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Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationThu, 16 Dec 2010 13:13:31 +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/2010/Dec/16/t1292505735ihb5cisiq9sig1e.htm/, Retrieved Fri, 03 May 2024 08:28:10 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=110904, Retrieved Fri, 03 May 2024 08:28:10 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact142
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Central Tendency] [s 0650692 paper] [2008-01-09 16:40:34] [d530bc48164a192180949b2df4f47d02]
-  M D    [Central Tendency] [] [2010-12-16 13:13:31] [44163a3390d803b6e1dc8c2f0815c192] [Current]
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Dataseries X:
-49.5493497703707
-34.5244589213124
-3.91006280789517
14.6313371136598
-16.7358782201586
-48.8615512151807
-77.8868483141492
-52.8243216396381
-45.4459004030628
-11.8820480510030
-25.5304783937354
20.2338922716193
-21.9420653281128
23.1907193380687
14.2843898128731
-36.3573860047354
33.4686325324833
-34.0974551131747
-5.09014031706005
-4.25345940866923
14.8564460348288
18.8607130375245
-2.46525460356892
-1.06098760087327
-17.290892109167
-15.5131820397076
-17.2049426803877
-36.6798487063743
-13.1060400146913
0.0857206259887766
53.7756017864013
56.6662296033538
3.76485816524712
54.9836940524584
-38.9231939514776
-19.5189269487819
31.9337349072222
11.4479582495412
-25.8786696625430
56.3992435318715
-2.89893769557475
14.1096472059418
-28.3133945167058
-20.4064607522117
66.8966785623235
-39.3512642805164
48.3239868281212
29.2125572581408
14.2248044635090
26.8845625839714
24.3119726420195
-17.2382153060072
-15.8952814463814
-2.91808969021696
-1.74390510248044
20.8180121971652
-40.0720823593368
-22.6110947584635
18.5949401206607
-28.866534980105
42.6237678369192
-11.4855992105612
8.39731269593327
19.2448693715856
15.1675048443228
71.6817281866418
59.2586864639942




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'RServer@AstonUniversity' @ vre.aston.ac.uk

\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 & 'RServer@AstonUniversity' @ vre.aston.ac.uk \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=110904&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]'RServer@AstonUniversity' @ vre.aston.ac.uk[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=110904&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=110904&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'RServer@AstonUniversity' @ vre.aston.ac.uk







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean-3.51480867628065e-153.98518676077935-8.81968371187023e-16
Geometric MeanNaN
Harmonic Mean7.73734700872154
Quadratic Mean32.3758102942182
Winsorized Mean ( 1 / 22 )0.3026489111969043.871632660562540.078170874597625
Winsorized Mean ( 2 / 22 )0.1724095013741613.795132440135280.0454291132374856
Winsorized Mean ( 3 / 22 )0.08712629366742653.762121402633280.0231588203417473
Winsorized Mean ( 4 / 22 )0.2751062781829843.719386907625290.073965490822957
Winsorized Mean ( 5 / 22 )0.5704994546242453.62383091631940.157429931969255
Winsorized Mean ( 6 / 22 )0.526862960244843.588442285726560.146822191439583
Winsorized Mean ( 7 / 22 )0.002015013906197423.456439762737120.000582973824083586
Winsorized Mean ( 8 / 22 )-0.4107460304040963.27103763795865-0.125570560741218
Winsorized Mean ( 9 / 22 )-1.597224439735043.03278867366454-0.526652072267567
Winsorized Mean ( 10 / 22 )-1.552742431054162.94603272089308-0.527062180960246
Winsorized Mean ( 11 / 22 )-1.929397837776262.8587481853712-0.674910034975932
Winsorized Mean ( 12 / 22 )-1.409470889913522.63639265945841-0.534621003763172
Winsorized Mean ( 13 / 22 )-1.801304370826722.53994506130542-0.709190288509993
Winsorized Mean ( 14 / 22 )-1.526847628991382.42462429411769-0.62972545177231
Winsorized Mean ( 15 / 22 )-1.980097451102412.33233654544929-0.848975871413519
Winsorized Mean ( 16 / 22 )-1.422422535346942.20754499633925-0.644345885454534
Winsorized Mean ( 17 / 22 )-1.503614908251582.14591629505292-0.700686653863403
Winsorized Mean ( 18 / 22 )-1.194270604473672.07202903135648-0.576377351089445
Winsorized Mean ( 19 / 22 )-1.017950353059442.02587953566451-0.502473288830343
Winsorized Mean ( 20 / 22 )-1.375980334170781.78798506172254-0.769570374847073
Winsorized Mean ( 21 / 22 )-1.45696573914121.77212437547988-0.82215772171559
Winsorized Mean ( 22 / 22 )-1.519956761560441.76035716369528-0.863436575774087
Trimmed Mean ( 1 / 22 )0.09546338657703333.766748289051030.0253437127334791
Trimmed Mean ( 2 / 22 )-0.1248767745266393.64016919501896-0.0343052116087115
Trimmed Mean ( 3 / 22 )-0.288140548996753.5369608459648-0.0814655749795704
Trimmed Mean ( 4 / 22 )-0.4301907097792353.42672182996723-0.125540014954569
Trimmed Mean ( 5 / 22 )-0.6374490351891853.30773958486088-0.192714395687832
Trimmed Mean ( 6 / 22 )-0.9317492127073663.19250790824238-0.291854942724429
Trimmed Mean ( 7 / 22 )-1.239066871788493.0594376872216-0.40499823773621
Trimmed Mean ( 8 / 22 )-1.471987001596742.93172247652019-0.502089475857863
Trimmed Mean ( 9 / 22 )-1.653372575754662.82207649854644-0.585870927526685
Trimmed Mean ( 10 / 22 )-1.662266015738862.74524841941136-0.605506592403498
Trimmed Mean ( 11 / 22 )-1.678572860569692.66714444594335-0.629352063448515
Trimmed Mean ( 12 / 22 )-1.64304374117682.58624713409469-0.635300362257122
Trimmed Mean ( 13 / 22 )-1.674851426206552.53328589714856-0.661137942658486
Trimmed Mean ( 14 / 22 )-1.65814068204572.48338928407394-0.667692613751463
Trimmed Mean ( 15 / 22 )-1.675122602035352.44084871821553-0.686286941724113
Trimmed Mean ( 16 / 22 )-1.636202002249662.40109233407971-0.681440683903052
Trimmed Mean ( 17 / 22 )-1.663329320966482.37218122161167-0.701181387750975
Trimmed Mean ( 18 / 22 )-1.683634568882792.34038336857143-0.719384093859153
Trimmed Mean ( 19 / 22 )-1.746445652437222.30688834083128-0.757056863795969
Trimmed Mean ( 20 / 22 )-1.841590262687342.26183823818777-0.814200693752026
Trimmed Mean ( 21 / 22 )-1.903981993108562.25952901188784-0.842645517314148
Trimmed Mean ( 22 / 22 )-1.965990458979812.24363117870165-0.876253850295258
Median-2.89893769557475
Midrange-3.1025600637537
Midmean - Weighted Average at Xnp-2.27944006912815
Midmean - Weighted Average at X(n+1)p-1.63620200224966
Midmean - Empirical Distribution Function-1.63620200224966
Midmean - Empirical Distribution Function - Averaging-1.63620200224966
Midmean - Empirical Distribution Function - Interpolation-1.66332932096648
Midmean - Closest Observation-2.27944006912815
Midmean - True Basic - Statistics Graphics Toolkit-1.63620200224966
Midmean - MS Excel (old versions)-1.63620200224966
Number of observations67

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & -3.51480867628065e-15 & 3.98518676077935 & -8.81968371187023e-16 \tabularnewline
Geometric Mean & NaN &  &  \tabularnewline
Harmonic Mean & 7.73734700872154 &  &  \tabularnewline
Quadratic Mean & 32.3758102942182 &  &  \tabularnewline
Winsorized Mean ( 1 / 22 ) & 0.302648911196904 & 3.87163266056254 & 0.078170874597625 \tabularnewline
Winsorized Mean ( 2 / 22 ) & 0.172409501374161 & 3.79513244013528 & 0.0454291132374856 \tabularnewline
Winsorized Mean ( 3 / 22 ) & 0.0871262936674265 & 3.76212140263328 & 0.0231588203417473 \tabularnewline
Winsorized Mean ( 4 / 22 ) & 0.275106278182984 & 3.71938690762529 & 0.073965490822957 \tabularnewline
Winsorized Mean ( 5 / 22 ) & 0.570499454624245 & 3.6238309163194 & 0.157429931969255 \tabularnewline
Winsorized Mean ( 6 / 22 ) & 0.52686296024484 & 3.58844228572656 & 0.146822191439583 \tabularnewline
Winsorized Mean ( 7 / 22 ) & 0.00201501390619742 & 3.45643976273712 & 0.000582973824083586 \tabularnewline
Winsorized Mean ( 8 / 22 ) & -0.410746030404096 & 3.27103763795865 & -0.125570560741218 \tabularnewline
Winsorized Mean ( 9 / 22 ) & -1.59722443973504 & 3.03278867366454 & -0.526652072267567 \tabularnewline
Winsorized Mean ( 10 / 22 ) & -1.55274243105416 & 2.94603272089308 & -0.527062180960246 \tabularnewline
Winsorized Mean ( 11 / 22 ) & -1.92939783777626 & 2.8587481853712 & -0.674910034975932 \tabularnewline
Winsorized Mean ( 12 / 22 ) & -1.40947088991352 & 2.63639265945841 & -0.534621003763172 \tabularnewline
Winsorized Mean ( 13 / 22 ) & -1.80130437082672 & 2.53994506130542 & -0.709190288509993 \tabularnewline
Winsorized Mean ( 14 / 22 ) & -1.52684762899138 & 2.42462429411769 & -0.62972545177231 \tabularnewline
Winsorized Mean ( 15 / 22 ) & -1.98009745110241 & 2.33233654544929 & -0.848975871413519 \tabularnewline
Winsorized Mean ( 16 / 22 ) & -1.42242253534694 & 2.20754499633925 & -0.644345885454534 \tabularnewline
Winsorized Mean ( 17 / 22 ) & -1.50361490825158 & 2.14591629505292 & -0.700686653863403 \tabularnewline
Winsorized Mean ( 18 / 22 ) & -1.19427060447367 & 2.07202903135648 & -0.576377351089445 \tabularnewline
Winsorized Mean ( 19 / 22 ) & -1.01795035305944 & 2.02587953566451 & -0.502473288830343 \tabularnewline
Winsorized Mean ( 20 / 22 ) & -1.37598033417078 & 1.78798506172254 & -0.769570374847073 \tabularnewline
Winsorized Mean ( 21 / 22 ) & -1.4569657391412 & 1.77212437547988 & -0.82215772171559 \tabularnewline
Winsorized Mean ( 22 / 22 ) & -1.51995676156044 & 1.76035716369528 & -0.863436575774087 \tabularnewline
Trimmed Mean ( 1 / 22 ) & 0.0954633865770333 & 3.76674828905103 & 0.0253437127334791 \tabularnewline
Trimmed Mean ( 2 / 22 ) & -0.124876774526639 & 3.64016919501896 & -0.0343052116087115 \tabularnewline
Trimmed Mean ( 3 / 22 ) & -0.28814054899675 & 3.5369608459648 & -0.0814655749795704 \tabularnewline
Trimmed Mean ( 4 / 22 ) & -0.430190709779235 & 3.42672182996723 & -0.125540014954569 \tabularnewline
Trimmed Mean ( 5 / 22 ) & -0.637449035189185 & 3.30773958486088 & -0.192714395687832 \tabularnewline
Trimmed Mean ( 6 / 22 ) & -0.931749212707366 & 3.19250790824238 & -0.291854942724429 \tabularnewline
Trimmed Mean ( 7 / 22 ) & -1.23906687178849 & 3.0594376872216 & -0.40499823773621 \tabularnewline
Trimmed Mean ( 8 / 22 ) & -1.47198700159674 & 2.93172247652019 & -0.502089475857863 \tabularnewline
Trimmed Mean ( 9 / 22 ) & -1.65337257575466 & 2.82207649854644 & -0.585870927526685 \tabularnewline
Trimmed Mean ( 10 / 22 ) & -1.66226601573886 & 2.74524841941136 & -0.605506592403498 \tabularnewline
Trimmed Mean ( 11 / 22 ) & -1.67857286056969 & 2.66714444594335 & -0.629352063448515 \tabularnewline
Trimmed Mean ( 12 / 22 ) & -1.6430437411768 & 2.58624713409469 & -0.635300362257122 \tabularnewline
Trimmed Mean ( 13 / 22 ) & -1.67485142620655 & 2.53328589714856 & -0.661137942658486 \tabularnewline
Trimmed Mean ( 14 / 22 ) & -1.6581406820457 & 2.48338928407394 & -0.667692613751463 \tabularnewline
Trimmed Mean ( 15 / 22 ) & -1.67512260203535 & 2.44084871821553 & -0.686286941724113 \tabularnewline
Trimmed Mean ( 16 / 22 ) & -1.63620200224966 & 2.40109233407971 & -0.681440683903052 \tabularnewline
Trimmed Mean ( 17 / 22 ) & -1.66332932096648 & 2.37218122161167 & -0.701181387750975 \tabularnewline
Trimmed Mean ( 18 / 22 ) & -1.68363456888279 & 2.34038336857143 & -0.719384093859153 \tabularnewline
Trimmed Mean ( 19 / 22 ) & -1.74644565243722 & 2.30688834083128 & -0.757056863795969 \tabularnewline
Trimmed Mean ( 20 / 22 ) & -1.84159026268734 & 2.26183823818777 & -0.814200693752026 \tabularnewline
Trimmed Mean ( 21 / 22 ) & -1.90398199310856 & 2.25952901188784 & -0.842645517314148 \tabularnewline
Trimmed Mean ( 22 / 22 ) & -1.96599045897981 & 2.24363117870165 & -0.876253850295258 \tabularnewline
Median & -2.89893769557475 &  &  \tabularnewline
Midrange & -3.1025600637537 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & -2.27944006912815 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & -1.63620200224966 &  &  \tabularnewline
Midmean - Empirical Distribution Function & -1.63620200224966 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & -1.63620200224966 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & -1.66332932096648 &  &  \tabularnewline
Midmean - Closest Observation & -2.27944006912815 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & -1.63620200224966 &  &  \tabularnewline
Midmean - MS Excel (old versions) & -1.63620200224966 &  &  \tabularnewline
Number of observations & 67 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=110904&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]-3.51480867628065e-15[/C][C]3.98518676077935[/C][C]-8.81968371187023e-16[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]NaN[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]7.73734700872154[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]32.3758102942182[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 22 )[/C][C]0.302648911196904[/C][C]3.87163266056254[/C][C]0.078170874597625[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 22 )[/C][C]0.172409501374161[/C][C]3.79513244013528[/C][C]0.0454291132374856[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 22 )[/C][C]0.0871262936674265[/C][C]3.76212140263328[/C][C]0.0231588203417473[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 22 )[/C][C]0.275106278182984[/C][C]3.71938690762529[/C][C]0.073965490822957[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 22 )[/C][C]0.570499454624245[/C][C]3.6238309163194[/C][C]0.157429931969255[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 22 )[/C][C]0.52686296024484[/C][C]3.58844228572656[/C][C]0.146822191439583[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 22 )[/C][C]0.00201501390619742[/C][C]3.45643976273712[/C][C]0.000582973824083586[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 22 )[/C][C]-0.410746030404096[/C][C]3.27103763795865[/C][C]-0.125570560741218[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 22 )[/C][C]-1.59722443973504[/C][C]3.03278867366454[/C][C]-0.526652072267567[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 22 )[/C][C]-1.55274243105416[/C][C]2.94603272089308[/C][C]-0.527062180960246[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 22 )[/C][C]-1.92939783777626[/C][C]2.8587481853712[/C][C]-0.674910034975932[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 22 )[/C][C]-1.40947088991352[/C][C]2.63639265945841[/C][C]-0.534621003763172[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 22 )[/C][C]-1.80130437082672[/C][C]2.53994506130542[/C][C]-0.709190288509993[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 22 )[/C][C]-1.52684762899138[/C][C]2.42462429411769[/C][C]-0.62972545177231[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 22 )[/C][C]-1.98009745110241[/C][C]2.33233654544929[/C][C]-0.848975871413519[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 22 )[/C][C]-1.42242253534694[/C][C]2.20754499633925[/C][C]-0.644345885454534[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 22 )[/C][C]-1.50361490825158[/C][C]2.14591629505292[/C][C]-0.700686653863403[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 22 )[/C][C]-1.19427060447367[/C][C]2.07202903135648[/C][C]-0.576377351089445[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 22 )[/C][C]-1.01795035305944[/C][C]2.02587953566451[/C][C]-0.502473288830343[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 22 )[/C][C]-1.37598033417078[/C][C]1.78798506172254[/C][C]-0.769570374847073[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 22 )[/C][C]-1.4569657391412[/C][C]1.77212437547988[/C][C]-0.82215772171559[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 22 )[/C][C]-1.51995676156044[/C][C]1.76035716369528[/C][C]-0.863436575774087[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 22 )[/C][C]0.0954633865770333[/C][C]3.76674828905103[/C][C]0.0253437127334791[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 22 )[/C][C]-0.124876774526639[/C][C]3.64016919501896[/C][C]-0.0343052116087115[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 22 )[/C][C]-0.28814054899675[/C][C]3.5369608459648[/C][C]-0.0814655749795704[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 22 )[/C][C]-0.430190709779235[/C][C]3.42672182996723[/C][C]-0.125540014954569[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 22 )[/C][C]-0.637449035189185[/C][C]3.30773958486088[/C][C]-0.192714395687832[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 22 )[/C][C]-0.931749212707366[/C][C]3.19250790824238[/C][C]-0.291854942724429[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 22 )[/C][C]-1.23906687178849[/C][C]3.0594376872216[/C][C]-0.40499823773621[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 22 )[/C][C]-1.47198700159674[/C][C]2.93172247652019[/C][C]-0.502089475857863[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 22 )[/C][C]-1.65337257575466[/C][C]2.82207649854644[/C][C]-0.585870927526685[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 22 )[/C][C]-1.66226601573886[/C][C]2.74524841941136[/C][C]-0.605506592403498[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 22 )[/C][C]-1.67857286056969[/C][C]2.66714444594335[/C][C]-0.629352063448515[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 22 )[/C][C]-1.6430437411768[/C][C]2.58624713409469[/C][C]-0.635300362257122[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 22 )[/C][C]-1.67485142620655[/C][C]2.53328589714856[/C][C]-0.661137942658486[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 22 )[/C][C]-1.6581406820457[/C][C]2.48338928407394[/C][C]-0.667692613751463[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 22 )[/C][C]-1.67512260203535[/C][C]2.44084871821553[/C][C]-0.686286941724113[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 22 )[/C][C]-1.63620200224966[/C][C]2.40109233407971[/C][C]-0.681440683903052[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 22 )[/C][C]-1.66332932096648[/C][C]2.37218122161167[/C][C]-0.701181387750975[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 22 )[/C][C]-1.68363456888279[/C][C]2.34038336857143[/C][C]-0.719384093859153[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 22 )[/C][C]-1.74644565243722[/C][C]2.30688834083128[/C][C]-0.757056863795969[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 22 )[/C][C]-1.84159026268734[/C][C]2.26183823818777[/C][C]-0.814200693752026[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 22 )[/C][C]-1.90398199310856[/C][C]2.25952901188784[/C][C]-0.842645517314148[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 22 )[/C][C]-1.96599045897981[/C][C]2.24363117870165[/C][C]-0.876253850295258[/C][/ROW]
[ROW][C]Median[/C][C]-2.89893769557475[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]-3.1025600637537[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]-2.27944006912815[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]-1.63620200224966[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]-1.63620200224966[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]-1.63620200224966[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]-1.66332932096648[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]-2.27944006912815[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]-1.63620200224966[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]-1.63620200224966[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]67[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=110904&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=110904&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 Mean-3.51480867628065e-153.98518676077935-8.81968371187023e-16
Geometric MeanNaN
Harmonic Mean7.73734700872154
Quadratic Mean32.3758102942182
Winsorized Mean ( 1 / 22 )0.3026489111969043.871632660562540.078170874597625
Winsorized Mean ( 2 / 22 )0.1724095013741613.795132440135280.0454291132374856
Winsorized Mean ( 3 / 22 )0.08712629366742653.762121402633280.0231588203417473
Winsorized Mean ( 4 / 22 )0.2751062781829843.719386907625290.073965490822957
Winsorized Mean ( 5 / 22 )0.5704994546242453.62383091631940.157429931969255
Winsorized Mean ( 6 / 22 )0.526862960244843.588442285726560.146822191439583
Winsorized Mean ( 7 / 22 )0.002015013906197423.456439762737120.000582973824083586
Winsorized Mean ( 8 / 22 )-0.4107460304040963.27103763795865-0.125570560741218
Winsorized Mean ( 9 / 22 )-1.597224439735043.03278867366454-0.526652072267567
Winsorized Mean ( 10 / 22 )-1.552742431054162.94603272089308-0.527062180960246
Winsorized Mean ( 11 / 22 )-1.929397837776262.8587481853712-0.674910034975932
Winsorized Mean ( 12 / 22 )-1.409470889913522.63639265945841-0.534621003763172
Winsorized Mean ( 13 / 22 )-1.801304370826722.53994506130542-0.709190288509993
Winsorized Mean ( 14 / 22 )-1.526847628991382.42462429411769-0.62972545177231
Winsorized Mean ( 15 / 22 )-1.980097451102412.33233654544929-0.848975871413519
Winsorized Mean ( 16 / 22 )-1.422422535346942.20754499633925-0.644345885454534
Winsorized Mean ( 17 / 22 )-1.503614908251582.14591629505292-0.700686653863403
Winsorized Mean ( 18 / 22 )-1.194270604473672.07202903135648-0.576377351089445
Winsorized Mean ( 19 / 22 )-1.017950353059442.02587953566451-0.502473288830343
Winsorized Mean ( 20 / 22 )-1.375980334170781.78798506172254-0.769570374847073
Winsorized Mean ( 21 / 22 )-1.45696573914121.77212437547988-0.82215772171559
Winsorized Mean ( 22 / 22 )-1.519956761560441.76035716369528-0.863436575774087
Trimmed Mean ( 1 / 22 )0.09546338657703333.766748289051030.0253437127334791
Trimmed Mean ( 2 / 22 )-0.1248767745266393.64016919501896-0.0343052116087115
Trimmed Mean ( 3 / 22 )-0.288140548996753.5369608459648-0.0814655749795704
Trimmed Mean ( 4 / 22 )-0.4301907097792353.42672182996723-0.125540014954569
Trimmed Mean ( 5 / 22 )-0.6374490351891853.30773958486088-0.192714395687832
Trimmed Mean ( 6 / 22 )-0.9317492127073663.19250790824238-0.291854942724429
Trimmed Mean ( 7 / 22 )-1.239066871788493.0594376872216-0.40499823773621
Trimmed Mean ( 8 / 22 )-1.471987001596742.93172247652019-0.502089475857863
Trimmed Mean ( 9 / 22 )-1.653372575754662.82207649854644-0.585870927526685
Trimmed Mean ( 10 / 22 )-1.662266015738862.74524841941136-0.605506592403498
Trimmed Mean ( 11 / 22 )-1.678572860569692.66714444594335-0.629352063448515
Trimmed Mean ( 12 / 22 )-1.64304374117682.58624713409469-0.635300362257122
Trimmed Mean ( 13 / 22 )-1.674851426206552.53328589714856-0.661137942658486
Trimmed Mean ( 14 / 22 )-1.65814068204572.48338928407394-0.667692613751463
Trimmed Mean ( 15 / 22 )-1.675122602035352.44084871821553-0.686286941724113
Trimmed Mean ( 16 / 22 )-1.636202002249662.40109233407971-0.681440683903052
Trimmed Mean ( 17 / 22 )-1.663329320966482.37218122161167-0.701181387750975
Trimmed Mean ( 18 / 22 )-1.683634568882792.34038336857143-0.719384093859153
Trimmed Mean ( 19 / 22 )-1.746445652437222.30688834083128-0.757056863795969
Trimmed Mean ( 20 / 22 )-1.841590262687342.26183823818777-0.814200693752026
Trimmed Mean ( 21 / 22 )-1.903981993108562.25952901188784-0.842645517314148
Trimmed Mean ( 22 / 22 )-1.965990458979812.24363117870165-0.876253850295258
Median-2.89893769557475
Midrange-3.1025600637537
Midmean - Weighted Average at Xnp-2.27944006912815
Midmean - Weighted Average at X(n+1)p-1.63620200224966
Midmean - Empirical Distribution Function-1.63620200224966
Midmean - Empirical Distribution Function - Averaging-1.63620200224966
Midmean - Empirical Distribution Function - Interpolation-1.66332932096648
Midmean - Closest Observation-2.27944006912815
Midmean - True Basic - Statistics Graphics Toolkit-1.63620200224966
Midmean - MS Excel (old versions)-1.63620200224966
Number of observations67



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')