Free Statistics

of Irreproducible Research!

Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationTue, 13 Dec 2011 09:30:48 -0500
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2011/Dec/13/t1323787329ecr9wthbeh92end.htm/, Retrieved Thu, 02 May 2024 14:12:51 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=154404, Retrieved Thu, 02 May 2024 14:12:51 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact130
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Recursive Partitioning (Regression Trees)] [] [2010-12-05 20:30:15] [b98453cac15ba1066b407e146608df68]
- RMPD    [Central Tendency] [] [2011-12-13 14:30:48] [885a9dbaf162325773a0a0afdf9f947e] [Current]
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Dataseries X:
28,23472222
28,05861111
1,993333333
26,82222222
48,84
94,88055556
28,77694444
31,28083333
23,77055556
61,33361111
25,73916667
37,03555556
17,04472222
34,98055556
22,86555556
28,33611111
28,20083333
11,54611111
27,75638889
6,291111111
12,97166667
36,58277778
25,48194444
22,18416667
30,01194444
27,46277778
33,45694444
32,23555556
69,4575
37,80111111
25,69416667
37,71694444
20,66888889
22,56666667
37,04666667
27,26277778
22,11638889
16,44277778
38,87277778
32,94777778
20,24444444
18,1875
27,67861111
19,99027778
21,46444444
13,69138889
37,53638889
30,12388889
24,92944444
12,30444444
21,56888889
50,42444444
37,2275
34,46222222
25,73055556
33,84666667
14,69861111
22,74222222
16,38361111
14,86527778
16,89222222
15,65972222
18,19166667
22,48583333
21,195
28,89194444
27,25111111
18,88583333
8,608055556
37,62722222
20,41777778
17,53416667
17,015
20,80944444
8,826111111
22,62138889
24,21833333
13,91388889
18,2625
15,73694444
43,99972222
12,90416667
20,45111111
10,66527778
25,5275
38,75722222
14,49
14,32416667
19,5975
23,57111111
28,48277778
24,07722222
23,80805556
9,628333333
41,82777778
27,66972222
5,374722222
27,60361111
23,95277778
8,565833333
8,807222222
24,94611111
17,24666667
11,15305556
7,676111111
21,38611111
10,40555556
15,04361111
13,85055556
23,42694444
17,82638889
16,495
33,14111111
21,30611111
28,72916667
19,54
12,05833333
29,12166667
17,28194444
19,25111111
14,75472222
5,49
24,07777778
23,3625
21,65138889
24,75361111
25,27916667
11,18
17,82972222
14,12694444
15,72583333
17,44222222
20,14861111




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'AstonUniversity' @ aston.wessa.net

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 1 seconds \tabularnewline
R Server & 'AstonUniversity' @ aston.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=154404&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]'AstonUniversity' @ aston.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=154404&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=154404&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'AstonUniversity' @ aston.wessa.net







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean23.80232038422561.0608025400101122.4380311004899
Geometric Mean21.081322936957
Harmonic Mean17.8919373131384
Quadratic Mean26.7411728143522
Winsorized Mean ( 1 / 44 )23.63659356715040.97380752075670624.2723464990118
Winsorized Mean ( 2 / 44 )23.51616332486470.93296230655282125.2059093488503
Winsorized Mean ( 3 / 44 )23.28816207165410.86286665916545526.9892941444486
Winsorized Mean ( 4 / 44 )23.28216374263160.84571142876686827.5296785057987
Winsorized Mean ( 5 / 44 )23.1336466163910.80223772394841428.8363983963917
Winsorized Mean ( 6 / 44 )23.0375689223910.78340948272697329.4068037601478
Winsorized Mean ( 7 / 44 )22.89252506270680.75531344100965330.3086425048991
Winsorized Mean ( 8 / 44 )22.88671052610530.75404175571495730.352046624268
Winsorized Mean ( 9 / 44 )22.87629699233080.73637896143916731.0659296235484
Winsorized Mean ( 10 / 44 )22.92840643270680.72761284835990131.5118218217137
Winsorized Mean ( 11 / 44 )22.94246658308270.72369038178745331.702047119124
Winsorized Mean ( 12 / 44 )22.97828111992480.71685158671618232.0544468976986
Winsorized Mean ( 13 / 44 )22.95072263984960.71190593036765332.2384203598319
Winsorized Mean ( 14 / 44 )22.97022556406010.70423684353333432.6171880596487
Winsorized Mean ( 15 / 44 )23.02674185466170.6970529984305433.0344204909926
Winsorized Mean ( 16 / 44 )23.00187969887220.68530171547290433.564602538605
Winsorized Mean ( 17 / 44 )22.8737406024060.64636100178792635.3884911669083
Winsorized Mean ( 18 / 44 )22.81272556390980.63544189376054235.9005690180485
Winsorized Mean ( 19 / 44 )22.82760651676690.61147620539147937.331962086983
Winsorized Mean ( 20 / 44 )22.79293650774440.60083133422216837.9356654846438
Winsorized Mean ( 21 / 44 )22.75306808669170.59304125288379838.3667543801545
Winsorized Mean ( 22 / 44 )22.7563304087970.58484887630465738.9097617021716
Winsorized Mean ( 23 / 44 )22.66727026015040.56500044181008540.1190310356776
Winsorized Mean ( 24 / 44 )22.52491436842110.53999684347047641.7130482164617
Winsorized Mean ( 25 / 44 )22.34665622368420.50960697214507743.8507662672293
Winsorized Mean ( 26 / 44 )22.33574143541350.5058376870374844.1559456872943
Winsorized Mean ( 27 / 44 )22.17745196421050.48303352430438345.9128628725062
Winsorized Mean ( 28 / 44 )22.16663324842110.47350543545094246.8138939678923
Winsorized Mean ( 29 / 44 )22.27589807691730.45575444420316148.8769739061225
Winsorized Mean ( 30 / 44 )22.28003341676690.45295356737432149.1883385441023
Winsorized Mean ( 31 / 44 )22.22519423496240.44652296399916249.773910922539
Winsorized Mean ( 32 / 44 )22.34549498684210.4259499479620652.4603773137036
Winsorized Mean ( 33 / 44 )22.33501879691730.42172138993924752.9615507530573
Winsorized Mean ( 34 / 44 )22.33970551285710.41939243781651153.2668295812979
Winsorized Mean ( 35 / 44 )22.4068107760150.40451221503551555.3921734453626
Winsorized Mean ( 36 / 44 )22.35823934864660.39249013302644556.9650991637544
Winsorized Mean ( 37 / 44 )22.34487050864660.38938749804615957.384663402824
Winsorized Mean ( 38 / 44 )22.40002924007520.38320919558830458.4537884214562
Winsorized Mean ( 39 / 44 )22.39098788473680.38013888580466158.9021242521417
Winsorized Mean ( 40 / 44 )22.39683583962410.37085354922560260.3926695224894
Winsorized Mean ( 41 / 44 )22.36352548210530.36163099266975361.8407325019511
Winsorized Mean ( 42 / 44 )22.45212197157890.35198902143226963.7864268613254
Winsorized Mean ( 43 / 44 )22.31453633939850.33770610899800566.0767920533244
Winsorized Mean ( 44 / 44 )22.07459482150380.29044011595319276.0039457671244
Trimmed Mean ( 1 / 44 )23.42621925350380.91344510471632325.6460066757695
Trimmed Mean ( 2 / 44 )23.20932170532560.8438790336544127.5031382220955
Trimmed Mean ( 3 / 44 )23.04865266832280.79004580852506629.1738180490474
Trimmed Mean ( 4 / 44 )22.9637066666080.76017210554584330.2085626387447
Trimmed Mean ( 5 / 44 )22.87761969280490.73254946635956331.2301363162494
Trimmed Mean ( 6 / 44 )22.82133608811570.7139546110090931.9646875812742
Trimmed Mean ( 7 / 44 )22.78105742290760.69782260483513632.6459149718856
Trimmed Mean ( 8 / 44 )22.76295584037610.6858207582651333.1908236460468
Trimmed Mean ( 9 / 44 )22.74506521733040.67275080645319533.80904935253
Trimmed Mean ( 10 / 44 )22.72790314646020.66130260348019134.3683860109602
Trimmed Mean ( 11 / 44 )22.70387887882880.64996444113801134.9309553597686
Trimmed Mean ( 12 / 44 )22.67741335366970.63791532549116435.5492530865428
Trimmed Mean ( 13 / 44 )22.64624870186920.62544262244390436.2083553138406
Trimmed Mean ( 14 / 44 )22.61658201047620.61219042346431636.9437043501784
Trimmed Mean ( 15 / 44 )22.5839644011650.59837283640224237.742295484121
Trimmed Mean ( 16 / 44 )22.54509350920790.58376414583169638.6202093262985
Trimmed Mean ( 17 / 44 )22.50673961828280.56888056861384539.563206866291
Trimmed Mean ( 18 / 44 )22.47713917505150.55727771020094240.3338205774403
Trimmed Mean ( 19 / 44 )22.45103801147370.5455571659070641.1524940271766
Trimmed Mean ( 20 / 44 )22.42269414548390.53524589745354341.8923232334164
Trimmed Mean ( 21 / 44 )22.39563797285710.52482800648570442.6723377870406
Trimmed Mean ( 22 / 44 )22.37020287112360.51390609642095243.5297479966061
Trimmed Mean ( 23 / 44 )22.34337164724140.50240374652390944.4729399448817
Trimmed Mean ( 24 / 44 )22.32133660094120.49171338242571245.3950154678035
Trimmed Mean ( 25 / 44 )22.3077443102410.48253452390711446.2303590831463
Trimmed Mean ( 26 / 44 )22.30518861419750.47559490656490446.8995531834056
Trimmed Mean ( 27 / 44 )22.3032102669620.46794533188596847.6619996978558
Trimmed Mean ( 28 / 44 )22.31125541090910.46170717819849548.3233886420478
Trimmed Mean ( 29 / 44 )22.32041481453330.45546946690006249.005293299783
Trimmed Mean ( 30 / 44 )22.32321156753420.45020476572351849.5845741029838
Trimmed Mean ( 31 / 44 )22.32590766802820.44422216686778650.2584277264872
Trimmed Mean ( 32 / 44 )22.33216988710150.43782732872965551.0067974785806
Trimmed Mean ( 33 / 44 )22.33134328343280.4327161614905751.607370537094
Trimmed Mean ( 34 / 44 )22.33111538446150.42699325520896652.2985202038682
Trimmed Mean ( 35 / 44 )22.33058201047620.42028409091845653.1321134751418
Trimmed Mean ( 36 / 44 )22.32583333327870.41408381282155753.9162185093665
Trimmed Mean ( 37 / 44 )22.32380414305080.40808144417435654.7042862686813
Trimmed Mean ( 38 / 44 )22.32247563350880.40101863065895855.6644353326634
Trimmed Mean ( 39 / 44 )22.3175404040.39310824967084356.7719970839759
Trimmed Mean ( 40 / 44 )22.31281446547170.38365806271863458.1580752072853
Trimmed Mean ( 41 / 44 )22.30733660137250.37333630411805159.7513189992872
Trimmed Mean ( 42 / 44 )22.303616780.36191969927949261.6258712206104
Trimmed Mean ( 43 / 44 )22.29361111106380.34914378433765363.8522354145762
Trimmed Mean ( 44 / 44 )22.29217283955560.33568569391342566.407872732595
Median22.48583333
Midrange48.4369444465
Midmean - Weighted Average at Xnp22.2418981480303
Midmean - Weighted Average at X(n+1)p22.3313432834328
Midmean - Empirical Distribution Function22.3313432834328
Midmean - Empirical Distribution Function - Averaging22.3313432834328
Midmean - Empirical Distribution Function - Interpolation22.3313432834328
Midmean - Closest Observation22.2438766338235
Midmean - True Basic - Statistics Graphics Toolkit22.3313432834328
Midmean - MS Excel (old versions)22.3313432834328
Number of observations133

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 23.8023203842256 & 1.06080254001011 & 22.4380311004899 \tabularnewline
Geometric Mean & 21.081322936957 &  &  \tabularnewline
Harmonic Mean & 17.8919373131384 &  &  \tabularnewline
Quadratic Mean & 26.7411728143522 &  &  \tabularnewline
Winsorized Mean ( 1 / 44 ) & 23.6365935671504 & 0.973807520756706 & 24.2723464990118 \tabularnewline
Winsorized Mean ( 2 / 44 ) & 23.5161633248647 & 0.932962306552821 & 25.2059093488503 \tabularnewline
Winsorized Mean ( 3 / 44 ) & 23.2881620716541 & 0.862866659165455 & 26.9892941444486 \tabularnewline
Winsorized Mean ( 4 / 44 ) & 23.2821637426316 & 0.845711428766868 & 27.5296785057987 \tabularnewline
Winsorized Mean ( 5 / 44 ) & 23.133646616391 & 0.802237723948414 & 28.8363983963917 \tabularnewline
Winsorized Mean ( 6 / 44 ) & 23.037568922391 & 0.783409482726973 & 29.4068037601478 \tabularnewline
Winsorized Mean ( 7 / 44 ) & 22.8925250627068 & 0.755313441009653 & 30.3086425048991 \tabularnewline
Winsorized Mean ( 8 / 44 ) & 22.8867105261053 & 0.754041755714957 & 30.352046624268 \tabularnewline
Winsorized Mean ( 9 / 44 ) & 22.8762969923308 & 0.736378961439167 & 31.0659296235484 \tabularnewline
Winsorized Mean ( 10 / 44 ) & 22.9284064327068 & 0.727612848359901 & 31.5118218217137 \tabularnewline
Winsorized Mean ( 11 / 44 ) & 22.9424665830827 & 0.723690381787453 & 31.702047119124 \tabularnewline
Winsorized Mean ( 12 / 44 ) & 22.9782811199248 & 0.716851586716182 & 32.0544468976986 \tabularnewline
Winsorized Mean ( 13 / 44 ) & 22.9507226398496 & 0.711905930367653 & 32.2384203598319 \tabularnewline
Winsorized Mean ( 14 / 44 ) & 22.9702255640601 & 0.704236843533334 & 32.6171880596487 \tabularnewline
Winsorized Mean ( 15 / 44 ) & 23.0267418546617 & 0.69705299843054 & 33.0344204909926 \tabularnewline
Winsorized Mean ( 16 / 44 ) & 23.0018796988722 & 0.685301715472904 & 33.564602538605 \tabularnewline
Winsorized Mean ( 17 / 44 ) & 22.873740602406 & 0.646361001787926 & 35.3884911669083 \tabularnewline
Winsorized Mean ( 18 / 44 ) & 22.8127255639098 & 0.635441893760542 & 35.9005690180485 \tabularnewline
Winsorized Mean ( 19 / 44 ) & 22.8276065167669 & 0.611476205391479 & 37.331962086983 \tabularnewline
Winsorized Mean ( 20 / 44 ) & 22.7929365077444 & 0.600831334222168 & 37.9356654846438 \tabularnewline
Winsorized Mean ( 21 / 44 ) & 22.7530680866917 & 0.593041252883798 & 38.3667543801545 \tabularnewline
Winsorized Mean ( 22 / 44 ) & 22.756330408797 & 0.584848876304657 & 38.9097617021716 \tabularnewline
Winsorized Mean ( 23 / 44 ) & 22.6672702601504 & 0.565000441810085 & 40.1190310356776 \tabularnewline
Winsorized Mean ( 24 / 44 ) & 22.5249143684211 & 0.539996843470476 & 41.7130482164617 \tabularnewline
Winsorized Mean ( 25 / 44 ) & 22.3466562236842 & 0.509606972145077 & 43.8507662672293 \tabularnewline
Winsorized Mean ( 26 / 44 ) & 22.3357414354135 & 0.50583768703748 & 44.1559456872943 \tabularnewline
Winsorized Mean ( 27 / 44 ) & 22.1774519642105 & 0.483033524304383 & 45.9128628725062 \tabularnewline
Winsorized Mean ( 28 / 44 ) & 22.1666332484211 & 0.473505435450942 & 46.8138939678923 \tabularnewline
Winsorized Mean ( 29 / 44 ) & 22.2758980769173 & 0.455754444203161 & 48.8769739061225 \tabularnewline
Winsorized Mean ( 30 / 44 ) & 22.2800334167669 & 0.452953567374321 & 49.1883385441023 \tabularnewline
Winsorized Mean ( 31 / 44 ) & 22.2251942349624 & 0.446522963999162 & 49.773910922539 \tabularnewline
Winsorized Mean ( 32 / 44 ) & 22.3454949868421 & 0.42594994796206 & 52.4603773137036 \tabularnewline
Winsorized Mean ( 33 / 44 ) & 22.3350187969173 & 0.421721389939247 & 52.9615507530573 \tabularnewline
Winsorized Mean ( 34 / 44 ) & 22.3397055128571 & 0.419392437816511 & 53.2668295812979 \tabularnewline
Winsorized Mean ( 35 / 44 ) & 22.406810776015 & 0.404512215035515 & 55.3921734453626 \tabularnewline
Winsorized Mean ( 36 / 44 ) & 22.3582393486466 & 0.392490133026445 & 56.9650991637544 \tabularnewline
Winsorized Mean ( 37 / 44 ) & 22.3448705086466 & 0.389387498046159 & 57.384663402824 \tabularnewline
Winsorized Mean ( 38 / 44 ) & 22.4000292400752 & 0.383209195588304 & 58.4537884214562 \tabularnewline
Winsorized Mean ( 39 / 44 ) & 22.3909878847368 & 0.380138885804661 & 58.9021242521417 \tabularnewline
Winsorized Mean ( 40 / 44 ) & 22.3968358396241 & 0.370853549225602 & 60.3926695224894 \tabularnewline
Winsorized Mean ( 41 / 44 ) & 22.3635254821053 & 0.361630992669753 & 61.8407325019511 \tabularnewline
Winsorized Mean ( 42 / 44 ) & 22.4521219715789 & 0.351989021432269 & 63.7864268613254 \tabularnewline
Winsorized Mean ( 43 / 44 ) & 22.3145363393985 & 0.337706108998005 & 66.0767920533244 \tabularnewline
Winsorized Mean ( 44 / 44 ) & 22.0745948215038 & 0.290440115953192 & 76.0039457671244 \tabularnewline
Trimmed Mean ( 1 / 44 ) & 23.4262192535038 & 0.913445104716323 & 25.6460066757695 \tabularnewline
Trimmed Mean ( 2 / 44 ) & 23.2093217053256 & 0.84387903365441 & 27.5031382220955 \tabularnewline
Trimmed Mean ( 3 / 44 ) & 23.0486526683228 & 0.790045808525066 & 29.1738180490474 \tabularnewline
Trimmed Mean ( 4 / 44 ) & 22.963706666608 & 0.760172105545843 & 30.2085626387447 \tabularnewline
Trimmed Mean ( 5 / 44 ) & 22.8776196928049 & 0.732549466359563 & 31.2301363162494 \tabularnewline
Trimmed Mean ( 6 / 44 ) & 22.8213360881157 & 0.71395461100909 & 31.9646875812742 \tabularnewline
Trimmed Mean ( 7 / 44 ) & 22.7810574229076 & 0.697822604835136 & 32.6459149718856 \tabularnewline
Trimmed Mean ( 8 / 44 ) & 22.7629558403761 & 0.68582075826513 & 33.1908236460468 \tabularnewline
Trimmed Mean ( 9 / 44 ) & 22.7450652173304 & 0.672750806453195 & 33.80904935253 \tabularnewline
Trimmed Mean ( 10 / 44 ) & 22.7279031464602 & 0.661302603480191 & 34.3683860109602 \tabularnewline
Trimmed Mean ( 11 / 44 ) & 22.7038788788288 & 0.649964441138011 & 34.9309553597686 \tabularnewline
Trimmed Mean ( 12 / 44 ) & 22.6774133536697 & 0.637915325491164 & 35.5492530865428 \tabularnewline
Trimmed Mean ( 13 / 44 ) & 22.6462487018692 & 0.625442622443904 & 36.2083553138406 \tabularnewline
Trimmed Mean ( 14 / 44 ) & 22.6165820104762 & 0.612190423464316 & 36.9437043501784 \tabularnewline
Trimmed Mean ( 15 / 44 ) & 22.583964401165 & 0.598372836402242 & 37.742295484121 \tabularnewline
Trimmed Mean ( 16 / 44 ) & 22.5450935092079 & 0.583764145831696 & 38.6202093262985 \tabularnewline
Trimmed Mean ( 17 / 44 ) & 22.5067396182828 & 0.568880568613845 & 39.563206866291 \tabularnewline
Trimmed Mean ( 18 / 44 ) & 22.4771391750515 & 0.557277710200942 & 40.3338205774403 \tabularnewline
Trimmed Mean ( 19 / 44 ) & 22.4510380114737 & 0.54555716590706 & 41.1524940271766 \tabularnewline
Trimmed Mean ( 20 / 44 ) & 22.4226941454839 & 0.535245897453543 & 41.8923232334164 \tabularnewline
Trimmed Mean ( 21 / 44 ) & 22.3956379728571 & 0.524828006485704 & 42.6723377870406 \tabularnewline
Trimmed Mean ( 22 / 44 ) & 22.3702028711236 & 0.513906096420952 & 43.5297479966061 \tabularnewline
Trimmed Mean ( 23 / 44 ) & 22.3433716472414 & 0.502403746523909 & 44.4729399448817 \tabularnewline
Trimmed Mean ( 24 / 44 ) & 22.3213366009412 & 0.491713382425712 & 45.3950154678035 \tabularnewline
Trimmed Mean ( 25 / 44 ) & 22.307744310241 & 0.482534523907114 & 46.2303590831463 \tabularnewline
Trimmed Mean ( 26 / 44 ) & 22.3051886141975 & 0.475594906564904 & 46.8995531834056 \tabularnewline
Trimmed Mean ( 27 / 44 ) & 22.303210266962 & 0.467945331885968 & 47.6619996978558 \tabularnewline
Trimmed Mean ( 28 / 44 ) & 22.3112554109091 & 0.461707178198495 & 48.3233886420478 \tabularnewline
Trimmed Mean ( 29 / 44 ) & 22.3204148145333 & 0.455469466900062 & 49.005293299783 \tabularnewline
Trimmed Mean ( 30 / 44 ) & 22.3232115675342 & 0.450204765723518 & 49.5845741029838 \tabularnewline
Trimmed Mean ( 31 / 44 ) & 22.3259076680282 & 0.444222166867786 & 50.2584277264872 \tabularnewline
Trimmed Mean ( 32 / 44 ) & 22.3321698871015 & 0.437827328729655 & 51.0067974785806 \tabularnewline
Trimmed Mean ( 33 / 44 ) & 22.3313432834328 & 0.43271616149057 & 51.607370537094 \tabularnewline
Trimmed Mean ( 34 / 44 ) & 22.3311153844615 & 0.426993255208966 & 52.2985202038682 \tabularnewline
Trimmed Mean ( 35 / 44 ) & 22.3305820104762 & 0.420284090918456 & 53.1321134751418 \tabularnewline
Trimmed Mean ( 36 / 44 ) & 22.3258333332787 & 0.414083812821557 & 53.9162185093665 \tabularnewline
Trimmed Mean ( 37 / 44 ) & 22.3238041430508 & 0.408081444174356 & 54.7042862686813 \tabularnewline
Trimmed Mean ( 38 / 44 ) & 22.3224756335088 & 0.401018630658958 & 55.6644353326634 \tabularnewline
Trimmed Mean ( 39 / 44 ) & 22.317540404 & 0.393108249670843 & 56.7719970839759 \tabularnewline
Trimmed Mean ( 40 / 44 ) & 22.3128144654717 & 0.383658062718634 & 58.1580752072853 \tabularnewline
Trimmed Mean ( 41 / 44 ) & 22.3073366013725 & 0.373336304118051 & 59.7513189992872 \tabularnewline
Trimmed Mean ( 42 / 44 ) & 22.30361678 & 0.361919699279492 & 61.6258712206104 \tabularnewline
Trimmed Mean ( 43 / 44 ) & 22.2936111110638 & 0.349143784337653 & 63.8522354145762 \tabularnewline
Trimmed Mean ( 44 / 44 ) & 22.2921728395556 & 0.335685693913425 & 66.407872732595 \tabularnewline
Median & 22.48583333 &  &  \tabularnewline
Midrange & 48.4369444465 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 22.2418981480303 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 22.3313432834328 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 22.3313432834328 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 22.3313432834328 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 22.3313432834328 &  &  \tabularnewline
Midmean - Closest Observation & 22.2438766338235 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 22.3313432834328 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 22.3313432834328 &  &  \tabularnewline
Number of observations & 133 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=154404&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]23.8023203842256[/C][C]1.06080254001011[/C][C]22.4380311004899[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]21.081322936957[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]17.8919373131384[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]26.7411728143522[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 44 )[/C][C]23.6365935671504[/C][C]0.973807520756706[/C][C]24.2723464990118[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 44 )[/C][C]23.5161633248647[/C][C]0.932962306552821[/C][C]25.2059093488503[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 44 )[/C][C]23.2881620716541[/C][C]0.862866659165455[/C][C]26.9892941444486[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 44 )[/C][C]23.2821637426316[/C][C]0.845711428766868[/C][C]27.5296785057987[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 44 )[/C][C]23.133646616391[/C][C]0.802237723948414[/C][C]28.8363983963917[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 44 )[/C][C]23.037568922391[/C][C]0.783409482726973[/C][C]29.4068037601478[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 44 )[/C][C]22.8925250627068[/C][C]0.755313441009653[/C][C]30.3086425048991[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 44 )[/C][C]22.8867105261053[/C][C]0.754041755714957[/C][C]30.352046624268[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 44 )[/C][C]22.8762969923308[/C][C]0.736378961439167[/C][C]31.0659296235484[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 44 )[/C][C]22.9284064327068[/C][C]0.727612848359901[/C][C]31.5118218217137[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 44 )[/C][C]22.9424665830827[/C][C]0.723690381787453[/C][C]31.702047119124[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 44 )[/C][C]22.9782811199248[/C][C]0.716851586716182[/C][C]32.0544468976986[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 44 )[/C][C]22.9507226398496[/C][C]0.711905930367653[/C][C]32.2384203598319[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 44 )[/C][C]22.9702255640601[/C][C]0.704236843533334[/C][C]32.6171880596487[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 44 )[/C][C]23.0267418546617[/C][C]0.69705299843054[/C][C]33.0344204909926[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 44 )[/C][C]23.0018796988722[/C][C]0.685301715472904[/C][C]33.564602538605[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 44 )[/C][C]22.873740602406[/C][C]0.646361001787926[/C][C]35.3884911669083[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 44 )[/C][C]22.8127255639098[/C][C]0.635441893760542[/C][C]35.9005690180485[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 44 )[/C][C]22.8276065167669[/C][C]0.611476205391479[/C][C]37.331962086983[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 44 )[/C][C]22.7929365077444[/C][C]0.600831334222168[/C][C]37.9356654846438[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 44 )[/C][C]22.7530680866917[/C][C]0.593041252883798[/C][C]38.3667543801545[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 44 )[/C][C]22.756330408797[/C][C]0.584848876304657[/C][C]38.9097617021716[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 44 )[/C][C]22.6672702601504[/C][C]0.565000441810085[/C][C]40.1190310356776[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 44 )[/C][C]22.5249143684211[/C][C]0.539996843470476[/C][C]41.7130482164617[/C][/ROW]
[ROW][C]Winsorized Mean ( 25 / 44 )[/C][C]22.3466562236842[/C][C]0.509606972145077[/C][C]43.8507662672293[/C][/ROW]
[ROW][C]Winsorized Mean ( 26 / 44 )[/C][C]22.3357414354135[/C][C]0.50583768703748[/C][C]44.1559456872943[/C][/ROW]
[ROW][C]Winsorized Mean ( 27 / 44 )[/C][C]22.1774519642105[/C][C]0.483033524304383[/C][C]45.9128628725062[/C][/ROW]
[ROW][C]Winsorized Mean ( 28 / 44 )[/C][C]22.1666332484211[/C][C]0.473505435450942[/C][C]46.8138939678923[/C][/ROW]
[ROW][C]Winsorized Mean ( 29 / 44 )[/C][C]22.2758980769173[/C][C]0.455754444203161[/C][C]48.8769739061225[/C][/ROW]
[ROW][C]Winsorized Mean ( 30 / 44 )[/C][C]22.2800334167669[/C][C]0.452953567374321[/C][C]49.1883385441023[/C][/ROW]
[ROW][C]Winsorized Mean ( 31 / 44 )[/C][C]22.2251942349624[/C][C]0.446522963999162[/C][C]49.773910922539[/C][/ROW]
[ROW][C]Winsorized Mean ( 32 / 44 )[/C][C]22.3454949868421[/C][C]0.42594994796206[/C][C]52.4603773137036[/C][/ROW]
[ROW][C]Winsorized Mean ( 33 / 44 )[/C][C]22.3350187969173[/C][C]0.421721389939247[/C][C]52.9615507530573[/C][/ROW]
[ROW][C]Winsorized Mean ( 34 / 44 )[/C][C]22.3397055128571[/C][C]0.419392437816511[/C][C]53.2668295812979[/C][/ROW]
[ROW][C]Winsorized Mean ( 35 / 44 )[/C][C]22.406810776015[/C][C]0.404512215035515[/C][C]55.3921734453626[/C][/ROW]
[ROW][C]Winsorized Mean ( 36 / 44 )[/C][C]22.3582393486466[/C][C]0.392490133026445[/C][C]56.9650991637544[/C][/ROW]
[ROW][C]Winsorized Mean ( 37 / 44 )[/C][C]22.3448705086466[/C][C]0.389387498046159[/C][C]57.384663402824[/C][/ROW]
[ROW][C]Winsorized Mean ( 38 / 44 )[/C][C]22.4000292400752[/C][C]0.383209195588304[/C][C]58.4537884214562[/C][/ROW]
[ROW][C]Winsorized Mean ( 39 / 44 )[/C][C]22.3909878847368[/C][C]0.380138885804661[/C][C]58.9021242521417[/C][/ROW]
[ROW][C]Winsorized Mean ( 40 / 44 )[/C][C]22.3968358396241[/C][C]0.370853549225602[/C][C]60.3926695224894[/C][/ROW]
[ROW][C]Winsorized Mean ( 41 / 44 )[/C][C]22.3635254821053[/C][C]0.361630992669753[/C][C]61.8407325019511[/C][/ROW]
[ROW][C]Winsorized Mean ( 42 / 44 )[/C][C]22.4521219715789[/C][C]0.351989021432269[/C][C]63.7864268613254[/C][/ROW]
[ROW][C]Winsorized Mean ( 43 / 44 )[/C][C]22.3145363393985[/C][C]0.337706108998005[/C][C]66.0767920533244[/C][/ROW]
[ROW][C]Winsorized Mean ( 44 / 44 )[/C][C]22.0745948215038[/C][C]0.290440115953192[/C][C]76.0039457671244[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 44 )[/C][C]23.4262192535038[/C][C]0.913445104716323[/C][C]25.6460066757695[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 44 )[/C][C]23.2093217053256[/C][C]0.84387903365441[/C][C]27.5031382220955[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 44 )[/C][C]23.0486526683228[/C][C]0.790045808525066[/C][C]29.1738180490474[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 44 )[/C][C]22.963706666608[/C][C]0.760172105545843[/C][C]30.2085626387447[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 44 )[/C][C]22.8776196928049[/C][C]0.732549466359563[/C][C]31.2301363162494[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 44 )[/C][C]22.8213360881157[/C][C]0.71395461100909[/C][C]31.9646875812742[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 44 )[/C][C]22.7810574229076[/C][C]0.697822604835136[/C][C]32.6459149718856[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 44 )[/C][C]22.7629558403761[/C][C]0.68582075826513[/C][C]33.1908236460468[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 44 )[/C][C]22.7450652173304[/C][C]0.672750806453195[/C][C]33.80904935253[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 44 )[/C][C]22.7279031464602[/C][C]0.661302603480191[/C][C]34.3683860109602[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 44 )[/C][C]22.7038788788288[/C][C]0.649964441138011[/C][C]34.9309553597686[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 44 )[/C][C]22.6774133536697[/C][C]0.637915325491164[/C][C]35.5492530865428[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 44 )[/C][C]22.6462487018692[/C][C]0.625442622443904[/C][C]36.2083553138406[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 44 )[/C][C]22.6165820104762[/C][C]0.612190423464316[/C][C]36.9437043501784[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 44 )[/C][C]22.583964401165[/C][C]0.598372836402242[/C][C]37.742295484121[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 44 )[/C][C]22.5450935092079[/C][C]0.583764145831696[/C][C]38.6202093262985[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 44 )[/C][C]22.5067396182828[/C][C]0.568880568613845[/C][C]39.563206866291[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 44 )[/C][C]22.4771391750515[/C][C]0.557277710200942[/C][C]40.3338205774403[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 44 )[/C][C]22.4510380114737[/C][C]0.54555716590706[/C][C]41.1524940271766[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 44 )[/C][C]22.4226941454839[/C][C]0.535245897453543[/C][C]41.8923232334164[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 44 )[/C][C]22.3956379728571[/C][C]0.524828006485704[/C][C]42.6723377870406[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 44 )[/C][C]22.3702028711236[/C][C]0.513906096420952[/C][C]43.5297479966061[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 44 )[/C][C]22.3433716472414[/C][C]0.502403746523909[/C][C]44.4729399448817[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 44 )[/C][C]22.3213366009412[/C][C]0.491713382425712[/C][C]45.3950154678035[/C][/ROW]
[ROW][C]Trimmed Mean ( 25 / 44 )[/C][C]22.307744310241[/C][C]0.482534523907114[/C][C]46.2303590831463[/C][/ROW]
[ROW][C]Trimmed Mean ( 26 / 44 )[/C][C]22.3051886141975[/C][C]0.475594906564904[/C][C]46.8995531834056[/C][/ROW]
[ROW][C]Trimmed Mean ( 27 / 44 )[/C][C]22.303210266962[/C][C]0.467945331885968[/C][C]47.6619996978558[/C][/ROW]
[ROW][C]Trimmed Mean ( 28 / 44 )[/C][C]22.3112554109091[/C][C]0.461707178198495[/C][C]48.3233886420478[/C][/ROW]
[ROW][C]Trimmed Mean ( 29 / 44 )[/C][C]22.3204148145333[/C][C]0.455469466900062[/C][C]49.005293299783[/C][/ROW]
[ROW][C]Trimmed Mean ( 30 / 44 )[/C][C]22.3232115675342[/C][C]0.450204765723518[/C][C]49.5845741029838[/C][/ROW]
[ROW][C]Trimmed Mean ( 31 / 44 )[/C][C]22.3259076680282[/C][C]0.444222166867786[/C][C]50.2584277264872[/C][/ROW]
[ROW][C]Trimmed Mean ( 32 / 44 )[/C][C]22.3321698871015[/C][C]0.437827328729655[/C][C]51.0067974785806[/C][/ROW]
[ROW][C]Trimmed Mean ( 33 / 44 )[/C][C]22.3313432834328[/C][C]0.43271616149057[/C][C]51.607370537094[/C][/ROW]
[ROW][C]Trimmed Mean ( 34 / 44 )[/C][C]22.3311153844615[/C][C]0.426993255208966[/C][C]52.2985202038682[/C][/ROW]
[ROW][C]Trimmed Mean ( 35 / 44 )[/C][C]22.3305820104762[/C][C]0.420284090918456[/C][C]53.1321134751418[/C][/ROW]
[ROW][C]Trimmed Mean ( 36 / 44 )[/C][C]22.3258333332787[/C][C]0.414083812821557[/C][C]53.9162185093665[/C][/ROW]
[ROW][C]Trimmed Mean ( 37 / 44 )[/C][C]22.3238041430508[/C][C]0.408081444174356[/C][C]54.7042862686813[/C][/ROW]
[ROW][C]Trimmed Mean ( 38 / 44 )[/C][C]22.3224756335088[/C][C]0.401018630658958[/C][C]55.6644353326634[/C][/ROW]
[ROW][C]Trimmed Mean ( 39 / 44 )[/C][C]22.317540404[/C][C]0.393108249670843[/C][C]56.7719970839759[/C][/ROW]
[ROW][C]Trimmed Mean ( 40 / 44 )[/C][C]22.3128144654717[/C][C]0.383658062718634[/C][C]58.1580752072853[/C][/ROW]
[ROW][C]Trimmed Mean ( 41 / 44 )[/C][C]22.3073366013725[/C][C]0.373336304118051[/C][C]59.7513189992872[/C][/ROW]
[ROW][C]Trimmed Mean ( 42 / 44 )[/C][C]22.30361678[/C][C]0.361919699279492[/C][C]61.6258712206104[/C][/ROW]
[ROW][C]Trimmed Mean ( 43 / 44 )[/C][C]22.2936111110638[/C][C]0.349143784337653[/C][C]63.8522354145762[/C][/ROW]
[ROW][C]Trimmed Mean ( 44 / 44 )[/C][C]22.2921728395556[/C][C]0.335685693913425[/C][C]66.407872732595[/C][/ROW]
[ROW][C]Median[/C][C]22.48583333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]48.4369444465[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]22.2418981480303[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]22.3313432834328[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]22.3313432834328[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]22.3313432834328[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]22.3313432834328[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]22.2438766338235[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]22.3313432834328[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]22.3313432834328[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]133[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=154404&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=154404&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 Mean23.80232038422561.0608025400101122.4380311004899
Geometric Mean21.081322936957
Harmonic Mean17.8919373131384
Quadratic Mean26.7411728143522
Winsorized Mean ( 1 / 44 )23.63659356715040.97380752075670624.2723464990118
Winsorized Mean ( 2 / 44 )23.51616332486470.93296230655282125.2059093488503
Winsorized Mean ( 3 / 44 )23.28816207165410.86286665916545526.9892941444486
Winsorized Mean ( 4 / 44 )23.28216374263160.84571142876686827.5296785057987
Winsorized Mean ( 5 / 44 )23.1336466163910.80223772394841428.8363983963917
Winsorized Mean ( 6 / 44 )23.0375689223910.78340948272697329.4068037601478
Winsorized Mean ( 7 / 44 )22.89252506270680.75531344100965330.3086425048991
Winsorized Mean ( 8 / 44 )22.88671052610530.75404175571495730.352046624268
Winsorized Mean ( 9 / 44 )22.87629699233080.73637896143916731.0659296235484
Winsorized Mean ( 10 / 44 )22.92840643270680.72761284835990131.5118218217137
Winsorized Mean ( 11 / 44 )22.94246658308270.72369038178745331.702047119124
Winsorized Mean ( 12 / 44 )22.97828111992480.71685158671618232.0544468976986
Winsorized Mean ( 13 / 44 )22.95072263984960.71190593036765332.2384203598319
Winsorized Mean ( 14 / 44 )22.97022556406010.70423684353333432.6171880596487
Winsorized Mean ( 15 / 44 )23.02674185466170.6970529984305433.0344204909926
Winsorized Mean ( 16 / 44 )23.00187969887220.68530171547290433.564602538605
Winsorized Mean ( 17 / 44 )22.8737406024060.64636100178792635.3884911669083
Winsorized Mean ( 18 / 44 )22.81272556390980.63544189376054235.9005690180485
Winsorized Mean ( 19 / 44 )22.82760651676690.61147620539147937.331962086983
Winsorized Mean ( 20 / 44 )22.79293650774440.60083133422216837.9356654846438
Winsorized Mean ( 21 / 44 )22.75306808669170.59304125288379838.3667543801545
Winsorized Mean ( 22 / 44 )22.7563304087970.58484887630465738.9097617021716
Winsorized Mean ( 23 / 44 )22.66727026015040.56500044181008540.1190310356776
Winsorized Mean ( 24 / 44 )22.52491436842110.53999684347047641.7130482164617
Winsorized Mean ( 25 / 44 )22.34665622368420.50960697214507743.8507662672293
Winsorized Mean ( 26 / 44 )22.33574143541350.5058376870374844.1559456872943
Winsorized Mean ( 27 / 44 )22.17745196421050.48303352430438345.9128628725062
Winsorized Mean ( 28 / 44 )22.16663324842110.47350543545094246.8138939678923
Winsorized Mean ( 29 / 44 )22.27589807691730.45575444420316148.8769739061225
Winsorized Mean ( 30 / 44 )22.28003341676690.45295356737432149.1883385441023
Winsorized Mean ( 31 / 44 )22.22519423496240.44652296399916249.773910922539
Winsorized Mean ( 32 / 44 )22.34549498684210.4259499479620652.4603773137036
Winsorized Mean ( 33 / 44 )22.33501879691730.42172138993924752.9615507530573
Winsorized Mean ( 34 / 44 )22.33970551285710.41939243781651153.2668295812979
Winsorized Mean ( 35 / 44 )22.4068107760150.40451221503551555.3921734453626
Winsorized Mean ( 36 / 44 )22.35823934864660.39249013302644556.9650991637544
Winsorized Mean ( 37 / 44 )22.34487050864660.38938749804615957.384663402824
Winsorized Mean ( 38 / 44 )22.40002924007520.38320919558830458.4537884214562
Winsorized Mean ( 39 / 44 )22.39098788473680.38013888580466158.9021242521417
Winsorized Mean ( 40 / 44 )22.39683583962410.37085354922560260.3926695224894
Winsorized Mean ( 41 / 44 )22.36352548210530.36163099266975361.8407325019511
Winsorized Mean ( 42 / 44 )22.45212197157890.35198902143226963.7864268613254
Winsorized Mean ( 43 / 44 )22.31453633939850.33770610899800566.0767920533244
Winsorized Mean ( 44 / 44 )22.07459482150380.29044011595319276.0039457671244
Trimmed Mean ( 1 / 44 )23.42621925350380.91344510471632325.6460066757695
Trimmed Mean ( 2 / 44 )23.20932170532560.8438790336544127.5031382220955
Trimmed Mean ( 3 / 44 )23.04865266832280.79004580852506629.1738180490474
Trimmed Mean ( 4 / 44 )22.9637066666080.76017210554584330.2085626387447
Trimmed Mean ( 5 / 44 )22.87761969280490.73254946635956331.2301363162494
Trimmed Mean ( 6 / 44 )22.82133608811570.7139546110090931.9646875812742
Trimmed Mean ( 7 / 44 )22.78105742290760.69782260483513632.6459149718856
Trimmed Mean ( 8 / 44 )22.76295584037610.6858207582651333.1908236460468
Trimmed Mean ( 9 / 44 )22.74506521733040.67275080645319533.80904935253
Trimmed Mean ( 10 / 44 )22.72790314646020.66130260348019134.3683860109602
Trimmed Mean ( 11 / 44 )22.70387887882880.64996444113801134.9309553597686
Trimmed Mean ( 12 / 44 )22.67741335366970.63791532549116435.5492530865428
Trimmed Mean ( 13 / 44 )22.64624870186920.62544262244390436.2083553138406
Trimmed Mean ( 14 / 44 )22.61658201047620.61219042346431636.9437043501784
Trimmed Mean ( 15 / 44 )22.5839644011650.59837283640224237.742295484121
Trimmed Mean ( 16 / 44 )22.54509350920790.58376414583169638.6202093262985
Trimmed Mean ( 17 / 44 )22.50673961828280.56888056861384539.563206866291
Trimmed Mean ( 18 / 44 )22.47713917505150.55727771020094240.3338205774403
Trimmed Mean ( 19 / 44 )22.45103801147370.5455571659070641.1524940271766
Trimmed Mean ( 20 / 44 )22.42269414548390.53524589745354341.8923232334164
Trimmed Mean ( 21 / 44 )22.39563797285710.52482800648570442.6723377870406
Trimmed Mean ( 22 / 44 )22.37020287112360.51390609642095243.5297479966061
Trimmed Mean ( 23 / 44 )22.34337164724140.50240374652390944.4729399448817
Trimmed Mean ( 24 / 44 )22.32133660094120.49171338242571245.3950154678035
Trimmed Mean ( 25 / 44 )22.3077443102410.48253452390711446.2303590831463
Trimmed Mean ( 26 / 44 )22.30518861419750.47559490656490446.8995531834056
Trimmed Mean ( 27 / 44 )22.3032102669620.46794533188596847.6619996978558
Trimmed Mean ( 28 / 44 )22.31125541090910.46170717819849548.3233886420478
Trimmed Mean ( 29 / 44 )22.32041481453330.45546946690006249.005293299783
Trimmed Mean ( 30 / 44 )22.32321156753420.45020476572351849.5845741029838
Trimmed Mean ( 31 / 44 )22.32590766802820.44422216686778650.2584277264872
Trimmed Mean ( 32 / 44 )22.33216988710150.43782732872965551.0067974785806
Trimmed Mean ( 33 / 44 )22.33134328343280.4327161614905751.607370537094
Trimmed Mean ( 34 / 44 )22.33111538446150.42699325520896652.2985202038682
Trimmed Mean ( 35 / 44 )22.33058201047620.42028409091845653.1321134751418
Trimmed Mean ( 36 / 44 )22.32583333327870.41408381282155753.9162185093665
Trimmed Mean ( 37 / 44 )22.32380414305080.40808144417435654.7042862686813
Trimmed Mean ( 38 / 44 )22.32247563350880.40101863065895855.6644353326634
Trimmed Mean ( 39 / 44 )22.3175404040.39310824967084356.7719970839759
Trimmed Mean ( 40 / 44 )22.31281446547170.38365806271863458.1580752072853
Trimmed Mean ( 41 / 44 )22.30733660137250.37333630411805159.7513189992872
Trimmed Mean ( 42 / 44 )22.303616780.36191969927949261.6258712206104
Trimmed Mean ( 43 / 44 )22.29361111106380.34914378433765363.8522354145762
Trimmed Mean ( 44 / 44 )22.29217283955560.33568569391342566.407872732595
Median22.48583333
Midrange48.4369444465
Midmean - Weighted Average at Xnp22.2418981480303
Midmean - Weighted Average at X(n+1)p22.3313432834328
Midmean - Empirical Distribution Function22.3313432834328
Midmean - Empirical Distribution Function - Averaging22.3313432834328
Midmean - Empirical Distribution Function - Interpolation22.3313432834328
Midmean - Closest Observation22.2438766338235
Midmean - True Basic - Statistics Graphics Toolkit22.3313432834328
Midmean - MS Excel (old versions)22.3313432834328
Number of observations133



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')