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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 computationSun, 06 Mar 2016 11:23:29 +0000
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/Mar/06/t1457263436fy3uck8ag9tfzeo.htm/, Retrieved Sun, 05 May 2024 01:29:50 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=293545, Retrieved Sun, 05 May 2024 01:29:50 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact185
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [] [2016-03-06 11:23:29] [9d122f8260d20611f07666190c7f1fd6] [Current]
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Dataseries X:
45564.6
47295.5
46465.5
50679.5
47452.8
49415.4
48165.3
51814
49030.7
50820.8
49729.5
53501.6
50524.9
52095
51290.3
55064
52505.2
54318.3
53039.6
57607.6
54236.4
56586.4
55614
60085.9
56963.5
59152.8
57804.6
62541.5
59449.3
61704.7
60399
65724.7
62679.4
65526.5
64274.8
68769.1
63542.8
66198
64544.9
71041.8
66087.2
69005.8
66897
73702
68485.3
71457
69774.6
76479.7
71204.7
73783.9
71651
78541.6
72714.4
75258
73168.1
79701.6
73944.5
76401.2
73948.1
80583.3




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gertrude Mary Cox' @ cox.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 & 1 seconds \tabularnewline
R Server & 'Gertrude Mary Cox' @ cox.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=293545&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]'Gertrude Mary Cox' @ cox.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=293545&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=293545&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'Gertrude Mary Cox' @ cox.wessa.net







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean61933.48666666671284.854721208948.2027155633551
Geometric Mean61142.2730178178
Harmonic Mean60353.7258700989
Quadratic Mean62714.8867360241
Winsorized Mean ( 1 / 20 )61933.80666666671278.1544920962948.4556499622278
Winsorized Mean ( 2 / 20 )61922.80666666671263.7366938233748.9997694688458
Winsorized Mean ( 3 / 20 )61827.57666666671240.3718613305549.84600069881
Winsorized Mean ( 4 / 20 )61869.84333333331230.1737808185450.2935798974404
Winsorized Mean ( 5 / 20 )61846.69333333331198.2455199138451.6143747716914
Winsorized Mean ( 6 / 20 )61754.17333333331167.2800039206252.9043358285207
Winsorized Mean ( 7 / 20 )61790.39833333331160.6957418625853.2356552236315
Winsorized Mean ( 8 / 20 )61875.03833333331138.5954399406454.3433041823521
Winsorized Mean ( 9 / 20 )61885.94333333331132.5165260498854.6446271730677
Winsorized Mean ( 10 / 20 )61820.511113.0115949662855.5434555035997
Winsorized Mean ( 11 / 20 )61823.40666666671084.4485307061257.0090741202918
Winsorized Mean ( 12 / 20 )61715.46666666671031.8322146065359.8115331088018
Winsorized Mean ( 13 / 20 )61734.31666666671015.1394412668860.8136322529476
Winsorized Mean ( 14 / 20 )61771.16990.31550453423962.3752326578508
Winsorized Mean ( 15 / 20 )61864.035962.76386164959864.2567066175524
Winsorized Mean ( 16 / 20 )61649.315890.15258079447169.2570198976195
Winsorized Mean ( 17 / 20 )61639.6816666667824.80476196070874.7324512532374
Winsorized Mean ( 18 / 20 )61593.2416666667810.36297700402376.0069788656705
Winsorized Mean ( 19 / 20 )61739.51761.34611134000281.0925662854386
Winsorized Mean ( 20 / 20 )61393.41656.52647963473893.512465840154
Trimmed Mean ( 1 / 20 )61894.16034482761257.5445842461649.2182632092764
Trimmed Mean ( 2 / 20 )61851.68214285711231.7393012751950.2149132359612
Trimmed Mean ( 3 / 20 )61812.16851851851208.8653924588651.1323832282029
Trimmed Mean ( 4 / 20 )61806.24230769231190.8825606817651.8995275842392
Trimmed Mean ( 5 / 20 )61787.1621171.422208501552.7454247935414
Trimmed Mean ( 6 / 20 )61772.27916666671156.5727306508253.4097662253428
Trimmed Mean ( 7 / 20 )61776.21521739131145.6319601535653.9232645090582
Trimmed Mean ( 8 / 20 )61773.45227272731131.8069659468654.5794946765043
Trimmed Mean ( 9 / 20 )61755.31190476191118.1204195763855.2313604362569
Trimmed Mean ( 10 / 20 )61733.541099.9466447188356.1241222893867
Trimmed Mean ( 11 / 20 )61719.80789473681079.2141478429757.1895837523038
Trimmed Mean ( 12 / 20 )61704.11111111111057.0654596103558.373027469705
Trimmed Mean ( 13 / 20 )61702.44117647061038.9702134005859.3880752120089
Trimmed Mean ( 14 / 20 )61697.843751015.8512315769160.73511734019
Trimmed Mean ( 15 / 20 )61687.37987.74664549246162.4526241435571
Trimmed Mean ( 16 / 20 )61662.1321428571952.92828270838164.7080512371855
Trimmed Mean ( 17 / 20 )61663.9807692308923.28523754986766.7875736136204
Trimmed Mean ( 18 / 20 )61667.5541666667897.88861359679968.6806283461333
Trimmed Mean ( 19 / 20 )61678.8136363636858.59331770495171.8370529615036
Trimmed Mean ( 20 / 20 )61669.23811.90558042889475.9561597882144
Median62123.1
Midrange63073.95
Midmean - Weighted Average at Xnp61391.1709677419
Midmean - Weighted Average at X(n+1)p61687.37
Midmean - Empirical Distribution Function61391.1709677419
Midmean - Empirical Distribution Function - Averaging61687.37
Midmean - Empirical Distribution Function - Interpolation61687.37
Midmean - Closest Observation61391.1709677419
Midmean - True Basic - Statistics Graphics Toolkit61687.37
Midmean - MS Excel (old versions)61697.84375
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 61933.4866666667 & 1284.8547212089 & 48.2027155633551 \tabularnewline
Geometric Mean & 61142.2730178178 &  &  \tabularnewline
Harmonic Mean & 60353.7258700989 &  &  \tabularnewline
Quadratic Mean & 62714.8867360241 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 61933.8066666667 & 1278.15449209629 & 48.4556499622278 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 61922.8066666667 & 1263.73669382337 & 48.9997694688458 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 61827.5766666667 & 1240.37186133055 & 49.84600069881 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 61869.8433333333 & 1230.17378081854 & 50.2935798974404 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 61846.6933333333 & 1198.24551991384 & 51.6143747716914 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 61754.1733333333 & 1167.28000392062 & 52.9043358285207 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 61790.3983333333 & 1160.69574186258 & 53.2356552236315 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 61875.0383333333 & 1138.59543994064 & 54.3433041823521 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 61885.9433333333 & 1132.51652604988 & 54.6446271730677 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 61820.51 & 1113.01159496628 & 55.5434555035997 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 61823.4066666667 & 1084.44853070612 & 57.0090741202918 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 61715.4666666667 & 1031.83221460653 & 59.8115331088018 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 61734.3166666667 & 1015.13944126688 & 60.8136322529476 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 61771.16 & 990.315504534239 & 62.3752326578508 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 61864.035 & 962.763861649598 & 64.2567066175524 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 61649.315 & 890.152580794471 & 69.2570198976195 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 61639.6816666667 & 824.804761960708 & 74.7324512532374 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 61593.2416666667 & 810.362977004023 & 76.0069788656705 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 61739.51 & 761.346111340002 & 81.0925662854386 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 61393.41 & 656.526479634738 & 93.512465840154 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 61894.1603448276 & 1257.54458424616 & 49.2182632092764 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 61851.6821428571 & 1231.73930127519 & 50.2149132359612 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 61812.1685185185 & 1208.86539245886 & 51.1323832282029 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 61806.2423076923 & 1190.88256068176 & 51.8995275842392 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 61787.162 & 1171.4222085015 & 52.7454247935414 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 61772.2791666667 & 1156.57273065082 & 53.4097662253428 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 61776.2152173913 & 1145.63196015356 & 53.9232645090582 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 61773.4522727273 & 1131.80696594686 & 54.5794946765043 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 61755.3119047619 & 1118.12041957638 & 55.2313604362569 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 61733.54 & 1099.94664471883 & 56.1241222893867 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 61719.8078947368 & 1079.21414784297 & 57.1895837523038 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 61704.1111111111 & 1057.06545961035 & 58.373027469705 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 61702.4411764706 & 1038.97021340058 & 59.3880752120089 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 61697.84375 & 1015.85123157691 & 60.73511734019 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 61687.37 & 987.746645492461 & 62.4526241435571 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 61662.1321428571 & 952.928282708381 & 64.7080512371855 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 61663.9807692308 & 923.285237549867 & 66.7875736136204 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 61667.5541666667 & 897.888613596799 & 68.6806283461333 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 61678.8136363636 & 858.593317704951 & 71.8370529615036 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 61669.23 & 811.905580428894 & 75.9561597882144 \tabularnewline
Median & 62123.1 &  &  \tabularnewline
Midrange & 63073.95 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 61391.1709677419 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 61687.37 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 61391.1709677419 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 61687.37 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 61687.37 &  &  \tabularnewline
Midmean - Closest Observation & 61391.1709677419 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 61687.37 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 61697.84375 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=293545&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]61933.4866666667[/C][C]1284.8547212089[/C][C]48.2027155633551[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]61142.2730178178[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]60353.7258700989[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]62714.8867360241[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]61933.8066666667[/C][C]1278.15449209629[/C][C]48.4556499622278[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]61922.8066666667[/C][C]1263.73669382337[/C][C]48.9997694688458[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]61827.5766666667[/C][C]1240.37186133055[/C][C]49.84600069881[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]61869.8433333333[/C][C]1230.17378081854[/C][C]50.2935798974404[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]61846.6933333333[/C][C]1198.24551991384[/C][C]51.6143747716914[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]61754.1733333333[/C][C]1167.28000392062[/C][C]52.9043358285207[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]61790.3983333333[/C][C]1160.69574186258[/C][C]53.2356552236315[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]61875.0383333333[/C][C]1138.59543994064[/C][C]54.3433041823521[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]61885.9433333333[/C][C]1132.51652604988[/C][C]54.6446271730677[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]61820.51[/C][C]1113.01159496628[/C][C]55.5434555035997[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]61823.4066666667[/C][C]1084.44853070612[/C][C]57.0090741202918[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]61715.4666666667[/C][C]1031.83221460653[/C][C]59.8115331088018[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]61734.3166666667[/C][C]1015.13944126688[/C][C]60.8136322529476[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]61771.16[/C][C]990.315504534239[/C][C]62.3752326578508[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]61864.035[/C][C]962.763861649598[/C][C]64.2567066175524[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]61649.315[/C][C]890.152580794471[/C][C]69.2570198976195[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]61639.6816666667[/C][C]824.804761960708[/C][C]74.7324512532374[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]61593.2416666667[/C][C]810.362977004023[/C][C]76.0069788656705[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]61739.51[/C][C]761.346111340002[/C][C]81.0925662854386[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]61393.41[/C][C]656.526479634738[/C][C]93.512465840154[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]61894.1603448276[/C][C]1257.54458424616[/C][C]49.2182632092764[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]61851.6821428571[/C][C]1231.73930127519[/C][C]50.2149132359612[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]61812.1685185185[/C][C]1208.86539245886[/C][C]51.1323832282029[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]61806.2423076923[/C][C]1190.88256068176[/C][C]51.8995275842392[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]61787.162[/C][C]1171.4222085015[/C][C]52.7454247935414[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]61772.2791666667[/C][C]1156.57273065082[/C][C]53.4097662253428[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]61776.2152173913[/C][C]1145.63196015356[/C][C]53.9232645090582[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]61773.4522727273[/C][C]1131.80696594686[/C][C]54.5794946765043[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]61755.3119047619[/C][C]1118.12041957638[/C][C]55.2313604362569[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]61733.54[/C][C]1099.94664471883[/C][C]56.1241222893867[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]61719.8078947368[/C][C]1079.21414784297[/C][C]57.1895837523038[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]61704.1111111111[/C][C]1057.06545961035[/C][C]58.373027469705[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]61702.4411764706[/C][C]1038.97021340058[/C][C]59.3880752120089[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]61697.84375[/C][C]1015.85123157691[/C][C]60.73511734019[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]61687.37[/C][C]987.746645492461[/C][C]62.4526241435571[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]61662.1321428571[/C][C]952.928282708381[/C][C]64.7080512371855[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]61663.9807692308[/C][C]923.285237549867[/C][C]66.7875736136204[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]61667.5541666667[/C][C]897.888613596799[/C][C]68.6806283461333[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]61678.8136363636[/C][C]858.593317704951[/C][C]71.8370529615036[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]61669.23[/C][C]811.905580428894[/C][C]75.9561597882144[/C][/ROW]
[ROW][C]Median[/C][C]62123.1[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]63073.95[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]61391.1709677419[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]61687.37[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]61391.1709677419[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]61687.37[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]61687.37[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]61391.1709677419[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]61687.37[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]61697.84375[/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=293545&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=293545&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 Mean61933.48666666671284.854721208948.2027155633551
Geometric Mean61142.2730178178
Harmonic Mean60353.7258700989
Quadratic Mean62714.8867360241
Winsorized Mean ( 1 / 20 )61933.80666666671278.1544920962948.4556499622278
Winsorized Mean ( 2 / 20 )61922.80666666671263.7366938233748.9997694688458
Winsorized Mean ( 3 / 20 )61827.57666666671240.3718613305549.84600069881
Winsorized Mean ( 4 / 20 )61869.84333333331230.1737808185450.2935798974404
Winsorized Mean ( 5 / 20 )61846.69333333331198.2455199138451.6143747716914
Winsorized Mean ( 6 / 20 )61754.17333333331167.2800039206252.9043358285207
Winsorized Mean ( 7 / 20 )61790.39833333331160.6957418625853.2356552236315
Winsorized Mean ( 8 / 20 )61875.03833333331138.5954399406454.3433041823521
Winsorized Mean ( 9 / 20 )61885.94333333331132.5165260498854.6446271730677
Winsorized Mean ( 10 / 20 )61820.511113.0115949662855.5434555035997
Winsorized Mean ( 11 / 20 )61823.40666666671084.4485307061257.0090741202918
Winsorized Mean ( 12 / 20 )61715.46666666671031.8322146065359.8115331088018
Winsorized Mean ( 13 / 20 )61734.31666666671015.1394412668860.8136322529476
Winsorized Mean ( 14 / 20 )61771.16990.31550453423962.3752326578508
Winsorized Mean ( 15 / 20 )61864.035962.76386164959864.2567066175524
Winsorized Mean ( 16 / 20 )61649.315890.15258079447169.2570198976195
Winsorized Mean ( 17 / 20 )61639.6816666667824.80476196070874.7324512532374
Winsorized Mean ( 18 / 20 )61593.2416666667810.36297700402376.0069788656705
Winsorized Mean ( 19 / 20 )61739.51761.34611134000281.0925662854386
Winsorized Mean ( 20 / 20 )61393.41656.52647963473893.512465840154
Trimmed Mean ( 1 / 20 )61894.16034482761257.5445842461649.2182632092764
Trimmed Mean ( 2 / 20 )61851.68214285711231.7393012751950.2149132359612
Trimmed Mean ( 3 / 20 )61812.16851851851208.8653924588651.1323832282029
Trimmed Mean ( 4 / 20 )61806.24230769231190.8825606817651.8995275842392
Trimmed Mean ( 5 / 20 )61787.1621171.422208501552.7454247935414
Trimmed Mean ( 6 / 20 )61772.27916666671156.5727306508253.4097662253428
Trimmed Mean ( 7 / 20 )61776.21521739131145.6319601535653.9232645090582
Trimmed Mean ( 8 / 20 )61773.45227272731131.8069659468654.5794946765043
Trimmed Mean ( 9 / 20 )61755.31190476191118.1204195763855.2313604362569
Trimmed Mean ( 10 / 20 )61733.541099.9466447188356.1241222893867
Trimmed Mean ( 11 / 20 )61719.80789473681079.2141478429757.1895837523038
Trimmed Mean ( 12 / 20 )61704.11111111111057.0654596103558.373027469705
Trimmed Mean ( 13 / 20 )61702.44117647061038.9702134005859.3880752120089
Trimmed Mean ( 14 / 20 )61697.843751015.8512315769160.73511734019
Trimmed Mean ( 15 / 20 )61687.37987.74664549246162.4526241435571
Trimmed Mean ( 16 / 20 )61662.1321428571952.92828270838164.7080512371855
Trimmed Mean ( 17 / 20 )61663.9807692308923.28523754986766.7875736136204
Trimmed Mean ( 18 / 20 )61667.5541666667897.88861359679968.6806283461333
Trimmed Mean ( 19 / 20 )61678.8136363636858.59331770495171.8370529615036
Trimmed Mean ( 20 / 20 )61669.23811.90558042889475.9561597882144
Median62123.1
Midrange63073.95
Midmean - Weighted Average at Xnp61391.1709677419
Midmean - Weighted Average at X(n+1)p61687.37
Midmean - Empirical Distribution Function61391.1709677419
Midmean - Empirical Distribution Function - Averaging61687.37
Midmean - Empirical Distribution Function - Interpolation61687.37
Midmean - Closest Observation61391.1709677419
Midmean - True Basic - Statistics Graphics Toolkit61687.37
Midmean - MS Excel (old versions)61697.84375
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')