Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationSun, 08 Mar 2009 09:20:45 -0600
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2009/Mar/08/t1236525719a3l3pc9vdyitkml.htm/, Retrieved Sun, 28 Apr 2024 11:31:57 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=38695, Retrieved Sun, 28 Apr 2024 11:31:57 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact137
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [RIA VANTHILLO PRI...] [2009-03-08 15:20:45] [822aa141fddc67f18188afbe1dd38d3f] [Current]
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Dataseries X:
1.38
1.38
1.38
1.38
1.38
1.38
1.38
1.38
1.38
1.38
1.38
1.38
1.38
1.38
1.38
1.38
1.38
1.38
1.38
1.38
1.38
1.38
1.38
1.43
1.43
1.43
1.43
1.43
1.43
1.43
1.43
1.43
1.43
1.43
1.43
1.43
1.43
1.43
1.43
1.43
1.43
1.43
1.44
1.48
1.48
1.48
1.48
1.48
1.48
1.48
1.48
1.48
1.48
1.48
1.48
1.48
1.48
1.48
1.48
1.48
1.48
1.48
1.48
1.48
1.48
1.48
1.48
1.48
1.48
1.48
1.48
1.48
1.48
1.57
1.58
1.58
1.58
1.58
1.59
1.6
1.6
1.61
1.61
1.61
1.62
1.63
1.63
1.64
1.64
1.64
1.64
1.64
1.65
1.65
1.65
1.65
1.65
1.66
1.66
1.67
1.68
1.68
1.68
1.68
1.69
1.7
1.7
1.71
1.72
1.73
1.74
1.74
1.75
1.75
1.75
1.76
1.79
1.83
1.84
1.85
1.87
1.87
1.87
1.88
1.88
1.88




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'Herman Ole Andreas Wold' @ 193.190.124.10:1001

\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 & 'Herman Ole Andreas Wold' @ 193.190.124.10:1001 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=38695&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]'Herman Ole Andreas Wold' @ 193.190.124.10:1001[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=38695&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=38695&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'Herman Ole Andreas Wold' @ 193.190.124.10:1001







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean1.544444444444440.0129984397381417118.817679318275
Geometric Mean1.53786042044277
Harmonic Mean1.53153584074654
Quadratic Mean1.55126676346416
Winsorized Mean ( 1 / 42 )1.544444444444440.0129984397381417118.817679318275
Winsorized Mean ( 2 / 42 )1.544444444444440.0129984397381417118.817679318275
Winsorized Mean ( 3 / 42 )1.544206349206350.0129498927737686119.244720877868
Winsorized Mean ( 4 / 42 )1.544206349206350.0129498927737686119.244720877868
Winsorized Mean ( 5 / 42 )1.544206349206350.0129498927737686119.244720877868
Winsorized Mean ( 6 / 42 )1.543253968253970.0127624595157006120.921360522667
Winsorized Mean ( 7 / 42 )1.542698412698410.0126568446622861121.886493344998
Winsorized Mean ( 8 / 42 )1.542063492063490.0125388627419385122.982723696765
Winsorized Mean ( 9 / 42 )1.539206349206350.012037825661706127.864150259526
Winsorized Mean ( 10 / 42 )1.536825396825400.0116568125969055131.839247139769
Winsorized Mean ( 11 / 42 )1.535952380952380.0115250884768445133.270333155214
Winsorized Mean ( 12 / 42 )1.535952380952380.0115250884768445133.270333155214
Winsorized Mean ( 13 / 42 )1.535952380952380.0115250884768445133.270333155214
Winsorized Mean ( 14 / 42 )1.534841269841270.0113622790732969135.082166169319
Winsorized Mean ( 15 / 42 )1.534841269841270.0113622790732969135.082166169319
Winsorized Mean ( 16 / 42 )1.533571428571430.0111813133713121137.154856289612
Winsorized Mean ( 17 / 42 )1.532222222222220.0109943066876200139.365061004489
Winsorized Mean ( 18 / 42 )1.530793650793650.0108018829484982141.715445176758
Winsorized Mean ( 19 / 42 )1.529285714285710.0106046881345393144.208457135562
Winsorized Mean ( 20 / 42 )1.529285714285710.0106046881345393144.208457135562
Winsorized Mean ( 21 / 42 )1.527619047619050.0103931775982887146.982867671826
Winsorized Mean ( 22 / 42 )1.525873015873020.0101782649478906149.914845377379
Winsorized Mean ( 23 / 42 )1.5350.00923468272759628166.221195170346
Winsorized Mean ( 24 / 42 )1.5350.00923468272759628166.221195170346
Winsorized Mean ( 25 / 42 )1.5350.00923468272759628166.221195170346
Winsorized Mean ( 26 / 42 )1.532936507936510.00897903551954073170.72396078626
Winsorized Mean ( 27 / 42 )1.530793650793650.00872114975280404175.526586996338
Winsorized Mean ( 28 / 42 )1.530793650793650.00872114975280404175.526586996338
Winsorized Mean ( 29 / 42 )1.528492063492060.00845234443691345180.836461989974
Winsorized Mean ( 30 / 42 )1.528492063492060.00845234443691345180.836461989974
Winsorized Mean ( 31 / 42 )1.528492063492060.00845234443691345180.836461989974
Winsorized Mean ( 32 / 42 )1.528492063492060.00845234443691345180.836461989974
Winsorized Mean ( 33 / 42 )1.528492063492060.00845234443691345180.836461989974
Winsorized Mean ( 34 / 42 )1.525793650793650.00814577750163065187.310990324522
Winsorized Mean ( 35 / 42 )1.525793650793650.00814577750163065187.310990324522
Winsorized Mean ( 36 / 42 )1.525793650793650.00814577750163065187.310990324522
Winsorized Mean ( 37 / 42 )1.525793650793650.00814577750163065187.310990324522
Winsorized Mean ( 38 / 42 )1.525793650793650.00814577750163065187.310990324522
Winsorized Mean ( 39 / 42 )1.522698412698410.00780184162094159195.171664163395
Winsorized Mean ( 40 / 42 )1.522698412698410.00780184162094159195.171664163395
Winsorized Mean ( 41 / 42 )1.519444444444440.00744700264029194204.034363600666
Winsorized Mean ( 42 / 42 )1.519444444444440.00677184231391392224.376820074868
Trimmed Mean ( 1 / 42 )1.543064516129030.0128571084462924120.016450244223
Trimmed Mean ( 2 / 42 )1.541639344262300.0126997577048778121.391240690377
Trimmed Mean ( 3 / 42 )1.540166666666670.0125244765028857122.972538318213
Trimmed Mean ( 4 / 42 )1.538728813559320.012348779109872124.605744411544
Trimmed Mean ( 5 / 42 )1.537241379310340.0121525697129510126.495170619931
Trimmed Mean ( 6 / 42 )1.535701754385960.0119331375483287128.692202546601
Trimmed Mean ( 7 / 42 )1.534285714285710.0117320156499904130.777673680223
Trimmed Mean ( 8 / 42 )1.532909090909090.0115289427678146132.961809402725
Trimmed Mean ( 9 / 42 )1.531574074074070.0113238935375634135.251543030987
Trimmed Mean ( 10 / 42 )1.530566037735850.0111832166226170136.862772973602
Trimmed Mean ( 11 / 42 )1.529807692307690.0110864118712196137.989433378267
Trimmed Mean ( 12 / 42 )1.529117647058820.0109959337900027139.06210025101
Trimmed Mean ( 13 / 42 )1.52840.0108922361377638140.320130840808
Trimmed Mean ( 14 / 42 )1.527653061224490.0107735728562710141.796327142791
Trimmed Mean ( 15 / 42 )1.526979166666670.0106603460491406143.239174378375
Trimmed Mean ( 16 / 42 )1.526276595744680.0105304126916404144.939865173216
Trimmed Mean ( 17 / 42 )1.525652173913040.0104054273342457146.620809016840
Trimmed Mean ( 18 / 42 )1.525111111111110.0102858574038796148.272628253224
Trimmed Mean ( 19 / 42 )1.524659090909090.0101721710226178149.885318239245
Trimmed Mean ( 20 / 42 )1.524302325581400.0100648250398478151.448467265601
Trimmed Mean ( 21 / 42 )1.523928571428570.0099396022544157153.318868544419
Trimmed Mean ( 22 / 42 )1.523658536585370.00981998802767366155.158899612866
Trimmed Mean ( 23 / 42 )1.52350.00970628792672336156.960107870435
Trimmed Mean ( 24 / 42 )1.522692307692310.0096744770947605157.392724462283
Trimmed Mean ( 25 / 42 )1.521842105263160.00963129133881774158.01018282248
Trimmed Mean ( 26 / 42 )1.520945945945950.00957475878984462158.849531286274
Trimmed Mean ( 27 / 42 )1.520138888888890.00953433186839356159.438428394565
Trimmed Mean ( 28 / 42 )1.519428571428570.00951164855051304159.743977435606
Trimmed Mean ( 29 / 42 )1.518676470588240.00947688934178001160.250522699782
Trimmed Mean ( 30 / 42 )1.518030303030300.0094615396100983160.442207673063
Trimmed Mean ( 31 / 42 )1.517343750.0094339868829114160.838017778941
Trimmed Mean ( 32 / 42 )1.516612903225810.00939171509617693161.484125923195
Trimmed Mean ( 33 / 42 )1.515833333333330.00933159285628155162.441006233245
Trimmed Mean ( 34 / 42 )1.5150.00924967912002095163.789465595707
Trimmed Mean ( 35 / 42 )1.514285714285710.00918729056782992164.823971017975
Trimmed Mean ( 36 / 42 )1.513518518518520.00910056174845734166.310449876908
Trimmed Mean ( 37 / 42 )1.512692307692310.00898345800310036168.386417253829
Trimmed Mean ( 38 / 42 )1.51180.00882801662611826171.250243857407
Trimmed Mean ( 39 / 42 )1.510833333333330.00862349448949798175.199663567163
Trimmed Mean ( 40 / 42 )1.510.00842700971600385179.185743328661
Trimmed Mean ( 41 / 42 )1.509090909090910.00816594655061256184.802937386078
Trimmed Mean ( 42 / 42 )1.508333333333330.00790416367046267190.827694898307
Median1.48
Midrange1.63
Midmean - Weighted Average at Xnp1.51148648648649
Midmean - Weighted Average at X(n+1)p1.51148648648649
Midmean - Empirical Distribution Function1.51148648648649
Midmean - Empirical Distribution Function - Averaging1.51148648648649
Midmean - Empirical Distribution Function - Interpolation1.51148648648649
Midmean - Closest Observation1.51148648648649
Midmean - True Basic - Statistics Graphics Toolkit1.51148648648649
Midmean - MS Excel (old versions)1.51148648648649
Number of observations126

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 1.54444444444444 & 0.0129984397381417 & 118.817679318275 \tabularnewline
Geometric Mean & 1.53786042044277 &  &  \tabularnewline
Harmonic Mean & 1.53153584074654 &  &  \tabularnewline
Quadratic Mean & 1.55126676346416 &  &  \tabularnewline
Winsorized Mean ( 1 / 42 ) & 1.54444444444444 & 0.0129984397381417 & 118.817679318275 \tabularnewline
Winsorized Mean ( 2 / 42 ) & 1.54444444444444 & 0.0129984397381417 & 118.817679318275 \tabularnewline
Winsorized Mean ( 3 / 42 ) & 1.54420634920635 & 0.0129498927737686 & 119.244720877868 \tabularnewline
Winsorized Mean ( 4 / 42 ) & 1.54420634920635 & 0.0129498927737686 & 119.244720877868 \tabularnewline
Winsorized Mean ( 5 / 42 ) & 1.54420634920635 & 0.0129498927737686 & 119.244720877868 \tabularnewline
Winsorized Mean ( 6 / 42 ) & 1.54325396825397 & 0.0127624595157006 & 120.921360522667 \tabularnewline
Winsorized Mean ( 7 / 42 ) & 1.54269841269841 & 0.0126568446622861 & 121.886493344998 \tabularnewline
Winsorized Mean ( 8 / 42 ) & 1.54206349206349 & 0.0125388627419385 & 122.982723696765 \tabularnewline
Winsorized Mean ( 9 / 42 ) & 1.53920634920635 & 0.012037825661706 & 127.864150259526 \tabularnewline
Winsorized Mean ( 10 / 42 ) & 1.53682539682540 & 0.0116568125969055 & 131.839247139769 \tabularnewline
Winsorized Mean ( 11 / 42 ) & 1.53595238095238 & 0.0115250884768445 & 133.270333155214 \tabularnewline
Winsorized Mean ( 12 / 42 ) & 1.53595238095238 & 0.0115250884768445 & 133.270333155214 \tabularnewline
Winsorized Mean ( 13 / 42 ) & 1.53595238095238 & 0.0115250884768445 & 133.270333155214 \tabularnewline
Winsorized Mean ( 14 / 42 ) & 1.53484126984127 & 0.0113622790732969 & 135.082166169319 \tabularnewline
Winsorized Mean ( 15 / 42 ) & 1.53484126984127 & 0.0113622790732969 & 135.082166169319 \tabularnewline
Winsorized Mean ( 16 / 42 ) & 1.53357142857143 & 0.0111813133713121 & 137.154856289612 \tabularnewline
Winsorized Mean ( 17 / 42 ) & 1.53222222222222 & 0.0109943066876200 & 139.365061004489 \tabularnewline
Winsorized Mean ( 18 / 42 ) & 1.53079365079365 & 0.0108018829484982 & 141.715445176758 \tabularnewline
Winsorized Mean ( 19 / 42 ) & 1.52928571428571 & 0.0106046881345393 & 144.208457135562 \tabularnewline
Winsorized Mean ( 20 / 42 ) & 1.52928571428571 & 0.0106046881345393 & 144.208457135562 \tabularnewline
Winsorized Mean ( 21 / 42 ) & 1.52761904761905 & 0.0103931775982887 & 146.982867671826 \tabularnewline
Winsorized Mean ( 22 / 42 ) & 1.52587301587302 & 0.0101782649478906 & 149.914845377379 \tabularnewline
Winsorized Mean ( 23 / 42 ) & 1.535 & 0.00923468272759628 & 166.221195170346 \tabularnewline
Winsorized Mean ( 24 / 42 ) & 1.535 & 0.00923468272759628 & 166.221195170346 \tabularnewline
Winsorized Mean ( 25 / 42 ) & 1.535 & 0.00923468272759628 & 166.221195170346 \tabularnewline
Winsorized Mean ( 26 / 42 ) & 1.53293650793651 & 0.00897903551954073 & 170.72396078626 \tabularnewline
Winsorized Mean ( 27 / 42 ) & 1.53079365079365 & 0.00872114975280404 & 175.526586996338 \tabularnewline
Winsorized Mean ( 28 / 42 ) & 1.53079365079365 & 0.00872114975280404 & 175.526586996338 \tabularnewline
Winsorized Mean ( 29 / 42 ) & 1.52849206349206 & 0.00845234443691345 & 180.836461989974 \tabularnewline
Winsorized Mean ( 30 / 42 ) & 1.52849206349206 & 0.00845234443691345 & 180.836461989974 \tabularnewline
Winsorized Mean ( 31 / 42 ) & 1.52849206349206 & 0.00845234443691345 & 180.836461989974 \tabularnewline
Winsorized Mean ( 32 / 42 ) & 1.52849206349206 & 0.00845234443691345 & 180.836461989974 \tabularnewline
Winsorized Mean ( 33 / 42 ) & 1.52849206349206 & 0.00845234443691345 & 180.836461989974 \tabularnewline
Winsorized Mean ( 34 / 42 ) & 1.52579365079365 & 0.00814577750163065 & 187.310990324522 \tabularnewline
Winsorized Mean ( 35 / 42 ) & 1.52579365079365 & 0.00814577750163065 & 187.310990324522 \tabularnewline
Winsorized Mean ( 36 / 42 ) & 1.52579365079365 & 0.00814577750163065 & 187.310990324522 \tabularnewline
Winsorized Mean ( 37 / 42 ) & 1.52579365079365 & 0.00814577750163065 & 187.310990324522 \tabularnewline
Winsorized Mean ( 38 / 42 ) & 1.52579365079365 & 0.00814577750163065 & 187.310990324522 \tabularnewline
Winsorized Mean ( 39 / 42 ) & 1.52269841269841 & 0.00780184162094159 & 195.171664163395 \tabularnewline
Winsorized Mean ( 40 / 42 ) & 1.52269841269841 & 0.00780184162094159 & 195.171664163395 \tabularnewline
Winsorized Mean ( 41 / 42 ) & 1.51944444444444 & 0.00744700264029194 & 204.034363600666 \tabularnewline
Winsorized Mean ( 42 / 42 ) & 1.51944444444444 & 0.00677184231391392 & 224.376820074868 \tabularnewline
Trimmed Mean ( 1 / 42 ) & 1.54306451612903 & 0.0128571084462924 & 120.016450244223 \tabularnewline
Trimmed Mean ( 2 / 42 ) & 1.54163934426230 & 0.0126997577048778 & 121.391240690377 \tabularnewline
Trimmed Mean ( 3 / 42 ) & 1.54016666666667 & 0.0125244765028857 & 122.972538318213 \tabularnewline
Trimmed Mean ( 4 / 42 ) & 1.53872881355932 & 0.012348779109872 & 124.605744411544 \tabularnewline
Trimmed Mean ( 5 / 42 ) & 1.53724137931034 & 0.0121525697129510 & 126.495170619931 \tabularnewline
Trimmed Mean ( 6 / 42 ) & 1.53570175438596 & 0.0119331375483287 & 128.692202546601 \tabularnewline
Trimmed Mean ( 7 / 42 ) & 1.53428571428571 & 0.0117320156499904 & 130.777673680223 \tabularnewline
Trimmed Mean ( 8 / 42 ) & 1.53290909090909 & 0.0115289427678146 & 132.961809402725 \tabularnewline
Trimmed Mean ( 9 / 42 ) & 1.53157407407407 & 0.0113238935375634 & 135.251543030987 \tabularnewline
Trimmed Mean ( 10 / 42 ) & 1.53056603773585 & 0.0111832166226170 & 136.862772973602 \tabularnewline
Trimmed Mean ( 11 / 42 ) & 1.52980769230769 & 0.0110864118712196 & 137.989433378267 \tabularnewline
Trimmed Mean ( 12 / 42 ) & 1.52911764705882 & 0.0109959337900027 & 139.06210025101 \tabularnewline
Trimmed Mean ( 13 / 42 ) & 1.5284 & 0.0108922361377638 & 140.320130840808 \tabularnewline
Trimmed Mean ( 14 / 42 ) & 1.52765306122449 & 0.0107735728562710 & 141.796327142791 \tabularnewline
Trimmed Mean ( 15 / 42 ) & 1.52697916666667 & 0.0106603460491406 & 143.239174378375 \tabularnewline
Trimmed Mean ( 16 / 42 ) & 1.52627659574468 & 0.0105304126916404 & 144.939865173216 \tabularnewline
Trimmed Mean ( 17 / 42 ) & 1.52565217391304 & 0.0104054273342457 & 146.620809016840 \tabularnewline
Trimmed Mean ( 18 / 42 ) & 1.52511111111111 & 0.0102858574038796 & 148.272628253224 \tabularnewline
Trimmed Mean ( 19 / 42 ) & 1.52465909090909 & 0.0101721710226178 & 149.885318239245 \tabularnewline
Trimmed Mean ( 20 / 42 ) & 1.52430232558140 & 0.0100648250398478 & 151.448467265601 \tabularnewline
Trimmed Mean ( 21 / 42 ) & 1.52392857142857 & 0.0099396022544157 & 153.318868544419 \tabularnewline
Trimmed Mean ( 22 / 42 ) & 1.52365853658537 & 0.00981998802767366 & 155.158899612866 \tabularnewline
Trimmed Mean ( 23 / 42 ) & 1.5235 & 0.00970628792672336 & 156.960107870435 \tabularnewline
Trimmed Mean ( 24 / 42 ) & 1.52269230769231 & 0.0096744770947605 & 157.392724462283 \tabularnewline
Trimmed Mean ( 25 / 42 ) & 1.52184210526316 & 0.00963129133881774 & 158.01018282248 \tabularnewline
Trimmed Mean ( 26 / 42 ) & 1.52094594594595 & 0.00957475878984462 & 158.849531286274 \tabularnewline
Trimmed Mean ( 27 / 42 ) & 1.52013888888889 & 0.00953433186839356 & 159.438428394565 \tabularnewline
Trimmed Mean ( 28 / 42 ) & 1.51942857142857 & 0.00951164855051304 & 159.743977435606 \tabularnewline
Trimmed Mean ( 29 / 42 ) & 1.51867647058824 & 0.00947688934178001 & 160.250522699782 \tabularnewline
Trimmed Mean ( 30 / 42 ) & 1.51803030303030 & 0.0094615396100983 & 160.442207673063 \tabularnewline
Trimmed Mean ( 31 / 42 ) & 1.51734375 & 0.0094339868829114 & 160.838017778941 \tabularnewline
Trimmed Mean ( 32 / 42 ) & 1.51661290322581 & 0.00939171509617693 & 161.484125923195 \tabularnewline
Trimmed Mean ( 33 / 42 ) & 1.51583333333333 & 0.00933159285628155 & 162.441006233245 \tabularnewline
Trimmed Mean ( 34 / 42 ) & 1.515 & 0.00924967912002095 & 163.789465595707 \tabularnewline
Trimmed Mean ( 35 / 42 ) & 1.51428571428571 & 0.00918729056782992 & 164.823971017975 \tabularnewline
Trimmed Mean ( 36 / 42 ) & 1.51351851851852 & 0.00910056174845734 & 166.310449876908 \tabularnewline
Trimmed Mean ( 37 / 42 ) & 1.51269230769231 & 0.00898345800310036 & 168.386417253829 \tabularnewline
Trimmed Mean ( 38 / 42 ) & 1.5118 & 0.00882801662611826 & 171.250243857407 \tabularnewline
Trimmed Mean ( 39 / 42 ) & 1.51083333333333 & 0.00862349448949798 & 175.199663567163 \tabularnewline
Trimmed Mean ( 40 / 42 ) & 1.51 & 0.00842700971600385 & 179.185743328661 \tabularnewline
Trimmed Mean ( 41 / 42 ) & 1.50909090909091 & 0.00816594655061256 & 184.802937386078 \tabularnewline
Trimmed Mean ( 42 / 42 ) & 1.50833333333333 & 0.00790416367046267 & 190.827694898307 \tabularnewline
Median & 1.48 &  &  \tabularnewline
Midrange & 1.63 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 1.51148648648649 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 1.51148648648649 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 1.51148648648649 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 1.51148648648649 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 1.51148648648649 &  &  \tabularnewline
Midmean - Closest Observation & 1.51148648648649 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 1.51148648648649 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 1.51148648648649 &  &  \tabularnewline
Number of observations & 126 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=38695&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]1.54444444444444[/C][C]0.0129984397381417[/C][C]118.817679318275[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]1.53786042044277[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]1.53153584074654[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]1.55126676346416[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 42 )[/C][C]1.54444444444444[/C][C]0.0129984397381417[/C][C]118.817679318275[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 42 )[/C][C]1.54444444444444[/C][C]0.0129984397381417[/C][C]118.817679318275[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 42 )[/C][C]1.54420634920635[/C][C]0.0129498927737686[/C][C]119.244720877868[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 42 )[/C][C]1.54420634920635[/C][C]0.0129498927737686[/C][C]119.244720877868[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 42 )[/C][C]1.54420634920635[/C][C]0.0129498927737686[/C][C]119.244720877868[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 42 )[/C][C]1.54325396825397[/C][C]0.0127624595157006[/C][C]120.921360522667[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 42 )[/C][C]1.54269841269841[/C][C]0.0126568446622861[/C][C]121.886493344998[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 42 )[/C][C]1.54206349206349[/C][C]0.0125388627419385[/C][C]122.982723696765[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 42 )[/C][C]1.53920634920635[/C][C]0.012037825661706[/C][C]127.864150259526[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 42 )[/C][C]1.53682539682540[/C][C]0.0116568125969055[/C][C]131.839247139769[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 42 )[/C][C]1.53595238095238[/C][C]0.0115250884768445[/C][C]133.270333155214[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 42 )[/C][C]1.53595238095238[/C][C]0.0115250884768445[/C][C]133.270333155214[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 42 )[/C][C]1.53595238095238[/C][C]0.0115250884768445[/C][C]133.270333155214[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 42 )[/C][C]1.53484126984127[/C][C]0.0113622790732969[/C][C]135.082166169319[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 42 )[/C][C]1.53484126984127[/C][C]0.0113622790732969[/C][C]135.082166169319[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 42 )[/C][C]1.53357142857143[/C][C]0.0111813133713121[/C][C]137.154856289612[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 42 )[/C][C]1.53222222222222[/C][C]0.0109943066876200[/C][C]139.365061004489[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 42 )[/C][C]1.53079365079365[/C][C]0.0108018829484982[/C][C]141.715445176758[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 42 )[/C][C]1.52928571428571[/C][C]0.0106046881345393[/C][C]144.208457135562[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 42 )[/C][C]1.52928571428571[/C][C]0.0106046881345393[/C][C]144.208457135562[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 42 )[/C][C]1.52761904761905[/C][C]0.0103931775982887[/C][C]146.982867671826[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 42 )[/C][C]1.52587301587302[/C][C]0.0101782649478906[/C][C]149.914845377379[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 42 )[/C][C]1.535[/C][C]0.00923468272759628[/C][C]166.221195170346[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 42 )[/C][C]1.535[/C][C]0.00923468272759628[/C][C]166.221195170346[/C][/ROW]
[ROW][C]Winsorized Mean ( 25 / 42 )[/C][C]1.535[/C][C]0.00923468272759628[/C][C]166.221195170346[/C][/ROW]
[ROW][C]Winsorized Mean ( 26 / 42 )[/C][C]1.53293650793651[/C][C]0.00897903551954073[/C][C]170.72396078626[/C][/ROW]
[ROW][C]Winsorized Mean ( 27 / 42 )[/C][C]1.53079365079365[/C][C]0.00872114975280404[/C][C]175.526586996338[/C][/ROW]
[ROW][C]Winsorized Mean ( 28 / 42 )[/C][C]1.53079365079365[/C][C]0.00872114975280404[/C][C]175.526586996338[/C][/ROW]
[ROW][C]Winsorized Mean ( 29 / 42 )[/C][C]1.52849206349206[/C][C]0.00845234443691345[/C][C]180.836461989974[/C][/ROW]
[ROW][C]Winsorized Mean ( 30 / 42 )[/C][C]1.52849206349206[/C][C]0.00845234443691345[/C][C]180.836461989974[/C][/ROW]
[ROW][C]Winsorized Mean ( 31 / 42 )[/C][C]1.52849206349206[/C][C]0.00845234443691345[/C][C]180.836461989974[/C][/ROW]
[ROW][C]Winsorized Mean ( 32 / 42 )[/C][C]1.52849206349206[/C][C]0.00845234443691345[/C][C]180.836461989974[/C][/ROW]
[ROW][C]Winsorized Mean ( 33 / 42 )[/C][C]1.52849206349206[/C][C]0.00845234443691345[/C][C]180.836461989974[/C][/ROW]
[ROW][C]Winsorized Mean ( 34 / 42 )[/C][C]1.52579365079365[/C][C]0.00814577750163065[/C][C]187.310990324522[/C][/ROW]
[ROW][C]Winsorized Mean ( 35 / 42 )[/C][C]1.52579365079365[/C][C]0.00814577750163065[/C][C]187.310990324522[/C][/ROW]
[ROW][C]Winsorized Mean ( 36 / 42 )[/C][C]1.52579365079365[/C][C]0.00814577750163065[/C][C]187.310990324522[/C][/ROW]
[ROW][C]Winsorized Mean ( 37 / 42 )[/C][C]1.52579365079365[/C][C]0.00814577750163065[/C][C]187.310990324522[/C][/ROW]
[ROW][C]Winsorized Mean ( 38 / 42 )[/C][C]1.52579365079365[/C][C]0.00814577750163065[/C][C]187.310990324522[/C][/ROW]
[ROW][C]Winsorized Mean ( 39 / 42 )[/C][C]1.52269841269841[/C][C]0.00780184162094159[/C][C]195.171664163395[/C][/ROW]
[ROW][C]Winsorized Mean ( 40 / 42 )[/C][C]1.52269841269841[/C][C]0.00780184162094159[/C][C]195.171664163395[/C][/ROW]
[ROW][C]Winsorized Mean ( 41 / 42 )[/C][C]1.51944444444444[/C][C]0.00744700264029194[/C][C]204.034363600666[/C][/ROW]
[ROW][C]Winsorized Mean ( 42 / 42 )[/C][C]1.51944444444444[/C][C]0.00677184231391392[/C][C]224.376820074868[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 42 )[/C][C]1.54306451612903[/C][C]0.0128571084462924[/C][C]120.016450244223[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 42 )[/C][C]1.54163934426230[/C][C]0.0126997577048778[/C][C]121.391240690377[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 42 )[/C][C]1.54016666666667[/C][C]0.0125244765028857[/C][C]122.972538318213[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 42 )[/C][C]1.53872881355932[/C][C]0.012348779109872[/C][C]124.605744411544[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 42 )[/C][C]1.53724137931034[/C][C]0.0121525697129510[/C][C]126.495170619931[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 42 )[/C][C]1.53570175438596[/C][C]0.0119331375483287[/C][C]128.692202546601[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 42 )[/C][C]1.53428571428571[/C][C]0.0117320156499904[/C][C]130.777673680223[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 42 )[/C][C]1.53290909090909[/C][C]0.0115289427678146[/C][C]132.961809402725[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 42 )[/C][C]1.53157407407407[/C][C]0.0113238935375634[/C][C]135.251543030987[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 42 )[/C][C]1.53056603773585[/C][C]0.0111832166226170[/C][C]136.862772973602[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 42 )[/C][C]1.52980769230769[/C][C]0.0110864118712196[/C][C]137.989433378267[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 42 )[/C][C]1.52911764705882[/C][C]0.0109959337900027[/C][C]139.06210025101[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 42 )[/C][C]1.5284[/C][C]0.0108922361377638[/C][C]140.320130840808[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 42 )[/C][C]1.52765306122449[/C][C]0.0107735728562710[/C][C]141.796327142791[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 42 )[/C][C]1.52697916666667[/C][C]0.0106603460491406[/C][C]143.239174378375[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 42 )[/C][C]1.52627659574468[/C][C]0.0105304126916404[/C][C]144.939865173216[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 42 )[/C][C]1.52565217391304[/C][C]0.0104054273342457[/C][C]146.620809016840[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 42 )[/C][C]1.52511111111111[/C][C]0.0102858574038796[/C][C]148.272628253224[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 42 )[/C][C]1.52465909090909[/C][C]0.0101721710226178[/C][C]149.885318239245[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 42 )[/C][C]1.52430232558140[/C][C]0.0100648250398478[/C][C]151.448467265601[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 42 )[/C][C]1.52392857142857[/C][C]0.0099396022544157[/C][C]153.318868544419[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 42 )[/C][C]1.52365853658537[/C][C]0.00981998802767366[/C][C]155.158899612866[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 42 )[/C][C]1.5235[/C][C]0.00970628792672336[/C][C]156.960107870435[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 42 )[/C][C]1.52269230769231[/C][C]0.0096744770947605[/C][C]157.392724462283[/C][/ROW]
[ROW][C]Trimmed Mean ( 25 / 42 )[/C][C]1.52184210526316[/C][C]0.00963129133881774[/C][C]158.01018282248[/C][/ROW]
[ROW][C]Trimmed Mean ( 26 / 42 )[/C][C]1.52094594594595[/C][C]0.00957475878984462[/C][C]158.849531286274[/C][/ROW]
[ROW][C]Trimmed Mean ( 27 / 42 )[/C][C]1.52013888888889[/C][C]0.00953433186839356[/C][C]159.438428394565[/C][/ROW]
[ROW][C]Trimmed Mean ( 28 / 42 )[/C][C]1.51942857142857[/C][C]0.00951164855051304[/C][C]159.743977435606[/C][/ROW]
[ROW][C]Trimmed Mean ( 29 / 42 )[/C][C]1.51867647058824[/C][C]0.00947688934178001[/C][C]160.250522699782[/C][/ROW]
[ROW][C]Trimmed Mean ( 30 / 42 )[/C][C]1.51803030303030[/C][C]0.0094615396100983[/C][C]160.442207673063[/C][/ROW]
[ROW][C]Trimmed Mean ( 31 / 42 )[/C][C]1.51734375[/C][C]0.0094339868829114[/C][C]160.838017778941[/C][/ROW]
[ROW][C]Trimmed Mean ( 32 / 42 )[/C][C]1.51661290322581[/C][C]0.00939171509617693[/C][C]161.484125923195[/C][/ROW]
[ROW][C]Trimmed Mean ( 33 / 42 )[/C][C]1.51583333333333[/C][C]0.00933159285628155[/C][C]162.441006233245[/C][/ROW]
[ROW][C]Trimmed Mean ( 34 / 42 )[/C][C]1.515[/C][C]0.00924967912002095[/C][C]163.789465595707[/C][/ROW]
[ROW][C]Trimmed Mean ( 35 / 42 )[/C][C]1.51428571428571[/C][C]0.00918729056782992[/C][C]164.823971017975[/C][/ROW]
[ROW][C]Trimmed Mean ( 36 / 42 )[/C][C]1.51351851851852[/C][C]0.00910056174845734[/C][C]166.310449876908[/C][/ROW]
[ROW][C]Trimmed Mean ( 37 / 42 )[/C][C]1.51269230769231[/C][C]0.00898345800310036[/C][C]168.386417253829[/C][/ROW]
[ROW][C]Trimmed Mean ( 38 / 42 )[/C][C]1.5118[/C][C]0.00882801662611826[/C][C]171.250243857407[/C][/ROW]
[ROW][C]Trimmed Mean ( 39 / 42 )[/C][C]1.51083333333333[/C][C]0.00862349448949798[/C][C]175.199663567163[/C][/ROW]
[ROW][C]Trimmed Mean ( 40 / 42 )[/C][C]1.51[/C][C]0.00842700971600385[/C][C]179.185743328661[/C][/ROW]
[ROW][C]Trimmed Mean ( 41 / 42 )[/C][C]1.50909090909091[/C][C]0.00816594655061256[/C][C]184.802937386078[/C][/ROW]
[ROW][C]Trimmed Mean ( 42 / 42 )[/C][C]1.50833333333333[/C][C]0.00790416367046267[/C][C]190.827694898307[/C][/ROW]
[ROW][C]Median[/C][C]1.48[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]1.63[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]1.51148648648649[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]1.51148648648649[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]1.51148648648649[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]1.51148648648649[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]1.51148648648649[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]1.51148648648649[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]1.51148648648649[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]1.51148648648649[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]126[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=38695&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=38695&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 Mean1.544444444444440.0129984397381417118.817679318275
Geometric Mean1.53786042044277
Harmonic Mean1.53153584074654
Quadratic Mean1.55126676346416
Winsorized Mean ( 1 / 42 )1.544444444444440.0129984397381417118.817679318275
Winsorized Mean ( 2 / 42 )1.544444444444440.0129984397381417118.817679318275
Winsorized Mean ( 3 / 42 )1.544206349206350.0129498927737686119.244720877868
Winsorized Mean ( 4 / 42 )1.544206349206350.0129498927737686119.244720877868
Winsorized Mean ( 5 / 42 )1.544206349206350.0129498927737686119.244720877868
Winsorized Mean ( 6 / 42 )1.543253968253970.0127624595157006120.921360522667
Winsorized Mean ( 7 / 42 )1.542698412698410.0126568446622861121.886493344998
Winsorized Mean ( 8 / 42 )1.542063492063490.0125388627419385122.982723696765
Winsorized Mean ( 9 / 42 )1.539206349206350.012037825661706127.864150259526
Winsorized Mean ( 10 / 42 )1.536825396825400.0116568125969055131.839247139769
Winsorized Mean ( 11 / 42 )1.535952380952380.0115250884768445133.270333155214
Winsorized Mean ( 12 / 42 )1.535952380952380.0115250884768445133.270333155214
Winsorized Mean ( 13 / 42 )1.535952380952380.0115250884768445133.270333155214
Winsorized Mean ( 14 / 42 )1.534841269841270.0113622790732969135.082166169319
Winsorized Mean ( 15 / 42 )1.534841269841270.0113622790732969135.082166169319
Winsorized Mean ( 16 / 42 )1.533571428571430.0111813133713121137.154856289612
Winsorized Mean ( 17 / 42 )1.532222222222220.0109943066876200139.365061004489
Winsorized Mean ( 18 / 42 )1.530793650793650.0108018829484982141.715445176758
Winsorized Mean ( 19 / 42 )1.529285714285710.0106046881345393144.208457135562
Winsorized Mean ( 20 / 42 )1.529285714285710.0106046881345393144.208457135562
Winsorized Mean ( 21 / 42 )1.527619047619050.0103931775982887146.982867671826
Winsorized Mean ( 22 / 42 )1.525873015873020.0101782649478906149.914845377379
Winsorized Mean ( 23 / 42 )1.5350.00923468272759628166.221195170346
Winsorized Mean ( 24 / 42 )1.5350.00923468272759628166.221195170346
Winsorized Mean ( 25 / 42 )1.5350.00923468272759628166.221195170346
Winsorized Mean ( 26 / 42 )1.532936507936510.00897903551954073170.72396078626
Winsorized Mean ( 27 / 42 )1.530793650793650.00872114975280404175.526586996338
Winsorized Mean ( 28 / 42 )1.530793650793650.00872114975280404175.526586996338
Winsorized Mean ( 29 / 42 )1.528492063492060.00845234443691345180.836461989974
Winsorized Mean ( 30 / 42 )1.528492063492060.00845234443691345180.836461989974
Winsorized Mean ( 31 / 42 )1.528492063492060.00845234443691345180.836461989974
Winsorized Mean ( 32 / 42 )1.528492063492060.00845234443691345180.836461989974
Winsorized Mean ( 33 / 42 )1.528492063492060.00845234443691345180.836461989974
Winsorized Mean ( 34 / 42 )1.525793650793650.00814577750163065187.310990324522
Winsorized Mean ( 35 / 42 )1.525793650793650.00814577750163065187.310990324522
Winsorized Mean ( 36 / 42 )1.525793650793650.00814577750163065187.310990324522
Winsorized Mean ( 37 / 42 )1.525793650793650.00814577750163065187.310990324522
Winsorized Mean ( 38 / 42 )1.525793650793650.00814577750163065187.310990324522
Winsorized Mean ( 39 / 42 )1.522698412698410.00780184162094159195.171664163395
Winsorized Mean ( 40 / 42 )1.522698412698410.00780184162094159195.171664163395
Winsorized Mean ( 41 / 42 )1.519444444444440.00744700264029194204.034363600666
Winsorized Mean ( 42 / 42 )1.519444444444440.00677184231391392224.376820074868
Trimmed Mean ( 1 / 42 )1.543064516129030.0128571084462924120.016450244223
Trimmed Mean ( 2 / 42 )1.541639344262300.0126997577048778121.391240690377
Trimmed Mean ( 3 / 42 )1.540166666666670.0125244765028857122.972538318213
Trimmed Mean ( 4 / 42 )1.538728813559320.012348779109872124.605744411544
Trimmed Mean ( 5 / 42 )1.537241379310340.0121525697129510126.495170619931
Trimmed Mean ( 6 / 42 )1.535701754385960.0119331375483287128.692202546601
Trimmed Mean ( 7 / 42 )1.534285714285710.0117320156499904130.777673680223
Trimmed Mean ( 8 / 42 )1.532909090909090.0115289427678146132.961809402725
Trimmed Mean ( 9 / 42 )1.531574074074070.0113238935375634135.251543030987
Trimmed Mean ( 10 / 42 )1.530566037735850.0111832166226170136.862772973602
Trimmed Mean ( 11 / 42 )1.529807692307690.0110864118712196137.989433378267
Trimmed Mean ( 12 / 42 )1.529117647058820.0109959337900027139.06210025101
Trimmed Mean ( 13 / 42 )1.52840.0108922361377638140.320130840808
Trimmed Mean ( 14 / 42 )1.527653061224490.0107735728562710141.796327142791
Trimmed Mean ( 15 / 42 )1.526979166666670.0106603460491406143.239174378375
Trimmed Mean ( 16 / 42 )1.526276595744680.0105304126916404144.939865173216
Trimmed Mean ( 17 / 42 )1.525652173913040.0104054273342457146.620809016840
Trimmed Mean ( 18 / 42 )1.525111111111110.0102858574038796148.272628253224
Trimmed Mean ( 19 / 42 )1.524659090909090.0101721710226178149.885318239245
Trimmed Mean ( 20 / 42 )1.524302325581400.0100648250398478151.448467265601
Trimmed Mean ( 21 / 42 )1.523928571428570.0099396022544157153.318868544419
Trimmed Mean ( 22 / 42 )1.523658536585370.00981998802767366155.158899612866
Trimmed Mean ( 23 / 42 )1.52350.00970628792672336156.960107870435
Trimmed Mean ( 24 / 42 )1.522692307692310.0096744770947605157.392724462283
Trimmed Mean ( 25 / 42 )1.521842105263160.00963129133881774158.01018282248
Trimmed Mean ( 26 / 42 )1.520945945945950.00957475878984462158.849531286274
Trimmed Mean ( 27 / 42 )1.520138888888890.00953433186839356159.438428394565
Trimmed Mean ( 28 / 42 )1.519428571428570.00951164855051304159.743977435606
Trimmed Mean ( 29 / 42 )1.518676470588240.00947688934178001160.250522699782
Trimmed Mean ( 30 / 42 )1.518030303030300.0094615396100983160.442207673063
Trimmed Mean ( 31 / 42 )1.517343750.0094339868829114160.838017778941
Trimmed Mean ( 32 / 42 )1.516612903225810.00939171509617693161.484125923195
Trimmed Mean ( 33 / 42 )1.515833333333330.00933159285628155162.441006233245
Trimmed Mean ( 34 / 42 )1.5150.00924967912002095163.789465595707
Trimmed Mean ( 35 / 42 )1.514285714285710.00918729056782992164.823971017975
Trimmed Mean ( 36 / 42 )1.513518518518520.00910056174845734166.310449876908
Trimmed Mean ( 37 / 42 )1.512692307692310.00898345800310036168.386417253829
Trimmed Mean ( 38 / 42 )1.51180.00882801662611826171.250243857407
Trimmed Mean ( 39 / 42 )1.510833333333330.00862349448949798175.199663567163
Trimmed Mean ( 40 / 42 )1.510.00842700971600385179.185743328661
Trimmed Mean ( 41 / 42 )1.509090909090910.00816594655061256184.802937386078
Trimmed Mean ( 42 / 42 )1.508333333333330.00790416367046267190.827694898307
Median1.48
Midrange1.63
Midmean - Weighted Average at Xnp1.51148648648649
Midmean - Weighted Average at X(n+1)p1.51148648648649
Midmean - Empirical Distribution Function1.51148648648649
Midmean - Empirical Distribution Function - Averaging1.51148648648649
Midmean - Empirical Distribution Function - Interpolation1.51148648648649
Midmean - Closest Observation1.51148648648649
Midmean - True Basic - Statistics Graphics Toolkit1.51148648648649
Midmean - MS Excel (old versions)1.51148648648649
Number of observations126



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')