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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, 24 Dec 2010 09:32:26 +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/Dec/24/t1293183060jac2v3i2658r8qh.htm/, Retrieved Tue, 30 Apr 2024 03:18:27 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=114659, Retrieved Tue, 30 Apr 2024 03:18:27 +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] [central tendency ...] [2010-12-24 09:32:26] [27f38de572a508a633f0ad2411de6a3e] [Current]
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Dataseries X:
0.217499822516866 
-9.78478953094158 
-4.69092289728636 
10.8303737739891 
17.4025635868567 
-18.695949344517 
-1.45165150662704 
24.2055636204555 
-7.85142459641661 
-9.4984274601968 
15.4524605741829 
-4.57316796503045 
-35.3790647494429 
-1.71841266886546 
16.4887231604473 
12.3672525241091 
-30.5270631334762 
14.0831320895415 
12.2671755298376 
7.6573009730872 
-10.2588701804503 
4.98218909929218 
18.2374731745486 
-18.1217207388952 
19.2509327179740 
20.7168346335646 
27.0084172311441 
-13.1935985382014 
3.91871968362315 
23.2274665865825 
39.0004011190054 
23.2030259046977 
50.985499051697 
26.9190549927636 
5.61997889463015 
-49.70729388275 
-6.42398274476005 
-41.6977425555609 
-7.92694134412627 
5.34208987982118 
27.7759340629904 
-6.52456657092852 
3.12509229100933 
-4.61574932357839 
11.4276121576526 
18.3833489895730 
-42.4568062507692 
7.51193809087255 
-16.7513836179227 
8.95264961600874 
8.81854600123269 
-18.5966360042492 
11.7598212958319 
-7.41354314708516 
17.5247266754596 
17.9797835233522 
-36.4653940696526 
4.31529911509816 
8.75602862255269 
7.65533116235876 
-1.38678324054813 




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=114659&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=114659&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=114659&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 Mean2.420628756821022.54045079436110.952834340343832
Geometric MeanNaN
Harmonic Mean15.6671824563002
Quadratic Mean19.8265694938016
Winsorized Mean ( 1 / 20 )2.343012194514282.445977391468520.957904272822237
Winsorized Mean ( 2 / 20 )1.999884215471442.358634481158610.847899168543086
Winsorized Mean ( 3 / 20 )2.219466100097442.275526907276730.975363592933127
Winsorized Mean ( 4 / 20 )2.284840990709192.254451409193321.01347981215827
Winsorized Mean ( 5 / 20 )2.460128715599242.107680927697931.16722065625287
Winsorized Mean ( 6 / 20 )3.527638560361821.817975823718671.94042105199509
Winsorized Mean ( 7 / 20 )3.536230504766431.815150324699341.94817501153915
Winsorized Mean ( 8 / 20 )3.272456602369171.745827477125781.87444443694788
Winsorized Mean ( 9 / 20 )3.258356878573051.669690436256691.95147364314911
Winsorized Mean ( 10 / 20 )3.699373493543591.535066093124192.40991154069111
Winsorized Mean ( 11 / 20 )4.202281329117261.437806105189442.92270377344348
Winsorized Mean ( 12 / 20 )4.244850050096731.414050505931663.00190837052172
Winsorized Mean ( 13 / 20 )4.20889870414721.388381757490793.03151397764971
Winsorized Mean ( 14 / 20 )4.541530218647971.325905382546213.4252294910566
Winsorized Mean ( 15 / 20 )4.335385051754591.287132232716943.36825148306887
Winsorized Mean ( 16 / 20 )4.178432622395131.22680994602563.40593311615354
Winsorized Mean ( 17 / 20 )4.044564057735441.130487858146423.57771561064531
Winsorized Mean ( 18 / 20 )3.567919413362481.053025831811983.38825440513936
Winsorized Mean ( 19 / 20 )4.076553416818890.965019733844134.22432130022881
Winsorized Mean ( 20 / 20 )3.93485483967210.9379483079589564.19517238453644
Trimmed Mean ( 1 / 20 )2.481019474527712.327958557180861.06574898718653
Trimmed Mean ( 2 / 20 )2.62871147594562.181521235151231.20499009296298
Trimmed Mean ( 3 / 20 )2.977424774935812.058646380727131.44630219294105
Trimmed Mean ( 4 / 20 )3.268213952075061.947163828752831.67844836875815
Trimmed Mean ( 5 / 20 )3.562261749346221.814089061462381.96366420206216
Trimmed Mean ( 6 / 20 )3.836670382238331.700330859602562.25642577770724
Trimmed Mean ( 7 / 20 )3.90351769122581.654192403785842.35977246799832
Trimmed Mean ( 8 / 20 )3.974643146381421.594979266344032.49197167026001
Trimmed Mean ( 9 / 20 )4.099158783546381.537249127269932.66655463374779
Trimmed Mean ( 10 / 20 )4.238153136401051.482151559753562.8594600251986
Trimmed Mean ( 11 / 20 )4.322423798489021.44593959644812.98935295022482
Trimmed Mean ( 12 / 20 )4.340430409377661.421685307990283.05301770017822
Trimmed Mean ( 13 / 20 )4.354312318701791.392254493733253.1275261371403
Trimmed Mean ( 14 / 20 )4.374988846645451.355855372276263.22673711083253
Trimmed Mean ( 15 / 20 )4.351580957953851.319913188316273.29686906417299
Trimmed Mean ( 16 / 20 )4.353852108018581.276924391436513.40963970710953
Trimmed Mean ( 17 / 20 )4.378621989090411.230157545112393.55939936838769
Trimmed Mean ( 18 / 20 )4.426569127473121.189687196256793.720784035838
Trimmed Mean ( 19 / 20 )4.553085148151261.149029751594143.96254765538874
Trimmed Mean ( 20 / 20 )4.625938370234661.115887396875424.14552434518723
Median5.34208987982118
Midrange0.639102584473498
Midmean - Weighted Average at Xnp3.94700955120407
Midmean - Weighted Average at X(n+1)p4.35158095795385
Midmean - Empirical Distribution Function4.35158095795385
Midmean - Empirical Distribution Function - Averaging4.35158095795385
Midmean - Empirical Distribution Function - Interpolation4.35158095795385
Midmean - Closest Observation3.96787713601385
Midmean - True Basic - Statistics Graphics Toolkit4.35158095795385
Midmean - MS Excel (old versions)4.35158095795385
Number of observations61

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 2.42062875682102 & 2.5404507943611 & 0.952834340343832 \tabularnewline
Geometric Mean & NaN &  &  \tabularnewline
Harmonic Mean & 15.6671824563002 &  &  \tabularnewline
Quadratic Mean & 19.8265694938016 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 2.34301219451428 & 2.44597739146852 & 0.957904272822237 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 1.99988421547144 & 2.35863448115861 & 0.847899168543086 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 2.21946610009744 & 2.27552690727673 & 0.975363592933127 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 2.28484099070919 & 2.25445140919332 & 1.01347981215827 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 2.46012871559924 & 2.10768092769793 & 1.16722065625287 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 3.52763856036182 & 1.81797582371867 & 1.94042105199509 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 3.53623050476643 & 1.81515032469934 & 1.94817501153915 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 3.27245660236917 & 1.74582747712578 & 1.87444443694788 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 3.25835687857305 & 1.66969043625669 & 1.95147364314911 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 3.69937349354359 & 1.53506609312419 & 2.40991154069111 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 4.20228132911726 & 1.43780610518944 & 2.92270377344348 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 4.24485005009673 & 1.41405050593166 & 3.00190837052172 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 4.2088987041472 & 1.38838175749079 & 3.03151397764971 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 4.54153021864797 & 1.32590538254621 & 3.4252294910566 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 4.33538505175459 & 1.28713223271694 & 3.36825148306887 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 4.17843262239513 & 1.2268099460256 & 3.40593311615354 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 4.04456405773544 & 1.13048785814642 & 3.57771561064531 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 3.56791941336248 & 1.05302583181198 & 3.38825440513936 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 4.07655341681889 & 0.96501973384413 & 4.22432130022881 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 3.9348548396721 & 0.937948307958956 & 4.19517238453644 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 2.48101947452771 & 2.32795855718086 & 1.06574898718653 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 2.6287114759456 & 2.18152123515123 & 1.20499009296298 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 2.97742477493581 & 2.05864638072713 & 1.44630219294105 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 3.26821395207506 & 1.94716382875283 & 1.67844836875815 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 3.56226174934622 & 1.81408906146238 & 1.96366420206216 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 3.83667038223833 & 1.70033085960256 & 2.25642577770724 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 3.9035176912258 & 1.65419240378584 & 2.35977246799832 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 3.97464314638142 & 1.59497926634403 & 2.49197167026001 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 4.09915878354638 & 1.53724912726993 & 2.66655463374779 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 4.23815313640105 & 1.48215155975356 & 2.8594600251986 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 4.32242379848902 & 1.4459395964481 & 2.98935295022482 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 4.34043040937766 & 1.42168530799028 & 3.05301770017822 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 4.35431231870179 & 1.39225449373325 & 3.1275261371403 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 4.37498884664545 & 1.35585537227626 & 3.22673711083253 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 4.35158095795385 & 1.31991318831627 & 3.29686906417299 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 4.35385210801858 & 1.27692439143651 & 3.40963970710953 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 4.37862198909041 & 1.23015754511239 & 3.55939936838769 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 4.42656912747312 & 1.18968719625679 & 3.720784035838 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 4.55308514815126 & 1.14902975159414 & 3.96254765538874 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 4.62593837023466 & 1.11588739687542 & 4.14552434518723 \tabularnewline
Median & 5.34208987982118 &  &  \tabularnewline
Midrange & 0.639102584473498 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 3.94700955120407 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 4.35158095795385 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 4.35158095795385 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 4.35158095795385 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 4.35158095795385 &  &  \tabularnewline
Midmean - Closest Observation & 3.96787713601385 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 4.35158095795385 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 4.35158095795385 &  &  \tabularnewline
Number of observations & 61 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=114659&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]2.42062875682102[/C][C]2.5404507943611[/C][C]0.952834340343832[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]NaN[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]15.6671824563002[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]19.8265694938016[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]2.34301219451428[/C][C]2.44597739146852[/C][C]0.957904272822237[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]1.99988421547144[/C][C]2.35863448115861[/C][C]0.847899168543086[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]2.21946610009744[/C][C]2.27552690727673[/C][C]0.975363592933127[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]2.28484099070919[/C][C]2.25445140919332[/C][C]1.01347981215827[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]2.46012871559924[/C][C]2.10768092769793[/C][C]1.16722065625287[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]3.52763856036182[/C][C]1.81797582371867[/C][C]1.94042105199509[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]3.53623050476643[/C][C]1.81515032469934[/C][C]1.94817501153915[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]3.27245660236917[/C][C]1.74582747712578[/C][C]1.87444443694788[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]3.25835687857305[/C][C]1.66969043625669[/C][C]1.95147364314911[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]3.69937349354359[/C][C]1.53506609312419[/C][C]2.40991154069111[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]4.20228132911726[/C][C]1.43780610518944[/C][C]2.92270377344348[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]4.24485005009673[/C][C]1.41405050593166[/C][C]3.00190837052172[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]4.2088987041472[/C][C]1.38838175749079[/C][C]3.03151397764971[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]4.54153021864797[/C][C]1.32590538254621[/C][C]3.4252294910566[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]4.33538505175459[/C][C]1.28713223271694[/C][C]3.36825148306887[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]4.17843262239513[/C][C]1.2268099460256[/C][C]3.40593311615354[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]4.04456405773544[/C][C]1.13048785814642[/C][C]3.57771561064531[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]3.56791941336248[/C][C]1.05302583181198[/C][C]3.38825440513936[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]4.07655341681889[/C][C]0.96501973384413[/C][C]4.22432130022881[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]3.9348548396721[/C][C]0.937948307958956[/C][C]4.19517238453644[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]2.48101947452771[/C][C]2.32795855718086[/C][C]1.06574898718653[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]2.6287114759456[/C][C]2.18152123515123[/C][C]1.20499009296298[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]2.97742477493581[/C][C]2.05864638072713[/C][C]1.44630219294105[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]3.26821395207506[/C][C]1.94716382875283[/C][C]1.67844836875815[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]3.56226174934622[/C][C]1.81408906146238[/C][C]1.96366420206216[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]3.83667038223833[/C][C]1.70033085960256[/C][C]2.25642577770724[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]3.9035176912258[/C][C]1.65419240378584[/C][C]2.35977246799832[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]3.97464314638142[/C][C]1.59497926634403[/C][C]2.49197167026001[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]4.09915878354638[/C][C]1.53724912726993[/C][C]2.66655463374779[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]4.23815313640105[/C][C]1.48215155975356[/C][C]2.8594600251986[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]4.32242379848902[/C][C]1.4459395964481[/C][C]2.98935295022482[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]4.34043040937766[/C][C]1.42168530799028[/C][C]3.05301770017822[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]4.35431231870179[/C][C]1.39225449373325[/C][C]3.1275261371403[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]4.37498884664545[/C][C]1.35585537227626[/C][C]3.22673711083253[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]4.35158095795385[/C][C]1.31991318831627[/C][C]3.29686906417299[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]4.35385210801858[/C][C]1.27692439143651[/C][C]3.40963970710953[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]4.37862198909041[/C][C]1.23015754511239[/C][C]3.55939936838769[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]4.42656912747312[/C][C]1.18968719625679[/C][C]3.720784035838[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]4.55308514815126[/C][C]1.14902975159414[/C][C]3.96254765538874[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]4.62593837023466[/C][C]1.11588739687542[/C][C]4.14552434518723[/C][/ROW]
[ROW][C]Median[/C][C]5.34208987982118[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]0.639102584473498[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]3.94700955120407[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]4.35158095795385[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]4.35158095795385[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]4.35158095795385[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]4.35158095795385[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]3.96787713601385[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]4.35158095795385[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]4.35158095795385[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]61[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=114659&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=114659&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 Mean2.420628756821022.54045079436110.952834340343832
Geometric MeanNaN
Harmonic Mean15.6671824563002
Quadratic Mean19.8265694938016
Winsorized Mean ( 1 / 20 )2.343012194514282.445977391468520.957904272822237
Winsorized Mean ( 2 / 20 )1.999884215471442.358634481158610.847899168543086
Winsorized Mean ( 3 / 20 )2.219466100097442.275526907276730.975363592933127
Winsorized Mean ( 4 / 20 )2.284840990709192.254451409193321.01347981215827
Winsorized Mean ( 5 / 20 )2.460128715599242.107680927697931.16722065625287
Winsorized Mean ( 6 / 20 )3.527638560361821.817975823718671.94042105199509
Winsorized Mean ( 7 / 20 )3.536230504766431.815150324699341.94817501153915
Winsorized Mean ( 8 / 20 )3.272456602369171.745827477125781.87444443694788
Winsorized Mean ( 9 / 20 )3.258356878573051.669690436256691.95147364314911
Winsorized Mean ( 10 / 20 )3.699373493543591.535066093124192.40991154069111
Winsorized Mean ( 11 / 20 )4.202281329117261.437806105189442.92270377344348
Winsorized Mean ( 12 / 20 )4.244850050096731.414050505931663.00190837052172
Winsorized Mean ( 13 / 20 )4.20889870414721.388381757490793.03151397764971
Winsorized Mean ( 14 / 20 )4.541530218647971.325905382546213.4252294910566
Winsorized Mean ( 15 / 20 )4.335385051754591.287132232716943.36825148306887
Winsorized Mean ( 16 / 20 )4.178432622395131.22680994602563.40593311615354
Winsorized Mean ( 17 / 20 )4.044564057735441.130487858146423.57771561064531
Winsorized Mean ( 18 / 20 )3.567919413362481.053025831811983.38825440513936
Winsorized Mean ( 19 / 20 )4.076553416818890.965019733844134.22432130022881
Winsorized Mean ( 20 / 20 )3.93485483967210.9379483079589564.19517238453644
Trimmed Mean ( 1 / 20 )2.481019474527712.327958557180861.06574898718653
Trimmed Mean ( 2 / 20 )2.62871147594562.181521235151231.20499009296298
Trimmed Mean ( 3 / 20 )2.977424774935812.058646380727131.44630219294105
Trimmed Mean ( 4 / 20 )3.268213952075061.947163828752831.67844836875815
Trimmed Mean ( 5 / 20 )3.562261749346221.814089061462381.96366420206216
Trimmed Mean ( 6 / 20 )3.836670382238331.700330859602562.25642577770724
Trimmed Mean ( 7 / 20 )3.90351769122581.654192403785842.35977246799832
Trimmed Mean ( 8 / 20 )3.974643146381421.594979266344032.49197167026001
Trimmed Mean ( 9 / 20 )4.099158783546381.537249127269932.66655463374779
Trimmed Mean ( 10 / 20 )4.238153136401051.482151559753562.8594600251986
Trimmed Mean ( 11 / 20 )4.322423798489021.44593959644812.98935295022482
Trimmed Mean ( 12 / 20 )4.340430409377661.421685307990283.05301770017822
Trimmed Mean ( 13 / 20 )4.354312318701791.392254493733253.1275261371403
Trimmed Mean ( 14 / 20 )4.374988846645451.355855372276263.22673711083253
Trimmed Mean ( 15 / 20 )4.351580957953851.319913188316273.29686906417299
Trimmed Mean ( 16 / 20 )4.353852108018581.276924391436513.40963970710953
Trimmed Mean ( 17 / 20 )4.378621989090411.230157545112393.55939936838769
Trimmed Mean ( 18 / 20 )4.426569127473121.189687196256793.720784035838
Trimmed Mean ( 19 / 20 )4.553085148151261.149029751594143.96254765538874
Trimmed Mean ( 20 / 20 )4.625938370234661.115887396875424.14552434518723
Median5.34208987982118
Midrange0.639102584473498
Midmean - Weighted Average at Xnp3.94700955120407
Midmean - Weighted Average at X(n+1)p4.35158095795385
Midmean - Empirical Distribution Function4.35158095795385
Midmean - Empirical Distribution Function - Averaging4.35158095795385
Midmean - Empirical Distribution Function - Interpolation4.35158095795385
Midmean - Closest Observation3.96787713601385
Midmean - True Basic - Statistics Graphics Toolkit4.35158095795385
Midmean - MS Excel (old versions)4.35158095795385
Number of observations61



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')