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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, 04 Apr 2011 18:29:06 +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/2011/Apr/04/t1301946305c2xzysl3rd4hivy.htm/, Retrieved Wed, 08 May 2024 12:08:47 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=120233, Retrieved Wed, 08 May 2024 12:08:47 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsKDGP1W52
Estimated Impact91
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [centrummaten eige...] [2011-04-04 18:29:06] [58d8a931f127f4dbe815c0a9b73ee0dc] [Current]
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Dataseries X:
10407
10463
10556
10646
10702
11353
11346
11451
11964
12574
13031
13812
14544
14931
14886
16005
17064
15168
16050
15839
15137
14954
15648
15305
15579
16348
15928
16171
15937
15713
15594
15683
16438
17032
17696
17745
19394
20148
20108
18584
18441
18391
19178
18079
18483
19644
19195
19650
20830
23595
22937
21814
21928
21777
21383
21467
22052
22680
24320
24977
25204
25739
26434
27525
30695
32436
30160
30236
31293
31077
32226
33865
32810




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'George Udny Yule' @ 216.218.223.82

\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 & 'George Udny Yule' @ 216.218.223.82 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=120233&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]'George Udny Yule' @ 216.218.223.82[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=120233&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=120233&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'George Udny Yule' @ 216.218.223.82







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean19293.904109589724.37996426933926.6350604120453
Geometric Mean18376.9930025913
Harmonic Mean17525.457155642
Quadratic Mean20249.321759993
Winsorized Mean ( 1 / 24 )19280.2191780822720.34520365071726.7652496058415
Winsorized Mean ( 2 / 24 )19272.5205479452717.27115769716226.8692255935965
Winsorized Mean ( 3 / 24 )19267.5890410959714.46218153346626.9679621106627
Winsorized Mean ( 4 / 24 )19219.5342465753701.3928990870427.4019515618026
Winsorized Mean ( 5 / 24 )19248.8493150685690.63813681555527.871106863317
Winsorized Mean ( 6 / 24 )19218.0273972603683.14881292321928.1315388883216
Winsorized Mean ( 7 / 24 )19183.4109589041671.47912103289728.568886742741
Winsorized Mean ( 8 / 24 )19231.301369863660.77936511562429.1039678070121
Winsorized Mean ( 9 / 24 )18981.6438356164578.34934391858632.8203775714639
Winsorized Mean ( 10 / 24 )18894.7945205479538.92042077052535.0604538115906
Winsorized Mean ( 11 / 24 )18907.7534246575501.61685563357637.6936165766913
Winsorized Mean ( 12 / 24 )18940.1369863014468.78688381122140.4024464855303
Winsorized Mean ( 13 / 24 )18960.6164383562453.54274878275441.8055772895584
Winsorized Mean ( 14 / 24 )18843.2465753425429.68675308481243.8534500774408
Winsorized Mean ( 15 / 24 )18699403.31898017783646.3628069072153
Winsorized Mean ( 16 / 24 )18594.8904109589374.3651818839749.6704589817387
Winsorized Mean ( 17 / 24 )18542.2602739726363.88935191429450.9557649225741
Winsorized Mean ( 18 / 24 )18421.1917808219335.65247441890954.8817398492687
Winsorized Mean ( 19 / 24 )18460.2328767123321.77675235537657.3696910717917
Winsorized Mean ( 20 / 24 )18433.1095890411316.61158530906558.2199465981238
Winsorized Mean ( 21 / 24 )18438313.1053941142558.8875194953431
Winsorized Mean ( 22 / 24 )18355.1232876712298.10125979314661.5734509153297
Winsorized Mean ( 23 / 24 )18338.1095890411293.09698770464862.5666941603654
Winsorized Mean ( 24 / 24 )18197.7260273973262.11246399675169.4271678267952
Trimmed Mean ( 1 / 24 )19213.8450704225704.42873715767527.2757825695033
Trimmed Mean ( 2 / 24 )19143.6231884058685.44104509483727.9289128151891
Trimmed Mean ( 3 / 24 )19073.4029850746664.68635311275828.6953431430523
Trimmed Mean ( 4 / 24 )19000.7076923077641.01019234781829.6418183659671
Trimmed Mean ( 5 / 24 )18937.3174603175617.44090634170330.6706557110377
Trimmed Mean ( 6 / 24 )18862.7540983607592.2445102499231.8496056475066
Trimmed Mean ( 7 / 24 )18789.4915254237563.6160342966133.3373970612332
Trimmed Mean ( 8 / 24 )18717.4210526316531.54584402745835.2131829510922
Trimmed Mean ( 9 / 24 )18632.1636363636494.04866495368337.7132152317635
Trimmed Mean ( 10 / 24 )18578.679245283470.07481399247739.5228135868185
Trimmed Mean ( 11 / 24 )18533.431372549450.01394597553541.184126710501
Trimmed Mean ( 12 / 24 )18482.7346938776433.53717187911842.6324105353324
Trimmed Mean ( 13 / 24 )18423.5319148936419.91098771650943.8748507513019
Trimmed Mean ( 14 / 24 )18356.5111111111405.486960796545.2702870520259
Trimmed Mean ( 15 / 24 )18297.488372093392.41410931780646.6280083657094
Trimmed Mean ( 16 / 24 )18249.8292682927381.56302567721447.8291344815241
Trimmed Mean ( 17 / 24 )18209.4615384615373.77359844736848.7178912959677
Trimmed Mean ( 18 / 24 )18170.8378378378365.30658380385249.7413368481596
Trimmed Mean ( 19 / 24 )18141.8285714286360.26138383383950.3574054436986
Trimmed Mean ( 20 / 24 )18104.7575757576355.55587622481850.9195847583459
Trimmed Mean ( 21 / 24 )18066.0967741935349.17842545911251.7388688904236
Trimmed Mean ( 22 / 24 )18021.5172413793339.72452481432653.0474426337894
Trimmed Mean ( 23 / 24 )17980.5185185185329.74512461753354.528534847555
Trimmed Mean ( 24 / 24 )17935.12315.06536528155656.9250764328616
Median18079
Midrange22136
Midmean - Weighted Average at Xnp18063.0277777778
Midmean - Weighted Average at X(n+1)p18170.8378378378
Midmean - Empirical Distribution Function18170.8378378378
Midmean - Empirical Distribution Function - Averaging18170.8378378378
Midmean - Empirical Distribution Function - Interpolation18170.8378378378
Midmean - Closest Observation18091.8157894737
Midmean - True Basic - Statistics Graphics Toolkit18170.8378378378
Midmean - MS Excel (old versions)18170.8378378378
Number of observations73

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 19293.904109589 & 724.379964269339 & 26.6350604120453 \tabularnewline
Geometric Mean & 18376.9930025913 &  &  \tabularnewline
Harmonic Mean & 17525.457155642 &  &  \tabularnewline
Quadratic Mean & 20249.321759993 &  &  \tabularnewline
Winsorized Mean ( 1 / 24 ) & 19280.2191780822 & 720.345203650717 & 26.7652496058415 \tabularnewline
Winsorized Mean ( 2 / 24 ) & 19272.5205479452 & 717.271157697162 & 26.8692255935965 \tabularnewline
Winsorized Mean ( 3 / 24 ) & 19267.5890410959 & 714.462181533466 & 26.9679621106627 \tabularnewline
Winsorized Mean ( 4 / 24 ) & 19219.5342465753 & 701.39289908704 & 27.4019515618026 \tabularnewline
Winsorized Mean ( 5 / 24 ) & 19248.8493150685 & 690.638136815555 & 27.871106863317 \tabularnewline
Winsorized Mean ( 6 / 24 ) & 19218.0273972603 & 683.148812923219 & 28.1315388883216 \tabularnewline
Winsorized Mean ( 7 / 24 ) & 19183.4109589041 & 671.479121032897 & 28.568886742741 \tabularnewline
Winsorized Mean ( 8 / 24 ) & 19231.301369863 & 660.779365115624 & 29.1039678070121 \tabularnewline
Winsorized Mean ( 9 / 24 ) & 18981.6438356164 & 578.349343918586 & 32.8203775714639 \tabularnewline
Winsorized Mean ( 10 / 24 ) & 18894.7945205479 & 538.920420770525 & 35.0604538115906 \tabularnewline
Winsorized Mean ( 11 / 24 ) & 18907.7534246575 & 501.616855633576 & 37.6936165766913 \tabularnewline
Winsorized Mean ( 12 / 24 ) & 18940.1369863014 & 468.786883811221 & 40.4024464855303 \tabularnewline
Winsorized Mean ( 13 / 24 ) & 18960.6164383562 & 453.542748782754 & 41.8055772895584 \tabularnewline
Winsorized Mean ( 14 / 24 ) & 18843.2465753425 & 429.686753084812 & 43.8534500774408 \tabularnewline
Winsorized Mean ( 15 / 24 ) & 18699 & 403.318980177836 & 46.3628069072153 \tabularnewline
Winsorized Mean ( 16 / 24 ) & 18594.8904109589 & 374.36518188397 & 49.6704589817387 \tabularnewline
Winsorized Mean ( 17 / 24 ) & 18542.2602739726 & 363.889351914294 & 50.9557649225741 \tabularnewline
Winsorized Mean ( 18 / 24 ) & 18421.1917808219 & 335.652474418909 & 54.8817398492687 \tabularnewline
Winsorized Mean ( 19 / 24 ) & 18460.2328767123 & 321.776752355376 & 57.3696910717917 \tabularnewline
Winsorized Mean ( 20 / 24 ) & 18433.1095890411 & 316.611585309065 & 58.2199465981238 \tabularnewline
Winsorized Mean ( 21 / 24 ) & 18438 & 313.10539411425 & 58.8875194953431 \tabularnewline
Winsorized Mean ( 22 / 24 ) & 18355.1232876712 & 298.101259793146 & 61.5734509153297 \tabularnewline
Winsorized Mean ( 23 / 24 ) & 18338.1095890411 & 293.096987704648 & 62.5666941603654 \tabularnewline
Winsorized Mean ( 24 / 24 ) & 18197.7260273973 & 262.112463996751 & 69.4271678267952 \tabularnewline
Trimmed Mean ( 1 / 24 ) & 19213.8450704225 & 704.428737157675 & 27.2757825695033 \tabularnewline
Trimmed Mean ( 2 / 24 ) & 19143.6231884058 & 685.441045094837 & 27.9289128151891 \tabularnewline
Trimmed Mean ( 3 / 24 ) & 19073.4029850746 & 664.686353112758 & 28.6953431430523 \tabularnewline
Trimmed Mean ( 4 / 24 ) & 19000.7076923077 & 641.010192347818 & 29.6418183659671 \tabularnewline
Trimmed Mean ( 5 / 24 ) & 18937.3174603175 & 617.440906341703 & 30.6706557110377 \tabularnewline
Trimmed Mean ( 6 / 24 ) & 18862.7540983607 & 592.24451024992 & 31.8496056475066 \tabularnewline
Trimmed Mean ( 7 / 24 ) & 18789.4915254237 & 563.61603429661 & 33.3373970612332 \tabularnewline
Trimmed Mean ( 8 / 24 ) & 18717.4210526316 & 531.545844027458 & 35.2131829510922 \tabularnewline
Trimmed Mean ( 9 / 24 ) & 18632.1636363636 & 494.048664953683 & 37.7132152317635 \tabularnewline
Trimmed Mean ( 10 / 24 ) & 18578.679245283 & 470.074813992477 & 39.5228135868185 \tabularnewline
Trimmed Mean ( 11 / 24 ) & 18533.431372549 & 450.013945975535 & 41.184126710501 \tabularnewline
Trimmed Mean ( 12 / 24 ) & 18482.7346938776 & 433.537171879118 & 42.6324105353324 \tabularnewline
Trimmed Mean ( 13 / 24 ) & 18423.5319148936 & 419.910987716509 & 43.8748507513019 \tabularnewline
Trimmed Mean ( 14 / 24 ) & 18356.5111111111 & 405.4869607965 & 45.2702870520259 \tabularnewline
Trimmed Mean ( 15 / 24 ) & 18297.488372093 & 392.414109317806 & 46.6280083657094 \tabularnewline
Trimmed Mean ( 16 / 24 ) & 18249.8292682927 & 381.563025677214 & 47.8291344815241 \tabularnewline
Trimmed Mean ( 17 / 24 ) & 18209.4615384615 & 373.773598447368 & 48.7178912959677 \tabularnewline
Trimmed Mean ( 18 / 24 ) & 18170.8378378378 & 365.306583803852 & 49.7413368481596 \tabularnewline
Trimmed Mean ( 19 / 24 ) & 18141.8285714286 & 360.261383833839 & 50.3574054436986 \tabularnewline
Trimmed Mean ( 20 / 24 ) & 18104.7575757576 & 355.555876224818 & 50.9195847583459 \tabularnewline
Trimmed Mean ( 21 / 24 ) & 18066.0967741935 & 349.178425459112 & 51.7388688904236 \tabularnewline
Trimmed Mean ( 22 / 24 ) & 18021.5172413793 & 339.724524814326 & 53.0474426337894 \tabularnewline
Trimmed Mean ( 23 / 24 ) & 17980.5185185185 & 329.745124617533 & 54.528534847555 \tabularnewline
Trimmed Mean ( 24 / 24 ) & 17935.12 & 315.065365281556 & 56.9250764328616 \tabularnewline
Median & 18079 &  &  \tabularnewline
Midrange & 22136 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 18063.0277777778 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 18170.8378378378 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 18170.8378378378 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 18170.8378378378 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 18170.8378378378 &  &  \tabularnewline
Midmean - Closest Observation & 18091.8157894737 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 18170.8378378378 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 18170.8378378378 &  &  \tabularnewline
Number of observations & 73 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=120233&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]19293.904109589[/C][C]724.379964269339[/C][C]26.6350604120453[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]18376.9930025913[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]17525.457155642[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]20249.321759993[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 24 )[/C][C]19280.2191780822[/C][C]720.345203650717[/C][C]26.7652496058415[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 24 )[/C][C]19272.5205479452[/C][C]717.271157697162[/C][C]26.8692255935965[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 24 )[/C][C]19267.5890410959[/C][C]714.462181533466[/C][C]26.9679621106627[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 24 )[/C][C]19219.5342465753[/C][C]701.39289908704[/C][C]27.4019515618026[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 24 )[/C][C]19248.8493150685[/C][C]690.638136815555[/C][C]27.871106863317[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 24 )[/C][C]19218.0273972603[/C][C]683.148812923219[/C][C]28.1315388883216[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 24 )[/C][C]19183.4109589041[/C][C]671.479121032897[/C][C]28.568886742741[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 24 )[/C][C]19231.301369863[/C][C]660.779365115624[/C][C]29.1039678070121[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 24 )[/C][C]18981.6438356164[/C][C]578.349343918586[/C][C]32.8203775714639[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 24 )[/C][C]18894.7945205479[/C][C]538.920420770525[/C][C]35.0604538115906[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 24 )[/C][C]18907.7534246575[/C][C]501.616855633576[/C][C]37.6936165766913[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 24 )[/C][C]18940.1369863014[/C][C]468.786883811221[/C][C]40.4024464855303[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 24 )[/C][C]18960.6164383562[/C][C]453.542748782754[/C][C]41.8055772895584[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 24 )[/C][C]18843.2465753425[/C][C]429.686753084812[/C][C]43.8534500774408[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 24 )[/C][C]18699[/C][C]403.318980177836[/C][C]46.3628069072153[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 24 )[/C][C]18594.8904109589[/C][C]374.36518188397[/C][C]49.6704589817387[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 24 )[/C][C]18542.2602739726[/C][C]363.889351914294[/C][C]50.9557649225741[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 24 )[/C][C]18421.1917808219[/C][C]335.652474418909[/C][C]54.8817398492687[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 24 )[/C][C]18460.2328767123[/C][C]321.776752355376[/C][C]57.3696910717917[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 24 )[/C][C]18433.1095890411[/C][C]316.611585309065[/C][C]58.2199465981238[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 24 )[/C][C]18438[/C][C]313.10539411425[/C][C]58.8875194953431[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 24 )[/C][C]18355.1232876712[/C][C]298.101259793146[/C][C]61.5734509153297[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 24 )[/C][C]18338.1095890411[/C][C]293.096987704648[/C][C]62.5666941603654[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 24 )[/C][C]18197.7260273973[/C][C]262.112463996751[/C][C]69.4271678267952[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 24 )[/C][C]19213.8450704225[/C][C]704.428737157675[/C][C]27.2757825695033[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 24 )[/C][C]19143.6231884058[/C][C]685.441045094837[/C][C]27.9289128151891[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 24 )[/C][C]19073.4029850746[/C][C]664.686353112758[/C][C]28.6953431430523[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 24 )[/C][C]19000.7076923077[/C][C]641.010192347818[/C][C]29.6418183659671[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 24 )[/C][C]18937.3174603175[/C][C]617.440906341703[/C][C]30.6706557110377[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 24 )[/C][C]18862.7540983607[/C][C]592.24451024992[/C][C]31.8496056475066[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 24 )[/C][C]18789.4915254237[/C][C]563.61603429661[/C][C]33.3373970612332[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 24 )[/C][C]18717.4210526316[/C][C]531.545844027458[/C][C]35.2131829510922[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 24 )[/C][C]18632.1636363636[/C][C]494.048664953683[/C][C]37.7132152317635[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 24 )[/C][C]18578.679245283[/C][C]470.074813992477[/C][C]39.5228135868185[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 24 )[/C][C]18533.431372549[/C][C]450.013945975535[/C][C]41.184126710501[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 24 )[/C][C]18482.7346938776[/C][C]433.537171879118[/C][C]42.6324105353324[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 24 )[/C][C]18423.5319148936[/C][C]419.910987716509[/C][C]43.8748507513019[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 24 )[/C][C]18356.5111111111[/C][C]405.4869607965[/C][C]45.2702870520259[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 24 )[/C][C]18297.488372093[/C][C]392.414109317806[/C][C]46.6280083657094[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 24 )[/C][C]18249.8292682927[/C][C]381.563025677214[/C][C]47.8291344815241[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 24 )[/C][C]18209.4615384615[/C][C]373.773598447368[/C][C]48.7178912959677[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 24 )[/C][C]18170.8378378378[/C][C]365.306583803852[/C][C]49.7413368481596[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 24 )[/C][C]18141.8285714286[/C][C]360.261383833839[/C][C]50.3574054436986[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 24 )[/C][C]18104.7575757576[/C][C]355.555876224818[/C][C]50.9195847583459[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 24 )[/C][C]18066.0967741935[/C][C]349.178425459112[/C][C]51.7388688904236[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 24 )[/C][C]18021.5172413793[/C][C]339.724524814326[/C][C]53.0474426337894[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 24 )[/C][C]17980.5185185185[/C][C]329.745124617533[/C][C]54.528534847555[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 24 )[/C][C]17935.12[/C][C]315.065365281556[/C][C]56.9250764328616[/C][/ROW]
[ROW][C]Median[/C][C]18079[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]22136[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]18063.0277777778[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]18170.8378378378[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]18170.8378378378[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]18170.8378378378[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]18170.8378378378[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]18091.8157894737[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]18170.8378378378[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]18170.8378378378[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]73[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=120233&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=120233&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 Mean19293.904109589724.37996426933926.6350604120453
Geometric Mean18376.9930025913
Harmonic Mean17525.457155642
Quadratic Mean20249.321759993
Winsorized Mean ( 1 / 24 )19280.2191780822720.34520365071726.7652496058415
Winsorized Mean ( 2 / 24 )19272.5205479452717.27115769716226.8692255935965
Winsorized Mean ( 3 / 24 )19267.5890410959714.46218153346626.9679621106627
Winsorized Mean ( 4 / 24 )19219.5342465753701.3928990870427.4019515618026
Winsorized Mean ( 5 / 24 )19248.8493150685690.63813681555527.871106863317
Winsorized Mean ( 6 / 24 )19218.0273972603683.14881292321928.1315388883216
Winsorized Mean ( 7 / 24 )19183.4109589041671.47912103289728.568886742741
Winsorized Mean ( 8 / 24 )19231.301369863660.77936511562429.1039678070121
Winsorized Mean ( 9 / 24 )18981.6438356164578.34934391858632.8203775714639
Winsorized Mean ( 10 / 24 )18894.7945205479538.92042077052535.0604538115906
Winsorized Mean ( 11 / 24 )18907.7534246575501.61685563357637.6936165766913
Winsorized Mean ( 12 / 24 )18940.1369863014468.78688381122140.4024464855303
Winsorized Mean ( 13 / 24 )18960.6164383562453.54274878275441.8055772895584
Winsorized Mean ( 14 / 24 )18843.2465753425429.68675308481243.8534500774408
Winsorized Mean ( 15 / 24 )18699403.31898017783646.3628069072153
Winsorized Mean ( 16 / 24 )18594.8904109589374.3651818839749.6704589817387
Winsorized Mean ( 17 / 24 )18542.2602739726363.88935191429450.9557649225741
Winsorized Mean ( 18 / 24 )18421.1917808219335.65247441890954.8817398492687
Winsorized Mean ( 19 / 24 )18460.2328767123321.77675235537657.3696910717917
Winsorized Mean ( 20 / 24 )18433.1095890411316.61158530906558.2199465981238
Winsorized Mean ( 21 / 24 )18438313.1053941142558.8875194953431
Winsorized Mean ( 22 / 24 )18355.1232876712298.10125979314661.5734509153297
Winsorized Mean ( 23 / 24 )18338.1095890411293.09698770464862.5666941603654
Winsorized Mean ( 24 / 24 )18197.7260273973262.11246399675169.4271678267952
Trimmed Mean ( 1 / 24 )19213.8450704225704.42873715767527.2757825695033
Trimmed Mean ( 2 / 24 )19143.6231884058685.44104509483727.9289128151891
Trimmed Mean ( 3 / 24 )19073.4029850746664.68635311275828.6953431430523
Trimmed Mean ( 4 / 24 )19000.7076923077641.01019234781829.6418183659671
Trimmed Mean ( 5 / 24 )18937.3174603175617.44090634170330.6706557110377
Trimmed Mean ( 6 / 24 )18862.7540983607592.2445102499231.8496056475066
Trimmed Mean ( 7 / 24 )18789.4915254237563.6160342966133.3373970612332
Trimmed Mean ( 8 / 24 )18717.4210526316531.54584402745835.2131829510922
Trimmed Mean ( 9 / 24 )18632.1636363636494.04866495368337.7132152317635
Trimmed Mean ( 10 / 24 )18578.679245283470.07481399247739.5228135868185
Trimmed Mean ( 11 / 24 )18533.431372549450.01394597553541.184126710501
Trimmed Mean ( 12 / 24 )18482.7346938776433.53717187911842.6324105353324
Trimmed Mean ( 13 / 24 )18423.5319148936419.91098771650943.8748507513019
Trimmed Mean ( 14 / 24 )18356.5111111111405.486960796545.2702870520259
Trimmed Mean ( 15 / 24 )18297.488372093392.41410931780646.6280083657094
Trimmed Mean ( 16 / 24 )18249.8292682927381.56302567721447.8291344815241
Trimmed Mean ( 17 / 24 )18209.4615384615373.77359844736848.7178912959677
Trimmed Mean ( 18 / 24 )18170.8378378378365.30658380385249.7413368481596
Trimmed Mean ( 19 / 24 )18141.8285714286360.26138383383950.3574054436986
Trimmed Mean ( 20 / 24 )18104.7575757576355.55587622481850.9195847583459
Trimmed Mean ( 21 / 24 )18066.0967741935349.17842545911251.7388688904236
Trimmed Mean ( 22 / 24 )18021.5172413793339.72452481432653.0474426337894
Trimmed Mean ( 23 / 24 )17980.5185185185329.74512461753354.528534847555
Trimmed Mean ( 24 / 24 )17935.12315.06536528155656.9250764328616
Median18079
Midrange22136
Midmean - Weighted Average at Xnp18063.0277777778
Midmean - Weighted Average at X(n+1)p18170.8378378378
Midmean - Empirical Distribution Function18170.8378378378
Midmean - Empirical Distribution Function - Averaging18170.8378378378
Midmean - Empirical Distribution Function - Interpolation18170.8378378378
Midmean - Closest Observation18091.8157894737
Midmean - True Basic - Statistics Graphics Toolkit18170.8378378378
Midmean - MS Excel (old versions)18170.8378378378
Number of observations73



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')