Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationThu, 03 Jun 2010 15:36:30 +0000
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2010/Jun/03/t1275579564ld8rekv5y2gpimi.htm/, Retrieved Sun, 05 May 2024 09:03:00 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=77396, Retrieved Sun, 05 May 2024 09:03:00 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsKDGP1W52
Estimated Impact199
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Univariate Data Series] [reeks 1] [2010-05-24 14:23:50] [d1b5c9274b6f3a044d3a238a9a6b4dd1]
- RMPD  [Quartiles] [] [2010-06-01 15:07:50] [d1b5c9274b6f3a044d3a238a9a6b4dd1]
- RM D      [Central Tendency] [] [2010-06-03 15:36:30] [07915b1f88a41fb8d82e27c5eaa7bbed] [Current]
Feedback Forum

Post a new message
Dataseries X:
25000
25284
12434,5
33955
14980,5
50831
4198,5
34566
35000
11055,5
20807
21887,29
16977,5
19613,5
14570
24416,5
16825,5
13980
21450,5
27239,5
19078,5
20459,1
20373,5
19306,5
16723,16
11638
20917
17903,5
28218,5
15268
21555
23143
16691
17932,5
30512
41931,5
10853,5
25939,5
14900
25127,76
22063,5
25306,5
31217,5
23201,5
38148
26264
16359
27945,5
16218,5
36003,5
20323,5
20100,5
18741
24426,75
19174,5
13766
18999
21745
34469
13248
16218,5
36003,5
20323,5
20100,5
18741
24426,75
19174,5
13766
18999
21745
34469
13248




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

\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 & 'RServer@AstonUniversity' @ vre.aston.ac.uk \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=77396&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]'RServer@AstonUniversity' @ vre.aston.ac.uk[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=77396&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=77396&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'RServer@AstonUniversity' @ vre.aston.ac.uk







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean22062.2195833333955.4175087444223.0917053344844
Geometric Mean20636.0632936084
Harmonic Mean19028.1610088962
Quadratic Mean23485.1429350624
Winsorized Mean ( 1 / 24 )22031.0459722222888.98094263344124.7823602460581
Winsorized Mean ( 2 / 24 )21931.5598611111857.36950123499625.5800560079637
Winsorized Mean ( 3 / 24 )21866.4765277778830.46246784390326.330481357633
Winsorized Mean ( 4 / 24 )21910.7265277778823.03533488318826.6218540068969
Winsorized Mean ( 5 / 24 )21897.5320833333797.66685006886527.4519770772007
Winsorized Mean ( 6 / 24 )21861.3654166667789.38364072073227.6942215279589
Winsorized Mean ( 7 / 24 )21902.2959722222779.67246163661228.0916629096365
Winsorized Mean ( 8 / 24 )21902.2959722222779.67246163661228.0916629096365
Winsorized Mean ( 9 / 24 )21864.7959722222761.27542086897528.7212687719041
Winsorized Mean ( 10 / 24 )21566.5320833333667.78741246954932.2955055465601
Winsorized Mean ( 11 / 24 )21509.1640277778638.71782976008333.6755340552449
Winsorized Mean ( 12 / 24 )21140.3306944444564.77480837637.4314335216776
Winsorized Mean ( 13 / 24 )21142.94875548.21073320165338.5671922665965
Winsorized Mean ( 14 / 24 )21190.4904166667497.4445483278842.5986986647996
Winsorized Mean ( 15 / 24 )20987.26125463.7159188233145.258875958487
Winsorized Mean ( 16 / 24 )20946.3723611111447.75831997001146.7805318782552
Winsorized Mean ( 17 / 24 )20875.3029166667413.478335106550.4870537202144
Winsorized Mean ( 18 / 24 )20877.7179166667411.48498551084350.7374962679326
Winsorized Mean ( 19 / 24 )20863.4943055556401.45816066317651.9692868394823
Winsorized Mean ( 20 / 24 )20870.2276388889390.20086376651653.4858570978894
Winsorized Mean ( 21 / 24 )20973.1130555556328.50245524617363.8446158335065
Winsorized Mean ( 22 / 24 )20981.9741666667327.33801215949364.0988012001592
Winsorized Mean ( 23 / 24 )21236.9706944444294.40189317173872.1359854912887
Winsorized Mean ( 24 / 24 )20831.9706944444234.56213226615388.8121645773871
Trimmed Mean ( 1 / 24 )21906.433853.42995056133825.6686948771732
Trimmed Mean ( 2 / 24 )21774.4898529412810.58903714865826.8625516199127
Trimmed Mean ( 3 / 24 )21688.8153030303780.00473260037627.8060047542586
Trimmed Mean ( 4 / 24 )21622.19234375755.90507920701928.6043749916759
Trimmed Mean ( 5 / 24 )21538.4243548387729.41225724005829.5284650635507
Trimmed Mean ( 6 / 24 )21452.2385705.46553139247830.4086274174964
Trimmed Mean ( 7 / 24 )21367.5915517241678.53108898290131.4909543551697
Trimmed Mean ( 8 / 24 )21269.3805357143647.70469720908732.8380828908027
Trimmed Mean ( 9 / 24 )21163.8946296296608.86597914197334.7595289515999
Trimmed Mean ( 10 / 24 )21056.0636538462564.52737152925937.2985699467627
Trimmed Mean ( 11 / 24 )20982.5562534.36017841457539.2666913583538
Trimmed Mean ( 12 / 24 )20910.7460416667503.32214159620241.5454523326785
Trimmed Mean ( 13 / 24 )20880.8002173913482.9995416258443.2315114567268
Trimmed Mean ( 14 / 24 )20847.8025460.63076913465745.2592486150345
Trimmed Mean ( 15 / 24 )20805.8407142857443.75110406803746.8862849546752
Trimmed Mean ( 16 / 24 )20784.07025429.84310435566348.3526897125764
Trimmed Mean ( 17 / 24 )20764.8502631579414.92411950912850.0449342104372
Trimmed Mean ( 18 / 24 )20751.8558333333403.19250787681651.4688527884886
Trimmed Mean ( 19 / 24 )20737.0485294118387.01369855196153.5822080897934
Trimmed Mean ( 20 / 24 )20722.0746875366.80148173998756.4939775848266
Trimmed Mean ( 21 / 24 )20704.2963333333340.95035153566760.7252529292888
Trimmed Mean ( 22 / 24 )20671.38324.08510775410463.7838009381294
Trimmed Mean ( 23 / 24 )20632.2842307692298.0953559198469.2137056852284
Trimmed Mean ( 24 / 24 )20553.4120833333268.22349737589776.6279326174364
Median20348.5
Midrange27514.75
Midmean - Weighted Average at Xnp20642.102972973
Midmean - Weighted Average at X(n+1)p20751.8558333333
Midmean - Empirical Distribution Function20642.102972973
Midmean - Empirical Distribution Function - Averaging20751.8558333333
Midmean - Empirical Distribution Function - Interpolation20751.8558333333
Midmean - Closest Observation20642.102972973
Midmean - True Basic - Statistics Graphics Toolkit20751.8558333333
Midmean - MS Excel (old versions)20764.8502631579
Number of observations72

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 22062.2195833333 & 955.41750874442 & 23.0917053344844 \tabularnewline
Geometric Mean & 20636.0632936084 &  &  \tabularnewline
Harmonic Mean & 19028.1610088962 &  &  \tabularnewline
Quadratic Mean & 23485.1429350624 &  &  \tabularnewline
Winsorized Mean ( 1 / 24 ) & 22031.0459722222 & 888.980942633441 & 24.7823602460581 \tabularnewline
Winsorized Mean ( 2 / 24 ) & 21931.5598611111 & 857.369501234996 & 25.5800560079637 \tabularnewline
Winsorized Mean ( 3 / 24 ) & 21866.4765277778 & 830.462467843903 & 26.330481357633 \tabularnewline
Winsorized Mean ( 4 / 24 ) & 21910.7265277778 & 823.035334883188 & 26.6218540068969 \tabularnewline
Winsorized Mean ( 5 / 24 ) & 21897.5320833333 & 797.666850068865 & 27.4519770772007 \tabularnewline
Winsorized Mean ( 6 / 24 ) & 21861.3654166667 & 789.383640720732 & 27.6942215279589 \tabularnewline
Winsorized Mean ( 7 / 24 ) & 21902.2959722222 & 779.672461636612 & 28.0916629096365 \tabularnewline
Winsorized Mean ( 8 / 24 ) & 21902.2959722222 & 779.672461636612 & 28.0916629096365 \tabularnewline
Winsorized Mean ( 9 / 24 ) & 21864.7959722222 & 761.275420868975 & 28.7212687719041 \tabularnewline
Winsorized Mean ( 10 / 24 ) & 21566.5320833333 & 667.787412469549 & 32.2955055465601 \tabularnewline
Winsorized Mean ( 11 / 24 ) & 21509.1640277778 & 638.717829760083 & 33.6755340552449 \tabularnewline
Winsorized Mean ( 12 / 24 ) & 21140.3306944444 & 564.774808376 & 37.4314335216776 \tabularnewline
Winsorized Mean ( 13 / 24 ) & 21142.94875 & 548.210733201653 & 38.5671922665965 \tabularnewline
Winsorized Mean ( 14 / 24 ) & 21190.4904166667 & 497.44454832788 & 42.5986986647996 \tabularnewline
Winsorized Mean ( 15 / 24 ) & 20987.26125 & 463.71591882331 & 45.258875958487 \tabularnewline
Winsorized Mean ( 16 / 24 ) & 20946.3723611111 & 447.758319970011 & 46.7805318782552 \tabularnewline
Winsorized Mean ( 17 / 24 ) & 20875.3029166667 & 413.4783351065 & 50.4870537202144 \tabularnewline
Winsorized Mean ( 18 / 24 ) & 20877.7179166667 & 411.484985510843 & 50.7374962679326 \tabularnewline
Winsorized Mean ( 19 / 24 ) & 20863.4943055556 & 401.458160663176 & 51.9692868394823 \tabularnewline
Winsorized Mean ( 20 / 24 ) & 20870.2276388889 & 390.200863766516 & 53.4858570978894 \tabularnewline
Winsorized Mean ( 21 / 24 ) & 20973.1130555556 & 328.502455246173 & 63.8446158335065 \tabularnewline
Winsorized Mean ( 22 / 24 ) & 20981.9741666667 & 327.338012159493 & 64.0988012001592 \tabularnewline
Winsorized Mean ( 23 / 24 ) & 21236.9706944444 & 294.401893171738 & 72.1359854912887 \tabularnewline
Winsorized Mean ( 24 / 24 ) & 20831.9706944444 & 234.562132266153 & 88.8121645773871 \tabularnewline
Trimmed Mean ( 1 / 24 ) & 21906.433 & 853.429950561338 & 25.6686948771732 \tabularnewline
Trimmed Mean ( 2 / 24 ) & 21774.4898529412 & 810.589037148658 & 26.8625516199127 \tabularnewline
Trimmed Mean ( 3 / 24 ) & 21688.8153030303 & 780.004732600376 & 27.8060047542586 \tabularnewline
Trimmed Mean ( 4 / 24 ) & 21622.19234375 & 755.905079207019 & 28.6043749916759 \tabularnewline
Trimmed Mean ( 5 / 24 ) & 21538.4243548387 & 729.412257240058 & 29.5284650635507 \tabularnewline
Trimmed Mean ( 6 / 24 ) & 21452.2385 & 705.465531392478 & 30.4086274174964 \tabularnewline
Trimmed Mean ( 7 / 24 ) & 21367.5915517241 & 678.531088982901 & 31.4909543551697 \tabularnewline
Trimmed Mean ( 8 / 24 ) & 21269.3805357143 & 647.704697209087 & 32.8380828908027 \tabularnewline
Trimmed Mean ( 9 / 24 ) & 21163.8946296296 & 608.865979141973 & 34.7595289515999 \tabularnewline
Trimmed Mean ( 10 / 24 ) & 21056.0636538462 & 564.527371529259 & 37.2985699467627 \tabularnewline
Trimmed Mean ( 11 / 24 ) & 20982.5562 & 534.360178414575 & 39.2666913583538 \tabularnewline
Trimmed Mean ( 12 / 24 ) & 20910.7460416667 & 503.322141596202 & 41.5454523326785 \tabularnewline
Trimmed Mean ( 13 / 24 ) & 20880.8002173913 & 482.99954162584 & 43.2315114567268 \tabularnewline
Trimmed Mean ( 14 / 24 ) & 20847.8025 & 460.630769134657 & 45.2592486150345 \tabularnewline
Trimmed Mean ( 15 / 24 ) & 20805.8407142857 & 443.751104068037 & 46.8862849546752 \tabularnewline
Trimmed Mean ( 16 / 24 ) & 20784.07025 & 429.843104355663 & 48.3526897125764 \tabularnewline
Trimmed Mean ( 17 / 24 ) & 20764.8502631579 & 414.924119509128 & 50.0449342104372 \tabularnewline
Trimmed Mean ( 18 / 24 ) & 20751.8558333333 & 403.192507876816 & 51.4688527884886 \tabularnewline
Trimmed Mean ( 19 / 24 ) & 20737.0485294118 & 387.013698551961 & 53.5822080897934 \tabularnewline
Trimmed Mean ( 20 / 24 ) & 20722.0746875 & 366.801481739987 & 56.4939775848266 \tabularnewline
Trimmed Mean ( 21 / 24 ) & 20704.2963333333 & 340.950351535667 & 60.7252529292888 \tabularnewline
Trimmed Mean ( 22 / 24 ) & 20671.38 & 324.085107754104 & 63.7838009381294 \tabularnewline
Trimmed Mean ( 23 / 24 ) & 20632.2842307692 & 298.09535591984 & 69.2137056852284 \tabularnewline
Trimmed Mean ( 24 / 24 ) & 20553.4120833333 & 268.223497375897 & 76.6279326174364 \tabularnewline
Median & 20348.5 &  &  \tabularnewline
Midrange & 27514.75 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 20642.102972973 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 20751.8558333333 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 20642.102972973 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 20751.8558333333 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 20751.8558333333 &  &  \tabularnewline
Midmean - Closest Observation & 20642.102972973 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 20751.8558333333 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 20764.8502631579 &  &  \tabularnewline
Number of observations & 72 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=77396&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]22062.2195833333[/C][C]955.41750874442[/C][C]23.0917053344844[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]20636.0632936084[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]19028.1610088962[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]23485.1429350624[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 24 )[/C][C]22031.0459722222[/C][C]888.980942633441[/C][C]24.7823602460581[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 24 )[/C][C]21931.5598611111[/C][C]857.369501234996[/C][C]25.5800560079637[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 24 )[/C][C]21866.4765277778[/C][C]830.462467843903[/C][C]26.330481357633[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 24 )[/C][C]21910.7265277778[/C][C]823.035334883188[/C][C]26.6218540068969[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 24 )[/C][C]21897.5320833333[/C][C]797.666850068865[/C][C]27.4519770772007[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 24 )[/C][C]21861.3654166667[/C][C]789.383640720732[/C][C]27.6942215279589[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 24 )[/C][C]21902.2959722222[/C][C]779.672461636612[/C][C]28.0916629096365[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 24 )[/C][C]21902.2959722222[/C][C]779.672461636612[/C][C]28.0916629096365[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 24 )[/C][C]21864.7959722222[/C][C]761.275420868975[/C][C]28.7212687719041[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 24 )[/C][C]21566.5320833333[/C][C]667.787412469549[/C][C]32.2955055465601[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 24 )[/C][C]21509.1640277778[/C][C]638.717829760083[/C][C]33.6755340552449[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 24 )[/C][C]21140.3306944444[/C][C]564.774808376[/C][C]37.4314335216776[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 24 )[/C][C]21142.94875[/C][C]548.210733201653[/C][C]38.5671922665965[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 24 )[/C][C]21190.4904166667[/C][C]497.44454832788[/C][C]42.5986986647996[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 24 )[/C][C]20987.26125[/C][C]463.71591882331[/C][C]45.258875958487[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 24 )[/C][C]20946.3723611111[/C][C]447.758319970011[/C][C]46.7805318782552[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 24 )[/C][C]20875.3029166667[/C][C]413.4783351065[/C][C]50.4870537202144[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 24 )[/C][C]20877.7179166667[/C][C]411.484985510843[/C][C]50.7374962679326[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 24 )[/C][C]20863.4943055556[/C][C]401.458160663176[/C][C]51.9692868394823[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 24 )[/C][C]20870.2276388889[/C][C]390.200863766516[/C][C]53.4858570978894[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 24 )[/C][C]20973.1130555556[/C][C]328.502455246173[/C][C]63.8446158335065[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 24 )[/C][C]20981.9741666667[/C][C]327.338012159493[/C][C]64.0988012001592[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 24 )[/C][C]21236.9706944444[/C][C]294.401893171738[/C][C]72.1359854912887[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 24 )[/C][C]20831.9706944444[/C][C]234.562132266153[/C][C]88.8121645773871[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 24 )[/C][C]21906.433[/C][C]853.429950561338[/C][C]25.6686948771732[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 24 )[/C][C]21774.4898529412[/C][C]810.589037148658[/C][C]26.8625516199127[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 24 )[/C][C]21688.8153030303[/C][C]780.004732600376[/C][C]27.8060047542586[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 24 )[/C][C]21622.19234375[/C][C]755.905079207019[/C][C]28.6043749916759[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 24 )[/C][C]21538.4243548387[/C][C]729.412257240058[/C][C]29.5284650635507[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 24 )[/C][C]21452.2385[/C][C]705.465531392478[/C][C]30.4086274174964[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 24 )[/C][C]21367.5915517241[/C][C]678.531088982901[/C][C]31.4909543551697[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 24 )[/C][C]21269.3805357143[/C][C]647.704697209087[/C][C]32.8380828908027[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 24 )[/C][C]21163.8946296296[/C][C]608.865979141973[/C][C]34.7595289515999[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 24 )[/C][C]21056.0636538462[/C][C]564.527371529259[/C][C]37.2985699467627[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 24 )[/C][C]20982.5562[/C][C]534.360178414575[/C][C]39.2666913583538[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 24 )[/C][C]20910.7460416667[/C][C]503.322141596202[/C][C]41.5454523326785[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 24 )[/C][C]20880.8002173913[/C][C]482.99954162584[/C][C]43.2315114567268[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 24 )[/C][C]20847.8025[/C][C]460.630769134657[/C][C]45.2592486150345[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 24 )[/C][C]20805.8407142857[/C][C]443.751104068037[/C][C]46.8862849546752[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 24 )[/C][C]20784.07025[/C][C]429.843104355663[/C][C]48.3526897125764[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 24 )[/C][C]20764.8502631579[/C][C]414.924119509128[/C][C]50.0449342104372[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 24 )[/C][C]20751.8558333333[/C][C]403.192507876816[/C][C]51.4688527884886[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 24 )[/C][C]20737.0485294118[/C][C]387.013698551961[/C][C]53.5822080897934[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 24 )[/C][C]20722.0746875[/C][C]366.801481739987[/C][C]56.4939775848266[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 24 )[/C][C]20704.2963333333[/C][C]340.950351535667[/C][C]60.7252529292888[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 24 )[/C][C]20671.38[/C][C]324.085107754104[/C][C]63.7838009381294[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 24 )[/C][C]20632.2842307692[/C][C]298.09535591984[/C][C]69.2137056852284[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 24 )[/C][C]20553.4120833333[/C][C]268.223497375897[/C][C]76.6279326174364[/C][/ROW]
[ROW][C]Median[/C][C]20348.5[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]27514.75[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]20642.102972973[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]20751.8558333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]20642.102972973[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]20751.8558333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]20751.8558333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]20642.102972973[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]20751.8558333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]20764.8502631579[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]72[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=77396&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=77396&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 Mean22062.2195833333955.4175087444223.0917053344844
Geometric Mean20636.0632936084
Harmonic Mean19028.1610088962
Quadratic Mean23485.1429350624
Winsorized Mean ( 1 / 24 )22031.0459722222888.98094263344124.7823602460581
Winsorized Mean ( 2 / 24 )21931.5598611111857.36950123499625.5800560079637
Winsorized Mean ( 3 / 24 )21866.4765277778830.46246784390326.330481357633
Winsorized Mean ( 4 / 24 )21910.7265277778823.03533488318826.6218540068969
Winsorized Mean ( 5 / 24 )21897.5320833333797.66685006886527.4519770772007
Winsorized Mean ( 6 / 24 )21861.3654166667789.38364072073227.6942215279589
Winsorized Mean ( 7 / 24 )21902.2959722222779.67246163661228.0916629096365
Winsorized Mean ( 8 / 24 )21902.2959722222779.67246163661228.0916629096365
Winsorized Mean ( 9 / 24 )21864.7959722222761.27542086897528.7212687719041
Winsorized Mean ( 10 / 24 )21566.5320833333667.78741246954932.2955055465601
Winsorized Mean ( 11 / 24 )21509.1640277778638.71782976008333.6755340552449
Winsorized Mean ( 12 / 24 )21140.3306944444564.77480837637.4314335216776
Winsorized Mean ( 13 / 24 )21142.94875548.21073320165338.5671922665965
Winsorized Mean ( 14 / 24 )21190.4904166667497.4445483278842.5986986647996
Winsorized Mean ( 15 / 24 )20987.26125463.7159188233145.258875958487
Winsorized Mean ( 16 / 24 )20946.3723611111447.75831997001146.7805318782552
Winsorized Mean ( 17 / 24 )20875.3029166667413.478335106550.4870537202144
Winsorized Mean ( 18 / 24 )20877.7179166667411.48498551084350.7374962679326
Winsorized Mean ( 19 / 24 )20863.4943055556401.45816066317651.9692868394823
Winsorized Mean ( 20 / 24 )20870.2276388889390.20086376651653.4858570978894
Winsorized Mean ( 21 / 24 )20973.1130555556328.50245524617363.8446158335065
Winsorized Mean ( 22 / 24 )20981.9741666667327.33801215949364.0988012001592
Winsorized Mean ( 23 / 24 )21236.9706944444294.40189317173872.1359854912887
Winsorized Mean ( 24 / 24 )20831.9706944444234.56213226615388.8121645773871
Trimmed Mean ( 1 / 24 )21906.433853.42995056133825.6686948771732
Trimmed Mean ( 2 / 24 )21774.4898529412810.58903714865826.8625516199127
Trimmed Mean ( 3 / 24 )21688.8153030303780.00473260037627.8060047542586
Trimmed Mean ( 4 / 24 )21622.19234375755.90507920701928.6043749916759
Trimmed Mean ( 5 / 24 )21538.4243548387729.41225724005829.5284650635507
Trimmed Mean ( 6 / 24 )21452.2385705.46553139247830.4086274174964
Trimmed Mean ( 7 / 24 )21367.5915517241678.53108898290131.4909543551697
Trimmed Mean ( 8 / 24 )21269.3805357143647.70469720908732.8380828908027
Trimmed Mean ( 9 / 24 )21163.8946296296608.86597914197334.7595289515999
Trimmed Mean ( 10 / 24 )21056.0636538462564.52737152925937.2985699467627
Trimmed Mean ( 11 / 24 )20982.5562534.36017841457539.2666913583538
Trimmed Mean ( 12 / 24 )20910.7460416667503.32214159620241.5454523326785
Trimmed Mean ( 13 / 24 )20880.8002173913482.9995416258443.2315114567268
Trimmed Mean ( 14 / 24 )20847.8025460.63076913465745.2592486150345
Trimmed Mean ( 15 / 24 )20805.8407142857443.75110406803746.8862849546752
Trimmed Mean ( 16 / 24 )20784.07025429.84310435566348.3526897125764
Trimmed Mean ( 17 / 24 )20764.8502631579414.92411950912850.0449342104372
Trimmed Mean ( 18 / 24 )20751.8558333333403.19250787681651.4688527884886
Trimmed Mean ( 19 / 24 )20737.0485294118387.01369855196153.5822080897934
Trimmed Mean ( 20 / 24 )20722.0746875366.80148173998756.4939775848266
Trimmed Mean ( 21 / 24 )20704.2963333333340.95035153566760.7252529292888
Trimmed Mean ( 22 / 24 )20671.38324.08510775410463.7838009381294
Trimmed Mean ( 23 / 24 )20632.2842307692298.0953559198469.2137056852284
Trimmed Mean ( 24 / 24 )20553.4120833333268.22349737589776.6279326174364
Median20348.5
Midrange27514.75
Midmean - Weighted Average at Xnp20642.102972973
Midmean - Weighted Average at X(n+1)p20751.8558333333
Midmean - Empirical Distribution Function20642.102972973
Midmean - Empirical Distribution Function - Averaging20751.8558333333
Midmean - Empirical Distribution Function - Interpolation20751.8558333333
Midmean - Closest Observation20642.102972973
Midmean - True Basic - Statistics Graphics Toolkit20751.8558333333
Midmean - MS Excel (old versions)20764.8502631579
Number of observations72



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')