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of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationMon, 17 Oct 2011 07:51:42 -0400
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2011/Oct/17/t1318852341yyjxismkploci09.htm/, Retrieved Wed, 15 May 2024 03:53:48 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=130349, Retrieved Wed, 15 May 2024 03:53:48 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsKDG2011W52a
Estimated Impact74
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [opgave 5] [2011-10-17 11:51:42] [824ef6e68de890e55183bcf963376e73] [Current]
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Dataseries X:
6,3
6,2
6,3
6,5
6,6
6,4
6,2
6,3
6,6
7,1
7,2
7,3
7,3
7,3
7,4
7,3
7,4
7,4
7,6
7,6
7,7
7,7
7,8
7,8
8
8,1
8,1
8,2
8,1
8,1
8,1
8,1
8,2
8,4
8,4
8,5
8,6
8,5
8,3
7,8
7,8
8
8,6
8,9
8,9
8,6
8,3
8,3
8,3
8,4
8,5
8,4
8,6
8,5
8,5
8,5
8,5
8,5
8,5
8,5
8,5
8,6
8,6
8,6
8,6
8,4
8,1
7,9
7,9
8
8
7,9
7,9
7,9
7,9
8
7,9
7,5
7,2
7
6,9
7,1
7,1
7,2
7,1
6,9
6,8
6,8
6,7
6,9
7,3
7,4
7,3
7,1
7
7,1
7,5
7,7
7,8
7,7
7,7
7,8
8
8,1
8,1
8
8,1
8,2
8,3
8,4
8,5
8,5
8,5
8,5
8,5
8,3
8,2
8,1
7,9
7,6




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 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 & 2 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=130349&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]'Gwilym Jenkins' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=130349&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=130349&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'Gwilym Jenkins' @ jenkins.wessa.net







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean7.808333333333330.0608366427863082128.349181935639
Geometric Mean7.77882353476357
Harmonic Mean7.74797595858816
Quadratic Mean7.83648518150835
Winsorized Mean ( 1 / 40 )7.808333333333330.0608366427863082128.349181935639
Winsorized Mean ( 2 / 40 )7.8050.0598182354179343130.478606489618
Winsorized Mean ( 3 / 40 )7.8050.0598182354179343130.478606489618
Winsorized Mean ( 4 / 40 )7.8050.0598182354179343130.478606489618
Winsorized Mean ( 5 / 40 )7.809166666666670.0589591777463261132.450399838781
Winsorized Mean ( 6 / 40 )7.814166666666670.0579806766967647134.771912158498
Winsorized Mean ( 7 / 40 )7.820.0568993410682901137.43568648035
Winsorized Mean ( 8 / 40 )7.820.0568993410682901137.43568648035
Winsorized Mean ( 9 / 40 )7.82750.0555840204855076140.822846775556
Winsorized Mean ( 10 / 40 )7.82750.0532680250525322146.945564290785
Winsorized Mean ( 11 / 40 )7.82750.0532680250525322146.945564290785
Winsorized Mean ( 12 / 40 )7.83750.0516948396126444151.610877579413
Winsorized Mean ( 13 / 40 )7.83750.0516948396126444151.610877579413
Winsorized Mean ( 14 / 40 )7.83750.0516948396126444151.610877579413
Winsorized Mean ( 15 / 40 )7.850.0498457002913492157.48600088105
Winsorized Mean ( 16 / 40 )7.850.0498457002913492157.48600088105
Winsorized Mean ( 17 / 40 )7.864166666666670.0478793393764191164.249690348481
Winsorized Mean ( 18 / 40 )7.864166666666670.0478793393764191164.249690348481
Winsorized Mean ( 19 / 40 )7.864166666666670.0478793393764191164.249690348481
Winsorized Mean ( 20 / 40 )7.864166666666670.0478793393764191164.249690348481
Winsorized Mean ( 21 / 40 )7.864166666666670.0478793393764191164.249690348481
Winsorized Mean ( 22 / 40 )7.864166666666670.0478793393764191164.249690348481
Winsorized Mean ( 23 / 40 )7.883333333333330.0453794048310442173.720509616299
Winsorized Mean ( 24 / 40 )7.883333333333330.0453794048310442173.720509616299
Winsorized Mean ( 25 / 40 )7.883333333333330.0453794048310442173.720509616299
Winsorized Mean ( 26 / 40 )7.883333333333330.0402779790071924195.723160090173
Winsorized Mean ( 27 / 40 )7.883333333333330.0402779790071924195.723160090173
Winsorized Mean ( 28 / 40 )7.883333333333330.0402779790071924195.723160090173
Winsorized Mean ( 29 / 40 )7.883333333333330.0402779790071924195.723160090173
Winsorized Mean ( 30 / 40 )7.883333333333330.0402779790071924195.723160090173
Winsorized Mean ( 31 / 40 )7.883333333333330.0402779790071924195.723160090173
Winsorized Mean ( 32 / 40 )7.883333333333330.0342656726359654230.065039641421
Winsorized Mean ( 33 / 40 )7.883333333333330.0342656726359654230.065039641421
Winsorized Mean ( 34 / 40 )7.883333333333330.0342656726359654230.065039641421
Winsorized Mean ( 35 / 40 )7.883333333333330.0342656726359654230.065039641421
Winsorized Mean ( 36 / 40 )7.913333333333330.030791003572912257.00147494689
Winsorized Mean ( 37 / 40 )7.913333333333330.030791003572912257.00147494689
Winsorized Mean ( 38 / 40 )7.913333333333330.0239903497560839329.854854714093
Winsorized Mean ( 39 / 40 )7.913333333333330.0239903497560839329.854854714093
Winsorized Mean ( 40 / 40 )7.913333333333330.0239903497560839329.854854714093
Trimmed Mean ( 1 / 40 )7.812711864406780.0596181121489419131.045945314212
Trimmed Mean ( 2 / 40 )7.817241379310350.0582641951363443134.168872684454
Trimmed Mean ( 3 / 40 )7.823684210526320.0573478780828093136.424999007445
Trimmed Mean ( 4 / 40 )7.830357142857140.0563222835393992139.027692962406
Trimmed Mean ( 5 / 40 )7.837272727272730.0551721710517536142.051193162601
Trimmed Mean ( 6 / 40 )7.843518518518520.0541185887462463144.932059394519
Trimmed Mean ( 7 / 40 )7.849056603773580.0531698744497357147.622251980183
Trimmed Mean ( 8 / 40 )7.853846153846150.0523339344619876150.071769580992
Trimmed Mean ( 9 / 40 )7.858823529411760.0513901665304645152.924655824048
Trimmed Mean ( 10 / 40 )7.8630.0505655889699585155.501006913446
Trimmed Mean ( 11 / 40 )7.867346938775510.0500110551675672157.312156530494
Trimmed Mean ( 12 / 40 )7.8718750.0493755551823107159.428587100124
Trimmed Mean ( 13 / 40 )7.875531914893620.048888028003957161.093262224776
Trimmed Mean ( 14 / 40 )7.879347826086960.04832448362701163.050843686263
Trimmed Mean ( 15 / 40 )7.883333333333330.0476737246287201165.360130653273
Trimmed Mean ( 16 / 40 )7.886363636363640.047182415138276167.1462474579
Trimmed Mean ( 17 / 40 )7.889534883720930.04660950713443169.268790184074
Trimmed Mean ( 18 / 40 )7.891666666666670.0462044253236362170.798935629865
Trimmed Mean ( 19 / 40 )7.893902439024390.0457250321335283172.638532346402
Trimmed Mean ( 20 / 40 )7.896250.0451594835632141174.852531007066
Trimmed Mean ( 21 / 40 )7.898717948717950.0444934335999346177.525475326084
Trimmed Mean ( 22 / 40 )7.901315789473680.0437093037208741180.769655813581
Trimmed Mean ( 23 / 40 )7.904054054054050.0427852575580247184.737792996447
Trimmed Mean ( 24 / 40 )7.905555555555560.0420470379385849188.016943478935
Trimmed Mean ( 25 / 40 )7.907142857142860.0411693180379245192.063974677912
Trimmed Mean ( 26 / 40 )7.908823529411770.0401235632186725197.111694350496
Trimmed Mean ( 27 / 40 )7.910606060606060.0395857799736836199.834538207028
Trimmed Mean ( 28 / 40 )7.91250.0389278433017678203.260682557276
Trimmed Mean ( 29 / 40 )7.914516129032260.0381240962784273207.598786636963
Trimmed Mean ( 30 / 40 )7.916666666666670.0371412532506917213.150229832894
Trimmed Mean ( 31 / 40 )7.918965517241380.0359350843559499220.368635810096
Trimmed Mean ( 32 / 40 )7.921428571428570.0344449764224352229.973406695935
Trimmed Mean ( 33 / 40 )7.924074074074070.033639597767835235.557931719707
Trimmed Mean ( 34 / 40 )7.926923076923080.0326223632933456242.990460428722
Trimmed Mean ( 35 / 40 )7.930.0313310174278019253.103813761351
Trimmed Mean ( 36 / 40 )7.933333333333330.0296751521851262267.339263631803
Trimmed Mean ( 37 / 40 )7.934782608695650.028355471539468279.832504201216
Trimmed Mean ( 38 / 40 )7.936363636363640.0266309261419243298.013054223813
Trimmed Mean ( 39 / 40 )7.938095238095240.0259438285730247305.972390148652
Trimmed Mean ( 40 / 40 )7.940.0250128172271942317.437253384139
Median7.95
Midrange7.55
Midmean - Weighted Average at Xnp7.90882352941177
Midmean - Weighted Average at X(n+1)p7.90882352941177
Midmean - Empirical Distribution Function7.90882352941177
Midmean - Empirical Distribution Function - Averaging7.90882352941177
Midmean - Empirical Distribution Function - Interpolation7.90882352941177
Midmean - Closest Observation7.90882352941177
Midmean - True Basic - Statistics Graphics Toolkit7.90882352941177
Midmean - MS Excel (old versions)7.90882352941177
Number of observations120

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 7.80833333333333 & 0.0608366427863082 & 128.349181935639 \tabularnewline
Geometric Mean & 7.77882353476357 &  &  \tabularnewline
Harmonic Mean & 7.74797595858816 &  &  \tabularnewline
Quadratic Mean & 7.83648518150835 &  &  \tabularnewline
Winsorized Mean ( 1 / 40 ) & 7.80833333333333 & 0.0608366427863082 & 128.349181935639 \tabularnewline
Winsorized Mean ( 2 / 40 ) & 7.805 & 0.0598182354179343 & 130.478606489618 \tabularnewline
Winsorized Mean ( 3 / 40 ) & 7.805 & 0.0598182354179343 & 130.478606489618 \tabularnewline
Winsorized Mean ( 4 / 40 ) & 7.805 & 0.0598182354179343 & 130.478606489618 \tabularnewline
Winsorized Mean ( 5 / 40 ) & 7.80916666666667 & 0.0589591777463261 & 132.450399838781 \tabularnewline
Winsorized Mean ( 6 / 40 ) & 7.81416666666667 & 0.0579806766967647 & 134.771912158498 \tabularnewline
Winsorized Mean ( 7 / 40 ) & 7.82 & 0.0568993410682901 & 137.43568648035 \tabularnewline
Winsorized Mean ( 8 / 40 ) & 7.82 & 0.0568993410682901 & 137.43568648035 \tabularnewline
Winsorized Mean ( 9 / 40 ) & 7.8275 & 0.0555840204855076 & 140.822846775556 \tabularnewline
Winsorized Mean ( 10 / 40 ) & 7.8275 & 0.0532680250525322 & 146.945564290785 \tabularnewline
Winsorized Mean ( 11 / 40 ) & 7.8275 & 0.0532680250525322 & 146.945564290785 \tabularnewline
Winsorized Mean ( 12 / 40 ) & 7.8375 & 0.0516948396126444 & 151.610877579413 \tabularnewline
Winsorized Mean ( 13 / 40 ) & 7.8375 & 0.0516948396126444 & 151.610877579413 \tabularnewline
Winsorized Mean ( 14 / 40 ) & 7.8375 & 0.0516948396126444 & 151.610877579413 \tabularnewline
Winsorized Mean ( 15 / 40 ) & 7.85 & 0.0498457002913492 & 157.48600088105 \tabularnewline
Winsorized Mean ( 16 / 40 ) & 7.85 & 0.0498457002913492 & 157.48600088105 \tabularnewline
Winsorized Mean ( 17 / 40 ) & 7.86416666666667 & 0.0478793393764191 & 164.249690348481 \tabularnewline
Winsorized Mean ( 18 / 40 ) & 7.86416666666667 & 0.0478793393764191 & 164.249690348481 \tabularnewline
Winsorized Mean ( 19 / 40 ) & 7.86416666666667 & 0.0478793393764191 & 164.249690348481 \tabularnewline
Winsorized Mean ( 20 / 40 ) & 7.86416666666667 & 0.0478793393764191 & 164.249690348481 \tabularnewline
Winsorized Mean ( 21 / 40 ) & 7.86416666666667 & 0.0478793393764191 & 164.249690348481 \tabularnewline
Winsorized Mean ( 22 / 40 ) & 7.86416666666667 & 0.0478793393764191 & 164.249690348481 \tabularnewline
Winsorized Mean ( 23 / 40 ) & 7.88333333333333 & 0.0453794048310442 & 173.720509616299 \tabularnewline
Winsorized Mean ( 24 / 40 ) & 7.88333333333333 & 0.0453794048310442 & 173.720509616299 \tabularnewline
Winsorized Mean ( 25 / 40 ) & 7.88333333333333 & 0.0453794048310442 & 173.720509616299 \tabularnewline
Winsorized Mean ( 26 / 40 ) & 7.88333333333333 & 0.0402779790071924 & 195.723160090173 \tabularnewline
Winsorized Mean ( 27 / 40 ) & 7.88333333333333 & 0.0402779790071924 & 195.723160090173 \tabularnewline
Winsorized Mean ( 28 / 40 ) & 7.88333333333333 & 0.0402779790071924 & 195.723160090173 \tabularnewline
Winsorized Mean ( 29 / 40 ) & 7.88333333333333 & 0.0402779790071924 & 195.723160090173 \tabularnewline
Winsorized Mean ( 30 / 40 ) & 7.88333333333333 & 0.0402779790071924 & 195.723160090173 \tabularnewline
Winsorized Mean ( 31 / 40 ) & 7.88333333333333 & 0.0402779790071924 & 195.723160090173 \tabularnewline
Winsorized Mean ( 32 / 40 ) & 7.88333333333333 & 0.0342656726359654 & 230.065039641421 \tabularnewline
Winsorized Mean ( 33 / 40 ) & 7.88333333333333 & 0.0342656726359654 & 230.065039641421 \tabularnewline
Winsorized Mean ( 34 / 40 ) & 7.88333333333333 & 0.0342656726359654 & 230.065039641421 \tabularnewline
Winsorized Mean ( 35 / 40 ) & 7.88333333333333 & 0.0342656726359654 & 230.065039641421 \tabularnewline
Winsorized Mean ( 36 / 40 ) & 7.91333333333333 & 0.030791003572912 & 257.00147494689 \tabularnewline
Winsorized Mean ( 37 / 40 ) & 7.91333333333333 & 0.030791003572912 & 257.00147494689 \tabularnewline
Winsorized Mean ( 38 / 40 ) & 7.91333333333333 & 0.0239903497560839 & 329.854854714093 \tabularnewline
Winsorized Mean ( 39 / 40 ) & 7.91333333333333 & 0.0239903497560839 & 329.854854714093 \tabularnewline
Winsorized Mean ( 40 / 40 ) & 7.91333333333333 & 0.0239903497560839 & 329.854854714093 \tabularnewline
Trimmed Mean ( 1 / 40 ) & 7.81271186440678 & 0.0596181121489419 & 131.045945314212 \tabularnewline
Trimmed Mean ( 2 / 40 ) & 7.81724137931035 & 0.0582641951363443 & 134.168872684454 \tabularnewline
Trimmed Mean ( 3 / 40 ) & 7.82368421052632 & 0.0573478780828093 & 136.424999007445 \tabularnewline
Trimmed Mean ( 4 / 40 ) & 7.83035714285714 & 0.0563222835393992 & 139.027692962406 \tabularnewline
Trimmed Mean ( 5 / 40 ) & 7.83727272727273 & 0.0551721710517536 & 142.051193162601 \tabularnewline
Trimmed Mean ( 6 / 40 ) & 7.84351851851852 & 0.0541185887462463 & 144.932059394519 \tabularnewline
Trimmed Mean ( 7 / 40 ) & 7.84905660377358 & 0.0531698744497357 & 147.622251980183 \tabularnewline
Trimmed Mean ( 8 / 40 ) & 7.85384615384615 & 0.0523339344619876 & 150.071769580992 \tabularnewline
Trimmed Mean ( 9 / 40 ) & 7.85882352941176 & 0.0513901665304645 & 152.924655824048 \tabularnewline
Trimmed Mean ( 10 / 40 ) & 7.863 & 0.0505655889699585 & 155.501006913446 \tabularnewline
Trimmed Mean ( 11 / 40 ) & 7.86734693877551 & 0.0500110551675672 & 157.312156530494 \tabularnewline
Trimmed Mean ( 12 / 40 ) & 7.871875 & 0.0493755551823107 & 159.428587100124 \tabularnewline
Trimmed Mean ( 13 / 40 ) & 7.87553191489362 & 0.048888028003957 & 161.093262224776 \tabularnewline
Trimmed Mean ( 14 / 40 ) & 7.87934782608696 & 0.04832448362701 & 163.050843686263 \tabularnewline
Trimmed Mean ( 15 / 40 ) & 7.88333333333333 & 0.0476737246287201 & 165.360130653273 \tabularnewline
Trimmed Mean ( 16 / 40 ) & 7.88636363636364 & 0.047182415138276 & 167.1462474579 \tabularnewline
Trimmed Mean ( 17 / 40 ) & 7.88953488372093 & 0.04660950713443 & 169.268790184074 \tabularnewline
Trimmed Mean ( 18 / 40 ) & 7.89166666666667 & 0.0462044253236362 & 170.798935629865 \tabularnewline
Trimmed Mean ( 19 / 40 ) & 7.89390243902439 & 0.0457250321335283 & 172.638532346402 \tabularnewline
Trimmed Mean ( 20 / 40 ) & 7.89625 & 0.0451594835632141 & 174.852531007066 \tabularnewline
Trimmed Mean ( 21 / 40 ) & 7.89871794871795 & 0.0444934335999346 & 177.525475326084 \tabularnewline
Trimmed Mean ( 22 / 40 ) & 7.90131578947368 & 0.0437093037208741 & 180.769655813581 \tabularnewline
Trimmed Mean ( 23 / 40 ) & 7.90405405405405 & 0.0427852575580247 & 184.737792996447 \tabularnewline
Trimmed Mean ( 24 / 40 ) & 7.90555555555556 & 0.0420470379385849 & 188.016943478935 \tabularnewline
Trimmed Mean ( 25 / 40 ) & 7.90714285714286 & 0.0411693180379245 & 192.063974677912 \tabularnewline
Trimmed Mean ( 26 / 40 ) & 7.90882352941177 & 0.0401235632186725 & 197.111694350496 \tabularnewline
Trimmed Mean ( 27 / 40 ) & 7.91060606060606 & 0.0395857799736836 & 199.834538207028 \tabularnewline
Trimmed Mean ( 28 / 40 ) & 7.9125 & 0.0389278433017678 & 203.260682557276 \tabularnewline
Trimmed Mean ( 29 / 40 ) & 7.91451612903226 & 0.0381240962784273 & 207.598786636963 \tabularnewline
Trimmed Mean ( 30 / 40 ) & 7.91666666666667 & 0.0371412532506917 & 213.150229832894 \tabularnewline
Trimmed Mean ( 31 / 40 ) & 7.91896551724138 & 0.0359350843559499 & 220.368635810096 \tabularnewline
Trimmed Mean ( 32 / 40 ) & 7.92142857142857 & 0.0344449764224352 & 229.973406695935 \tabularnewline
Trimmed Mean ( 33 / 40 ) & 7.92407407407407 & 0.033639597767835 & 235.557931719707 \tabularnewline
Trimmed Mean ( 34 / 40 ) & 7.92692307692308 & 0.0326223632933456 & 242.990460428722 \tabularnewline
Trimmed Mean ( 35 / 40 ) & 7.93 & 0.0313310174278019 & 253.103813761351 \tabularnewline
Trimmed Mean ( 36 / 40 ) & 7.93333333333333 & 0.0296751521851262 & 267.339263631803 \tabularnewline
Trimmed Mean ( 37 / 40 ) & 7.93478260869565 & 0.028355471539468 & 279.832504201216 \tabularnewline
Trimmed Mean ( 38 / 40 ) & 7.93636363636364 & 0.0266309261419243 & 298.013054223813 \tabularnewline
Trimmed Mean ( 39 / 40 ) & 7.93809523809524 & 0.0259438285730247 & 305.972390148652 \tabularnewline
Trimmed Mean ( 40 / 40 ) & 7.94 & 0.0250128172271942 & 317.437253384139 \tabularnewline
Median & 7.95 &  &  \tabularnewline
Midrange & 7.55 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 7.90882352941177 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 7.90882352941177 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 7.90882352941177 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 7.90882352941177 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 7.90882352941177 &  &  \tabularnewline
Midmean - Closest Observation & 7.90882352941177 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 7.90882352941177 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 7.90882352941177 &  &  \tabularnewline
Number of observations & 120 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=130349&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]7.80833333333333[/C][C]0.0608366427863082[/C][C]128.349181935639[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]7.77882353476357[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]7.74797595858816[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]7.83648518150835[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 40 )[/C][C]7.80833333333333[/C][C]0.0608366427863082[/C][C]128.349181935639[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 40 )[/C][C]7.805[/C][C]0.0598182354179343[/C][C]130.478606489618[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 40 )[/C][C]7.805[/C][C]0.0598182354179343[/C][C]130.478606489618[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 40 )[/C][C]7.805[/C][C]0.0598182354179343[/C][C]130.478606489618[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 40 )[/C][C]7.80916666666667[/C][C]0.0589591777463261[/C][C]132.450399838781[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 40 )[/C][C]7.81416666666667[/C][C]0.0579806766967647[/C][C]134.771912158498[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 40 )[/C][C]7.82[/C][C]0.0568993410682901[/C][C]137.43568648035[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 40 )[/C][C]7.82[/C][C]0.0568993410682901[/C][C]137.43568648035[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 40 )[/C][C]7.8275[/C][C]0.0555840204855076[/C][C]140.822846775556[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 40 )[/C][C]7.8275[/C][C]0.0532680250525322[/C][C]146.945564290785[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 40 )[/C][C]7.8275[/C][C]0.0532680250525322[/C][C]146.945564290785[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 40 )[/C][C]7.8375[/C][C]0.0516948396126444[/C][C]151.610877579413[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 40 )[/C][C]7.8375[/C][C]0.0516948396126444[/C][C]151.610877579413[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 40 )[/C][C]7.8375[/C][C]0.0516948396126444[/C][C]151.610877579413[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 40 )[/C][C]7.85[/C][C]0.0498457002913492[/C][C]157.48600088105[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 40 )[/C][C]7.85[/C][C]0.0498457002913492[/C][C]157.48600088105[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 40 )[/C][C]7.86416666666667[/C][C]0.0478793393764191[/C][C]164.249690348481[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 40 )[/C][C]7.86416666666667[/C][C]0.0478793393764191[/C][C]164.249690348481[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 40 )[/C][C]7.86416666666667[/C][C]0.0478793393764191[/C][C]164.249690348481[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 40 )[/C][C]7.86416666666667[/C][C]0.0478793393764191[/C][C]164.249690348481[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 40 )[/C][C]7.86416666666667[/C][C]0.0478793393764191[/C][C]164.249690348481[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 40 )[/C][C]7.86416666666667[/C][C]0.0478793393764191[/C][C]164.249690348481[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 40 )[/C][C]7.88333333333333[/C][C]0.0453794048310442[/C][C]173.720509616299[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 40 )[/C][C]7.88333333333333[/C][C]0.0453794048310442[/C][C]173.720509616299[/C][/ROW]
[ROW][C]Winsorized Mean ( 25 / 40 )[/C][C]7.88333333333333[/C][C]0.0453794048310442[/C][C]173.720509616299[/C][/ROW]
[ROW][C]Winsorized Mean ( 26 / 40 )[/C][C]7.88333333333333[/C][C]0.0402779790071924[/C][C]195.723160090173[/C][/ROW]
[ROW][C]Winsorized Mean ( 27 / 40 )[/C][C]7.88333333333333[/C][C]0.0402779790071924[/C][C]195.723160090173[/C][/ROW]
[ROW][C]Winsorized Mean ( 28 / 40 )[/C][C]7.88333333333333[/C][C]0.0402779790071924[/C][C]195.723160090173[/C][/ROW]
[ROW][C]Winsorized Mean ( 29 / 40 )[/C][C]7.88333333333333[/C][C]0.0402779790071924[/C][C]195.723160090173[/C][/ROW]
[ROW][C]Winsorized Mean ( 30 / 40 )[/C][C]7.88333333333333[/C][C]0.0402779790071924[/C][C]195.723160090173[/C][/ROW]
[ROW][C]Winsorized Mean ( 31 / 40 )[/C][C]7.88333333333333[/C][C]0.0402779790071924[/C][C]195.723160090173[/C][/ROW]
[ROW][C]Winsorized Mean ( 32 / 40 )[/C][C]7.88333333333333[/C][C]0.0342656726359654[/C][C]230.065039641421[/C][/ROW]
[ROW][C]Winsorized Mean ( 33 / 40 )[/C][C]7.88333333333333[/C][C]0.0342656726359654[/C][C]230.065039641421[/C][/ROW]
[ROW][C]Winsorized Mean ( 34 / 40 )[/C][C]7.88333333333333[/C][C]0.0342656726359654[/C][C]230.065039641421[/C][/ROW]
[ROW][C]Winsorized Mean ( 35 / 40 )[/C][C]7.88333333333333[/C][C]0.0342656726359654[/C][C]230.065039641421[/C][/ROW]
[ROW][C]Winsorized Mean ( 36 / 40 )[/C][C]7.91333333333333[/C][C]0.030791003572912[/C][C]257.00147494689[/C][/ROW]
[ROW][C]Winsorized Mean ( 37 / 40 )[/C][C]7.91333333333333[/C][C]0.030791003572912[/C][C]257.00147494689[/C][/ROW]
[ROW][C]Winsorized Mean ( 38 / 40 )[/C][C]7.91333333333333[/C][C]0.0239903497560839[/C][C]329.854854714093[/C][/ROW]
[ROW][C]Winsorized Mean ( 39 / 40 )[/C][C]7.91333333333333[/C][C]0.0239903497560839[/C][C]329.854854714093[/C][/ROW]
[ROW][C]Winsorized Mean ( 40 / 40 )[/C][C]7.91333333333333[/C][C]0.0239903497560839[/C][C]329.854854714093[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 40 )[/C][C]7.81271186440678[/C][C]0.0596181121489419[/C][C]131.045945314212[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 40 )[/C][C]7.81724137931035[/C][C]0.0582641951363443[/C][C]134.168872684454[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 40 )[/C][C]7.82368421052632[/C][C]0.0573478780828093[/C][C]136.424999007445[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 40 )[/C][C]7.83035714285714[/C][C]0.0563222835393992[/C][C]139.027692962406[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 40 )[/C][C]7.83727272727273[/C][C]0.0551721710517536[/C][C]142.051193162601[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 40 )[/C][C]7.84351851851852[/C][C]0.0541185887462463[/C][C]144.932059394519[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 40 )[/C][C]7.84905660377358[/C][C]0.0531698744497357[/C][C]147.622251980183[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 40 )[/C][C]7.85384615384615[/C][C]0.0523339344619876[/C][C]150.071769580992[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 40 )[/C][C]7.85882352941176[/C][C]0.0513901665304645[/C][C]152.924655824048[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 40 )[/C][C]7.863[/C][C]0.0505655889699585[/C][C]155.501006913446[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 40 )[/C][C]7.86734693877551[/C][C]0.0500110551675672[/C][C]157.312156530494[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 40 )[/C][C]7.871875[/C][C]0.0493755551823107[/C][C]159.428587100124[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 40 )[/C][C]7.87553191489362[/C][C]0.048888028003957[/C][C]161.093262224776[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 40 )[/C][C]7.87934782608696[/C][C]0.04832448362701[/C][C]163.050843686263[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 40 )[/C][C]7.88333333333333[/C][C]0.0476737246287201[/C][C]165.360130653273[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 40 )[/C][C]7.88636363636364[/C][C]0.047182415138276[/C][C]167.1462474579[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 40 )[/C][C]7.88953488372093[/C][C]0.04660950713443[/C][C]169.268790184074[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 40 )[/C][C]7.89166666666667[/C][C]0.0462044253236362[/C][C]170.798935629865[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 40 )[/C][C]7.89390243902439[/C][C]0.0457250321335283[/C][C]172.638532346402[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 40 )[/C][C]7.89625[/C][C]0.0451594835632141[/C][C]174.852531007066[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 40 )[/C][C]7.89871794871795[/C][C]0.0444934335999346[/C][C]177.525475326084[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 40 )[/C][C]7.90131578947368[/C][C]0.0437093037208741[/C][C]180.769655813581[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 40 )[/C][C]7.90405405405405[/C][C]0.0427852575580247[/C][C]184.737792996447[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 40 )[/C][C]7.90555555555556[/C][C]0.0420470379385849[/C][C]188.016943478935[/C][/ROW]
[ROW][C]Trimmed Mean ( 25 / 40 )[/C][C]7.90714285714286[/C][C]0.0411693180379245[/C][C]192.063974677912[/C][/ROW]
[ROW][C]Trimmed Mean ( 26 / 40 )[/C][C]7.90882352941177[/C][C]0.0401235632186725[/C][C]197.111694350496[/C][/ROW]
[ROW][C]Trimmed Mean ( 27 / 40 )[/C][C]7.91060606060606[/C][C]0.0395857799736836[/C][C]199.834538207028[/C][/ROW]
[ROW][C]Trimmed Mean ( 28 / 40 )[/C][C]7.9125[/C][C]0.0389278433017678[/C][C]203.260682557276[/C][/ROW]
[ROW][C]Trimmed Mean ( 29 / 40 )[/C][C]7.91451612903226[/C][C]0.0381240962784273[/C][C]207.598786636963[/C][/ROW]
[ROW][C]Trimmed Mean ( 30 / 40 )[/C][C]7.91666666666667[/C][C]0.0371412532506917[/C][C]213.150229832894[/C][/ROW]
[ROW][C]Trimmed Mean ( 31 / 40 )[/C][C]7.91896551724138[/C][C]0.0359350843559499[/C][C]220.368635810096[/C][/ROW]
[ROW][C]Trimmed Mean ( 32 / 40 )[/C][C]7.92142857142857[/C][C]0.0344449764224352[/C][C]229.973406695935[/C][/ROW]
[ROW][C]Trimmed Mean ( 33 / 40 )[/C][C]7.92407407407407[/C][C]0.033639597767835[/C][C]235.557931719707[/C][/ROW]
[ROW][C]Trimmed Mean ( 34 / 40 )[/C][C]7.92692307692308[/C][C]0.0326223632933456[/C][C]242.990460428722[/C][/ROW]
[ROW][C]Trimmed Mean ( 35 / 40 )[/C][C]7.93[/C][C]0.0313310174278019[/C][C]253.103813761351[/C][/ROW]
[ROW][C]Trimmed Mean ( 36 / 40 )[/C][C]7.93333333333333[/C][C]0.0296751521851262[/C][C]267.339263631803[/C][/ROW]
[ROW][C]Trimmed Mean ( 37 / 40 )[/C][C]7.93478260869565[/C][C]0.028355471539468[/C][C]279.832504201216[/C][/ROW]
[ROW][C]Trimmed Mean ( 38 / 40 )[/C][C]7.93636363636364[/C][C]0.0266309261419243[/C][C]298.013054223813[/C][/ROW]
[ROW][C]Trimmed Mean ( 39 / 40 )[/C][C]7.93809523809524[/C][C]0.0259438285730247[/C][C]305.972390148652[/C][/ROW]
[ROW][C]Trimmed Mean ( 40 / 40 )[/C][C]7.94[/C][C]0.0250128172271942[/C][C]317.437253384139[/C][/ROW]
[ROW][C]Median[/C][C]7.95[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]7.55[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]7.90882352941177[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]7.90882352941177[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]7.90882352941177[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]7.90882352941177[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]7.90882352941177[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]7.90882352941177[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]7.90882352941177[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]7.90882352941177[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]120[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=130349&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=130349&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 Mean7.808333333333330.0608366427863082128.349181935639
Geometric Mean7.77882353476357
Harmonic Mean7.74797595858816
Quadratic Mean7.83648518150835
Winsorized Mean ( 1 / 40 )7.808333333333330.0608366427863082128.349181935639
Winsorized Mean ( 2 / 40 )7.8050.0598182354179343130.478606489618
Winsorized Mean ( 3 / 40 )7.8050.0598182354179343130.478606489618
Winsorized Mean ( 4 / 40 )7.8050.0598182354179343130.478606489618
Winsorized Mean ( 5 / 40 )7.809166666666670.0589591777463261132.450399838781
Winsorized Mean ( 6 / 40 )7.814166666666670.0579806766967647134.771912158498
Winsorized Mean ( 7 / 40 )7.820.0568993410682901137.43568648035
Winsorized Mean ( 8 / 40 )7.820.0568993410682901137.43568648035
Winsorized Mean ( 9 / 40 )7.82750.0555840204855076140.822846775556
Winsorized Mean ( 10 / 40 )7.82750.0532680250525322146.945564290785
Winsorized Mean ( 11 / 40 )7.82750.0532680250525322146.945564290785
Winsorized Mean ( 12 / 40 )7.83750.0516948396126444151.610877579413
Winsorized Mean ( 13 / 40 )7.83750.0516948396126444151.610877579413
Winsorized Mean ( 14 / 40 )7.83750.0516948396126444151.610877579413
Winsorized Mean ( 15 / 40 )7.850.0498457002913492157.48600088105
Winsorized Mean ( 16 / 40 )7.850.0498457002913492157.48600088105
Winsorized Mean ( 17 / 40 )7.864166666666670.0478793393764191164.249690348481
Winsorized Mean ( 18 / 40 )7.864166666666670.0478793393764191164.249690348481
Winsorized Mean ( 19 / 40 )7.864166666666670.0478793393764191164.249690348481
Winsorized Mean ( 20 / 40 )7.864166666666670.0478793393764191164.249690348481
Winsorized Mean ( 21 / 40 )7.864166666666670.0478793393764191164.249690348481
Winsorized Mean ( 22 / 40 )7.864166666666670.0478793393764191164.249690348481
Winsorized Mean ( 23 / 40 )7.883333333333330.0453794048310442173.720509616299
Winsorized Mean ( 24 / 40 )7.883333333333330.0453794048310442173.720509616299
Winsorized Mean ( 25 / 40 )7.883333333333330.0453794048310442173.720509616299
Winsorized Mean ( 26 / 40 )7.883333333333330.0402779790071924195.723160090173
Winsorized Mean ( 27 / 40 )7.883333333333330.0402779790071924195.723160090173
Winsorized Mean ( 28 / 40 )7.883333333333330.0402779790071924195.723160090173
Winsorized Mean ( 29 / 40 )7.883333333333330.0402779790071924195.723160090173
Winsorized Mean ( 30 / 40 )7.883333333333330.0402779790071924195.723160090173
Winsorized Mean ( 31 / 40 )7.883333333333330.0402779790071924195.723160090173
Winsorized Mean ( 32 / 40 )7.883333333333330.0342656726359654230.065039641421
Winsorized Mean ( 33 / 40 )7.883333333333330.0342656726359654230.065039641421
Winsorized Mean ( 34 / 40 )7.883333333333330.0342656726359654230.065039641421
Winsorized Mean ( 35 / 40 )7.883333333333330.0342656726359654230.065039641421
Winsorized Mean ( 36 / 40 )7.913333333333330.030791003572912257.00147494689
Winsorized Mean ( 37 / 40 )7.913333333333330.030791003572912257.00147494689
Winsorized Mean ( 38 / 40 )7.913333333333330.0239903497560839329.854854714093
Winsorized Mean ( 39 / 40 )7.913333333333330.0239903497560839329.854854714093
Winsorized Mean ( 40 / 40 )7.913333333333330.0239903497560839329.854854714093
Trimmed Mean ( 1 / 40 )7.812711864406780.0596181121489419131.045945314212
Trimmed Mean ( 2 / 40 )7.817241379310350.0582641951363443134.168872684454
Trimmed Mean ( 3 / 40 )7.823684210526320.0573478780828093136.424999007445
Trimmed Mean ( 4 / 40 )7.830357142857140.0563222835393992139.027692962406
Trimmed Mean ( 5 / 40 )7.837272727272730.0551721710517536142.051193162601
Trimmed Mean ( 6 / 40 )7.843518518518520.0541185887462463144.932059394519
Trimmed Mean ( 7 / 40 )7.849056603773580.0531698744497357147.622251980183
Trimmed Mean ( 8 / 40 )7.853846153846150.0523339344619876150.071769580992
Trimmed Mean ( 9 / 40 )7.858823529411760.0513901665304645152.924655824048
Trimmed Mean ( 10 / 40 )7.8630.0505655889699585155.501006913446
Trimmed Mean ( 11 / 40 )7.867346938775510.0500110551675672157.312156530494
Trimmed Mean ( 12 / 40 )7.8718750.0493755551823107159.428587100124
Trimmed Mean ( 13 / 40 )7.875531914893620.048888028003957161.093262224776
Trimmed Mean ( 14 / 40 )7.879347826086960.04832448362701163.050843686263
Trimmed Mean ( 15 / 40 )7.883333333333330.0476737246287201165.360130653273
Trimmed Mean ( 16 / 40 )7.886363636363640.047182415138276167.1462474579
Trimmed Mean ( 17 / 40 )7.889534883720930.04660950713443169.268790184074
Trimmed Mean ( 18 / 40 )7.891666666666670.0462044253236362170.798935629865
Trimmed Mean ( 19 / 40 )7.893902439024390.0457250321335283172.638532346402
Trimmed Mean ( 20 / 40 )7.896250.0451594835632141174.852531007066
Trimmed Mean ( 21 / 40 )7.898717948717950.0444934335999346177.525475326084
Trimmed Mean ( 22 / 40 )7.901315789473680.0437093037208741180.769655813581
Trimmed Mean ( 23 / 40 )7.904054054054050.0427852575580247184.737792996447
Trimmed Mean ( 24 / 40 )7.905555555555560.0420470379385849188.016943478935
Trimmed Mean ( 25 / 40 )7.907142857142860.0411693180379245192.063974677912
Trimmed Mean ( 26 / 40 )7.908823529411770.0401235632186725197.111694350496
Trimmed Mean ( 27 / 40 )7.910606060606060.0395857799736836199.834538207028
Trimmed Mean ( 28 / 40 )7.91250.0389278433017678203.260682557276
Trimmed Mean ( 29 / 40 )7.914516129032260.0381240962784273207.598786636963
Trimmed Mean ( 30 / 40 )7.916666666666670.0371412532506917213.150229832894
Trimmed Mean ( 31 / 40 )7.918965517241380.0359350843559499220.368635810096
Trimmed Mean ( 32 / 40 )7.921428571428570.0344449764224352229.973406695935
Trimmed Mean ( 33 / 40 )7.924074074074070.033639597767835235.557931719707
Trimmed Mean ( 34 / 40 )7.926923076923080.0326223632933456242.990460428722
Trimmed Mean ( 35 / 40 )7.930.0313310174278019253.103813761351
Trimmed Mean ( 36 / 40 )7.933333333333330.0296751521851262267.339263631803
Trimmed Mean ( 37 / 40 )7.934782608695650.028355471539468279.832504201216
Trimmed Mean ( 38 / 40 )7.936363636363640.0266309261419243298.013054223813
Trimmed Mean ( 39 / 40 )7.938095238095240.0259438285730247305.972390148652
Trimmed Mean ( 40 / 40 )7.940.0250128172271942317.437253384139
Median7.95
Midrange7.55
Midmean - Weighted Average at Xnp7.90882352941177
Midmean - Weighted Average at X(n+1)p7.90882352941177
Midmean - Empirical Distribution Function7.90882352941177
Midmean - Empirical Distribution Function - Averaging7.90882352941177
Midmean - Empirical Distribution Function - Interpolation7.90882352941177
Midmean - Closest Observation7.90882352941177
Midmean - True Basic - Statistics Graphics Toolkit7.90882352941177
Midmean - MS Excel (old versions)7.90882352941177
Number of observations120



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')