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of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationMon, 20 Oct 2008 13:39:13 -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/2008/Oct/20/t1224531753ajn5eeh4x0plhgc.htm/, Retrieved Sat, 18 May 2024 17:36:31 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=17989, Retrieved Sat, 18 May 2024 17:36:31 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact148
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Pearson Correlation] [investigating Ass...] [2007-10-22 22:15:01] [8cd6641b921d30ebe00b648d1481bba0]
F RM D    [Central Tendency] [Centrale tendens ...] [2008-10-20 19:39:13] [84a986a411c52e49a8807521f8b9f7a0] [Current]
Feedback Forum
2008-10-27 10:26:26 [dbd46bd47d5f87b1007a5a1708bef00e] [reply
Correcte toepassing van de central tendency-techniek. Zo kan de student zien of er al dan niet outliers aanwezig zijn. Ook had hij hier door gebruik van een back-to-back histogram gemakkelijk een vergelijking kunnen maken tussen zijn reeksen.

Post a new message
Dataseries X:
105.15
105.24
105.57
105.62
106.17
106.27
106.41
106.94
107.16
107.32
107.32
107.35
107.55
107.87
108.37
108.38
107.92
108.03
108.14
108.3
108.64
108.66
109.04
109.03
109.03
109.54
109.75
109.83
109.65
109.82
109.95
110.12
110.15
110.21
109.99
110.14
110.14
110.81
110.97
110.99
109.73
109.81
110.02
110.18
110.21
110.25
110.36
110.51
110.6
110.95
111.18
111.19
111.69
111.7
111.83
111.77
111.73
112.01
111.86
112.04




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=17989&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=17989&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=17989&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 Mean109.2860.241384448499486452.746648259043
Geometric Mean109.270172476283
Harmonic Mean109.254245693435
Quadratic Mean109.301726961044
Winsorized Mean ( 1 / 20 )109.2870.240856792202924453.742653468226
Winsorized Mean ( 2 / 20 )109.2930.236886143954728461.3735450094
Winsorized Mean ( 3 / 20 )109.2940.235948883672321463.210498388219
Winsorized Mean ( 4 / 20 )109.3266666666670.226029304968032483.683594399979
Winsorized Mean ( 5 / 20 )109.3316666666670.22346679965073489.252393812181
Winsorized Mean ( 6 / 20 )109.3426666666670.21971165832979497.664382026291
Winsorized Mean ( 7 / 20 )109.4033333333330.206218942762417530.520290075272
Winsorized Mean ( 8 / 20 )109.3660.188573473220016579.964923658158
Winsorized Mean ( 9 / 20 )109.38850.183655263060217595.618650820442
Winsorized Mean ( 10 / 20 )109.3568333333330.178580955651157612.365595953874
Winsorized Mean ( 11 / 20 )109.3586666666670.176953099002827618.009332884978
Winsorized Mean ( 12 / 20 )109.3946666666670.168775829438449648.165480985307
Winsorized Mean ( 13 / 20 )109.4336666666670.151567696025052722.011810805506
Winsorized Mean ( 14 / 20 )109.3963333333330.142228424270372769.159427129515
Winsorized Mean ( 15 / 20 )109.4013333333330.134237850014993814.981268853114
Winsorized Mean ( 16 / 20 )109.3906666666670.123723052003201884.157518712328
Winsorized Mean ( 17 / 20 )109.4048333333330.111977724698376977.023185888328
Winsorized Mean ( 18 / 20 )109.4138333333330.1069598086158241022.94342846409
Winsorized Mean ( 19 / 20 )109.4170.1064364482408371028.00311179512
Winsorized Mean ( 20 / 20 )109.4936666666670.09110835625801681201.79609383560
Trimmed Mean ( 1 / 20 )109.3098275862070.234333242293959466.471707198431
Trimmed Mean ( 2 / 20 )109.3342857142860.22624214948608483.262230148732
Trimmed Mean ( 3 / 20 )109.3572222222220.218847980618993499.694911110967
Trimmed Mean ( 4 / 20 )109.3815384615380.210007610401384520.84559341673
Trimmed Mean ( 5 / 20 )109.3980.202967173378820538.99356323901
Trimmed Mean ( 6 / 20 )109.4145833333330.194896762618562561.397643877089
Trimmed Mean ( 7 / 20 )109.4302173913040.185763469451479589.083621846797
Trimmed Mean ( 8 / 20 )109.4354545454550.178261944274360613.902507295803
Trimmed Mean ( 9 / 20 )109.4478571428570.173540215047098630.67720132278
Trimmed Mean ( 10 / 20 )109.457750.16856882011625649.335683339984
Trimmed Mean ( 11 / 20 )109.4736842105260.163097428340370671.21649510049
Trimmed Mean ( 12 / 20 )109.4911111111110.155942489286040702.124941139521
Trimmed Mean ( 13 / 20 )109.5052941176470.148485062474033737.483571027874
Trimmed Mean ( 14 / 20 )109.5156250.143254888941513764.480890035888
Trimmed Mean ( 15 / 20 )109.5326666666670.138245104116784792.307744758451
Trimmed Mean ( 16 / 20 )109.5514285714290.133155351731102822.733950586232
Trimmed Mean ( 17 / 20 )109.5746153846150.128567528822233852.272859161209
Trimmed Mean ( 18 / 20 )109.5995833333330.125170143866095875.604836330468
Trimmed Mean ( 19 / 20 )109.6277272727270.120842876443304907.19230209785
Trimmed Mean ( 20 / 20 )109.6610.112724396089242972.824018619569
Median109.815
Midrange108.595
Midmean - Weighted Average at Xnp109.480645161290
Midmean - Weighted Average at X(n+1)p109.532666666667
Midmean - Empirical Distribution Function109.480645161290
Midmean - Empirical Distribution Function - Averaging109.532666666667
Midmean - Empirical Distribution Function - Interpolation109.532666666667
Midmean - Closest Observation109.480645161290
Midmean - True Basic - Statistics Graphics Toolkit109.532666666667
Midmean - MS Excel (old versions)109.515625
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 109.286 & 0.241384448499486 & 452.746648259043 \tabularnewline
Geometric Mean & 109.270172476283 &  &  \tabularnewline
Harmonic Mean & 109.254245693435 &  &  \tabularnewline
Quadratic Mean & 109.301726961044 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 109.287 & 0.240856792202924 & 453.742653468226 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 109.293 & 0.236886143954728 & 461.3735450094 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 109.294 & 0.235948883672321 & 463.210498388219 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 109.326666666667 & 0.226029304968032 & 483.683594399979 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 109.331666666667 & 0.22346679965073 & 489.252393812181 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 109.342666666667 & 0.21971165832979 & 497.664382026291 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 109.403333333333 & 0.206218942762417 & 530.520290075272 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 109.366 & 0.188573473220016 & 579.964923658158 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 109.3885 & 0.183655263060217 & 595.618650820442 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 109.356833333333 & 0.178580955651157 & 612.365595953874 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 109.358666666667 & 0.176953099002827 & 618.009332884978 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 109.394666666667 & 0.168775829438449 & 648.165480985307 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 109.433666666667 & 0.151567696025052 & 722.011810805506 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 109.396333333333 & 0.142228424270372 & 769.159427129515 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 109.401333333333 & 0.134237850014993 & 814.981268853114 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 109.390666666667 & 0.123723052003201 & 884.157518712328 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 109.404833333333 & 0.111977724698376 & 977.023185888328 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 109.413833333333 & 0.106959808615824 & 1022.94342846409 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 109.417 & 0.106436448240837 & 1028.00311179512 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 109.493666666667 & 0.0911083562580168 & 1201.79609383560 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 109.309827586207 & 0.234333242293959 & 466.471707198431 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 109.334285714286 & 0.22624214948608 & 483.262230148732 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 109.357222222222 & 0.218847980618993 & 499.694911110967 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 109.381538461538 & 0.210007610401384 & 520.84559341673 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 109.398 & 0.202967173378820 & 538.99356323901 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 109.414583333333 & 0.194896762618562 & 561.397643877089 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 109.430217391304 & 0.185763469451479 & 589.083621846797 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 109.435454545455 & 0.178261944274360 & 613.902507295803 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 109.447857142857 & 0.173540215047098 & 630.67720132278 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 109.45775 & 0.16856882011625 & 649.335683339984 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 109.473684210526 & 0.163097428340370 & 671.21649510049 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 109.491111111111 & 0.155942489286040 & 702.124941139521 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 109.505294117647 & 0.148485062474033 & 737.483571027874 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 109.515625 & 0.143254888941513 & 764.480890035888 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 109.532666666667 & 0.138245104116784 & 792.307744758451 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 109.551428571429 & 0.133155351731102 & 822.733950586232 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 109.574615384615 & 0.128567528822233 & 852.272859161209 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 109.599583333333 & 0.125170143866095 & 875.604836330468 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 109.627727272727 & 0.120842876443304 & 907.19230209785 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 109.661 & 0.112724396089242 & 972.824018619569 \tabularnewline
Median & 109.815 &  &  \tabularnewline
Midrange & 108.595 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 109.480645161290 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 109.532666666667 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 109.480645161290 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 109.532666666667 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 109.532666666667 &  &  \tabularnewline
Midmean - Closest Observation & 109.480645161290 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 109.532666666667 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 109.515625 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=17989&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]109.286[/C][C]0.241384448499486[/C][C]452.746648259043[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]109.270172476283[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]109.254245693435[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]109.301726961044[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]109.287[/C][C]0.240856792202924[/C][C]453.742653468226[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]109.293[/C][C]0.236886143954728[/C][C]461.3735450094[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]109.294[/C][C]0.235948883672321[/C][C]463.210498388219[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]109.326666666667[/C][C]0.226029304968032[/C][C]483.683594399979[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]109.331666666667[/C][C]0.22346679965073[/C][C]489.252393812181[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]109.342666666667[/C][C]0.21971165832979[/C][C]497.664382026291[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]109.403333333333[/C][C]0.206218942762417[/C][C]530.520290075272[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]109.366[/C][C]0.188573473220016[/C][C]579.964923658158[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]109.3885[/C][C]0.183655263060217[/C][C]595.618650820442[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]109.356833333333[/C][C]0.178580955651157[/C][C]612.365595953874[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]109.358666666667[/C][C]0.176953099002827[/C][C]618.009332884978[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]109.394666666667[/C][C]0.168775829438449[/C][C]648.165480985307[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]109.433666666667[/C][C]0.151567696025052[/C][C]722.011810805506[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]109.396333333333[/C][C]0.142228424270372[/C][C]769.159427129515[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]109.401333333333[/C][C]0.134237850014993[/C][C]814.981268853114[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]109.390666666667[/C][C]0.123723052003201[/C][C]884.157518712328[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]109.404833333333[/C][C]0.111977724698376[/C][C]977.023185888328[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]109.413833333333[/C][C]0.106959808615824[/C][C]1022.94342846409[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]109.417[/C][C]0.106436448240837[/C][C]1028.00311179512[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]109.493666666667[/C][C]0.0911083562580168[/C][C]1201.79609383560[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]109.309827586207[/C][C]0.234333242293959[/C][C]466.471707198431[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]109.334285714286[/C][C]0.22624214948608[/C][C]483.262230148732[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]109.357222222222[/C][C]0.218847980618993[/C][C]499.694911110967[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]109.381538461538[/C][C]0.210007610401384[/C][C]520.84559341673[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]109.398[/C][C]0.202967173378820[/C][C]538.99356323901[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]109.414583333333[/C][C]0.194896762618562[/C][C]561.397643877089[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]109.430217391304[/C][C]0.185763469451479[/C][C]589.083621846797[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]109.435454545455[/C][C]0.178261944274360[/C][C]613.902507295803[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]109.447857142857[/C][C]0.173540215047098[/C][C]630.67720132278[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]109.45775[/C][C]0.16856882011625[/C][C]649.335683339984[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]109.473684210526[/C][C]0.163097428340370[/C][C]671.21649510049[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]109.491111111111[/C][C]0.155942489286040[/C][C]702.124941139521[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]109.505294117647[/C][C]0.148485062474033[/C][C]737.483571027874[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]109.515625[/C][C]0.143254888941513[/C][C]764.480890035888[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]109.532666666667[/C][C]0.138245104116784[/C][C]792.307744758451[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]109.551428571429[/C][C]0.133155351731102[/C][C]822.733950586232[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]109.574615384615[/C][C]0.128567528822233[/C][C]852.272859161209[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]109.599583333333[/C][C]0.125170143866095[/C][C]875.604836330468[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]109.627727272727[/C][C]0.120842876443304[/C][C]907.19230209785[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]109.661[/C][C]0.112724396089242[/C][C]972.824018619569[/C][/ROW]
[ROW][C]Median[/C][C]109.815[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]108.595[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]109.480645161290[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]109.532666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]109.480645161290[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]109.532666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]109.532666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]109.480645161290[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]109.532666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]109.515625[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]60[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=17989&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=17989&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 Mean109.2860.241384448499486452.746648259043
Geometric Mean109.270172476283
Harmonic Mean109.254245693435
Quadratic Mean109.301726961044
Winsorized Mean ( 1 / 20 )109.2870.240856792202924453.742653468226
Winsorized Mean ( 2 / 20 )109.2930.236886143954728461.3735450094
Winsorized Mean ( 3 / 20 )109.2940.235948883672321463.210498388219
Winsorized Mean ( 4 / 20 )109.3266666666670.226029304968032483.683594399979
Winsorized Mean ( 5 / 20 )109.3316666666670.22346679965073489.252393812181
Winsorized Mean ( 6 / 20 )109.3426666666670.21971165832979497.664382026291
Winsorized Mean ( 7 / 20 )109.4033333333330.206218942762417530.520290075272
Winsorized Mean ( 8 / 20 )109.3660.188573473220016579.964923658158
Winsorized Mean ( 9 / 20 )109.38850.183655263060217595.618650820442
Winsorized Mean ( 10 / 20 )109.3568333333330.178580955651157612.365595953874
Winsorized Mean ( 11 / 20 )109.3586666666670.176953099002827618.009332884978
Winsorized Mean ( 12 / 20 )109.3946666666670.168775829438449648.165480985307
Winsorized Mean ( 13 / 20 )109.4336666666670.151567696025052722.011810805506
Winsorized Mean ( 14 / 20 )109.3963333333330.142228424270372769.159427129515
Winsorized Mean ( 15 / 20 )109.4013333333330.134237850014993814.981268853114
Winsorized Mean ( 16 / 20 )109.3906666666670.123723052003201884.157518712328
Winsorized Mean ( 17 / 20 )109.4048333333330.111977724698376977.023185888328
Winsorized Mean ( 18 / 20 )109.4138333333330.1069598086158241022.94342846409
Winsorized Mean ( 19 / 20 )109.4170.1064364482408371028.00311179512
Winsorized Mean ( 20 / 20 )109.4936666666670.09110835625801681201.79609383560
Trimmed Mean ( 1 / 20 )109.3098275862070.234333242293959466.471707198431
Trimmed Mean ( 2 / 20 )109.3342857142860.22624214948608483.262230148732
Trimmed Mean ( 3 / 20 )109.3572222222220.218847980618993499.694911110967
Trimmed Mean ( 4 / 20 )109.3815384615380.210007610401384520.84559341673
Trimmed Mean ( 5 / 20 )109.3980.202967173378820538.99356323901
Trimmed Mean ( 6 / 20 )109.4145833333330.194896762618562561.397643877089
Trimmed Mean ( 7 / 20 )109.4302173913040.185763469451479589.083621846797
Trimmed Mean ( 8 / 20 )109.4354545454550.178261944274360613.902507295803
Trimmed Mean ( 9 / 20 )109.4478571428570.173540215047098630.67720132278
Trimmed Mean ( 10 / 20 )109.457750.16856882011625649.335683339984
Trimmed Mean ( 11 / 20 )109.4736842105260.163097428340370671.21649510049
Trimmed Mean ( 12 / 20 )109.4911111111110.155942489286040702.124941139521
Trimmed Mean ( 13 / 20 )109.5052941176470.148485062474033737.483571027874
Trimmed Mean ( 14 / 20 )109.5156250.143254888941513764.480890035888
Trimmed Mean ( 15 / 20 )109.5326666666670.138245104116784792.307744758451
Trimmed Mean ( 16 / 20 )109.5514285714290.133155351731102822.733950586232
Trimmed Mean ( 17 / 20 )109.5746153846150.128567528822233852.272859161209
Trimmed Mean ( 18 / 20 )109.5995833333330.125170143866095875.604836330468
Trimmed Mean ( 19 / 20 )109.6277272727270.120842876443304907.19230209785
Trimmed Mean ( 20 / 20 )109.6610.112724396089242972.824018619569
Median109.815
Midrange108.595
Midmean - Weighted Average at Xnp109.480645161290
Midmean - Weighted Average at X(n+1)p109.532666666667
Midmean - Empirical Distribution Function109.480645161290
Midmean - Empirical Distribution Function - Averaging109.532666666667
Midmean - Empirical Distribution Function - Interpolation109.532666666667
Midmean - Closest Observation109.480645161290
Midmean - True Basic - Statistics Graphics Toolkit109.532666666667
Midmean - MS Excel (old versions)109.515625
Number of observations60



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')