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of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationMon, 02 May 2016 20:39:22 +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/May/02/t1462218021dlfe9clpcjsloxv.htm/, Retrieved Sun, 05 May 2024 14:34:05 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=295156, Retrieved Sun, 05 May 2024 14:34:05 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact69
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [] [2016-05-02 19:39:22] [517bf63cbd197750110a40d4d2cd39d6] [Current]
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Dataseries X:
74787
49019
56601
47637
49806
50499
42092
39062
44382
43635
41082
17244
70170
43949
52333
41032
47758
76116
30917
32996
31951
26775
30268
18214
47957
31901
35559
30408
30083
35043
30475
28309
31394
36313
40357
38918
44368
33298
29366
28282
30943
32699
29764
25524
29807
35112
32192
36214
47639
33421
28642
26996
27757
36839
33821
30839
35032
38821
40347
68799




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'George Udny Yule' @ yule.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 & 'George Udny Yule' @ yule.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=295156&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'George Udny Yule' @ yule.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=295156&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=295156&T=0

As an alternative you can also use a QR Code:  

The GUIDs for individual cells are displayed in the table below:

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







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean38526.06666666671579.0474779998824.3982953036132
Geometric Mean36868.1901402245
Harmonic Mean35371.8653509587
Quadratic Mean40390.1953218022
Winsorized Mean ( 1 / 20 )38520.08333333331566.6102580826424.5881725429768
Winsorized Mean ( 2 / 20 )38609.851462.6810054246126.3966304729525
Winsorized Mean ( 3 / 20 )38603.851428.7304272673127.0196877334211
Winsorized Mean ( 4 / 20 )37805.38333333331166.3512517353732.4133774256117
Winsorized Mean ( 5 / 20 )37513.13333333331065.6583537031635.2018385657799
Winsorized Mean ( 6 / 20 )37382.23333333331015.8781629777636.7979494940199
Winsorized Mean ( 7 / 20 )37304.5333333333997.96625608597237.3805558112174
Winsorized Mean ( 8 / 20 )37244969.28701037132238.4241195863465
Winsorized Mean ( 9 / 20 )37193.3921.09813156150840.3793024060828
Winsorized Mean ( 10 / 20 )37226.4666666667905.13011720813541.1283040514565
Winsorized Mean ( 11 / 20 )37212.5333333333899.73563080962841.3594083184719
Winsorized Mean ( 12 / 20 )37267.3333333333892.03869550314541.777709331671
Winsorized Mean ( 13 / 20 )36602.1666666667754.71902511717848.4977394878628
Winsorized Mean ( 14 / 20 )36631.5666666667749.52574661576848.8729931320761
Winsorized Mean ( 15 / 20 )36543.5666666667728.98278418779250.1295331787324
Winsorized Mean ( 16 / 20 )36556.9701.04897823690352.1459999726959
Winsorized Mean ( 17 / 20 )36141.8166666667625.16612232571157.811540606541
Winsorized Mean ( 18 / 20 )35846.6166666667576.23705794095262.2081071890033
Winsorized Mean ( 19 / 20 )35973.6553.47214302740264.9962251094162
Winsorized Mean ( 20 / 20 )35917.6495.46743164330172.4923530914499
Trimmed Mean ( 1 / 20 )38244.89655172411450.5447988129726.3658844477062
Trimmed Mean ( 2 / 20 )37950.05357142861301.1806365658129.1658609918987
Trimmed Mean ( 3 / 20 )37583.51184.4071298760431.731909621258
Trimmed Mean ( 4 / 20 )37191.05769230771048.5269187802635.4698167745388
Trimmed Mean ( 5 / 20 )37006.76996.57546835681937.1339263056693
Trimmed Mean ( 6 / 20 )36880.1666666667967.56521411113238.116466082906
Trimmed Mean ( 7 / 20 )36771.0217391304945.89847403297138.874173865988
Trimmed Mean ( 8 / 20 )36667.0909090909922.49511696409739.7477344159405
Trimmed Mean ( 9 / 20 )36564.0714285714899.3058656237340.6581040180492
Trimmed Mean ( 10 / 20 )36459.2880.92983960568241.3871779122838
Trimmed Mean ( 11 / 20 )36338.0526315789859.04608923178442.3004691914433
Trimmed Mean ( 12 / 20 )36205.5555555556829.31122735471243.6573801985557
Trimmed Mean ( 13 / 20 )36049.4117647059788.4987666588645.7190464830524
Trimmed Mean ( 14 / 20 )35969.6875774.15488707913546.4631666096079
Trimmed Mean ( 15 / 20 )35875.1333333333752.61156614944247.6675285723815
Trimmed Mean ( 16 / 20 )35779.6428571429725.74077137333349.3008581968412
Trimmed Mean ( 17 / 20 )35667.5384615385692.53337432661951.5029885689186
Trimmed Mean ( 18 / 20 )35597.7916666667669.9874754917653.1320255509828
Trimmed Mean ( 19 / 20 )35560.0909090909651.35330286072854.5941668721289
Trimmed Mean ( 20 / 20 )35494.8625.39519968534656.7557922060458
Median35077.5
Midrange46680
Midmean - Weighted Average at Xnp35698.7741935484
Midmean - Weighted Average at X(n+1)p35875.1333333333
Midmean - Empirical Distribution Function35698.7741935484
Midmean - Empirical Distribution Function - Averaging35875.1333333333
Midmean - Empirical Distribution Function - Interpolation35875.1333333333
Midmean - Closest Observation35698.7741935484
Midmean - True Basic - Statistics Graphics Toolkit35875.1333333333
Midmean - MS Excel (old versions)35969.6875
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 38526.0666666667 & 1579.04747799988 & 24.3982953036132 \tabularnewline
Geometric Mean & 36868.1901402245 &  &  \tabularnewline
Harmonic Mean & 35371.8653509587 &  &  \tabularnewline
Quadratic Mean & 40390.1953218022 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 38520.0833333333 & 1566.61025808264 & 24.5881725429768 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 38609.85 & 1462.68100542461 & 26.3966304729525 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 38603.85 & 1428.73042726731 & 27.0196877334211 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 37805.3833333333 & 1166.35125173537 & 32.4133774256117 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 37513.1333333333 & 1065.65835370316 & 35.2018385657799 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 37382.2333333333 & 1015.87816297776 & 36.7979494940199 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 37304.5333333333 & 997.966256085972 & 37.3805558112174 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 37244 & 969.287010371322 & 38.4241195863465 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 37193.3 & 921.098131561508 & 40.3793024060828 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 37226.4666666667 & 905.130117208135 & 41.1283040514565 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 37212.5333333333 & 899.735630809628 & 41.3594083184719 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 37267.3333333333 & 892.038695503145 & 41.777709331671 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 36602.1666666667 & 754.719025117178 & 48.4977394878628 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 36631.5666666667 & 749.525746615768 & 48.8729931320761 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 36543.5666666667 & 728.982784187792 & 50.1295331787324 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 36556.9 & 701.048978236903 & 52.1459999726959 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 36141.8166666667 & 625.166122325711 & 57.811540606541 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 35846.6166666667 & 576.237057940952 & 62.2081071890033 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 35973.6 & 553.472143027402 & 64.9962251094162 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 35917.6 & 495.467431643301 & 72.4923530914499 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 38244.8965517241 & 1450.54479881297 & 26.3658844477062 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 37950.0535714286 & 1301.18063656581 & 29.1658609918987 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 37583.5 & 1184.40712987604 & 31.731909621258 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 37191.0576923077 & 1048.52691878026 & 35.4698167745388 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 37006.76 & 996.575468356819 & 37.1339263056693 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 36880.1666666667 & 967.565214111132 & 38.116466082906 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 36771.0217391304 & 945.898474032971 & 38.874173865988 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 36667.0909090909 & 922.495116964097 & 39.7477344159405 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 36564.0714285714 & 899.30586562373 & 40.6581040180492 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 36459.2 & 880.929839605682 & 41.3871779122838 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 36338.0526315789 & 859.046089231784 & 42.3004691914433 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 36205.5555555556 & 829.311227354712 & 43.6573801985557 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 36049.4117647059 & 788.49876665886 & 45.7190464830524 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 35969.6875 & 774.154887079135 & 46.4631666096079 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 35875.1333333333 & 752.611566149442 & 47.6675285723815 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 35779.6428571429 & 725.740771373333 & 49.3008581968412 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 35667.5384615385 & 692.533374326619 & 51.5029885689186 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 35597.7916666667 & 669.98747549176 & 53.1320255509828 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 35560.0909090909 & 651.353302860728 & 54.5941668721289 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 35494.8 & 625.395199685346 & 56.7557922060458 \tabularnewline
Median & 35077.5 &  &  \tabularnewline
Midrange & 46680 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 35698.7741935484 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 35875.1333333333 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 35698.7741935484 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 35875.1333333333 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 35875.1333333333 &  &  \tabularnewline
Midmean - Closest Observation & 35698.7741935484 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 35875.1333333333 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 35969.6875 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=295156&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]38526.0666666667[/C][C]1579.04747799988[/C][C]24.3982953036132[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]36868.1901402245[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]35371.8653509587[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]40390.1953218022[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]38520.0833333333[/C][C]1566.61025808264[/C][C]24.5881725429768[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]38609.85[/C][C]1462.68100542461[/C][C]26.3966304729525[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]38603.85[/C][C]1428.73042726731[/C][C]27.0196877334211[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]37805.3833333333[/C][C]1166.35125173537[/C][C]32.4133774256117[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]37513.1333333333[/C][C]1065.65835370316[/C][C]35.2018385657799[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]37382.2333333333[/C][C]1015.87816297776[/C][C]36.7979494940199[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]37304.5333333333[/C][C]997.966256085972[/C][C]37.3805558112174[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]37244[/C][C]969.287010371322[/C][C]38.4241195863465[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]37193.3[/C][C]921.098131561508[/C][C]40.3793024060828[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]37226.4666666667[/C][C]905.130117208135[/C][C]41.1283040514565[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]37212.5333333333[/C][C]899.735630809628[/C][C]41.3594083184719[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]37267.3333333333[/C][C]892.038695503145[/C][C]41.777709331671[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]36602.1666666667[/C][C]754.719025117178[/C][C]48.4977394878628[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]36631.5666666667[/C][C]749.525746615768[/C][C]48.8729931320761[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]36543.5666666667[/C][C]728.982784187792[/C][C]50.1295331787324[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]36556.9[/C][C]701.048978236903[/C][C]52.1459999726959[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]36141.8166666667[/C][C]625.166122325711[/C][C]57.811540606541[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]35846.6166666667[/C][C]576.237057940952[/C][C]62.2081071890033[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]35973.6[/C][C]553.472143027402[/C][C]64.9962251094162[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]35917.6[/C][C]495.467431643301[/C][C]72.4923530914499[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]38244.8965517241[/C][C]1450.54479881297[/C][C]26.3658844477062[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]37950.0535714286[/C][C]1301.18063656581[/C][C]29.1658609918987[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]37583.5[/C][C]1184.40712987604[/C][C]31.731909621258[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]37191.0576923077[/C][C]1048.52691878026[/C][C]35.4698167745388[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]37006.76[/C][C]996.575468356819[/C][C]37.1339263056693[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]36880.1666666667[/C][C]967.565214111132[/C][C]38.116466082906[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]36771.0217391304[/C][C]945.898474032971[/C][C]38.874173865988[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]36667.0909090909[/C][C]922.495116964097[/C][C]39.7477344159405[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]36564.0714285714[/C][C]899.30586562373[/C][C]40.6581040180492[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]36459.2[/C][C]880.929839605682[/C][C]41.3871779122838[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]36338.0526315789[/C][C]859.046089231784[/C][C]42.3004691914433[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]36205.5555555556[/C][C]829.311227354712[/C][C]43.6573801985557[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]36049.4117647059[/C][C]788.49876665886[/C][C]45.7190464830524[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]35969.6875[/C][C]774.154887079135[/C][C]46.4631666096079[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]35875.1333333333[/C][C]752.611566149442[/C][C]47.6675285723815[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]35779.6428571429[/C][C]725.740771373333[/C][C]49.3008581968412[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]35667.5384615385[/C][C]692.533374326619[/C][C]51.5029885689186[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]35597.7916666667[/C][C]669.98747549176[/C][C]53.1320255509828[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]35560.0909090909[/C][C]651.353302860728[/C][C]54.5941668721289[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]35494.8[/C][C]625.395199685346[/C][C]56.7557922060458[/C][/ROW]
[ROW][C]Median[/C][C]35077.5[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]46680[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]35698.7741935484[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]35875.1333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]35698.7741935484[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]35875.1333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]35875.1333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]35698.7741935484[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]35875.1333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]35969.6875[/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=295156&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=295156&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 Mean38526.06666666671579.0474779998824.3982953036132
Geometric Mean36868.1901402245
Harmonic Mean35371.8653509587
Quadratic Mean40390.1953218022
Winsorized Mean ( 1 / 20 )38520.08333333331566.6102580826424.5881725429768
Winsorized Mean ( 2 / 20 )38609.851462.6810054246126.3966304729525
Winsorized Mean ( 3 / 20 )38603.851428.7304272673127.0196877334211
Winsorized Mean ( 4 / 20 )37805.38333333331166.3512517353732.4133774256117
Winsorized Mean ( 5 / 20 )37513.13333333331065.6583537031635.2018385657799
Winsorized Mean ( 6 / 20 )37382.23333333331015.8781629777636.7979494940199
Winsorized Mean ( 7 / 20 )37304.5333333333997.96625608597237.3805558112174
Winsorized Mean ( 8 / 20 )37244969.28701037132238.4241195863465
Winsorized Mean ( 9 / 20 )37193.3921.09813156150840.3793024060828
Winsorized Mean ( 10 / 20 )37226.4666666667905.13011720813541.1283040514565
Winsorized Mean ( 11 / 20 )37212.5333333333899.73563080962841.3594083184719
Winsorized Mean ( 12 / 20 )37267.3333333333892.03869550314541.777709331671
Winsorized Mean ( 13 / 20 )36602.1666666667754.71902511717848.4977394878628
Winsorized Mean ( 14 / 20 )36631.5666666667749.52574661576848.8729931320761
Winsorized Mean ( 15 / 20 )36543.5666666667728.98278418779250.1295331787324
Winsorized Mean ( 16 / 20 )36556.9701.04897823690352.1459999726959
Winsorized Mean ( 17 / 20 )36141.8166666667625.16612232571157.811540606541
Winsorized Mean ( 18 / 20 )35846.6166666667576.23705794095262.2081071890033
Winsorized Mean ( 19 / 20 )35973.6553.47214302740264.9962251094162
Winsorized Mean ( 20 / 20 )35917.6495.46743164330172.4923530914499
Trimmed Mean ( 1 / 20 )38244.89655172411450.5447988129726.3658844477062
Trimmed Mean ( 2 / 20 )37950.05357142861301.1806365658129.1658609918987
Trimmed Mean ( 3 / 20 )37583.51184.4071298760431.731909621258
Trimmed Mean ( 4 / 20 )37191.05769230771048.5269187802635.4698167745388
Trimmed Mean ( 5 / 20 )37006.76996.57546835681937.1339263056693
Trimmed Mean ( 6 / 20 )36880.1666666667967.56521411113238.116466082906
Trimmed Mean ( 7 / 20 )36771.0217391304945.89847403297138.874173865988
Trimmed Mean ( 8 / 20 )36667.0909090909922.49511696409739.7477344159405
Trimmed Mean ( 9 / 20 )36564.0714285714899.3058656237340.6581040180492
Trimmed Mean ( 10 / 20 )36459.2880.92983960568241.3871779122838
Trimmed Mean ( 11 / 20 )36338.0526315789859.04608923178442.3004691914433
Trimmed Mean ( 12 / 20 )36205.5555555556829.31122735471243.6573801985557
Trimmed Mean ( 13 / 20 )36049.4117647059788.4987666588645.7190464830524
Trimmed Mean ( 14 / 20 )35969.6875774.15488707913546.4631666096079
Trimmed Mean ( 15 / 20 )35875.1333333333752.61156614944247.6675285723815
Trimmed Mean ( 16 / 20 )35779.6428571429725.74077137333349.3008581968412
Trimmed Mean ( 17 / 20 )35667.5384615385692.53337432661951.5029885689186
Trimmed Mean ( 18 / 20 )35597.7916666667669.9874754917653.1320255509828
Trimmed Mean ( 19 / 20 )35560.0909090909651.35330286072854.5941668721289
Trimmed Mean ( 20 / 20 )35494.8625.39519968534656.7557922060458
Median35077.5
Midrange46680
Midmean - Weighted Average at Xnp35698.7741935484
Midmean - Weighted Average at X(n+1)p35875.1333333333
Midmean - Empirical Distribution Function35698.7741935484
Midmean - Empirical Distribution Function - Averaging35875.1333333333
Midmean - Empirical Distribution Function - Interpolation35875.1333333333
Midmean - Closest Observation35698.7741935484
Midmean - True Basic - Statistics Graphics Toolkit35875.1333333333
Midmean - MS Excel (old versions)35969.6875
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')