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of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationSat, 24 Oct 2009 06:52:20 -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/24/t1256388784tub7p8ewwmn5u90.htm/, Retrieved Fri, 03 May 2024 14:41:41 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=50116, Retrieved Fri, 03 May 2024 14:41:41 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsKDGP1W52
Estimated Impact146
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [central tendency ...] [2009-10-24 12:52:20] [ddb1c76c3acba5bf82e5ed3b5a08f68d] [Current]
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Dataseries X:
35,75
36,25
35,32
33,80
31,54
30,74
30,55
30,06
30,30
32,24
33,42
33,31
33,76
33,61
33,68
34,17
34,17
34,07
32,36
31,57
31,34
30,81
29,95
29,74
29,56
29,91
29,82
31,46
32,55
32,82
32,74
33,05
32,63
31,85
31,99
31,39
30,16
30,04
29,55
29,12
29,31
29,36
29,67
30,69
31,08
31,08
31,10
30,96
31,94
31,59
32,01
32,13
32,20
32,05
32,12
31,66
32,99
36,02
37,10
37,96
38,96
41,66
47,29
49,42
48,17
46,25
45,43
43,83
41,51
38,25
35,23
34,18




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'Sir Ronald Aylmer Fisher' @ 193.190.124.24

\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 & 3 seconds \tabularnewline
R Server & 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=50116&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]3 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Sir Ronald Aylmer Fisher' @ 193.190.124.24[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=50116&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=50116&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 time3 seconds
R Server'Sir Ronald Aylmer Fisher' @ 193.190.124.24







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean33.81041666666670.56141617676449660.223445753772
Geometric Mean33.5224032992703
Harmonic Mean33.271584130383
Quadratic Mean34.1397514921308
Winsorized Mean ( 1 / 24 )33.79569444444440.5545406474469960.9435838473411
Winsorized Mean ( 2 / 24 )33.77263888888890.5456541921225361.8938503111602
Winsorized Mean ( 3 / 24 )33.73722222222220.52999306924862163.6559686904057
Winsorized Mean ( 4 / 24 )33.69222222222220.51504148541533565.4165211469372
Winsorized Mean ( 5 / 24 )33.588750.47958894181405970.0365397770633
Winsorized Mean ( 6 / 24 )33.413750.42696024219532878.2596286440968
Winsorized Mean ( 7 / 24 )33.40694444444440.42206816412494079.1505905537936
Winsorized Mean ( 8 / 24 )33.13361111111110.34870520087713395.0189759939536
Winsorized Mean ( 9 / 24 )33.04986111111110.327668799935717100.86361935465
Winsorized Mean ( 10 / 24 )33.02208333333330.317088052811083104.141682540803
Winsorized Mean ( 11 / 24 )32.893750.288743530132315113.920301469358
Winsorized Mean ( 12 / 24 )32.768750.258372474507139126.827558014871
Winsorized Mean ( 13 / 24 )32.75250.246996096317825132.603310288173
Winsorized Mean ( 14 / 24 )32.74861111111110.230623458051392142.000347179832
Winsorized Mean ( 15 / 24 )32.68819444444440.210607524085545155.209053363009
Winsorized Mean ( 16 / 24 )32.67930555555560.205619728779646158.930788156893
Winsorized Mean ( 17 / 24 )32.44791666666670.162764283404773199.355263869366
Winsorized Mean ( 18 / 24 )32.48291666666670.157169858861134206.673957093558
Winsorized Mean ( 19 / 24 )32.51458333333330.152915963079319212.630406130115
Winsorized Mean ( 20 / 24 )32.48680555555550.148715263219457218.449706185271
Winsorized Mean ( 21 / 24 )32.41388888888890.136379171380264237.674775120239
Winsorized Mean ( 22 / 24 )32.4750.124940361359785259.924012117136
Winsorized Mean ( 23 / 24 )32.46541666666670.119218887323608272.317729140874
Winsorized Mean ( 24 / 24 )32.46541666666670.112933556417487287.473605689439
Trimmed Mean ( 1 / 24 )33.65442857142860.52748069683811563.8021993471302
Trimmed Mean ( 2 / 24 )33.50485294117650.49421191033795267.7945072555316
Trimmed Mean ( 3 / 24 )33.35878787878790.45908693790738672.6633348159374
Trimmed Mean ( 4 / 24 )33.2168750.4232177778052378.4864831819207
Trimmed Mean ( 5 / 24 )33.07887096774190.38427265522078786.0817716752085
Trimmed Mean ( 6 / 24 )32.95650.34867188086863994.520096997487
Trimmed Mean ( 7 / 24 )32.86189655172410.322455271489092101.911488064588
Trimmed Mean ( 8 / 24 )32.76178571428570.290065611380219112.946121253034
Trimmed Mean ( 9 / 24 )32.69981481481480.272414020150606120.037194843116
Trimmed Mean ( 10 / 24 )32.64596153846150.256050796774905127.497988483749
Trimmed Mean ( 11 / 24 )32.59180.237927907105476136.981829481448
Trimmed Mean ( 12 / 24 )32.5506250.222691547609632146.169108569220
Trimmed Mean ( 13 / 24 )32.52217391304350.211322935108217153.897985073836
Trimmed Mean ( 14 / 24 )32.49318181818180.199405769637761162.950058452213
Trimmed Mean ( 15 / 24 )32.46190476190480.187914539999525172.748233116962
Trimmed Mean ( 16 / 24 )32.434750.178075894040888182.140037396374
Trimmed Mean ( 17 / 24 )32.40578947368420.166017116625523195.195472204113
Trimmed Mean ( 18 / 24 )32.40083333333330.161973138572566200.038312641682
Trimmed Mean ( 19 / 24 )32.39117647058820.157541701298759205.603825549416
Trimmed Mean ( 20 / 24 )32.37656250.152125803053384212.827553578392
Trimmed Mean ( 21 / 24 )32.36333333333330.145440538336362222.519345043170
Trimmed Mean ( 22 / 24 )32.35714285714290.139642265117353231.714537356942
Trimmed Mean ( 23 / 24 )32.34230769230770.134356938720144240.719295932117
Trimmed Mean ( 24 / 24 )32.326250.127909349269062252.727812194562
Median32.165
Midrange39.27
Midmean - Weighted Average at Xnp32.3578378378378
Midmean - Weighted Average at X(n+1)p32.4008333333333
Midmean - Empirical Distribution Function32.3578378378378
Midmean - Empirical Distribution Function - Averaging32.4008333333333
Midmean - Empirical Distribution Function - Interpolation32.4008333333333
Midmean - Closest Observation32.3578378378378
Midmean - True Basic - Statistics Graphics Toolkit32.4008333333333
Midmean - MS Excel (old versions)32.4057894736842
Number of observations72

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 33.8104166666667 & 0.561416176764496 & 60.223445753772 \tabularnewline
Geometric Mean & 33.5224032992703 &  &  \tabularnewline
Harmonic Mean & 33.271584130383 &  &  \tabularnewline
Quadratic Mean & 34.1397514921308 &  &  \tabularnewline
Winsorized Mean ( 1 / 24 ) & 33.7956944444444 & 0.55454064744699 & 60.9435838473411 \tabularnewline
Winsorized Mean ( 2 / 24 ) & 33.7726388888889 & 0.54565419212253 & 61.8938503111602 \tabularnewline
Winsorized Mean ( 3 / 24 ) & 33.7372222222222 & 0.529993069248621 & 63.6559686904057 \tabularnewline
Winsorized Mean ( 4 / 24 ) & 33.6922222222222 & 0.515041485415335 & 65.4165211469372 \tabularnewline
Winsorized Mean ( 5 / 24 ) & 33.58875 & 0.479588941814059 & 70.0365397770633 \tabularnewline
Winsorized Mean ( 6 / 24 ) & 33.41375 & 0.426960242195328 & 78.2596286440968 \tabularnewline
Winsorized Mean ( 7 / 24 ) & 33.4069444444444 & 0.422068164124940 & 79.1505905537936 \tabularnewline
Winsorized Mean ( 8 / 24 ) & 33.1336111111111 & 0.348705200877133 & 95.0189759939536 \tabularnewline
Winsorized Mean ( 9 / 24 ) & 33.0498611111111 & 0.327668799935717 & 100.86361935465 \tabularnewline
Winsorized Mean ( 10 / 24 ) & 33.0220833333333 & 0.317088052811083 & 104.141682540803 \tabularnewline
Winsorized Mean ( 11 / 24 ) & 32.89375 & 0.288743530132315 & 113.920301469358 \tabularnewline
Winsorized Mean ( 12 / 24 ) & 32.76875 & 0.258372474507139 & 126.827558014871 \tabularnewline
Winsorized Mean ( 13 / 24 ) & 32.7525 & 0.246996096317825 & 132.603310288173 \tabularnewline
Winsorized Mean ( 14 / 24 ) & 32.7486111111111 & 0.230623458051392 & 142.000347179832 \tabularnewline
Winsorized Mean ( 15 / 24 ) & 32.6881944444444 & 0.210607524085545 & 155.209053363009 \tabularnewline
Winsorized Mean ( 16 / 24 ) & 32.6793055555556 & 0.205619728779646 & 158.930788156893 \tabularnewline
Winsorized Mean ( 17 / 24 ) & 32.4479166666667 & 0.162764283404773 & 199.355263869366 \tabularnewline
Winsorized Mean ( 18 / 24 ) & 32.4829166666667 & 0.157169858861134 & 206.673957093558 \tabularnewline
Winsorized Mean ( 19 / 24 ) & 32.5145833333333 & 0.152915963079319 & 212.630406130115 \tabularnewline
Winsorized Mean ( 20 / 24 ) & 32.4868055555555 & 0.148715263219457 & 218.449706185271 \tabularnewline
Winsorized Mean ( 21 / 24 ) & 32.4138888888889 & 0.136379171380264 & 237.674775120239 \tabularnewline
Winsorized Mean ( 22 / 24 ) & 32.475 & 0.124940361359785 & 259.924012117136 \tabularnewline
Winsorized Mean ( 23 / 24 ) & 32.4654166666667 & 0.119218887323608 & 272.317729140874 \tabularnewline
Winsorized Mean ( 24 / 24 ) & 32.4654166666667 & 0.112933556417487 & 287.473605689439 \tabularnewline
Trimmed Mean ( 1 / 24 ) & 33.6544285714286 & 0.527480696838115 & 63.8021993471302 \tabularnewline
Trimmed Mean ( 2 / 24 ) & 33.5048529411765 & 0.494211910337952 & 67.7945072555316 \tabularnewline
Trimmed Mean ( 3 / 24 ) & 33.3587878787879 & 0.459086937907386 & 72.6633348159374 \tabularnewline
Trimmed Mean ( 4 / 24 ) & 33.216875 & 0.42321777780523 & 78.4864831819207 \tabularnewline
Trimmed Mean ( 5 / 24 ) & 33.0788709677419 & 0.384272655220787 & 86.0817716752085 \tabularnewline
Trimmed Mean ( 6 / 24 ) & 32.9565 & 0.348671880868639 & 94.520096997487 \tabularnewline
Trimmed Mean ( 7 / 24 ) & 32.8618965517241 & 0.322455271489092 & 101.911488064588 \tabularnewline
Trimmed Mean ( 8 / 24 ) & 32.7617857142857 & 0.290065611380219 & 112.946121253034 \tabularnewline
Trimmed Mean ( 9 / 24 ) & 32.6998148148148 & 0.272414020150606 & 120.037194843116 \tabularnewline
Trimmed Mean ( 10 / 24 ) & 32.6459615384615 & 0.256050796774905 & 127.497988483749 \tabularnewline
Trimmed Mean ( 11 / 24 ) & 32.5918 & 0.237927907105476 & 136.981829481448 \tabularnewline
Trimmed Mean ( 12 / 24 ) & 32.550625 & 0.222691547609632 & 146.169108569220 \tabularnewline
Trimmed Mean ( 13 / 24 ) & 32.5221739130435 & 0.211322935108217 & 153.897985073836 \tabularnewline
Trimmed Mean ( 14 / 24 ) & 32.4931818181818 & 0.199405769637761 & 162.950058452213 \tabularnewline
Trimmed Mean ( 15 / 24 ) & 32.4619047619048 & 0.187914539999525 & 172.748233116962 \tabularnewline
Trimmed Mean ( 16 / 24 ) & 32.43475 & 0.178075894040888 & 182.140037396374 \tabularnewline
Trimmed Mean ( 17 / 24 ) & 32.4057894736842 & 0.166017116625523 & 195.195472204113 \tabularnewline
Trimmed Mean ( 18 / 24 ) & 32.4008333333333 & 0.161973138572566 & 200.038312641682 \tabularnewline
Trimmed Mean ( 19 / 24 ) & 32.3911764705882 & 0.157541701298759 & 205.603825549416 \tabularnewline
Trimmed Mean ( 20 / 24 ) & 32.3765625 & 0.152125803053384 & 212.827553578392 \tabularnewline
Trimmed Mean ( 21 / 24 ) & 32.3633333333333 & 0.145440538336362 & 222.519345043170 \tabularnewline
Trimmed Mean ( 22 / 24 ) & 32.3571428571429 & 0.139642265117353 & 231.714537356942 \tabularnewline
Trimmed Mean ( 23 / 24 ) & 32.3423076923077 & 0.134356938720144 & 240.719295932117 \tabularnewline
Trimmed Mean ( 24 / 24 ) & 32.32625 & 0.127909349269062 & 252.727812194562 \tabularnewline
Median & 32.165 &  &  \tabularnewline
Midrange & 39.27 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 32.3578378378378 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 32.4008333333333 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 32.3578378378378 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 32.4008333333333 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 32.4008333333333 &  &  \tabularnewline
Midmean - Closest Observation & 32.3578378378378 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 32.4008333333333 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 32.4057894736842 &  &  \tabularnewline
Number of observations & 72 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=50116&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]33.8104166666667[/C][C]0.561416176764496[/C][C]60.223445753772[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]33.5224032992703[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]33.271584130383[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]34.1397514921308[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 24 )[/C][C]33.7956944444444[/C][C]0.55454064744699[/C][C]60.9435838473411[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 24 )[/C][C]33.7726388888889[/C][C]0.54565419212253[/C][C]61.8938503111602[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 24 )[/C][C]33.7372222222222[/C][C]0.529993069248621[/C][C]63.6559686904057[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 24 )[/C][C]33.6922222222222[/C][C]0.515041485415335[/C][C]65.4165211469372[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 24 )[/C][C]33.58875[/C][C]0.479588941814059[/C][C]70.0365397770633[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 24 )[/C][C]33.41375[/C][C]0.426960242195328[/C][C]78.2596286440968[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 24 )[/C][C]33.4069444444444[/C][C]0.422068164124940[/C][C]79.1505905537936[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 24 )[/C][C]33.1336111111111[/C][C]0.348705200877133[/C][C]95.0189759939536[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 24 )[/C][C]33.0498611111111[/C][C]0.327668799935717[/C][C]100.86361935465[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 24 )[/C][C]33.0220833333333[/C][C]0.317088052811083[/C][C]104.141682540803[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 24 )[/C][C]32.89375[/C][C]0.288743530132315[/C][C]113.920301469358[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 24 )[/C][C]32.76875[/C][C]0.258372474507139[/C][C]126.827558014871[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 24 )[/C][C]32.7525[/C][C]0.246996096317825[/C][C]132.603310288173[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 24 )[/C][C]32.7486111111111[/C][C]0.230623458051392[/C][C]142.000347179832[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 24 )[/C][C]32.6881944444444[/C][C]0.210607524085545[/C][C]155.209053363009[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 24 )[/C][C]32.6793055555556[/C][C]0.205619728779646[/C][C]158.930788156893[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 24 )[/C][C]32.4479166666667[/C][C]0.162764283404773[/C][C]199.355263869366[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 24 )[/C][C]32.4829166666667[/C][C]0.157169858861134[/C][C]206.673957093558[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 24 )[/C][C]32.5145833333333[/C][C]0.152915963079319[/C][C]212.630406130115[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 24 )[/C][C]32.4868055555555[/C][C]0.148715263219457[/C][C]218.449706185271[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 24 )[/C][C]32.4138888888889[/C][C]0.136379171380264[/C][C]237.674775120239[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 24 )[/C][C]32.475[/C][C]0.124940361359785[/C][C]259.924012117136[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 24 )[/C][C]32.4654166666667[/C][C]0.119218887323608[/C][C]272.317729140874[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 24 )[/C][C]32.4654166666667[/C][C]0.112933556417487[/C][C]287.473605689439[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 24 )[/C][C]33.6544285714286[/C][C]0.527480696838115[/C][C]63.8021993471302[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 24 )[/C][C]33.5048529411765[/C][C]0.494211910337952[/C][C]67.7945072555316[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 24 )[/C][C]33.3587878787879[/C][C]0.459086937907386[/C][C]72.6633348159374[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 24 )[/C][C]33.216875[/C][C]0.42321777780523[/C][C]78.4864831819207[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 24 )[/C][C]33.0788709677419[/C][C]0.384272655220787[/C][C]86.0817716752085[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 24 )[/C][C]32.9565[/C][C]0.348671880868639[/C][C]94.520096997487[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 24 )[/C][C]32.8618965517241[/C][C]0.322455271489092[/C][C]101.911488064588[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 24 )[/C][C]32.7617857142857[/C][C]0.290065611380219[/C][C]112.946121253034[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 24 )[/C][C]32.6998148148148[/C][C]0.272414020150606[/C][C]120.037194843116[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 24 )[/C][C]32.6459615384615[/C][C]0.256050796774905[/C][C]127.497988483749[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 24 )[/C][C]32.5918[/C][C]0.237927907105476[/C][C]136.981829481448[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 24 )[/C][C]32.550625[/C][C]0.222691547609632[/C][C]146.169108569220[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 24 )[/C][C]32.5221739130435[/C][C]0.211322935108217[/C][C]153.897985073836[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 24 )[/C][C]32.4931818181818[/C][C]0.199405769637761[/C][C]162.950058452213[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 24 )[/C][C]32.4619047619048[/C][C]0.187914539999525[/C][C]172.748233116962[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 24 )[/C][C]32.43475[/C][C]0.178075894040888[/C][C]182.140037396374[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 24 )[/C][C]32.4057894736842[/C][C]0.166017116625523[/C][C]195.195472204113[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 24 )[/C][C]32.4008333333333[/C][C]0.161973138572566[/C][C]200.038312641682[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 24 )[/C][C]32.3911764705882[/C][C]0.157541701298759[/C][C]205.603825549416[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 24 )[/C][C]32.3765625[/C][C]0.152125803053384[/C][C]212.827553578392[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 24 )[/C][C]32.3633333333333[/C][C]0.145440538336362[/C][C]222.519345043170[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 24 )[/C][C]32.3571428571429[/C][C]0.139642265117353[/C][C]231.714537356942[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 24 )[/C][C]32.3423076923077[/C][C]0.134356938720144[/C][C]240.719295932117[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 24 )[/C][C]32.32625[/C][C]0.127909349269062[/C][C]252.727812194562[/C][/ROW]
[ROW][C]Median[/C][C]32.165[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]39.27[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]32.3578378378378[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]32.4008333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]32.3578378378378[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]32.4008333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]32.4008333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]32.3578378378378[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]32.4008333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]32.4057894736842[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]72[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=50116&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=50116&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 Mean33.81041666666670.56141617676449660.223445753772
Geometric Mean33.5224032992703
Harmonic Mean33.271584130383
Quadratic Mean34.1397514921308
Winsorized Mean ( 1 / 24 )33.79569444444440.5545406474469960.9435838473411
Winsorized Mean ( 2 / 24 )33.77263888888890.5456541921225361.8938503111602
Winsorized Mean ( 3 / 24 )33.73722222222220.52999306924862163.6559686904057
Winsorized Mean ( 4 / 24 )33.69222222222220.51504148541533565.4165211469372
Winsorized Mean ( 5 / 24 )33.588750.47958894181405970.0365397770633
Winsorized Mean ( 6 / 24 )33.413750.42696024219532878.2596286440968
Winsorized Mean ( 7 / 24 )33.40694444444440.42206816412494079.1505905537936
Winsorized Mean ( 8 / 24 )33.13361111111110.34870520087713395.0189759939536
Winsorized Mean ( 9 / 24 )33.04986111111110.327668799935717100.86361935465
Winsorized Mean ( 10 / 24 )33.02208333333330.317088052811083104.141682540803
Winsorized Mean ( 11 / 24 )32.893750.288743530132315113.920301469358
Winsorized Mean ( 12 / 24 )32.768750.258372474507139126.827558014871
Winsorized Mean ( 13 / 24 )32.75250.246996096317825132.603310288173
Winsorized Mean ( 14 / 24 )32.74861111111110.230623458051392142.000347179832
Winsorized Mean ( 15 / 24 )32.68819444444440.210607524085545155.209053363009
Winsorized Mean ( 16 / 24 )32.67930555555560.205619728779646158.930788156893
Winsorized Mean ( 17 / 24 )32.44791666666670.162764283404773199.355263869366
Winsorized Mean ( 18 / 24 )32.48291666666670.157169858861134206.673957093558
Winsorized Mean ( 19 / 24 )32.51458333333330.152915963079319212.630406130115
Winsorized Mean ( 20 / 24 )32.48680555555550.148715263219457218.449706185271
Winsorized Mean ( 21 / 24 )32.41388888888890.136379171380264237.674775120239
Winsorized Mean ( 22 / 24 )32.4750.124940361359785259.924012117136
Winsorized Mean ( 23 / 24 )32.46541666666670.119218887323608272.317729140874
Winsorized Mean ( 24 / 24 )32.46541666666670.112933556417487287.473605689439
Trimmed Mean ( 1 / 24 )33.65442857142860.52748069683811563.8021993471302
Trimmed Mean ( 2 / 24 )33.50485294117650.49421191033795267.7945072555316
Trimmed Mean ( 3 / 24 )33.35878787878790.45908693790738672.6633348159374
Trimmed Mean ( 4 / 24 )33.2168750.4232177778052378.4864831819207
Trimmed Mean ( 5 / 24 )33.07887096774190.38427265522078786.0817716752085
Trimmed Mean ( 6 / 24 )32.95650.34867188086863994.520096997487
Trimmed Mean ( 7 / 24 )32.86189655172410.322455271489092101.911488064588
Trimmed Mean ( 8 / 24 )32.76178571428570.290065611380219112.946121253034
Trimmed Mean ( 9 / 24 )32.69981481481480.272414020150606120.037194843116
Trimmed Mean ( 10 / 24 )32.64596153846150.256050796774905127.497988483749
Trimmed Mean ( 11 / 24 )32.59180.237927907105476136.981829481448
Trimmed Mean ( 12 / 24 )32.5506250.222691547609632146.169108569220
Trimmed Mean ( 13 / 24 )32.52217391304350.211322935108217153.897985073836
Trimmed Mean ( 14 / 24 )32.49318181818180.199405769637761162.950058452213
Trimmed Mean ( 15 / 24 )32.46190476190480.187914539999525172.748233116962
Trimmed Mean ( 16 / 24 )32.434750.178075894040888182.140037396374
Trimmed Mean ( 17 / 24 )32.40578947368420.166017116625523195.195472204113
Trimmed Mean ( 18 / 24 )32.40083333333330.161973138572566200.038312641682
Trimmed Mean ( 19 / 24 )32.39117647058820.157541701298759205.603825549416
Trimmed Mean ( 20 / 24 )32.37656250.152125803053384212.827553578392
Trimmed Mean ( 21 / 24 )32.36333333333330.145440538336362222.519345043170
Trimmed Mean ( 22 / 24 )32.35714285714290.139642265117353231.714537356942
Trimmed Mean ( 23 / 24 )32.34230769230770.134356938720144240.719295932117
Trimmed Mean ( 24 / 24 )32.326250.127909349269062252.727812194562
Median32.165
Midrange39.27
Midmean - Weighted Average at Xnp32.3578378378378
Midmean - Weighted Average at X(n+1)p32.4008333333333
Midmean - Empirical Distribution Function32.3578378378378
Midmean - Empirical Distribution Function - Averaging32.4008333333333
Midmean - Empirical Distribution Function - Interpolation32.4008333333333
Midmean - Closest Observation32.3578378378378
Midmean - True Basic - Statistics Graphics Toolkit32.4008333333333
Midmean - MS Excel (old versions)32.4057894736842
Number of observations72



Parameters (Session):
Parameters (R input):
R code (references can be found in the software module):
geomean <- function(x) {
return(exp(mean(log(x))))
}
harmean <- function(x) {
return(1/mean(1/x))
}
quamean <- function(x) {
return(sqrt(mean(x*x)))
}
winmean <- function(x) {
x <-sort(x[!is.na(x)])
n<-length(x)
denom <- 3
nodenom <- n/denom
if (nodenom>40) denom <- n/40
sqrtn = sqrt(n)
roundnodenom = floor(nodenom)
win <- array(NA,dim=c(roundnodenom,2))
for (j in 1:roundnodenom) {
win[j,1] <- (j*x[j+1]+sum(x[(j+1):(n-j)])+j*x[n-j])/n
win[j,2] <- sd(c(rep(x[j+1],j),x[(j+1):(n-j)],rep(x[n-j],j)))/sqrtn
}
return(win)
}
trimean <- function(x) {
x <-sort(x[!is.na(x)])
n<-length(x)
denom <- 3
nodenom <- n/denom
if (nodenom>40) denom <- n/40
sqrtn = sqrt(n)
roundnodenom = floor(nodenom)
tri <- array(NA,dim=c(roundnodenom,2))
for (j in 1:roundnodenom) {
tri[j,1] <- mean(x,trim=j/n)
tri[j,2] <- sd(x[(j+1):(n-j)]) / sqrt(n-j*2)
}
return(tri)
}
midrange <- function(x) {
return((max(x)+min(x))/2)
}
q1 <- function(data,n,p,i,f) {
np <- n*p;
i <<- floor(np)
f <<- np - i
qvalue <- (1-f)*data[i] + f*data[i+1]
}
q2 <- function(data,n,p,i,f) {
np <- (n+1)*p
i <<- floor(np)
f <<- np - i
qvalue <- (1-f)*data[i] + f*data[i+1]
}
q3 <- function(data,n,p,i,f) {
np <- n*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- data[i]
} else {
qvalue <- data[i+1]
}
}
q4 <- function(data,n,p,i,f) {
np <- n*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- (data[i]+data[i+1])/2
} else {
qvalue <- data[i+1]
}
}
q5 <- function(data,n,p,i,f) {
np <- (n-1)*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- data[i+1]
} else {
qvalue <- data[i+1] + f*(data[i+2]-data[i+1])
}
}
q6 <- function(data,n,p,i,f) {
np <- n*p+0.5
i <<- floor(np)
f <<- np - i
qvalue <- data[i]
}
q7 <- function(data,n,p,i,f) {
np <- (n+1)*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- data[i]
} else {
qvalue <- f*data[i] + (1-f)*data[i+1]
}
}
q8 <- function(data,n,p,i,f) {
np <- (n+1)*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- data[i]
} else {
if (f == 0.5) {
qvalue <- (data[i]+data[i+1])/2
} else {
if (f < 0.5) {
qvalue <- data[i]
} else {
qvalue <- data[i+1]
}
}
}
}
midmean <- function(x,def) {
x <-sort(x[!is.na(x)])
n<-length(x)
if (def==1) {
qvalue1 <- q1(x,n,0.25,i,f)
qvalue3 <- q1(x,n,0.75,i,f)
}
if (def==2) {
qvalue1 <- q2(x,n,0.25,i,f)
qvalue3 <- q2(x,n,0.75,i,f)
}
if (def==3) {
qvalue1 <- q3(x,n,0.25,i,f)
qvalue3 <- q3(x,n,0.75,i,f)
}
if (def==4) {
qvalue1 <- q4(x,n,0.25,i,f)
qvalue3 <- q4(x,n,0.75,i,f)
}
if (def==5) {
qvalue1 <- q5(x,n,0.25,i,f)
qvalue3 <- q5(x,n,0.75,i,f)
}
if (def==6) {
qvalue1 <- q6(x,n,0.25,i,f)
qvalue3 <- q6(x,n,0.75,i,f)
}
if (def==7) {
qvalue1 <- q7(x,n,0.25,i,f)
qvalue3 <- q7(x,n,0.75,i,f)
}
if (def==8) {
qvalue1 <- q8(x,n,0.25,i,f)
qvalue3 <- q8(x,n,0.75,i,f)
}
midm <- 0
myn <- 0
roundno4 <- round(n/4)
round3no4 <- round(3*n/4)
for (i in 1:n) {
if ((x[i]>=qvalue1) & (x[i]<=qvalue3)){
midm = midm + x[i]
myn = myn + 1
}
}
midm = midm / myn
return(midm)
}
(arm <- mean(x))
sqrtn <- sqrt(length(x))
(armse <- sd(x) / sqrtn)
(armose <- arm / armse)
(geo <- geomean(x))
(har <- harmean(x))
(qua <- quamean(x))
(win <- winmean(x))
(tri <- trimean(x))
(midr <- midrange(x))
midm <- array(NA,dim=8)
for (j in 1:8) midm[j] <- midmean(x,j)
midm
bitmap(file='test1.png')
lb <- win[,1] - 2*win[,2]
ub <- win[,1] + 2*win[,2]
if ((ylimmin == '') | (ylimmax == '')) plot(win[,1],type='b',main=main, xlab='j', pch=19, ylab='Winsorized Mean(j/n)', ylim=c(min(lb),max(ub))) else plot(win[,1],type='l',main=main, xlab='j', pch=19, ylab='Winsorized Mean(j/n)', ylim=c(ylimmin,ylimmax))
lines(ub,lty=3)
lines(lb,lty=3)
grid()
dev.off()
bitmap(file='test2.png')
lb <- tri[,1] - 2*tri[,2]
ub <- tri[,1] + 2*tri[,2]
if ((ylimmin == '') | (ylimmax == '')) plot(tri[,1],type='b',main=main, xlab='j', pch=19, ylab='Trimmed Mean(j/n)', ylim=c(min(lb),max(ub))) else plot(tri[,1],type='l',main=main, xlab='j', pch=19, ylab='Trimmed Mean(j/n)', ylim=c(ylimmin,ylimmax))
lines(ub,lty=3)
lines(lb,lty=3)
grid()
dev.off()
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Central Tendency - Ungrouped Data',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Measure',header=TRUE)
a<-table.element(a,'Value',header=TRUE)
a<-table.element(a,'S.E.',header=TRUE)
a<-table.element(a,'Value/S.E.',header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('arithmetic_mean.htm', 'Arithmetic Mean', 'click to view the definition of the Arithmetic Mean'),header=TRUE)
a<-table.element(a,arm)
a<-table.element(a,hyperlink('arithmetic_mean_standard_error.htm', armse, 'click to view the definition of the Standard Error of the Arithmetic Mean'))
a<-table.element(a,armose)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('geometric_mean.htm', 'Geometric Mean', 'click to view the definition of the Geometric Mean'),header=TRUE)
a<-table.element(a,geo)
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('harmonic_mean.htm', 'Harmonic Mean', 'click to view the definition of the Harmonic Mean'),header=TRUE)
a<-table.element(a,har)
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('quadratic_mean.htm', 'Quadratic Mean', 'click to view the definition of the Quadratic Mean'),header=TRUE)
a<-table.element(a,qua)
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
for (j in 1:length(win[,1])) {
a<-table.row.start(a)
mylabel <- paste('Winsorized Mean (',j)
mylabel <- paste(mylabel,'/')
mylabel <- paste(mylabel,length(win[,1]))
mylabel <- paste(mylabel,')')
a<-table.element(a,hyperlink('winsorized_mean.htm', mylabel, 'click to view the definition of the Winsorized Mean'),header=TRUE)
a<-table.element(a,win[j,1])
a<-table.element(a,win[j,2])
a<-table.element(a,win[j,1]/win[j,2])
a<-table.row.end(a)
}
for (j in 1:length(tri[,1])) {
a<-table.row.start(a)
mylabel <- paste('Trimmed Mean (',j)
mylabel <- paste(mylabel,'/')
mylabel <- paste(mylabel,length(tri[,1]))
mylabel <- paste(mylabel,')')
a<-table.element(a,hyperlink('arithmetic_mean.htm', mylabel, 'click to view the definition of the Trimmed Mean'),header=TRUE)
a<-table.element(a,tri[j,1])
a<-table.element(a,tri[j,2])
a<-table.element(a,tri[j,1]/tri[j,2])
a<-table.row.end(a)
}
a<-table.row.start(a)
a<-table.element(a,hyperlink('median_1.htm', 'Median', 'click to view the definition of the Median'),header=TRUE)
a<-table.element(a,median(x))
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('midrange.htm', 'Midrange', 'click to view the definition of the Midrange'),header=TRUE)
a<-table.element(a,midr)
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_1.htm','Weighted Average at Xnp',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[1])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_2.htm','Weighted Average at X(n+1)p',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[2])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_3.htm','Empirical Distribution Function',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[3])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_4.htm','Empirical Distribution Function - Averaging',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[4])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_5.htm','Empirical Distribution Function - Interpolation',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[5])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_6.htm','Closest Observation',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[6])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_7.htm','True Basic - Statistics Graphics Toolkit',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[7])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_8.htm','MS Excel (old versions)',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[8])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Number of observations',header=TRUE)
a<-table.element(a,length(x))
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable.tab')