Free Statistics

of Irreproducible Research!

Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationTue, 24 Nov 2015 15:02:15 +0000
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2015/Nov/24/t14483774286nv55ifn7exch7s.htm/, Retrieved Tue, 14 May 2024 23:21:26 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=284032, Retrieved Tue, 14 May 2024 23:21:26 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact129
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [Mediaan jongens j...] [2015-11-24 15:02:15] [d7b41ff8615e11945ad30de5daa5ba50] [Current]
- RMPD    [Kendall tau Correlation Matrix] [Kendall tau corre...] [2015-12-02 20:25:52] [48fd8bb62b0a9b06295d017de30951c4]
- RM D    [Tukey lambda PPCC Plot] [Tukey Lambda jongens] [2015-12-02 21:04:42] [48fd8bb62b0a9b06295d017de30951c4]
- RM D    [Tukey lambda PPCC Plot] [Tukey Lambda meisjes] [2015-12-02 21:07:16] [48fd8bb62b0a9b06295d017de30951c4]
Feedback Forum

Post a new message
Dataseries X:
4,35
12,7
18,1
12,6
19,1
18,4
14,7
10,6
12,6
16,2
18,9
14,1
16,15
14,75
14,8
12,45
12,65
17,35
18,4
11,6
17,75
15,25
17,65
14,75
9,9
16
13,85
17,1
14,6
15,4
17,6
13,9
16,25
15,65
14,6
11,2
16,35
15,85
7,65
12,35
15,6
13,1
12,85
9,5
11,85
13,6
17,6
16,1
13,35
15,15




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gwilym Jenkins' @ jenkins.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 & 1 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=284032&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' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=284032&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=284032&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' @ jenkins.wessa.net







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean14.4570.41885658253714234.5153940578647
Geometric Mean14.0736762150636
Harmonic Mean13.5308045306283
Quadratic Mean14.7513202798936
Winsorized Mean ( 1 / 16 )14.5190.38966466483427537.2602427427566
Winsorized Mean ( 2 / 16 )14.5730.36118345725672240.3479165703921
Winsorized Mean ( 3 / 16 )14.5970.3544970855641441.1766431782383
Winsorized Mean ( 4 / 16 )14.6290.3348624146342743.6865989154904
Winsorized Mean ( 5 / 16 )14.6540.31349523968654246.7439314697482
Winsorized Mean ( 6 / 16 )14.690.30064216983935348.8620741656087
Winsorized Mean ( 7 / 16 )14.7180.29205381108869150.3948226018199
Winsorized Mean ( 8 / 16 )14.7980.27679639610724653.461678721664
Winsorized Mean ( 9 / 16 )14.7710.26442888014182855.8600104197298
Winsorized Mean ( 10 / 16 )14.7510.24931125534322859.1670038309831
Winsorized Mean ( 11 / 16 )14.5860.21978672407957866.364335976539
Winsorized Mean ( 12 / 16 )14.5740.21369079320841368.2013472886777
Winsorized Mean ( 13 / 16 )14.5740.20923690313291669.6531050774634
Winsorized Mean ( 14 / 16 )14.6020.1994121974448873.225209827178
Winsorized Mean ( 15 / 16 )14.6620.18378980895999479.7759140344475
Winsorized Mean ( 16 / 16 )14.710.16500463815373589.1490091708496
Trimmed Mean ( 1 / 16 )14.57083333333330.36798953420080339.5957818881403
Trimmed Mean ( 2 / 16 )14.62717391304350.33958879126667243.0731940782965
Trimmed Mean ( 3 / 16 )14.65795454545450.32362060166323245.293638507934
Trimmed Mean ( 4 / 16 )14.68214285714290.30623041276844247.9447574276198
Trimmed Mean ( 5 / 16 )14.698750.2921268576518450.3163253052142
Trimmed Mean ( 6 / 16 )14.71052631578950.28169724054344252.2210522453482
Trimmed Mean ( 7 / 16 )14.71527777777780.27204997384966854.0903480693194
Trimmed Mean ( 8 / 16 )14.71470588235290.26149618705758256.2712062761846
Trimmed Mean ( 9 / 16 )14.69843750.25160256893873858.4192663930187
Trimmed Mean ( 10 / 16 )14.6850.24141762832147960.8282009151585
Trimmed Mean ( 11 / 16 )14.67321428571430.23151905401800963.3779986185193
Trimmed Mean ( 12 / 16 )14.68846153846150.22670393590807664.7913829975031
Trimmed Mean ( 13 / 16 )14.70833333333330.22035599216954466.7480524968733
Trimmed Mean ( 14 / 16 )14.73181818181820.21081539940182569.8801805922091
Trimmed Mean ( 15 / 16 )14.7550.19847775959192974.340823023881
Trimmed Mean ( 16 / 16 )14.77222222222220.18449818100588680.0670344915267
Median14.75
Midrange11.725
Midmean - Weighted Average at Xnp14.626
Midmean - Weighted Average at X(n+1)p14.6884615384615
Midmean - Empirical Distribution Function14.6884615384615
Midmean - Empirical Distribution Function - Averaging14.6884615384615
Midmean - Empirical Distribution Function - Interpolation14.7083333333333
Midmean - Closest Observation14.6884615384615
Midmean - True Basic - Statistics Graphics Toolkit14.6884615384615
Midmean - MS Excel (old versions)14.6884615384615
Number of observations50

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 14.457 & 0.418856582537142 & 34.5153940578647 \tabularnewline
Geometric Mean & 14.0736762150636 &  &  \tabularnewline
Harmonic Mean & 13.5308045306283 &  &  \tabularnewline
Quadratic Mean & 14.7513202798936 &  &  \tabularnewline
Winsorized Mean ( 1 / 16 ) & 14.519 & 0.389664664834275 & 37.2602427427566 \tabularnewline
Winsorized Mean ( 2 / 16 ) & 14.573 & 0.361183457256722 & 40.3479165703921 \tabularnewline
Winsorized Mean ( 3 / 16 ) & 14.597 & 0.35449708556414 & 41.1766431782383 \tabularnewline
Winsorized Mean ( 4 / 16 ) & 14.629 & 0.33486241463427 & 43.6865989154904 \tabularnewline
Winsorized Mean ( 5 / 16 ) & 14.654 & 0.313495239686542 & 46.7439314697482 \tabularnewline
Winsorized Mean ( 6 / 16 ) & 14.69 & 0.300642169839353 & 48.8620741656087 \tabularnewline
Winsorized Mean ( 7 / 16 ) & 14.718 & 0.292053811088691 & 50.3948226018199 \tabularnewline
Winsorized Mean ( 8 / 16 ) & 14.798 & 0.276796396107246 & 53.461678721664 \tabularnewline
Winsorized Mean ( 9 / 16 ) & 14.771 & 0.264428880141828 & 55.8600104197298 \tabularnewline
Winsorized Mean ( 10 / 16 ) & 14.751 & 0.249311255343228 & 59.1670038309831 \tabularnewline
Winsorized Mean ( 11 / 16 ) & 14.586 & 0.219786724079578 & 66.364335976539 \tabularnewline
Winsorized Mean ( 12 / 16 ) & 14.574 & 0.213690793208413 & 68.2013472886777 \tabularnewline
Winsorized Mean ( 13 / 16 ) & 14.574 & 0.209236903132916 & 69.6531050774634 \tabularnewline
Winsorized Mean ( 14 / 16 ) & 14.602 & 0.19941219744488 & 73.225209827178 \tabularnewline
Winsorized Mean ( 15 / 16 ) & 14.662 & 0.183789808959994 & 79.7759140344475 \tabularnewline
Winsorized Mean ( 16 / 16 ) & 14.71 & 0.165004638153735 & 89.1490091708496 \tabularnewline
Trimmed Mean ( 1 / 16 ) & 14.5708333333333 & 0.367989534200803 & 39.5957818881403 \tabularnewline
Trimmed Mean ( 2 / 16 ) & 14.6271739130435 & 0.339588791266672 & 43.0731940782965 \tabularnewline
Trimmed Mean ( 3 / 16 ) & 14.6579545454545 & 0.323620601663232 & 45.293638507934 \tabularnewline
Trimmed Mean ( 4 / 16 ) & 14.6821428571429 & 0.306230412768442 & 47.9447574276198 \tabularnewline
Trimmed Mean ( 5 / 16 ) & 14.69875 & 0.29212685765184 & 50.3163253052142 \tabularnewline
Trimmed Mean ( 6 / 16 ) & 14.7105263157895 & 0.281697240543442 & 52.2210522453482 \tabularnewline
Trimmed Mean ( 7 / 16 ) & 14.7152777777778 & 0.272049973849668 & 54.0903480693194 \tabularnewline
Trimmed Mean ( 8 / 16 ) & 14.7147058823529 & 0.261496187057582 & 56.2712062761846 \tabularnewline
Trimmed Mean ( 9 / 16 ) & 14.6984375 & 0.251602568938738 & 58.4192663930187 \tabularnewline
Trimmed Mean ( 10 / 16 ) & 14.685 & 0.241417628321479 & 60.8282009151585 \tabularnewline
Trimmed Mean ( 11 / 16 ) & 14.6732142857143 & 0.231519054018009 & 63.3779986185193 \tabularnewline
Trimmed Mean ( 12 / 16 ) & 14.6884615384615 & 0.226703935908076 & 64.7913829975031 \tabularnewline
Trimmed Mean ( 13 / 16 ) & 14.7083333333333 & 0.220355992169544 & 66.7480524968733 \tabularnewline
Trimmed Mean ( 14 / 16 ) & 14.7318181818182 & 0.210815399401825 & 69.8801805922091 \tabularnewline
Trimmed Mean ( 15 / 16 ) & 14.755 & 0.198477759591929 & 74.340823023881 \tabularnewline
Trimmed Mean ( 16 / 16 ) & 14.7722222222222 & 0.184498181005886 & 80.0670344915267 \tabularnewline
Median & 14.75 &  &  \tabularnewline
Midrange & 11.725 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 14.626 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 14.6884615384615 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 14.6884615384615 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 14.6884615384615 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 14.7083333333333 &  &  \tabularnewline
Midmean - Closest Observation & 14.6884615384615 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 14.6884615384615 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 14.6884615384615 &  &  \tabularnewline
Number of observations & 50 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=284032&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]14.457[/C][C]0.418856582537142[/C][C]34.5153940578647[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]14.0736762150636[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]13.5308045306283[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]14.7513202798936[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 16 )[/C][C]14.519[/C][C]0.389664664834275[/C][C]37.2602427427566[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 16 )[/C][C]14.573[/C][C]0.361183457256722[/C][C]40.3479165703921[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 16 )[/C][C]14.597[/C][C]0.35449708556414[/C][C]41.1766431782383[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 16 )[/C][C]14.629[/C][C]0.33486241463427[/C][C]43.6865989154904[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 16 )[/C][C]14.654[/C][C]0.313495239686542[/C][C]46.7439314697482[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 16 )[/C][C]14.69[/C][C]0.300642169839353[/C][C]48.8620741656087[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 16 )[/C][C]14.718[/C][C]0.292053811088691[/C][C]50.3948226018199[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 16 )[/C][C]14.798[/C][C]0.276796396107246[/C][C]53.461678721664[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 16 )[/C][C]14.771[/C][C]0.264428880141828[/C][C]55.8600104197298[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 16 )[/C][C]14.751[/C][C]0.249311255343228[/C][C]59.1670038309831[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 16 )[/C][C]14.586[/C][C]0.219786724079578[/C][C]66.364335976539[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 16 )[/C][C]14.574[/C][C]0.213690793208413[/C][C]68.2013472886777[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 16 )[/C][C]14.574[/C][C]0.209236903132916[/C][C]69.6531050774634[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 16 )[/C][C]14.602[/C][C]0.19941219744488[/C][C]73.225209827178[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 16 )[/C][C]14.662[/C][C]0.183789808959994[/C][C]79.7759140344475[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 16 )[/C][C]14.71[/C][C]0.165004638153735[/C][C]89.1490091708496[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 16 )[/C][C]14.5708333333333[/C][C]0.367989534200803[/C][C]39.5957818881403[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 16 )[/C][C]14.6271739130435[/C][C]0.339588791266672[/C][C]43.0731940782965[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 16 )[/C][C]14.6579545454545[/C][C]0.323620601663232[/C][C]45.293638507934[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 16 )[/C][C]14.6821428571429[/C][C]0.306230412768442[/C][C]47.9447574276198[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 16 )[/C][C]14.69875[/C][C]0.29212685765184[/C][C]50.3163253052142[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 16 )[/C][C]14.7105263157895[/C][C]0.281697240543442[/C][C]52.2210522453482[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 16 )[/C][C]14.7152777777778[/C][C]0.272049973849668[/C][C]54.0903480693194[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 16 )[/C][C]14.7147058823529[/C][C]0.261496187057582[/C][C]56.2712062761846[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 16 )[/C][C]14.6984375[/C][C]0.251602568938738[/C][C]58.4192663930187[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 16 )[/C][C]14.685[/C][C]0.241417628321479[/C][C]60.8282009151585[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 16 )[/C][C]14.6732142857143[/C][C]0.231519054018009[/C][C]63.3779986185193[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 16 )[/C][C]14.6884615384615[/C][C]0.226703935908076[/C][C]64.7913829975031[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 16 )[/C][C]14.7083333333333[/C][C]0.220355992169544[/C][C]66.7480524968733[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 16 )[/C][C]14.7318181818182[/C][C]0.210815399401825[/C][C]69.8801805922091[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 16 )[/C][C]14.755[/C][C]0.198477759591929[/C][C]74.340823023881[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 16 )[/C][C]14.7722222222222[/C][C]0.184498181005886[/C][C]80.0670344915267[/C][/ROW]
[ROW][C]Median[/C][C]14.75[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]11.725[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]14.626[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]14.6884615384615[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]14.6884615384615[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]14.6884615384615[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]14.7083333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]14.6884615384615[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]14.6884615384615[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]14.6884615384615[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]50[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=284032&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=284032&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 Mean14.4570.41885658253714234.5153940578647
Geometric Mean14.0736762150636
Harmonic Mean13.5308045306283
Quadratic Mean14.7513202798936
Winsorized Mean ( 1 / 16 )14.5190.38966466483427537.2602427427566
Winsorized Mean ( 2 / 16 )14.5730.36118345725672240.3479165703921
Winsorized Mean ( 3 / 16 )14.5970.3544970855641441.1766431782383
Winsorized Mean ( 4 / 16 )14.6290.3348624146342743.6865989154904
Winsorized Mean ( 5 / 16 )14.6540.31349523968654246.7439314697482
Winsorized Mean ( 6 / 16 )14.690.30064216983935348.8620741656087
Winsorized Mean ( 7 / 16 )14.7180.29205381108869150.3948226018199
Winsorized Mean ( 8 / 16 )14.7980.27679639610724653.461678721664
Winsorized Mean ( 9 / 16 )14.7710.26442888014182855.8600104197298
Winsorized Mean ( 10 / 16 )14.7510.24931125534322859.1670038309831
Winsorized Mean ( 11 / 16 )14.5860.21978672407957866.364335976539
Winsorized Mean ( 12 / 16 )14.5740.21369079320841368.2013472886777
Winsorized Mean ( 13 / 16 )14.5740.20923690313291669.6531050774634
Winsorized Mean ( 14 / 16 )14.6020.1994121974448873.225209827178
Winsorized Mean ( 15 / 16 )14.6620.18378980895999479.7759140344475
Winsorized Mean ( 16 / 16 )14.710.16500463815373589.1490091708496
Trimmed Mean ( 1 / 16 )14.57083333333330.36798953420080339.5957818881403
Trimmed Mean ( 2 / 16 )14.62717391304350.33958879126667243.0731940782965
Trimmed Mean ( 3 / 16 )14.65795454545450.32362060166323245.293638507934
Trimmed Mean ( 4 / 16 )14.68214285714290.30623041276844247.9447574276198
Trimmed Mean ( 5 / 16 )14.698750.2921268576518450.3163253052142
Trimmed Mean ( 6 / 16 )14.71052631578950.28169724054344252.2210522453482
Trimmed Mean ( 7 / 16 )14.71527777777780.27204997384966854.0903480693194
Trimmed Mean ( 8 / 16 )14.71470588235290.26149618705758256.2712062761846
Trimmed Mean ( 9 / 16 )14.69843750.25160256893873858.4192663930187
Trimmed Mean ( 10 / 16 )14.6850.24141762832147960.8282009151585
Trimmed Mean ( 11 / 16 )14.67321428571430.23151905401800963.3779986185193
Trimmed Mean ( 12 / 16 )14.68846153846150.22670393590807664.7913829975031
Trimmed Mean ( 13 / 16 )14.70833333333330.22035599216954466.7480524968733
Trimmed Mean ( 14 / 16 )14.73181818181820.21081539940182569.8801805922091
Trimmed Mean ( 15 / 16 )14.7550.19847775959192974.340823023881
Trimmed Mean ( 16 / 16 )14.77222222222220.18449818100588680.0670344915267
Median14.75
Midrange11.725
Midmean - Weighted Average at Xnp14.626
Midmean - Weighted Average at X(n+1)p14.6884615384615
Midmean - Empirical Distribution Function14.6884615384615
Midmean - Empirical Distribution Function - Averaging14.6884615384615
Midmean - Empirical Distribution Function - Interpolation14.7083333333333
Midmean - Closest Observation14.6884615384615
Midmean - True Basic - Statistics Graphics Toolkit14.6884615384615
Midmean - MS Excel (old versions)14.6884615384615
Number of observations50



Parameters (Session):
par1 = 8 ; par2 = 0 ;
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')