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Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationFri, 26 Nov 2010 21:56:35 +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/2010/Nov/26/t1290808562ksd9a6nwvwt2pph.htm/, Retrieved Sat, 04 May 2024 04:02:53 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=102252, Retrieved Sat, 04 May 2024 04:02:53 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact128
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Central Tendency] [Arabica Price in ...] [2008-01-06 21:28:17] [74be16979710d4c4e7c6647856088456]
- RM D    [Central Tendency] [S&P] [2010-11-26 21:56:35] [0956ee981dded61b2e7128dae94e5715] [Current]
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Dataseries X:
1198.35
1183.26
1141.2
1049.33
1101.6
1030.71
1089.41
1186.69
1169.43
1104.49
1073.87
1115.1
1095.63
1036.19
1057.08
1020.62
987.48
919.32
919.14
872.81
797.87
735.09
825.88
903.25
896.24
968.75
1166.36
1282.83
1267.38
1280
1400.38
1385.59
1322.7
1330.63
1378.55
1468.36
1481.14
1549.38
1526.75
1473.99
1455.27
1503.35
1530.62
1482.37
1420.86
1406.82
1438.24
1418.3
1400.63
1377.94
1335.85
1303.82
1276.66
1270.2
1270.09
1310.61
1294.87
1280.66
1280.08
1248.29
1249.48
1207.01
1228.81
1220.33
1234.18
1191.33
1191.5
1156.85
1180.59
1203.6
1181.27




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'RServer@AstonUniversity' @ vre.aston.ac.uk

\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 & 'RServer@AstonUniversity' @ vre.aston.ac.uk \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=102252&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]'RServer@AstonUniversity' @ vre.aston.ac.uk[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=102252&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=102252&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'RServer@AstonUniversity' @ vre.aston.ac.uk







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean1216.1029577464822.693298644223453.5886376331649
Geometric Mean1200.20561010002
Harmonic Mean1183.1162781983
Quadratic Mean1230.83524895684
Winsorized Mean ( 1 / 23 )1216.7229577464822.386961185531854.3496255549332
Winsorized Mean ( 2 / 23 )1217.4029577464822.160125639216354.9366451060218
Winsorized Mean ( 3 / 23 )1218.3971830985921.489439266000656.6974860542906
Winsorized Mean ( 4 / 23 )1218.5352112676120.974632210663558.095665231646
Winsorized Mean ( 5 / 23 )1218.9422535211320.851498338142558.4582572318739
Winsorized Mean ( 6 / 23 )1219.6808450704220.457403138445359.6205117930288
Winsorized Mean ( 7 / 23 )1219.1435211267620.355844187838159.8915726548525
Winsorized Mean ( 8 / 23 )1223.2381690140818.97672944039464.4599045824139
Winsorized Mean ( 9 / 23 )1223.4536619718318.15768646707567.3793803076344
Winsorized Mean ( 10 / 23 )1225.6733802816916.910268450624372.4810125788654
Winsorized Mean ( 11 / 23 )1226.8416.577310302373174.0071807562394
Winsorized Mean ( 12 / 23 )1225.8259154929616.105253816880276.1134179834003
Winsorized Mean ( 13 / 23 )1227.0984507042315.524537175484379.0425142362382
Winsorized Mean ( 14 / 23 )1228.5773239436615.26902895371780.4620469099699
Winsorized Mean ( 15 / 23 )1228.9998591549314.210312562305986.4864761958129
Winsorized Mean ( 16 / 23 )1230.9153521126813.423781915643391.6966142513266
Winsorized Mean ( 17 / 23 )1232.258591549313.1783318303593.5064170042658
Winsorized Mean ( 18 / 23 )1223.101408450711.3442715479467107.816654712579
Winsorized Mean ( 19 / 23 )1222.4778873239411.0289761102681110.842373317483
Winsorized Mean ( 20 / 23 )1223.2328169014110.2644233999639119.172092696966
Winsorized Mean ( 21 / 23 )1227.376619718318.63692343582856142.108081522036
Winsorized Mean ( 22 / 23 )1230.121971830997.67031665121907160.374340169578
Winsorized Mean ( 23 / 23 )1230.303380281696.86062575515237179.328158128685
Trimmed Mean ( 1 / 23 )1218.2440579710121.735820224505156.0477610408996
Trimmed Mean ( 2 / 23 )1219.8559701492520.95767369606658.2056953381345
Trimmed Mean ( 3 / 23 )1221.1956923076920.171924721495360.5393738658155
Trimmed Mean ( 4 / 23 )1222.2469841269819.542108374617462.5442741743528
Trimmed Mean ( 5 / 23 )1223.3270491803318.974114282508664.4734732259971
Trimmed Mean ( 6 / 23 )1224.3823728813618.321434520992466.8278660974105
Trimmed Mean ( 7 / 23 )1224.3823728813617.639069218472969.4130941784103
Trimmed Mean ( 8 / 23 )1226.5045454545516.821172890997672.9143296607424
Trimmed Mean ( 9 / 23 )1227.0515094339616.180899992183975.8333288028902
Trimmed Mean ( 10 / 23 )1227.6080392156915.587441387897778.756224877857
Trimmed Mean ( 11 / 23 )1227.8883673469415.143517220415281.083433225909
Trimmed Mean ( 12 / 23 )1228.0323404255314.653540441672883.8044802424103
Trimmed Mean ( 13 / 23 )1228.3224444444414.132594481672186.9141505501623
Trimmed Mean ( 14 / 23 )1228.3224444444413.593868335346390.3585656520303
Trimmed Mean ( 15 / 23 )1228.465609756112.944747560157194.9007003842407
Trimmed Mean ( 16 / 23 )1228.4007692307712.354988886651799.4254855670434
Trimmed Mean ( 17 / 23 )1228.0991891891911.7645319847232104.389974100451
Trimmed Mean ( 18 / 23 )1227.6028571428611.013568206256111.46277338579
Trimmed Mean ( 19 / 23 )1228.1409090909110.5143173163775116.806528863068
Trimmed Mean ( 20 / 23 )1228.82354838719.8882851460041124.270642507075
Trimmed Mean ( 21 / 23 )1229.507931034489.22984381461543133.21004729111
Trimmed Mean ( 22 / 23 )1229.774814814818.8350292094118139.193067240203
Trimmed Mean ( 23 / 23 )1229.738.56307635529818143.608435680845
Median1228.81
Midrange1142.235
Midmean - Weighted Average at Xnp1223.93694444444
Midmean - Weighted Average at X(n+1)p1228.09918918919
Midmean - Empirical Distribution Function1228.09918918919
Midmean - Empirical Distribution Function - Averaging1228.09918918919
Midmean - Empirical Distribution Function - Interpolation1227.60285714286
Midmean - Closest Observation1223.93694444444
Midmean - True Basic - Statistics Graphics Toolkit1228.09918918919
Midmean - MS Excel (old versions)1228.09918918919
Number of observations71

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 1216.10295774648 & 22.6932986442234 & 53.5886376331649 \tabularnewline
Geometric Mean & 1200.20561010002 &  &  \tabularnewline
Harmonic Mean & 1183.1162781983 &  &  \tabularnewline
Quadratic Mean & 1230.83524895684 &  &  \tabularnewline
Winsorized Mean ( 1 / 23 ) & 1216.72295774648 & 22.3869611855318 & 54.3496255549332 \tabularnewline
Winsorized Mean ( 2 / 23 ) & 1217.40295774648 & 22.1601256392163 & 54.9366451060218 \tabularnewline
Winsorized Mean ( 3 / 23 ) & 1218.39718309859 & 21.4894392660006 & 56.6974860542906 \tabularnewline
Winsorized Mean ( 4 / 23 ) & 1218.53521126761 & 20.9746322106635 & 58.095665231646 \tabularnewline
Winsorized Mean ( 5 / 23 ) & 1218.94225352113 & 20.8514983381425 & 58.4582572318739 \tabularnewline
Winsorized Mean ( 6 / 23 ) & 1219.68084507042 & 20.4574031384453 & 59.6205117930288 \tabularnewline
Winsorized Mean ( 7 / 23 ) & 1219.14352112676 & 20.3558441878381 & 59.8915726548525 \tabularnewline
Winsorized Mean ( 8 / 23 ) & 1223.23816901408 & 18.976729440394 & 64.4599045824139 \tabularnewline
Winsorized Mean ( 9 / 23 ) & 1223.45366197183 & 18.157686467075 & 67.3793803076344 \tabularnewline
Winsorized Mean ( 10 / 23 ) & 1225.67338028169 & 16.9102684506243 & 72.4810125788654 \tabularnewline
Winsorized Mean ( 11 / 23 ) & 1226.84 & 16.5773103023731 & 74.0071807562394 \tabularnewline
Winsorized Mean ( 12 / 23 ) & 1225.82591549296 & 16.1052538168802 & 76.1134179834003 \tabularnewline
Winsorized Mean ( 13 / 23 ) & 1227.09845070423 & 15.5245371754843 & 79.0425142362382 \tabularnewline
Winsorized Mean ( 14 / 23 ) & 1228.57732394366 & 15.269028953717 & 80.4620469099699 \tabularnewline
Winsorized Mean ( 15 / 23 ) & 1228.99985915493 & 14.2103125623059 & 86.4864761958129 \tabularnewline
Winsorized Mean ( 16 / 23 ) & 1230.91535211268 & 13.4237819156433 & 91.6966142513266 \tabularnewline
Winsorized Mean ( 17 / 23 ) & 1232.2585915493 & 13.17833183035 & 93.5064170042658 \tabularnewline
Winsorized Mean ( 18 / 23 ) & 1223.1014084507 & 11.3442715479467 & 107.816654712579 \tabularnewline
Winsorized Mean ( 19 / 23 ) & 1222.47788732394 & 11.0289761102681 & 110.842373317483 \tabularnewline
Winsorized Mean ( 20 / 23 ) & 1223.23281690141 & 10.2644233999639 & 119.172092696966 \tabularnewline
Winsorized Mean ( 21 / 23 ) & 1227.37661971831 & 8.63692343582856 & 142.108081522036 \tabularnewline
Winsorized Mean ( 22 / 23 ) & 1230.12197183099 & 7.67031665121907 & 160.374340169578 \tabularnewline
Winsorized Mean ( 23 / 23 ) & 1230.30338028169 & 6.86062575515237 & 179.328158128685 \tabularnewline
Trimmed Mean ( 1 / 23 ) & 1218.24405797101 & 21.7358202245051 & 56.0477610408996 \tabularnewline
Trimmed Mean ( 2 / 23 ) & 1219.85597014925 & 20.957673696066 & 58.2056953381345 \tabularnewline
Trimmed Mean ( 3 / 23 ) & 1221.19569230769 & 20.1719247214953 & 60.5393738658155 \tabularnewline
Trimmed Mean ( 4 / 23 ) & 1222.24698412698 & 19.5421083746174 & 62.5442741743528 \tabularnewline
Trimmed Mean ( 5 / 23 ) & 1223.32704918033 & 18.9741142825086 & 64.4734732259971 \tabularnewline
Trimmed Mean ( 6 / 23 ) & 1224.38237288136 & 18.3214345209924 & 66.8278660974105 \tabularnewline
Trimmed Mean ( 7 / 23 ) & 1224.38237288136 & 17.6390692184729 & 69.4130941784103 \tabularnewline
Trimmed Mean ( 8 / 23 ) & 1226.50454545455 & 16.8211728909976 & 72.9143296607424 \tabularnewline
Trimmed Mean ( 9 / 23 ) & 1227.05150943396 & 16.1808999921839 & 75.8333288028902 \tabularnewline
Trimmed Mean ( 10 / 23 ) & 1227.60803921569 & 15.5874413878977 & 78.756224877857 \tabularnewline
Trimmed Mean ( 11 / 23 ) & 1227.88836734694 & 15.1435172204152 & 81.083433225909 \tabularnewline
Trimmed Mean ( 12 / 23 ) & 1228.03234042553 & 14.6535404416728 & 83.8044802424103 \tabularnewline
Trimmed Mean ( 13 / 23 ) & 1228.32244444444 & 14.1325944816721 & 86.9141505501623 \tabularnewline
Trimmed Mean ( 14 / 23 ) & 1228.32244444444 & 13.5938683353463 & 90.3585656520303 \tabularnewline
Trimmed Mean ( 15 / 23 ) & 1228.4656097561 & 12.9447475601571 & 94.9007003842407 \tabularnewline
Trimmed Mean ( 16 / 23 ) & 1228.40076923077 & 12.3549888866517 & 99.4254855670434 \tabularnewline
Trimmed Mean ( 17 / 23 ) & 1228.09918918919 & 11.7645319847232 & 104.389974100451 \tabularnewline
Trimmed Mean ( 18 / 23 ) & 1227.60285714286 & 11.013568206256 & 111.46277338579 \tabularnewline
Trimmed Mean ( 19 / 23 ) & 1228.14090909091 & 10.5143173163775 & 116.806528863068 \tabularnewline
Trimmed Mean ( 20 / 23 ) & 1228.8235483871 & 9.8882851460041 & 124.270642507075 \tabularnewline
Trimmed Mean ( 21 / 23 ) & 1229.50793103448 & 9.22984381461543 & 133.21004729111 \tabularnewline
Trimmed Mean ( 22 / 23 ) & 1229.77481481481 & 8.8350292094118 & 139.193067240203 \tabularnewline
Trimmed Mean ( 23 / 23 ) & 1229.73 & 8.56307635529818 & 143.608435680845 \tabularnewline
Median & 1228.81 &  &  \tabularnewline
Midrange & 1142.235 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 1223.93694444444 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 1228.09918918919 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 1228.09918918919 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 1228.09918918919 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 1227.60285714286 &  &  \tabularnewline
Midmean - Closest Observation & 1223.93694444444 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 1228.09918918919 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 1228.09918918919 &  &  \tabularnewline
Number of observations & 71 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=102252&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]1216.10295774648[/C][C]22.6932986442234[/C][C]53.5886376331649[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]1200.20561010002[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]1183.1162781983[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]1230.83524895684[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 23 )[/C][C]1216.72295774648[/C][C]22.3869611855318[/C][C]54.3496255549332[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 23 )[/C][C]1217.40295774648[/C][C]22.1601256392163[/C][C]54.9366451060218[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 23 )[/C][C]1218.39718309859[/C][C]21.4894392660006[/C][C]56.6974860542906[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 23 )[/C][C]1218.53521126761[/C][C]20.9746322106635[/C][C]58.095665231646[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 23 )[/C][C]1218.94225352113[/C][C]20.8514983381425[/C][C]58.4582572318739[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 23 )[/C][C]1219.68084507042[/C][C]20.4574031384453[/C][C]59.6205117930288[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 23 )[/C][C]1219.14352112676[/C][C]20.3558441878381[/C][C]59.8915726548525[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 23 )[/C][C]1223.23816901408[/C][C]18.976729440394[/C][C]64.4599045824139[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 23 )[/C][C]1223.45366197183[/C][C]18.157686467075[/C][C]67.3793803076344[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 23 )[/C][C]1225.67338028169[/C][C]16.9102684506243[/C][C]72.4810125788654[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 23 )[/C][C]1226.84[/C][C]16.5773103023731[/C][C]74.0071807562394[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 23 )[/C][C]1225.82591549296[/C][C]16.1052538168802[/C][C]76.1134179834003[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 23 )[/C][C]1227.09845070423[/C][C]15.5245371754843[/C][C]79.0425142362382[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 23 )[/C][C]1228.57732394366[/C][C]15.269028953717[/C][C]80.4620469099699[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 23 )[/C][C]1228.99985915493[/C][C]14.2103125623059[/C][C]86.4864761958129[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 23 )[/C][C]1230.91535211268[/C][C]13.4237819156433[/C][C]91.6966142513266[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 23 )[/C][C]1232.2585915493[/C][C]13.17833183035[/C][C]93.5064170042658[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 23 )[/C][C]1223.1014084507[/C][C]11.3442715479467[/C][C]107.816654712579[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 23 )[/C][C]1222.47788732394[/C][C]11.0289761102681[/C][C]110.842373317483[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 23 )[/C][C]1223.23281690141[/C][C]10.2644233999639[/C][C]119.172092696966[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 23 )[/C][C]1227.37661971831[/C][C]8.63692343582856[/C][C]142.108081522036[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 23 )[/C][C]1230.12197183099[/C][C]7.67031665121907[/C][C]160.374340169578[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 23 )[/C][C]1230.30338028169[/C][C]6.86062575515237[/C][C]179.328158128685[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 23 )[/C][C]1218.24405797101[/C][C]21.7358202245051[/C][C]56.0477610408996[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 23 )[/C][C]1219.85597014925[/C][C]20.957673696066[/C][C]58.2056953381345[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 23 )[/C][C]1221.19569230769[/C][C]20.1719247214953[/C][C]60.5393738658155[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 23 )[/C][C]1222.24698412698[/C][C]19.5421083746174[/C][C]62.5442741743528[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 23 )[/C][C]1223.32704918033[/C][C]18.9741142825086[/C][C]64.4734732259971[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 23 )[/C][C]1224.38237288136[/C][C]18.3214345209924[/C][C]66.8278660974105[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 23 )[/C][C]1224.38237288136[/C][C]17.6390692184729[/C][C]69.4130941784103[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 23 )[/C][C]1226.50454545455[/C][C]16.8211728909976[/C][C]72.9143296607424[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 23 )[/C][C]1227.05150943396[/C][C]16.1808999921839[/C][C]75.8333288028902[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 23 )[/C][C]1227.60803921569[/C][C]15.5874413878977[/C][C]78.756224877857[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 23 )[/C][C]1227.88836734694[/C][C]15.1435172204152[/C][C]81.083433225909[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 23 )[/C][C]1228.03234042553[/C][C]14.6535404416728[/C][C]83.8044802424103[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 23 )[/C][C]1228.32244444444[/C][C]14.1325944816721[/C][C]86.9141505501623[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 23 )[/C][C]1228.32244444444[/C][C]13.5938683353463[/C][C]90.3585656520303[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 23 )[/C][C]1228.4656097561[/C][C]12.9447475601571[/C][C]94.9007003842407[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 23 )[/C][C]1228.40076923077[/C][C]12.3549888866517[/C][C]99.4254855670434[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 23 )[/C][C]1228.09918918919[/C][C]11.7645319847232[/C][C]104.389974100451[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 23 )[/C][C]1227.60285714286[/C][C]11.013568206256[/C][C]111.46277338579[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 23 )[/C][C]1228.14090909091[/C][C]10.5143173163775[/C][C]116.806528863068[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 23 )[/C][C]1228.8235483871[/C][C]9.8882851460041[/C][C]124.270642507075[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 23 )[/C][C]1229.50793103448[/C][C]9.22984381461543[/C][C]133.21004729111[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 23 )[/C][C]1229.77481481481[/C][C]8.8350292094118[/C][C]139.193067240203[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 23 )[/C][C]1229.73[/C][C]8.56307635529818[/C][C]143.608435680845[/C][/ROW]
[ROW][C]Median[/C][C]1228.81[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]1142.235[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]1223.93694444444[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]1228.09918918919[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]1228.09918918919[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]1228.09918918919[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]1227.60285714286[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]1223.93694444444[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]1228.09918918919[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]1228.09918918919[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]71[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=102252&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=102252&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 Mean1216.1029577464822.693298644223453.5886376331649
Geometric Mean1200.20561010002
Harmonic Mean1183.1162781983
Quadratic Mean1230.83524895684
Winsorized Mean ( 1 / 23 )1216.7229577464822.386961185531854.3496255549332
Winsorized Mean ( 2 / 23 )1217.4029577464822.160125639216354.9366451060218
Winsorized Mean ( 3 / 23 )1218.3971830985921.489439266000656.6974860542906
Winsorized Mean ( 4 / 23 )1218.5352112676120.974632210663558.095665231646
Winsorized Mean ( 5 / 23 )1218.9422535211320.851498338142558.4582572318739
Winsorized Mean ( 6 / 23 )1219.6808450704220.457403138445359.6205117930288
Winsorized Mean ( 7 / 23 )1219.1435211267620.355844187838159.8915726548525
Winsorized Mean ( 8 / 23 )1223.2381690140818.97672944039464.4599045824139
Winsorized Mean ( 9 / 23 )1223.4536619718318.15768646707567.3793803076344
Winsorized Mean ( 10 / 23 )1225.6733802816916.910268450624372.4810125788654
Winsorized Mean ( 11 / 23 )1226.8416.577310302373174.0071807562394
Winsorized Mean ( 12 / 23 )1225.8259154929616.105253816880276.1134179834003
Winsorized Mean ( 13 / 23 )1227.0984507042315.524537175484379.0425142362382
Winsorized Mean ( 14 / 23 )1228.5773239436615.26902895371780.4620469099699
Winsorized Mean ( 15 / 23 )1228.9998591549314.210312562305986.4864761958129
Winsorized Mean ( 16 / 23 )1230.9153521126813.423781915643391.6966142513266
Winsorized Mean ( 17 / 23 )1232.258591549313.1783318303593.5064170042658
Winsorized Mean ( 18 / 23 )1223.101408450711.3442715479467107.816654712579
Winsorized Mean ( 19 / 23 )1222.4778873239411.0289761102681110.842373317483
Winsorized Mean ( 20 / 23 )1223.2328169014110.2644233999639119.172092696966
Winsorized Mean ( 21 / 23 )1227.376619718318.63692343582856142.108081522036
Winsorized Mean ( 22 / 23 )1230.121971830997.67031665121907160.374340169578
Winsorized Mean ( 23 / 23 )1230.303380281696.86062575515237179.328158128685
Trimmed Mean ( 1 / 23 )1218.2440579710121.735820224505156.0477610408996
Trimmed Mean ( 2 / 23 )1219.8559701492520.95767369606658.2056953381345
Trimmed Mean ( 3 / 23 )1221.1956923076920.171924721495360.5393738658155
Trimmed Mean ( 4 / 23 )1222.2469841269819.542108374617462.5442741743528
Trimmed Mean ( 5 / 23 )1223.3270491803318.974114282508664.4734732259971
Trimmed Mean ( 6 / 23 )1224.3823728813618.321434520992466.8278660974105
Trimmed Mean ( 7 / 23 )1224.3823728813617.639069218472969.4130941784103
Trimmed Mean ( 8 / 23 )1226.5045454545516.821172890997672.9143296607424
Trimmed Mean ( 9 / 23 )1227.0515094339616.180899992183975.8333288028902
Trimmed Mean ( 10 / 23 )1227.6080392156915.587441387897778.756224877857
Trimmed Mean ( 11 / 23 )1227.8883673469415.143517220415281.083433225909
Trimmed Mean ( 12 / 23 )1228.0323404255314.653540441672883.8044802424103
Trimmed Mean ( 13 / 23 )1228.3224444444414.132594481672186.9141505501623
Trimmed Mean ( 14 / 23 )1228.3224444444413.593868335346390.3585656520303
Trimmed Mean ( 15 / 23 )1228.465609756112.944747560157194.9007003842407
Trimmed Mean ( 16 / 23 )1228.4007692307712.354988886651799.4254855670434
Trimmed Mean ( 17 / 23 )1228.0991891891911.7645319847232104.389974100451
Trimmed Mean ( 18 / 23 )1227.6028571428611.013568206256111.46277338579
Trimmed Mean ( 19 / 23 )1228.1409090909110.5143173163775116.806528863068
Trimmed Mean ( 20 / 23 )1228.82354838719.8882851460041124.270642507075
Trimmed Mean ( 21 / 23 )1229.507931034489.22984381461543133.21004729111
Trimmed Mean ( 22 / 23 )1229.774814814818.8350292094118139.193067240203
Trimmed Mean ( 23 / 23 )1229.738.56307635529818143.608435680845
Median1228.81
Midrange1142.235
Midmean - Weighted Average at Xnp1223.93694444444
Midmean - Weighted Average at X(n+1)p1228.09918918919
Midmean - Empirical Distribution Function1228.09918918919
Midmean - Empirical Distribution Function - Averaging1228.09918918919
Midmean - Empirical Distribution Function - Interpolation1227.60285714286
Midmean - Closest Observation1223.93694444444
Midmean - True Basic - Statistics Graphics Toolkit1228.09918918919
Midmean - MS Excel (old versions)1228.09918918919
Number of observations71



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')