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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 computationMon, 14 Dec 2009 14:36:13 -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/2009/Dec/14/t12608266777kg8tw5izxn7zm2.htm/, Retrieved Wed, 08 May 2024 03:22:30 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=67700, Retrieved Wed, 08 May 2024 03:22:30 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact98
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [Central tendancy ...] [2009-12-14 21:36:13] [95223d06eb2c638c714cd6fbd03e9e6c] [Current]
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Dataseries X:
15
13
14
14
8
7
6
3
1
1
5
0
3
8
16
14
12
14
16
18
22
22
19
21
17
24
23
23
24
26
27
27
24
26
24
17
26
27
23
23
23
23
19
21
20
23
24
20
16
17
11
15
14
14
14
20
23
22
19
19
18
19
23
23
21
25
19
21
22
24
22
19
19
10
20
14
12
15
16
14
7
12
16
17
21
22
22
22
24
25
26
25
27
26
24
17
7
11
21
25
29
29
28
28
32
33
38
40
39
39
35
41
38
40
38
37
38
36
34
33




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 1 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=67700&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=67700&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=67700&T=0

As an alternative you can also use a QR Code:  

The GUIDs for individual cells are displayed in the table below:

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean20.90.81952708915565725.5025127009930
Geometric Mean0
Harmonic Mean0
Quadratic Mean22.7317692521575
Winsorized Mean ( 1 / 40 )20.90.81610195990671725.6095451631913
Winsorized Mean ( 2 / 40 )20.90.81610195990671725.6095451631913
Winsorized Mean ( 3 / 40 )20.9250.8014484873472226.1089768467358
Winsorized Mean ( 4 / 40 )20.9250.8014484873472226.1089768467358
Winsorized Mean ( 5 / 40 )20.96666666666670.77864830568122526.9270048026667
Winsorized Mean ( 6 / 40 )21.01666666666670.77024345284937627.2857452912054
Winsorized Mean ( 7 / 40 )21.0750.76092992827348927.6963741560515
Winsorized Mean ( 8 / 40 )21.0750.76092992827348927.6963741560515
Winsorized Mean ( 9 / 40 )210.74717019836321728.106046046809
Winsorized Mean ( 10 / 40 )210.71947693418450129.1878710799849
Winsorized Mean ( 11 / 40 )20.90833333333330.70373113592574229.7106839046263
Winsorized Mean ( 12 / 40 )21.00833333333330.65748180932897831.9527217867432
Winsorized Mean ( 13 / 40 )21.00833333333330.62482443846109833.6227779199474
Winsorized Mean ( 14 / 40 )21.00833333333330.62482443846109833.6227779199474
Winsorized Mean ( 15 / 40 )21.00833333333330.58846234530291135.7003867809406
Winsorized Mean ( 16 / 40 )20.60833333333330.53022058637396638.8674711298331
Winsorized Mean ( 17 / 40 )20.60833333333330.53022058637396638.8674711298331
Winsorized Mean ( 18 / 40 )20.60833333333330.49071145876265341.9968455297498
Winsorized Mean ( 19 / 40 )20.76666666666670.4708198542975344.1074574003487
Winsorized Mean ( 20 / 40 )20.60.4500855816534545.7690733489464
Winsorized Mean ( 21 / 40 )20.60.4500855816534545.7690733489464
Winsorized Mean ( 22 / 40 )20.60.4500855816534545.7690733489464
Winsorized Mean ( 23 / 40 )20.60.4500855816534545.7690733489464
Winsorized Mean ( 24 / 40 )20.40.42709362391100447.7647027674917
Winsorized Mean ( 25 / 40 )20.40.42709362391100447.7647027674917
Winsorized Mean ( 26 / 40 )20.40.42709362391100447.7647027674917
Winsorized Mean ( 27 / 40 )20.40.42709362391100447.7647027674917
Winsorized Mean ( 28 / 40 )20.63333333333330.39851498383825451.7755521626956
Winsorized Mean ( 29 / 40 )20.39166666666670.37223223853184454.7821079310469
Winsorized Mean ( 30 / 40 )20.39166666666670.37223223853184454.7821079310469
Winsorized Mean ( 31 / 40 )20.650.34169826321073560.4334356457193
Winsorized Mean ( 32 / 40 )20.650.34169826321073560.4334356457193
Winsorized Mean ( 33 / 40 )20.3750.31357308754498264.9768771915964
Winsorized Mean ( 34 / 40 )20.3750.31357308754498264.9768771915964
Winsorized Mean ( 35 / 40 )20.3750.31357308754498264.9768771915964
Winsorized Mean ( 36 / 40 )20.6750.2793455988295474.0122632560828
Winsorized Mean ( 37 / 40 )20.6750.2793455988295474.0122632560828
Winsorized Mean ( 38 / 40 )20.6750.2793455988295474.0122632560828
Winsorized Mean ( 39 / 40 )20.6750.2793455988295474.0122632560828
Winsorized Mean ( 40 / 40 )20.6750.2793455988295474.0122632560828
Trimmed Mean ( 1 / 40 )20.90677966101690.79610336762564526.2613882960586
Trimmed Mean ( 2 / 40 )20.91379310344830.77387718785130827.0246925891640
Trimmed Mean ( 3 / 40 )20.92105263157890.74907641076013727.9291302343228
Trimmed Mean ( 4 / 40 )20.91964285714290.7275311287171428.7542924713484
Trimmed Mean ( 5 / 40 )20.91818181818180.70339719175686629.7387906339727
Trimmed Mean ( 6 / 40 )20.90740740740740.68276729044646430.6215715075278
Trimmed Mean ( 7 / 40 )20.88679245283020.66165964583106531.5672756898990
Trimmed Mean ( 8 / 40 )20.85576923076920.63994174918564232.5901056733824
Trimmed Mean ( 9 / 40 )20.82352941176470.61534316221217733.8405148387503
Trimmed Mean ( 10 / 40 )20.80.59015491888387135.244982858633
Trimmed Mean ( 11 / 40 )20.77551020408160.56672040747558636.6591884287785
Trimmed Mean ( 12 / 40 )20.76041666666670.54284516702785338.2437164916336
Trimmed Mean ( 13 / 40 )20.73404255319150.52356405184475639.6017306385646
Trimmed Mean ( 14 / 40 )20.70652173913040.50688947811053840.8501707636846
Trimmed Mean ( 15 / 40 )20.67777777777780.48775973337040942.3933678061016
Trimmed Mean ( 16 / 40 )20.64772727272730.47150788948347443.7908415389324
Trimmed Mean ( 17 / 40 )20.65116279069770.46159405059043344.7387975739341
Trimmed Mean ( 18 / 40 )20.65476190476190.45018452505976245.8806572749696
Trimmed Mean ( 19 / 40 )20.65853658536590.44248195181947846.6878626357941
Trimmed Mean ( 20 / 40 )20.650.43614392003940847.346756543423
Trimmed Mean ( 21 / 40 )20.65384615384620.4313809818178947.8784346653587
Trimmed Mean ( 22 / 40 )20.65789473684210.42573059250671948.5233974265453
Trimmed Mean ( 23 / 40 )20.66216216216220.41903833197920149.3085252238636
Trimmed Mean ( 24 / 40 )20.66666666666670.41111322589651950.2700116776799
Trimmed Mean ( 25 / 40 )20.68571428571430.40470466042653351.1131111361872
Trimmed Mean ( 26 / 40 )20.70588235294120.39701410992666952.1540213187024
Trimmed Mean ( 27 / 40 )20.72727272727270.38777679311677853.4515553668803
Trimmed Mean ( 28 / 40 )20.750.37664980998943755.0909610191544
Trimmed Mean ( 29 / 40 )20.75806451612900.36771155023048656.452032858684
Trimmed Mean ( 30 / 40 )20.78333333333330.36054859853017357.6436392155164
Trimmed Mean ( 31 / 40 )20.81034482758620.35169359202140759.1718055139303
Trimmed Mean ( 32 / 40 )20.82142857142860.3457601665379960.2192808382421
Trimmed Mean ( 33 / 40 )20.83333333333330.33827572807408661.5868405692134
Trimmed Mean ( 34 / 40 )20.86538461538460.33298871267750762.6609366053568
Trimmed Mean ( 35 / 40 )20.90.32607749172895264.0951937196967
Trimmed Mean ( 36 / 40 )20.93750.31707641929629366.0329773070727
Trimmed Mean ( 37 / 40 )20.95652173913040.31231799993161767.0999485899594
Trimmed Mean ( 38 / 40 )20.97727272727270.30584274511515468.588426772636
Trimmed Mean ( 39 / 40 )210.29710175718617570.6828535747793
Trimmed Mean ( 40 / 40 )21.0250.28529674160289873.6951984865797
Median21
Midrange20.5
Midmean - Weighted Average at Xnp20.6666666666667
Midmean - Weighted Average at X(n+1)p20.6666666666667
Midmean - Empirical Distribution Function20.6666666666667
Midmean - Empirical Distribution Function - Averaging20.6666666666667
Midmean - Empirical Distribution Function - Interpolation20.6666666666667
Midmean - Closest Observation20.6666666666667
Midmean - True Basic - Statistics Graphics Toolkit20.6666666666667
Midmean - MS Excel (old versions)20.6666666666667
Number of observations120

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 20.9 & 0.819527089155657 & 25.5025127009930 \tabularnewline
Geometric Mean & 0 &  &  \tabularnewline
Harmonic Mean & 0 &  &  \tabularnewline
Quadratic Mean & 22.7317692521575 &  &  \tabularnewline
Winsorized Mean ( 1 / 40 ) & 20.9 & 0.816101959906717 & 25.6095451631913 \tabularnewline
Winsorized Mean ( 2 / 40 ) & 20.9 & 0.816101959906717 & 25.6095451631913 \tabularnewline
Winsorized Mean ( 3 / 40 ) & 20.925 & 0.80144848734722 & 26.1089768467358 \tabularnewline
Winsorized Mean ( 4 / 40 ) & 20.925 & 0.80144848734722 & 26.1089768467358 \tabularnewline
Winsorized Mean ( 5 / 40 ) & 20.9666666666667 & 0.778648305681225 & 26.9270048026667 \tabularnewline
Winsorized Mean ( 6 / 40 ) & 21.0166666666667 & 0.770243452849376 & 27.2857452912054 \tabularnewline
Winsorized Mean ( 7 / 40 ) & 21.075 & 0.760929928273489 & 27.6963741560515 \tabularnewline
Winsorized Mean ( 8 / 40 ) & 21.075 & 0.760929928273489 & 27.6963741560515 \tabularnewline
Winsorized Mean ( 9 / 40 ) & 21 & 0.747170198363217 & 28.106046046809 \tabularnewline
Winsorized Mean ( 10 / 40 ) & 21 & 0.719476934184501 & 29.1878710799849 \tabularnewline
Winsorized Mean ( 11 / 40 ) & 20.9083333333333 & 0.703731135925742 & 29.7106839046263 \tabularnewline
Winsorized Mean ( 12 / 40 ) & 21.0083333333333 & 0.657481809328978 & 31.9527217867432 \tabularnewline
Winsorized Mean ( 13 / 40 ) & 21.0083333333333 & 0.624824438461098 & 33.6227779199474 \tabularnewline
Winsorized Mean ( 14 / 40 ) & 21.0083333333333 & 0.624824438461098 & 33.6227779199474 \tabularnewline
Winsorized Mean ( 15 / 40 ) & 21.0083333333333 & 0.588462345302911 & 35.7003867809406 \tabularnewline
Winsorized Mean ( 16 / 40 ) & 20.6083333333333 & 0.530220586373966 & 38.8674711298331 \tabularnewline
Winsorized Mean ( 17 / 40 ) & 20.6083333333333 & 0.530220586373966 & 38.8674711298331 \tabularnewline
Winsorized Mean ( 18 / 40 ) & 20.6083333333333 & 0.490711458762653 & 41.9968455297498 \tabularnewline
Winsorized Mean ( 19 / 40 ) & 20.7666666666667 & 0.47081985429753 & 44.1074574003487 \tabularnewline
Winsorized Mean ( 20 / 40 ) & 20.6 & 0.45008558165345 & 45.7690733489464 \tabularnewline
Winsorized Mean ( 21 / 40 ) & 20.6 & 0.45008558165345 & 45.7690733489464 \tabularnewline
Winsorized Mean ( 22 / 40 ) & 20.6 & 0.45008558165345 & 45.7690733489464 \tabularnewline
Winsorized Mean ( 23 / 40 ) & 20.6 & 0.45008558165345 & 45.7690733489464 \tabularnewline
Winsorized Mean ( 24 / 40 ) & 20.4 & 0.427093623911004 & 47.7647027674917 \tabularnewline
Winsorized Mean ( 25 / 40 ) & 20.4 & 0.427093623911004 & 47.7647027674917 \tabularnewline
Winsorized Mean ( 26 / 40 ) & 20.4 & 0.427093623911004 & 47.7647027674917 \tabularnewline
Winsorized Mean ( 27 / 40 ) & 20.4 & 0.427093623911004 & 47.7647027674917 \tabularnewline
Winsorized Mean ( 28 / 40 ) & 20.6333333333333 & 0.398514983838254 & 51.7755521626956 \tabularnewline
Winsorized Mean ( 29 / 40 ) & 20.3916666666667 & 0.372232238531844 & 54.7821079310469 \tabularnewline
Winsorized Mean ( 30 / 40 ) & 20.3916666666667 & 0.372232238531844 & 54.7821079310469 \tabularnewline
Winsorized Mean ( 31 / 40 ) & 20.65 & 0.341698263210735 & 60.4334356457193 \tabularnewline
Winsorized Mean ( 32 / 40 ) & 20.65 & 0.341698263210735 & 60.4334356457193 \tabularnewline
Winsorized Mean ( 33 / 40 ) & 20.375 & 0.313573087544982 & 64.9768771915964 \tabularnewline
Winsorized Mean ( 34 / 40 ) & 20.375 & 0.313573087544982 & 64.9768771915964 \tabularnewline
Winsorized Mean ( 35 / 40 ) & 20.375 & 0.313573087544982 & 64.9768771915964 \tabularnewline
Winsorized Mean ( 36 / 40 ) & 20.675 & 0.27934559882954 & 74.0122632560828 \tabularnewline
Winsorized Mean ( 37 / 40 ) & 20.675 & 0.27934559882954 & 74.0122632560828 \tabularnewline
Winsorized Mean ( 38 / 40 ) & 20.675 & 0.27934559882954 & 74.0122632560828 \tabularnewline
Winsorized Mean ( 39 / 40 ) & 20.675 & 0.27934559882954 & 74.0122632560828 \tabularnewline
Winsorized Mean ( 40 / 40 ) & 20.675 & 0.27934559882954 & 74.0122632560828 \tabularnewline
Trimmed Mean ( 1 / 40 ) & 20.9067796610169 & 0.796103367625645 & 26.2613882960586 \tabularnewline
Trimmed Mean ( 2 / 40 ) & 20.9137931034483 & 0.773877187851308 & 27.0246925891640 \tabularnewline
Trimmed Mean ( 3 / 40 ) & 20.9210526315789 & 0.749076410760137 & 27.9291302343228 \tabularnewline
Trimmed Mean ( 4 / 40 ) & 20.9196428571429 & 0.72753112871714 & 28.7542924713484 \tabularnewline
Trimmed Mean ( 5 / 40 ) & 20.9181818181818 & 0.703397191756866 & 29.7387906339727 \tabularnewline
Trimmed Mean ( 6 / 40 ) & 20.9074074074074 & 0.682767290446464 & 30.6215715075278 \tabularnewline
Trimmed Mean ( 7 / 40 ) & 20.8867924528302 & 0.661659645831065 & 31.5672756898990 \tabularnewline
Trimmed Mean ( 8 / 40 ) & 20.8557692307692 & 0.639941749185642 & 32.5901056733824 \tabularnewline
Trimmed Mean ( 9 / 40 ) & 20.8235294117647 & 0.615343162212177 & 33.8405148387503 \tabularnewline
Trimmed Mean ( 10 / 40 ) & 20.8 & 0.590154918883871 & 35.244982858633 \tabularnewline
Trimmed Mean ( 11 / 40 ) & 20.7755102040816 & 0.566720407475586 & 36.6591884287785 \tabularnewline
Trimmed Mean ( 12 / 40 ) & 20.7604166666667 & 0.542845167027853 & 38.2437164916336 \tabularnewline
Trimmed Mean ( 13 / 40 ) & 20.7340425531915 & 0.523564051844756 & 39.6017306385646 \tabularnewline
Trimmed Mean ( 14 / 40 ) & 20.7065217391304 & 0.506889478110538 & 40.8501707636846 \tabularnewline
Trimmed Mean ( 15 / 40 ) & 20.6777777777778 & 0.487759733370409 & 42.3933678061016 \tabularnewline
Trimmed Mean ( 16 / 40 ) & 20.6477272727273 & 0.471507889483474 & 43.7908415389324 \tabularnewline
Trimmed Mean ( 17 / 40 ) & 20.6511627906977 & 0.461594050590433 & 44.7387975739341 \tabularnewline
Trimmed Mean ( 18 / 40 ) & 20.6547619047619 & 0.450184525059762 & 45.8806572749696 \tabularnewline
Trimmed Mean ( 19 / 40 ) & 20.6585365853659 & 0.442481951819478 & 46.6878626357941 \tabularnewline
Trimmed Mean ( 20 / 40 ) & 20.65 & 0.436143920039408 & 47.346756543423 \tabularnewline
Trimmed Mean ( 21 / 40 ) & 20.6538461538462 & 0.43138098181789 & 47.8784346653587 \tabularnewline
Trimmed Mean ( 22 / 40 ) & 20.6578947368421 & 0.425730592506719 & 48.5233974265453 \tabularnewline
Trimmed Mean ( 23 / 40 ) & 20.6621621621622 & 0.419038331979201 & 49.3085252238636 \tabularnewline
Trimmed Mean ( 24 / 40 ) & 20.6666666666667 & 0.411113225896519 & 50.2700116776799 \tabularnewline
Trimmed Mean ( 25 / 40 ) & 20.6857142857143 & 0.404704660426533 & 51.1131111361872 \tabularnewline
Trimmed Mean ( 26 / 40 ) & 20.7058823529412 & 0.397014109926669 & 52.1540213187024 \tabularnewline
Trimmed Mean ( 27 / 40 ) & 20.7272727272727 & 0.387776793116778 & 53.4515553668803 \tabularnewline
Trimmed Mean ( 28 / 40 ) & 20.75 & 0.376649809989437 & 55.0909610191544 \tabularnewline
Trimmed Mean ( 29 / 40 ) & 20.7580645161290 & 0.367711550230486 & 56.452032858684 \tabularnewline
Trimmed Mean ( 30 / 40 ) & 20.7833333333333 & 0.360548598530173 & 57.6436392155164 \tabularnewline
Trimmed Mean ( 31 / 40 ) & 20.8103448275862 & 0.351693592021407 & 59.1718055139303 \tabularnewline
Trimmed Mean ( 32 / 40 ) & 20.8214285714286 & 0.34576016653799 & 60.2192808382421 \tabularnewline
Trimmed Mean ( 33 / 40 ) & 20.8333333333333 & 0.338275728074086 & 61.5868405692134 \tabularnewline
Trimmed Mean ( 34 / 40 ) & 20.8653846153846 & 0.332988712677507 & 62.6609366053568 \tabularnewline
Trimmed Mean ( 35 / 40 ) & 20.9 & 0.326077491728952 & 64.0951937196967 \tabularnewline
Trimmed Mean ( 36 / 40 ) & 20.9375 & 0.317076419296293 & 66.0329773070727 \tabularnewline
Trimmed Mean ( 37 / 40 ) & 20.9565217391304 & 0.312317999931617 & 67.0999485899594 \tabularnewline
Trimmed Mean ( 38 / 40 ) & 20.9772727272727 & 0.305842745115154 & 68.588426772636 \tabularnewline
Trimmed Mean ( 39 / 40 ) & 21 & 0.297101757186175 & 70.6828535747793 \tabularnewline
Trimmed Mean ( 40 / 40 ) & 21.025 & 0.285296741602898 & 73.6951984865797 \tabularnewline
Median & 21 &  &  \tabularnewline
Midrange & 20.5 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 20.6666666666667 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 20.6666666666667 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 20.6666666666667 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 20.6666666666667 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 20.6666666666667 &  &  \tabularnewline
Midmean - Closest Observation & 20.6666666666667 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 20.6666666666667 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 20.6666666666667 &  &  \tabularnewline
Number of observations & 120 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=67700&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]20.9[/C][C]0.819527089155657[/C][C]25.5025127009930[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]0[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]0[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]22.7317692521575[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 40 )[/C][C]20.9[/C][C]0.816101959906717[/C][C]25.6095451631913[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 40 )[/C][C]20.9[/C][C]0.816101959906717[/C][C]25.6095451631913[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 40 )[/C][C]20.925[/C][C]0.80144848734722[/C][C]26.1089768467358[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 40 )[/C][C]20.925[/C][C]0.80144848734722[/C][C]26.1089768467358[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 40 )[/C][C]20.9666666666667[/C][C]0.778648305681225[/C][C]26.9270048026667[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 40 )[/C][C]21.0166666666667[/C][C]0.770243452849376[/C][C]27.2857452912054[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 40 )[/C][C]21.075[/C][C]0.760929928273489[/C][C]27.6963741560515[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 40 )[/C][C]21.075[/C][C]0.760929928273489[/C][C]27.6963741560515[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 40 )[/C][C]21[/C][C]0.747170198363217[/C][C]28.106046046809[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 40 )[/C][C]21[/C][C]0.719476934184501[/C][C]29.1878710799849[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 40 )[/C][C]20.9083333333333[/C][C]0.703731135925742[/C][C]29.7106839046263[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 40 )[/C][C]21.0083333333333[/C][C]0.657481809328978[/C][C]31.9527217867432[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 40 )[/C][C]21.0083333333333[/C][C]0.624824438461098[/C][C]33.6227779199474[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 40 )[/C][C]21.0083333333333[/C][C]0.624824438461098[/C][C]33.6227779199474[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 40 )[/C][C]21.0083333333333[/C][C]0.588462345302911[/C][C]35.7003867809406[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 40 )[/C][C]20.6083333333333[/C][C]0.530220586373966[/C][C]38.8674711298331[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 40 )[/C][C]20.6083333333333[/C][C]0.530220586373966[/C][C]38.8674711298331[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 40 )[/C][C]20.6083333333333[/C][C]0.490711458762653[/C][C]41.9968455297498[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 40 )[/C][C]20.7666666666667[/C][C]0.47081985429753[/C][C]44.1074574003487[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 40 )[/C][C]20.6[/C][C]0.45008558165345[/C][C]45.7690733489464[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 40 )[/C][C]20.6[/C][C]0.45008558165345[/C][C]45.7690733489464[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 40 )[/C][C]20.6[/C][C]0.45008558165345[/C][C]45.7690733489464[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 40 )[/C][C]20.6[/C][C]0.45008558165345[/C][C]45.7690733489464[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 40 )[/C][C]20.4[/C][C]0.427093623911004[/C][C]47.7647027674917[/C][/ROW]
[ROW][C]Winsorized Mean ( 25 / 40 )[/C][C]20.4[/C][C]0.427093623911004[/C][C]47.7647027674917[/C][/ROW]
[ROW][C]Winsorized Mean ( 26 / 40 )[/C][C]20.4[/C][C]0.427093623911004[/C][C]47.7647027674917[/C][/ROW]
[ROW][C]Winsorized Mean ( 27 / 40 )[/C][C]20.4[/C][C]0.427093623911004[/C][C]47.7647027674917[/C][/ROW]
[ROW][C]Winsorized Mean ( 28 / 40 )[/C][C]20.6333333333333[/C][C]0.398514983838254[/C][C]51.7755521626956[/C][/ROW]
[ROW][C]Winsorized Mean ( 29 / 40 )[/C][C]20.3916666666667[/C][C]0.372232238531844[/C][C]54.7821079310469[/C][/ROW]
[ROW][C]Winsorized Mean ( 30 / 40 )[/C][C]20.3916666666667[/C][C]0.372232238531844[/C][C]54.7821079310469[/C][/ROW]
[ROW][C]Winsorized Mean ( 31 / 40 )[/C][C]20.65[/C][C]0.341698263210735[/C][C]60.4334356457193[/C][/ROW]
[ROW][C]Winsorized Mean ( 32 / 40 )[/C][C]20.65[/C][C]0.341698263210735[/C][C]60.4334356457193[/C][/ROW]
[ROW][C]Winsorized Mean ( 33 / 40 )[/C][C]20.375[/C][C]0.313573087544982[/C][C]64.9768771915964[/C][/ROW]
[ROW][C]Winsorized Mean ( 34 / 40 )[/C][C]20.375[/C][C]0.313573087544982[/C][C]64.9768771915964[/C][/ROW]
[ROW][C]Winsorized Mean ( 35 / 40 )[/C][C]20.375[/C][C]0.313573087544982[/C][C]64.9768771915964[/C][/ROW]
[ROW][C]Winsorized Mean ( 36 / 40 )[/C][C]20.675[/C][C]0.27934559882954[/C][C]74.0122632560828[/C][/ROW]
[ROW][C]Winsorized Mean ( 37 / 40 )[/C][C]20.675[/C][C]0.27934559882954[/C][C]74.0122632560828[/C][/ROW]
[ROW][C]Winsorized Mean ( 38 / 40 )[/C][C]20.675[/C][C]0.27934559882954[/C][C]74.0122632560828[/C][/ROW]
[ROW][C]Winsorized Mean ( 39 / 40 )[/C][C]20.675[/C][C]0.27934559882954[/C][C]74.0122632560828[/C][/ROW]
[ROW][C]Winsorized Mean ( 40 / 40 )[/C][C]20.675[/C][C]0.27934559882954[/C][C]74.0122632560828[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 40 )[/C][C]20.9067796610169[/C][C]0.796103367625645[/C][C]26.2613882960586[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 40 )[/C][C]20.9137931034483[/C][C]0.773877187851308[/C][C]27.0246925891640[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 40 )[/C][C]20.9210526315789[/C][C]0.749076410760137[/C][C]27.9291302343228[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 40 )[/C][C]20.9196428571429[/C][C]0.72753112871714[/C][C]28.7542924713484[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 40 )[/C][C]20.9181818181818[/C][C]0.703397191756866[/C][C]29.7387906339727[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 40 )[/C][C]20.9074074074074[/C][C]0.682767290446464[/C][C]30.6215715075278[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 40 )[/C][C]20.8867924528302[/C][C]0.661659645831065[/C][C]31.5672756898990[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 40 )[/C][C]20.8557692307692[/C][C]0.639941749185642[/C][C]32.5901056733824[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 40 )[/C][C]20.8235294117647[/C][C]0.615343162212177[/C][C]33.8405148387503[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 40 )[/C][C]20.8[/C][C]0.590154918883871[/C][C]35.244982858633[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 40 )[/C][C]20.7755102040816[/C][C]0.566720407475586[/C][C]36.6591884287785[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 40 )[/C][C]20.7604166666667[/C][C]0.542845167027853[/C][C]38.2437164916336[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 40 )[/C][C]20.7340425531915[/C][C]0.523564051844756[/C][C]39.6017306385646[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 40 )[/C][C]20.7065217391304[/C][C]0.506889478110538[/C][C]40.8501707636846[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 40 )[/C][C]20.6777777777778[/C][C]0.487759733370409[/C][C]42.3933678061016[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 40 )[/C][C]20.6477272727273[/C][C]0.471507889483474[/C][C]43.7908415389324[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 40 )[/C][C]20.6511627906977[/C][C]0.461594050590433[/C][C]44.7387975739341[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 40 )[/C][C]20.6547619047619[/C][C]0.450184525059762[/C][C]45.8806572749696[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 40 )[/C][C]20.6585365853659[/C][C]0.442481951819478[/C][C]46.6878626357941[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 40 )[/C][C]20.65[/C][C]0.436143920039408[/C][C]47.346756543423[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 40 )[/C][C]20.6538461538462[/C][C]0.43138098181789[/C][C]47.8784346653587[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 40 )[/C][C]20.6578947368421[/C][C]0.425730592506719[/C][C]48.5233974265453[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 40 )[/C][C]20.6621621621622[/C][C]0.419038331979201[/C][C]49.3085252238636[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 40 )[/C][C]20.6666666666667[/C][C]0.411113225896519[/C][C]50.2700116776799[/C][/ROW]
[ROW][C]Trimmed Mean ( 25 / 40 )[/C][C]20.6857142857143[/C][C]0.404704660426533[/C][C]51.1131111361872[/C][/ROW]
[ROW][C]Trimmed Mean ( 26 / 40 )[/C][C]20.7058823529412[/C][C]0.397014109926669[/C][C]52.1540213187024[/C][/ROW]
[ROW][C]Trimmed Mean ( 27 / 40 )[/C][C]20.7272727272727[/C][C]0.387776793116778[/C][C]53.4515553668803[/C][/ROW]
[ROW][C]Trimmed Mean ( 28 / 40 )[/C][C]20.75[/C][C]0.376649809989437[/C][C]55.0909610191544[/C][/ROW]
[ROW][C]Trimmed Mean ( 29 / 40 )[/C][C]20.7580645161290[/C][C]0.367711550230486[/C][C]56.452032858684[/C][/ROW]
[ROW][C]Trimmed Mean ( 30 / 40 )[/C][C]20.7833333333333[/C][C]0.360548598530173[/C][C]57.6436392155164[/C][/ROW]
[ROW][C]Trimmed Mean ( 31 / 40 )[/C][C]20.8103448275862[/C][C]0.351693592021407[/C][C]59.1718055139303[/C][/ROW]
[ROW][C]Trimmed Mean ( 32 / 40 )[/C][C]20.8214285714286[/C][C]0.34576016653799[/C][C]60.2192808382421[/C][/ROW]
[ROW][C]Trimmed Mean ( 33 / 40 )[/C][C]20.8333333333333[/C][C]0.338275728074086[/C][C]61.5868405692134[/C][/ROW]
[ROW][C]Trimmed Mean ( 34 / 40 )[/C][C]20.8653846153846[/C][C]0.332988712677507[/C][C]62.6609366053568[/C][/ROW]
[ROW][C]Trimmed Mean ( 35 / 40 )[/C][C]20.9[/C][C]0.326077491728952[/C][C]64.0951937196967[/C][/ROW]
[ROW][C]Trimmed Mean ( 36 / 40 )[/C][C]20.9375[/C][C]0.317076419296293[/C][C]66.0329773070727[/C][/ROW]
[ROW][C]Trimmed Mean ( 37 / 40 )[/C][C]20.9565217391304[/C][C]0.312317999931617[/C][C]67.0999485899594[/C][/ROW]
[ROW][C]Trimmed Mean ( 38 / 40 )[/C][C]20.9772727272727[/C][C]0.305842745115154[/C][C]68.588426772636[/C][/ROW]
[ROW][C]Trimmed Mean ( 39 / 40 )[/C][C]21[/C][C]0.297101757186175[/C][C]70.6828535747793[/C][/ROW]
[ROW][C]Trimmed Mean ( 40 / 40 )[/C][C]21.025[/C][C]0.285296741602898[/C][C]73.6951984865797[/C][/ROW]
[ROW][C]Median[/C][C]21[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]20.5[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]20.6666666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]20.6666666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]20.6666666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]20.6666666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]20.6666666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]20.6666666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]20.6666666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]20.6666666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]120[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=67700&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=67700&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 Mean20.90.81952708915565725.5025127009930
Geometric Mean0
Harmonic Mean0
Quadratic Mean22.7317692521575
Winsorized Mean ( 1 / 40 )20.90.81610195990671725.6095451631913
Winsorized Mean ( 2 / 40 )20.90.81610195990671725.6095451631913
Winsorized Mean ( 3 / 40 )20.9250.8014484873472226.1089768467358
Winsorized Mean ( 4 / 40 )20.9250.8014484873472226.1089768467358
Winsorized Mean ( 5 / 40 )20.96666666666670.77864830568122526.9270048026667
Winsorized Mean ( 6 / 40 )21.01666666666670.77024345284937627.2857452912054
Winsorized Mean ( 7 / 40 )21.0750.76092992827348927.6963741560515
Winsorized Mean ( 8 / 40 )21.0750.76092992827348927.6963741560515
Winsorized Mean ( 9 / 40 )210.74717019836321728.106046046809
Winsorized Mean ( 10 / 40 )210.71947693418450129.1878710799849
Winsorized Mean ( 11 / 40 )20.90833333333330.70373113592574229.7106839046263
Winsorized Mean ( 12 / 40 )21.00833333333330.65748180932897831.9527217867432
Winsorized Mean ( 13 / 40 )21.00833333333330.62482443846109833.6227779199474
Winsorized Mean ( 14 / 40 )21.00833333333330.62482443846109833.6227779199474
Winsorized Mean ( 15 / 40 )21.00833333333330.58846234530291135.7003867809406
Winsorized Mean ( 16 / 40 )20.60833333333330.53022058637396638.8674711298331
Winsorized Mean ( 17 / 40 )20.60833333333330.53022058637396638.8674711298331
Winsorized Mean ( 18 / 40 )20.60833333333330.49071145876265341.9968455297498
Winsorized Mean ( 19 / 40 )20.76666666666670.4708198542975344.1074574003487
Winsorized Mean ( 20 / 40 )20.60.4500855816534545.7690733489464
Winsorized Mean ( 21 / 40 )20.60.4500855816534545.7690733489464
Winsorized Mean ( 22 / 40 )20.60.4500855816534545.7690733489464
Winsorized Mean ( 23 / 40 )20.60.4500855816534545.7690733489464
Winsorized Mean ( 24 / 40 )20.40.42709362391100447.7647027674917
Winsorized Mean ( 25 / 40 )20.40.42709362391100447.7647027674917
Winsorized Mean ( 26 / 40 )20.40.42709362391100447.7647027674917
Winsorized Mean ( 27 / 40 )20.40.42709362391100447.7647027674917
Winsorized Mean ( 28 / 40 )20.63333333333330.39851498383825451.7755521626956
Winsorized Mean ( 29 / 40 )20.39166666666670.37223223853184454.7821079310469
Winsorized Mean ( 30 / 40 )20.39166666666670.37223223853184454.7821079310469
Winsorized Mean ( 31 / 40 )20.650.34169826321073560.4334356457193
Winsorized Mean ( 32 / 40 )20.650.34169826321073560.4334356457193
Winsorized Mean ( 33 / 40 )20.3750.31357308754498264.9768771915964
Winsorized Mean ( 34 / 40 )20.3750.31357308754498264.9768771915964
Winsorized Mean ( 35 / 40 )20.3750.31357308754498264.9768771915964
Winsorized Mean ( 36 / 40 )20.6750.2793455988295474.0122632560828
Winsorized Mean ( 37 / 40 )20.6750.2793455988295474.0122632560828
Winsorized Mean ( 38 / 40 )20.6750.2793455988295474.0122632560828
Winsorized Mean ( 39 / 40 )20.6750.2793455988295474.0122632560828
Winsorized Mean ( 40 / 40 )20.6750.2793455988295474.0122632560828
Trimmed Mean ( 1 / 40 )20.90677966101690.79610336762564526.2613882960586
Trimmed Mean ( 2 / 40 )20.91379310344830.77387718785130827.0246925891640
Trimmed Mean ( 3 / 40 )20.92105263157890.74907641076013727.9291302343228
Trimmed Mean ( 4 / 40 )20.91964285714290.7275311287171428.7542924713484
Trimmed Mean ( 5 / 40 )20.91818181818180.70339719175686629.7387906339727
Trimmed Mean ( 6 / 40 )20.90740740740740.68276729044646430.6215715075278
Trimmed Mean ( 7 / 40 )20.88679245283020.66165964583106531.5672756898990
Trimmed Mean ( 8 / 40 )20.85576923076920.63994174918564232.5901056733824
Trimmed Mean ( 9 / 40 )20.82352941176470.61534316221217733.8405148387503
Trimmed Mean ( 10 / 40 )20.80.59015491888387135.244982858633
Trimmed Mean ( 11 / 40 )20.77551020408160.56672040747558636.6591884287785
Trimmed Mean ( 12 / 40 )20.76041666666670.54284516702785338.2437164916336
Trimmed Mean ( 13 / 40 )20.73404255319150.52356405184475639.6017306385646
Trimmed Mean ( 14 / 40 )20.70652173913040.50688947811053840.8501707636846
Trimmed Mean ( 15 / 40 )20.67777777777780.48775973337040942.3933678061016
Trimmed Mean ( 16 / 40 )20.64772727272730.47150788948347443.7908415389324
Trimmed Mean ( 17 / 40 )20.65116279069770.46159405059043344.7387975739341
Trimmed Mean ( 18 / 40 )20.65476190476190.45018452505976245.8806572749696
Trimmed Mean ( 19 / 40 )20.65853658536590.44248195181947846.6878626357941
Trimmed Mean ( 20 / 40 )20.650.43614392003940847.346756543423
Trimmed Mean ( 21 / 40 )20.65384615384620.4313809818178947.8784346653587
Trimmed Mean ( 22 / 40 )20.65789473684210.42573059250671948.5233974265453
Trimmed Mean ( 23 / 40 )20.66216216216220.41903833197920149.3085252238636
Trimmed Mean ( 24 / 40 )20.66666666666670.41111322589651950.2700116776799
Trimmed Mean ( 25 / 40 )20.68571428571430.40470466042653351.1131111361872
Trimmed Mean ( 26 / 40 )20.70588235294120.39701410992666952.1540213187024
Trimmed Mean ( 27 / 40 )20.72727272727270.38777679311677853.4515553668803
Trimmed Mean ( 28 / 40 )20.750.37664980998943755.0909610191544
Trimmed Mean ( 29 / 40 )20.75806451612900.36771155023048656.452032858684
Trimmed Mean ( 30 / 40 )20.78333333333330.36054859853017357.6436392155164
Trimmed Mean ( 31 / 40 )20.81034482758620.35169359202140759.1718055139303
Trimmed Mean ( 32 / 40 )20.82142857142860.3457601665379960.2192808382421
Trimmed Mean ( 33 / 40 )20.83333333333330.33827572807408661.5868405692134
Trimmed Mean ( 34 / 40 )20.86538461538460.33298871267750762.6609366053568
Trimmed Mean ( 35 / 40 )20.90.32607749172895264.0951937196967
Trimmed Mean ( 36 / 40 )20.93750.31707641929629366.0329773070727
Trimmed Mean ( 37 / 40 )20.95652173913040.31231799993161767.0999485899594
Trimmed Mean ( 38 / 40 )20.97727272727270.30584274511515468.588426772636
Trimmed Mean ( 39 / 40 )210.29710175718617570.6828535747793
Trimmed Mean ( 40 / 40 )21.0250.28529674160289873.6951984865797
Median21
Midrange20.5
Midmean - Weighted Average at Xnp20.6666666666667
Midmean - Weighted Average at X(n+1)p20.6666666666667
Midmean - Empirical Distribution Function20.6666666666667
Midmean - Empirical Distribution Function - Averaging20.6666666666667
Midmean - Empirical Distribution Function - Interpolation20.6666666666667
Midmean - Closest Observation20.6666666666667
Midmean - True Basic - Statistics Graphics Toolkit20.6666666666667
Midmean - MS Excel (old versions)20.6666666666667
Number of observations120



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')