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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 computationSun, 21 Oct 2007 05:34:27 -0700
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2007/Oct/21/ibgum76zlxbiihg1192970011.htm/, Retrieved Thu, 09 May 2024 10:13:14 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=1256, Retrieved Thu, 09 May 2024 10:13:14 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsWS2Q9METAALVERWERKEND
Estimated Impact161
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [WS2Q9METAALVERWER...] [2007-10-21 12:34:27] [e0964b90cb3acfe235da067e79729c23] [Current]
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Dataseries X:
7,322
7,141
6,907
6,834
6,751
6,507
6,785
6,913
6,903
7,067
6,808
7,011
7,506
7,594
7,702
7,656
7,549
7,452
8,126
8,37
8,29
8,492
8,548
9,026
9,513
9,565
9,602
9,846
9,612
9,789
10,583
10,7
10,384
10,486
10,24
10,819
11,38
11,702
11,787
11,676
11,58
11,355
11,991
12,338
11,963
12,317
12,098
12,551
12,551
12,447
12,5
12,326
12,206
12,142
12,66
12,727
12,641
12,61
12,249
12,657
12,221
12,359
12,155
12,509
12,363
12,251
12,742
12,487
12,108
11,463
11,193
11,368




Summary of compuational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'Herman Ole Andreas Wold' @ 193.190.124.10:1001

\begin{tabular}{lllllllll}
\hline
Summary of compuational 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 & 'Herman Ole Andreas Wold' @ 193.190.124.10:1001 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=1256&T=0

[TABLE]
[ROW][C]Summary of compuational 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]'Herman Ole Andreas Wold' @ 193.190.124.10:1001[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=1256&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=1256&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 compuational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'Herman Ole Andreas Wold' @ 193.190.124.10:1001







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean10.2510.25682658727464839.9140918733529
Geometric Mean10.0017634921678
Harmonic Mean9.73702969565045
Quadratic Mean10.4769343613058
Winsorized Mean ( 1 / 24 )10.25418055555560.25612383097705340.0360267782902
Winsorized Mean ( 2 / 24 )10.25326388888890.2556927363607440.099941964809
Winsorized Mean ( 3 / 24 )10.25409722222220.25549360091680940.1344581055126
Winsorized Mean ( 4 / 24 )10.25465277777780.2551025708587340.1981553665195
Winsorized Mean ( 5 / 24 )10.25729166666670.25392203607782440.3954372180717
Winsorized Mean ( 6 / 24 )10.25270833333330.25322493699429940.4885413539037
Winsorized Mean ( 7 / 24 )10.25329166666670.2531164490721340.5081997011771
Winsorized Mean ( 8 / 24 )10.25951388888890.25051660707389940.9534282326539
Winsorized Mean ( 9 / 24 )10.26538888888890.2491022068359341.2095461508703
Winsorized Mean ( 10 / 24 )10.27386111111110.24702693388846541.5900442489799
Winsorized Mean ( 11 / 24 )10.29540277777780.24138844812296942.650768327294
Winsorized Mean ( 12 / 24 )10.30306944444440.23592481787533643.670986110027
Winsorized Mean ( 13 / 24 )10.31209722222220.23418343227680144.034273142062
Winsorized Mean ( 14 / 24 )10.3163750.23227472506063944.4145397107101
Winsorized Mean ( 15 / 24 )10.323250.23039977822290644.8058156983663
Winsorized Mean ( 16 / 24 )10.33502777777780.22786469330610745.3559857291889
Winsorized Mean ( 17 / 24 )10.33030555555560.22417374165396746.0816930624343
Winsorized Mean ( 18 / 24 )10.43580555555560.20701492752615150.4108842790443
Winsorized Mean ( 19 / 24 )10.47169444444440.19936563974121652.5250713113708
Winsorized Mean ( 20 / 24 )10.489750.19544046573199753.6723547025535
Winsorized Mean ( 21 / 24 )10.51045833333330.18819910973520955.8475454433407
Winsorized Mean ( 22 / 24 )10.52359722222220.18513179087360156.8438147363207
Winsorized Mean ( 23 / 24 )10.66543055555560.16134112936871966.1048462799677
Winsorized Mean ( 24 / 24 )10.82443055555560.13840750433419778.2069628928432
Trimmed Mean ( 1 / 24 )10.26890.25616293594420140.0873762714714
Trimmed Mean ( 2 / 24 )10.28448529411760.25596807452640440.1787813310162
Trimmed Mean ( 3 / 24 )10.30151515151520.25574924913809040.2797473941084
Trimmed Mean ( 4 / 24 )10.3192968750.25531344888662840.4181484367566
Trimmed Mean ( 5 / 24 )10.33806451612900.25465850555829140.5957951157561
Trimmed Mean ( 6 / 24 )10.357450.25394202975758340.7866709181122
Trimmed Mean ( 7 / 24 )10.37912068965520.25295465028016041.0315472680963
Trimmed Mean ( 8 / 24 )10.40223214285710.25147418213390541.3650103346122
Trimmed Mean ( 9 / 24 )10.42601851851850.24995279427243641.711950245912
Trimmed Mean ( 10 / 24 )10.45073076923080.24806285255968642.1293662529186
Trimmed Mean ( 11 / 24 )10.47620.24582900146073842.6158017880294
Trimmed Mean ( 12 / 24 )10.50085416666670.24389345567534643.0550878767517
Trimmed Mean ( 13 / 24 )10.52665217391300.24217435970782543.4672447843491
Trimmed Mean ( 14 / 24 )10.55365909090910.23989988649950543.9919303210294
Trimmed Mean ( 15 / 24 )10.58271428571430.23689948785706344.671748265237
Trimmed Mean ( 16 / 24 )10.613850.23291733856148245.5691708721732
Trimmed Mean ( 17 / 24 )10.64686842105260.22776627975833946.7447087968816
Trimmed Mean ( 18 / 24 )10.68411111111110.22118783505750348.3033395952067
Trimmed Mean ( 19 / 24 )10.71332352941180.21656549696385649.4692076051237
Trimmed Mean ( 20 / 24 )10.74193750.21168178309279950.7456869601805
Trimmed Mean ( 21 / 24 )10.77220.20525751361777752.4813918386424
Trimmed Mean ( 22 / 24 )10.804250.19758279106591554.6821407963391
Trimmed Mean ( 23 / 24 )10.83957692307690.18646825403621358.130950917639
Trimmed Mean ( 24 / 24 )10.86229166666670.17901919255020860.6766878563604
Median11.006
Midrange9.6245
Midmean - Weighted Average at Xnp10.6035135135135
Midmean - Weighted Average at X(n+1)p10.6841111111111
Midmean - Empirical Distribution Function10.6035135135135
Midmean - Empirical Distribution Function - Averaging10.6841111111111
Midmean - Empirical Distribution Function - Interpolation10.6841111111111
Midmean - Closest Observation10.6035135135135
Midmean - True Basic - Statistics Graphics Toolkit10.6841111111111
Midmean - MS Excel (old versions)10.6468684210526
Number of observations72

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 10.251 & 0.256826587274648 & 39.9140918733529 \tabularnewline
Geometric Mean & 10.0017634921678 &  &  \tabularnewline
Harmonic Mean & 9.73702969565045 &  &  \tabularnewline
Quadratic Mean & 10.4769343613058 &  &  \tabularnewline
Winsorized Mean ( 1 / 24 ) & 10.2541805555556 & 0.256123830977053 & 40.0360267782902 \tabularnewline
Winsorized Mean ( 2 / 24 ) & 10.2532638888889 & 0.25569273636074 & 40.099941964809 \tabularnewline
Winsorized Mean ( 3 / 24 ) & 10.2540972222222 & 0.255493600916809 & 40.1344581055126 \tabularnewline
Winsorized Mean ( 4 / 24 ) & 10.2546527777778 & 0.25510257085873 & 40.1981553665195 \tabularnewline
Winsorized Mean ( 5 / 24 ) & 10.2572916666667 & 0.253922036077824 & 40.3954372180717 \tabularnewline
Winsorized Mean ( 6 / 24 ) & 10.2527083333333 & 0.253224936994299 & 40.4885413539037 \tabularnewline
Winsorized Mean ( 7 / 24 ) & 10.2532916666667 & 0.25311644907213 & 40.5081997011771 \tabularnewline
Winsorized Mean ( 8 / 24 ) & 10.2595138888889 & 0.250516607073899 & 40.9534282326539 \tabularnewline
Winsorized Mean ( 9 / 24 ) & 10.2653888888889 & 0.24910220683593 & 41.2095461508703 \tabularnewline
Winsorized Mean ( 10 / 24 ) & 10.2738611111111 & 0.247026933888465 & 41.5900442489799 \tabularnewline
Winsorized Mean ( 11 / 24 ) & 10.2954027777778 & 0.241388448122969 & 42.650768327294 \tabularnewline
Winsorized Mean ( 12 / 24 ) & 10.3030694444444 & 0.235924817875336 & 43.670986110027 \tabularnewline
Winsorized Mean ( 13 / 24 ) & 10.3120972222222 & 0.234183432276801 & 44.034273142062 \tabularnewline
Winsorized Mean ( 14 / 24 ) & 10.316375 & 0.232274725060639 & 44.4145397107101 \tabularnewline
Winsorized Mean ( 15 / 24 ) & 10.32325 & 0.230399778222906 & 44.8058156983663 \tabularnewline
Winsorized Mean ( 16 / 24 ) & 10.3350277777778 & 0.227864693306107 & 45.3559857291889 \tabularnewline
Winsorized Mean ( 17 / 24 ) & 10.3303055555556 & 0.224173741653967 & 46.0816930624343 \tabularnewline
Winsorized Mean ( 18 / 24 ) & 10.4358055555556 & 0.207014927526151 & 50.4108842790443 \tabularnewline
Winsorized Mean ( 19 / 24 ) & 10.4716944444444 & 0.199365639741216 & 52.5250713113708 \tabularnewline
Winsorized Mean ( 20 / 24 ) & 10.48975 & 0.195440465731997 & 53.6723547025535 \tabularnewline
Winsorized Mean ( 21 / 24 ) & 10.5104583333333 & 0.188199109735209 & 55.8475454433407 \tabularnewline
Winsorized Mean ( 22 / 24 ) & 10.5235972222222 & 0.185131790873601 & 56.8438147363207 \tabularnewline
Winsorized Mean ( 23 / 24 ) & 10.6654305555556 & 0.161341129368719 & 66.1048462799677 \tabularnewline
Winsorized Mean ( 24 / 24 ) & 10.8244305555556 & 0.138407504334197 & 78.2069628928432 \tabularnewline
Trimmed Mean ( 1 / 24 ) & 10.2689 & 0.256162935944201 & 40.0873762714714 \tabularnewline
Trimmed Mean ( 2 / 24 ) & 10.2844852941176 & 0.255968074526404 & 40.1787813310162 \tabularnewline
Trimmed Mean ( 3 / 24 ) & 10.3015151515152 & 0.255749249138090 & 40.2797473941084 \tabularnewline
Trimmed Mean ( 4 / 24 ) & 10.319296875 & 0.255313448886628 & 40.4181484367566 \tabularnewline
Trimmed Mean ( 5 / 24 ) & 10.3380645161290 & 0.254658505558291 & 40.5957951157561 \tabularnewline
Trimmed Mean ( 6 / 24 ) & 10.35745 & 0.253942029757583 & 40.7866709181122 \tabularnewline
Trimmed Mean ( 7 / 24 ) & 10.3791206896552 & 0.252954650280160 & 41.0315472680963 \tabularnewline
Trimmed Mean ( 8 / 24 ) & 10.4022321428571 & 0.251474182133905 & 41.3650103346122 \tabularnewline
Trimmed Mean ( 9 / 24 ) & 10.4260185185185 & 0.249952794272436 & 41.711950245912 \tabularnewline
Trimmed Mean ( 10 / 24 ) & 10.4507307692308 & 0.248062852559686 & 42.1293662529186 \tabularnewline
Trimmed Mean ( 11 / 24 ) & 10.4762 & 0.245829001460738 & 42.6158017880294 \tabularnewline
Trimmed Mean ( 12 / 24 ) & 10.5008541666667 & 0.243893455675346 & 43.0550878767517 \tabularnewline
Trimmed Mean ( 13 / 24 ) & 10.5266521739130 & 0.242174359707825 & 43.4672447843491 \tabularnewline
Trimmed Mean ( 14 / 24 ) & 10.5536590909091 & 0.239899886499505 & 43.9919303210294 \tabularnewline
Trimmed Mean ( 15 / 24 ) & 10.5827142857143 & 0.236899487857063 & 44.671748265237 \tabularnewline
Trimmed Mean ( 16 / 24 ) & 10.61385 & 0.232917338561482 & 45.5691708721732 \tabularnewline
Trimmed Mean ( 17 / 24 ) & 10.6468684210526 & 0.227766279758339 & 46.7447087968816 \tabularnewline
Trimmed Mean ( 18 / 24 ) & 10.6841111111111 & 0.221187835057503 & 48.3033395952067 \tabularnewline
Trimmed Mean ( 19 / 24 ) & 10.7133235294118 & 0.216565496963856 & 49.4692076051237 \tabularnewline
Trimmed Mean ( 20 / 24 ) & 10.7419375 & 0.211681783092799 & 50.7456869601805 \tabularnewline
Trimmed Mean ( 21 / 24 ) & 10.7722 & 0.205257513617777 & 52.4813918386424 \tabularnewline
Trimmed Mean ( 22 / 24 ) & 10.80425 & 0.197582791065915 & 54.6821407963391 \tabularnewline
Trimmed Mean ( 23 / 24 ) & 10.8395769230769 & 0.186468254036213 & 58.130950917639 \tabularnewline
Trimmed Mean ( 24 / 24 ) & 10.8622916666667 & 0.179019192550208 & 60.6766878563604 \tabularnewline
Median & 11.006 &  &  \tabularnewline
Midrange & 9.6245 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 10.6035135135135 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 10.6841111111111 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 10.6035135135135 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 10.6841111111111 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 10.6841111111111 &  &  \tabularnewline
Midmean - Closest Observation & 10.6035135135135 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 10.6841111111111 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 10.6468684210526 &  &  \tabularnewline
Number of observations & 72 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=1256&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]10.251[/C][C]0.256826587274648[/C][C]39.9140918733529[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]10.0017634921678[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]9.73702969565045[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]10.4769343613058[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 24 )[/C][C]10.2541805555556[/C][C]0.256123830977053[/C][C]40.0360267782902[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 24 )[/C][C]10.2532638888889[/C][C]0.25569273636074[/C][C]40.099941964809[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 24 )[/C][C]10.2540972222222[/C][C]0.255493600916809[/C][C]40.1344581055126[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 24 )[/C][C]10.2546527777778[/C][C]0.25510257085873[/C][C]40.1981553665195[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 24 )[/C][C]10.2572916666667[/C][C]0.253922036077824[/C][C]40.3954372180717[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 24 )[/C][C]10.2527083333333[/C][C]0.253224936994299[/C][C]40.4885413539037[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 24 )[/C][C]10.2532916666667[/C][C]0.25311644907213[/C][C]40.5081997011771[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 24 )[/C][C]10.2595138888889[/C][C]0.250516607073899[/C][C]40.9534282326539[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 24 )[/C][C]10.2653888888889[/C][C]0.24910220683593[/C][C]41.2095461508703[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 24 )[/C][C]10.2738611111111[/C][C]0.247026933888465[/C][C]41.5900442489799[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 24 )[/C][C]10.2954027777778[/C][C]0.241388448122969[/C][C]42.650768327294[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 24 )[/C][C]10.3030694444444[/C][C]0.235924817875336[/C][C]43.670986110027[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 24 )[/C][C]10.3120972222222[/C][C]0.234183432276801[/C][C]44.034273142062[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 24 )[/C][C]10.316375[/C][C]0.232274725060639[/C][C]44.4145397107101[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 24 )[/C][C]10.32325[/C][C]0.230399778222906[/C][C]44.8058156983663[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 24 )[/C][C]10.3350277777778[/C][C]0.227864693306107[/C][C]45.3559857291889[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 24 )[/C][C]10.3303055555556[/C][C]0.224173741653967[/C][C]46.0816930624343[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 24 )[/C][C]10.4358055555556[/C][C]0.207014927526151[/C][C]50.4108842790443[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 24 )[/C][C]10.4716944444444[/C][C]0.199365639741216[/C][C]52.5250713113708[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 24 )[/C][C]10.48975[/C][C]0.195440465731997[/C][C]53.6723547025535[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 24 )[/C][C]10.5104583333333[/C][C]0.188199109735209[/C][C]55.8475454433407[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 24 )[/C][C]10.5235972222222[/C][C]0.185131790873601[/C][C]56.8438147363207[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 24 )[/C][C]10.6654305555556[/C][C]0.161341129368719[/C][C]66.1048462799677[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 24 )[/C][C]10.8244305555556[/C][C]0.138407504334197[/C][C]78.2069628928432[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 24 )[/C][C]10.2689[/C][C]0.256162935944201[/C][C]40.0873762714714[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 24 )[/C][C]10.2844852941176[/C][C]0.255968074526404[/C][C]40.1787813310162[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 24 )[/C][C]10.3015151515152[/C][C]0.255749249138090[/C][C]40.2797473941084[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 24 )[/C][C]10.319296875[/C][C]0.255313448886628[/C][C]40.4181484367566[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 24 )[/C][C]10.3380645161290[/C][C]0.254658505558291[/C][C]40.5957951157561[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 24 )[/C][C]10.35745[/C][C]0.253942029757583[/C][C]40.7866709181122[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 24 )[/C][C]10.3791206896552[/C][C]0.252954650280160[/C][C]41.0315472680963[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 24 )[/C][C]10.4022321428571[/C][C]0.251474182133905[/C][C]41.3650103346122[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 24 )[/C][C]10.4260185185185[/C][C]0.249952794272436[/C][C]41.711950245912[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 24 )[/C][C]10.4507307692308[/C][C]0.248062852559686[/C][C]42.1293662529186[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 24 )[/C][C]10.4762[/C][C]0.245829001460738[/C][C]42.6158017880294[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 24 )[/C][C]10.5008541666667[/C][C]0.243893455675346[/C][C]43.0550878767517[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 24 )[/C][C]10.5266521739130[/C][C]0.242174359707825[/C][C]43.4672447843491[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 24 )[/C][C]10.5536590909091[/C][C]0.239899886499505[/C][C]43.9919303210294[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 24 )[/C][C]10.5827142857143[/C][C]0.236899487857063[/C][C]44.671748265237[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 24 )[/C][C]10.61385[/C][C]0.232917338561482[/C][C]45.5691708721732[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 24 )[/C][C]10.6468684210526[/C][C]0.227766279758339[/C][C]46.7447087968816[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 24 )[/C][C]10.6841111111111[/C][C]0.221187835057503[/C][C]48.3033395952067[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 24 )[/C][C]10.7133235294118[/C][C]0.216565496963856[/C][C]49.4692076051237[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 24 )[/C][C]10.7419375[/C][C]0.211681783092799[/C][C]50.7456869601805[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 24 )[/C][C]10.7722[/C][C]0.205257513617777[/C][C]52.4813918386424[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 24 )[/C][C]10.80425[/C][C]0.197582791065915[/C][C]54.6821407963391[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 24 )[/C][C]10.8395769230769[/C][C]0.186468254036213[/C][C]58.130950917639[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 24 )[/C][C]10.8622916666667[/C][C]0.179019192550208[/C][C]60.6766878563604[/C][/ROW]
[ROW][C]Median[/C][C]11.006[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]9.6245[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]10.6035135135135[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]10.6841111111111[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]10.6035135135135[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]10.6841111111111[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]10.6841111111111[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]10.6035135135135[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]10.6841111111111[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]10.6468684210526[/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=1256&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=1256&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 Mean10.2510.25682658727464839.9140918733529
Geometric Mean10.0017634921678
Harmonic Mean9.73702969565045
Quadratic Mean10.4769343613058
Winsorized Mean ( 1 / 24 )10.25418055555560.25612383097705340.0360267782902
Winsorized Mean ( 2 / 24 )10.25326388888890.2556927363607440.099941964809
Winsorized Mean ( 3 / 24 )10.25409722222220.25549360091680940.1344581055126
Winsorized Mean ( 4 / 24 )10.25465277777780.2551025708587340.1981553665195
Winsorized Mean ( 5 / 24 )10.25729166666670.25392203607782440.3954372180717
Winsorized Mean ( 6 / 24 )10.25270833333330.25322493699429940.4885413539037
Winsorized Mean ( 7 / 24 )10.25329166666670.2531164490721340.5081997011771
Winsorized Mean ( 8 / 24 )10.25951388888890.25051660707389940.9534282326539
Winsorized Mean ( 9 / 24 )10.26538888888890.2491022068359341.2095461508703
Winsorized Mean ( 10 / 24 )10.27386111111110.24702693388846541.5900442489799
Winsorized Mean ( 11 / 24 )10.29540277777780.24138844812296942.650768327294
Winsorized Mean ( 12 / 24 )10.30306944444440.23592481787533643.670986110027
Winsorized Mean ( 13 / 24 )10.31209722222220.23418343227680144.034273142062
Winsorized Mean ( 14 / 24 )10.3163750.23227472506063944.4145397107101
Winsorized Mean ( 15 / 24 )10.323250.23039977822290644.8058156983663
Winsorized Mean ( 16 / 24 )10.33502777777780.22786469330610745.3559857291889
Winsorized Mean ( 17 / 24 )10.33030555555560.22417374165396746.0816930624343
Winsorized Mean ( 18 / 24 )10.43580555555560.20701492752615150.4108842790443
Winsorized Mean ( 19 / 24 )10.47169444444440.19936563974121652.5250713113708
Winsorized Mean ( 20 / 24 )10.489750.19544046573199753.6723547025535
Winsorized Mean ( 21 / 24 )10.51045833333330.18819910973520955.8475454433407
Winsorized Mean ( 22 / 24 )10.52359722222220.18513179087360156.8438147363207
Winsorized Mean ( 23 / 24 )10.66543055555560.16134112936871966.1048462799677
Winsorized Mean ( 24 / 24 )10.82443055555560.13840750433419778.2069628928432
Trimmed Mean ( 1 / 24 )10.26890.25616293594420140.0873762714714
Trimmed Mean ( 2 / 24 )10.28448529411760.25596807452640440.1787813310162
Trimmed Mean ( 3 / 24 )10.30151515151520.25574924913809040.2797473941084
Trimmed Mean ( 4 / 24 )10.3192968750.25531344888662840.4181484367566
Trimmed Mean ( 5 / 24 )10.33806451612900.25465850555829140.5957951157561
Trimmed Mean ( 6 / 24 )10.357450.25394202975758340.7866709181122
Trimmed Mean ( 7 / 24 )10.37912068965520.25295465028016041.0315472680963
Trimmed Mean ( 8 / 24 )10.40223214285710.25147418213390541.3650103346122
Trimmed Mean ( 9 / 24 )10.42601851851850.24995279427243641.711950245912
Trimmed Mean ( 10 / 24 )10.45073076923080.24806285255968642.1293662529186
Trimmed Mean ( 11 / 24 )10.47620.24582900146073842.6158017880294
Trimmed Mean ( 12 / 24 )10.50085416666670.24389345567534643.0550878767517
Trimmed Mean ( 13 / 24 )10.52665217391300.24217435970782543.4672447843491
Trimmed Mean ( 14 / 24 )10.55365909090910.23989988649950543.9919303210294
Trimmed Mean ( 15 / 24 )10.58271428571430.23689948785706344.671748265237
Trimmed Mean ( 16 / 24 )10.613850.23291733856148245.5691708721732
Trimmed Mean ( 17 / 24 )10.64686842105260.22776627975833946.7447087968816
Trimmed Mean ( 18 / 24 )10.68411111111110.22118783505750348.3033395952067
Trimmed Mean ( 19 / 24 )10.71332352941180.21656549696385649.4692076051237
Trimmed Mean ( 20 / 24 )10.74193750.21168178309279950.7456869601805
Trimmed Mean ( 21 / 24 )10.77220.20525751361777752.4813918386424
Trimmed Mean ( 22 / 24 )10.804250.19758279106591554.6821407963391
Trimmed Mean ( 23 / 24 )10.83957692307690.18646825403621358.130950917639
Trimmed Mean ( 24 / 24 )10.86229166666670.17901919255020860.6766878563604
Median11.006
Midrange9.6245
Midmean - Weighted Average at Xnp10.6035135135135
Midmean - Weighted Average at X(n+1)p10.6841111111111
Midmean - Empirical Distribution Function10.6035135135135
Midmean - Empirical Distribution Function - Averaging10.6841111111111
Midmean - Empirical Distribution Function - Interpolation10.6841111111111
Midmean - Closest Observation10.6035135135135
Midmean - True Basic - Statistics Graphics Toolkit10.6841111111111
Midmean - MS Excel (old versions)10.6468684210526
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')