Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationSun, 12 Oct 2014 19:12:34 +0100
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2014/Oct/12/t1413137688spv0fsmumluqe5x.htm/, Retrieved Wed, 15 May 2024 09:09:25 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=240648, Retrieved Wed, 15 May 2024 09:09:25 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact75
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [] [2014-10-12 18:12:34] [10cb439e718ee6ebb3ca27a8e32cf1a7] [Current]
Feedback Forum

Post a new message
Dataseries X:
27,88
28,06
28,08
28,12
28,11
28,18
28,2
28,37
28,64
28,75
28,97
29,08
29,16
29,24
29,36
29,35
29,43
29,49
29,61
29,66
29,75
29,74
29,97
30,02
30,09
30,16
30,33
30,41
30,44
30,45
30,46
30,51
30,54
30,82
30,88
30,89
31,13
31,41
31,47
31,56
31,62
31,65
31,79
31,98
32,14
32,32
32,5
32,55
32,66
32,68
32,72
32,8
32,93
32,96
32,98
33,09
33,46
33,65
33,82
33,83
33,92
33,87
34,03
34,11
34,29
34,44
34,64
34,77
35,01
35,19
35,32
35,35




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Gertrude Mary Cox' @ cox.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 & 'Gertrude Mary Cox' @ cox.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=240648&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]'Gertrude Mary Cox' @ cox.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=240648&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=240648&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'Gertrude Mary Cox' @ cox.wessa.net







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean31.33111111111110.254276456358118123.216720729287
Geometric Mean31.2582083078024
Harmonic Mean31.1857678988184
Quadratic Mean31.4042853144457
Winsorized Mean ( 1 / 24 )31.33319444444440.253717881042615123.496201039065
Winsorized Mean ( 2 / 24 )31.33013888888890.252829256116954123.918170587015
Winsorized Mean ( 3 / 24 )31.32388888888890.251021353077625124.785754298768
Winsorized Mean ( 4 / 24 )31.31111111111110.248233394797056126.13577289514
Winsorized Mean ( 5 / 24 )31.306250.24573437870741127.398739096558
Winsorized Mean ( 6 / 24 )31.291250.242317396320338129.133320492738
Winsorized Mean ( 7 / 24 )31.29319444444440.236760117302525132.172575351697
Winsorized Mean ( 8 / 24 )31.30319444444440.228166796673873137.194345981844
Winsorized Mean ( 9 / 24 )31.30694444444440.224210372276444139.63200777279
Winsorized Mean ( 10 / 24 )31.32222222222220.21682399688883144.459205031082
Winsorized Mean ( 11 / 24 )31.33138888888890.213003183643796147.093523922554
Winsorized Mean ( 12 / 24 )31.33805555555560.209919468023147149.286085043337
Winsorized Mean ( 13 / 24 )31.35069444444440.207527109150658151.06794756961
Winsorized Mean ( 14 / 24 )31.33902777777780.199014803489368157.470837486982
Winsorized Mean ( 15 / 24 )31.30152777777780.192353297525529162.729353644813
Winsorized Mean ( 16 / 24 )31.23486111111110.177569664199156175.902011483668
Winsorized Mean ( 17 / 24 )31.22305555555560.171766532655715181.776129917801
Winsorized Mean ( 18 / 24 )31.24805555555560.166838366825815187.295381452514
Winsorized Mean ( 19 / 24 )31.25333333333330.163880109045744190.708521707229
Winsorized Mean ( 20 / 24 )31.23944444444440.155699100994277200.639851129216
Winsorized Mean ( 21 / 24 )31.21902777777780.152033318320644205.343329492656
Winsorized Mean ( 22 / 24 )31.27402777777780.141379667824852221.205978617248
Winsorized Mean ( 23 / 24 )31.28361111111110.138420458105181226.004244887989
Winsorized Mean ( 24 / 24 )31.27027777777780.130327919784522239.935370943376
Trimmed Mean ( 1 / 24 )31.3230.250241237646063125.171215962026
Trimmed Mean ( 2 / 24 )31.31220588235290.246051687824193127.258651055163
Trimmed Mean ( 3 / 24 )31.30242424242420.241564448499437129.582082284336
Trimmed Mean ( 4 / 24 )31.2943750.236958538479484132.066880564042
Trimmed Mean ( 5 / 24 )31.28951612903230.232383600724622134.645973431278
Trimmed Mean ( 6 / 24 )31.28550.227576450803795137.472484035586
Trimmed Mean ( 7 / 24 )31.28431034482760.222636828523361140.517229572128
Trimmed Mean ( 8 / 24 )31.28267857142860.217975855190883143.51442064092
Trimmed Mean ( 9 / 24 )31.27925925925930.21424087162072146.000429435492
Trimmed Mean ( 10 / 24 )31.2750.210399587512284148.64572868126
Trimmed Mean ( 11 / 24 )31.26820.207105748400203150.976977903957
Trimmed Mean ( 12 / 24 )31.25958333333330.203609050001017153.527474997684
Trimmed Mean ( 13 / 24 )31.2493478260870.199644709100631156.524798312264
Trimmed Mean ( 14 / 24 )31.23659090909090.194877839759598160.288060190037
Trimmed Mean ( 15 / 24 )31.22404761904760.190455795220515163.943804297976
Trimmed Mean ( 16 / 24 )31.214750.186026599800494167.79723992954
Trimmed Mean ( 17 / 24 )31.21236842105260.183383497076686170.202711359575
Trimmed Mean ( 18 / 24 )31.21111111111110.180809369831032172.618881091606
Trimmed Mean ( 19 / 24 )31.20676470588240.17804930348658175.270355428459
Trimmed Mean ( 20 / 24 )31.201250.174498561552441178.805198864767
Trimmed Mean ( 21 / 24 )31.19666666666670.171250527867855182.169754774358
Trimmed Mean ( 22 / 24 )31.19392857142860.167065664691977186.716574162271
Trimmed Mean ( 23 / 24 )31.18384615384620.163573626727987190.641039008709
Trimmed Mean ( 24 / 24 )31.17083333333330.158422838927093196.757194508288
Median31.01
Midrange31.615
Midmean - Weighted Average at Xnp31.1645945945946
Midmean - Weighted Average at X(n+1)p31.2111111111111
Midmean - Empirical Distribution Function31.1645945945946
Midmean - Empirical Distribution Function - Averaging31.2111111111111
Midmean - Empirical Distribution Function - Interpolation31.2111111111111
Midmean - Closest Observation31.1645945945946
Midmean - True Basic - Statistics Graphics Toolkit31.2111111111111
Midmean - MS Excel (old versions)31.2123684210526
Number of observations72

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 31.3311111111111 & 0.254276456358118 & 123.216720729287 \tabularnewline
Geometric Mean & 31.2582083078024 &  &  \tabularnewline
Harmonic Mean & 31.1857678988184 &  &  \tabularnewline
Quadratic Mean & 31.4042853144457 &  &  \tabularnewline
Winsorized Mean ( 1 / 24 ) & 31.3331944444444 & 0.253717881042615 & 123.496201039065 \tabularnewline
Winsorized Mean ( 2 / 24 ) & 31.3301388888889 & 0.252829256116954 & 123.918170587015 \tabularnewline
Winsorized Mean ( 3 / 24 ) & 31.3238888888889 & 0.251021353077625 & 124.785754298768 \tabularnewline
Winsorized Mean ( 4 / 24 ) & 31.3111111111111 & 0.248233394797056 & 126.13577289514 \tabularnewline
Winsorized Mean ( 5 / 24 ) & 31.30625 & 0.24573437870741 & 127.398739096558 \tabularnewline
Winsorized Mean ( 6 / 24 ) & 31.29125 & 0.242317396320338 & 129.133320492738 \tabularnewline
Winsorized Mean ( 7 / 24 ) & 31.2931944444444 & 0.236760117302525 & 132.172575351697 \tabularnewline
Winsorized Mean ( 8 / 24 ) & 31.3031944444444 & 0.228166796673873 & 137.194345981844 \tabularnewline
Winsorized Mean ( 9 / 24 ) & 31.3069444444444 & 0.224210372276444 & 139.63200777279 \tabularnewline
Winsorized Mean ( 10 / 24 ) & 31.3222222222222 & 0.21682399688883 & 144.459205031082 \tabularnewline
Winsorized Mean ( 11 / 24 ) & 31.3313888888889 & 0.213003183643796 & 147.093523922554 \tabularnewline
Winsorized Mean ( 12 / 24 ) & 31.3380555555556 & 0.209919468023147 & 149.286085043337 \tabularnewline
Winsorized Mean ( 13 / 24 ) & 31.3506944444444 & 0.207527109150658 & 151.06794756961 \tabularnewline
Winsorized Mean ( 14 / 24 ) & 31.3390277777778 & 0.199014803489368 & 157.470837486982 \tabularnewline
Winsorized Mean ( 15 / 24 ) & 31.3015277777778 & 0.192353297525529 & 162.729353644813 \tabularnewline
Winsorized Mean ( 16 / 24 ) & 31.2348611111111 & 0.177569664199156 & 175.902011483668 \tabularnewline
Winsorized Mean ( 17 / 24 ) & 31.2230555555556 & 0.171766532655715 & 181.776129917801 \tabularnewline
Winsorized Mean ( 18 / 24 ) & 31.2480555555556 & 0.166838366825815 & 187.295381452514 \tabularnewline
Winsorized Mean ( 19 / 24 ) & 31.2533333333333 & 0.163880109045744 & 190.708521707229 \tabularnewline
Winsorized Mean ( 20 / 24 ) & 31.2394444444444 & 0.155699100994277 & 200.639851129216 \tabularnewline
Winsorized Mean ( 21 / 24 ) & 31.2190277777778 & 0.152033318320644 & 205.343329492656 \tabularnewline
Winsorized Mean ( 22 / 24 ) & 31.2740277777778 & 0.141379667824852 & 221.205978617248 \tabularnewline
Winsorized Mean ( 23 / 24 ) & 31.2836111111111 & 0.138420458105181 & 226.004244887989 \tabularnewline
Winsorized Mean ( 24 / 24 ) & 31.2702777777778 & 0.130327919784522 & 239.935370943376 \tabularnewline
Trimmed Mean ( 1 / 24 ) & 31.323 & 0.250241237646063 & 125.171215962026 \tabularnewline
Trimmed Mean ( 2 / 24 ) & 31.3122058823529 & 0.246051687824193 & 127.258651055163 \tabularnewline
Trimmed Mean ( 3 / 24 ) & 31.3024242424242 & 0.241564448499437 & 129.582082284336 \tabularnewline
Trimmed Mean ( 4 / 24 ) & 31.294375 & 0.236958538479484 & 132.066880564042 \tabularnewline
Trimmed Mean ( 5 / 24 ) & 31.2895161290323 & 0.232383600724622 & 134.645973431278 \tabularnewline
Trimmed Mean ( 6 / 24 ) & 31.2855 & 0.227576450803795 & 137.472484035586 \tabularnewline
Trimmed Mean ( 7 / 24 ) & 31.2843103448276 & 0.222636828523361 & 140.517229572128 \tabularnewline
Trimmed Mean ( 8 / 24 ) & 31.2826785714286 & 0.217975855190883 & 143.51442064092 \tabularnewline
Trimmed Mean ( 9 / 24 ) & 31.2792592592593 & 0.21424087162072 & 146.000429435492 \tabularnewline
Trimmed Mean ( 10 / 24 ) & 31.275 & 0.210399587512284 & 148.64572868126 \tabularnewline
Trimmed Mean ( 11 / 24 ) & 31.2682 & 0.207105748400203 & 150.976977903957 \tabularnewline
Trimmed Mean ( 12 / 24 ) & 31.2595833333333 & 0.203609050001017 & 153.527474997684 \tabularnewline
Trimmed Mean ( 13 / 24 ) & 31.249347826087 & 0.199644709100631 & 156.524798312264 \tabularnewline
Trimmed Mean ( 14 / 24 ) & 31.2365909090909 & 0.194877839759598 & 160.288060190037 \tabularnewline
Trimmed Mean ( 15 / 24 ) & 31.2240476190476 & 0.190455795220515 & 163.943804297976 \tabularnewline
Trimmed Mean ( 16 / 24 ) & 31.21475 & 0.186026599800494 & 167.79723992954 \tabularnewline
Trimmed Mean ( 17 / 24 ) & 31.2123684210526 & 0.183383497076686 & 170.202711359575 \tabularnewline
Trimmed Mean ( 18 / 24 ) & 31.2111111111111 & 0.180809369831032 & 172.618881091606 \tabularnewline
Trimmed Mean ( 19 / 24 ) & 31.2067647058824 & 0.17804930348658 & 175.270355428459 \tabularnewline
Trimmed Mean ( 20 / 24 ) & 31.20125 & 0.174498561552441 & 178.805198864767 \tabularnewline
Trimmed Mean ( 21 / 24 ) & 31.1966666666667 & 0.171250527867855 & 182.169754774358 \tabularnewline
Trimmed Mean ( 22 / 24 ) & 31.1939285714286 & 0.167065664691977 & 186.716574162271 \tabularnewline
Trimmed Mean ( 23 / 24 ) & 31.1838461538462 & 0.163573626727987 & 190.641039008709 \tabularnewline
Trimmed Mean ( 24 / 24 ) & 31.1708333333333 & 0.158422838927093 & 196.757194508288 \tabularnewline
Median & 31.01 &  &  \tabularnewline
Midrange & 31.615 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 31.1645945945946 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 31.2111111111111 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 31.1645945945946 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 31.2111111111111 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 31.2111111111111 &  &  \tabularnewline
Midmean - Closest Observation & 31.1645945945946 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 31.2111111111111 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 31.2123684210526 &  &  \tabularnewline
Number of observations & 72 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=240648&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]31.3311111111111[/C][C]0.254276456358118[/C][C]123.216720729287[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]31.2582083078024[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]31.1857678988184[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]31.4042853144457[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 24 )[/C][C]31.3331944444444[/C][C]0.253717881042615[/C][C]123.496201039065[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 24 )[/C][C]31.3301388888889[/C][C]0.252829256116954[/C][C]123.918170587015[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 24 )[/C][C]31.3238888888889[/C][C]0.251021353077625[/C][C]124.785754298768[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 24 )[/C][C]31.3111111111111[/C][C]0.248233394797056[/C][C]126.13577289514[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 24 )[/C][C]31.30625[/C][C]0.24573437870741[/C][C]127.398739096558[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 24 )[/C][C]31.29125[/C][C]0.242317396320338[/C][C]129.133320492738[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 24 )[/C][C]31.2931944444444[/C][C]0.236760117302525[/C][C]132.172575351697[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 24 )[/C][C]31.3031944444444[/C][C]0.228166796673873[/C][C]137.194345981844[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 24 )[/C][C]31.3069444444444[/C][C]0.224210372276444[/C][C]139.63200777279[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 24 )[/C][C]31.3222222222222[/C][C]0.21682399688883[/C][C]144.459205031082[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 24 )[/C][C]31.3313888888889[/C][C]0.213003183643796[/C][C]147.093523922554[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 24 )[/C][C]31.3380555555556[/C][C]0.209919468023147[/C][C]149.286085043337[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 24 )[/C][C]31.3506944444444[/C][C]0.207527109150658[/C][C]151.06794756961[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 24 )[/C][C]31.3390277777778[/C][C]0.199014803489368[/C][C]157.470837486982[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 24 )[/C][C]31.3015277777778[/C][C]0.192353297525529[/C][C]162.729353644813[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 24 )[/C][C]31.2348611111111[/C][C]0.177569664199156[/C][C]175.902011483668[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 24 )[/C][C]31.2230555555556[/C][C]0.171766532655715[/C][C]181.776129917801[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 24 )[/C][C]31.2480555555556[/C][C]0.166838366825815[/C][C]187.295381452514[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 24 )[/C][C]31.2533333333333[/C][C]0.163880109045744[/C][C]190.708521707229[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 24 )[/C][C]31.2394444444444[/C][C]0.155699100994277[/C][C]200.639851129216[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 24 )[/C][C]31.2190277777778[/C][C]0.152033318320644[/C][C]205.343329492656[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 24 )[/C][C]31.2740277777778[/C][C]0.141379667824852[/C][C]221.205978617248[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 24 )[/C][C]31.2836111111111[/C][C]0.138420458105181[/C][C]226.004244887989[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 24 )[/C][C]31.2702777777778[/C][C]0.130327919784522[/C][C]239.935370943376[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 24 )[/C][C]31.323[/C][C]0.250241237646063[/C][C]125.171215962026[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 24 )[/C][C]31.3122058823529[/C][C]0.246051687824193[/C][C]127.258651055163[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 24 )[/C][C]31.3024242424242[/C][C]0.241564448499437[/C][C]129.582082284336[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 24 )[/C][C]31.294375[/C][C]0.236958538479484[/C][C]132.066880564042[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 24 )[/C][C]31.2895161290323[/C][C]0.232383600724622[/C][C]134.645973431278[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 24 )[/C][C]31.2855[/C][C]0.227576450803795[/C][C]137.472484035586[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 24 )[/C][C]31.2843103448276[/C][C]0.222636828523361[/C][C]140.517229572128[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 24 )[/C][C]31.2826785714286[/C][C]0.217975855190883[/C][C]143.51442064092[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 24 )[/C][C]31.2792592592593[/C][C]0.21424087162072[/C][C]146.000429435492[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 24 )[/C][C]31.275[/C][C]0.210399587512284[/C][C]148.64572868126[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 24 )[/C][C]31.2682[/C][C]0.207105748400203[/C][C]150.976977903957[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 24 )[/C][C]31.2595833333333[/C][C]0.203609050001017[/C][C]153.527474997684[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 24 )[/C][C]31.249347826087[/C][C]0.199644709100631[/C][C]156.524798312264[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 24 )[/C][C]31.2365909090909[/C][C]0.194877839759598[/C][C]160.288060190037[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 24 )[/C][C]31.2240476190476[/C][C]0.190455795220515[/C][C]163.943804297976[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 24 )[/C][C]31.21475[/C][C]0.186026599800494[/C][C]167.79723992954[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 24 )[/C][C]31.2123684210526[/C][C]0.183383497076686[/C][C]170.202711359575[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 24 )[/C][C]31.2111111111111[/C][C]0.180809369831032[/C][C]172.618881091606[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 24 )[/C][C]31.2067647058824[/C][C]0.17804930348658[/C][C]175.270355428459[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 24 )[/C][C]31.20125[/C][C]0.174498561552441[/C][C]178.805198864767[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 24 )[/C][C]31.1966666666667[/C][C]0.171250527867855[/C][C]182.169754774358[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 24 )[/C][C]31.1939285714286[/C][C]0.167065664691977[/C][C]186.716574162271[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 24 )[/C][C]31.1838461538462[/C][C]0.163573626727987[/C][C]190.641039008709[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 24 )[/C][C]31.1708333333333[/C][C]0.158422838927093[/C][C]196.757194508288[/C][/ROW]
[ROW][C]Median[/C][C]31.01[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]31.615[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]31.1645945945946[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]31.2111111111111[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]31.1645945945946[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]31.2111111111111[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]31.2111111111111[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]31.1645945945946[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]31.2111111111111[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]31.2123684210526[/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=240648&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=240648&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 Mean31.33111111111110.254276456358118123.216720729287
Geometric Mean31.2582083078024
Harmonic Mean31.1857678988184
Quadratic Mean31.4042853144457
Winsorized Mean ( 1 / 24 )31.33319444444440.253717881042615123.496201039065
Winsorized Mean ( 2 / 24 )31.33013888888890.252829256116954123.918170587015
Winsorized Mean ( 3 / 24 )31.32388888888890.251021353077625124.785754298768
Winsorized Mean ( 4 / 24 )31.31111111111110.248233394797056126.13577289514
Winsorized Mean ( 5 / 24 )31.306250.24573437870741127.398739096558
Winsorized Mean ( 6 / 24 )31.291250.242317396320338129.133320492738
Winsorized Mean ( 7 / 24 )31.29319444444440.236760117302525132.172575351697
Winsorized Mean ( 8 / 24 )31.30319444444440.228166796673873137.194345981844
Winsorized Mean ( 9 / 24 )31.30694444444440.224210372276444139.63200777279
Winsorized Mean ( 10 / 24 )31.32222222222220.21682399688883144.459205031082
Winsorized Mean ( 11 / 24 )31.33138888888890.213003183643796147.093523922554
Winsorized Mean ( 12 / 24 )31.33805555555560.209919468023147149.286085043337
Winsorized Mean ( 13 / 24 )31.35069444444440.207527109150658151.06794756961
Winsorized Mean ( 14 / 24 )31.33902777777780.199014803489368157.470837486982
Winsorized Mean ( 15 / 24 )31.30152777777780.192353297525529162.729353644813
Winsorized Mean ( 16 / 24 )31.23486111111110.177569664199156175.902011483668
Winsorized Mean ( 17 / 24 )31.22305555555560.171766532655715181.776129917801
Winsorized Mean ( 18 / 24 )31.24805555555560.166838366825815187.295381452514
Winsorized Mean ( 19 / 24 )31.25333333333330.163880109045744190.708521707229
Winsorized Mean ( 20 / 24 )31.23944444444440.155699100994277200.639851129216
Winsorized Mean ( 21 / 24 )31.21902777777780.152033318320644205.343329492656
Winsorized Mean ( 22 / 24 )31.27402777777780.141379667824852221.205978617248
Winsorized Mean ( 23 / 24 )31.28361111111110.138420458105181226.004244887989
Winsorized Mean ( 24 / 24 )31.27027777777780.130327919784522239.935370943376
Trimmed Mean ( 1 / 24 )31.3230.250241237646063125.171215962026
Trimmed Mean ( 2 / 24 )31.31220588235290.246051687824193127.258651055163
Trimmed Mean ( 3 / 24 )31.30242424242420.241564448499437129.582082284336
Trimmed Mean ( 4 / 24 )31.2943750.236958538479484132.066880564042
Trimmed Mean ( 5 / 24 )31.28951612903230.232383600724622134.645973431278
Trimmed Mean ( 6 / 24 )31.28550.227576450803795137.472484035586
Trimmed Mean ( 7 / 24 )31.28431034482760.222636828523361140.517229572128
Trimmed Mean ( 8 / 24 )31.28267857142860.217975855190883143.51442064092
Trimmed Mean ( 9 / 24 )31.27925925925930.21424087162072146.000429435492
Trimmed Mean ( 10 / 24 )31.2750.210399587512284148.64572868126
Trimmed Mean ( 11 / 24 )31.26820.207105748400203150.976977903957
Trimmed Mean ( 12 / 24 )31.25958333333330.203609050001017153.527474997684
Trimmed Mean ( 13 / 24 )31.2493478260870.199644709100631156.524798312264
Trimmed Mean ( 14 / 24 )31.23659090909090.194877839759598160.288060190037
Trimmed Mean ( 15 / 24 )31.22404761904760.190455795220515163.943804297976
Trimmed Mean ( 16 / 24 )31.214750.186026599800494167.79723992954
Trimmed Mean ( 17 / 24 )31.21236842105260.183383497076686170.202711359575
Trimmed Mean ( 18 / 24 )31.21111111111110.180809369831032172.618881091606
Trimmed Mean ( 19 / 24 )31.20676470588240.17804930348658175.270355428459
Trimmed Mean ( 20 / 24 )31.201250.174498561552441178.805198864767
Trimmed Mean ( 21 / 24 )31.19666666666670.171250527867855182.169754774358
Trimmed Mean ( 22 / 24 )31.19392857142860.167065664691977186.716574162271
Trimmed Mean ( 23 / 24 )31.18384615384620.163573626727987190.641039008709
Trimmed Mean ( 24 / 24 )31.17083333333330.158422838927093196.757194508288
Median31.01
Midrange31.615
Midmean - Weighted Average at Xnp31.1645945945946
Midmean - Weighted Average at X(n+1)p31.2111111111111
Midmean - Empirical Distribution Function31.1645945945946
Midmean - Empirical Distribution Function - Averaging31.2111111111111
Midmean - Empirical Distribution Function - Interpolation31.2111111111111
Midmean - Closest Observation31.1645945945946
Midmean - True Basic - Statistics Graphics Toolkit31.2111111111111
Midmean - MS Excel (old versions)31.2123684210526
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')