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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, 15 Nov 2011 16:00:58 -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/2011/Nov/15/t1321390883op3duarizrtjgn6.htm/, Retrieved Thu, 28 Mar 2024 13:32:34 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=143545, Retrieved Thu, 28 Mar 2024 13:32:34 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact75
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Central Tendency] [Arabica Price in ...] [2008-01-06 21:28:17] [74be16979710d4c4e7c6647856088456]
- RM D  [Central Tendency] [winsorized and tr...] [2011-11-13 14:50:39] [74be16979710d4c4e7c6647856088456]
-           [Central Tendency] [W6 T3] [2011-11-15 21:00:58] [7c363341293f6644b8647ab9153ed4f7] [Current]
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Dataseries X:
330123
334728
338414
338582
339904
341396
343496
344591
346099
347258
348503
348628
349913
352797
354539
353032
355576
355603
357889
359310
361253
364253
364872
364201
368830
368755
370117
372895
374215
375539
380550
382839
386678
389265
393978
397923
394691
394410
398981
399827
403635
402425
406939
404544
406309
407884
407151
414154
408459
407609
408503
409068
412860
415113
418053
415780
413562
414521
413948
413106




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Gwilym Jenkins' @ jenkins.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 & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=143545&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]'Gwilym Jenkins' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=143545&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=143545&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'Gwilym Jenkins' @ jenkins.wessa.net







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean379134.63561.86138811375106.442828254128
Geometric Mean378139.556086526
Harmonic Mean377139.106807599
Quadratic Mean380120.467027888
Winsorized Mean ( 1 / 20 )379173.4666666673537.90747847543107.174500456429
Winsorized Mean ( 2 / 20 )379274.13508.82339677762108.091533004571
Winsorized Mean ( 3 / 20 )379252.93502.07935461851108.293634037688
Winsorized Mean ( 4 / 20 )379316.5666666673480.78443569517108.974449200819
Winsorized Mean ( 5 / 20 )379423.7333333333454.34297307475109.839624001089
Winsorized Mean ( 6 / 20 )379595.1333333333409.37450751117111.338643641832
Winsorized Mean ( 7 / 20 )379669.6833333333377.71214813297112.404392879718
Winsorized Mean ( 8 / 20 )379837.953337.28463512379113.81646803582
Winsorized Mean ( 9 / 20 )3794433215.47143040861118.005402384117
Winsorized Mean ( 10 / 20 )379556.3333333333165.97022879909119.88626105221
Winsorized Mean ( 11 / 20 )379571.1833333333160.91436267852120.082716512348
Winsorized Mean ( 12 / 20 )379713.1833333333100.89819906358122.452644026818
Winsorized Mean ( 13 / 20 )380278.4666666672992.13165803591127.092825492943
Winsorized Mean ( 14 / 20 )380226.4333333332967.11392086927128.146894077441
Winsorized Mean ( 15 / 20 )380550.1833333332901.05565458718131.176450452305
Winsorized Mean ( 16 / 20 )380658.7166666672833.45502537851134.344365185685
Winsorized Mean ( 17 / 20 )380166.2833333332756.44580343663137.919012541207
Winsorized Mean ( 18 / 20 )380579.3833333332613.3295211143145.630078510366
Winsorized Mean ( 19 / 20 )380646.22490.48935787626152.839922321367
Winsorized Mean ( 20 / 20 )380427.8666666672270.1151299193167.580869204722
Trimmed Mean ( 1 / 20 )379308.6206896553521.30053526617107.718332159054
Trimmed Mean ( 2 / 20 )379453.4285714293497.4094972516108.495567610718
Trimmed Mean ( 3 / 20 )379553.0555555563482.9019181969108.976096505195
Trimmed Mean ( 4 / 20 )379668.53463.65073014985109.615122764868
Trimmed Mean ( 5 / 20 )379774.083443.10571916384110.299860351726
Trimmed Mean ( 6 / 20 )379861.6666666673421.06995963766111.035924768665
Trimmed Mean ( 7 / 20 )379919.6086956523401.14096790384111.703576029605
Trimmed Mean ( 8 / 20 )379968.2954545453378.49431519752112.466755899316
Trimmed Mean ( 9 / 20 )379991.5714285713353.59942745019113.308574756493
Trimmed Mean ( 10 / 20 )3800833344.4783790907113.644926627792
Trimmed Mean ( 11 / 20 )380166.1578947373335.67509029331113.9697805104
Trimmed Mean ( 12 / 20 )380256.3055555563315.27814026704114.698160898478
Trimmed Mean ( 13 / 20 )380336.1764705883292.69224551206115.509178541963
Trimmed Mean ( 14 / 20 )380344.53278.45932387554116.013182542825
Trimmed Mean ( 15 / 20 )380361.3666666673251.47880431416116.98103833923
Trimmed Mean ( 16 / 20 )380334.3928571433217.13212247961118.221564541776
Trimmed Mean ( 17 / 20 )380287.6153846153171.22612301829119.918164341642
Trimmed Mean ( 18 / 20 )380305.4583333333110.03773392643122.28322961638
Trimmed Mean ( 19 / 20 )380263.9545454553048.07289305447124.755531736773
Trimmed Mean ( 20 / 20 )380203.62974.48480404148127.821664942921
Median378044.5
Midrange374088
Midmean - Weighted Average at Xnp379479.774193548
Midmean - Weighted Average at X(n+1)p380361.366666667
Midmean - Empirical Distribution Function379479.774193548
Midmean - Empirical Distribution Function - Averaging380361.366666667
Midmean - Empirical Distribution Function - Interpolation380361.366666667
Midmean - Closest Observation379479.774193548
Midmean - True Basic - Statistics Graphics Toolkit380361.366666667
Midmean - MS Excel (old versions)380344.5
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 379134.6 & 3561.86138811375 & 106.442828254128 \tabularnewline
Geometric Mean & 378139.556086526 &  &  \tabularnewline
Harmonic Mean & 377139.106807599 &  &  \tabularnewline
Quadratic Mean & 380120.467027888 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 379173.466666667 & 3537.90747847543 & 107.174500456429 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 379274.1 & 3508.82339677762 & 108.091533004571 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 379252.9 & 3502.07935461851 & 108.293634037688 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 379316.566666667 & 3480.78443569517 & 108.974449200819 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 379423.733333333 & 3454.34297307475 & 109.839624001089 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 379595.133333333 & 3409.37450751117 & 111.338643641832 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 379669.683333333 & 3377.71214813297 & 112.404392879718 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 379837.95 & 3337.28463512379 & 113.81646803582 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 379443 & 3215.47143040861 & 118.005402384117 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 379556.333333333 & 3165.97022879909 & 119.88626105221 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 379571.183333333 & 3160.91436267852 & 120.082716512348 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 379713.183333333 & 3100.89819906358 & 122.452644026818 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 380278.466666667 & 2992.13165803591 & 127.092825492943 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 380226.433333333 & 2967.11392086927 & 128.146894077441 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 380550.183333333 & 2901.05565458718 & 131.176450452305 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 380658.716666667 & 2833.45502537851 & 134.344365185685 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 380166.283333333 & 2756.44580343663 & 137.919012541207 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 380579.383333333 & 2613.3295211143 & 145.630078510366 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 380646.2 & 2490.48935787626 & 152.839922321367 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 380427.866666667 & 2270.1151299193 & 167.580869204722 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 379308.620689655 & 3521.30053526617 & 107.718332159054 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 379453.428571429 & 3497.4094972516 & 108.495567610718 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 379553.055555556 & 3482.9019181969 & 108.976096505195 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 379668.5 & 3463.65073014985 & 109.615122764868 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 379774.08 & 3443.10571916384 & 110.299860351726 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 379861.666666667 & 3421.06995963766 & 111.035924768665 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 379919.608695652 & 3401.14096790384 & 111.703576029605 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 379968.295454545 & 3378.49431519752 & 112.466755899316 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 379991.571428571 & 3353.59942745019 & 113.308574756493 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 380083 & 3344.4783790907 & 113.644926627792 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 380166.157894737 & 3335.67509029331 & 113.9697805104 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 380256.305555556 & 3315.27814026704 & 114.698160898478 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 380336.176470588 & 3292.69224551206 & 115.509178541963 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 380344.5 & 3278.45932387554 & 116.013182542825 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 380361.366666667 & 3251.47880431416 & 116.98103833923 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 380334.392857143 & 3217.13212247961 & 118.221564541776 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 380287.615384615 & 3171.22612301829 & 119.918164341642 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 380305.458333333 & 3110.03773392643 & 122.28322961638 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 380263.954545455 & 3048.07289305447 & 124.755531736773 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 380203.6 & 2974.48480404148 & 127.821664942921 \tabularnewline
Median & 378044.5 &  &  \tabularnewline
Midrange & 374088 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 379479.774193548 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 380361.366666667 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 379479.774193548 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 380361.366666667 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 380361.366666667 &  &  \tabularnewline
Midmean - Closest Observation & 379479.774193548 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 380361.366666667 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 380344.5 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=143545&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]379134.6[/C][C]3561.86138811375[/C][C]106.442828254128[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]378139.556086526[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]377139.106807599[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]380120.467027888[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]379173.466666667[/C][C]3537.90747847543[/C][C]107.174500456429[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]379274.1[/C][C]3508.82339677762[/C][C]108.091533004571[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]379252.9[/C][C]3502.07935461851[/C][C]108.293634037688[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]379316.566666667[/C][C]3480.78443569517[/C][C]108.974449200819[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]379423.733333333[/C][C]3454.34297307475[/C][C]109.839624001089[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]379595.133333333[/C][C]3409.37450751117[/C][C]111.338643641832[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]379669.683333333[/C][C]3377.71214813297[/C][C]112.404392879718[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]379837.95[/C][C]3337.28463512379[/C][C]113.81646803582[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]379443[/C][C]3215.47143040861[/C][C]118.005402384117[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]379556.333333333[/C][C]3165.97022879909[/C][C]119.88626105221[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]379571.183333333[/C][C]3160.91436267852[/C][C]120.082716512348[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]379713.183333333[/C][C]3100.89819906358[/C][C]122.452644026818[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]380278.466666667[/C][C]2992.13165803591[/C][C]127.092825492943[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]380226.433333333[/C][C]2967.11392086927[/C][C]128.146894077441[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]380550.183333333[/C][C]2901.05565458718[/C][C]131.176450452305[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]380658.716666667[/C][C]2833.45502537851[/C][C]134.344365185685[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]380166.283333333[/C][C]2756.44580343663[/C][C]137.919012541207[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]380579.383333333[/C][C]2613.3295211143[/C][C]145.630078510366[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]380646.2[/C][C]2490.48935787626[/C][C]152.839922321367[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]380427.866666667[/C][C]2270.1151299193[/C][C]167.580869204722[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]379308.620689655[/C][C]3521.30053526617[/C][C]107.718332159054[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]379453.428571429[/C][C]3497.4094972516[/C][C]108.495567610718[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]379553.055555556[/C][C]3482.9019181969[/C][C]108.976096505195[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]379668.5[/C][C]3463.65073014985[/C][C]109.615122764868[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]379774.08[/C][C]3443.10571916384[/C][C]110.299860351726[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]379861.666666667[/C][C]3421.06995963766[/C][C]111.035924768665[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]379919.608695652[/C][C]3401.14096790384[/C][C]111.703576029605[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]379968.295454545[/C][C]3378.49431519752[/C][C]112.466755899316[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]379991.571428571[/C][C]3353.59942745019[/C][C]113.308574756493[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]380083[/C][C]3344.4783790907[/C][C]113.644926627792[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]380166.157894737[/C][C]3335.67509029331[/C][C]113.9697805104[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]380256.305555556[/C][C]3315.27814026704[/C][C]114.698160898478[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]380336.176470588[/C][C]3292.69224551206[/C][C]115.509178541963[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]380344.5[/C][C]3278.45932387554[/C][C]116.013182542825[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]380361.366666667[/C][C]3251.47880431416[/C][C]116.98103833923[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]380334.392857143[/C][C]3217.13212247961[/C][C]118.221564541776[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]380287.615384615[/C][C]3171.22612301829[/C][C]119.918164341642[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]380305.458333333[/C][C]3110.03773392643[/C][C]122.28322961638[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]380263.954545455[/C][C]3048.07289305447[/C][C]124.755531736773[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]380203.6[/C][C]2974.48480404148[/C][C]127.821664942921[/C][/ROW]
[ROW][C]Median[/C][C]378044.5[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]374088[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]379479.774193548[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]380361.366666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]379479.774193548[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]380361.366666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]380361.366666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]379479.774193548[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]380361.366666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]380344.5[/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=143545&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=143545&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 Mean379134.63561.86138811375106.442828254128
Geometric Mean378139.556086526
Harmonic Mean377139.106807599
Quadratic Mean380120.467027888
Winsorized Mean ( 1 / 20 )379173.4666666673537.90747847543107.174500456429
Winsorized Mean ( 2 / 20 )379274.13508.82339677762108.091533004571
Winsorized Mean ( 3 / 20 )379252.93502.07935461851108.293634037688
Winsorized Mean ( 4 / 20 )379316.5666666673480.78443569517108.974449200819
Winsorized Mean ( 5 / 20 )379423.7333333333454.34297307475109.839624001089
Winsorized Mean ( 6 / 20 )379595.1333333333409.37450751117111.338643641832
Winsorized Mean ( 7 / 20 )379669.6833333333377.71214813297112.404392879718
Winsorized Mean ( 8 / 20 )379837.953337.28463512379113.81646803582
Winsorized Mean ( 9 / 20 )3794433215.47143040861118.005402384117
Winsorized Mean ( 10 / 20 )379556.3333333333165.97022879909119.88626105221
Winsorized Mean ( 11 / 20 )379571.1833333333160.91436267852120.082716512348
Winsorized Mean ( 12 / 20 )379713.1833333333100.89819906358122.452644026818
Winsorized Mean ( 13 / 20 )380278.4666666672992.13165803591127.092825492943
Winsorized Mean ( 14 / 20 )380226.4333333332967.11392086927128.146894077441
Winsorized Mean ( 15 / 20 )380550.1833333332901.05565458718131.176450452305
Winsorized Mean ( 16 / 20 )380658.7166666672833.45502537851134.344365185685
Winsorized Mean ( 17 / 20 )380166.2833333332756.44580343663137.919012541207
Winsorized Mean ( 18 / 20 )380579.3833333332613.3295211143145.630078510366
Winsorized Mean ( 19 / 20 )380646.22490.48935787626152.839922321367
Winsorized Mean ( 20 / 20 )380427.8666666672270.1151299193167.580869204722
Trimmed Mean ( 1 / 20 )379308.6206896553521.30053526617107.718332159054
Trimmed Mean ( 2 / 20 )379453.4285714293497.4094972516108.495567610718
Trimmed Mean ( 3 / 20 )379553.0555555563482.9019181969108.976096505195
Trimmed Mean ( 4 / 20 )379668.53463.65073014985109.615122764868
Trimmed Mean ( 5 / 20 )379774.083443.10571916384110.299860351726
Trimmed Mean ( 6 / 20 )379861.6666666673421.06995963766111.035924768665
Trimmed Mean ( 7 / 20 )379919.6086956523401.14096790384111.703576029605
Trimmed Mean ( 8 / 20 )379968.2954545453378.49431519752112.466755899316
Trimmed Mean ( 9 / 20 )379991.5714285713353.59942745019113.308574756493
Trimmed Mean ( 10 / 20 )3800833344.4783790907113.644926627792
Trimmed Mean ( 11 / 20 )380166.1578947373335.67509029331113.9697805104
Trimmed Mean ( 12 / 20 )380256.3055555563315.27814026704114.698160898478
Trimmed Mean ( 13 / 20 )380336.1764705883292.69224551206115.509178541963
Trimmed Mean ( 14 / 20 )380344.53278.45932387554116.013182542825
Trimmed Mean ( 15 / 20 )380361.3666666673251.47880431416116.98103833923
Trimmed Mean ( 16 / 20 )380334.3928571433217.13212247961118.221564541776
Trimmed Mean ( 17 / 20 )380287.6153846153171.22612301829119.918164341642
Trimmed Mean ( 18 / 20 )380305.4583333333110.03773392643122.28322961638
Trimmed Mean ( 19 / 20 )380263.9545454553048.07289305447124.755531736773
Trimmed Mean ( 20 / 20 )380203.62974.48480404148127.821664942921
Median378044.5
Midrange374088
Midmean - Weighted Average at Xnp379479.774193548
Midmean - Weighted Average at X(n+1)p380361.366666667
Midmean - Empirical Distribution Function379479.774193548
Midmean - Empirical Distribution Function - Averaging380361.366666667
Midmean - Empirical Distribution Function - Interpolation380361.366666667
Midmean - Closest Observation379479.774193548
Midmean - True Basic - Statistics Graphics Toolkit380361.366666667
Midmean - MS Excel (old versions)380344.5
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')