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Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationTue, 20 Oct 2009 14:12:04 -0600
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2009/Oct/20/t1256069648jbrm5s8ydnlazhj.htm/, Retrieved Fri, 03 May 2024 02:35:03 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=49118, Retrieved Fri, 03 May 2024 02:35:03 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact119
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [onderzoek tijdree...] [2009-10-20 20:12:04] [99bf2a1e962091d45abf4c2600a412f9] [Current]
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Dataseries X:
-4252
-3347
-4695
-3393
-3467
-5017
-3328
-3148
-3525
-4023
-3402
-3713
-3552
-3840
-4635
-4356
-5188
-5023
-3542
-4333
-4580
-4143
-3896
-5135
-5138
-4450
-5522
-4330
-4796
-5005
-3999
-4105
-4391
-4711
-3580
-4068
-4175
-3670
-4584
-3679
-3610
-4604
-3745
-4013
-3267
-4999
-3737
-3316
-3877
-4318
-3916
-4079
-3637
-4316
-3386
-3259
-3887
-3516
-3598
-4272




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'George Udny Yule' @ 72.249.76.132

\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 & 1 seconds \tabularnewline
R Server & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=49118&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]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'George Udny Yule' @ 72.249.76.132[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=49118&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=49118&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 time1 seconds
R Server'George Udny Yule' @ 72.249.76.132







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean-4084.876.4456374178801-53.4340498421247
Geometric MeanNaN
Harmonic Mean-4003.94810082758
Quadratic Mean4126.7884890473
Winsorized Mean ( 1 / 20 )-4081.0833333333374.4899048696888-54.7870659852862
Winsorized Mean ( 2 / 20 )-4079.6833333333374.0283213923783-55.1097641632242
Winsorized Mean ( 3 / 20 )-4081.9833333333373.5477380298211-55.5011403841982
Winsorized Mean ( 4 / 20 )-4075.3166666666771.6627833332331-56.8679651712156
Winsorized Mean ( 5 / 20 )-4076.471.2735765334139-57.1937062550655
Winsorized Mean ( 6 / 20 )-4079.170.3415264192003-57.9899272542169
Winsorized Mean ( 7 / 20 )-4079.2166666666770.0495550648498-58.2332987395887
Winsorized Mean ( 8 / 20 )-4053.3564.1644947537628-63.1712291284317
Winsorized Mean ( 9 / 20 )-4050.3560.0815069031346-67.4142545480776
Winsorized Mean ( 10 / 20 )-4055.8558.271504723251-69.6026302952439
Winsorized Mean ( 11 / 20 )-4046.556.0089505558967-72.2473811745787
Winsorized Mean ( 12 / 20 )-4043.754.3812202754229-74.3583902589901
Winsorized Mean ( 13 / 20 )-4041.5333333333353.290916041855-75.8390666461633
Winsorized Mean ( 14 / 20 )-4047.1333333333352.1246087747877-77.6434284777003
Winsorized Mean ( 15 / 20 )-4019.1333333333346.0255975614127-87.3238707649702
Winsorized Mean ( 16 / 20 )-4006.643.088276224776-92.9858502368257
Winsorized Mean ( 17 / 20 )-4004.3333333333340.4206600042467-99.0665004706165
Winsorized Mean ( 18 / 20 )-4007.3333333333337.8995450881771-105.735657882169
Winsorized Mean ( 19 / 20 )-4009.2333333333337.3325592635652-107.392405246810
Winsorized Mean ( 20 / 20 )-4016.5666666666735.0683623464909-114.535336066772
Trimmed Mean ( 1 / 20 )-4076.172413793173.2531520268579-55.645010501372
Trimmed Mean ( 2 / 20 )-4070.9107142857171.7014792579828-56.7758260556735
Trimmed Mean ( 3 / 20 )-4066.0370370370470.0612687989473-58.0354467845168
Trimmed Mean ( 4 / 20 )-4059.9038461538568.2168004966263-59.5147209572608
Trimmed Mean ( 5 / 20 )-4055.2866.629833607256-60.8628264615445
Trimmed Mean ( 6 / 20 )-405064.717594371829-62.5795819407485
Trimmed Mean ( 7 / 20 )-4043.6739130434862.5319014572-64.6657756890884
Trimmed Mean ( 8 / 20 )-4036.7559.7566428853042-67.5531590311735
Trimmed Mean ( 9 / 20 )-4033.7857142857157.9174142270552-69.6471996914771
Trimmed Mean ( 10 / 20 )-4031.02556.5920680260188-71.2295051339473
Trimmed Mean ( 11 / 20 )-4027.1052631578955.2342456374958-72.9095729773866
Trimmed Mean ( 12 / 20 )-4024.1666666666753.9510286469451-74.5892482050855
Trimmed Mean ( 13 / 20 )-4021.2941176470652.5510282426656-76.5217018985409
Trimmed Mean ( 14 / 20 )-4018.37550.8137361969214-79.0804869066773
Trimmed Mean ( 15 / 20 )-4014.2666666666748.5807523811201-82.6308047922849
Trimmed Mean ( 16 / 20 )-4013.5714285714347.2822614190349-84.885352521562
Trimmed Mean ( 17 / 20 )-4014.5769230769246.1564954367846-86.9775073927621
Trimmed Mean ( 18 / 20 )-4016.0833333333345.1564477182539-88.9370961682152
Trimmed Mean ( 19 / 20 )-4017.4090909090944.2674212577278-90.7531764165677
Trimmed Mean ( 20 / 20 )-4018.742.7067787051239-94.0998155760656
Median-4018
Midrange-4335
Midmean - Weighted Average at Xnp-4032.51612903226
Midmean - Weighted Average at X(n+1)p-4014.26666666667
Midmean - Empirical Distribution Function-4032.51612903226
Midmean - Empirical Distribution Function - Averaging-4014.26666666667
Midmean - Empirical Distribution Function - Interpolation-4014.26666666667
Midmean - Closest Observation-4032.51612903226
Midmean - True Basic - Statistics Graphics Toolkit-4014.26666666667
Midmean - MS Excel (old versions)-4018.375
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & -4084.8 & 76.4456374178801 & -53.4340498421247 \tabularnewline
Geometric Mean & NaN &  &  \tabularnewline
Harmonic Mean & -4003.94810082758 &  &  \tabularnewline
Quadratic Mean & 4126.7884890473 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & -4081.08333333333 & 74.4899048696888 & -54.7870659852862 \tabularnewline
Winsorized Mean ( 2 / 20 ) & -4079.68333333333 & 74.0283213923783 & -55.1097641632242 \tabularnewline
Winsorized Mean ( 3 / 20 ) & -4081.98333333333 & 73.5477380298211 & -55.5011403841982 \tabularnewline
Winsorized Mean ( 4 / 20 ) & -4075.31666666667 & 71.6627833332331 & -56.8679651712156 \tabularnewline
Winsorized Mean ( 5 / 20 ) & -4076.4 & 71.2735765334139 & -57.1937062550655 \tabularnewline
Winsorized Mean ( 6 / 20 ) & -4079.1 & 70.3415264192003 & -57.9899272542169 \tabularnewline
Winsorized Mean ( 7 / 20 ) & -4079.21666666667 & 70.0495550648498 & -58.2332987395887 \tabularnewline
Winsorized Mean ( 8 / 20 ) & -4053.35 & 64.1644947537628 & -63.1712291284317 \tabularnewline
Winsorized Mean ( 9 / 20 ) & -4050.35 & 60.0815069031346 & -67.4142545480776 \tabularnewline
Winsorized Mean ( 10 / 20 ) & -4055.85 & 58.271504723251 & -69.6026302952439 \tabularnewline
Winsorized Mean ( 11 / 20 ) & -4046.5 & 56.0089505558967 & -72.2473811745787 \tabularnewline
Winsorized Mean ( 12 / 20 ) & -4043.7 & 54.3812202754229 & -74.3583902589901 \tabularnewline
Winsorized Mean ( 13 / 20 ) & -4041.53333333333 & 53.290916041855 & -75.8390666461633 \tabularnewline
Winsorized Mean ( 14 / 20 ) & -4047.13333333333 & 52.1246087747877 & -77.6434284777003 \tabularnewline
Winsorized Mean ( 15 / 20 ) & -4019.13333333333 & 46.0255975614127 & -87.3238707649702 \tabularnewline
Winsorized Mean ( 16 / 20 ) & -4006.6 & 43.088276224776 & -92.9858502368257 \tabularnewline
Winsorized Mean ( 17 / 20 ) & -4004.33333333333 & 40.4206600042467 & -99.0665004706165 \tabularnewline
Winsorized Mean ( 18 / 20 ) & -4007.33333333333 & 37.8995450881771 & -105.735657882169 \tabularnewline
Winsorized Mean ( 19 / 20 ) & -4009.23333333333 & 37.3325592635652 & -107.392405246810 \tabularnewline
Winsorized Mean ( 20 / 20 ) & -4016.56666666667 & 35.0683623464909 & -114.535336066772 \tabularnewline
Trimmed Mean ( 1 / 20 ) & -4076.1724137931 & 73.2531520268579 & -55.645010501372 \tabularnewline
Trimmed Mean ( 2 / 20 ) & -4070.91071428571 & 71.7014792579828 & -56.7758260556735 \tabularnewline
Trimmed Mean ( 3 / 20 ) & -4066.03703703704 & 70.0612687989473 & -58.0354467845168 \tabularnewline
Trimmed Mean ( 4 / 20 ) & -4059.90384615385 & 68.2168004966263 & -59.5147209572608 \tabularnewline
Trimmed Mean ( 5 / 20 ) & -4055.28 & 66.629833607256 & -60.8628264615445 \tabularnewline
Trimmed Mean ( 6 / 20 ) & -4050 & 64.717594371829 & -62.5795819407485 \tabularnewline
Trimmed Mean ( 7 / 20 ) & -4043.67391304348 & 62.5319014572 & -64.6657756890884 \tabularnewline
Trimmed Mean ( 8 / 20 ) & -4036.75 & 59.7566428853042 & -67.5531590311735 \tabularnewline
Trimmed Mean ( 9 / 20 ) & -4033.78571428571 & 57.9174142270552 & -69.6471996914771 \tabularnewline
Trimmed Mean ( 10 / 20 ) & -4031.025 & 56.5920680260188 & -71.2295051339473 \tabularnewline
Trimmed Mean ( 11 / 20 ) & -4027.10526315789 & 55.2342456374958 & -72.9095729773866 \tabularnewline
Trimmed Mean ( 12 / 20 ) & -4024.16666666667 & 53.9510286469451 & -74.5892482050855 \tabularnewline
Trimmed Mean ( 13 / 20 ) & -4021.29411764706 & 52.5510282426656 & -76.5217018985409 \tabularnewline
Trimmed Mean ( 14 / 20 ) & -4018.375 & 50.8137361969214 & -79.0804869066773 \tabularnewline
Trimmed Mean ( 15 / 20 ) & -4014.26666666667 & 48.5807523811201 & -82.6308047922849 \tabularnewline
Trimmed Mean ( 16 / 20 ) & -4013.57142857143 & 47.2822614190349 & -84.885352521562 \tabularnewline
Trimmed Mean ( 17 / 20 ) & -4014.57692307692 & 46.1564954367846 & -86.9775073927621 \tabularnewline
Trimmed Mean ( 18 / 20 ) & -4016.08333333333 & 45.1564477182539 & -88.9370961682152 \tabularnewline
Trimmed Mean ( 19 / 20 ) & -4017.40909090909 & 44.2674212577278 & -90.7531764165677 \tabularnewline
Trimmed Mean ( 20 / 20 ) & -4018.7 & 42.7067787051239 & -94.0998155760656 \tabularnewline
Median & -4018 &  &  \tabularnewline
Midrange & -4335 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & -4032.51612903226 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & -4014.26666666667 &  &  \tabularnewline
Midmean - Empirical Distribution Function & -4032.51612903226 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & -4014.26666666667 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & -4014.26666666667 &  &  \tabularnewline
Midmean - Closest Observation & -4032.51612903226 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & -4014.26666666667 &  &  \tabularnewline
Midmean - MS Excel (old versions) & -4018.375 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=49118&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]-4084.8[/C][C]76.4456374178801[/C][C]-53.4340498421247[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]NaN[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]-4003.94810082758[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]4126.7884890473[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]-4081.08333333333[/C][C]74.4899048696888[/C][C]-54.7870659852862[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]-4079.68333333333[/C][C]74.0283213923783[/C][C]-55.1097641632242[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]-4081.98333333333[/C][C]73.5477380298211[/C][C]-55.5011403841982[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]-4075.31666666667[/C][C]71.6627833332331[/C][C]-56.8679651712156[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]-4076.4[/C][C]71.2735765334139[/C][C]-57.1937062550655[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]-4079.1[/C][C]70.3415264192003[/C][C]-57.9899272542169[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]-4079.21666666667[/C][C]70.0495550648498[/C][C]-58.2332987395887[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]-4053.35[/C][C]64.1644947537628[/C][C]-63.1712291284317[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]-4050.35[/C][C]60.0815069031346[/C][C]-67.4142545480776[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]-4055.85[/C][C]58.271504723251[/C][C]-69.6026302952439[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]-4046.5[/C][C]56.0089505558967[/C][C]-72.2473811745787[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]-4043.7[/C][C]54.3812202754229[/C][C]-74.3583902589901[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]-4041.53333333333[/C][C]53.290916041855[/C][C]-75.8390666461633[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]-4047.13333333333[/C][C]52.1246087747877[/C][C]-77.6434284777003[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]-4019.13333333333[/C][C]46.0255975614127[/C][C]-87.3238707649702[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]-4006.6[/C][C]43.088276224776[/C][C]-92.9858502368257[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]-4004.33333333333[/C][C]40.4206600042467[/C][C]-99.0665004706165[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]-4007.33333333333[/C][C]37.8995450881771[/C][C]-105.735657882169[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]-4009.23333333333[/C][C]37.3325592635652[/C][C]-107.392405246810[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]-4016.56666666667[/C][C]35.0683623464909[/C][C]-114.535336066772[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]-4076.1724137931[/C][C]73.2531520268579[/C][C]-55.645010501372[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]-4070.91071428571[/C][C]71.7014792579828[/C][C]-56.7758260556735[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]-4066.03703703704[/C][C]70.0612687989473[/C][C]-58.0354467845168[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]-4059.90384615385[/C][C]68.2168004966263[/C][C]-59.5147209572608[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]-4055.28[/C][C]66.629833607256[/C][C]-60.8628264615445[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]-4050[/C][C]64.717594371829[/C][C]-62.5795819407485[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]-4043.67391304348[/C][C]62.5319014572[/C][C]-64.6657756890884[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]-4036.75[/C][C]59.7566428853042[/C][C]-67.5531590311735[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]-4033.78571428571[/C][C]57.9174142270552[/C][C]-69.6471996914771[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]-4031.025[/C][C]56.5920680260188[/C][C]-71.2295051339473[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]-4027.10526315789[/C][C]55.2342456374958[/C][C]-72.9095729773866[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]-4024.16666666667[/C][C]53.9510286469451[/C][C]-74.5892482050855[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]-4021.29411764706[/C][C]52.5510282426656[/C][C]-76.5217018985409[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]-4018.375[/C][C]50.8137361969214[/C][C]-79.0804869066773[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]-4014.26666666667[/C][C]48.5807523811201[/C][C]-82.6308047922849[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]-4013.57142857143[/C][C]47.2822614190349[/C][C]-84.885352521562[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]-4014.57692307692[/C][C]46.1564954367846[/C][C]-86.9775073927621[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]-4016.08333333333[/C][C]45.1564477182539[/C][C]-88.9370961682152[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]-4017.40909090909[/C][C]44.2674212577278[/C][C]-90.7531764165677[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]-4018.7[/C][C]42.7067787051239[/C][C]-94.0998155760656[/C][/ROW]
[ROW][C]Median[/C][C]-4018[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]-4335[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]-4032.51612903226[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]-4014.26666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]-4032.51612903226[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]-4014.26666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]-4014.26666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]-4032.51612903226[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]-4014.26666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]-4018.375[/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=49118&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=49118&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 Mean-4084.876.4456374178801-53.4340498421247
Geometric MeanNaN
Harmonic Mean-4003.94810082758
Quadratic Mean4126.7884890473
Winsorized Mean ( 1 / 20 )-4081.0833333333374.4899048696888-54.7870659852862
Winsorized Mean ( 2 / 20 )-4079.6833333333374.0283213923783-55.1097641632242
Winsorized Mean ( 3 / 20 )-4081.9833333333373.5477380298211-55.5011403841982
Winsorized Mean ( 4 / 20 )-4075.3166666666771.6627833332331-56.8679651712156
Winsorized Mean ( 5 / 20 )-4076.471.2735765334139-57.1937062550655
Winsorized Mean ( 6 / 20 )-4079.170.3415264192003-57.9899272542169
Winsorized Mean ( 7 / 20 )-4079.2166666666770.0495550648498-58.2332987395887
Winsorized Mean ( 8 / 20 )-4053.3564.1644947537628-63.1712291284317
Winsorized Mean ( 9 / 20 )-4050.3560.0815069031346-67.4142545480776
Winsorized Mean ( 10 / 20 )-4055.8558.271504723251-69.6026302952439
Winsorized Mean ( 11 / 20 )-4046.556.0089505558967-72.2473811745787
Winsorized Mean ( 12 / 20 )-4043.754.3812202754229-74.3583902589901
Winsorized Mean ( 13 / 20 )-4041.5333333333353.290916041855-75.8390666461633
Winsorized Mean ( 14 / 20 )-4047.1333333333352.1246087747877-77.6434284777003
Winsorized Mean ( 15 / 20 )-4019.1333333333346.0255975614127-87.3238707649702
Winsorized Mean ( 16 / 20 )-4006.643.088276224776-92.9858502368257
Winsorized Mean ( 17 / 20 )-4004.3333333333340.4206600042467-99.0665004706165
Winsorized Mean ( 18 / 20 )-4007.3333333333337.8995450881771-105.735657882169
Winsorized Mean ( 19 / 20 )-4009.2333333333337.3325592635652-107.392405246810
Winsorized Mean ( 20 / 20 )-4016.5666666666735.0683623464909-114.535336066772
Trimmed Mean ( 1 / 20 )-4076.172413793173.2531520268579-55.645010501372
Trimmed Mean ( 2 / 20 )-4070.9107142857171.7014792579828-56.7758260556735
Trimmed Mean ( 3 / 20 )-4066.0370370370470.0612687989473-58.0354467845168
Trimmed Mean ( 4 / 20 )-4059.9038461538568.2168004966263-59.5147209572608
Trimmed Mean ( 5 / 20 )-4055.2866.629833607256-60.8628264615445
Trimmed Mean ( 6 / 20 )-405064.717594371829-62.5795819407485
Trimmed Mean ( 7 / 20 )-4043.6739130434862.5319014572-64.6657756890884
Trimmed Mean ( 8 / 20 )-4036.7559.7566428853042-67.5531590311735
Trimmed Mean ( 9 / 20 )-4033.7857142857157.9174142270552-69.6471996914771
Trimmed Mean ( 10 / 20 )-4031.02556.5920680260188-71.2295051339473
Trimmed Mean ( 11 / 20 )-4027.1052631578955.2342456374958-72.9095729773866
Trimmed Mean ( 12 / 20 )-4024.1666666666753.9510286469451-74.5892482050855
Trimmed Mean ( 13 / 20 )-4021.2941176470652.5510282426656-76.5217018985409
Trimmed Mean ( 14 / 20 )-4018.37550.8137361969214-79.0804869066773
Trimmed Mean ( 15 / 20 )-4014.2666666666748.5807523811201-82.6308047922849
Trimmed Mean ( 16 / 20 )-4013.5714285714347.2822614190349-84.885352521562
Trimmed Mean ( 17 / 20 )-4014.5769230769246.1564954367846-86.9775073927621
Trimmed Mean ( 18 / 20 )-4016.0833333333345.1564477182539-88.9370961682152
Trimmed Mean ( 19 / 20 )-4017.4090909090944.2674212577278-90.7531764165677
Trimmed Mean ( 20 / 20 )-4018.742.7067787051239-94.0998155760656
Median-4018
Midrange-4335
Midmean - Weighted Average at Xnp-4032.51612903226
Midmean - Weighted Average at X(n+1)p-4014.26666666667
Midmean - Empirical Distribution Function-4032.51612903226
Midmean - Empirical Distribution Function - Averaging-4014.26666666667
Midmean - Empirical Distribution Function - Interpolation-4014.26666666667
Midmean - Closest Observation-4032.51612903226
Midmean - True Basic - Statistics Graphics Toolkit-4014.26666666667
Midmean - MS Excel (old versions)-4018.375
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')