Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationWed, 12 Oct 2016 17:11:09 +0100
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2016/Oct/12/t1476288691jtfttuack8810mh.htm/, Retrieved Sun, 05 May 2024 12:03:23 +0200
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=, Retrieved Sun, 05 May 2024 12:03:23 +0200
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact0
Dataseries X:
662
670
659
663
673
699
712
700
692
699
700
702
693
696
696
694
695
715
731
715
707
712
699
703
695
694
691
694
699
720
732
712
705
707
700
687
674
676
666
669
669
688
705
684
679
689
691
685
690
685
688
696
693
721
726
704
700
707
696
687




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=&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=&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&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 Mean694.852.12701549483172326.678391242736
Geometric Mean694.657573957622
Harmonic Mean694.464774355789
Quadratic Mean695.042049087679
Winsorized Mean ( 1 / 20 )694.8833333333332.10837604074563329.582256629888
Winsorized Mean ( 2 / 20 )694.752.05388222724426338.261849089645
Winsorized Mean ( 3 / 20 )694.651.95468797631381355.376412203643
Winsorized Mean ( 4 / 20 )694.7833333333331.89156493168279367.306097557663
Winsorized Mean ( 5 / 20 )694.3666666666671.80394524743515384.915599657981
Winsorized Mean ( 6 / 20 )694.4666666666671.78038062753663390.066402613887
Winsorized Mean ( 7 / 20 )694.4666666666671.63445712521374424.891333001991
Winsorized Mean ( 8 / 20 )694.61.60511189042726432.742417611216
Winsorized Mean ( 9 / 20 )694.91.54127762689395450.859720451787
Winsorized Mean ( 10 / 20 )694.5666666666671.29085585997202538.066788248319
Winsorized Mean ( 11 / 20 )695.4833333333331.11626183740294623.046770954227
Winsorized Mean ( 12 / 20 )695.6833333333331.08208097973503642.912449587353
Winsorized Mean ( 13 / 20 )695.251.00805372693333689.69538172838
Winsorized Mean ( 14 / 20 )695.7166666666670.930673672128135747.540934596118
Winsorized Mean ( 15 / 20 )695.4666666666670.889190156102721782.134914442671
Winsorized Mean ( 16 / 20 )695.4666666666670.803757653368476865.269106616937
Winsorized Mean ( 17 / 20 )695.1833333333330.759680153729099915.100032455546
Winsorized Mean ( 18 / 20 )694.8833333333330.6239529836457041113.6789975315
Winsorized Mean ( 19 / 20 )695.20.5743087222692831210.49876667907
Winsorized Mean ( 20 / 20 )695.5333333333330.5242517760298321326.71621754078
Trimmed Mean ( 1 / 20 )694.8275862068972.00952630376865345.766853065731
Trimmed Mean ( 2 / 20 )694.7678571428571.88672585766099368.23996147706
Trimmed Mean ( 3 / 20 )694.7777777777781.7712800542305392.246147704527
Trimmed Mean ( 4 / 20 )694.8269230769231.67757841747919414.184467228068
Trimmed Mean ( 5 / 20 )694.841.58599997426461438.108456037132
Trimmed Mean ( 6 / 20 )694.9583333333331.50175970461385462.762671816412
Trimmed Mean ( 7 / 20 )695.0652173913041.40096660003325496.132611137771
Trimmed Mean ( 8 / 20 )695.1818181818181.3183822840934527.299119966456
Trimmed Mean ( 9 / 20 )695.2857142857141.21846312933317570.625156845102
Trimmed Mean ( 10 / 20 )695.351.10508730366336629.226304288285
Trimmed Mean ( 11 / 20 )695.4736842105261.03339463399348672.999124761194
Trimmed Mean ( 12 / 20 )695.4722222222220.990819855418054701.915911776701
Trimmed Mean ( 13 / 20 )695.4411764705880.941413183245009738.720456488015
Trimmed Mean ( 14 / 20 )695.468750.894634966782722777.377115608434
Trimmed Mean ( 15 / 20 )695.4333333333330.851885445503406816.34606742504
Trimmed Mean ( 16 / 20 )695.4285714285710.802490454588225866.587966813152
Trimmed Mean ( 17 / 20 )695.4230769230770.758892060680116916.366256750454
Trimmed Mean ( 18 / 20 )695.4583333333330.707053404565887983.600855101358
Trimmed Mean ( 19 / 20 )695.5454545454550.6797226093482471023.278385888
Trimmed Mean ( 20 / 20 )695.60.6545388091103381062.73301188278
Median695.5
Midrange695.5
Midmean - Weighted Average at Xnp695.161290322581
Midmean - Weighted Average at X(n+1)p695.161290322581
Midmean - Empirical Distribution Function695.161290322581
Midmean - Empirical Distribution Function - Averaging695.161290322581
Midmean - Empirical Distribution Function - Interpolation695.161290322581
Midmean - Closest Observation695.161290322581
Midmean - True Basic - Statistics Graphics Toolkit695.161290322581
Midmean - MS Excel (old versions)695.757575757576
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 694.85 & 2.12701549483172 & 326.678391242736 \tabularnewline
Geometric Mean & 694.657573957622 &  &  \tabularnewline
Harmonic Mean & 694.464774355789 &  &  \tabularnewline
Quadratic Mean & 695.042049087679 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 694.883333333333 & 2.10837604074563 & 329.582256629888 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 694.75 & 2.05388222724426 & 338.261849089645 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 694.65 & 1.95468797631381 & 355.376412203643 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 694.783333333333 & 1.89156493168279 & 367.306097557663 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 694.366666666667 & 1.80394524743515 & 384.915599657981 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 694.466666666667 & 1.78038062753663 & 390.066402613887 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 694.466666666667 & 1.63445712521374 & 424.891333001991 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 694.6 & 1.60511189042726 & 432.742417611216 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 694.9 & 1.54127762689395 & 450.859720451787 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 694.566666666667 & 1.29085585997202 & 538.066788248319 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 695.483333333333 & 1.11626183740294 & 623.046770954227 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 695.683333333333 & 1.08208097973503 & 642.912449587353 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 695.25 & 1.00805372693333 & 689.69538172838 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 695.716666666667 & 0.930673672128135 & 747.540934596118 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 695.466666666667 & 0.889190156102721 & 782.134914442671 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 695.466666666667 & 0.803757653368476 & 865.269106616937 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 695.183333333333 & 0.759680153729099 & 915.100032455546 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 694.883333333333 & 0.623952983645704 & 1113.6789975315 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 695.2 & 0.574308722269283 & 1210.49876667907 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 695.533333333333 & 0.524251776029832 & 1326.71621754078 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 694.827586206897 & 2.00952630376865 & 345.766853065731 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 694.767857142857 & 1.88672585766099 & 368.23996147706 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 694.777777777778 & 1.7712800542305 & 392.246147704527 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 694.826923076923 & 1.67757841747919 & 414.184467228068 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 694.84 & 1.58599997426461 & 438.108456037132 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 694.958333333333 & 1.50175970461385 & 462.762671816412 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 695.065217391304 & 1.40096660003325 & 496.132611137771 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 695.181818181818 & 1.3183822840934 & 527.299119966456 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 695.285714285714 & 1.21846312933317 & 570.625156845102 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 695.35 & 1.10508730366336 & 629.226304288285 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 695.473684210526 & 1.03339463399348 & 672.999124761194 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 695.472222222222 & 0.990819855418054 & 701.915911776701 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 695.441176470588 & 0.941413183245009 & 738.720456488015 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 695.46875 & 0.894634966782722 & 777.377115608434 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 695.433333333333 & 0.851885445503406 & 816.34606742504 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 695.428571428571 & 0.802490454588225 & 866.587966813152 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 695.423076923077 & 0.758892060680116 & 916.366256750454 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 695.458333333333 & 0.707053404565887 & 983.600855101358 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 695.545454545455 & 0.679722609348247 & 1023.278385888 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 695.6 & 0.654538809110338 & 1062.73301188278 \tabularnewline
Median & 695.5 &  &  \tabularnewline
Midrange & 695.5 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 695.161290322581 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 695.161290322581 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 695.161290322581 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 695.161290322581 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 695.161290322581 &  &  \tabularnewline
Midmean - Closest Observation & 695.161290322581 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 695.161290322581 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 695.757575757576 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&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]694.85[/C][C]2.12701549483172[/C][C]326.678391242736[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]694.657573957622[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]694.464774355789[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]695.042049087679[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]694.883333333333[/C][C]2.10837604074563[/C][C]329.582256629888[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]694.75[/C][C]2.05388222724426[/C][C]338.261849089645[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]694.65[/C][C]1.95468797631381[/C][C]355.376412203643[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]694.783333333333[/C][C]1.89156493168279[/C][C]367.306097557663[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]694.366666666667[/C][C]1.80394524743515[/C][C]384.915599657981[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]694.466666666667[/C][C]1.78038062753663[/C][C]390.066402613887[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]694.466666666667[/C][C]1.63445712521374[/C][C]424.891333001991[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]694.6[/C][C]1.60511189042726[/C][C]432.742417611216[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]694.9[/C][C]1.54127762689395[/C][C]450.859720451787[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]694.566666666667[/C][C]1.29085585997202[/C][C]538.066788248319[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]695.483333333333[/C][C]1.11626183740294[/C][C]623.046770954227[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]695.683333333333[/C][C]1.08208097973503[/C][C]642.912449587353[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]695.25[/C][C]1.00805372693333[/C][C]689.69538172838[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]695.716666666667[/C][C]0.930673672128135[/C][C]747.540934596118[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]695.466666666667[/C][C]0.889190156102721[/C][C]782.134914442671[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]695.466666666667[/C][C]0.803757653368476[/C][C]865.269106616937[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]695.183333333333[/C][C]0.759680153729099[/C][C]915.100032455546[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]694.883333333333[/C][C]0.623952983645704[/C][C]1113.6789975315[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]695.2[/C][C]0.574308722269283[/C][C]1210.49876667907[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]695.533333333333[/C][C]0.524251776029832[/C][C]1326.71621754078[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]694.827586206897[/C][C]2.00952630376865[/C][C]345.766853065731[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]694.767857142857[/C][C]1.88672585766099[/C][C]368.23996147706[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]694.777777777778[/C][C]1.7712800542305[/C][C]392.246147704527[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]694.826923076923[/C][C]1.67757841747919[/C][C]414.184467228068[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]694.84[/C][C]1.58599997426461[/C][C]438.108456037132[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]694.958333333333[/C][C]1.50175970461385[/C][C]462.762671816412[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]695.065217391304[/C][C]1.40096660003325[/C][C]496.132611137771[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]695.181818181818[/C][C]1.3183822840934[/C][C]527.299119966456[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]695.285714285714[/C][C]1.21846312933317[/C][C]570.625156845102[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]695.35[/C][C]1.10508730366336[/C][C]629.226304288285[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]695.473684210526[/C][C]1.03339463399348[/C][C]672.999124761194[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]695.472222222222[/C][C]0.990819855418054[/C][C]701.915911776701[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]695.441176470588[/C][C]0.941413183245009[/C][C]738.720456488015[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]695.46875[/C][C]0.894634966782722[/C][C]777.377115608434[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]695.433333333333[/C][C]0.851885445503406[/C][C]816.34606742504[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]695.428571428571[/C][C]0.802490454588225[/C][C]866.587966813152[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]695.423076923077[/C][C]0.758892060680116[/C][C]916.366256750454[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]695.458333333333[/C][C]0.707053404565887[/C][C]983.600855101358[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]695.545454545455[/C][C]0.679722609348247[/C][C]1023.278385888[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]695.6[/C][C]0.654538809110338[/C][C]1062.73301188278[/C][/ROW]
[ROW][C]Median[/C][C]695.5[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]695.5[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]695.161290322581[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]695.161290322581[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]695.161290322581[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]695.161290322581[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]695.161290322581[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]695.161290322581[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]695.161290322581[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]695.757575757576[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]60[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&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 Mean694.852.12701549483172326.678391242736
Geometric Mean694.657573957622
Harmonic Mean694.464774355789
Quadratic Mean695.042049087679
Winsorized Mean ( 1 / 20 )694.8833333333332.10837604074563329.582256629888
Winsorized Mean ( 2 / 20 )694.752.05388222724426338.261849089645
Winsorized Mean ( 3 / 20 )694.651.95468797631381355.376412203643
Winsorized Mean ( 4 / 20 )694.7833333333331.89156493168279367.306097557663
Winsorized Mean ( 5 / 20 )694.3666666666671.80394524743515384.915599657981
Winsorized Mean ( 6 / 20 )694.4666666666671.78038062753663390.066402613887
Winsorized Mean ( 7 / 20 )694.4666666666671.63445712521374424.891333001991
Winsorized Mean ( 8 / 20 )694.61.60511189042726432.742417611216
Winsorized Mean ( 9 / 20 )694.91.54127762689395450.859720451787
Winsorized Mean ( 10 / 20 )694.5666666666671.29085585997202538.066788248319
Winsorized Mean ( 11 / 20 )695.4833333333331.11626183740294623.046770954227
Winsorized Mean ( 12 / 20 )695.6833333333331.08208097973503642.912449587353
Winsorized Mean ( 13 / 20 )695.251.00805372693333689.69538172838
Winsorized Mean ( 14 / 20 )695.7166666666670.930673672128135747.540934596118
Winsorized Mean ( 15 / 20 )695.4666666666670.889190156102721782.134914442671
Winsorized Mean ( 16 / 20 )695.4666666666670.803757653368476865.269106616937
Winsorized Mean ( 17 / 20 )695.1833333333330.759680153729099915.100032455546
Winsorized Mean ( 18 / 20 )694.8833333333330.6239529836457041113.6789975315
Winsorized Mean ( 19 / 20 )695.20.5743087222692831210.49876667907
Winsorized Mean ( 20 / 20 )695.5333333333330.5242517760298321326.71621754078
Trimmed Mean ( 1 / 20 )694.8275862068972.00952630376865345.766853065731
Trimmed Mean ( 2 / 20 )694.7678571428571.88672585766099368.23996147706
Trimmed Mean ( 3 / 20 )694.7777777777781.7712800542305392.246147704527
Trimmed Mean ( 4 / 20 )694.8269230769231.67757841747919414.184467228068
Trimmed Mean ( 5 / 20 )694.841.58599997426461438.108456037132
Trimmed Mean ( 6 / 20 )694.9583333333331.50175970461385462.762671816412
Trimmed Mean ( 7 / 20 )695.0652173913041.40096660003325496.132611137771
Trimmed Mean ( 8 / 20 )695.1818181818181.3183822840934527.299119966456
Trimmed Mean ( 9 / 20 )695.2857142857141.21846312933317570.625156845102
Trimmed Mean ( 10 / 20 )695.351.10508730366336629.226304288285
Trimmed Mean ( 11 / 20 )695.4736842105261.03339463399348672.999124761194
Trimmed Mean ( 12 / 20 )695.4722222222220.990819855418054701.915911776701
Trimmed Mean ( 13 / 20 )695.4411764705880.941413183245009738.720456488015
Trimmed Mean ( 14 / 20 )695.468750.894634966782722777.377115608434
Trimmed Mean ( 15 / 20 )695.4333333333330.851885445503406816.34606742504
Trimmed Mean ( 16 / 20 )695.4285714285710.802490454588225866.587966813152
Trimmed Mean ( 17 / 20 )695.4230769230770.758892060680116916.366256750454
Trimmed Mean ( 18 / 20 )695.4583333333330.707053404565887983.600855101358
Trimmed Mean ( 19 / 20 )695.5454545454550.6797226093482471023.278385888
Trimmed Mean ( 20 / 20 )695.60.6545388091103381062.73301188278
Median695.5
Midrange695.5
Midmean - Weighted Average at Xnp695.161290322581
Midmean - Weighted Average at X(n+1)p695.161290322581
Midmean - Empirical Distribution Function695.161290322581
Midmean - Empirical Distribution Function - Averaging695.161290322581
Midmean - Empirical Distribution Function - Interpolation695.161290322581
Midmean - Closest Observation695.161290322581
Midmean - True Basic - Statistics Graphics Toolkit695.161290322581
Midmean - MS Excel (old versions)695.757575757576
Number of observations60



Parameters (Session):
Parameters (R input):
R code (references can be found in the software module):
geomean <- function(x) {
return(exp(mean(log(x))))
}
harmean <- function(x) {
return(1/mean(1/x))
}
quamean <- function(x) {
return(sqrt(mean(x*x)))
}
winmean <- function(x) {
x <-sort(x[!is.na(x)])
n<-length(x)
denom <- 3
nodenom <- n/denom
if (nodenom>40) denom <- n/40
sqrtn = sqrt(n)
roundnodenom = floor(nodenom)
win <- array(NA,dim=c(roundnodenom,2))
for (j in 1:roundnodenom) {
win[j,1] <- (j*x[j+1]+sum(x[(j+1):(n-j)])+j*x[n-j])/n
win[j,2] <- sd(c(rep(x[j+1],j),x[(j+1):(n-j)],rep(x[n-j],j)))/sqrtn
}
return(win)
}
trimean <- function(x) {
x <-sort(x[!is.na(x)])
n<-length(x)
denom <- 3
nodenom <- n/denom
if (nodenom>40) denom <- n/40
sqrtn = sqrt(n)
roundnodenom = floor(nodenom)
tri <- array(NA,dim=c(roundnodenom,2))
for (j in 1:roundnodenom) {
tri[j,1] <- mean(x,trim=j/n)
tri[j,2] <- sd(x[(j+1):(n-j)]) / sqrt(n-j*2)
}
return(tri)
}
midrange <- function(x) {
return((max(x)+min(x))/2)
}
q1 <- function(data,n,p,i,f) {
np <- n*p;
i <<- floor(np)
f <<- np - i
qvalue <- (1-f)*data[i] + f*data[i+1]
}
q2 <- function(data,n,p,i,f) {
np <- (n+1)*p
i <<- floor(np)
f <<- np - i
qvalue <- (1-f)*data[i] + f*data[i+1]
}
q3 <- function(data,n,p,i,f) {
np <- n*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- data[i]
} else {
qvalue <- data[i+1]
}
}
q4 <- function(data,n,p,i,f) {
np <- n*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- (data[i]+data[i+1])/2
} else {
qvalue <- data[i+1]
}
}
q5 <- function(data,n,p,i,f) {
np <- (n-1)*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- data[i+1]
} else {
qvalue <- data[i+1] + f*(data[i+2]-data[i+1])
}
}
q6 <- function(data,n,p,i,f) {
np <- n*p+0.5
i <<- floor(np)
f <<- np - i
qvalue <- data[i]
}
q7 <- function(data,n,p,i,f) {
np <- (n+1)*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- data[i]
} else {
qvalue <- f*data[i] + (1-f)*data[i+1]
}
}
q8 <- function(data,n,p,i,f) {
np <- (n+1)*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- data[i]
} else {
if (f == 0.5) {
qvalue <- (data[i]+data[i+1])/2
} else {
if (f < 0.5) {
qvalue <- data[i]
} else {
qvalue <- data[i+1]
}
}
}
}
midmean <- function(x,def) {
x <-sort(x[!is.na(x)])
n<-length(x)
if (def==1) {
qvalue1 <- q1(x,n,0.25,i,f)
qvalue3 <- q1(x,n,0.75,i,f)
}
if (def==2) {
qvalue1 <- q2(x,n,0.25,i,f)
qvalue3 <- q2(x,n,0.75,i,f)
}
if (def==3) {
qvalue1 <- q3(x,n,0.25,i,f)
qvalue3 <- q3(x,n,0.75,i,f)
}
if (def==4) {
qvalue1 <- q4(x,n,0.25,i,f)
qvalue3 <- q4(x,n,0.75,i,f)
}
if (def==5) {
qvalue1 <- q5(x,n,0.25,i,f)
qvalue3 <- q5(x,n,0.75,i,f)
}
if (def==6) {
qvalue1 <- q6(x,n,0.25,i,f)
qvalue3 <- q6(x,n,0.75,i,f)
}
if (def==7) {
qvalue1 <- q7(x,n,0.25,i,f)
qvalue3 <- q7(x,n,0.75,i,f)
}
if (def==8) {
qvalue1 <- q8(x,n,0.25,i,f)
qvalue3 <- q8(x,n,0.75,i,f)
}
midm <- 0
myn <- 0
roundno4 <- round(n/4)
round3no4 <- round(3*n/4)
for (i in 1:n) {
if ((x[i]>=qvalue1) & (x[i]<=qvalue3)){
midm = midm + x[i]
myn = myn + 1
}
}
midm = midm / myn
return(midm)
}
(arm <- mean(x))
sqrtn <- sqrt(length(x))
(armse <- sd(x) / sqrtn)
(armose <- arm / armse)
(geo <- geomean(x))
(har <- harmean(x))
(qua <- quamean(x))
(win <- winmean(x))
(tri <- trimean(x))
(midr <- midrange(x))
midm <- array(NA,dim=8)
for (j in 1:8) midm[j] <- midmean(x,j)
midm
bitmap(file='test1.png')
lb <- win[,1] - 2*win[,2]
ub <- win[,1] + 2*win[,2]
if ((ylimmin == '') | (ylimmax == '')) plot(win[,1],type='b',main=main, xlab='j', pch=19, ylab='Winsorized Mean(j/n)', ylim=c(min(lb),max(ub))) else plot(win[,1],type='l',main=main, xlab='j', pch=19, ylab='Winsorized Mean(j/n)', ylim=c(ylimmin,ylimmax))
lines(ub,lty=3)
lines(lb,lty=3)
grid()
dev.off()
bitmap(file='test2.png')
lb <- tri[,1] - 2*tri[,2]
ub <- tri[,1] + 2*tri[,2]
if ((ylimmin == '') | (ylimmax == '')) plot(tri[,1],type='b',main=main, xlab='j', pch=19, ylab='Trimmed Mean(j/n)', ylim=c(min(lb),max(ub))) else plot(tri[,1],type='l',main=main, xlab='j', pch=19, ylab='Trimmed Mean(j/n)', ylim=c(ylimmin,ylimmax))
lines(ub,lty=3)
lines(lb,lty=3)
grid()
dev.off()
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Central Tendency - Ungrouped Data',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Measure',header=TRUE)
a<-table.element(a,'Value',header=TRUE)
a<-table.element(a,'S.E.',header=TRUE)
a<-table.element(a,'Value/S.E.',header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('arithmetic_mean.htm', 'Arithmetic Mean', 'click to view the definition of the Arithmetic Mean'),header=TRUE)
a<-table.element(a,arm)
a<-table.element(a,hyperlink('arithmetic_mean_standard_error.htm', armse, 'click to view the definition of the Standard Error of the Arithmetic Mean'))
a<-table.element(a,armose)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('geometric_mean.htm', 'Geometric Mean', 'click to view the definition of the Geometric Mean'),header=TRUE)
a<-table.element(a,geo)
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('harmonic_mean.htm', 'Harmonic Mean', 'click to view the definition of the Harmonic Mean'),header=TRUE)
a<-table.element(a,har)
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('quadratic_mean.htm', 'Quadratic Mean', 'click to view the definition of the Quadratic Mean'),header=TRUE)
a<-table.element(a,qua)
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
for (j in 1:length(win[,1])) {
a<-table.row.start(a)
mylabel <- paste('Winsorized Mean (',j)
mylabel <- paste(mylabel,'/')
mylabel <- paste(mylabel,length(win[,1]))
mylabel <- paste(mylabel,')')
a<-table.element(a,hyperlink('winsorized_mean.htm', mylabel, 'click to view the definition of the Winsorized Mean'),header=TRUE)
a<-table.element(a,win[j,1])
a<-table.element(a,win[j,2])
a<-table.element(a,win[j,1]/win[j,2])
a<-table.row.end(a)
}
for (j in 1:length(tri[,1])) {
a<-table.row.start(a)
mylabel <- paste('Trimmed Mean (',j)
mylabel <- paste(mylabel,'/')
mylabel <- paste(mylabel,length(tri[,1]))
mylabel <- paste(mylabel,')')
a<-table.element(a,hyperlink('arithmetic_mean.htm', mylabel, 'click to view the definition of the Trimmed Mean'),header=TRUE)
a<-table.element(a,tri[j,1])
a<-table.element(a,tri[j,2])
a<-table.element(a,tri[j,1]/tri[j,2])
a<-table.row.end(a)
}
a<-table.row.start(a)
a<-table.element(a,hyperlink('median_1.htm', 'Median', 'click to view the definition of the Median'),header=TRUE)
a<-table.element(a,median(x))
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('midrange.htm', 'Midrange', 'click to view the definition of the Midrange'),header=TRUE)
a<-table.element(a,midr)
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_1.htm','Weighted Average at Xnp',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[1])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_2.htm','Weighted Average at X(n+1)p',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[2])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_3.htm','Empirical Distribution Function',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[3])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_4.htm','Empirical Distribution Function - Averaging',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[4])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_5.htm','Empirical Distribution Function - Interpolation',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[5])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_6.htm','Closest Observation',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[6])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_7.htm','True Basic - Statistics Graphics Toolkit',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[7])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_8.htm','MS Excel (old versions)',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[8])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Number of observations',header=TRUE)
a<-table.element(a,length(x))
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable.tab')