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Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationSat, 18 Dec 2010 15:50:39 +0000
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2010/Dec/18/t1292689011m8ulc6qampbv95g.htm/, Retrieved Tue, 30 Apr 2024 07:25:15 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=112079, Retrieved Tue, 30 Apr 2024 07:25:15 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact116
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Central Tendency] [Arabica Price in ...] [2008-01-06 21:28:17] [74be16979710d4c4e7c6647856088456]
-  M D    [Central Tendency] [Winsorized & trim...] [2010-12-18 15:50:39] [dfb0309aec67f282200eef05efe0d5bd] [Current]
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Dataseries X:
25
24
21
23
17
19
18
27
23
23
29
21
26
25
25
23
26
20
29
24
23
24
30
22
22
13
24
17
24
21
23
24
24
24
23
26
24
21
23
28
23
22
24
21
23
23
20
23
21
27
12
15
22
21
21
20
24
24
29
25
14
30
19
29
25
25
25
16
25
28
24
25
21
22
20
25
27
21
13
26
26
25
22
19
23
25
15
21
23
25
24
24
21
24
22
24
28
21
17
28
24
10
20
22
19
22
22
26
24
22
20
20
15
20
20
24
22
29
23
24
22
16
23
27
16
21
26
22
23
19
18
24
24
29
22
24
22
12
26
18
22
24
21
15
23
22
22
24
23
13




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 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 & 3 seconds \tabularnewline
R Server & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=112079&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]'George Udny Yule' @ 72.249.76.132[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=112079&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=112079&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'George Udny Yule' @ 72.249.76.132







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean22.37333333333330.31282027584758271.521365655449
Geometric Mean21.9977076567226
Harmonic Mean21.555039556858
Quadratic Mean22.6968426585432
Winsorized Mean ( 1 / 50 )22.38666666666670.30954779266427672.3205501612036
Winsorized Mean ( 2 / 50 )22.37333333333330.30748262229380972.7629196291781
Winsorized Mean ( 3 / 50 )22.39333333333330.30313745919104573.871877771531
Winsorized Mean ( 4 / 50 )22.39333333333330.30313745919104573.871877771531
Winsorized Mean ( 5 / 50 )22.39333333333330.30313745919104573.871877771531
Winsorized Mean ( 6 / 50 )22.43333333333330.29513833508743176.009554389767
Winsorized Mean ( 7 / 50 )22.480.28657040160892478.4449471187117
Winsorized Mean ( 8 / 50 )22.42666666666670.27891555202306080.4066553621668
Winsorized Mean ( 9 / 50 )22.42666666666670.27891555202306080.4066553621668
Winsorized Mean ( 10 / 50 )22.42666666666670.27891555202306080.4066553621668
Winsorized Mean ( 11 / 50 )22.50.26634488415480584.476937003688
Winsorized Mean ( 12 / 50 )22.420.25598343067183887.5837937680494
Winsorized Mean ( 13 / 50 )22.420.25598343067183887.5837937680494
Winsorized Mean ( 14 / 50 )22.51333333333330.24094086024524793.4392502393228
Winsorized Mean ( 15 / 50 )22.51333333333330.24094086024524793.4392502393228
Winsorized Mean ( 16 / 50 )22.40666666666670.228622304447798.007351998293
Winsorized Mean ( 17 / 50 )22.520.211465537093107106.494894201529
Winsorized Mean ( 18 / 50 )22.520.211465537093107106.494894201529
Winsorized Mean ( 19 / 50 )22.520.211465537093107106.494894201529
Winsorized Mean ( 20 / 50 )22.65333333333330.193400435782279117.131759510797
Winsorized Mean ( 21 / 50 )22.65333333333330.193400435782279117.131759510797
Winsorized Mean ( 22 / 50 )22.65333333333330.193400435782279117.131759510797
Winsorized Mean ( 23 / 50 )22.65333333333330.193400435782279117.131759510797
Winsorized Mean ( 24 / 50 )22.49333333333330.176403712964892127.510543600689
Winsorized Mean ( 25 / 50 )22.660.155677059183915145.557734188888
Winsorized Mean ( 26 / 50 )22.660.155677059183915145.557734188888
Winsorized Mean ( 27 / 50 )22.660.155677059183915145.557734188888
Winsorized Mean ( 28 / 50 )22.660.155677059183915145.557734188888
Winsorized Mean ( 29 / 50 )22.660.155677059183915145.557734188888
Winsorized Mean ( 30 / 50 )22.660.155677059183915145.557734188888
Winsorized Mean ( 31 / 50 )22.660.155677059183915145.557734188888
Winsorized Mean ( 32 / 50 )22.660.155677059183915145.557734188888
Winsorized Mean ( 33 / 50 )22.660.155677059183915145.557734188888
Winsorized Mean ( 34 / 50 )22.88666666666670.131600597928327173.910050766876
Winsorized Mean ( 35 / 50 )22.88666666666670.131600597928327173.910050766876
Winsorized Mean ( 36 / 50 )22.88666666666670.131600597928327173.910050766876
Winsorized Mean ( 37 / 50 )22.640.107557798831537210.491477567888
Winsorized Mean ( 38 / 50 )22.640.107557798831537210.491477567888
Winsorized Mean ( 39 / 50 )22.640.107557798831537210.491477567888
Winsorized Mean ( 40 / 50 )22.640.107557798831537210.491477567888
Winsorized Mean ( 41 / 50 )22.640.107557798831537210.491477567888
Winsorized Mean ( 42 / 50 )22.640.107557798831537210.491477567888
Winsorized Mean ( 43 / 50 )22.640.107557798831537210.491477567888
Winsorized Mean ( 44 / 50 )22.640.107557798831537210.491477567888
Winsorized Mean ( 45 / 50 )22.640.107557798831537210.491477567888
Winsorized Mean ( 46 / 50 )22.640.107557798831537210.491477567888
Winsorized Mean ( 47 / 50 )22.640.107557798831537210.491477567888
Winsorized Mean ( 48 / 50 )22.640.107557798831537210.491477567888
Winsorized Mean ( 49 / 50 )22.96666666666670.0765103941801296300.177079372979
Winsorized Mean ( 50 / 50 )22.96666666666670.0765103941801296300.177079372979
Trimmed Mean ( 1 / 50 )22.40540540540540.30134799160793074.3506047140212
Trimmed Mean ( 2 / 50 )22.42465753424660.29237444631441876.6984181310128
Trimmed Mean ( 3 / 50 )22.45138888888890.28372553773074079.1306593987166
Trimmed Mean ( 4 / 50 )22.47183098591550.27601732206312081.4145678175103
Trimmed Mean ( 5 / 50 )22.49285714285710.26754881191972084.0701066151859
Trimmed Mean ( 6 / 50 )22.51449275362320.2582061634717487.1957990889994
Trimmed Mean ( 7 / 50 )22.52941176470590.24982372357668590.1812343605965
Trimmed Mean ( 8 / 50 )22.53731343283580.24241535049713892.9698279692973
Trimmed Mean ( 9 / 50 )22.55303030303030.2356976135163095.6862904404021
Trimmed Mean ( 10 / 50 )22.56923076923080.22827513281083698.8685473153713
Trimmed Mean ( 11 / 50 )22.58593750.220036946541389102.646114005002
Trimmed Mean ( 12 / 50 )22.59523809523810.212969502676545106.096120858936
Trimmed Mean ( 13 / 50 )22.61290322580650.206664999216862109.418156492372
Trimmed Mean ( 14 / 50 )22.63114754098360.199647711569348113.355406696573
Trimmed Mean ( 15 / 50 )22.64166666666670.194026996206119116.693383443477
Trimmed Mean ( 16 / 50 )22.65254237288140.187767721328330120.641301990725
Trimmed Mean ( 17 / 50 )22.67241379310340.182345151932066124.33790288842
Trimmed Mean ( 18 / 50 )22.68421052631580.178539586703157127.054234554889
Trimmed Mean ( 19 / 50 )22.69642857142860.174297304823787130.216750020171
Trimmed Mean ( 20 / 50 )22.70909090909090.169552939393443133.935105993032
Trimmed Mean ( 21 / 50 )22.71296296296300.166433339232519136.468829308480
Trimmed Mean ( 22 / 50 )22.71698113207550.162943894775986139.415969915943
Trimmed Mean ( 23 / 50 )22.72115384615380.159030348516553142.873068304877
Trimmed Mean ( 24 / 50 )22.72549019607840.154626360451120146.970349232674
Trimmed Mean ( 25 / 50 )22.740.151504242031487150.094807215193
Trimmed Mean ( 26 / 50 )22.74489795918370.150258368193735151.371921794450
Trimmed Mean ( 27 / 50 )22.750.148825813644736152.863266410939
Trimmed Mean ( 28 / 50 )22.75531914893620.147181380536590154.607322379878
Trimmed Mean ( 29 / 50 )22.76086956521740.145295360594118156.652418027303
Trimmed Mean ( 30 / 50 )22.76666666666670.143132426045840159.060160549332
Trimmed Mean ( 31 / 50 )22.77272727272730.140650148026338161.910439429206
Trimmed Mean ( 32 / 50 )22.77906976744190.137796974696417165.308925087991
Trimmed Mean ( 33 / 50 )22.78571428571430.134509402200690169.398673348631
Trimmed Mean ( 34 / 50 )22.79268292682930.130707896909016174.378774854705
Trimmed Mean ( 35 / 50 )22.78750.129132634689191176.465848891313
Trimmed Mean ( 36 / 50 )22.78205128205130.127277697785034178.994841032787
Trimmed Mean ( 37 / 50 )22.77631578947370.125094608702775182.072721004230
Trimmed Mean ( 38 / 50 )22.78378378378380.125099398125767182.125446845702
Trimmed Mean ( 39 / 50 )22.79166666666670.125182.333333333333
Trimmed Mean ( 40 / 50 )22.80.124777234213833182.725640167077
Trimmed Mean ( 41 / 50 )22.80882352941180.124407909287975183.339014858089
Trimmed Mean ( 42 / 50 )22.81818181818180.123863770021955184.219984698813
Trimmed Mean ( 43 / 50 )22.8281250.123110092965928185.428541641326
Trimmed Mean ( 44 / 50 )22.83870967741940.122103778946206187.043430387861
Trimmed Mean ( 45 / 50 )22.850.120790709411883189.170177998409
Trimmed Mean ( 46 / 50 )22.86206896551720.119101993488926191.953705356266
Trimmed Mean ( 47 / 50 )22.8750.116948484607318195.598943216821
Trimmed Mean ( 48 / 50 )22.88888888888890.114212481944455200.406194657608
Trimmed Mean ( 49 / 50 )22.90384615384620.110734607878761206.835483437326
Trimmed Mean ( 50 / 50 )22.90.111574995370095205.243118532432
Median23
Midrange20
Midmean - Weighted Average at Xnp22.7088607594937
Midmean - Weighted Average at X(n+1)p22.7088607594937
Midmean - Empirical Distribution Function22.7088607594937
Midmean - Empirical Distribution Function - Averaging22.7088607594937
Midmean - Empirical Distribution Function - Interpolation22.7088607594937
Midmean - Closest Observation22.7088607594937
Midmean - True Basic - Statistics Graphics Toolkit22.7088607594937
Midmean - MS Excel (old versions)22.7088607594937
Number of observations150

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 22.3733333333333 & 0.312820275847582 & 71.521365655449 \tabularnewline
Geometric Mean & 21.9977076567226 &  &  \tabularnewline
Harmonic Mean & 21.555039556858 &  &  \tabularnewline
Quadratic Mean & 22.6968426585432 &  &  \tabularnewline
Winsorized Mean ( 1 / 50 ) & 22.3866666666667 & 0.309547792664276 & 72.3205501612036 \tabularnewline
Winsorized Mean ( 2 / 50 ) & 22.3733333333333 & 0.307482622293809 & 72.7629196291781 \tabularnewline
Winsorized Mean ( 3 / 50 ) & 22.3933333333333 & 0.303137459191045 & 73.871877771531 \tabularnewline
Winsorized Mean ( 4 / 50 ) & 22.3933333333333 & 0.303137459191045 & 73.871877771531 \tabularnewline
Winsorized Mean ( 5 / 50 ) & 22.3933333333333 & 0.303137459191045 & 73.871877771531 \tabularnewline
Winsorized Mean ( 6 / 50 ) & 22.4333333333333 & 0.295138335087431 & 76.009554389767 \tabularnewline
Winsorized Mean ( 7 / 50 ) & 22.48 & 0.286570401608924 & 78.4449471187117 \tabularnewline
Winsorized Mean ( 8 / 50 ) & 22.4266666666667 & 0.278915552023060 & 80.4066553621668 \tabularnewline
Winsorized Mean ( 9 / 50 ) & 22.4266666666667 & 0.278915552023060 & 80.4066553621668 \tabularnewline
Winsorized Mean ( 10 / 50 ) & 22.4266666666667 & 0.278915552023060 & 80.4066553621668 \tabularnewline
Winsorized Mean ( 11 / 50 ) & 22.5 & 0.266344884154805 & 84.476937003688 \tabularnewline
Winsorized Mean ( 12 / 50 ) & 22.42 & 0.255983430671838 & 87.5837937680494 \tabularnewline
Winsorized Mean ( 13 / 50 ) & 22.42 & 0.255983430671838 & 87.5837937680494 \tabularnewline
Winsorized Mean ( 14 / 50 ) & 22.5133333333333 & 0.240940860245247 & 93.4392502393228 \tabularnewline
Winsorized Mean ( 15 / 50 ) & 22.5133333333333 & 0.240940860245247 & 93.4392502393228 \tabularnewline
Winsorized Mean ( 16 / 50 ) & 22.4066666666667 & 0.2286223044477 & 98.007351998293 \tabularnewline
Winsorized Mean ( 17 / 50 ) & 22.52 & 0.211465537093107 & 106.494894201529 \tabularnewline
Winsorized Mean ( 18 / 50 ) & 22.52 & 0.211465537093107 & 106.494894201529 \tabularnewline
Winsorized Mean ( 19 / 50 ) & 22.52 & 0.211465537093107 & 106.494894201529 \tabularnewline
Winsorized Mean ( 20 / 50 ) & 22.6533333333333 & 0.193400435782279 & 117.131759510797 \tabularnewline
Winsorized Mean ( 21 / 50 ) & 22.6533333333333 & 0.193400435782279 & 117.131759510797 \tabularnewline
Winsorized Mean ( 22 / 50 ) & 22.6533333333333 & 0.193400435782279 & 117.131759510797 \tabularnewline
Winsorized Mean ( 23 / 50 ) & 22.6533333333333 & 0.193400435782279 & 117.131759510797 \tabularnewline
Winsorized Mean ( 24 / 50 ) & 22.4933333333333 & 0.176403712964892 & 127.510543600689 \tabularnewline
Winsorized Mean ( 25 / 50 ) & 22.66 & 0.155677059183915 & 145.557734188888 \tabularnewline
Winsorized Mean ( 26 / 50 ) & 22.66 & 0.155677059183915 & 145.557734188888 \tabularnewline
Winsorized Mean ( 27 / 50 ) & 22.66 & 0.155677059183915 & 145.557734188888 \tabularnewline
Winsorized Mean ( 28 / 50 ) & 22.66 & 0.155677059183915 & 145.557734188888 \tabularnewline
Winsorized Mean ( 29 / 50 ) & 22.66 & 0.155677059183915 & 145.557734188888 \tabularnewline
Winsorized Mean ( 30 / 50 ) & 22.66 & 0.155677059183915 & 145.557734188888 \tabularnewline
Winsorized Mean ( 31 / 50 ) & 22.66 & 0.155677059183915 & 145.557734188888 \tabularnewline
Winsorized Mean ( 32 / 50 ) & 22.66 & 0.155677059183915 & 145.557734188888 \tabularnewline
Winsorized Mean ( 33 / 50 ) & 22.66 & 0.155677059183915 & 145.557734188888 \tabularnewline
Winsorized Mean ( 34 / 50 ) & 22.8866666666667 & 0.131600597928327 & 173.910050766876 \tabularnewline
Winsorized Mean ( 35 / 50 ) & 22.8866666666667 & 0.131600597928327 & 173.910050766876 \tabularnewline
Winsorized Mean ( 36 / 50 ) & 22.8866666666667 & 0.131600597928327 & 173.910050766876 \tabularnewline
Winsorized Mean ( 37 / 50 ) & 22.64 & 0.107557798831537 & 210.491477567888 \tabularnewline
Winsorized Mean ( 38 / 50 ) & 22.64 & 0.107557798831537 & 210.491477567888 \tabularnewline
Winsorized Mean ( 39 / 50 ) & 22.64 & 0.107557798831537 & 210.491477567888 \tabularnewline
Winsorized Mean ( 40 / 50 ) & 22.64 & 0.107557798831537 & 210.491477567888 \tabularnewline
Winsorized Mean ( 41 / 50 ) & 22.64 & 0.107557798831537 & 210.491477567888 \tabularnewline
Winsorized Mean ( 42 / 50 ) & 22.64 & 0.107557798831537 & 210.491477567888 \tabularnewline
Winsorized Mean ( 43 / 50 ) & 22.64 & 0.107557798831537 & 210.491477567888 \tabularnewline
Winsorized Mean ( 44 / 50 ) & 22.64 & 0.107557798831537 & 210.491477567888 \tabularnewline
Winsorized Mean ( 45 / 50 ) & 22.64 & 0.107557798831537 & 210.491477567888 \tabularnewline
Winsorized Mean ( 46 / 50 ) & 22.64 & 0.107557798831537 & 210.491477567888 \tabularnewline
Winsorized Mean ( 47 / 50 ) & 22.64 & 0.107557798831537 & 210.491477567888 \tabularnewline
Winsorized Mean ( 48 / 50 ) & 22.64 & 0.107557798831537 & 210.491477567888 \tabularnewline
Winsorized Mean ( 49 / 50 ) & 22.9666666666667 & 0.0765103941801296 & 300.177079372979 \tabularnewline
Winsorized Mean ( 50 / 50 ) & 22.9666666666667 & 0.0765103941801296 & 300.177079372979 \tabularnewline
Trimmed Mean ( 1 / 50 ) & 22.4054054054054 & 0.301347991607930 & 74.3506047140212 \tabularnewline
Trimmed Mean ( 2 / 50 ) & 22.4246575342466 & 0.292374446314418 & 76.6984181310128 \tabularnewline
Trimmed Mean ( 3 / 50 ) & 22.4513888888889 & 0.283725537730740 & 79.1306593987166 \tabularnewline
Trimmed Mean ( 4 / 50 ) & 22.4718309859155 & 0.276017322063120 & 81.4145678175103 \tabularnewline
Trimmed Mean ( 5 / 50 ) & 22.4928571428571 & 0.267548811919720 & 84.0701066151859 \tabularnewline
Trimmed Mean ( 6 / 50 ) & 22.5144927536232 & 0.25820616347174 & 87.1957990889994 \tabularnewline
Trimmed Mean ( 7 / 50 ) & 22.5294117647059 & 0.249823723576685 & 90.1812343605965 \tabularnewline
Trimmed Mean ( 8 / 50 ) & 22.5373134328358 & 0.242415350497138 & 92.9698279692973 \tabularnewline
Trimmed Mean ( 9 / 50 ) & 22.5530303030303 & 0.23569761351630 & 95.6862904404021 \tabularnewline
Trimmed Mean ( 10 / 50 ) & 22.5692307692308 & 0.228275132810836 & 98.8685473153713 \tabularnewline
Trimmed Mean ( 11 / 50 ) & 22.5859375 & 0.220036946541389 & 102.646114005002 \tabularnewline
Trimmed Mean ( 12 / 50 ) & 22.5952380952381 & 0.212969502676545 & 106.096120858936 \tabularnewline
Trimmed Mean ( 13 / 50 ) & 22.6129032258065 & 0.206664999216862 & 109.418156492372 \tabularnewline
Trimmed Mean ( 14 / 50 ) & 22.6311475409836 & 0.199647711569348 & 113.355406696573 \tabularnewline
Trimmed Mean ( 15 / 50 ) & 22.6416666666667 & 0.194026996206119 & 116.693383443477 \tabularnewline
Trimmed Mean ( 16 / 50 ) & 22.6525423728814 & 0.187767721328330 & 120.641301990725 \tabularnewline
Trimmed Mean ( 17 / 50 ) & 22.6724137931034 & 0.182345151932066 & 124.33790288842 \tabularnewline
Trimmed Mean ( 18 / 50 ) & 22.6842105263158 & 0.178539586703157 & 127.054234554889 \tabularnewline
Trimmed Mean ( 19 / 50 ) & 22.6964285714286 & 0.174297304823787 & 130.216750020171 \tabularnewline
Trimmed Mean ( 20 / 50 ) & 22.7090909090909 & 0.169552939393443 & 133.935105993032 \tabularnewline
Trimmed Mean ( 21 / 50 ) & 22.7129629629630 & 0.166433339232519 & 136.468829308480 \tabularnewline
Trimmed Mean ( 22 / 50 ) & 22.7169811320755 & 0.162943894775986 & 139.415969915943 \tabularnewline
Trimmed Mean ( 23 / 50 ) & 22.7211538461538 & 0.159030348516553 & 142.873068304877 \tabularnewline
Trimmed Mean ( 24 / 50 ) & 22.7254901960784 & 0.154626360451120 & 146.970349232674 \tabularnewline
Trimmed Mean ( 25 / 50 ) & 22.74 & 0.151504242031487 & 150.094807215193 \tabularnewline
Trimmed Mean ( 26 / 50 ) & 22.7448979591837 & 0.150258368193735 & 151.371921794450 \tabularnewline
Trimmed Mean ( 27 / 50 ) & 22.75 & 0.148825813644736 & 152.863266410939 \tabularnewline
Trimmed Mean ( 28 / 50 ) & 22.7553191489362 & 0.147181380536590 & 154.607322379878 \tabularnewline
Trimmed Mean ( 29 / 50 ) & 22.7608695652174 & 0.145295360594118 & 156.652418027303 \tabularnewline
Trimmed Mean ( 30 / 50 ) & 22.7666666666667 & 0.143132426045840 & 159.060160549332 \tabularnewline
Trimmed Mean ( 31 / 50 ) & 22.7727272727273 & 0.140650148026338 & 161.910439429206 \tabularnewline
Trimmed Mean ( 32 / 50 ) & 22.7790697674419 & 0.137796974696417 & 165.308925087991 \tabularnewline
Trimmed Mean ( 33 / 50 ) & 22.7857142857143 & 0.134509402200690 & 169.398673348631 \tabularnewline
Trimmed Mean ( 34 / 50 ) & 22.7926829268293 & 0.130707896909016 & 174.378774854705 \tabularnewline
Trimmed Mean ( 35 / 50 ) & 22.7875 & 0.129132634689191 & 176.465848891313 \tabularnewline
Trimmed Mean ( 36 / 50 ) & 22.7820512820513 & 0.127277697785034 & 178.994841032787 \tabularnewline
Trimmed Mean ( 37 / 50 ) & 22.7763157894737 & 0.125094608702775 & 182.072721004230 \tabularnewline
Trimmed Mean ( 38 / 50 ) & 22.7837837837838 & 0.125099398125767 & 182.125446845702 \tabularnewline
Trimmed Mean ( 39 / 50 ) & 22.7916666666667 & 0.125 & 182.333333333333 \tabularnewline
Trimmed Mean ( 40 / 50 ) & 22.8 & 0.124777234213833 & 182.725640167077 \tabularnewline
Trimmed Mean ( 41 / 50 ) & 22.8088235294118 & 0.124407909287975 & 183.339014858089 \tabularnewline
Trimmed Mean ( 42 / 50 ) & 22.8181818181818 & 0.123863770021955 & 184.219984698813 \tabularnewline
Trimmed Mean ( 43 / 50 ) & 22.828125 & 0.123110092965928 & 185.428541641326 \tabularnewline
Trimmed Mean ( 44 / 50 ) & 22.8387096774194 & 0.122103778946206 & 187.043430387861 \tabularnewline
Trimmed Mean ( 45 / 50 ) & 22.85 & 0.120790709411883 & 189.170177998409 \tabularnewline
Trimmed Mean ( 46 / 50 ) & 22.8620689655172 & 0.119101993488926 & 191.953705356266 \tabularnewline
Trimmed Mean ( 47 / 50 ) & 22.875 & 0.116948484607318 & 195.598943216821 \tabularnewline
Trimmed Mean ( 48 / 50 ) & 22.8888888888889 & 0.114212481944455 & 200.406194657608 \tabularnewline
Trimmed Mean ( 49 / 50 ) & 22.9038461538462 & 0.110734607878761 & 206.835483437326 \tabularnewline
Trimmed Mean ( 50 / 50 ) & 22.9 & 0.111574995370095 & 205.243118532432 \tabularnewline
Median & 23 &  &  \tabularnewline
Midrange & 20 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 22.7088607594937 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 22.7088607594937 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 22.7088607594937 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 22.7088607594937 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 22.7088607594937 &  &  \tabularnewline
Midmean - Closest Observation & 22.7088607594937 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 22.7088607594937 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 22.7088607594937 &  &  \tabularnewline
Number of observations & 150 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=112079&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]22.3733333333333[/C][C]0.312820275847582[/C][C]71.521365655449[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]21.9977076567226[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]21.555039556858[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]22.6968426585432[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 50 )[/C][C]22.3866666666667[/C][C]0.309547792664276[/C][C]72.3205501612036[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 50 )[/C][C]22.3733333333333[/C][C]0.307482622293809[/C][C]72.7629196291781[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 50 )[/C][C]22.3933333333333[/C][C]0.303137459191045[/C][C]73.871877771531[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 50 )[/C][C]22.3933333333333[/C][C]0.303137459191045[/C][C]73.871877771531[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 50 )[/C][C]22.3933333333333[/C][C]0.303137459191045[/C][C]73.871877771531[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 50 )[/C][C]22.4333333333333[/C][C]0.295138335087431[/C][C]76.009554389767[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 50 )[/C][C]22.48[/C][C]0.286570401608924[/C][C]78.4449471187117[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 50 )[/C][C]22.4266666666667[/C][C]0.278915552023060[/C][C]80.4066553621668[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 50 )[/C][C]22.4266666666667[/C][C]0.278915552023060[/C][C]80.4066553621668[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 50 )[/C][C]22.4266666666667[/C][C]0.278915552023060[/C][C]80.4066553621668[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 50 )[/C][C]22.5[/C][C]0.266344884154805[/C][C]84.476937003688[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 50 )[/C][C]22.42[/C][C]0.255983430671838[/C][C]87.5837937680494[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 50 )[/C][C]22.42[/C][C]0.255983430671838[/C][C]87.5837937680494[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 50 )[/C][C]22.5133333333333[/C][C]0.240940860245247[/C][C]93.4392502393228[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 50 )[/C][C]22.5133333333333[/C][C]0.240940860245247[/C][C]93.4392502393228[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 50 )[/C][C]22.4066666666667[/C][C]0.2286223044477[/C][C]98.007351998293[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 50 )[/C][C]22.52[/C][C]0.211465537093107[/C][C]106.494894201529[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 50 )[/C][C]22.52[/C][C]0.211465537093107[/C][C]106.494894201529[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 50 )[/C][C]22.52[/C][C]0.211465537093107[/C][C]106.494894201529[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 50 )[/C][C]22.6533333333333[/C][C]0.193400435782279[/C][C]117.131759510797[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 50 )[/C][C]22.6533333333333[/C][C]0.193400435782279[/C][C]117.131759510797[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 50 )[/C][C]22.6533333333333[/C][C]0.193400435782279[/C][C]117.131759510797[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 50 )[/C][C]22.6533333333333[/C][C]0.193400435782279[/C][C]117.131759510797[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 50 )[/C][C]22.4933333333333[/C][C]0.176403712964892[/C][C]127.510543600689[/C][/ROW]
[ROW][C]Winsorized Mean ( 25 / 50 )[/C][C]22.66[/C][C]0.155677059183915[/C][C]145.557734188888[/C][/ROW]
[ROW][C]Winsorized Mean ( 26 / 50 )[/C][C]22.66[/C][C]0.155677059183915[/C][C]145.557734188888[/C][/ROW]
[ROW][C]Winsorized Mean ( 27 / 50 )[/C][C]22.66[/C][C]0.155677059183915[/C][C]145.557734188888[/C][/ROW]
[ROW][C]Winsorized Mean ( 28 / 50 )[/C][C]22.66[/C][C]0.155677059183915[/C][C]145.557734188888[/C][/ROW]
[ROW][C]Winsorized Mean ( 29 / 50 )[/C][C]22.66[/C][C]0.155677059183915[/C][C]145.557734188888[/C][/ROW]
[ROW][C]Winsorized Mean ( 30 / 50 )[/C][C]22.66[/C][C]0.155677059183915[/C][C]145.557734188888[/C][/ROW]
[ROW][C]Winsorized Mean ( 31 / 50 )[/C][C]22.66[/C][C]0.155677059183915[/C][C]145.557734188888[/C][/ROW]
[ROW][C]Winsorized Mean ( 32 / 50 )[/C][C]22.66[/C][C]0.155677059183915[/C][C]145.557734188888[/C][/ROW]
[ROW][C]Winsorized Mean ( 33 / 50 )[/C][C]22.66[/C][C]0.155677059183915[/C][C]145.557734188888[/C][/ROW]
[ROW][C]Winsorized Mean ( 34 / 50 )[/C][C]22.8866666666667[/C][C]0.131600597928327[/C][C]173.910050766876[/C][/ROW]
[ROW][C]Winsorized Mean ( 35 / 50 )[/C][C]22.8866666666667[/C][C]0.131600597928327[/C][C]173.910050766876[/C][/ROW]
[ROW][C]Winsorized Mean ( 36 / 50 )[/C][C]22.8866666666667[/C][C]0.131600597928327[/C][C]173.910050766876[/C][/ROW]
[ROW][C]Winsorized Mean ( 37 / 50 )[/C][C]22.64[/C][C]0.107557798831537[/C][C]210.491477567888[/C][/ROW]
[ROW][C]Winsorized Mean ( 38 / 50 )[/C][C]22.64[/C][C]0.107557798831537[/C][C]210.491477567888[/C][/ROW]
[ROW][C]Winsorized Mean ( 39 / 50 )[/C][C]22.64[/C][C]0.107557798831537[/C][C]210.491477567888[/C][/ROW]
[ROW][C]Winsorized Mean ( 40 / 50 )[/C][C]22.64[/C][C]0.107557798831537[/C][C]210.491477567888[/C][/ROW]
[ROW][C]Winsorized Mean ( 41 / 50 )[/C][C]22.64[/C][C]0.107557798831537[/C][C]210.491477567888[/C][/ROW]
[ROW][C]Winsorized Mean ( 42 / 50 )[/C][C]22.64[/C][C]0.107557798831537[/C][C]210.491477567888[/C][/ROW]
[ROW][C]Winsorized Mean ( 43 / 50 )[/C][C]22.64[/C][C]0.107557798831537[/C][C]210.491477567888[/C][/ROW]
[ROW][C]Winsorized Mean ( 44 / 50 )[/C][C]22.64[/C][C]0.107557798831537[/C][C]210.491477567888[/C][/ROW]
[ROW][C]Winsorized Mean ( 45 / 50 )[/C][C]22.64[/C][C]0.107557798831537[/C][C]210.491477567888[/C][/ROW]
[ROW][C]Winsorized Mean ( 46 / 50 )[/C][C]22.64[/C][C]0.107557798831537[/C][C]210.491477567888[/C][/ROW]
[ROW][C]Winsorized Mean ( 47 / 50 )[/C][C]22.64[/C][C]0.107557798831537[/C][C]210.491477567888[/C][/ROW]
[ROW][C]Winsorized Mean ( 48 / 50 )[/C][C]22.64[/C][C]0.107557798831537[/C][C]210.491477567888[/C][/ROW]
[ROW][C]Winsorized Mean ( 49 / 50 )[/C][C]22.9666666666667[/C][C]0.0765103941801296[/C][C]300.177079372979[/C][/ROW]
[ROW][C]Winsorized Mean ( 50 / 50 )[/C][C]22.9666666666667[/C][C]0.0765103941801296[/C][C]300.177079372979[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 50 )[/C][C]22.4054054054054[/C][C]0.301347991607930[/C][C]74.3506047140212[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 50 )[/C][C]22.4246575342466[/C][C]0.292374446314418[/C][C]76.6984181310128[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 50 )[/C][C]22.4513888888889[/C][C]0.283725537730740[/C][C]79.1306593987166[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 50 )[/C][C]22.4718309859155[/C][C]0.276017322063120[/C][C]81.4145678175103[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 50 )[/C][C]22.4928571428571[/C][C]0.267548811919720[/C][C]84.0701066151859[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 50 )[/C][C]22.5144927536232[/C][C]0.25820616347174[/C][C]87.1957990889994[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 50 )[/C][C]22.5294117647059[/C][C]0.249823723576685[/C][C]90.1812343605965[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 50 )[/C][C]22.5373134328358[/C][C]0.242415350497138[/C][C]92.9698279692973[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 50 )[/C][C]22.5530303030303[/C][C]0.23569761351630[/C][C]95.6862904404021[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 50 )[/C][C]22.5692307692308[/C][C]0.228275132810836[/C][C]98.8685473153713[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 50 )[/C][C]22.5859375[/C][C]0.220036946541389[/C][C]102.646114005002[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 50 )[/C][C]22.5952380952381[/C][C]0.212969502676545[/C][C]106.096120858936[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 50 )[/C][C]22.6129032258065[/C][C]0.206664999216862[/C][C]109.418156492372[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 50 )[/C][C]22.6311475409836[/C][C]0.199647711569348[/C][C]113.355406696573[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 50 )[/C][C]22.6416666666667[/C][C]0.194026996206119[/C][C]116.693383443477[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 50 )[/C][C]22.6525423728814[/C][C]0.187767721328330[/C][C]120.641301990725[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 50 )[/C][C]22.6724137931034[/C][C]0.182345151932066[/C][C]124.33790288842[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 50 )[/C][C]22.6842105263158[/C][C]0.178539586703157[/C][C]127.054234554889[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 50 )[/C][C]22.6964285714286[/C][C]0.174297304823787[/C][C]130.216750020171[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 50 )[/C][C]22.7090909090909[/C][C]0.169552939393443[/C][C]133.935105993032[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 50 )[/C][C]22.7129629629630[/C][C]0.166433339232519[/C][C]136.468829308480[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 50 )[/C][C]22.7169811320755[/C][C]0.162943894775986[/C][C]139.415969915943[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 50 )[/C][C]22.7211538461538[/C][C]0.159030348516553[/C][C]142.873068304877[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 50 )[/C][C]22.7254901960784[/C][C]0.154626360451120[/C][C]146.970349232674[/C][/ROW]
[ROW][C]Trimmed Mean ( 25 / 50 )[/C][C]22.74[/C][C]0.151504242031487[/C][C]150.094807215193[/C][/ROW]
[ROW][C]Trimmed Mean ( 26 / 50 )[/C][C]22.7448979591837[/C][C]0.150258368193735[/C][C]151.371921794450[/C][/ROW]
[ROW][C]Trimmed Mean ( 27 / 50 )[/C][C]22.75[/C][C]0.148825813644736[/C][C]152.863266410939[/C][/ROW]
[ROW][C]Trimmed Mean ( 28 / 50 )[/C][C]22.7553191489362[/C][C]0.147181380536590[/C][C]154.607322379878[/C][/ROW]
[ROW][C]Trimmed Mean ( 29 / 50 )[/C][C]22.7608695652174[/C][C]0.145295360594118[/C][C]156.652418027303[/C][/ROW]
[ROW][C]Trimmed Mean ( 30 / 50 )[/C][C]22.7666666666667[/C][C]0.143132426045840[/C][C]159.060160549332[/C][/ROW]
[ROW][C]Trimmed Mean ( 31 / 50 )[/C][C]22.7727272727273[/C][C]0.140650148026338[/C][C]161.910439429206[/C][/ROW]
[ROW][C]Trimmed Mean ( 32 / 50 )[/C][C]22.7790697674419[/C][C]0.137796974696417[/C][C]165.308925087991[/C][/ROW]
[ROW][C]Trimmed Mean ( 33 / 50 )[/C][C]22.7857142857143[/C][C]0.134509402200690[/C][C]169.398673348631[/C][/ROW]
[ROW][C]Trimmed Mean ( 34 / 50 )[/C][C]22.7926829268293[/C][C]0.130707896909016[/C][C]174.378774854705[/C][/ROW]
[ROW][C]Trimmed Mean ( 35 / 50 )[/C][C]22.7875[/C][C]0.129132634689191[/C][C]176.465848891313[/C][/ROW]
[ROW][C]Trimmed Mean ( 36 / 50 )[/C][C]22.7820512820513[/C][C]0.127277697785034[/C][C]178.994841032787[/C][/ROW]
[ROW][C]Trimmed Mean ( 37 / 50 )[/C][C]22.7763157894737[/C][C]0.125094608702775[/C][C]182.072721004230[/C][/ROW]
[ROW][C]Trimmed Mean ( 38 / 50 )[/C][C]22.7837837837838[/C][C]0.125099398125767[/C][C]182.125446845702[/C][/ROW]
[ROW][C]Trimmed Mean ( 39 / 50 )[/C][C]22.7916666666667[/C][C]0.125[/C][C]182.333333333333[/C][/ROW]
[ROW][C]Trimmed Mean ( 40 / 50 )[/C][C]22.8[/C][C]0.124777234213833[/C][C]182.725640167077[/C][/ROW]
[ROW][C]Trimmed Mean ( 41 / 50 )[/C][C]22.8088235294118[/C][C]0.124407909287975[/C][C]183.339014858089[/C][/ROW]
[ROW][C]Trimmed Mean ( 42 / 50 )[/C][C]22.8181818181818[/C][C]0.123863770021955[/C][C]184.219984698813[/C][/ROW]
[ROW][C]Trimmed Mean ( 43 / 50 )[/C][C]22.828125[/C][C]0.123110092965928[/C][C]185.428541641326[/C][/ROW]
[ROW][C]Trimmed Mean ( 44 / 50 )[/C][C]22.8387096774194[/C][C]0.122103778946206[/C][C]187.043430387861[/C][/ROW]
[ROW][C]Trimmed Mean ( 45 / 50 )[/C][C]22.85[/C][C]0.120790709411883[/C][C]189.170177998409[/C][/ROW]
[ROW][C]Trimmed Mean ( 46 / 50 )[/C][C]22.8620689655172[/C][C]0.119101993488926[/C][C]191.953705356266[/C][/ROW]
[ROW][C]Trimmed Mean ( 47 / 50 )[/C][C]22.875[/C][C]0.116948484607318[/C][C]195.598943216821[/C][/ROW]
[ROW][C]Trimmed Mean ( 48 / 50 )[/C][C]22.8888888888889[/C][C]0.114212481944455[/C][C]200.406194657608[/C][/ROW]
[ROW][C]Trimmed Mean ( 49 / 50 )[/C][C]22.9038461538462[/C][C]0.110734607878761[/C][C]206.835483437326[/C][/ROW]
[ROW][C]Trimmed Mean ( 50 / 50 )[/C][C]22.9[/C][C]0.111574995370095[/C][C]205.243118532432[/C][/ROW]
[ROW][C]Median[/C][C]23[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]20[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]22.7088607594937[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]22.7088607594937[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]22.7088607594937[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]22.7088607594937[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]22.7088607594937[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]22.7088607594937[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]22.7088607594937[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]22.7088607594937[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]150[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=112079&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=112079&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 Mean22.37333333333330.31282027584758271.521365655449
Geometric Mean21.9977076567226
Harmonic Mean21.555039556858
Quadratic Mean22.6968426585432
Winsorized Mean ( 1 / 50 )22.38666666666670.30954779266427672.3205501612036
Winsorized Mean ( 2 / 50 )22.37333333333330.30748262229380972.7629196291781
Winsorized Mean ( 3 / 50 )22.39333333333330.30313745919104573.871877771531
Winsorized Mean ( 4 / 50 )22.39333333333330.30313745919104573.871877771531
Winsorized Mean ( 5 / 50 )22.39333333333330.30313745919104573.871877771531
Winsorized Mean ( 6 / 50 )22.43333333333330.29513833508743176.009554389767
Winsorized Mean ( 7 / 50 )22.480.28657040160892478.4449471187117
Winsorized Mean ( 8 / 50 )22.42666666666670.27891555202306080.4066553621668
Winsorized Mean ( 9 / 50 )22.42666666666670.27891555202306080.4066553621668
Winsorized Mean ( 10 / 50 )22.42666666666670.27891555202306080.4066553621668
Winsorized Mean ( 11 / 50 )22.50.26634488415480584.476937003688
Winsorized Mean ( 12 / 50 )22.420.25598343067183887.5837937680494
Winsorized Mean ( 13 / 50 )22.420.25598343067183887.5837937680494
Winsorized Mean ( 14 / 50 )22.51333333333330.24094086024524793.4392502393228
Winsorized Mean ( 15 / 50 )22.51333333333330.24094086024524793.4392502393228
Winsorized Mean ( 16 / 50 )22.40666666666670.228622304447798.007351998293
Winsorized Mean ( 17 / 50 )22.520.211465537093107106.494894201529
Winsorized Mean ( 18 / 50 )22.520.211465537093107106.494894201529
Winsorized Mean ( 19 / 50 )22.520.211465537093107106.494894201529
Winsorized Mean ( 20 / 50 )22.65333333333330.193400435782279117.131759510797
Winsorized Mean ( 21 / 50 )22.65333333333330.193400435782279117.131759510797
Winsorized Mean ( 22 / 50 )22.65333333333330.193400435782279117.131759510797
Winsorized Mean ( 23 / 50 )22.65333333333330.193400435782279117.131759510797
Winsorized Mean ( 24 / 50 )22.49333333333330.176403712964892127.510543600689
Winsorized Mean ( 25 / 50 )22.660.155677059183915145.557734188888
Winsorized Mean ( 26 / 50 )22.660.155677059183915145.557734188888
Winsorized Mean ( 27 / 50 )22.660.155677059183915145.557734188888
Winsorized Mean ( 28 / 50 )22.660.155677059183915145.557734188888
Winsorized Mean ( 29 / 50 )22.660.155677059183915145.557734188888
Winsorized Mean ( 30 / 50 )22.660.155677059183915145.557734188888
Winsorized Mean ( 31 / 50 )22.660.155677059183915145.557734188888
Winsorized Mean ( 32 / 50 )22.660.155677059183915145.557734188888
Winsorized Mean ( 33 / 50 )22.660.155677059183915145.557734188888
Winsorized Mean ( 34 / 50 )22.88666666666670.131600597928327173.910050766876
Winsorized Mean ( 35 / 50 )22.88666666666670.131600597928327173.910050766876
Winsorized Mean ( 36 / 50 )22.88666666666670.131600597928327173.910050766876
Winsorized Mean ( 37 / 50 )22.640.107557798831537210.491477567888
Winsorized Mean ( 38 / 50 )22.640.107557798831537210.491477567888
Winsorized Mean ( 39 / 50 )22.640.107557798831537210.491477567888
Winsorized Mean ( 40 / 50 )22.640.107557798831537210.491477567888
Winsorized Mean ( 41 / 50 )22.640.107557798831537210.491477567888
Winsorized Mean ( 42 / 50 )22.640.107557798831537210.491477567888
Winsorized Mean ( 43 / 50 )22.640.107557798831537210.491477567888
Winsorized Mean ( 44 / 50 )22.640.107557798831537210.491477567888
Winsorized Mean ( 45 / 50 )22.640.107557798831537210.491477567888
Winsorized Mean ( 46 / 50 )22.640.107557798831537210.491477567888
Winsorized Mean ( 47 / 50 )22.640.107557798831537210.491477567888
Winsorized Mean ( 48 / 50 )22.640.107557798831537210.491477567888
Winsorized Mean ( 49 / 50 )22.96666666666670.0765103941801296300.177079372979
Winsorized Mean ( 50 / 50 )22.96666666666670.0765103941801296300.177079372979
Trimmed Mean ( 1 / 50 )22.40540540540540.30134799160793074.3506047140212
Trimmed Mean ( 2 / 50 )22.42465753424660.29237444631441876.6984181310128
Trimmed Mean ( 3 / 50 )22.45138888888890.28372553773074079.1306593987166
Trimmed Mean ( 4 / 50 )22.47183098591550.27601732206312081.4145678175103
Trimmed Mean ( 5 / 50 )22.49285714285710.26754881191972084.0701066151859
Trimmed Mean ( 6 / 50 )22.51449275362320.2582061634717487.1957990889994
Trimmed Mean ( 7 / 50 )22.52941176470590.24982372357668590.1812343605965
Trimmed Mean ( 8 / 50 )22.53731343283580.24241535049713892.9698279692973
Trimmed Mean ( 9 / 50 )22.55303030303030.2356976135163095.6862904404021
Trimmed Mean ( 10 / 50 )22.56923076923080.22827513281083698.8685473153713
Trimmed Mean ( 11 / 50 )22.58593750.220036946541389102.646114005002
Trimmed Mean ( 12 / 50 )22.59523809523810.212969502676545106.096120858936
Trimmed Mean ( 13 / 50 )22.61290322580650.206664999216862109.418156492372
Trimmed Mean ( 14 / 50 )22.63114754098360.199647711569348113.355406696573
Trimmed Mean ( 15 / 50 )22.64166666666670.194026996206119116.693383443477
Trimmed Mean ( 16 / 50 )22.65254237288140.187767721328330120.641301990725
Trimmed Mean ( 17 / 50 )22.67241379310340.182345151932066124.33790288842
Trimmed Mean ( 18 / 50 )22.68421052631580.178539586703157127.054234554889
Trimmed Mean ( 19 / 50 )22.69642857142860.174297304823787130.216750020171
Trimmed Mean ( 20 / 50 )22.70909090909090.169552939393443133.935105993032
Trimmed Mean ( 21 / 50 )22.71296296296300.166433339232519136.468829308480
Trimmed Mean ( 22 / 50 )22.71698113207550.162943894775986139.415969915943
Trimmed Mean ( 23 / 50 )22.72115384615380.159030348516553142.873068304877
Trimmed Mean ( 24 / 50 )22.72549019607840.154626360451120146.970349232674
Trimmed Mean ( 25 / 50 )22.740.151504242031487150.094807215193
Trimmed Mean ( 26 / 50 )22.74489795918370.150258368193735151.371921794450
Trimmed Mean ( 27 / 50 )22.750.148825813644736152.863266410939
Trimmed Mean ( 28 / 50 )22.75531914893620.147181380536590154.607322379878
Trimmed Mean ( 29 / 50 )22.76086956521740.145295360594118156.652418027303
Trimmed Mean ( 30 / 50 )22.76666666666670.143132426045840159.060160549332
Trimmed Mean ( 31 / 50 )22.77272727272730.140650148026338161.910439429206
Trimmed Mean ( 32 / 50 )22.77906976744190.137796974696417165.308925087991
Trimmed Mean ( 33 / 50 )22.78571428571430.134509402200690169.398673348631
Trimmed Mean ( 34 / 50 )22.79268292682930.130707896909016174.378774854705
Trimmed Mean ( 35 / 50 )22.78750.129132634689191176.465848891313
Trimmed Mean ( 36 / 50 )22.78205128205130.127277697785034178.994841032787
Trimmed Mean ( 37 / 50 )22.77631578947370.125094608702775182.072721004230
Trimmed Mean ( 38 / 50 )22.78378378378380.125099398125767182.125446845702
Trimmed Mean ( 39 / 50 )22.79166666666670.125182.333333333333
Trimmed Mean ( 40 / 50 )22.80.124777234213833182.725640167077
Trimmed Mean ( 41 / 50 )22.80882352941180.124407909287975183.339014858089
Trimmed Mean ( 42 / 50 )22.81818181818180.123863770021955184.219984698813
Trimmed Mean ( 43 / 50 )22.8281250.123110092965928185.428541641326
Trimmed Mean ( 44 / 50 )22.83870967741940.122103778946206187.043430387861
Trimmed Mean ( 45 / 50 )22.850.120790709411883189.170177998409
Trimmed Mean ( 46 / 50 )22.86206896551720.119101993488926191.953705356266
Trimmed Mean ( 47 / 50 )22.8750.116948484607318195.598943216821
Trimmed Mean ( 48 / 50 )22.88888888888890.114212481944455200.406194657608
Trimmed Mean ( 49 / 50 )22.90384615384620.110734607878761206.835483437326
Trimmed Mean ( 50 / 50 )22.90.111574995370095205.243118532432
Median23
Midrange20
Midmean - Weighted Average at Xnp22.7088607594937
Midmean - Weighted Average at X(n+1)p22.7088607594937
Midmean - Empirical Distribution Function22.7088607594937
Midmean - Empirical Distribution Function - Averaging22.7088607594937
Midmean - Empirical Distribution Function - Interpolation22.7088607594937
Midmean - Closest Observation22.7088607594937
Midmean - True Basic - Statistics Graphics Toolkit22.7088607594937
Midmean - MS Excel (old versions)22.7088607594937
Number of observations150



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')