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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, 06 Jun 2010 10:24:46 +0000
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2010/Jun/06/t1275819892ruf9pnztbh519is.htm/, Retrieved Sat, 27 Apr 2024 18:29:09 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=77644, Retrieved Sat, 27 Apr 2024 18:29:09 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact169
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [] [2010-06-06 10:24:46] [d41d8cd98f00b204e9800998ecf8427e] [Current]
-    D    [Central Tendency] [] [2010-06-06 23:08:34] [df79fc70699bb35257862e03e3412eb1]
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Dataseries X:
10.383
10.431
10.574
10.653
10.805
10.872
10.625
10.407
10.463
10.556
10.646
10.702
11.353
11.346
11.451
11.964
12.574
13.031
13.812
14.544
14.931
14.886
16.005
17.064
15.168
16.050
15.839
15.137
14.954
15.648
15.305
15.579
16.348
15.928
16.171
15.937
15.713
15.594
15.683
16.438
17.032
17.696
17.745
19.394
20.148
20.108
18.584
18.441
18.391
19.178
18.079
18.483
19.644
19.195
19.650
20.830
23.595
22.937
21.814
21.928
21.777
21.383
21.467
22.052
22.680
24.320
24.977
25.204
25.739
26.434
27.525
30.695




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time9 seconds
R Server'George Udny Yule' @ 72.249.76.132

\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 & 9 seconds \tabularnewline
R Server & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=77644&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]9 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'George Udny Yule' @ 72.249.76.132[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=77644&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=77644&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 time9 seconds
R Server'George Udny Yule' @ 72.249.76.132







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean17.06520833333330.571826816470729.8433159162757
Geometric Mean16.3963647274193
Harmonic Mean15.746636233899
Quadratic Mean17.7323809718423
Winsorized Mean ( 1 / 24 )17.02151388888890.55853218902657430.4754394165795
Winsorized Mean ( 2 / 24 )16.9918750.55074579679095430.8524823957024
Winsorized Mean ( 3 / 24 )16.964250.54373305011985931.1995932494088
Winsorized Mean ( 4 / 24 )16.93969444444440.53626024934078431.5885700371567
Winsorized Mean ( 5 / 24 )16.92518055555560.53266146439549431.7747419080965
Winsorized Mean ( 6 / 24 )16.87468055555560.52059936635100332.4139475501746
Winsorized Mean ( 7 / 24 )16.80623611111110.50649361639411333.1815358913306
Winsorized Mean ( 8 / 24 )16.73390277777780.4929741635056433.9447865964812
Winsorized Mean ( 9 / 24 )16.70790277777780.48628384645900534.3583339225444
Winsorized Mean ( 10 / 24 )16.63498611111110.46914378086638735.4581831616538
Winsorized Mean ( 11 / 24 )16.62627777777780.46429060946781335.8100668821095
Winsorized Mean ( 12 / 24 )16.68627777777780.44769425462791937.2715923988032
Winsorized Mean ( 13 / 24 )16.68086111111110.44640592790302737.367024200303
Winsorized Mean ( 14 / 24 )16.63963888888890.43362526249390638.3733152288901
Winsorized Mean ( 15 / 24 )16.72901388888890.41317171395967540.4892525883842
Winsorized Mean ( 16 / 24 )16.74168055555560.37218923810584744.981635258337
Winsorized Mean ( 17 / 24 )16.68855555555560.33092909110081450.429400147452
Winsorized Mean ( 18 / 24 )16.87380555555560.30015505033326856.2169636553515
Winsorized Mean ( 19 / 24 )16.94611111111110.25518501799643766.4071552639024
Winsorized Mean ( 20 / 24 )17.03944444444440.24269182182155370.2102127568734
Winsorized Mean ( 21 / 24 )16.97965277777780.23014807113634273.777080528817
Winsorized Mean ( 22 / 24 )16.9258750.22036145255489976.8095998812826
Winsorized Mean ( 23 / 24 )16.97890277777780.21231417831336779.9706496883952
Winsorized Mean ( 24 / 24 )16.79123611111110.18286815449932991.8215429968301
Trimmed Mean ( 1 / 24 )16.96595714285710.54610218233876531.0673674113476
Trimmed Mean ( 2 / 24 )16.90713235294120.53122241038906331.8268431871286
Trimmed Mean ( 3 / 24 )16.86090909090910.51839094683995832.5254698093995
Trimmed Mean ( 4 / 24 )16.822156250.50616200549127733.2347273550739
Trimmed Mean ( 5 / 24 )16.78803225806450.49412360867424233.9753696511438
Trimmed Mean ( 6 / 24 )16.75511666666670.48060334379099834.8626718543037
Trimmed Mean ( 7 / 24 )16.73037931034480.46759039475824035.7799892767151
Trimmed Mean ( 8 / 24 )16.71644642857140.4553694268205636.7096371517243
Trimmed Mean ( 9 / 24 )16.71353703703700.44360969437723837.6762213470117
Trimmed Mean ( 10 / 24 )16.71440384615380.43049062933519438.8264057500296
Trimmed Mean ( 11 / 24 )16.725840.41799174912274740.0147611408671
Trimmed Mean ( 12 / 24 )16.73941666666670.40317783639486841.5186926353567
Trimmed Mean ( 13 / 24 )16.74634782608700.38815530063121343.143421715108
Trimmed Mean ( 14 / 24 )16.75459090909090.36889995652777845.4177090905385
Trimmed Mean ( 15 / 24 )16.76866666666670.34682376890059048.3492429593921
Trimmed Mean ( 16 / 24 )16.7734250.32300268294412451.9296770141739
Trimmed Mean ( 17 / 24 )16.77718421052630.30250781553042455.4603330863001
Trimmed Mean ( 18 / 24 )16.78761111111110.28627912142095258.6407106036427
Trimmed Mean ( 19 / 24 )16.77747058823530.27260786916428661.5443370716654
Trimmed Mean ( 20 / 24 )16.75750.26588430512100163.0255328247896
Trimmed Mean ( 21 / 24 )16.72366666666670.25877734775055664.625697774703
Trimmed Mean ( 22 / 24 )16.69232142857140.2516830334926766.3227917946148
Trimmed Mean ( 23 / 24 )16.66292307692310.24362864504485268.394761518521
Trimmed Mean ( 24 / 24 )16.62170833333330.23268235391423171.4351907384443
Median16.1105
Midrange20.539
Midmean - Weighted Average at Xnp16.6860810810811
Midmean - Weighted Average at X(n+1)p16.7876111111111
Midmean - Empirical Distribution Function16.6860810810811
Midmean - Empirical Distribution Function - Averaging16.7876111111111
Midmean - Empirical Distribution Function - Interpolation16.7876111111111
Midmean - Closest Observation16.6860810810811
Midmean - True Basic - Statistics Graphics Toolkit16.7876111111111
Midmean - MS Excel (old versions)16.7771842105263
Number of observations72

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 17.0652083333333 & 0.5718268164707 & 29.8433159162757 \tabularnewline
Geometric Mean & 16.3963647274193 &  &  \tabularnewline
Harmonic Mean & 15.746636233899 &  &  \tabularnewline
Quadratic Mean & 17.7323809718423 &  &  \tabularnewline
Winsorized Mean ( 1 / 24 ) & 17.0215138888889 & 0.558532189026574 & 30.4754394165795 \tabularnewline
Winsorized Mean ( 2 / 24 ) & 16.991875 & 0.550745796790954 & 30.8524823957024 \tabularnewline
Winsorized Mean ( 3 / 24 ) & 16.96425 & 0.543733050119859 & 31.1995932494088 \tabularnewline
Winsorized Mean ( 4 / 24 ) & 16.9396944444444 & 0.536260249340784 & 31.5885700371567 \tabularnewline
Winsorized Mean ( 5 / 24 ) & 16.9251805555556 & 0.532661464395494 & 31.7747419080965 \tabularnewline
Winsorized Mean ( 6 / 24 ) & 16.8746805555556 & 0.520599366351003 & 32.4139475501746 \tabularnewline
Winsorized Mean ( 7 / 24 ) & 16.8062361111111 & 0.506493616394113 & 33.1815358913306 \tabularnewline
Winsorized Mean ( 8 / 24 ) & 16.7339027777778 & 0.49297416350564 & 33.9447865964812 \tabularnewline
Winsorized Mean ( 9 / 24 ) & 16.7079027777778 & 0.486283846459005 & 34.3583339225444 \tabularnewline
Winsorized Mean ( 10 / 24 ) & 16.6349861111111 & 0.469143780866387 & 35.4581831616538 \tabularnewline
Winsorized Mean ( 11 / 24 ) & 16.6262777777778 & 0.464290609467813 & 35.8100668821095 \tabularnewline
Winsorized Mean ( 12 / 24 ) & 16.6862777777778 & 0.447694254627919 & 37.2715923988032 \tabularnewline
Winsorized Mean ( 13 / 24 ) & 16.6808611111111 & 0.446405927903027 & 37.367024200303 \tabularnewline
Winsorized Mean ( 14 / 24 ) & 16.6396388888889 & 0.433625262493906 & 38.3733152288901 \tabularnewline
Winsorized Mean ( 15 / 24 ) & 16.7290138888889 & 0.413171713959675 & 40.4892525883842 \tabularnewline
Winsorized Mean ( 16 / 24 ) & 16.7416805555556 & 0.372189238105847 & 44.981635258337 \tabularnewline
Winsorized Mean ( 17 / 24 ) & 16.6885555555556 & 0.330929091100814 & 50.429400147452 \tabularnewline
Winsorized Mean ( 18 / 24 ) & 16.8738055555556 & 0.300155050333268 & 56.2169636553515 \tabularnewline
Winsorized Mean ( 19 / 24 ) & 16.9461111111111 & 0.255185017996437 & 66.4071552639024 \tabularnewline
Winsorized Mean ( 20 / 24 ) & 17.0394444444444 & 0.242691821821553 & 70.2102127568734 \tabularnewline
Winsorized Mean ( 21 / 24 ) & 16.9796527777778 & 0.230148071136342 & 73.777080528817 \tabularnewline
Winsorized Mean ( 22 / 24 ) & 16.925875 & 0.220361452554899 & 76.8095998812826 \tabularnewline
Winsorized Mean ( 23 / 24 ) & 16.9789027777778 & 0.212314178313367 & 79.9706496883952 \tabularnewline
Winsorized Mean ( 24 / 24 ) & 16.7912361111111 & 0.182868154499329 & 91.8215429968301 \tabularnewline
Trimmed Mean ( 1 / 24 ) & 16.9659571428571 & 0.546102182338765 & 31.0673674113476 \tabularnewline
Trimmed Mean ( 2 / 24 ) & 16.9071323529412 & 0.531222410389063 & 31.8268431871286 \tabularnewline
Trimmed Mean ( 3 / 24 ) & 16.8609090909091 & 0.518390946839958 & 32.5254698093995 \tabularnewline
Trimmed Mean ( 4 / 24 ) & 16.82215625 & 0.506162005491277 & 33.2347273550739 \tabularnewline
Trimmed Mean ( 5 / 24 ) & 16.7880322580645 & 0.494123608674242 & 33.9753696511438 \tabularnewline
Trimmed Mean ( 6 / 24 ) & 16.7551166666667 & 0.480603343790998 & 34.8626718543037 \tabularnewline
Trimmed Mean ( 7 / 24 ) & 16.7303793103448 & 0.467590394758240 & 35.7799892767151 \tabularnewline
Trimmed Mean ( 8 / 24 ) & 16.7164464285714 & 0.45536942682056 & 36.7096371517243 \tabularnewline
Trimmed Mean ( 9 / 24 ) & 16.7135370370370 & 0.443609694377238 & 37.6762213470117 \tabularnewline
Trimmed Mean ( 10 / 24 ) & 16.7144038461538 & 0.430490629335194 & 38.8264057500296 \tabularnewline
Trimmed Mean ( 11 / 24 ) & 16.72584 & 0.417991749122747 & 40.0147611408671 \tabularnewline
Trimmed Mean ( 12 / 24 ) & 16.7394166666667 & 0.403177836394868 & 41.5186926353567 \tabularnewline
Trimmed Mean ( 13 / 24 ) & 16.7463478260870 & 0.388155300631213 & 43.143421715108 \tabularnewline
Trimmed Mean ( 14 / 24 ) & 16.7545909090909 & 0.368899956527778 & 45.4177090905385 \tabularnewline
Trimmed Mean ( 15 / 24 ) & 16.7686666666667 & 0.346823768900590 & 48.3492429593921 \tabularnewline
Trimmed Mean ( 16 / 24 ) & 16.773425 & 0.323002682944124 & 51.9296770141739 \tabularnewline
Trimmed Mean ( 17 / 24 ) & 16.7771842105263 & 0.302507815530424 & 55.4603330863001 \tabularnewline
Trimmed Mean ( 18 / 24 ) & 16.7876111111111 & 0.286279121420952 & 58.6407106036427 \tabularnewline
Trimmed Mean ( 19 / 24 ) & 16.7774705882353 & 0.272607869164286 & 61.5443370716654 \tabularnewline
Trimmed Mean ( 20 / 24 ) & 16.7575 & 0.265884305121001 & 63.0255328247896 \tabularnewline
Trimmed Mean ( 21 / 24 ) & 16.7236666666667 & 0.258777347750556 & 64.625697774703 \tabularnewline
Trimmed Mean ( 22 / 24 ) & 16.6923214285714 & 0.25168303349267 & 66.3227917946148 \tabularnewline
Trimmed Mean ( 23 / 24 ) & 16.6629230769231 & 0.243628645044852 & 68.394761518521 \tabularnewline
Trimmed Mean ( 24 / 24 ) & 16.6217083333333 & 0.232682353914231 & 71.4351907384443 \tabularnewline
Median & 16.1105 &  &  \tabularnewline
Midrange & 20.539 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 16.6860810810811 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 16.7876111111111 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 16.6860810810811 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 16.7876111111111 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 16.7876111111111 &  &  \tabularnewline
Midmean - Closest Observation & 16.6860810810811 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 16.7876111111111 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 16.7771842105263 &  &  \tabularnewline
Number of observations & 72 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=77644&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]17.0652083333333[/C][C]0.5718268164707[/C][C]29.8433159162757[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]16.3963647274193[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]15.746636233899[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]17.7323809718423[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 24 )[/C][C]17.0215138888889[/C][C]0.558532189026574[/C][C]30.4754394165795[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 24 )[/C][C]16.991875[/C][C]0.550745796790954[/C][C]30.8524823957024[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 24 )[/C][C]16.96425[/C][C]0.543733050119859[/C][C]31.1995932494088[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 24 )[/C][C]16.9396944444444[/C][C]0.536260249340784[/C][C]31.5885700371567[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 24 )[/C][C]16.9251805555556[/C][C]0.532661464395494[/C][C]31.7747419080965[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 24 )[/C][C]16.8746805555556[/C][C]0.520599366351003[/C][C]32.4139475501746[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 24 )[/C][C]16.8062361111111[/C][C]0.506493616394113[/C][C]33.1815358913306[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 24 )[/C][C]16.7339027777778[/C][C]0.49297416350564[/C][C]33.9447865964812[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 24 )[/C][C]16.7079027777778[/C][C]0.486283846459005[/C][C]34.3583339225444[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 24 )[/C][C]16.6349861111111[/C][C]0.469143780866387[/C][C]35.4581831616538[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 24 )[/C][C]16.6262777777778[/C][C]0.464290609467813[/C][C]35.8100668821095[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 24 )[/C][C]16.6862777777778[/C][C]0.447694254627919[/C][C]37.2715923988032[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 24 )[/C][C]16.6808611111111[/C][C]0.446405927903027[/C][C]37.367024200303[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 24 )[/C][C]16.6396388888889[/C][C]0.433625262493906[/C][C]38.3733152288901[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 24 )[/C][C]16.7290138888889[/C][C]0.413171713959675[/C][C]40.4892525883842[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 24 )[/C][C]16.7416805555556[/C][C]0.372189238105847[/C][C]44.981635258337[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 24 )[/C][C]16.6885555555556[/C][C]0.330929091100814[/C][C]50.429400147452[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 24 )[/C][C]16.8738055555556[/C][C]0.300155050333268[/C][C]56.2169636553515[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 24 )[/C][C]16.9461111111111[/C][C]0.255185017996437[/C][C]66.4071552639024[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 24 )[/C][C]17.0394444444444[/C][C]0.242691821821553[/C][C]70.2102127568734[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 24 )[/C][C]16.9796527777778[/C][C]0.230148071136342[/C][C]73.777080528817[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 24 )[/C][C]16.925875[/C][C]0.220361452554899[/C][C]76.8095998812826[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 24 )[/C][C]16.9789027777778[/C][C]0.212314178313367[/C][C]79.9706496883952[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 24 )[/C][C]16.7912361111111[/C][C]0.182868154499329[/C][C]91.8215429968301[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 24 )[/C][C]16.9659571428571[/C][C]0.546102182338765[/C][C]31.0673674113476[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 24 )[/C][C]16.9071323529412[/C][C]0.531222410389063[/C][C]31.8268431871286[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 24 )[/C][C]16.8609090909091[/C][C]0.518390946839958[/C][C]32.5254698093995[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 24 )[/C][C]16.82215625[/C][C]0.506162005491277[/C][C]33.2347273550739[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 24 )[/C][C]16.7880322580645[/C][C]0.494123608674242[/C][C]33.9753696511438[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 24 )[/C][C]16.7551166666667[/C][C]0.480603343790998[/C][C]34.8626718543037[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 24 )[/C][C]16.7303793103448[/C][C]0.467590394758240[/C][C]35.7799892767151[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 24 )[/C][C]16.7164464285714[/C][C]0.45536942682056[/C][C]36.7096371517243[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 24 )[/C][C]16.7135370370370[/C][C]0.443609694377238[/C][C]37.6762213470117[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 24 )[/C][C]16.7144038461538[/C][C]0.430490629335194[/C][C]38.8264057500296[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 24 )[/C][C]16.72584[/C][C]0.417991749122747[/C][C]40.0147611408671[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 24 )[/C][C]16.7394166666667[/C][C]0.403177836394868[/C][C]41.5186926353567[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 24 )[/C][C]16.7463478260870[/C][C]0.388155300631213[/C][C]43.143421715108[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 24 )[/C][C]16.7545909090909[/C][C]0.368899956527778[/C][C]45.4177090905385[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 24 )[/C][C]16.7686666666667[/C][C]0.346823768900590[/C][C]48.3492429593921[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 24 )[/C][C]16.773425[/C][C]0.323002682944124[/C][C]51.9296770141739[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 24 )[/C][C]16.7771842105263[/C][C]0.302507815530424[/C][C]55.4603330863001[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 24 )[/C][C]16.7876111111111[/C][C]0.286279121420952[/C][C]58.6407106036427[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 24 )[/C][C]16.7774705882353[/C][C]0.272607869164286[/C][C]61.5443370716654[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 24 )[/C][C]16.7575[/C][C]0.265884305121001[/C][C]63.0255328247896[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 24 )[/C][C]16.7236666666667[/C][C]0.258777347750556[/C][C]64.625697774703[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 24 )[/C][C]16.6923214285714[/C][C]0.25168303349267[/C][C]66.3227917946148[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 24 )[/C][C]16.6629230769231[/C][C]0.243628645044852[/C][C]68.394761518521[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 24 )[/C][C]16.6217083333333[/C][C]0.232682353914231[/C][C]71.4351907384443[/C][/ROW]
[ROW][C]Median[/C][C]16.1105[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]20.539[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]16.6860810810811[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]16.7876111111111[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]16.6860810810811[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]16.7876111111111[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]16.7876111111111[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]16.6860810810811[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]16.7876111111111[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]16.7771842105263[/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=77644&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=77644&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 Mean17.06520833333330.571826816470729.8433159162757
Geometric Mean16.3963647274193
Harmonic Mean15.746636233899
Quadratic Mean17.7323809718423
Winsorized Mean ( 1 / 24 )17.02151388888890.55853218902657430.4754394165795
Winsorized Mean ( 2 / 24 )16.9918750.55074579679095430.8524823957024
Winsorized Mean ( 3 / 24 )16.964250.54373305011985931.1995932494088
Winsorized Mean ( 4 / 24 )16.93969444444440.53626024934078431.5885700371567
Winsorized Mean ( 5 / 24 )16.92518055555560.53266146439549431.7747419080965
Winsorized Mean ( 6 / 24 )16.87468055555560.52059936635100332.4139475501746
Winsorized Mean ( 7 / 24 )16.80623611111110.50649361639411333.1815358913306
Winsorized Mean ( 8 / 24 )16.73390277777780.4929741635056433.9447865964812
Winsorized Mean ( 9 / 24 )16.70790277777780.48628384645900534.3583339225444
Winsorized Mean ( 10 / 24 )16.63498611111110.46914378086638735.4581831616538
Winsorized Mean ( 11 / 24 )16.62627777777780.46429060946781335.8100668821095
Winsorized Mean ( 12 / 24 )16.68627777777780.44769425462791937.2715923988032
Winsorized Mean ( 13 / 24 )16.68086111111110.44640592790302737.367024200303
Winsorized Mean ( 14 / 24 )16.63963888888890.43362526249390638.3733152288901
Winsorized Mean ( 15 / 24 )16.72901388888890.41317171395967540.4892525883842
Winsorized Mean ( 16 / 24 )16.74168055555560.37218923810584744.981635258337
Winsorized Mean ( 17 / 24 )16.68855555555560.33092909110081450.429400147452
Winsorized Mean ( 18 / 24 )16.87380555555560.30015505033326856.2169636553515
Winsorized Mean ( 19 / 24 )16.94611111111110.25518501799643766.4071552639024
Winsorized Mean ( 20 / 24 )17.03944444444440.24269182182155370.2102127568734
Winsorized Mean ( 21 / 24 )16.97965277777780.23014807113634273.777080528817
Winsorized Mean ( 22 / 24 )16.9258750.22036145255489976.8095998812826
Winsorized Mean ( 23 / 24 )16.97890277777780.21231417831336779.9706496883952
Winsorized Mean ( 24 / 24 )16.79123611111110.18286815449932991.8215429968301
Trimmed Mean ( 1 / 24 )16.96595714285710.54610218233876531.0673674113476
Trimmed Mean ( 2 / 24 )16.90713235294120.53122241038906331.8268431871286
Trimmed Mean ( 3 / 24 )16.86090909090910.51839094683995832.5254698093995
Trimmed Mean ( 4 / 24 )16.822156250.50616200549127733.2347273550739
Trimmed Mean ( 5 / 24 )16.78803225806450.49412360867424233.9753696511438
Trimmed Mean ( 6 / 24 )16.75511666666670.48060334379099834.8626718543037
Trimmed Mean ( 7 / 24 )16.73037931034480.46759039475824035.7799892767151
Trimmed Mean ( 8 / 24 )16.71644642857140.4553694268205636.7096371517243
Trimmed Mean ( 9 / 24 )16.71353703703700.44360969437723837.6762213470117
Trimmed Mean ( 10 / 24 )16.71440384615380.43049062933519438.8264057500296
Trimmed Mean ( 11 / 24 )16.725840.41799174912274740.0147611408671
Trimmed Mean ( 12 / 24 )16.73941666666670.40317783639486841.5186926353567
Trimmed Mean ( 13 / 24 )16.74634782608700.38815530063121343.143421715108
Trimmed Mean ( 14 / 24 )16.75459090909090.36889995652777845.4177090905385
Trimmed Mean ( 15 / 24 )16.76866666666670.34682376890059048.3492429593921
Trimmed Mean ( 16 / 24 )16.7734250.32300268294412451.9296770141739
Trimmed Mean ( 17 / 24 )16.77718421052630.30250781553042455.4603330863001
Trimmed Mean ( 18 / 24 )16.78761111111110.28627912142095258.6407106036427
Trimmed Mean ( 19 / 24 )16.77747058823530.27260786916428661.5443370716654
Trimmed Mean ( 20 / 24 )16.75750.26588430512100163.0255328247896
Trimmed Mean ( 21 / 24 )16.72366666666670.25877734775055664.625697774703
Trimmed Mean ( 22 / 24 )16.69232142857140.2516830334926766.3227917946148
Trimmed Mean ( 23 / 24 )16.66292307692310.24362864504485268.394761518521
Trimmed Mean ( 24 / 24 )16.62170833333330.23268235391423171.4351907384443
Median16.1105
Midrange20.539
Midmean - Weighted Average at Xnp16.6860810810811
Midmean - Weighted Average at X(n+1)p16.7876111111111
Midmean - Empirical Distribution Function16.6860810810811
Midmean - Empirical Distribution Function - Averaging16.7876111111111
Midmean - Empirical Distribution Function - Interpolation16.7876111111111
Midmean - Closest Observation16.6860810810811
Midmean - True Basic - Statistics Graphics Toolkit16.7876111111111
Midmean - MS Excel (old versions)16.7771842105263
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')