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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 computationMon, 22 Dec 2008 06:24:16 -0700
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2008/Dec/22/t12299523829ny9oi42y59k1vd.htm/, Retrieved Sun, 12 May 2024 15:56:08 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=36051, Retrieved Sun, 12 May 2024 15:56:08 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact166
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [ARIMA Backward Selection] [ARMA backward sel...] [2008-12-21 12:09:36] [82d201ca7b4e7cd2c6f885d29b5b6937]
- RMPD    [Central Tendency] [central tendency] [2008-12-22 13:24:16] [00a0a665d7a07edd2e460056b0c0c354] [Current]
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Dataseries X:
1.99499881671212 
-44.0713152253927 
-160.978734424716 
-94.2145782865758 
208.335903573322 
52.5495842727748 
72.661373122602 
-62.4712626246549 
124.821402543340 
-30.3289038334678 
62.3393617788071 
1.18465758313622 
38.2020088461955 
128.574985864437 
51.115301712882 
-33.7041148859667 
43.0655264119969 
-87.520733496075 
89.5265555708561 
-65.8856549991207 
109.266277081459 
79.4239223229955 
119.047912261890 
42.4658492333484 
50.0743781398157 
32.4110610202947 
82.6074244456106 
-7.52320761164093 
16.7593231945769 
-85.4661718426825 
68.3227235846736 
27.654340089409 
115.423686036618 
-30.968532050421 
36.0387266766301 
30.3329159680057 
133.808966479107 
127.664777824372 
113.445538569978 
58.2209947148251 
-55.0913953958727 
-94.6873011242496 
-224.999990770574 
201.022601208512 
89.6359105550153 
160.889095655410 
69.9830938784715 
50.1740293728778 
58.117154554652 
114.652321250987 
28.923326531499 
-160.486994985916 
256.041094445984 
7.58277618525696 
-4.16118309950070 
-137.639065031518 
-306.153135940507 
176.456660406577 
61.8112124666031 
-238.688317592266 
23.3002938224372 




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=36051&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=36051&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=36051&T=0

As an alternative you can also use a QR Code:  

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

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







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean24.440810735308813.85474622679191.76407494841341
Geometric MeanNaN
Harmonic Mean39.7601076954351
Quadratic Mean110.066310967196
Winsorized Mean ( 1 / 20 )24.764739054580613.25113159473581.86887730134827
Winsorized Mean ( 2 / 20 )24.973756249888213.05047557445691.91362805956038
Winsorized Mean ( 3 / 20 )26.914181604507311.86512186048412.26834430534953
Winsorized Mean ( 4 / 20 )25.925602895499711.65072740623872.22523469921861
Winsorized Mean ( 5 / 20 )25.578701319933710.76241361585252.37666960525078
Winsorized Mean ( 6 / 20 )29.28864721756639.686428655589993.0236786187099
Winsorized Mean ( 7 / 20 )29.23844399761989.657070506948783.02767220934974
Winsorized Mean ( 8 / 20 )29.74342360541909.409269771054463.16107671786795
Winsorized Mean ( 9 / 20 )29.19472921767289.205277731968373.17152073709677
Winsorized Mean ( 10 / 20 )31.81051456493348.465140676686323.75782468122971
Winsorized Mean ( 11 / 20 )32.28712609734628.32459491714883.87852218860935
Winsorized Mean ( 12 / 20 )33.50150338543288.013754249427914.18050046740882
Winsorized Mean ( 13 / 20 )34.95938277667047.44105608779794.69817487789105
Winsorized Mean ( 14 / 20 )32.83341020915816.304904193468055.20759859335752
Winsorized Mean ( 15 / 20 )33.47920394310566.183260584476315.41449021688629
Winsorized Mean ( 16 / 20 )31.83212121306175.88621813634645.40790716139176
Winsorized Mean ( 17 / 20 )37.30060153579294.684142879434637.96316476586534
Winsorized Mean ( 18 / 20 )36.29716802122634.233287148149398.57422772208917
Winsorized Mean ( 19 / 20 )37.1280478135483.852018670696469.63859497774322
Winsorized Mean ( 20 / 20 )36.84934976101623.733750534061969.86925865154886
Trimmed Mean ( 1 / 20 )26.118669429633212.55559778200642.08024101146855
Trimmed Mean ( 2 / 20 )27.567612462584311.68735552896062.35875535695593
Trimmed Mean ( 3 / 20 )29.006023635079410.73115160094002.70297398766956
Trimmed Mean ( 4 / 20 )29.808554225424610.15389709933992.93567621710117
Trimmed Mean ( 5 / 20 )30.96963280937279.511289977152293.25609174820313
Trimmed Mean ( 6 / 20 )32.31186473123319.02546767844013.58007649935074
Trimmed Mean ( 7 / 20 )32.96582312957948.767113525679373.76016838757941
Trimmed Mean ( 8 / 20 )33.68763305672088.439028394444513.99188526002563
Trimmed Mean ( 9 / 20 )34.38704229081808.082910275334184.2542897445928
Trimmed Mean ( 10 / 20 )35.24539214843827.668025423141514.59641044512845
Trimmed Mean ( 11 / 20 )35.7826422320127.336265933214224.87750070100507
Trimmed Mean ( 12 / 20 )36.30654022762536.925060626673085.2427757943063
Trimmed Mean ( 13 / 20 )36.7139384356586.453986729009265.68856738899646
Trimmed Mean ( 14 / 20 )36.96342070884745.981033879006266.18010555643079
Trimmed Mean ( 15 / 20 )37.54390605557795.679363088862346.61058387501308
Trimmed Mean ( 16 / 20 )38.11389876560285.274687632712127.22581153985899
Trimmed Mean ( 17 / 20 )39.00090902186434.76011404019458.19327198729691
Trimmed Mean ( 18 / 20 )39.24495315515934.491917736884928.73679249130131
Trimmed Mean ( 19 / 20 )39.67928864590794.241081387716289.35593661579652
Trimmed Mean ( 20 / 20 )40.06932797115593.9934333957457210.0338039977936
Median42.4658492333484
Midrange-25.0560207472615
Midmean - Weighted Average at Xnp35.8111510717353
Midmean - Weighted Average at X(n+1)p37.5439060555779
Midmean - Empirical Distribution Function37.5439060555779
Midmean - Empirical Distribution Function - Averaging37.5439060555779
Midmean - Empirical Distribution Function - Interpolation37.5439060555779
Midmean - Closest Observation35.3174054011546
Midmean - True Basic - Statistics Graphics Toolkit37.5439060555779
Midmean - MS Excel (old versions)37.5439060555779
Number of observations61

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 24.4408107353088 & 13.8547462267919 & 1.76407494841341 \tabularnewline
Geometric Mean & NaN &  &  \tabularnewline
Harmonic Mean & 39.7601076954351 &  &  \tabularnewline
Quadratic Mean & 110.066310967196 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 24.7647390545806 & 13.2511315947358 & 1.86887730134827 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 24.9737562498882 & 13.0504755744569 & 1.91362805956038 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 26.9141816045073 & 11.8651218604841 & 2.26834430534953 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 25.9256028954997 & 11.6507274062387 & 2.22523469921861 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 25.5787013199337 & 10.7624136158525 & 2.37666960525078 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 29.2886472175663 & 9.68642865558999 & 3.0236786187099 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 29.2384439976198 & 9.65707050694878 & 3.02767220934974 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 29.7434236054190 & 9.40926977105446 & 3.16107671786795 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 29.1947292176728 & 9.20527773196837 & 3.17152073709677 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 31.8105145649334 & 8.46514067668632 & 3.75782468122971 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 32.2871260973462 & 8.3245949171488 & 3.87852218860935 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 33.5015033854328 & 8.01375424942791 & 4.18050046740882 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 34.9593827766704 & 7.4410560877979 & 4.69817487789105 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 32.8334102091581 & 6.30490419346805 & 5.20759859335752 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 33.4792039431056 & 6.18326058447631 & 5.41449021688629 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 31.8321212130617 & 5.8862181363464 & 5.40790716139176 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 37.3006015357929 & 4.68414287943463 & 7.96316476586534 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 36.2971680212263 & 4.23328714814939 & 8.57422772208917 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 37.128047813548 & 3.85201867069646 & 9.63859497774322 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 36.8493497610162 & 3.73375053406196 & 9.86925865154886 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 26.1186694296332 & 12.5555977820064 & 2.08024101146855 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 27.5676124625843 & 11.6873555289606 & 2.35875535695593 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 29.0060236350794 & 10.7311516009400 & 2.70297398766956 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 29.8085542254246 & 10.1538970993399 & 2.93567621710117 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 30.9696328093727 & 9.51128997715229 & 3.25609174820313 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 32.3118647312331 & 9.0254676784401 & 3.58007649935074 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 32.9658231295794 & 8.76711352567937 & 3.76016838757941 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 33.6876330567208 & 8.43902839444451 & 3.99188526002563 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 34.3870422908180 & 8.08291027533418 & 4.2542897445928 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 35.2453921484382 & 7.66802542314151 & 4.59641044512845 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 35.782642232012 & 7.33626593321422 & 4.87750070100507 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 36.3065402276253 & 6.92506062667308 & 5.2427757943063 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 36.713938435658 & 6.45398672900926 & 5.68856738899646 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 36.9634207088474 & 5.98103387900626 & 6.18010555643079 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 37.5439060555779 & 5.67936308886234 & 6.61058387501308 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 38.1138987656028 & 5.27468763271212 & 7.22581153985899 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 39.0009090218643 & 4.7601140401945 & 8.19327198729691 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 39.2449531551593 & 4.49191773688492 & 8.73679249130131 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 39.6792886459079 & 4.24108138771628 & 9.35593661579652 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 40.0693279711559 & 3.99343339574572 & 10.0338039977936 \tabularnewline
Median & 42.4658492333484 &  &  \tabularnewline
Midrange & -25.0560207472615 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 35.8111510717353 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 37.5439060555779 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 37.5439060555779 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 37.5439060555779 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 37.5439060555779 &  &  \tabularnewline
Midmean - Closest Observation & 35.3174054011546 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 37.5439060555779 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 37.5439060555779 &  &  \tabularnewline
Number of observations & 61 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=36051&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]24.4408107353088[/C][C]13.8547462267919[/C][C]1.76407494841341[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]NaN[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]39.7601076954351[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]110.066310967196[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]24.7647390545806[/C][C]13.2511315947358[/C][C]1.86887730134827[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]24.9737562498882[/C][C]13.0504755744569[/C][C]1.91362805956038[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]26.9141816045073[/C][C]11.8651218604841[/C][C]2.26834430534953[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]25.9256028954997[/C][C]11.6507274062387[/C][C]2.22523469921861[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]25.5787013199337[/C][C]10.7624136158525[/C][C]2.37666960525078[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]29.2886472175663[/C][C]9.68642865558999[/C][C]3.0236786187099[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]29.2384439976198[/C][C]9.65707050694878[/C][C]3.02767220934974[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]29.7434236054190[/C][C]9.40926977105446[/C][C]3.16107671786795[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]29.1947292176728[/C][C]9.20527773196837[/C][C]3.17152073709677[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]31.8105145649334[/C][C]8.46514067668632[/C][C]3.75782468122971[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]32.2871260973462[/C][C]8.3245949171488[/C][C]3.87852218860935[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]33.5015033854328[/C][C]8.01375424942791[/C][C]4.18050046740882[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]34.9593827766704[/C][C]7.4410560877979[/C][C]4.69817487789105[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]32.8334102091581[/C][C]6.30490419346805[/C][C]5.20759859335752[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]33.4792039431056[/C][C]6.18326058447631[/C][C]5.41449021688629[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]31.8321212130617[/C][C]5.8862181363464[/C][C]5.40790716139176[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]37.3006015357929[/C][C]4.68414287943463[/C][C]7.96316476586534[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]36.2971680212263[/C][C]4.23328714814939[/C][C]8.57422772208917[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]37.128047813548[/C][C]3.85201867069646[/C][C]9.63859497774322[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]36.8493497610162[/C][C]3.73375053406196[/C][C]9.86925865154886[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]26.1186694296332[/C][C]12.5555977820064[/C][C]2.08024101146855[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]27.5676124625843[/C][C]11.6873555289606[/C][C]2.35875535695593[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]29.0060236350794[/C][C]10.7311516009400[/C][C]2.70297398766956[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]29.8085542254246[/C][C]10.1538970993399[/C][C]2.93567621710117[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]30.9696328093727[/C][C]9.51128997715229[/C][C]3.25609174820313[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]32.3118647312331[/C][C]9.0254676784401[/C][C]3.58007649935074[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]32.9658231295794[/C][C]8.76711352567937[/C][C]3.76016838757941[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]33.6876330567208[/C][C]8.43902839444451[/C][C]3.99188526002563[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]34.3870422908180[/C][C]8.08291027533418[/C][C]4.2542897445928[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]35.2453921484382[/C][C]7.66802542314151[/C][C]4.59641044512845[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]35.782642232012[/C][C]7.33626593321422[/C][C]4.87750070100507[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]36.3065402276253[/C][C]6.92506062667308[/C][C]5.2427757943063[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]36.713938435658[/C][C]6.45398672900926[/C][C]5.68856738899646[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]36.9634207088474[/C][C]5.98103387900626[/C][C]6.18010555643079[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]37.5439060555779[/C][C]5.67936308886234[/C][C]6.61058387501308[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]38.1138987656028[/C][C]5.27468763271212[/C][C]7.22581153985899[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]39.0009090218643[/C][C]4.7601140401945[/C][C]8.19327198729691[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]39.2449531551593[/C][C]4.49191773688492[/C][C]8.73679249130131[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]39.6792886459079[/C][C]4.24108138771628[/C][C]9.35593661579652[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]40.0693279711559[/C][C]3.99343339574572[/C][C]10.0338039977936[/C][/ROW]
[ROW][C]Median[/C][C]42.4658492333484[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]-25.0560207472615[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]35.8111510717353[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]37.5439060555779[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]37.5439060555779[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]37.5439060555779[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]37.5439060555779[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]35.3174054011546[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]37.5439060555779[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]37.5439060555779[/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=36051&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=36051&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 Mean24.440810735308813.85474622679191.76407494841341
Geometric MeanNaN
Harmonic Mean39.7601076954351
Quadratic Mean110.066310967196
Winsorized Mean ( 1 / 20 )24.764739054580613.25113159473581.86887730134827
Winsorized Mean ( 2 / 20 )24.973756249888213.05047557445691.91362805956038
Winsorized Mean ( 3 / 20 )26.914181604507311.86512186048412.26834430534953
Winsorized Mean ( 4 / 20 )25.925602895499711.65072740623872.22523469921861
Winsorized Mean ( 5 / 20 )25.578701319933710.76241361585252.37666960525078
Winsorized Mean ( 6 / 20 )29.28864721756639.686428655589993.0236786187099
Winsorized Mean ( 7 / 20 )29.23844399761989.657070506948783.02767220934974
Winsorized Mean ( 8 / 20 )29.74342360541909.409269771054463.16107671786795
Winsorized Mean ( 9 / 20 )29.19472921767289.205277731968373.17152073709677
Winsorized Mean ( 10 / 20 )31.81051456493348.465140676686323.75782468122971
Winsorized Mean ( 11 / 20 )32.28712609734628.32459491714883.87852218860935
Winsorized Mean ( 12 / 20 )33.50150338543288.013754249427914.18050046740882
Winsorized Mean ( 13 / 20 )34.95938277667047.44105608779794.69817487789105
Winsorized Mean ( 14 / 20 )32.83341020915816.304904193468055.20759859335752
Winsorized Mean ( 15 / 20 )33.47920394310566.183260584476315.41449021688629
Winsorized Mean ( 16 / 20 )31.83212121306175.88621813634645.40790716139176
Winsorized Mean ( 17 / 20 )37.30060153579294.684142879434637.96316476586534
Winsorized Mean ( 18 / 20 )36.29716802122634.233287148149398.57422772208917
Winsorized Mean ( 19 / 20 )37.1280478135483.852018670696469.63859497774322
Winsorized Mean ( 20 / 20 )36.84934976101623.733750534061969.86925865154886
Trimmed Mean ( 1 / 20 )26.118669429633212.55559778200642.08024101146855
Trimmed Mean ( 2 / 20 )27.567612462584311.68735552896062.35875535695593
Trimmed Mean ( 3 / 20 )29.006023635079410.73115160094002.70297398766956
Trimmed Mean ( 4 / 20 )29.808554225424610.15389709933992.93567621710117
Trimmed Mean ( 5 / 20 )30.96963280937279.511289977152293.25609174820313
Trimmed Mean ( 6 / 20 )32.31186473123319.02546767844013.58007649935074
Trimmed Mean ( 7 / 20 )32.96582312957948.767113525679373.76016838757941
Trimmed Mean ( 8 / 20 )33.68763305672088.439028394444513.99188526002563
Trimmed Mean ( 9 / 20 )34.38704229081808.082910275334184.2542897445928
Trimmed Mean ( 10 / 20 )35.24539214843827.668025423141514.59641044512845
Trimmed Mean ( 11 / 20 )35.7826422320127.336265933214224.87750070100507
Trimmed Mean ( 12 / 20 )36.30654022762536.925060626673085.2427757943063
Trimmed Mean ( 13 / 20 )36.7139384356586.453986729009265.68856738899646
Trimmed Mean ( 14 / 20 )36.96342070884745.981033879006266.18010555643079
Trimmed Mean ( 15 / 20 )37.54390605557795.679363088862346.61058387501308
Trimmed Mean ( 16 / 20 )38.11389876560285.274687632712127.22581153985899
Trimmed Mean ( 17 / 20 )39.00090902186434.76011404019458.19327198729691
Trimmed Mean ( 18 / 20 )39.24495315515934.491917736884928.73679249130131
Trimmed Mean ( 19 / 20 )39.67928864590794.241081387716289.35593661579652
Trimmed Mean ( 20 / 20 )40.06932797115593.9934333957457210.0338039977936
Median42.4658492333484
Midrange-25.0560207472615
Midmean - Weighted Average at Xnp35.8111510717353
Midmean - Weighted Average at X(n+1)p37.5439060555779
Midmean - Empirical Distribution Function37.5439060555779
Midmean - Empirical Distribution Function - Averaging37.5439060555779
Midmean - Empirical Distribution Function - Interpolation37.5439060555779
Midmean - Closest Observation35.3174054011546
Midmean - True Basic - Statistics Graphics Toolkit37.5439060555779
Midmean - MS Excel (old versions)37.5439060555779
Number of observations61



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')