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Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationSat, 12 Oct 2013 11:09:10 -0400
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2013/Oct/12/t1381590560uqv62teze0qy7uj.htm/, Retrieved Sun, 28 Apr 2024 22:02:48 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=214949, Retrieved Sun, 28 Apr 2024 22:02:48 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact106
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [] [2013-10-12 15:09:10] [a51ebb1a550b3d5f2cc4b9cf02171f8b] [Current]
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Dataseries X:
71,4
75,8
79,2
84,4
84,4
87,2
92,4
88,5
94,8
100,9
110
107,9
111,2
116,7
125,8
131,5
146,2
155,4
157,5
137,2
121,3
89,1
69,6
56,7
58,5
56,4
60,5
64,6
73,2
84,6
80,4
88,4
84,6
90,8
94,9
93,1
96,6
93,1
98,3
105
95,6
94,3
95,3
97,1
98,1
104,4
107,8
114,3
118,7
124,1
134,2
142,4
133,8
131
133,2
125,9
126,2
122,7
126,6
124,8
128
134,1
138,8
134
124
110,4
116,7
124,7
126
122,8
120,2
121,2




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Sir Ronald Aylmer Fisher' @ fisher.wessa.net

\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 & 2 seconds \tabularnewline
R Server & 'Sir Ronald Aylmer Fisher' @ fisher.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=214949&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]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Sir Ronald Aylmer Fisher' @ fisher.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=214949&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=214949&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 time2 seconds
R Server'Sir Ronald Aylmer Fisher' @ fisher.wessa.net







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean106.5208333333332.8809957806606836.9736165697908
Geometric Mean103.528025255018
Harmonic Mean100.29979854534
Quadratic Mean109.251991464178
Winsorized Mean ( 1 / 24 )106.4958333333332.8728454793598937.0698090441892
Winsorized Mean ( 2 / 24 )106.2902777777782.8044329427477237.9008091645211
Winsorized Mean ( 3 / 24 )106.2152777777782.7541607872645638.5653874199811
Winsorized Mean ( 4 / 24 )106.2430555555562.6667406286609939.8400408400054
Winsorized Mean ( 5 / 24 )106.4791666666672.5745815235719441.3578539625885
Winsorized Mean ( 6 / 24 )106.3791666666672.5041014380668242.4819717961553
Winsorized Mean ( 7 / 24 )106.5444444444442.4687117908842843.157911279016
Winsorized Mean ( 8 / 24 )106.8222222222222.4133117575993144.2637474772368
Winsorized Mean ( 9 / 24 )107.2222222222222.3348898415288145.9217477052436
Winsorized Mean ( 10 / 24 )107.3055555555562.2937273184278946.7821761956877
Winsorized Mean ( 11 / 24 )107.6569444444442.1558023265870349.9382263005915
Winsorized Mean ( 12 / 24 )107.5736111111112.1428959617119250.2001091201705
Winsorized Mean ( 13 / 24 )107.0680555555562.0567875212633852.0559632186941
Winsorized Mean ( 14 / 24 )106.7958333333332.018461775744352.9095148675543
Winsorized Mean ( 15 / 24 )107.2541666666671.9251952906853455.7107983722971
Winsorized Mean ( 16 / 24 )107.4763888888891.8804128890320157.1557393143669
Winsorized Mean ( 17 / 24 )107.4763888888891.8737692810705757.3583898373459
Winsorized Mean ( 18 / 24 )107.6013888888891.8490369834749258.1932053552936
Winsorized Mean ( 19 / 24 )107.7861111111111.7503814759218161.5786401957592
Winsorized Mean ( 20 / 24 )108.2027777777781.6868530722189164.1447554382706
Winsorized Mean ( 21 / 24 )108.2319444444441.6360758645913466.1533775950411
Winsorized Mean ( 22 / 24 )108.2013888888891.6319056866173166.3037023378317
Winsorized Mean ( 23 / 24 )108.2013888888891.5304940198059670.6970347408526
Winsorized Mean ( 24 / 24 )108.3347222222221.5047956200322271.9929808274577
Trimmed Mean ( 1 / 24 )106.5085714285712.7796701644279638.3169819180652
Trimmed Mean ( 2 / 24 )106.5220588235292.6687159789388139.9150976215486
Trimmed Mean ( 3 / 24 )106.6484848484852.580477397894741.3289746058208
Trimmed Mean ( 4 / 24 )106.81093752.4978652762769442.7608880728754
Trimmed Mean ( 5 / 24 )106.9758064516132.4309737658950544.0053315064163
Trimmed Mean ( 6 / 24 )107.0952.379225560037745.0125460144699
Trimmed Mean ( 7 / 24 )107.2431034482762.3352452352905445.9237007863687
Trimmed Mean ( 8 / 24 )107.3714285714292.289706943032746.893087736903
Trimmed Mean ( 9 / 24 )107.4629629629632.2463112028923547.8397484839117
Trimmed Mean ( 10 / 24 )107.52.2096814946259448.6495453129538
Trimmed Mean ( 11 / 24 )107.5282.171612849323549.515271579599
Trimmed Mean ( 12 / 24 )107.5104166666672.1516512700239149.9664690856116
Trimmed Mean ( 13 / 24 )107.5021739130432.1262711211149250.5590151911927
Trimmed Mean ( 14 / 24 )107.5568181818182.108791618472651.0040049664658
Trimmed Mean ( 15 / 24 )107.652.0902551678363751.5008892964148
Trimmed Mean ( 16 / 24 )107.69752.081867651092851.7311943165398
Trimmed Mean ( 17 / 24 )107.7236842105262.0750342649505251.9141712645865
Trimmed Mean ( 18 / 24 )107.7527777777782.061350636405252.2729010168248
Trimmed Mean ( 19 / 24 )107.7705882352942.042400502169352.7666283477837
Trimmed Mean ( 20 / 24 )107.768752.0335662971933452.9949528317511
Trimmed Mean ( 21 / 24 )107.7166666666672.0283512546550153.1055291431699
Trimmed Mean ( 22 / 24 )107.6535714285712.0240582246815453.1869933956615
Trimmed Mean ( 23 / 24 )107.5846153846152.0069317746074553.6065135575716
Trimmed Mean ( 24 / 24 )107.5041666666672.0008646606146653.7288547210593
Median107.85
Midrange106.95
Midmean - Weighted Average at Xnp107.232432432432
Midmean - Weighted Average at X(n+1)p107.752777777778
Midmean - Empirical Distribution Function107.232432432432
Midmean - Empirical Distribution Function - Averaging107.752777777778
Midmean - Empirical Distribution Function - Interpolation107.752777777778
Midmean - Closest Observation107.232432432432
Midmean - True Basic - Statistics Graphics Toolkit107.752777777778
Midmean - MS Excel (old versions)107.723684210526
Number of observations72

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 106.520833333333 & 2.88099578066068 & 36.9736165697908 \tabularnewline
Geometric Mean & 103.528025255018 &  &  \tabularnewline
Harmonic Mean & 100.29979854534 &  &  \tabularnewline
Quadratic Mean & 109.251991464178 &  &  \tabularnewline
Winsorized Mean ( 1 / 24 ) & 106.495833333333 & 2.87284547935989 & 37.0698090441892 \tabularnewline
Winsorized Mean ( 2 / 24 ) & 106.290277777778 & 2.80443294274772 & 37.9008091645211 \tabularnewline
Winsorized Mean ( 3 / 24 ) & 106.215277777778 & 2.75416078726456 & 38.5653874199811 \tabularnewline
Winsorized Mean ( 4 / 24 ) & 106.243055555556 & 2.66674062866099 & 39.8400408400054 \tabularnewline
Winsorized Mean ( 5 / 24 ) & 106.479166666667 & 2.57458152357194 & 41.3578539625885 \tabularnewline
Winsorized Mean ( 6 / 24 ) & 106.379166666667 & 2.50410143806682 & 42.4819717961553 \tabularnewline
Winsorized Mean ( 7 / 24 ) & 106.544444444444 & 2.46871179088428 & 43.157911279016 \tabularnewline
Winsorized Mean ( 8 / 24 ) & 106.822222222222 & 2.41331175759931 & 44.2637474772368 \tabularnewline
Winsorized Mean ( 9 / 24 ) & 107.222222222222 & 2.33488984152881 & 45.9217477052436 \tabularnewline
Winsorized Mean ( 10 / 24 ) & 107.305555555556 & 2.29372731842789 & 46.7821761956877 \tabularnewline
Winsorized Mean ( 11 / 24 ) & 107.656944444444 & 2.15580232658703 & 49.9382263005915 \tabularnewline
Winsorized Mean ( 12 / 24 ) & 107.573611111111 & 2.14289596171192 & 50.2001091201705 \tabularnewline
Winsorized Mean ( 13 / 24 ) & 107.068055555556 & 2.05678752126338 & 52.0559632186941 \tabularnewline
Winsorized Mean ( 14 / 24 ) & 106.795833333333 & 2.0184617757443 & 52.9095148675543 \tabularnewline
Winsorized Mean ( 15 / 24 ) & 107.254166666667 & 1.92519529068534 & 55.7107983722971 \tabularnewline
Winsorized Mean ( 16 / 24 ) & 107.476388888889 & 1.88041288903201 & 57.1557393143669 \tabularnewline
Winsorized Mean ( 17 / 24 ) & 107.476388888889 & 1.87376928107057 & 57.3583898373459 \tabularnewline
Winsorized Mean ( 18 / 24 ) & 107.601388888889 & 1.84903698347492 & 58.1932053552936 \tabularnewline
Winsorized Mean ( 19 / 24 ) & 107.786111111111 & 1.75038147592181 & 61.5786401957592 \tabularnewline
Winsorized Mean ( 20 / 24 ) & 108.202777777778 & 1.68685307221891 & 64.1447554382706 \tabularnewline
Winsorized Mean ( 21 / 24 ) & 108.231944444444 & 1.63607586459134 & 66.1533775950411 \tabularnewline
Winsorized Mean ( 22 / 24 ) & 108.201388888889 & 1.63190568661731 & 66.3037023378317 \tabularnewline
Winsorized Mean ( 23 / 24 ) & 108.201388888889 & 1.53049401980596 & 70.6970347408526 \tabularnewline
Winsorized Mean ( 24 / 24 ) & 108.334722222222 & 1.50479562003222 & 71.9929808274577 \tabularnewline
Trimmed Mean ( 1 / 24 ) & 106.508571428571 & 2.77967016442796 & 38.3169819180652 \tabularnewline
Trimmed Mean ( 2 / 24 ) & 106.522058823529 & 2.66871597893881 & 39.9150976215486 \tabularnewline
Trimmed Mean ( 3 / 24 ) & 106.648484848485 & 2.5804773978947 & 41.3289746058208 \tabularnewline
Trimmed Mean ( 4 / 24 ) & 106.8109375 & 2.49786527627694 & 42.7608880728754 \tabularnewline
Trimmed Mean ( 5 / 24 ) & 106.975806451613 & 2.43097376589505 & 44.0053315064163 \tabularnewline
Trimmed Mean ( 6 / 24 ) & 107.095 & 2.3792255600377 & 45.0125460144699 \tabularnewline
Trimmed Mean ( 7 / 24 ) & 107.243103448276 & 2.33524523529054 & 45.9237007863687 \tabularnewline
Trimmed Mean ( 8 / 24 ) & 107.371428571429 & 2.2897069430327 & 46.893087736903 \tabularnewline
Trimmed Mean ( 9 / 24 ) & 107.462962962963 & 2.24631120289235 & 47.8397484839117 \tabularnewline
Trimmed Mean ( 10 / 24 ) & 107.5 & 2.20968149462594 & 48.6495453129538 \tabularnewline
Trimmed Mean ( 11 / 24 ) & 107.528 & 2.1716128493235 & 49.515271579599 \tabularnewline
Trimmed Mean ( 12 / 24 ) & 107.510416666667 & 2.15165127002391 & 49.9664690856116 \tabularnewline
Trimmed Mean ( 13 / 24 ) & 107.502173913043 & 2.12627112111492 & 50.5590151911927 \tabularnewline
Trimmed Mean ( 14 / 24 ) & 107.556818181818 & 2.1087916184726 & 51.0040049664658 \tabularnewline
Trimmed Mean ( 15 / 24 ) & 107.65 & 2.09025516783637 & 51.5008892964148 \tabularnewline
Trimmed Mean ( 16 / 24 ) & 107.6975 & 2.0818676510928 & 51.7311943165398 \tabularnewline
Trimmed Mean ( 17 / 24 ) & 107.723684210526 & 2.07503426495052 & 51.9141712645865 \tabularnewline
Trimmed Mean ( 18 / 24 ) & 107.752777777778 & 2.0613506364052 & 52.2729010168248 \tabularnewline
Trimmed Mean ( 19 / 24 ) & 107.770588235294 & 2.0424005021693 & 52.7666283477837 \tabularnewline
Trimmed Mean ( 20 / 24 ) & 107.76875 & 2.03356629719334 & 52.9949528317511 \tabularnewline
Trimmed Mean ( 21 / 24 ) & 107.716666666667 & 2.02835125465501 & 53.1055291431699 \tabularnewline
Trimmed Mean ( 22 / 24 ) & 107.653571428571 & 2.02405822468154 & 53.1869933956615 \tabularnewline
Trimmed Mean ( 23 / 24 ) & 107.584615384615 & 2.00693177460745 & 53.6065135575716 \tabularnewline
Trimmed Mean ( 24 / 24 ) & 107.504166666667 & 2.00086466061466 & 53.7288547210593 \tabularnewline
Median & 107.85 &  &  \tabularnewline
Midrange & 106.95 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 107.232432432432 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 107.752777777778 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 107.232432432432 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 107.752777777778 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 107.752777777778 &  &  \tabularnewline
Midmean - Closest Observation & 107.232432432432 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 107.752777777778 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 107.723684210526 &  &  \tabularnewline
Number of observations & 72 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=214949&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]106.520833333333[/C][C]2.88099578066068[/C][C]36.9736165697908[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]103.528025255018[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]100.29979854534[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]109.251991464178[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 24 )[/C][C]106.495833333333[/C][C]2.87284547935989[/C][C]37.0698090441892[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 24 )[/C][C]106.290277777778[/C][C]2.80443294274772[/C][C]37.9008091645211[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 24 )[/C][C]106.215277777778[/C][C]2.75416078726456[/C][C]38.5653874199811[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 24 )[/C][C]106.243055555556[/C][C]2.66674062866099[/C][C]39.8400408400054[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 24 )[/C][C]106.479166666667[/C][C]2.57458152357194[/C][C]41.3578539625885[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 24 )[/C][C]106.379166666667[/C][C]2.50410143806682[/C][C]42.4819717961553[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 24 )[/C][C]106.544444444444[/C][C]2.46871179088428[/C][C]43.157911279016[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 24 )[/C][C]106.822222222222[/C][C]2.41331175759931[/C][C]44.2637474772368[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 24 )[/C][C]107.222222222222[/C][C]2.33488984152881[/C][C]45.9217477052436[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 24 )[/C][C]107.305555555556[/C][C]2.29372731842789[/C][C]46.7821761956877[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 24 )[/C][C]107.656944444444[/C][C]2.15580232658703[/C][C]49.9382263005915[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 24 )[/C][C]107.573611111111[/C][C]2.14289596171192[/C][C]50.2001091201705[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 24 )[/C][C]107.068055555556[/C][C]2.05678752126338[/C][C]52.0559632186941[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 24 )[/C][C]106.795833333333[/C][C]2.0184617757443[/C][C]52.9095148675543[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 24 )[/C][C]107.254166666667[/C][C]1.92519529068534[/C][C]55.7107983722971[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 24 )[/C][C]107.476388888889[/C][C]1.88041288903201[/C][C]57.1557393143669[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 24 )[/C][C]107.476388888889[/C][C]1.87376928107057[/C][C]57.3583898373459[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 24 )[/C][C]107.601388888889[/C][C]1.84903698347492[/C][C]58.1932053552936[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 24 )[/C][C]107.786111111111[/C][C]1.75038147592181[/C][C]61.5786401957592[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 24 )[/C][C]108.202777777778[/C][C]1.68685307221891[/C][C]64.1447554382706[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 24 )[/C][C]108.231944444444[/C][C]1.63607586459134[/C][C]66.1533775950411[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 24 )[/C][C]108.201388888889[/C][C]1.63190568661731[/C][C]66.3037023378317[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 24 )[/C][C]108.201388888889[/C][C]1.53049401980596[/C][C]70.6970347408526[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 24 )[/C][C]108.334722222222[/C][C]1.50479562003222[/C][C]71.9929808274577[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 24 )[/C][C]106.508571428571[/C][C]2.77967016442796[/C][C]38.3169819180652[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 24 )[/C][C]106.522058823529[/C][C]2.66871597893881[/C][C]39.9150976215486[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 24 )[/C][C]106.648484848485[/C][C]2.5804773978947[/C][C]41.3289746058208[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 24 )[/C][C]106.8109375[/C][C]2.49786527627694[/C][C]42.7608880728754[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 24 )[/C][C]106.975806451613[/C][C]2.43097376589505[/C][C]44.0053315064163[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 24 )[/C][C]107.095[/C][C]2.3792255600377[/C][C]45.0125460144699[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 24 )[/C][C]107.243103448276[/C][C]2.33524523529054[/C][C]45.9237007863687[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 24 )[/C][C]107.371428571429[/C][C]2.2897069430327[/C][C]46.893087736903[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 24 )[/C][C]107.462962962963[/C][C]2.24631120289235[/C][C]47.8397484839117[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 24 )[/C][C]107.5[/C][C]2.20968149462594[/C][C]48.6495453129538[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 24 )[/C][C]107.528[/C][C]2.1716128493235[/C][C]49.515271579599[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 24 )[/C][C]107.510416666667[/C][C]2.15165127002391[/C][C]49.9664690856116[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 24 )[/C][C]107.502173913043[/C][C]2.12627112111492[/C][C]50.5590151911927[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 24 )[/C][C]107.556818181818[/C][C]2.1087916184726[/C][C]51.0040049664658[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 24 )[/C][C]107.65[/C][C]2.09025516783637[/C][C]51.5008892964148[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 24 )[/C][C]107.6975[/C][C]2.0818676510928[/C][C]51.7311943165398[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 24 )[/C][C]107.723684210526[/C][C]2.07503426495052[/C][C]51.9141712645865[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 24 )[/C][C]107.752777777778[/C][C]2.0613506364052[/C][C]52.2729010168248[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 24 )[/C][C]107.770588235294[/C][C]2.0424005021693[/C][C]52.7666283477837[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 24 )[/C][C]107.76875[/C][C]2.03356629719334[/C][C]52.9949528317511[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 24 )[/C][C]107.716666666667[/C][C]2.02835125465501[/C][C]53.1055291431699[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 24 )[/C][C]107.653571428571[/C][C]2.02405822468154[/C][C]53.1869933956615[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 24 )[/C][C]107.584615384615[/C][C]2.00693177460745[/C][C]53.6065135575716[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 24 )[/C][C]107.504166666667[/C][C]2.00086466061466[/C][C]53.7288547210593[/C][/ROW]
[ROW][C]Median[/C][C]107.85[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]106.95[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]107.232432432432[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]107.752777777778[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]107.232432432432[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]107.752777777778[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]107.752777777778[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]107.232432432432[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]107.752777777778[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]107.723684210526[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]72[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=214949&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=214949&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 Mean106.5208333333332.8809957806606836.9736165697908
Geometric Mean103.528025255018
Harmonic Mean100.29979854534
Quadratic Mean109.251991464178
Winsorized Mean ( 1 / 24 )106.4958333333332.8728454793598937.0698090441892
Winsorized Mean ( 2 / 24 )106.2902777777782.8044329427477237.9008091645211
Winsorized Mean ( 3 / 24 )106.2152777777782.7541607872645638.5653874199811
Winsorized Mean ( 4 / 24 )106.2430555555562.6667406286609939.8400408400054
Winsorized Mean ( 5 / 24 )106.4791666666672.5745815235719441.3578539625885
Winsorized Mean ( 6 / 24 )106.3791666666672.5041014380668242.4819717961553
Winsorized Mean ( 7 / 24 )106.5444444444442.4687117908842843.157911279016
Winsorized Mean ( 8 / 24 )106.8222222222222.4133117575993144.2637474772368
Winsorized Mean ( 9 / 24 )107.2222222222222.3348898415288145.9217477052436
Winsorized Mean ( 10 / 24 )107.3055555555562.2937273184278946.7821761956877
Winsorized Mean ( 11 / 24 )107.6569444444442.1558023265870349.9382263005915
Winsorized Mean ( 12 / 24 )107.5736111111112.1428959617119250.2001091201705
Winsorized Mean ( 13 / 24 )107.0680555555562.0567875212633852.0559632186941
Winsorized Mean ( 14 / 24 )106.7958333333332.018461775744352.9095148675543
Winsorized Mean ( 15 / 24 )107.2541666666671.9251952906853455.7107983722971
Winsorized Mean ( 16 / 24 )107.4763888888891.8804128890320157.1557393143669
Winsorized Mean ( 17 / 24 )107.4763888888891.8737692810705757.3583898373459
Winsorized Mean ( 18 / 24 )107.6013888888891.8490369834749258.1932053552936
Winsorized Mean ( 19 / 24 )107.7861111111111.7503814759218161.5786401957592
Winsorized Mean ( 20 / 24 )108.2027777777781.6868530722189164.1447554382706
Winsorized Mean ( 21 / 24 )108.2319444444441.6360758645913466.1533775950411
Winsorized Mean ( 22 / 24 )108.2013888888891.6319056866173166.3037023378317
Winsorized Mean ( 23 / 24 )108.2013888888891.5304940198059670.6970347408526
Winsorized Mean ( 24 / 24 )108.3347222222221.5047956200322271.9929808274577
Trimmed Mean ( 1 / 24 )106.5085714285712.7796701644279638.3169819180652
Trimmed Mean ( 2 / 24 )106.5220588235292.6687159789388139.9150976215486
Trimmed Mean ( 3 / 24 )106.6484848484852.580477397894741.3289746058208
Trimmed Mean ( 4 / 24 )106.81093752.4978652762769442.7608880728754
Trimmed Mean ( 5 / 24 )106.9758064516132.4309737658950544.0053315064163
Trimmed Mean ( 6 / 24 )107.0952.379225560037745.0125460144699
Trimmed Mean ( 7 / 24 )107.2431034482762.3352452352905445.9237007863687
Trimmed Mean ( 8 / 24 )107.3714285714292.289706943032746.893087736903
Trimmed Mean ( 9 / 24 )107.4629629629632.2463112028923547.8397484839117
Trimmed Mean ( 10 / 24 )107.52.2096814946259448.6495453129538
Trimmed Mean ( 11 / 24 )107.5282.171612849323549.515271579599
Trimmed Mean ( 12 / 24 )107.5104166666672.1516512700239149.9664690856116
Trimmed Mean ( 13 / 24 )107.5021739130432.1262711211149250.5590151911927
Trimmed Mean ( 14 / 24 )107.5568181818182.108791618472651.0040049664658
Trimmed Mean ( 15 / 24 )107.652.0902551678363751.5008892964148
Trimmed Mean ( 16 / 24 )107.69752.081867651092851.7311943165398
Trimmed Mean ( 17 / 24 )107.7236842105262.0750342649505251.9141712645865
Trimmed Mean ( 18 / 24 )107.7527777777782.061350636405252.2729010168248
Trimmed Mean ( 19 / 24 )107.7705882352942.042400502169352.7666283477837
Trimmed Mean ( 20 / 24 )107.768752.0335662971933452.9949528317511
Trimmed Mean ( 21 / 24 )107.7166666666672.0283512546550153.1055291431699
Trimmed Mean ( 22 / 24 )107.6535714285712.0240582246815453.1869933956615
Trimmed Mean ( 23 / 24 )107.5846153846152.0069317746074553.6065135575716
Trimmed Mean ( 24 / 24 )107.5041666666672.0008646606146653.7288547210593
Median107.85
Midrange106.95
Midmean - Weighted Average at Xnp107.232432432432
Midmean - Weighted Average at X(n+1)p107.752777777778
Midmean - Empirical Distribution Function107.232432432432
Midmean - Empirical Distribution Function - Averaging107.752777777778
Midmean - Empirical Distribution Function - Interpolation107.752777777778
Midmean - Closest Observation107.232432432432
Midmean - True Basic - Statistics Graphics Toolkit107.752777777778
Midmean - MS Excel (old versions)107.723684210526
Number of observations72



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