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Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationFri, 10 Oct 2014 09:36:16 +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/2014/Oct/10/t14129302322jandz3z41j0p3o.htm/, Retrieved Sun, 12 May 2024 21:35:49 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=240238, Retrieved Sun, 12 May 2024 21:35:49 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact102
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [] [2014-10-10 08:36:16] [345c72938773a86f996d724d064c8f2d] [Current]
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Dataseries X:
82303
79596
74472
73562
66618
69029
89899
93774
90305
83799
80320
82497
84420
84646
84186
83269
77793
81145
101691
107357
104253
95963
91432
94324
93855
92183
87600
83641
78195
79604
100846
105293
102518
93132
87479
85476
85460
82868
79941
76909
72613
72496
93244
99126
96748
89318
84724
83111
87497
86961
82319
79196
76898
77971
97335
106855
105401
99108
93456
92506
94602
93027
89722
87391
83030
83390
104501
110393
111017
103434
97817
96893




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Sir Ronald Aylmer Fisher' @ fisher.wessa.net

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 2 seconds \tabularnewline
R Server & 'Sir Ronald Aylmer Fisher' @ fisher.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=240238&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Sir Ronald Aylmer Fisher' @ fisher.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=240238&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=240238&T=0

As an alternative you can also use a QR Code:  

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

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Sir Ronald Aylmer Fisher' @ fisher.wessa.net







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean88941.01388888891215.0705102470873.1982326447898
Geometric Mean88353.0986347619
Harmonic Mean87766.8181941782
Quadratic Mean89528.3647346998
Winsorized Mean ( 1 / 24 )88965.83333333331204.6388928989673.8526988110418
Winsorized Mean ( 2 / 24 )88977.80555555561163.8188405749476.4533125375422
Winsorized Mean ( 3 / 24 )88961.76388888891158.2461698371976.807302459195
Winsorized Mean ( 4 / 24 )88933.70833333331130.8789216971678.6412290715143
Winsorized Mean ( 5 / 24 )88989.40277777781117.5071552532279.6320653156027
Winsorized Mean ( 6 / 24 )89125.56944444441069.214674734583.3561038306695
Winsorized Mean ( 7 / 24 )89102.52777777781064.1831558114283.7285642900806
Winsorized Mean ( 8 / 24 )89109.751030.6230822641386.4620165543339
Winsorized Mean ( 9 / 24 )89017.51005.1385118542288.5624209501093
Winsorized Mean ( 10 / 24 )88933.75978.91709150783990.8491135475163
Winsorized Mean ( 11 / 24 )88957.5833333333932.36766038271895.4104127730235
Winsorized Mean ( 12 / 24 )88737.5833333333872.706124619932101.680944856413
Winsorized Mean ( 13 / 24 )88735.7777777778871.948341642914101.76724186502
Winsorized Mean ( 14 / 24 )88550.2777777778821.270186943217107.821127791529
Winsorized Mean ( 15 / 24 )88528.8194444444793.864372146781111.516302469959
Winsorized Mean ( 16 / 24 )88613.9305555556752.397671185261117.775391856225
Winsorized Mean ( 17 / 24 )88853.1111111111710.152602832437125.118334787088
Winsorized Mean ( 18 / 24 )88660.8611111111679.400133928327130.498739525512
Winsorized Mean ( 19 / 24 )88348.6805555556620.441281140816142.396522025593
Winsorized Mean ( 20 / 24 )88374.5138888889595.977258953537148.285043701271
Winsorized Mean ( 21 / 24 )88284.9722222222570.818015617183154.663955598469
Winsorized Mean ( 22 / 24 )88284.9722222222564.218638243962156.472980929866
Winsorized Mean ( 23 / 24 )88233.8611111111543.884363107208162.229082312703
Winsorized Mean ( 24 / 24 )88203.5277777778529.188918230995166.676823227194
Trimmed Mean ( 1 / 24 )88944.54285714291165.5573961681276.3107360903519
Trimmed Mean ( 2 / 24 )889221119.0123473181179.4647174475915
Trimmed Mean ( 3 / 24 )88891.56060606061089.8180554567181.5655055089073
Trimmed Mean ( 4 / 24 )88865.2343751057.325930536184.0471531138394
Trimmed Mean ( 5 / 24 )88845.35483870971028.4017321735686.3916814404152
Trimmed Mean ( 6 / 24 )88810.7833333333997.55228856104189.0286999004753
Trimmed Mean ( 7 / 24 )88745.6551724138973.69331508443891.1433341459449
Trimmed Mean ( 8 / 24 )88680.1071428571945.51630459702493.790140594828
Trimmed Mean ( 9 / 24 )88608.5918.98220740078496.4202563296814
Trimmed Mean ( 10 / 24 )88545.5769230769892.02168120972999.263929104273
Trimmed Mean ( 11 / 24 )88489.68864.282335974507102.385153921056
Trimmed Mean ( 12 / 24 )88425.875839.744174688263105.300968634675
Trimmed Mean ( 13 / 24 )88385.2173913044821.900925487343107.537556718161
Trimmed Mean ( 14 / 24 )88341.0909090909798.437699416859110.642434561408
Trimmed Mean ( 15 / 24 )88315.4761904762779.295553002366113.327319590399
Trimmed Mean ( 16 / 24 )88289.875759.751822828788116.208836026572
Trimmed Mean ( 17 / 24 )88251.5742.601564481528118.840983134227
Trimmed Mean ( 18 / 24 )88180.7222222222727.898231822727121.144300627588
Trimmed Mean ( 19 / 24 )88124.2352941177714.35561885799123.361856430832
Trimmed Mean ( 20 / 24 )88097.65625709.178884869472124.224872073306
Trimmed Mean ( 21 / 24 )88064.4333333333705.285007497513124.863611727411
Trimmed Mean ( 22 / 24 )88037.4285714286703.228419596717125.190373594281
Trimmed Mean ( 23 / 24 )88006.2692307692697.976906291302126.087651951682
Trimmed Mean ( 24 / 24 )87976.5833333333692.217621276224127.093822273887
Median87488
Midrange88817.5
Midmean - Weighted Average at Xnp88021.8648648649
Midmean - Weighted Average at X(n+1)p88180.7222222222
Midmean - Empirical Distribution Function88021.8648648649
Midmean - Empirical Distribution Function - Averaging88180.7222222222
Midmean - Empirical Distribution Function - Interpolation88180.7222222222
Midmean - Closest Observation88021.8648648649
Midmean - True Basic - Statistics Graphics Toolkit88180.7222222222
Midmean - MS Excel (old versions)88251.5
Number of observations72

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 88941.0138888889 & 1215.07051024708 & 73.1982326447898 \tabularnewline
Geometric Mean & 88353.0986347619 &  &  \tabularnewline
Harmonic Mean & 87766.8181941782 &  &  \tabularnewline
Quadratic Mean & 89528.3647346998 &  &  \tabularnewline
Winsorized Mean ( 1 / 24 ) & 88965.8333333333 & 1204.63889289896 & 73.8526988110418 \tabularnewline
Winsorized Mean ( 2 / 24 ) & 88977.8055555556 & 1163.81884057494 & 76.4533125375422 \tabularnewline
Winsorized Mean ( 3 / 24 ) & 88961.7638888889 & 1158.24616983719 & 76.807302459195 \tabularnewline
Winsorized Mean ( 4 / 24 ) & 88933.7083333333 & 1130.87892169716 & 78.6412290715143 \tabularnewline
Winsorized Mean ( 5 / 24 ) & 88989.4027777778 & 1117.50715525322 & 79.6320653156027 \tabularnewline
Winsorized Mean ( 6 / 24 ) & 89125.5694444444 & 1069.2146747345 & 83.3561038306695 \tabularnewline
Winsorized Mean ( 7 / 24 ) & 89102.5277777778 & 1064.18315581142 & 83.7285642900806 \tabularnewline
Winsorized Mean ( 8 / 24 ) & 89109.75 & 1030.62308226413 & 86.4620165543339 \tabularnewline
Winsorized Mean ( 9 / 24 ) & 89017.5 & 1005.13851185422 & 88.5624209501093 \tabularnewline
Winsorized Mean ( 10 / 24 ) & 88933.75 & 978.917091507839 & 90.8491135475163 \tabularnewline
Winsorized Mean ( 11 / 24 ) & 88957.5833333333 & 932.367660382718 & 95.4104127730235 \tabularnewline
Winsorized Mean ( 12 / 24 ) & 88737.5833333333 & 872.706124619932 & 101.680944856413 \tabularnewline
Winsorized Mean ( 13 / 24 ) & 88735.7777777778 & 871.948341642914 & 101.76724186502 \tabularnewline
Winsorized Mean ( 14 / 24 ) & 88550.2777777778 & 821.270186943217 & 107.821127791529 \tabularnewline
Winsorized Mean ( 15 / 24 ) & 88528.8194444444 & 793.864372146781 & 111.516302469959 \tabularnewline
Winsorized Mean ( 16 / 24 ) & 88613.9305555556 & 752.397671185261 & 117.775391856225 \tabularnewline
Winsorized Mean ( 17 / 24 ) & 88853.1111111111 & 710.152602832437 & 125.118334787088 \tabularnewline
Winsorized Mean ( 18 / 24 ) & 88660.8611111111 & 679.400133928327 & 130.498739525512 \tabularnewline
Winsorized Mean ( 19 / 24 ) & 88348.6805555556 & 620.441281140816 & 142.396522025593 \tabularnewline
Winsorized Mean ( 20 / 24 ) & 88374.5138888889 & 595.977258953537 & 148.285043701271 \tabularnewline
Winsorized Mean ( 21 / 24 ) & 88284.9722222222 & 570.818015617183 & 154.663955598469 \tabularnewline
Winsorized Mean ( 22 / 24 ) & 88284.9722222222 & 564.218638243962 & 156.472980929866 \tabularnewline
Winsorized Mean ( 23 / 24 ) & 88233.8611111111 & 543.884363107208 & 162.229082312703 \tabularnewline
Winsorized Mean ( 24 / 24 ) & 88203.5277777778 & 529.188918230995 & 166.676823227194 \tabularnewline
Trimmed Mean ( 1 / 24 ) & 88944.5428571429 & 1165.55739616812 & 76.3107360903519 \tabularnewline
Trimmed Mean ( 2 / 24 ) & 88922 & 1119.01234731811 & 79.4647174475915 \tabularnewline
Trimmed Mean ( 3 / 24 ) & 88891.5606060606 & 1089.81805545671 & 81.5655055089073 \tabularnewline
Trimmed Mean ( 4 / 24 ) & 88865.234375 & 1057.3259305361 & 84.0471531138394 \tabularnewline
Trimmed Mean ( 5 / 24 ) & 88845.3548387097 & 1028.40173217356 & 86.3916814404152 \tabularnewline
Trimmed Mean ( 6 / 24 ) & 88810.7833333333 & 997.552288561041 & 89.0286999004753 \tabularnewline
Trimmed Mean ( 7 / 24 ) & 88745.6551724138 & 973.693315084438 & 91.1433341459449 \tabularnewline
Trimmed Mean ( 8 / 24 ) & 88680.1071428571 & 945.516304597024 & 93.790140594828 \tabularnewline
Trimmed Mean ( 9 / 24 ) & 88608.5 & 918.982207400784 & 96.4202563296814 \tabularnewline
Trimmed Mean ( 10 / 24 ) & 88545.5769230769 & 892.021681209729 & 99.263929104273 \tabularnewline
Trimmed Mean ( 11 / 24 ) & 88489.68 & 864.282335974507 & 102.385153921056 \tabularnewline
Trimmed Mean ( 12 / 24 ) & 88425.875 & 839.744174688263 & 105.300968634675 \tabularnewline
Trimmed Mean ( 13 / 24 ) & 88385.2173913044 & 821.900925487343 & 107.537556718161 \tabularnewline
Trimmed Mean ( 14 / 24 ) & 88341.0909090909 & 798.437699416859 & 110.642434561408 \tabularnewline
Trimmed Mean ( 15 / 24 ) & 88315.4761904762 & 779.295553002366 & 113.327319590399 \tabularnewline
Trimmed Mean ( 16 / 24 ) & 88289.875 & 759.751822828788 & 116.208836026572 \tabularnewline
Trimmed Mean ( 17 / 24 ) & 88251.5 & 742.601564481528 & 118.840983134227 \tabularnewline
Trimmed Mean ( 18 / 24 ) & 88180.7222222222 & 727.898231822727 & 121.144300627588 \tabularnewline
Trimmed Mean ( 19 / 24 ) & 88124.2352941177 & 714.35561885799 & 123.361856430832 \tabularnewline
Trimmed Mean ( 20 / 24 ) & 88097.65625 & 709.178884869472 & 124.224872073306 \tabularnewline
Trimmed Mean ( 21 / 24 ) & 88064.4333333333 & 705.285007497513 & 124.863611727411 \tabularnewline
Trimmed Mean ( 22 / 24 ) & 88037.4285714286 & 703.228419596717 & 125.190373594281 \tabularnewline
Trimmed Mean ( 23 / 24 ) & 88006.2692307692 & 697.976906291302 & 126.087651951682 \tabularnewline
Trimmed Mean ( 24 / 24 ) & 87976.5833333333 & 692.217621276224 & 127.093822273887 \tabularnewline
Median & 87488 &  &  \tabularnewline
Midrange & 88817.5 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 88021.8648648649 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 88180.7222222222 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 88021.8648648649 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 88180.7222222222 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 88180.7222222222 &  &  \tabularnewline
Midmean - Closest Observation & 88021.8648648649 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 88180.7222222222 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 88251.5 &  &  \tabularnewline
Number of observations & 72 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=240238&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]88941.0138888889[/C][C]1215.07051024708[/C][C]73.1982326447898[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]88353.0986347619[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]87766.8181941782[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]89528.3647346998[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 24 )[/C][C]88965.8333333333[/C][C]1204.63889289896[/C][C]73.8526988110418[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 24 )[/C][C]88977.8055555556[/C][C]1163.81884057494[/C][C]76.4533125375422[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 24 )[/C][C]88961.7638888889[/C][C]1158.24616983719[/C][C]76.807302459195[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 24 )[/C][C]88933.7083333333[/C][C]1130.87892169716[/C][C]78.6412290715143[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 24 )[/C][C]88989.4027777778[/C][C]1117.50715525322[/C][C]79.6320653156027[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 24 )[/C][C]89125.5694444444[/C][C]1069.2146747345[/C][C]83.3561038306695[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 24 )[/C][C]89102.5277777778[/C][C]1064.18315581142[/C][C]83.7285642900806[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 24 )[/C][C]89109.75[/C][C]1030.62308226413[/C][C]86.4620165543339[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 24 )[/C][C]89017.5[/C][C]1005.13851185422[/C][C]88.5624209501093[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 24 )[/C][C]88933.75[/C][C]978.917091507839[/C][C]90.8491135475163[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 24 )[/C][C]88957.5833333333[/C][C]932.367660382718[/C][C]95.4104127730235[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 24 )[/C][C]88737.5833333333[/C][C]872.706124619932[/C][C]101.680944856413[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 24 )[/C][C]88735.7777777778[/C][C]871.948341642914[/C][C]101.76724186502[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 24 )[/C][C]88550.2777777778[/C][C]821.270186943217[/C][C]107.821127791529[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 24 )[/C][C]88528.8194444444[/C][C]793.864372146781[/C][C]111.516302469959[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 24 )[/C][C]88613.9305555556[/C][C]752.397671185261[/C][C]117.775391856225[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 24 )[/C][C]88853.1111111111[/C][C]710.152602832437[/C][C]125.118334787088[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 24 )[/C][C]88660.8611111111[/C][C]679.400133928327[/C][C]130.498739525512[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 24 )[/C][C]88348.6805555556[/C][C]620.441281140816[/C][C]142.396522025593[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 24 )[/C][C]88374.5138888889[/C][C]595.977258953537[/C][C]148.285043701271[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 24 )[/C][C]88284.9722222222[/C][C]570.818015617183[/C][C]154.663955598469[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 24 )[/C][C]88284.9722222222[/C][C]564.218638243962[/C][C]156.472980929866[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 24 )[/C][C]88233.8611111111[/C][C]543.884363107208[/C][C]162.229082312703[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 24 )[/C][C]88203.5277777778[/C][C]529.188918230995[/C][C]166.676823227194[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 24 )[/C][C]88944.5428571429[/C][C]1165.55739616812[/C][C]76.3107360903519[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 24 )[/C][C]88922[/C][C]1119.01234731811[/C][C]79.4647174475915[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 24 )[/C][C]88891.5606060606[/C][C]1089.81805545671[/C][C]81.5655055089073[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 24 )[/C][C]88865.234375[/C][C]1057.3259305361[/C][C]84.0471531138394[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 24 )[/C][C]88845.3548387097[/C][C]1028.40173217356[/C][C]86.3916814404152[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 24 )[/C][C]88810.7833333333[/C][C]997.552288561041[/C][C]89.0286999004753[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 24 )[/C][C]88745.6551724138[/C][C]973.693315084438[/C][C]91.1433341459449[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 24 )[/C][C]88680.1071428571[/C][C]945.516304597024[/C][C]93.790140594828[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 24 )[/C][C]88608.5[/C][C]918.982207400784[/C][C]96.4202563296814[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 24 )[/C][C]88545.5769230769[/C][C]892.021681209729[/C][C]99.263929104273[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 24 )[/C][C]88489.68[/C][C]864.282335974507[/C][C]102.385153921056[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 24 )[/C][C]88425.875[/C][C]839.744174688263[/C][C]105.300968634675[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 24 )[/C][C]88385.2173913044[/C][C]821.900925487343[/C][C]107.537556718161[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 24 )[/C][C]88341.0909090909[/C][C]798.437699416859[/C][C]110.642434561408[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 24 )[/C][C]88315.4761904762[/C][C]779.295553002366[/C][C]113.327319590399[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 24 )[/C][C]88289.875[/C][C]759.751822828788[/C][C]116.208836026572[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 24 )[/C][C]88251.5[/C][C]742.601564481528[/C][C]118.840983134227[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 24 )[/C][C]88180.7222222222[/C][C]727.898231822727[/C][C]121.144300627588[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 24 )[/C][C]88124.2352941177[/C][C]714.35561885799[/C][C]123.361856430832[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 24 )[/C][C]88097.65625[/C][C]709.178884869472[/C][C]124.224872073306[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 24 )[/C][C]88064.4333333333[/C][C]705.285007497513[/C][C]124.863611727411[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 24 )[/C][C]88037.4285714286[/C][C]703.228419596717[/C][C]125.190373594281[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 24 )[/C][C]88006.2692307692[/C][C]697.976906291302[/C][C]126.087651951682[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 24 )[/C][C]87976.5833333333[/C][C]692.217621276224[/C][C]127.093822273887[/C][/ROW]
[ROW][C]Median[/C][C]87488[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]88817.5[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]88021.8648648649[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]88180.7222222222[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]88021.8648648649[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]88180.7222222222[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]88180.7222222222[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]88021.8648648649[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]88180.7222222222[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]88251.5[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]72[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=240238&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=240238&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 Mean88941.01388888891215.0705102470873.1982326447898
Geometric Mean88353.0986347619
Harmonic Mean87766.8181941782
Quadratic Mean89528.3647346998
Winsorized Mean ( 1 / 24 )88965.83333333331204.6388928989673.8526988110418
Winsorized Mean ( 2 / 24 )88977.80555555561163.8188405749476.4533125375422
Winsorized Mean ( 3 / 24 )88961.76388888891158.2461698371976.807302459195
Winsorized Mean ( 4 / 24 )88933.70833333331130.8789216971678.6412290715143
Winsorized Mean ( 5 / 24 )88989.40277777781117.5071552532279.6320653156027
Winsorized Mean ( 6 / 24 )89125.56944444441069.214674734583.3561038306695
Winsorized Mean ( 7 / 24 )89102.52777777781064.1831558114283.7285642900806
Winsorized Mean ( 8 / 24 )89109.751030.6230822641386.4620165543339
Winsorized Mean ( 9 / 24 )89017.51005.1385118542288.5624209501093
Winsorized Mean ( 10 / 24 )88933.75978.91709150783990.8491135475163
Winsorized Mean ( 11 / 24 )88957.5833333333932.36766038271895.4104127730235
Winsorized Mean ( 12 / 24 )88737.5833333333872.706124619932101.680944856413
Winsorized Mean ( 13 / 24 )88735.7777777778871.948341642914101.76724186502
Winsorized Mean ( 14 / 24 )88550.2777777778821.270186943217107.821127791529
Winsorized Mean ( 15 / 24 )88528.8194444444793.864372146781111.516302469959
Winsorized Mean ( 16 / 24 )88613.9305555556752.397671185261117.775391856225
Winsorized Mean ( 17 / 24 )88853.1111111111710.152602832437125.118334787088
Winsorized Mean ( 18 / 24 )88660.8611111111679.400133928327130.498739525512
Winsorized Mean ( 19 / 24 )88348.6805555556620.441281140816142.396522025593
Winsorized Mean ( 20 / 24 )88374.5138888889595.977258953537148.285043701271
Winsorized Mean ( 21 / 24 )88284.9722222222570.818015617183154.663955598469
Winsorized Mean ( 22 / 24 )88284.9722222222564.218638243962156.472980929866
Winsorized Mean ( 23 / 24 )88233.8611111111543.884363107208162.229082312703
Winsorized Mean ( 24 / 24 )88203.5277777778529.188918230995166.676823227194
Trimmed Mean ( 1 / 24 )88944.54285714291165.5573961681276.3107360903519
Trimmed Mean ( 2 / 24 )889221119.0123473181179.4647174475915
Trimmed Mean ( 3 / 24 )88891.56060606061089.8180554567181.5655055089073
Trimmed Mean ( 4 / 24 )88865.2343751057.325930536184.0471531138394
Trimmed Mean ( 5 / 24 )88845.35483870971028.4017321735686.3916814404152
Trimmed Mean ( 6 / 24 )88810.7833333333997.55228856104189.0286999004753
Trimmed Mean ( 7 / 24 )88745.6551724138973.69331508443891.1433341459449
Trimmed Mean ( 8 / 24 )88680.1071428571945.51630459702493.790140594828
Trimmed Mean ( 9 / 24 )88608.5918.98220740078496.4202563296814
Trimmed Mean ( 10 / 24 )88545.5769230769892.02168120972999.263929104273
Trimmed Mean ( 11 / 24 )88489.68864.282335974507102.385153921056
Trimmed Mean ( 12 / 24 )88425.875839.744174688263105.300968634675
Trimmed Mean ( 13 / 24 )88385.2173913044821.900925487343107.537556718161
Trimmed Mean ( 14 / 24 )88341.0909090909798.437699416859110.642434561408
Trimmed Mean ( 15 / 24 )88315.4761904762779.295553002366113.327319590399
Trimmed Mean ( 16 / 24 )88289.875759.751822828788116.208836026572
Trimmed Mean ( 17 / 24 )88251.5742.601564481528118.840983134227
Trimmed Mean ( 18 / 24 )88180.7222222222727.898231822727121.144300627588
Trimmed Mean ( 19 / 24 )88124.2352941177714.35561885799123.361856430832
Trimmed Mean ( 20 / 24 )88097.65625709.178884869472124.224872073306
Trimmed Mean ( 21 / 24 )88064.4333333333705.285007497513124.863611727411
Trimmed Mean ( 22 / 24 )88037.4285714286703.228419596717125.190373594281
Trimmed Mean ( 23 / 24 )88006.2692307692697.976906291302126.087651951682
Trimmed Mean ( 24 / 24 )87976.5833333333692.217621276224127.093822273887
Median87488
Midrange88817.5
Midmean - Weighted Average at Xnp88021.8648648649
Midmean - Weighted Average at X(n+1)p88180.7222222222
Midmean - Empirical Distribution Function88021.8648648649
Midmean - Empirical Distribution Function - Averaging88180.7222222222
Midmean - Empirical Distribution Function - Interpolation88180.7222222222
Midmean - Closest Observation88021.8648648649
Midmean - True Basic - Statistics Graphics Toolkit88180.7222222222
Midmean - MS Excel (old versions)88251.5
Number of observations72



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')