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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 computationThu, 15 Oct 2009 11:00:13 -0600
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2009/Oct/15/t12556260587tk9qry1y4s5s7k.htm/, Retrieved Sat, 04 May 2024 18:52:56 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=46815, Retrieved Sat, 04 May 2024 18:52:56 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact144
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [Shw3: Part 2] [2009-10-15 17:00:13] [7a39e26d7a09dd77604df90cb29f8d39] [Current]
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Dataseries X:
26442.90
24863.62
25152.29
27539.80
27920.04
26945.05
26129.44
25406.62
25663.17
26066.60
26306.23
27105.07
27239.67
26296.19
25873.03
25917.65
25853.93
24803.73
23821.36
22950.51
22765.47
24710.92
23983.59
24434.12
23939.23
24290.02
24117.63
23724.64
22989.44
23716.86
25058.83
25059.00
23579.18
24209.03
24173.67
24706.39
24522.12
24766.15
25940.04
24985.78
24788.00
26544.56
28019.08
27285.71
29161.16
28357.73
27979.91
27543.95
27397.53
27623.59
27736.07
27803.79
27779.55
27524.13
27582.72
28638.95
28825.78
30132.61
29326.85
29075.62
28230.63
28118.36
28173.29
27396.91
24578.55
24504.77
27582.37
26920.31
25426.68
25390.80
25041.16
22769.42
22921.89
26267.63
27364.67
28382.59
29132.81
28214.51
28865.73
24405.35




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135

\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 & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=46815&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]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=46815&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=46815&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'Gwilym Jenkins' @ 72.249.127.135







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean26159.809125208.435470317083125.505553758217
Geometric Mean26093.9918962458
Harmonic Mean26028.0496767391
Quadratic Mean26225.3273713418
Winsorized Mean ( 1 / 26 )26149.7865206.226934806736126.801023952114
Winsorized Mean ( 2 / 26 )26149.456204.661224665933127.769468997772
Winsorized Mean ( 3 / 26 )26149.466125204.250416652542128.026500770786
Winsorized Mean ( 4 / 26 )26148.553125203.341191795411128.594471656825
Winsorized Mean ( 5 / 26 )26172.29375194.243525454418134.739593964699
Winsorized Mean ( 6 / 26 )26179.6235192.008289774734136.346318852765
Winsorized Mean ( 7 / 26 )26163.956625189.116927037112138.348042319161
Winsorized Mean ( 8 / 26 )26147.992625183.448693398228142.535725606059
Winsorized Mean ( 9 / 26 )26158.45625180.923796924878144.582728721205
Winsorized Mean ( 10 / 26 )26148.11375177.664360374261147.177034802688
Winsorized Mean ( 11 / 26 )26164.32775174.545715122684149.899570617415
Winsorized Mean ( 12 / 26 )26166.55075172.391579732179151.785550028902
Winsorized Mean ( 13 / 26 )26163.370625170.247253748306153.678664700695
Winsorized Mean ( 14 / 26 )26160.169875165.708219829513157.868872780811
Winsorized Mean ( 15 / 26 )26174.449875161.624228383279161.946325354942
Winsorized Mean ( 16 / 26 )26168.229875159.147916308583164.427097017473
Winsorized Mean ( 17 / 26 )26158.539875153.694420469943170.198370214198
Winsorized Mean ( 18 / 26 )26156.989625152.42658954763171.603850106654
Winsorized Mean ( 19 / 26 )26160.06525149.231744679310175.298260475453
Winsorized Mean ( 20 / 26 )26163.90525141.280221252821185.191564806369
Winsorized Mean ( 21 / 26 )26154.366139.729141428871187.179036044631
Winsorized Mean ( 22 / 26 )26169.458137.744200681916189.985914981869
Winsorized Mean ( 23 / 26 )26164.694125135.506481079260193.088138047772
Winsorized Mean ( 24 / 26 )26168.168125134.740174175362194.212069897896
Winsorized Mean ( 25 / 26 )26181.986875131.723668332876198.764483303305
Winsorized Mean ( 26 / 26 )26180.543875121.471316044171215.528609778788
Trimmed Mean ( 1 / 26 )26152.3929487179202.903338545913128.890895222013
Trimmed Mean ( 2 / 26 )26155.1365789474199.007780732361131.427708417705
Trimmed Mean ( 3 / 26 )26158.2071621622195.399037201098133.870706513467
Trimmed Mean ( 4 / 26 )26161.4445833333191.318962019772136.742559687469
Trimmed Mean ( 5 / 26 )26165.1278571429186.811136187654140.06192773679
Trimmed Mean ( 6 / 26 )26163.4417647059184.197177999222142.040405009985
Trimmed Mean ( 7 / 26 )26160.1727272727181.616794004064144.040494001273
Trimmed Mean ( 8 / 26 )26159.49703125179.165285961136146.007620231323
Trimmed Mean ( 9 / 26 )26161.3525806452177.397280047397147.473245213542
Trimmed Mean ( 10 / 26 )26161.7816666667175.680156048320148.917113094270
Trimmed Mean ( 11 / 26 )26163.6668965517174.121242371577150.261200415272
Trimmed Mean ( 12 / 26 )26163.5810714286172.679200784433151.515532574709
Trimmed Mean ( 13 / 26 )26163.2144444444171.15659128336152.861273108260
Trimmed Mean ( 14 / 26 )26163.1959615385169.507819764107154.348017678170
Trimmed Mean ( 15 / 26 )26163.5418168.118706387612155.625405180538
Trimmed Mean ( 16 / 26 )26162.3297916667166.918317906668156.737319904549
Trimmed Mean ( 17 / 26 )26161.6884782609165.619577608285157.962535927590
Trimmed Mean ( 18 / 26 )26162.0252272727164.724603356963158.822815135750
Trimmed Mean ( 19 / 26 )26162.5580952381163.498712246964160.016906162048
Trimmed Mean ( 20 / 26 )26162.8205162.210660084724161.289156251106
Trimmed Mean ( 21 / 26 )26162.7063157895161.765128883884161.732670670755
Trimmed Mean ( 22 / 26 )26163.5888888889161.018575833033162.488015767939
Trimmed Mean ( 23 / 26 )26162.9611764706159.941523225370163.578291921136
Trimmed Mean ( 24 / 26 )26162.7728125158.446842975931165.120189971058
Trimmed Mean ( 25 / 26 )26162.1733333333155.959568920947167.749715611194
Trimmed Mean ( 26 / 26 )26159.9089285714152.666062407256171.35379347629
Median26098.02
Midrange26449.04
Midmean - Weighted Average at Xnp26124.1797560976
Midmean - Weighted Average at X(n+1)p26162.8205
Midmean - Empirical Distribution Function26124.1797560976
Midmean - Empirical Distribution Function - Averaging26162.8205
Midmean - Empirical Distribution Function - Interpolation26162.8205
Midmean - Closest Observation26124.1797560976
Midmean - True Basic - Statistics Graphics Toolkit26162.8205
Midmean - MS Excel (old versions)26162.5580952381
Number of observations80

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 26159.809125 & 208.435470317083 & 125.505553758217 \tabularnewline
Geometric Mean & 26093.9918962458 &  &  \tabularnewline
Harmonic Mean & 26028.0496767391 &  &  \tabularnewline
Quadratic Mean & 26225.3273713418 &  &  \tabularnewline
Winsorized Mean ( 1 / 26 ) & 26149.7865 & 206.226934806736 & 126.801023952114 \tabularnewline
Winsorized Mean ( 2 / 26 ) & 26149.456 & 204.661224665933 & 127.769468997772 \tabularnewline
Winsorized Mean ( 3 / 26 ) & 26149.466125 & 204.250416652542 & 128.026500770786 \tabularnewline
Winsorized Mean ( 4 / 26 ) & 26148.553125 & 203.341191795411 & 128.594471656825 \tabularnewline
Winsorized Mean ( 5 / 26 ) & 26172.29375 & 194.243525454418 & 134.739593964699 \tabularnewline
Winsorized Mean ( 6 / 26 ) & 26179.6235 & 192.008289774734 & 136.346318852765 \tabularnewline
Winsorized Mean ( 7 / 26 ) & 26163.956625 & 189.116927037112 & 138.348042319161 \tabularnewline
Winsorized Mean ( 8 / 26 ) & 26147.992625 & 183.448693398228 & 142.535725606059 \tabularnewline
Winsorized Mean ( 9 / 26 ) & 26158.45625 & 180.923796924878 & 144.582728721205 \tabularnewline
Winsorized Mean ( 10 / 26 ) & 26148.11375 & 177.664360374261 & 147.177034802688 \tabularnewline
Winsorized Mean ( 11 / 26 ) & 26164.32775 & 174.545715122684 & 149.899570617415 \tabularnewline
Winsorized Mean ( 12 / 26 ) & 26166.55075 & 172.391579732179 & 151.785550028902 \tabularnewline
Winsorized Mean ( 13 / 26 ) & 26163.370625 & 170.247253748306 & 153.678664700695 \tabularnewline
Winsorized Mean ( 14 / 26 ) & 26160.169875 & 165.708219829513 & 157.868872780811 \tabularnewline
Winsorized Mean ( 15 / 26 ) & 26174.449875 & 161.624228383279 & 161.946325354942 \tabularnewline
Winsorized Mean ( 16 / 26 ) & 26168.229875 & 159.147916308583 & 164.427097017473 \tabularnewline
Winsorized Mean ( 17 / 26 ) & 26158.539875 & 153.694420469943 & 170.198370214198 \tabularnewline
Winsorized Mean ( 18 / 26 ) & 26156.989625 & 152.42658954763 & 171.603850106654 \tabularnewline
Winsorized Mean ( 19 / 26 ) & 26160.06525 & 149.231744679310 & 175.298260475453 \tabularnewline
Winsorized Mean ( 20 / 26 ) & 26163.90525 & 141.280221252821 & 185.191564806369 \tabularnewline
Winsorized Mean ( 21 / 26 ) & 26154.366 & 139.729141428871 & 187.179036044631 \tabularnewline
Winsorized Mean ( 22 / 26 ) & 26169.458 & 137.744200681916 & 189.985914981869 \tabularnewline
Winsorized Mean ( 23 / 26 ) & 26164.694125 & 135.506481079260 & 193.088138047772 \tabularnewline
Winsorized Mean ( 24 / 26 ) & 26168.168125 & 134.740174175362 & 194.212069897896 \tabularnewline
Winsorized Mean ( 25 / 26 ) & 26181.986875 & 131.723668332876 & 198.764483303305 \tabularnewline
Winsorized Mean ( 26 / 26 ) & 26180.543875 & 121.471316044171 & 215.528609778788 \tabularnewline
Trimmed Mean ( 1 / 26 ) & 26152.3929487179 & 202.903338545913 & 128.890895222013 \tabularnewline
Trimmed Mean ( 2 / 26 ) & 26155.1365789474 & 199.007780732361 & 131.427708417705 \tabularnewline
Trimmed Mean ( 3 / 26 ) & 26158.2071621622 & 195.399037201098 & 133.870706513467 \tabularnewline
Trimmed Mean ( 4 / 26 ) & 26161.4445833333 & 191.318962019772 & 136.742559687469 \tabularnewline
Trimmed Mean ( 5 / 26 ) & 26165.1278571429 & 186.811136187654 & 140.06192773679 \tabularnewline
Trimmed Mean ( 6 / 26 ) & 26163.4417647059 & 184.197177999222 & 142.040405009985 \tabularnewline
Trimmed Mean ( 7 / 26 ) & 26160.1727272727 & 181.616794004064 & 144.040494001273 \tabularnewline
Trimmed Mean ( 8 / 26 ) & 26159.49703125 & 179.165285961136 & 146.007620231323 \tabularnewline
Trimmed Mean ( 9 / 26 ) & 26161.3525806452 & 177.397280047397 & 147.473245213542 \tabularnewline
Trimmed Mean ( 10 / 26 ) & 26161.7816666667 & 175.680156048320 & 148.917113094270 \tabularnewline
Trimmed Mean ( 11 / 26 ) & 26163.6668965517 & 174.121242371577 & 150.261200415272 \tabularnewline
Trimmed Mean ( 12 / 26 ) & 26163.5810714286 & 172.679200784433 & 151.515532574709 \tabularnewline
Trimmed Mean ( 13 / 26 ) & 26163.2144444444 & 171.15659128336 & 152.861273108260 \tabularnewline
Trimmed Mean ( 14 / 26 ) & 26163.1959615385 & 169.507819764107 & 154.348017678170 \tabularnewline
Trimmed Mean ( 15 / 26 ) & 26163.5418 & 168.118706387612 & 155.625405180538 \tabularnewline
Trimmed Mean ( 16 / 26 ) & 26162.3297916667 & 166.918317906668 & 156.737319904549 \tabularnewline
Trimmed Mean ( 17 / 26 ) & 26161.6884782609 & 165.619577608285 & 157.962535927590 \tabularnewline
Trimmed Mean ( 18 / 26 ) & 26162.0252272727 & 164.724603356963 & 158.822815135750 \tabularnewline
Trimmed Mean ( 19 / 26 ) & 26162.5580952381 & 163.498712246964 & 160.016906162048 \tabularnewline
Trimmed Mean ( 20 / 26 ) & 26162.8205 & 162.210660084724 & 161.289156251106 \tabularnewline
Trimmed Mean ( 21 / 26 ) & 26162.7063157895 & 161.765128883884 & 161.732670670755 \tabularnewline
Trimmed Mean ( 22 / 26 ) & 26163.5888888889 & 161.018575833033 & 162.488015767939 \tabularnewline
Trimmed Mean ( 23 / 26 ) & 26162.9611764706 & 159.941523225370 & 163.578291921136 \tabularnewline
Trimmed Mean ( 24 / 26 ) & 26162.7728125 & 158.446842975931 & 165.120189971058 \tabularnewline
Trimmed Mean ( 25 / 26 ) & 26162.1733333333 & 155.959568920947 & 167.749715611194 \tabularnewline
Trimmed Mean ( 26 / 26 ) & 26159.9089285714 & 152.666062407256 & 171.35379347629 \tabularnewline
Median & 26098.02 &  &  \tabularnewline
Midrange & 26449.04 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 26124.1797560976 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 26162.8205 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 26124.1797560976 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 26162.8205 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 26162.8205 &  &  \tabularnewline
Midmean - Closest Observation & 26124.1797560976 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 26162.8205 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 26162.5580952381 &  &  \tabularnewline
Number of observations & 80 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=46815&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]26159.809125[/C][C]208.435470317083[/C][C]125.505553758217[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]26093.9918962458[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]26028.0496767391[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]26225.3273713418[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 26 )[/C][C]26149.7865[/C][C]206.226934806736[/C][C]126.801023952114[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 26 )[/C][C]26149.456[/C][C]204.661224665933[/C][C]127.769468997772[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 26 )[/C][C]26149.466125[/C][C]204.250416652542[/C][C]128.026500770786[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 26 )[/C][C]26148.553125[/C][C]203.341191795411[/C][C]128.594471656825[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 26 )[/C][C]26172.29375[/C][C]194.243525454418[/C][C]134.739593964699[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 26 )[/C][C]26179.6235[/C][C]192.008289774734[/C][C]136.346318852765[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 26 )[/C][C]26163.956625[/C][C]189.116927037112[/C][C]138.348042319161[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 26 )[/C][C]26147.992625[/C][C]183.448693398228[/C][C]142.535725606059[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 26 )[/C][C]26158.45625[/C][C]180.923796924878[/C][C]144.582728721205[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 26 )[/C][C]26148.11375[/C][C]177.664360374261[/C][C]147.177034802688[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 26 )[/C][C]26164.32775[/C][C]174.545715122684[/C][C]149.899570617415[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 26 )[/C][C]26166.55075[/C][C]172.391579732179[/C][C]151.785550028902[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 26 )[/C][C]26163.370625[/C][C]170.247253748306[/C][C]153.678664700695[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 26 )[/C][C]26160.169875[/C][C]165.708219829513[/C][C]157.868872780811[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 26 )[/C][C]26174.449875[/C][C]161.624228383279[/C][C]161.946325354942[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 26 )[/C][C]26168.229875[/C][C]159.147916308583[/C][C]164.427097017473[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 26 )[/C][C]26158.539875[/C][C]153.694420469943[/C][C]170.198370214198[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 26 )[/C][C]26156.989625[/C][C]152.42658954763[/C][C]171.603850106654[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 26 )[/C][C]26160.06525[/C][C]149.231744679310[/C][C]175.298260475453[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 26 )[/C][C]26163.90525[/C][C]141.280221252821[/C][C]185.191564806369[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 26 )[/C][C]26154.366[/C][C]139.729141428871[/C][C]187.179036044631[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 26 )[/C][C]26169.458[/C][C]137.744200681916[/C][C]189.985914981869[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 26 )[/C][C]26164.694125[/C][C]135.506481079260[/C][C]193.088138047772[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 26 )[/C][C]26168.168125[/C][C]134.740174175362[/C][C]194.212069897896[/C][/ROW]
[ROW][C]Winsorized Mean ( 25 / 26 )[/C][C]26181.986875[/C][C]131.723668332876[/C][C]198.764483303305[/C][/ROW]
[ROW][C]Winsorized Mean ( 26 / 26 )[/C][C]26180.543875[/C][C]121.471316044171[/C][C]215.528609778788[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 26 )[/C][C]26152.3929487179[/C][C]202.903338545913[/C][C]128.890895222013[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 26 )[/C][C]26155.1365789474[/C][C]199.007780732361[/C][C]131.427708417705[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 26 )[/C][C]26158.2071621622[/C][C]195.399037201098[/C][C]133.870706513467[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 26 )[/C][C]26161.4445833333[/C][C]191.318962019772[/C][C]136.742559687469[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 26 )[/C][C]26165.1278571429[/C][C]186.811136187654[/C][C]140.06192773679[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 26 )[/C][C]26163.4417647059[/C][C]184.197177999222[/C][C]142.040405009985[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 26 )[/C][C]26160.1727272727[/C][C]181.616794004064[/C][C]144.040494001273[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 26 )[/C][C]26159.49703125[/C][C]179.165285961136[/C][C]146.007620231323[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 26 )[/C][C]26161.3525806452[/C][C]177.397280047397[/C][C]147.473245213542[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 26 )[/C][C]26161.7816666667[/C][C]175.680156048320[/C][C]148.917113094270[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 26 )[/C][C]26163.6668965517[/C][C]174.121242371577[/C][C]150.261200415272[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 26 )[/C][C]26163.5810714286[/C][C]172.679200784433[/C][C]151.515532574709[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 26 )[/C][C]26163.2144444444[/C][C]171.15659128336[/C][C]152.861273108260[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 26 )[/C][C]26163.1959615385[/C][C]169.507819764107[/C][C]154.348017678170[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 26 )[/C][C]26163.5418[/C][C]168.118706387612[/C][C]155.625405180538[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 26 )[/C][C]26162.3297916667[/C][C]166.918317906668[/C][C]156.737319904549[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 26 )[/C][C]26161.6884782609[/C][C]165.619577608285[/C][C]157.962535927590[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 26 )[/C][C]26162.0252272727[/C][C]164.724603356963[/C][C]158.822815135750[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 26 )[/C][C]26162.5580952381[/C][C]163.498712246964[/C][C]160.016906162048[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 26 )[/C][C]26162.8205[/C][C]162.210660084724[/C][C]161.289156251106[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 26 )[/C][C]26162.7063157895[/C][C]161.765128883884[/C][C]161.732670670755[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 26 )[/C][C]26163.5888888889[/C][C]161.018575833033[/C][C]162.488015767939[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 26 )[/C][C]26162.9611764706[/C][C]159.941523225370[/C][C]163.578291921136[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 26 )[/C][C]26162.7728125[/C][C]158.446842975931[/C][C]165.120189971058[/C][/ROW]
[ROW][C]Trimmed Mean ( 25 / 26 )[/C][C]26162.1733333333[/C][C]155.959568920947[/C][C]167.749715611194[/C][/ROW]
[ROW][C]Trimmed Mean ( 26 / 26 )[/C][C]26159.9089285714[/C][C]152.666062407256[/C][C]171.35379347629[/C][/ROW]
[ROW][C]Median[/C][C]26098.02[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]26449.04[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]26124.1797560976[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]26162.8205[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]26124.1797560976[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]26162.8205[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]26162.8205[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]26124.1797560976[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]26162.8205[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]26162.5580952381[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]80[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=46815&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=46815&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 Mean26159.809125208.435470317083125.505553758217
Geometric Mean26093.9918962458
Harmonic Mean26028.0496767391
Quadratic Mean26225.3273713418
Winsorized Mean ( 1 / 26 )26149.7865206.226934806736126.801023952114
Winsorized Mean ( 2 / 26 )26149.456204.661224665933127.769468997772
Winsorized Mean ( 3 / 26 )26149.466125204.250416652542128.026500770786
Winsorized Mean ( 4 / 26 )26148.553125203.341191795411128.594471656825
Winsorized Mean ( 5 / 26 )26172.29375194.243525454418134.739593964699
Winsorized Mean ( 6 / 26 )26179.6235192.008289774734136.346318852765
Winsorized Mean ( 7 / 26 )26163.956625189.116927037112138.348042319161
Winsorized Mean ( 8 / 26 )26147.992625183.448693398228142.535725606059
Winsorized Mean ( 9 / 26 )26158.45625180.923796924878144.582728721205
Winsorized Mean ( 10 / 26 )26148.11375177.664360374261147.177034802688
Winsorized Mean ( 11 / 26 )26164.32775174.545715122684149.899570617415
Winsorized Mean ( 12 / 26 )26166.55075172.391579732179151.785550028902
Winsorized Mean ( 13 / 26 )26163.370625170.247253748306153.678664700695
Winsorized Mean ( 14 / 26 )26160.169875165.708219829513157.868872780811
Winsorized Mean ( 15 / 26 )26174.449875161.624228383279161.946325354942
Winsorized Mean ( 16 / 26 )26168.229875159.147916308583164.427097017473
Winsorized Mean ( 17 / 26 )26158.539875153.694420469943170.198370214198
Winsorized Mean ( 18 / 26 )26156.989625152.42658954763171.603850106654
Winsorized Mean ( 19 / 26 )26160.06525149.231744679310175.298260475453
Winsorized Mean ( 20 / 26 )26163.90525141.280221252821185.191564806369
Winsorized Mean ( 21 / 26 )26154.366139.729141428871187.179036044631
Winsorized Mean ( 22 / 26 )26169.458137.744200681916189.985914981869
Winsorized Mean ( 23 / 26 )26164.694125135.506481079260193.088138047772
Winsorized Mean ( 24 / 26 )26168.168125134.740174175362194.212069897896
Winsorized Mean ( 25 / 26 )26181.986875131.723668332876198.764483303305
Winsorized Mean ( 26 / 26 )26180.543875121.471316044171215.528609778788
Trimmed Mean ( 1 / 26 )26152.3929487179202.903338545913128.890895222013
Trimmed Mean ( 2 / 26 )26155.1365789474199.007780732361131.427708417705
Trimmed Mean ( 3 / 26 )26158.2071621622195.399037201098133.870706513467
Trimmed Mean ( 4 / 26 )26161.4445833333191.318962019772136.742559687469
Trimmed Mean ( 5 / 26 )26165.1278571429186.811136187654140.06192773679
Trimmed Mean ( 6 / 26 )26163.4417647059184.197177999222142.040405009985
Trimmed Mean ( 7 / 26 )26160.1727272727181.616794004064144.040494001273
Trimmed Mean ( 8 / 26 )26159.49703125179.165285961136146.007620231323
Trimmed Mean ( 9 / 26 )26161.3525806452177.397280047397147.473245213542
Trimmed Mean ( 10 / 26 )26161.7816666667175.680156048320148.917113094270
Trimmed Mean ( 11 / 26 )26163.6668965517174.121242371577150.261200415272
Trimmed Mean ( 12 / 26 )26163.5810714286172.679200784433151.515532574709
Trimmed Mean ( 13 / 26 )26163.2144444444171.15659128336152.861273108260
Trimmed Mean ( 14 / 26 )26163.1959615385169.507819764107154.348017678170
Trimmed Mean ( 15 / 26 )26163.5418168.118706387612155.625405180538
Trimmed Mean ( 16 / 26 )26162.3297916667166.918317906668156.737319904549
Trimmed Mean ( 17 / 26 )26161.6884782609165.619577608285157.962535927590
Trimmed Mean ( 18 / 26 )26162.0252272727164.724603356963158.822815135750
Trimmed Mean ( 19 / 26 )26162.5580952381163.498712246964160.016906162048
Trimmed Mean ( 20 / 26 )26162.8205162.210660084724161.289156251106
Trimmed Mean ( 21 / 26 )26162.7063157895161.765128883884161.732670670755
Trimmed Mean ( 22 / 26 )26163.5888888889161.018575833033162.488015767939
Trimmed Mean ( 23 / 26 )26162.9611764706159.941523225370163.578291921136
Trimmed Mean ( 24 / 26 )26162.7728125158.446842975931165.120189971058
Trimmed Mean ( 25 / 26 )26162.1733333333155.959568920947167.749715611194
Trimmed Mean ( 26 / 26 )26159.9089285714152.666062407256171.35379347629
Median26098.02
Midrange26449.04
Midmean - Weighted Average at Xnp26124.1797560976
Midmean - Weighted Average at X(n+1)p26162.8205
Midmean - Empirical Distribution Function26124.1797560976
Midmean - Empirical Distribution Function - Averaging26162.8205
Midmean - Empirical Distribution Function - Interpolation26162.8205
Midmean - Closest Observation26124.1797560976
Midmean - True Basic - Statistics Graphics Toolkit26162.8205
Midmean - MS Excel (old versions)26162.5580952381
Number of observations80



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')