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Description of Statistical Computation

Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationWed, 21 Oct 2009 11:48:52 -0600
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2009/Oct/21/t1256147447zvceln34j79ookk.htm/, Retrieved Thu, 02 May 2024 08:45:05 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=49542, Retrieved Thu, 02 May 2024 08:45:05 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsWS3 verschil
Estimated Impact132

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Bivariate Data Series] [Bivariate dataset] [2008-01-05 23:51:08] [74be16979710d4c4e7c6647856088456]
F RMPD  [Univariate Explorative Data Analysis] [Colombia Coffee] [2008-01-07 14:21:11] [74be16979710d4c4e7c6647856088456]
F RMPD    [Univariate Data Series] [] [2009-10-14 08:30:28] [74be16979710d4c4e7c6647856088456]
-           [Univariate Data Series] [WS3 deel 1 -EDA] [2009-10-20 19:35:12] [c620fe7250af73a91c51407172a85dab]
- RMPD          [Central Tendency] [WS3 deel 2 verschil] [2009-10-21 17:48:52] [b4ff140915b3f24d4faed3d78f95eba4] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
0,9
1,2
1,7
2,3
2,4
2,3
2,2
2,3
2,4
2,6
2,1
1,4
1,2
1,4
2,1
2,5
2,6
2,7
2,8
3
3,2
2,9
2,3
1,1
0,6
0,9
1,6
2
2,1
2,1
2
1,8
1,8
2
2,1
2,3
2,5
2,7
2,4
2,3
2,5
2,9
3,2
3,3
3,3
3,3
3,2
3
2,6
2,6
2,2
2,3
2,4
2,8
3,3
3,7
4
4,2
4,2
3,9
3,6

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'George Udny Yule' @ 72.249.76.132

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 1 seconds \tabularnewline
R Server & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=49542&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]'George Udny Yule' @ 72.249.76.132[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=49542&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=49542&T=0

As an alternative you can also use a QR Code:  
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'George Udny Yule' @ 72.249.76.132






Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean2.447540983606560.10268543288969223.8353280960093
Geometric Mean2.29598932070683
Harmonic Mean2.10723895594887
Quadratic Mean2.57354128665121
Winsorized Mean ( 1 / 20 )2.452459016393440.10131934466405424.2052396265008
Winsorized Mean ( 2 / 20 )2.445901639344260.09952273459939224.5763106207816
Winsorized Mean ( 3 / 20 )2.450819672131150.095831789984807225.5741823513856
Winsorized Mean ( 4 / 20 )2.444262295081970.091153044611134226.8149276363656
Winsorized Mean ( 5 / 20 )2.436065573770490.089321448934788827.2730189984826
Winsorized Mean ( 6 / 20 )2.426229508196720.078958439622839330.7279312988718
Winsorized Mean ( 7 / 20 )2.426229508196720.078958439622839330.7279312988718
Winsorized Mean ( 8 / 20 )2.452459016393440.073574116282561133.3331766701048
Winsorized Mean ( 9 / 20 )2.46721311475410.070815750751583834.8398920941881
Winsorized Mean ( 10 / 20 )2.46721311475410.064770351422258838.0917049325476
Winsorized Mean ( 11 / 20 )2.46721311475410.064770351422258838.0917049325476
Winsorized Mean ( 12 / 20 )2.506557377049180.058527881005272242.82672350334
Winsorized Mean ( 13 / 20 )2.463934426229510.050518231675439448.7731724669098
Winsorized Mean ( 14 / 20 )2.463934426229510.050518231675439448.7731724669098
Winsorized Mean ( 15 / 20 )2.463934426229510.042595619652501657.8447841897942
Winsorized Mean ( 16 / 20 )2.463934426229510.042595619652501657.8447841897942
Winsorized Mean ( 17 / 20 )2.436065573770490.037984235073606964.1335956627748
Winsorized Mean ( 18 / 20 )2.436065573770490.037984235073606964.1335956627748
Winsorized Mean ( 19 / 20 )2.404918032786890.033176645079533272.4882828574637
Winsorized Mean ( 20 / 20 )2.437704918032790.028357970750061985.9618954937906
Trimmed Mean ( 1 / 20 )2.449152542372880.096864124267806725.284413201337
Trimmed Mean ( 2 / 20 )2.445614035087720.091358110517811726.7695338840322
Trimmed Mean ( 3 / 20 )2.445454545454550.085745617897794828.5198778131079
Trimmed Mean ( 4 / 20 )2.443396226415090.080614000536226630.3098247222835
Trimmed Mean ( 5 / 20 )2.443137254901960.07614510924831332.0852813663287
Trimmed Mean ( 6 / 20 )2.444897959183670.071133989245181834.3703198024885
Trimmed Mean ( 7 / 20 )2.448936170212770.068272752519518535.8698906934013
Trimmed Mean ( 8 / 20 )2.453333333333330.064557546171433538.0022705141003
Trimmed Mean ( 9 / 20 )2.453488372093020.061392915821451539.9637049204257
Trimmed Mean ( 10 / 20 )2.451219512195120.058028793443691742.2414351002088
Trimmed Mean ( 11 / 20 )2.448717948717950.055332609161293144.2545180108894
Trimmed Mean ( 12 / 20 )2.445945945945950.051638992093410847.3662603933366
Trimmed Mean ( 13 / 20 )2.437142857142860.048348474950219550.4078538082573
Trimmed Mean ( 14 / 20 )2.433333333333330.046398036356916852.4447481918183
Trimmed Mean ( 15 / 20 )2.429032258064520.043550378289802255.7752275284667
Trimmed Mean ( 16 / 20 )2.424137931034480.042010781050554957.7027579686587
Trimmed Mean ( 17 / 20 )2.418518518518520.039598065018280161.0766843632897
Trimmed Mean ( 18 / 20 )2.4160.037718253759508464.0538667406084
Trimmed Mean ( 19 / 20 )2.413043478260870.034609251788091369.7224977019345
Trimmed Mean ( 20 / 20 )2.414285714285710.031837170762755875.8322946557182
Median2.4
Midrange2.4
Midmean - Weighted Average at Xnp2.42903225806452
Midmean - Weighted Average at X(n+1)p2.42903225806452
Midmean - Empirical Distribution Function2.42903225806452
Midmean - Empirical Distribution Function - Averaging2.42903225806452
Midmean - Empirical Distribution Function - Interpolation2.42903225806452
Midmean - Closest Observation2.39117647058824
Midmean - True Basic - Statistics Graphics Toolkit2.42903225806452
Midmean - MS Excel (old versions)2.42903225806452
Number of observations61

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 2.44754098360656 & 0.102685432889692 & 23.8353280960093 \tabularnewline
Geometric Mean & 2.29598932070683 &  &  \tabularnewline
Harmonic Mean & 2.10723895594887 &  &  \tabularnewline
Quadratic Mean & 2.57354128665121 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 2.45245901639344 & 0.101319344664054 & 24.2052396265008 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 2.44590163934426 & 0.099522734599392 & 24.5763106207816 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 2.45081967213115 & 0.0958317899848072 & 25.5741823513856 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 2.44426229508197 & 0.0911530446111342 & 26.8149276363656 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 2.43606557377049 & 0.0893214489347888 & 27.2730189984826 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 2.42622950819672 & 0.0789584396228393 & 30.7279312988718 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 2.42622950819672 & 0.0789584396228393 & 30.7279312988718 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 2.45245901639344 & 0.0735741162825611 & 33.3331766701048 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 2.4672131147541 & 0.0708157507515838 & 34.8398920941881 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 2.4672131147541 & 0.0647703514222588 & 38.0917049325476 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 2.4672131147541 & 0.0647703514222588 & 38.0917049325476 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 2.50655737704918 & 0.0585278810052722 & 42.82672350334 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 2.46393442622951 & 0.0505182316754394 & 48.7731724669098 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 2.46393442622951 & 0.0505182316754394 & 48.7731724669098 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 2.46393442622951 & 0.0425956196525016 & 57.8447841897942 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 2.46393442622951 & 0.0425956196525016 & 57.8447841897942 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 2.43606557377049 & 0.0379842350736069 & 64.1335956627748 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 2.43606557377049 & 0.0379842350736069 & 64.1335956627748 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 2.40491803278689 & 0.0331766450795332 & 72.4882828574637 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 2.43770491803279 & 0.0283579707500619 & 85.9618954937906 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 2.44915254237288 & 0.0968641242678067 & 25.284413201337 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 2.44561403508772 & 0.0913581105178117 & 26.7695338840322 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 2.44545454545455 & 0.0857456178977948 & 28.5198778131079 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 2.44339622641509 & 0.0806140005362266 & 30.3098247222835 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 2.44313725490196 & 0.076145109248313 & 32.0852813663287 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 2.44489795918367 & 0.0711339892451818 & 34.3703198024885 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 2.44893617021277 & 0.0682727525195185 & 35.8698906934013 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 2.45333333333333 & 0.0645575461714335 & 38.0022705141003 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 2.45348837209302 & 0.0613929158214515 & 39.9637049204257 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 2.45121951219512 & 0.0580287934436917 & 42.2414351002088 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 2.44871794871795 & 0.0553326091612931 & 44.2545180108894 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 2.44594594594595 & 0.0516389920934108 & 47.3662603933366 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 2.43714285714286 & 0.0483484749502195 & 50.4078538082573 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 2.43333333333333 & 0.0463980363569168 & 52.4447481918183 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 2.42903225806452 & 0.0435503782898022 & 55.7752275284667 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 2.42413793103448 & 0.0420107810505549 & 57.7027579686587 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 2.41851851851852 & 0.0395980650182801 & 61.0766843632897 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 2.416 & 0.0377182537595084 & 64.0538667406084 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 2.41304347826087 & 0.0346092517880913 & 69.7224977019345 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 2.41428571428571 & 0.0318371707627558 & 75.8322946557182 \tabularnewline
Median & 2.4 &  &  \tabularnewline
Midrange & 2.4 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 2.42903225806452 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 2.42903225806452 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 2.42903225806452 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 2.42903225806452 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 2.42903225806452 &  &  \tabularnewline
Midmean - Closest Observation & 2.39117647058824 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 2.42903225806452 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 2.42903225806452 &  &  \tabularnewline
Number of observations & 61 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=49542&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]2.44754098360656[/C][C]0.102685432889692[/C][C]23.8353280960093[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]2.29598932070683[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]2.10723895594887[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]2.57354128665121[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]2.45245901639344[/C][C]0.101319344664054[/C][C]24.2052396265008[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]2.44590163934426[/C][C]0.099522734599392[/C][C]24.5763106207816[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]2.45081967213115[/C][C]0.0958317899848072[/C][C]25.5741823513856[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]2.44426229508197[/C][C]0.0911530446111342[/C][C]26.8149276363656[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]2.43606557377049[/C][C]0.0893214489347888[/C][C]27.2730189984826[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]2.42622950819672[/C][C]0.0789584396228393[/C][C]30.7279312988718[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]2.42622950819672[/C][C]0.0789584396228393[/C][C]30.7279312988718[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]2.45245901639344[/C][C]0.0735741162825611[/C][C]33.3331766701048[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]2.4672131147541[/C][C]0.0708157507515838[/C][C]34.8398920941881[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]2.4672131147541[/C][C]0.0647703514222588[/C][C]38.0917049325476[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]2.4672131147541[/C][C]0.0647703514222588[/C][C]38.0917049325476[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]2.50655737704918[/C][C]0.0585278810052722[/C][C]42.82672350334[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]2.46393442622951[/C][C]0.0505182316754394[/C][C]48.7731724669098[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]2.46393442622951[/C][C]0.0505182316754394[/C][C]48.7731724669098[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]2.46393442622951[/C][C]0.0425956196525016[/C][C]57.8447841897942[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]2.46393442622951[/C][C]0.0425956196525016[/C][C]57.8447841897942[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]2.43606557377049[/C][C]0.0379842350736069[/C][C]64.1335956627748[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]2.43606557377049[/C][C]0.0379842350736069[/C][C]64.1335956627748[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]2.40491803278689[/C][C]0.0331766450795332[/C][C]72.4882828574637[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]2.43770491803279[/C][C]0.0283579707500619[/C][C]85.9618954937906[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]2.44915254237288[/C][C]0.0968641242678067[/C][C]25.284413201337[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]2.44561403508772[/C][C]0.0913581105178117[/C][C]26.7695338840322[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]2.44545454545455[/C][C]0.0857456178977948[/C][C]28.5198778131079[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]2.44339622641509[/C][C]0.0806140005362266[/C][C]30.3098247222835[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]2.44313725490196[/C][C]0.076145109248313[/C][C]32.0852813663287[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]2.44489795918367[/C][C]0.0711339892451818[/C][C]34.3703198024885[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]2.44893617021277[/C][C]0.0682727525195185[/C][C]35.8698906934013[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]2.45333333333333[/C][C]0.0645575461714335[/C][C]38.0022705141003[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]2.45348837209302[/C][C]0.0613929158214515[/C][C]39.9637049204257[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]2.45121951219512[/C][C]0.0580287934436917[/C][C]42.2414351002088[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]2.44871794871795[/C][C]0.0553326091612931[/C][C]44.2545180108894[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]2.44594594594595[/C][C]0.0516389920934108[/C][C]47.3662603933366[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]2.43714285714286[/C][C]0.0483484749502195[/C][C]50.4078538082573[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]2.43333333333333[/C][C]0.0463980363569168[/C][C]52.4447481918183[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]2.42903225806452[/C][C]0.0435503782898022[/C][C]55.7752275284667[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]2.42413793103448[/C][C]0.0420107810505549[/C][C]57.7027579686587[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]2.41851851851852[/C][C]0.0395980650182801[/C][C]61.0766843632897[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]2.416[/C][C]0.0377182537595084[/C][C]64.0538667406084[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]2.41304347826087[/C][C]0.0346092517880913[/C][C]69.7224977019345[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]2.41428571428571[/C][C]0.0318371707627558[/C][C]75.8322946557182[/C][/ROW]
[ROW][C]Median[/C][C]2.4[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]2.4[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]2.42903225806452[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]2.42903225806452[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]2.42903225806452[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]2.42903225806452[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]2.42903225806452[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]2.39117647058824[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]2.42903225806452[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]2.42903225806452[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]61[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=49542&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=49542&T=1

As an alternative you can also use a QR Code:  
QR Code


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

Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean2.447540983606560.10268543288969223.8353280960093
Geometric Mean2.29598932070683
Harmonic Mean2.10723895594887
Quadratic Mean2.57354128665121
Winsorized Mean ( 1 / 20 )2.452459016393440.10131934466405424.2052396265008
Winsorized Mean ( 2 / 20 )2.445901639344260.09952273459939224.5763106207816
Winsorized Mean ( 3 / 20 )2.450819672131150.095831789984807225.5741823513856
Winsorized Mean ( 4 / 20 )2.444262295081970.091153044611134226.8149276363656
Winsorized Mean ( 5 / 20 )2.436065573770490.089321448934788827.2730189984826
Winsorized Mean ( 6 / 20 )2.426229508196720.078958439622839330.7279312988718
Winsorized Mean ( 7 / 20 )2.426229508196720.078958439622839330.7279312988718
Winsorized Mean ( 8 / 20 )2.452459016393440.073574116282561133.3331766701048
Winsorized Mean ( 9 / 20 )2.46721311475410.070815750751583834.8398920941881
Winsorized Mean ( 10 / 20 )2.46721311475410.064770351422258838.0917049325476
Winsorized Mean ( 11 / 20 )2.46721311475410.064770351422258838.0917049325476
Winsorized Mean ( 12 / 20 )2.506557377049180.058527881005272242.82672350334
Winsorized Mean ( 13 / 20 )2.463934426229510.050518231675439448.7731724669098
Winsorized Mean ( 14 / 20 )2.463934426229510.050518231675439448.7731724669098
Winsorized Mean ( 15 / 20 )2.463934426229510.042595619652501657.8447841897942
Winsorized Mean ( 16 / 20 )2.463934426229510.042595619652501657.8447841897942
Winsorized Mean ( 17 / 20 )2.436065573770490.037984235073606964.1335956627748
Winsorized Mean ( 18 / 20 )2.436065573770490.037984235073606964.1335956627748
Winsorized Mean ( 19 / 20 )2.404918032786890.033176645079533272.4882828574637
Winsorized Mean ( 20 / 20 )2.437704918032790.028357970750061985.9618954937906
Trimmed Mean ( 1 / 20 )2.449152542372880.096864124267806725.284413201337
Trimmed Mean ( 2 / 20 )2.445614035087720.091358110517811726.7695338840322
Trimmed Mean ( 3 / 20 )2.445454545454550.085745617897794828.5198778131079
Trimmed Mean ( 4 / 20 )2.443396226415090.080614000536226630.3098247222835
Trimmed Mean ( 5 / 20 )2.443137254901960.07614510924831332.0852813663287
Trimmed Mean ( 6 / 20 )2.444897959183670.071133989245181834.3703198024885
Trimmed Mean ( 7 / 20 )2.448936170212770.068272752519518535.8698906934013
Trimmed Mean ( 8 / 20 )2.453333333333330.064557546171433538.0022705141003
Trimmed Mean ( 9 / 20 )2.453488372093020.061392915821451539.9637049204257
Trimmed Mean ( 10 / 20 )2.451219512195120.058028793443691742.2414351002088
Trimmed Mean ( 11 / 20 )2.448717948717950.055332609161293144.2545180108894
Trimmed Mean ( 12 / 20 )2.445945945945950.051638992093410847.3662603933366
Trimmed Mean ( 13 / 20 )2.437142857142860.048348474950219550.4078538082573
Trimmed Mean ( 14 / 20 )2.433333333333330.046398036356916852.4447481918183
Trimmed Mean ( 15 / 20 )2.429032258064520.043550378289802255.7752275284667
Trimmed Mean ( 16 / 20 )2.424137931034480.042010781050554957.7027579686587
Trimmed Mean ( 17 / 20 )2.418518518518520.039598065018280161.0766843632897
Trimmed Mean ( 18 / 20 )2.4160.037718253759508464.0538667406084
Trimmed Mean ( 19 / 20 )2.413043478260870.034609251788091369.7224977019345
Trimmed Mean ( 20 / 20 )2.414285714285710.031837170762755875.8322946557182
Median2.4
Midrange2.4
Midmean - Weighted Average at Xnp2.42903225806452
Midmean - Weighted Average at X(n+1)p2.42903225806452
Midmean - Empirical Distribution Function2.42903225806452
Midmean - Empirical Distribution Function - Averaging2.42903225806452
Midmean - Empirical Distribution Function - Interpolation2.42903225806452
Midmean - Closest Observation2.39117647058824
Midmean - True Basic - Statistics Graphics Toolkit2.42903225806452
Midmean - MS Excel (old versions)2.42903225806452
Number of observations61


Figures (Output of Computation)

Input Parameters & R Code

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')