301517414392657[/C][C]66.1791515652923[/C][/ROW]
[ROW][C]Trimmed Mean ( 37 / 40 )[/C][C]19.9478260869565[/C][C]0.296464499270777[/C][C]67.2857159492042[/C][/ROW]
[ROW][C]Trimmed Mean ( 38 / 40 )[/C][C]19.9431818181818[/C][C]0.291518545990062[/C][C]68.4113655632108[/C][/ROW]
[ROW][C]Trimmed Mean ( 39 / 40 )[/C][C]19.9357142857143[/C][C]0.285393984225239[/C][C]69.8533094165733[/C][/ROW]
[ROW][C]Trimmed Mean ( 40 / 40 )[/C][C]19.9225[/C][C]0.27837641690197[/C][C]71.5667664011053[/C][/ROW]
[ROW][C]Median[/C][C]20.15[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]22.7[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]19.9114754098361[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]19.9833333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]19.9114754098361[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]19.9833333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]19.9833333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]19.9114754098361[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]19.9833333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]19.9822580645161[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]120[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=29180&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=29180&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 Mean19.62083333333330.64833539906636330.2633997180909
Geometric Mean17.9919193482532
Harmonic Mean15.6543697921414
Quadratic Mean20.8565916838458
Winsorized Mean ( 1 / 40 )19.56333333333330.62781236529163131.1611150319503
Winsorized Mean ( 2 / 40 )19.53833333333330.614099262194831.8162462262258
Winsorized Mean ( 3 / 40 )19.55583333333330.60809063786265432.1594053841531
Winsorized Mean ( 4 / 40 )19.56250.60686786283438732.2351885773503
Winsorized Mean ( 5 / 40 )19.51250.58937910939720133.1068741475360
Winsorized Mean ( 6 / 40 )19.53250.58588337681870933.3385461558231
Winsorized Mean ( 7 / 40 )19.53250.58220719128625933.5490531417986
Winsorized Mean ( 8 / 40 )19.51916666666670.5761959865294333.8759157005507
Winsorized Mean ( 9 / 40 )19.48916666666670.56984050527076934.2010904567166
Winsorized Mean ( 10 / 40 )19.54750.55522847456122535.2062275182259
Winsorized Mean ( 11 / 40 )19.5750.54289174112066836.0569124879155
Winsorized Mean ( 12 / 40 )19.5250.5365078622671936.3927565152367
Winsorized Mean ( 13 / 40 )19.53583333333330.53177309749323936.7371599379973
Winsorized Mean ( 14 / 40 )19.53583333333330.51885836195109537.6515726948517
Winsorized Mean ( 15 / 40 )19.54833333333330.51016280058419338.317833662016
Winsorized Mean ( 16 / 40 )19.68166666666670.48714279211195340.4022536828247
Winsorized Mean ( 17 / 40 )19.73833333333330.47924892120698441.1859734261321
Winsorized Mean ( 18 / 40 )19.75333333333330.47332179336546141.7334118357009
Winsorized Mean ( 19 / 40 )19.76916666666670.47117737362232541.9569524629015
Winsorized Mean ( 20 / 40 )19.81916666666670.46025096039583143.0616519509737
Winsorized Mean ( 21 / 40 )19.76666666666670.4539221131213843.5463840497698
Winsorized Mean ( 22 / 40 )19.80333333333330.44908704984446244.0968701729255
Winsorized Mean ( 23 / 40 )19.84166666666670.43931698855523445.1648062414322
Winsorized Mean ( 24 / 40 )20.00166666666670.41432335464410948.2754989369293
Winsorized Mean ( 25 / 40 )20.04333333333330.39425448799879250.8385673301321
Winsorized Mean ( 26 / 40 )20.0650.38655747395732651.9068996250091
Winsorized Mean ( 27 / 40 )20.110.38134988015264552.7337257637276
Winsorized Mean ( 28 / 40 )20.06333333333330.35403226152929656.6709182001287
Winsorized Mean ( 29 / 40 )19.96666666666670.3264942665179561.1547237248925
Winsorized Mean ( 30 / 40 )20.04166666666670.31264791084081864.1029924452965
Winsorized Mean ( 31 / 40 )20.04166666666670.31264791084081864.1029924452965
Winsorized Mean ( 32 / 40 )20.0150.30967962572348164.6313103525635
Winsorized Mean ( 33 / 40 )19.98750.29465253358187667.834135878713
Winsorized Mean ( 34 / 40 )20.07250.28559231903024970.2837529670186
Winsorized Mean ( 35 / 40 )20.10166666666670.28254045428927671.1461539807881
Winsorized Mean ( 36 / 40 )20.04166666666670.26961322887414274.334878708872
Winsorized Mean ( 37 / 40 )20.01083333333330.25980168000195777.0234947409985
Winsorized Mean ( 38 / 40 )20.04250.25652728899670778.1300893109165
Winsorized Mean ( 39 / 40 )20.10750.24989399012885680.4641199639563
Winsorized Mean ( 40 / 40 )20.00750.2323794904698786.0983900065576
Trimmed Mean ( 1 / 40 )19.56864406779660.61080817592286532.0372988430132
Trimmed Mean ( 2 / 40 )19.57413793103450.59187542842484733.0713812248077
Trimmed Mean ( 3 / 40 )19.59298245614040.5789007664033733.8451485871557
Trimmed Mean ( 4 / 40 )19.606250.56694143338049234.5824962608468
Trimmed Mean ( 5 / 40 )19.61818181818180.55400909266840535.4112993411176
Trimmed Mean ( 6 / 40 )19.64166666666670.54430263639463936.0859296893535
Trimmed Mean ( 7 / 40 )19.66226415094340.53427105260002736.8020390684786
Trimmed Mean ( 8 / 40 )19.68365384615380.52380257587485737.5783830640354
Trimmed Mean ( 9 / 40 )19.70784313725490.51320494655690138.4015065900574
Trimmed Mean ( 10 / 40 )19.7370.50240563715231639.2849891411873
Trimmed Mean ( 11 / 40 )19.76020408163270.49274718586430340.1021145295275
Trimmed Mean ( 12 / 40 )19.781250.48382230068523240.8853621918296
Trimmed Mean ( 13 / 40 )19.80851063829790.47464820281622241.7330362166514
Trimmed Mean ( 14 / 40 )19.83586956521740.4649198398963442.6651389401667
Trimmed Mean ( 15 / 40 )19.86444444444440.45570680476912643.5904055777888
Trimmed Mean ( 16 / 40 )19.89318181818180.44640616317982944.5629640874114
Trimmed Mean ( 17 / 40 )19.91162790697670.439012131323445.3555300327425
Trimmed Mean ( 18 / 40 )19.92619047619050.43157478597694746.1708865384339
Trimmed Mean ( 19 / 40 )19.94024390243900.42377001908567547.0543998026619
Trimmed Mean ( 20 / 40 )19.953750.41500702964154648.0805108704657
Trimmed Mean ( 21 / 40 )19.96410256410260.40631861846364449.1341072176068
Trimmed Mean ( 22 / 40 )19.97894736842110.39701215585028450.323263592854
Trimmed Mean ( 23 / 40 )19.99189189189190.38679019143571951.6866568350256
Trimmed Mean ( 24 / 40 )20.00277777777780.37616783320891353.175141550896
Trimmed Mean ( 25 / 40 )20.00285714285710.36722884493044754.4697330261344
Trimmed Mean ( 26 / 40 )200.35943937422063755.6422068210126
Trimmed Mean ( 27 / 40 )19.99545454545450.35121123627483256.9328440557282
Trimmed Mean ( 28 / 40 )19.98750.34206930398701258.4311417804356
Trimmed Mean ( 29 / 40 )19.98225806451610.33510082930972259.6305837430418
Trimmed Mean ( 30 / 40 )19.98333333333330.33057189502100460.4507934108059
Trimmed Mean ( 31 / 40 )19.97931034482760.32685561859400761.125797472199
Trimmed Mean ( 32 / 40 )19.9750.32209994818903162.0149121796109
Trimmed Mean ( 33 / 40 )19.97222222222220.31651951415645163.0994972788637
Trimmed Mean ( 34 / 40 )19.97115384615380.31181288306565064.0485205415616
Trimmed Mean ( 35 / 40 )19.9640.30714963447672264.9976355466347
Trimmed Mean ( 36 / 40 )19.95416666666670.30151741439265766.1791515652923
Trimmed Mean ( 37 / 40 )19.94782608695650.29646449927077767.2857159492042
Trimmed Mean ( 38 / 40 )19.94318181818180.29151854599006268.4113655632108
Trimmed Mean ( 39 / 40 )19.93571428571430.28539398422523969.8533094165733
Trimmed Mean ( 40 / 40 )19.92250.2783764169019771.5667664011053
Median20.15
Midrange22.7
Midmean - Weighted Average at Xnp19.9114754098361
Midmean - Weighted Average at X(n+1)p19.9833333333333
Midmean - Empirical Distribution Function19.9114754098361
Midmean - Empirical Distribution Function - Averaging19.9833333333333
Midmean - Empirical Distribution Function - Interpolation19.9833333333333
Midmean - Closest Observation19.9114754098361
Midmean - True Basic - Statistics Graphics Toolkit19.9833333333333
Midmean - MS Excel (old versions)19.9822580645161
Number of observations120



Parameters (Session):
par1 = Inflatie indexcijfer der consumptieprijzen ; par2 = http://ecodata.mineco.fgov.be/mdn/ts_structur.jsp?table=EI0_ ; par3 = Economische indicator voor België. Maandelijks, volledige tijdreeks van januari 1998 tot december 2007 - Inflatie op jaarbasis: indexcijfer der consumptieprijzen ;
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')