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Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationTue, 15 Nov 2011 14:47:07 -0500
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2011/Nov/15/t1321386449f3kt6awx1mf2t3o.htm/, Retrieved Thu, 28 Mar 2024 22:54:33 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=143452, Retrieved Thu, 28 Mar 2024 22:54:33 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact74
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Histogram] [Histogram] [2011-11-15 19:20:24] [74b1e5a3104ff0b2404b2865a63336ad]
- RMPD    [Central Tendency] [Rekenkundig gemid...] [2011-11-15 19:47:07] [f9bdb25068ab2a4592adc645515299ca] [Current]
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Dataseries X:
76035
74427
73354
73081
75309
75463
75910
76151
76882
78632
80137
82490
79896
81303
79344
81355
82328
79669
77249
75101
72520
72438
72653
71429
69189
66451
63354
61379
61880
62274
62429
63905
63917
64295
61930
60440
59353
58695
60569
60386
60938
61795
63304
64270
63492
61333
59341
58412
58725
59277
58562
57858
58790
58243
57044
57339
59429
60575
61950
61712




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

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 2 seconds \tabularnewline
R Server & 'AstonUniversity' @ aston.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=143452&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'AstonUniversity' @ aston.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=143452&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=143452&T=0

As an alternative you can also use a QR Code:  

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

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







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean67433.18333333331065.5924090376663.2823420675759
Geometric Mean66950.306416377
Harmonic Mean66484.3851753748
Quadratic Mean67928.1087490051
Winsorized Mean ( 1 / 20 )67435.41064.1473035857563.3703621413783
Winsorized Mean ( 2 / 20 )67420.26666666671053.9441507053563.9694870184019
Winsorized Mean ( 3 / 20 )67436.91666666671050.4539732336264.1978786172565
Winsorized Mean ( 4 / 20 )67370.451031.9390946927965.2852967258272
Winsorized Mean ( 5 / 20 )67362.86666666671025.9258405007465.6605614239988
Winsorized Mean ( 6 / 20 )67353.46666666671019.3270637903866.0764037954726
Winsorized Mean ( 7 / 20 )67319.051011.1190169024766.5787596461493
Winsorized Mean ( 8 / 20 )67232.7833333333991.0442321653967.8403457194161
Winsorized Mean ( 9 / 20 )67098.3833333333941.41384149360471.2740565051372
Winsorized Mean ( 10 / 20 )67047.8833333333928.83476180699472.1849419189433
Winsorized Mean ( 11 / 20 )66916.0666666667904.90323915933473.9483115662538
Winsorized Mean ( 12 / 20 )66908.0666666667898.75155150747974.4455645772645
Winsorized Mean ( 13 / 20 )67088.3333333333865.83833698928877.4836715669282
Winsorized Mean ( 14 / 20 )66996.6333333333846.33487647916979.1609033200257
Winsorized Mean ( 15 / 20 )66990.3833333333835.60510673527680.1699065663516
Winsorized Mean ( 16 / 20 )66936.5166666667826.0709793895781.0299820920109
Winsorized Mean ( 17 / 20 )66848.4781.05352298207685.5874764443436
Winsorized Mean ( 18 / 20 )66645713.82947804697393.3626335834992
Winsorized Mean ( 19 / 20 )66573.1166666667698.27827288228995.3389490294066
Winsorized Mean ( 20 / 20 )66541.45661.981768496712100.518553782997
Trimmed Mean ( 1 / 20 )67352.70689655171055.708724542963.7985699376635
Trimmed Mean ( 2 / 20 )67264.10714285711044.4088627154464.4039988017453
Trimmed Mean ( 3 / 20 )67177.35185185191036.0716851635564.8385172704028
Trimmed Mean ( 4 / 20 )67077.51923076921026.1151504723865.3703623807619
Trimmed Mean ( 5 / 20 )66989.641019.4628488631965.7107221461781
Trimmed Mean ( 6 / 20 )66896.33333333331011.5202743229866.1344463689646
Trimmed Mean ( 7 / 20 )66796.95652173911001.79108198266.6775315962927
Trimmed Mean ( 8 / 20 )66695.25990.00870013741867.3683473597175
Trimmed Mean ( 9 / 20 )66599.2619047619978.5788832440468.057121449404
Trimmed Mean ( 10 / 20 )66516.075974.58294656102268.250809471593
Trimmed Mean ( 11 / 20 )66432.1052631579969.85303310201368.4970846053644
Trimmed Mean ( 12 / 20 )66358.7777777778966.80637012755868.6370920053233
Trimmed Mean ( 13 / 20 )66278960.85012956209868.9784993110276
Trimmed Mean ( 14 / 20 )66161.125956.69288895139269.1560748115496
Trimmed Mean ( 15 / 20 )66041.7666666667951.86184847506969.3816721118395
Trimmed Mean ( 16 / 20 )65906.25942.74495732594269.9088862664834
Trimmed Mean ( 17 / 20 )65757.6538461538926.83820999934770.948363087232
Trimmed Mean ( 18 / 20 )65597.25912.24039636538271.9078548388753
Trimmed Mean ( 19 / 20 )65438.5907.47178590179472.1107818630095
Trimmed Mean ( 20 / 20 )65259.35895.79439686089272.8508128971186
Median63698.5
Midrange69767
Midmean - Weighted Average at Xnp65861.064516129
Midmean - Weighted Average at X(n+1)p66041.7666666667
Midmean - Empirical Distribution Function65861.064516129
Midmean - Empirical Distribution Function - Averaging66041.7666666667
Midmean - Empirical Distribution Function - Interpolation66041.7666666667
Midmean - Closest Observation65861.064516129
Midmean - True Basic - Statistics Graphics Toolkit66041.7666666667
Midmean - MS Excel (old versions)66161.125
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 67433.1833333333 & 1065.59240903766 & 63.2823420675759 \tabularnewline
Geometric Mean & 66950.306416377 &  &  \tabularnewline
Harmonic Mean & 66484.3851753748 &  &  \tabularnewline
Quadratic Mean & 67928.1087490051 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 67435.4 & 1064.14730358575 & 63.3703621413783 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 67420.2666666667 & 1053.94415070535 & 63.9694870184019 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 67436.9166666667 & 1050.45397323362 & 64.1978786172565 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 67370.45 & 1031.93909469279 & 65.2852967258272 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 67362.8666666667 & 1025.92584050074 & 65.6605614239988 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 67353.4666666667 & 1019.32706379038 & 66.0764037954726 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 67319.05 & 1011.11901690247 & 66.5787596461493 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 67232.7833333333 & 991.04423216539 & 67.8403457194161 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 67098.3833333333 & 941.413841493604 & 71.2740565051372 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 67047.8833333333 & 928.834761806994 & 72.1849419189433 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 66916.0666666667 & 904.903239159334 & 73.9483115662538 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 66908.0666666667 & 898.751551507479 & 74.4455645772645 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 67088.3333333333 & 865.838336989288 & 77.4836715669282 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 66996.6333333333 & 846.334876479169 & 79.1609033200257 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 66990.3833333333 & 835.605106735276 & 80.1699065663516 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 66936.5166666667 & 826.07097938957 & 81.0299820920109 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 66848.4 & 781.053522982076 & 85.5874764443436 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 66645 & 713.829478046973 & 93.3626335834992 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 66573.1166666667 & 698.278272882289 & 95.3389490294066 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 66541.45 & 661.981768496712 & 100.518553782997 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 67352.7068965517 & 1055.7087245429 & 63.7985699376635 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 67264.1071428571 & 1044.40886271544 & 64.4039988017453 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 67177.3518518519 & 1036.07168516355 & 64.8385172704028 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 67077.5192307692 & 1026.11515047238 & 65.3703623807619 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 66989.64 & 1019.46284886319 & 65.7107221461781 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 66896.3333333333 & 1011.52027432298 & 66.1344463689646 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 66796.9565217391 & 1001.791081982 & 66.6775315962927 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 66695.25 & 990.008700137418 & 67.3683473597175 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 66599.2619047619 & 978.57888324404 & 68.057121449404 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 66516.075 & 974.582946561022 & 68.250809471593 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 66432.1052631579 & 969.853033102013 & 68.4970846053644 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 66358.7777777778 & 966.806370127558 & 68.6370920053233 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 66278 & 960.850129562098 & 68.9784993110276 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 66161.125 & 956.692888951392 & 69.1560748115496 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 66041.7666666667 & 951.861848475069 & 69.3816721118395 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 65906.25 & 942.744957325942 & 69.9088862664834 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 65757.6538461538 & 926.838209999347 & 70.948363087232 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 65597.25 & 912.240396365382 & 71.9078548388753 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 65438.5 & 907.471785901794 & 72.1107818630095 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 65259.35 & 895.794396860892 & 72.8508128971186 \tabularnewline
Median & 63698.5 &  &  \tabularnewline
Midrange & 69767 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 65861.064516129 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 66041.7666666667 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 65861.064516129 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 66041.7666666667 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 66041.7666666667 &  &  \tabularnewline
Midmean - Closest Observation & 65861.064516129 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 66041.7666666667 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 66161.125 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=143452&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]67433.1833333333[/C][C]1065.59240903766[/C][C]63.2823420675759[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]66950.306416377[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]66484.3851753748[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]67928.1087490051[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]67435.4[/C][C]1064.14730358575[/C][C]63.3703621413783[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]67420.2666666667[/C][C]1053.94415070535[/C][C]63.9694870184019[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]67436.9166666667[/C][C]1050.45397323362[/C][C]64.1978786172565[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]67370.45[/C][C]1031.93909469279[/C][C]65.2852967258272[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]67362.8666666667[/C][C]1025.92584050074[/C][C]65.6605614239988[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]67353.4666666667[/C][C]1019.32706379038[/C][C]66.0764037954726[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]67319.05[/C][C]1011.11901690247[/C][C]66.5787596461493[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]67232.7833333333[/C][C]991.04423216539[/C][C]67.8403457194161[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]67098.3833333333[/C][C]941.413841493604[/C][C]71.2740565051372[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]67047.8833333333[/C][C]928.834761806994[/C][C]72.1849419189433[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]66916.0666666667[/C][C]904.903239159334[/C][C]73.9483115662538[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]66908.0666666667[/C][C]898.751551507479[/C][C]74.4455645772645[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]67088.3333333333[/C][C]865.838336989288[/C][C]77.4836715669282[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]66996.6333333333[/C][C]846.334876479169[/C][C]79.1609033200257[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]66990.3833333333[/C][C]835.605106735276[/C][C]80.1699065663516[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]66936.5166666667[/C][C]826.07097938957[/C][C]81.0299820920109[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]66848.4[/C][C]781.053522982076[/C][C]85.5874764443436[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]66645[/C][C]713.829478046973[/C][C]93.3626335834992[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]66573.1166666667[/C][C]698.278272882289[/C][C]95.3389490294066[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]66541.45[/C][C]661.981768496712[/C][C]100.518553782997[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]67352.7068965517[/C][C]1055.7087245429[/C][C]63.7985699376635[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]67264.1071428571[/C][C]1044.40886271544[/C][C]64.4039988017453[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]67177.3518518519[/C][C]1036.07168516355[/C][C]64.8385172704028[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]67077.5192307692[/C][C]1026.11515047238[/C][C]65.3703623807619[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]66989.64[/C][C]1019.46284886319[/C][C]65.7107221461781[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]66896.3333333333[/C][C]1011.52027432298[/C][C]66.1344463689646[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]66796.9565217391[/C][C]1001.791081982[/C][C]66.6775315962927[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]66695.25[/C][C]990.008700137418[/C][C]67.3683473597175[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]66599.2619047619[/C][C]978.57888324404[/C][C]68.057121449404[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]66516.075[/C][C]974.582946561022[/C][C]68.250809471593[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]66432.1052631579[/C][C]969.853033102013[/C][C]68.4970846053644[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]66358.7777777778[/C][C]966.806370127558[/C][C]68.6370920053233[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]66278[/C][C]960.850129562098[/C][C]68.9784993110276[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]66161.125[/C][C]956.692888951392[/C][C]69.1560748115496[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]66041.7666666667[/C][C]951.861848475069[/C][C]69.3816721118395[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]65906.25[/C][C]942.744957325942[/C][C]69.9088862664834[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]65757.6538461538[/C][C]926.838209999347[/C][C]70.948363087232[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]65597.25[/C][C]912.240396365382[/C][C]71.9078548388753[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]65438.5[/C][C]907.471785901794[/C][C]72.1107818630095[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]65259.35[/C][C]895.794396860892[/C][C]72.8508128971186[/C][/ROW]
[ROW][C]Median[/C][C]63698.5[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]69767[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]65861.064516129[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]66041.7666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]65861.064516129[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]66041.7666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]66041.7666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]65861.064516129[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]66041.7666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]66161.125[/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=143452&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=143452&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 Mean67433.18333333331065.5924090376663.2823420675759
Geometric Mean66950.306416377
Harmonic Mean66484.3851753748
Quadratic Mean67928.1087490051
Winsorized Mean ( 1 / 20 )67435.41064.1473035857563.3703621413783
Winsorized Mean ( 2 / 20 )67420.26666666671053.9441507053563.9694870184019
Winsorized Mean ( 3 / 20 )67436.91666666671050.4539732336264.1978786172565
Winsorized Mean ( 4 / 20 )67370.451031.9390946927965.2852967258272
Winsorized Mean ( 5 / 20 )67362.86666666671025.9258405007465.6605614239988
Winsorized Mean ( 6 / 20 )67353.46666666671019.3270637903866.0764037954726
Winsorized Mean ( 7 / 20 )67319.051011.1190169024766.5787596461493
Winsorized Mean ( 8 / 20 )67232.7833333333991.0442321653967.8403457194161
Winsorized Mean ( 9 / 20 )67098.3833333333941.41384149360471.2740565051372
Winsorized Mean ( 10 / 20 )67047.8833333333928.83476180699472.1849419189433
Winsorized Mean ( 11 / 20 )66916.0666666667904.90323915933473.9483115662538
Winsorized Mean ( 12 / 20 )66908.0666666667898.75155150747974.4455645772645
Winsorized Mean ( 13 / 20 )67088.3333333333865.83833698928877.4836715669282
Winsorized Mean ( 14 / 20 )66996.6333333333846.33487647916979.1609033200257
Winsorized Mean ( 15 / 20 )66990.3833333333835.60510673527680.1699065663516
Winsorized Mean ( 16 / 20 )66936.5166666667826.0709793895781.0299820920109
Winsorized Mean ( 17 / 20 )66848.4781.05352298207685.5874764443436
Winsorized Mean ( 18 / 20 )66645713.82947804697393.3626335834992
Winsorized Mean ( 19 / 20 )66573.1166666667698.27827288228995.3389490294066
Winsorized Mean ( 20 / 20 )66541.45661.981768496712100.518553782997
Trimmed Mean ( 1 / 20 )67352.70689655171055.708724542963.7985699376635
Trimmed Mean ( 2 / 20 )67264.10714285711044.4088627154464.4039988017453
Trimmed Mean ( 3 / 20 )67177.35185185191036.0716851635564.8385172704028
Trimmed Mean ( 4 / 20 )67077.51923076921026.1151504723865.3703623807619
Trimmed Mean ( 5 / 20 )66989.641019.4628488631965.7107221461781
Trimmed Mean ( 6 / 20 )66896.33333333331011.5202743229866.1344463689646
Trimmed Mean ( 7 / 20 )66796.95652173911001.79108198266.6775315962927
Trimmed Mean ( 8 / 20 )66695.25990.00870013741867.3683473597175
Trimmed Mean ( 9 / 20 )66599.2619047619978.5788832440468.057121449404
Trimmed Mean ( 10 / 20 )66516.075974.58294656102268.250809471593
Trimmed Mean ( 11 / 20 )66432.1052631579969.85303310201368.4970846053644
Trimmed Mean ( 12 / 20 )66358.7777777778966.80637012755868.6370920053233
Trimmed Mean ( 13 / 20 )66278960.85012956209868.9784993110276
Trimmed Mean ( 14 / 20 )66161.125956.69288895139269.1560748115496
Trimmed Mean ( 15 / 20 )66041.7666666667951.86184847506969.3816721118395
Trimmed Mean ( 16 / 20 )65906.25942.74495732594269.9088862664834
Trimmed Mean ( 17 / 20 )65757.6538461538926.83820999934770.948363087232
Trimmed Mean ( 18 / 20 )65597.25912.24039636538271.9078548388753
Trimmed Mean ( 19 / 20 )65438.5907.47178590179472.1107818630095
Trimmed Mean ( 20 / 20 )65259.35895.79439686089272.8508128971186
Median63698.5
Midrange69767
Midmean - Weighted Average at Xnp65861.064516129
Midmean - Weighted Average at X(n+1)p66041.7666666667
Midmean - Empirical Distribution Function65861.064516129
Midmean - Empirical Distribution Function - Averaging66041.7666666667
Midmean - Empirical Distribution Function - Interpolation66041.7666666667
Midmean - Closest Observation65861.064516129
Midmean - True Basic - Statistics Graphics Toolkit66041.7666666667
Midmean - MS Excel (old versions)66161.125
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')