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Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationTue, 15 Jan 2013 19:12:11 -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/2013/Jan/15/t1358295138sw10ecy2qthi88m.htm/, Retrieved Sun, 28 Apr 2024 11:53:36 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=205572, Retrieved Sun, 28 Apr 2024 11:53:36 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact69
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [] [2013-01-16 00:12:11] [38a0db91cd47487c7649642dcb33e029] [Current]
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Dataseries X:
435
431
434
439
455
452
426
428
433
438
442
446
442
436
444
454
469
471
443
437
444
451
457
460
454
439
441
446
459
456
433
424
430
428
424
419
409
397
397
401
413
413
390
385
397
398
406
412
409
404
412
418
434
431
406
416
424
427
438
444
442
443
453
471
476
476
461
462
460
463
467
468
465
459
465
471
472
472
456
455
456
462
463
461




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Sir Maurice George Kendall' @ kendall.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 & 'Sir Maurice George Kendall' @ kendall.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=205572&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]'Sir Maurice George Kendall' @ kendall.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=205572&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=205572&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'Sir Maurice George Kendall' @ kendall.wessa.net







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean439.2857142857142.52142690551711174.22107828092
Geometric Mean438.674955309611
Harmonic Mean438.054198868343
Quadratic Mean439.885915945963
Winsorized Mean ( 1 / 28 )439.3452380952382.50664601678747175.272150576053
Winsorized Mean ( 2 / 28 )439.4166666666672.45348045858956179.099313845473
Winsorized Mean ( 3 / 28 )439.4166666666672.45348045858956179.099313845473
Winsorized Mean ( 4 / 28 )439.3690476190482.44596098050638179.630440191277
Winsorized Mean ( 5 / 28 )439.4285714285712.43364526845654180.563937203249
Winsorized Mean ( 6 / 28 )439.6428571428572.39079577422723183.889758331601
Winsorized Mean ( 7 / 28 )439.726190476192.31735892304588189.753165167105
Winsorized Mean ( 8 / 28 )439.8214285714292.26817645169671193.909705853096
Winsorized Mean ( 9 / 28 )439.7142857142862.25233807433118195.225703781106
Winsorized Mean ( 10 / 28 )439.8333333333332.15518383547596204.081585103481
Winsorized Mean ( 11 / 28 )439.8333333333332.15518383547596204.081585103481
Winsorized Mean ( 12 / 28 )439.976190476192.04334668830445215.321361271923
Winsorized Mean ( 13 / 28 )439.976190476192.04334668830445215.321361271923
Winsorized Mean ( 14 / 28 )439.976190476191.9936053961989220.693719687492
Winsorized Mean ( 15 / 28 )439.976190476191.9936053961989220.693719687492
Winsorized Mean ( 16 / 28 )440.3571428571431.87700115869049234.606750676895
Winsorized Mean ( 17 / 28 )440.7619047619051.81475901205522242.876272735927
Winsorized Mean ( 18 / 28 )440.7619047619051.75399053644999251.290925237254
Winsorized Mean ( 19 / 28 )441.8928571428571.5925293406541277.478628407159
Winsorized Mean ( 20 / 28 )441.6547619047621.56027253599502283.062575105258
Winsorized Mean ( 21 / 28 )441.6547619047621.56027253599502283.062575105258
Winsorized Mean ( 22 / 28 )441.6547619047621.42053762737211310.906767546728
Winsorized Mean ( 23 / 28 )441.6547619047621.34907099711432327.376960033583
Winsorized Mean ( 24 / 28 )441.9404761904761.31208155261414336.823938504411
Winsorized Mean ( 25 / 28 )441.9404761904761.31208155261414336.823938504411
Winsorized Mean ( 26 / 28 )442.251.19425318797719370.315109435945
Winsorized Mean ( 27 / 28 )442.5714285714291.15498442296581383.183893887485
Winsorized Mean ( 28 / 28 )442.2380952380951.11213241590406397.648777172452
Trimmed Mean ( 1 / 28 )439.52.4548466769162179.03358451376
Trimmed Mean ( 2 / 28 )439.66252.3946765690283183.599950693301
Trimmed Mean ( 3 / 28 )439.7948717948722.35730695823807186.566654061713
Trimmed Mean ( 4 / 28 )439.9342105263162.31337344064902190.169992788926
Trimmed Mean ( 5 / 28 )440.0945945945952.26421781413697194.369371995397
Trimmed Mean ( 6 / 28 )440.252.20991063344759199.216200572412
Trimmed Mean ( 7 / 28 )440.3714285714292.15729024766233204.131747709249
Trimmed Mean ( 8 / 28 )440.4852941176472.11266225689359208.497734401393
Trimmed Mean ( 9 / 28 )440.5909090909092.07032279869153212.812663498353
Trimmed Mean ( 10 / 28 )440.718752.02250099942095217.907803321818
Trimmed Mean ( 11 / 28 )440.8387096774191.98463073334706222.126314114843
Trimmed Mean ( 12 / 28 )440.9666666666671.93816365221039227.517767224539
Trimmed Mean ( 13 / 28 )441.0862068965521.90301516460915231.782812401889
Trimmed Mean ( 14 / 28 )441.2142857142861.8591148371568237.32492307417
Trimmed Mean ( 15 / 28 )441.3518518518521.81386796275486243.320826495848
Trimmed Mean ( 16 / 28 )441.51.75680104866351251.309048532201
Trimmed Mean ( 17 / 28 )441.621.70877447431826258.442530970151
Trimmed Mean ( 18 / 28 )441.7083333333331.66043827348302266.019123015505
Trimmed Mean ( 19 / 28 )441.8043478260871.61053883179278274.32082921856
Trimmed Mean ( 20 / 28 )441.7954545454551.57966047461732279.677476042743
Trimmed Mean ( 21 / 28 )441.8095238095241.54462768169979286.029785069844
Trimmed Mean ( 22 / 28 )441.8251.4969573842486295.1486826873
Trimmed Mean ( 23 / 28 )441.8421052631581.46438337087118301.725705202663
Trimmed Mean ( 24 / 28 )441.8611111111111.43491207505524307.936018375273
Trimmed Mean ( 25 / 28 )441.8529411764711.40100063103701315.383827378733
Trimmed Mean ( 26 / 28 )441.843751.35085798228624327.083791037906
Trimmed Mean ( 27 / 28 )441.81.31166297886116336.824326919395
Trimmed Mean ( 28 / 28 )441.7142857142861.26287773212166349.768053137019
Median442
Midrange430.5
Midmean - Weighted Average at Xnp441.4
Midmean - Weighted Average at X(n+1)p441.4
Midmean - Empirical Distribution Function441.4
Midmean - Empirical Distribution Function - Averaging441.4
Midmean - Empirical Distribution Function - Interpolation441.4
Midmean - Closest Observation441.4
Midmean - True Basic - Statistics Graphics Toolkit441.4
Midmean - MS Excel (old versions)441.4
Number of observations84

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 439.285714285714 & 2.52142690551711 & 174.22107828092 \tabularnewline
Geometric Mean & 438.674955309611 &  &  \tabularnewline
Harmonic Mean & 438.054198868343 &  &  \tabularnewline
Quadratic Mean & 439.885915945963 &  &  \tabularnewline
Winsorized Mean ( 1 / 28 ) & 439.345238095238 & 2.50664601678747 & 175.272150576053 \tabularnewline
Winsorized Mean ( 2 / 28 ) & 439.416666666667 & 2.45348045858956 & 179.099313845473 \tabularnewline
Winsorized Mean ( 3 / 28 ) & 439.416666666667 & 2.45348045858956 & 179.099313845473 \tabularnewline
Winsorized Mean ( 4 / 28 ) & 439.369047619048 & 2.44596098050638 & 179.630440191277 \tabularnewline
Winsorized Mean ( 5 / 28 ) & 439.428571428571 & 2.43364526845654 & 180.563937203249 \tabularnewline
Winsorized Mean ( 6 / 28 ) & 439.642857142857 & 2.39079577422723 & 183.889758331601 \tabularnewline
Winsorized Mean ( 7 / 28 ) & 439.72619047619 & 2.31735892304588 & 189.753165167105 \tabularnewline
Winsorized Mean ( 8 / 28 ) & 439.821428571429 & 2.26817645169671 & 193.909705853096 \tabularnewline
Winsorized Mean ( 9 / 28 ) & 439.714285714286 & 2.25233807433118 & 195.225703781106 \tabularnewline
Winsorized Mean ( 10 / 28 ) & 439.833333333333 & 2.15518383547596 & 204.081585103481 \tabularnewline
Winsorized Mean ( 11 / 28 ) & 439.833333333333 & 2.15518383547596 & 204.081585103481 \tabularnewline
Winsorized Mean ( 12 / 28 ) & 439.97619047619 & 2.04334668830445 & 215.321361271923 \tabularnewline
Winsorized Mean ( 13 / 28 ) & 439.97619047619 & 2.04334668830445 & 215.321361271923 \tabularnewline
Winsorized Mean ( 14 / 28 ) & 439.97619047619 & 1.9936053961989 & 220.693719687492 \tabularnewline
Winsorized Mean ( 15 / 28 ) & 439.97619047619 & 1.9936053961989 & 220.693719687492 \tabularnewline
Winsorized Mean ( 16 / 28 ) & 440.357142857143 & 1.87700115869049 & 234.606750676895 \tabularnewline
Winsorized Mean ( 17 / 28 ) & 440.761904761905 & 1.81475901205522 & 242.876272735927 \tabularnewline
Winsorized Mean ( 18 / 28 ) & 440.761904761905 & 1.75399053644999 & 251.290925237254 \tabularnewline
Winsorized Mean ( 19 / 28 ) & 441.892857142857 & 1.5925293406541 & 277.478628407159 \tabularnewline
Winsorized Mean ( 20 / 28 ) & 441.654761904762 & 1.56027253599502 & 283.062575105258 \tabularnewline
Winsorized Mean ( 21 / 28 ) & 441.654761904762 & 1.56027253599502 & 283.062575105258 \tabularnewline
Winsorized Mean ( 22 / 28 ) & 441.654761904762 & 1.42053762737211 & 310.906767546728 \tabularnewline
Winsorized Mean ( 23 / 28 ) & 441.654761904762 & 1.34907099711432 & 327.376960033583 \tabularnewline
Winsorized Mean ( 24 / 28 ) & 441.940476190476 & 1.31208155261414 & 336.823938504411 \tabularnewline
Winsorized Mean ( 25 / 28 ) & 441.940476190476 & 1.31208155261414 & 336.823938504411 \tabularnewline
Winsorized Mean ( 26 / 28 ) & 442.25 & 1.19425318797719 & 370.315109435945 \tabularnewline
Winsorized Mean ( 27 / 28 ) & 442.571428571429 & 1.15498442296581 & 383.183893887485 \tabularnewline
Winsorized Mean ( 28 / 28 ) & 442.238095238095 & 1.11213241590406 & 397.648777172452 \tabularnewline
Trimmed Mean ( 1 / 28 ) & 439.5 & 2.4548466769162 & 179.03358451376 \tabularnewline
Trimmed Mean ( 2 / 28 ) & 439.6625 & 2.3946765690283 & 183.599950693301 \tabularnewline
Trimmed Mean ( 3 / 28 ) & 439.794871794872 & 2.35730695823807 & 186.566654061713 \tabularnewline
Trimmed Mean ( 4 / 28 ) & 439.934210526316 & 2.31337344064902 & 190.169992788926 \tabularnewline
Trimmed Mean ( 5 / 28 ) & 440.094594594595 & 2.26421781413697 & 194.369371995397 \tabularnewline
Trimmed Mean ( 6 / 28 ) & 440.25 & 2.20991063344759 & 199.216200572412 \tabularnewline
Trimmed Mean ( 7 / 28 ) & 440.371428571429 & 2.15729024766233 & 204.131747709249 \tabularnewline
Trimmed Mean ( 8 / 28 ) & 440.485294117647 & 2.11266225689359 & 208.497734401393 \tabularnewline
Trimmed Mean ( 9 / 28 ) & 440.590909090909 & 2.07032279869153 & 212.812663498353 \tabularnewline
Trimmed Mean ( 10 / 28 ) & 440.71875 & 2.02250099942095 & 217.907803321818 \tabularnewline
Trimmed Mean ( 11 / 28 ) & 440.838709677419 & 1.98463073334706 & 222.126314114843 \tabularnewline
Trimmed Mean ( 12 / 28 ) & 440.966666666667 & 1.93816365221039 & 227.517767224539 \tabularnewline
Trimmed Mean ( 13 / 28 ) & 441.086206896552 & 1.90301516460915 & 231.782812401889 \tabularnewline
Trimmed Mean ( 14 / 28 ) & 441.214285714286 & 1.8591148371568 & 237.32492307417 \tabularnewline
Trimmed Mean ( 15 / 28 ) & 441.351851851852 & 1.81386796275486 & 243.320826495848 \tabularnewline
Trimmed Mean ( 16 / 28 ) & 441.5 & 1.75680104866351 & 251.309048532201 \tabularnewline
Trimmed Mean ( 17 / 28 ) & 441.62 & 1.70877447431826 & 258.442530970151 \tabularnewline
Trimmed Mean ( 18 / 28 ) & 441.708333333333 & 1.66043827348302 & 266.019123015505 \tabularnewline
Trimmed Mean ( 19 / 28 ) & 441.804347826087 & 1.61053883179278 & 274.32082921856 \tabularnewline
Trimmed Mean ( 20 / 28 ) & 441.795454545455 & 1.57966047461732 & 279.677476042743 \tabularnewline
Trimmed Mean ( 21 / 28 ) & 441.809523809524 & 1.54462768169979 & 286.029785069844 \tabularnewline
Trimmed Mean ( 22 / 28 ) & 441.825 & 1.4969573842486 & 295.1486826873 \tabularnewline
Trimmed Mean ( 23 / 28 ) & 441.842105263158 & 1.46438337087118 & 301.725705202663 \tabularnewline
Trimmed Mean ( 24 / 28 ) & 441.861111111111 & 1.43491207505524 & 307.936018375273 \tabularnewline
Trimmed Mean ( 25 / 28 ) & 441.852941176471 & 1.40100063103701 & 315.383827378733 \tabularnewline
Trimmed Mean ( 26 / 28 ) & 441.84375 & 1.35085798228624 & 327.083791037906 \tabularnewline
Trimmed Mean ( 27 / 28 ) & 441.8 & 1.31166297886116 & 336.824326919395 \tabularnewline
Trimmed Mean ( 28 / 28 ) & 441.714285714286 & 1.26287773212166 & 349.768053137019 \tabularnewline
Median & 442 &  &  \tabularnewline
Midrange & 430.5 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 441.4 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 441.4 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 441.4 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 441.4 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 441.4 &  &  \tabularnewline
Midmean - Closest Observation & 441.4 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 441.4 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 441.4 &  &  \tabularnewline
Number of observations & 84 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=205572&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]439.285714285714[/C][C]2.52142690551711[/C][C]174.22107828092[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]438.674955309611[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]438.054198868343[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]439.885915945963[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 28 )[/C][C]439.345238095238[/C][C]2.50664601678747[/C][C]175.272150576053[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 28 )[/C][C]439.416666666667[/C][C]2.45348045858956[/C][C]179.099313845473[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 28 )[/C][C]439.416666666667[/C][C]2.45348045858956[/C][C]179.099313845473[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 28 )[/C][C]439.369047619048[/C][C]2.44596098050638[/C][C]179.630440191277[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 28 )[/C][C]439.428571428571[/C][C]2.43364526845654[/C][C]180.563937203249[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 28 )[/C][C]439.642857142857[/C][C]2.39079577422723[/C][C]183.889758331601[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 28 )[/C][C]439.72619047619[/C][C]2.31735892304588[/C][C]189.753165167105[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 28 )[/C][C]439.821428571429[/C][C]2.26817645169671[/C][C]193.909705853096[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 28 )[/C][C]439.714285714286[/C][C]2.25233807433118[/C][C]195.225703781106[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 28 )[/C][C]439.833333333333[/C][C]2.15518383547596[/C][C]204.081585103481[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 28 )[/C][C]439.833333333333[/C][C]2.15518383547596[/C][C]204.081585103481[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 28 )[/C][C]439.97619047619[/C][C]2.04334668830445[/C][C]215.321361271923[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 28 )[/C][C]439.97619047619[/C][C]2.04334668830445[/C][C]215.321361271923[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 28 )[/C][C]439.97619047619[/C][C]1.9936053961989[/C][C]220.693719687492[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 28 )[/C][C]439.97619047619[/C][C]1.9936053961989[/C][C]220.693719687492[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 28 )[/C][C]440.357142857143[/C][C]1.87700115869049[/C][C]234.606750676895[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 28 )[/C][C]440.761904761905[/C][C]1.81475901205522[/C][C]242.876272735927[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 28 )[/C][C]440.761904761905[/C][C]1.75399053644999[/C][C]251.290925237254[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 28 )[/C][C]441.892857142857[/C][C]1.5925293406541[/C][C]277.478628407159[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 28 )[/C][C]441.654761904762[/C][C]1.56027253599502[/C][C]283.062575105258[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 28 )[/C][C]441.654761904762[/C][C]1.56027253599502[/C][C]283.062575105258[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 28 )[/C][C]441.654761904762[/C][C]1.42053762737211[/C][C]310.906767546728[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 28 )[/C][C]441.654761904762[/C][C]1.34907099711432[/C][C]327.376960033583[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 28 )[/C][C]441.940476190476[/C][C]1.31208155261414[/C][C]336.823938504411[/C][/ROW]
[ROW][C]Winsorized Mean ( 25 / 28 )[/C][C]441.940476190476[/C][C]1.31208155261414[/C][C]336.823938504411[/C][/ROW]
[ROW][C]Winsorized Mean ( 26 / 28 )[/C][C]442.25[/C][C]1.19425318797719[/C][C]370.315109435945[/C][/ROW]
[ROW][C]Winsorized Mean ( 27 / 28 )[/C][C]442.571428571429[/C][C]1.15498442296581[/C][C]383.183893887485[/C][/ROW]
[ROW][C]Winsorized Mean ( 28 / 28 )[/C][C]442.238095238095[/C][C]1.11213241590406[/C][C]397.648777172452[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 28 )[/C][C]439.5[/C][C]2.4548466769162[/C][C]179.03358451376[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 28 )[/C][C]439.6625[/C][C]2.3946765690283[/C][C]183.599950693301[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 28 )[/C][C]439.794871794872[/C][C]2.35730695823807[/C][C]186.566654061713[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 28 )[/C][C]439.934210526316[/C][C]2.31337344064902[/C][C]190.169992788926[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 28 )[/C][C]440.094594594595[/C][C]2.26421781413697[/C][C]194.369371995397[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 28 )[/C][C]440.25[/C][C]2.20991063344759[/C][C]199.216200572412[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 28 )[/C][C]440.371428571429[/C][C]2.15729024766233[/C][C]204.131747709249[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 28 )[/C][C]440.485294117647[/C][C]2.11266225689359[/C][C]208.497734401393[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 28 )[/C][C]440.590909090909[/C][C]2.07032279869153[/C][C]212.812663498353[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 28 )[/C][C]440.71875[/C][C]2.02250099942095[/C][C]217.907803321818[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 28 )[/C][C]440.838709677419[/C][C]1.98463073334706[/C][C]222.126314114843[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 28 )[/C][C]440.966666666667[/C][C]1.93816365221039[/C][C]227.517767224539[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 28 )[/C][C]441.086206896552[/C][C]1.90301516460915[/C][C]231.782812401889[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 28 )[/C][C]441.214285714286[/C][C]1.8591148371568[/C][C]237.32492307417[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 28 )[/C][C]441.351851851852[/C][C]1.81386796275486[/C][C]243.320826495848[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 28 )[/C][C]441.5[/C][C]1.75680104866351[/C][C]251.309048532201[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 28 )[/C][C]441.62[/C][C]1.70877447431826[/C][C]258.442530970151[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 28 )[/C][C]441.708333333333[/C][C]1.66043827348302[/C][C]266.019123015505[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 28 )[/C][C]441.804347826087[/C][C]1.61053883179278[/C][C]274.32082921856[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 28 )[/C][C]441.795454545455[/C][C]1.57966047461732[/C][C]279.677476042743[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 28 )[/C][C]441.809523809524[/C][C]1.54462768169979[/C][C]286.029785069844[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 28 )[/C][C]441.825[/C][C]1.4969573842486[/C][C]295.1486826873[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 28 )[/C][C]441.842105263158[/C][C]1.46438337087118[/C][C]301.725705202663[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 28 )[/C][C]441.861111111111[/C][C]1.43491207505524[/C][C]307.936018375273[/C][/ROW]
[ROW][C]Trimmed Mean ( 25 / 28 )[/C][C]441.852941176471[/C][C]1.40100063103701[/C][C]315.383827378733[/C][/ROW]
[ROW][C]Trimmed Mean ( 26 / 28 )[/C][C]441.84375[/C][C]1.35085798228624[/C][C]327.083791037906[/C][/ROW]
[ROW][C]Trimmed Mean ( 27 / 28 )[/C][C]441.8[/C][C]1.31166297886116[/C][C]336.824326919395[/C][/ROW]
[ROW][C]Trimmed Mean ( 28 / 28 )[/C][C]441.714285714286[/C][C]1.26287773212166[/C][C]349.768053137019[/C][/ROW]
[ROW][C]Median[/C][C]442[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]430.5[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]441.4[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]441.4[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]441.4[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]441.4[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]441.4[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]441.4[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]441.4[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]441.4[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]84[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=205572&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=205572&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 Mean439.2857142857142.52142690551711174.22107828092
Geometric Mean438.674955309611
Harmonic Mean438.054198868343
Quadratic Mean439.885915945963
Winsorized Mean ( 1 / 28 )439.3452380952382.50664601678747175.272150576053
Winsorized Mean ( 2 / 28 )439.4166666666672.45348045858956179.099313845473
Winsorized Mean ( 3 / 28 )439.4166666666672.45348045858956179.099313845473
Winsorized Mean ( 4 / 28 )439.3690476190482.44596098050638179.630440191277
Winsorized Mean ( 5 / 28 )439.4285714285712.43364526845654180.563937203249
Winsorized Mean ( 6 / 28 )439.6428571428572.39079577422723183.889758331601
Winsorized Mean ( 7 / 28 )439.726190476192.31735892304588189.753165167105
Winsorized Mean ( 8 / 28 )439.8214285714292.26817645169671193.909705853096
Winsorized Mean ( 9 / 28 )439.7142857142862.25233807433118195.225703781106
Winsorized Mean ( 10 / 28 )439.8333333333332.15518383547596204.081585103481
Winsorized Mean ( 11 / 28 )439.8333333333332.15518383547596204.081585103481
Winsorized Mean ( 12 / 28 )439.976190476192.04334668830445215.321361271923
Winsorized Mean ( 13 / 28 )439.976190476192.04334668830445215.321361271923
Winsorized Mean ( 14 / 28 )439.976190476191.9936053961989220.693719687492
Winsorized Mean ( 15 / 28 )439.976190476191.9936053961989220.693719687492
Winsorized Mean ( 16 / 28 )440.3571428571431.87700115869049234.606750676895
Winsorized Mean ( 17 / 28 )440.7619047619051.81475901205522242.876272735927
Winsorized Mean ( 18 / 28 )440.7619047619051.75399053644999251.290925237254
Winsorized Mean ( 19 / 28 )441.8928571428571.5925293406541277.478628407159
Winsorized Mean ( 20 / 28 )441.6547619047621.56027253599502283.062575105258
Winsorized Mean ( 21 / 28 )441.6547619047621.56027253599502283.062575105258
Winsorized Mean ( 22 / 28 )441.6547619047621.42053762737211310.906767546728
Winsorized Mean ( 23 / 28 )441.6547619047621.34907099711432327.376960033583
Winsorized Mean ( 24 / 28 )441.9404761904761.31208155261414336.823938504411
Winsorized Mean ( 25 / 28 )441.9404761904761.31208155261414336.823938504411
Winsorized Mean ( 26 / 28 )442.251.19425318797719370.315109435945
Winsorized Mean ( 27 / 28 )442.5714285714291.15498442296581383.183893887485
Winsorized Mean ( 28 / 28 )442.2380952380951.11213241590406397.648777172452
Trimmed Mean ( 1 / 28 )439.52.4548466769162179.03358451376
Trimmed Mean ( 2 / 28 )439.66252.3946765690283183.599950693301
Trimmed Mean ( 3 / 28 )439.7948717948722.35730695823807186.566654061713
Trimmed Mean ( 4 / 28 )439.9342105263162.31337344064902190.169992788926
Trimmed Mean ( 5 / 28 )440.0945945945952.26421781413697194.369371995397
Trimmed Mean ( 6 / 28 )440.252.20991063344759199.216200572412
Trimmed Mean ( 7 / 28 )440.3714285714292.15729024766233204.131747709249
Trimmed Mean ( 8 / 28 )440.4852941176472.11266225689359208.497734401393
Trimmed Mean ( 9 / 28 )440.5909090909092.07032279869153212.812663498353
Trimmed Mean ( 10 / 28 )440.718752.02250099942095217.907803321818
Trimmed Mean ( 11 / 28 )440.8387096774191.98463073334706222.126314114843
Trimmed Mean ( 12 / 28 )440.9666666666671.93816365221039227.517767224539
Trimmed Mean ( 13 / 28 )441.0862068965521.90301516460915231.782812401889
Trimmed Mean ( 14 / 28 )441.2142857142861.8591148371568237.32492307417
Trimmed Mean ( 15 / 28 )441.3518518518521.81386796275486243.320826495848
Trimmed Mean ( 16 / 28 )441.51.75680104866351251.309048532201
Trimmed Mean ( 17 / 28 )441.621.70877447431826258.442530970151
Trimmed Mean ( 18 / 28 )441.7083333333331.66043827348302266.019123015505
Trimmed Mean ( 19 / 28 )441.8043478260871.61053883179278274.32082921856
Trimmed Mean ( 20 / 28 )441.7954545454551.57966047461732279.677476042743
Trimmed Mean ( 21 / 28 )441.8095238095241.54462768169979286.029785069844
Trimmed Mean ( 22 / 28 )441.8251.4969573842486295.1486826873
Trimmed Mean ( 23 / 28 )441.8421052631581.46438337087118301.725705202663
Trimmed Mean ( 24 / 28 )441.8611111111111.43491207505524307.936018375273
Trimmed Mean ( 25 / 28 )441.8529411764711.40100063103701315.383827378733
Trimmed Mean ( 26 / 28 )441.843751.35085798228624327.083791037906
Trimmed Mean ( 27 / 28 )441.81.31166297886116336.824326919395
Trimmed Mean ( 28 / 28 )441.7142857142861.26287773212166349.768053137019
Median442
Midrange430.5
Midmean - Weighted Average at Xnp441.4
Midmean - Weighted Average at X(n+1)p441.4
Midmean - Empirical Distribution Function441.4
Midmean - Empirical Distribution Function - Averaging441.4
Midmean - Empirical Distribution Function - Interpolation441.4
Midmean - Closest Observation441.4
Midmean - True Basic - Statistics Graphics Toolkit441.4
Midmean - MS Excel (old versions)441.4
Number of observations84



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')