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of Irreproducible Research!

Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationSun, 18 Oct 2009 13:15:43 -0600
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2009/Oct/18/t12558933948usnb13s8bao5b5.htm/, Retrieved Mon, 29 Apr 2024 15:53:42 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=47472, Retrieved Mon, 29 Apr 2024 15:53:42 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact87
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Bivariate Data Series] [Bivariate dataset] [2008-01-05 23:51:08] [74be16979710d4c4e7c6647856088456]
F RMPD  [Univariate Explorative Data Analysis] [Colombia Coffee] [2008-01-07 14:21:11] [74be16979710d4c4e7c6647856088456]
F RMPD    [Univariate Data Series] [] [2009-10-14 08:30:28] [74be16979710d4c4e7c6647856088456]
- RMPD        [Central Tendency] [WS3 part 3] [2009-10-18 19:15:43] [a18540c86166a2b66550d1fef0503cc2] [Current]
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Post a new message
Dataseries X:
17460,225
20289,225
22705,225
19092,225
13730,225
29666,225
25514,225
29019,225
26405,225
22328,225
26967,225
17893,225
18653,225
19607,225
19708,225
18402,225
10621,225
31879,225
29429,225
34429,225
27088,225
26659,225
23614,225
18080,225
17251,225
18128,225
20918,225
17305,225
9290,225
31047,225
26474,225
30574,225
25782,225
25023,225
25701,225
20341,225
18611,225
20347,225
24699,225
19737,225
12661,225
31489,225
30034,225
29942,225
31857,225
25749,225
26758,225
20128,225
17712,225
20443,225
22441,225
15495,225
11432,225
25370,225
24013,225
27709,225
26118,225
20439,225
22682,225
18951,225
16894,225




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=47472&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=47472&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=47472&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 Mean22603.2086065574735.93266482334630.7136911934505
Geometric Mean21809.2175706781
Harmonic Mean20918.4698488398
Quadratic Mean23310.9599231947
Winsorized Mean ( 1 / 20 )22583.225719.50621767136931.3871158377047
Winsorized Mean ( 2 / 20 )22609.093852459712.18805364668631.7459605460826
Winsorized Mean ( 3 / 20 )22651.4381147541693.1328636916432.6797924341836
Winsorized Mean ( 4 / 20 )22692.5528688525670.80981510740633.8285939737168
Winsorized Mean ( 5 / 20 )22798.4545081967632.72677672553736.0320684169277
Winsorized Mean ( 6 / 20 )22882.9463114754597.19740314491638.3172234021296
Winsorized Mean ( 7 / 20 )22913.3561475410588.38304104726538.9429241651109
Winsorized Mean ( 8 / 20 )22884.2413934426580.11721751823139.4476162789005
Winsorized Mean ( 9 / 20 )22872.1430327869569.71307335675340.1467758112414
Winsorized Mean ( 10 / 20 )22846.2413934426550.50103978490741.5008142443639
Winsorized Mean ( 11 / 20 )22642.6512295082503.41135417038444.9784277647512
Winsorized Mean ( 12 / 20 )22557.2741803279477.72891255827847.2177286895445
Winsorized Mean ( 13 / 20 )22541.7168032787472.08032139521247.749748891582
Winsorized Mean ( 14 / 20 )22556.6348360656454.95379479381749.5800564676862
Winsorized Mean ( 15 / 20 )22583.6840163934443.46756559448750.9252215235156
Winsorized Mean ( 16 / 20 )22546.1758196721434.44964269313351.8959474334227
Winsorized Mean ( 17 / 20 )22609.9954918033419.3071747208453.9222719164207
Winsorized Mean ( 18 / 20 )22566.9135245902400.62750816140956.3289166741346
Winsorized Mean ( 19 / 20 )22622.6676229508362.55418477612962.3980319987755
Winsorized Mean ( 20 / 20 )22644.9627049180356.41396228901763.5355656649477
Trimmed Mean ( 1 / 20 )22628.4114406780697.56128060231732.4393169029382
Trimmed Mean ( 2 / 20 )22676.7688596491670.54796685882633.8182650316250
Trimmed Mean ( 3 / 20 )22714.2977272727642.08088734622635.3760689266937
Trimmed Mean ( 4 / 20 )22738.4136792453616.16501984544336.9031232654994
Trimmed Mean ( 5 / 20 )22752.1269607843592.81571997289538.3797632117863
Trimmed Mean ( 6 / 20 )22740.5923469388576.72152649909539.4308020458023
Trimmed Mean ( 7 / 20 )22709.7994680851566.92351080975940.0579602628365
Trimmed Mean ( 8 / 20 )22670.3805555556556.27629385640940.7538138977525
Trimmed Mean ( 9 / 20 )22632.4575581395544.22834399418741.5863264159231
Trimmed Mean ( 10 / 20 )22592.8347560976530.70178098352442.5716203820296
Trimmed Mean ( 11 / 20 )22553.1993589744517.38772959525743.5905184234217
Trimmed Mean ( 12 / 20 )22539.7925675676511.43828066125144.0713834295417
Trimmed Mean ( 13 / 20 )22537.2535714286508.60978337100144.3114826106068
Trimmed Mean ( 14 / 20 )22536.6189393939504.49650669157644.6715064236742
Trimmed Mean ( 15 / 20 )22533.8056451613501.45406370775244.9369289752012
Trimmed Mean ( 16 / 20 )22526.8112068965498.08389385062745.2269416558413
Trimmed Mean ( 17 / 20 )22524.0768518518493.34626254628445.6557159987378
Trimmed Mean ( 18 / 20 )22511.745488.24135465976346.1078210298012
Trimmed Mean ( 19 / 20 )22503.6163043478483.57699943640346.5357457666002
Trimmed Mean ( 20 / 20 )22485.4154761905485.94807492084446.2712306862274
Median22441.225
Midrange21859.725
Midmean - Weighted Average at Xnp22396.2916666667
Midmean - Weighted Average at X(n+1)p22533.8056451613
Midmean - Empirical Distribution Function22533.8056451613
Midmean - Empirical Distribution Function - Averaging22533.8056451613
Midmean - Empirical Distribution Function - Interpolation22533.8056451613
Midmean - Closest Observation22404.69375
Midmean - True Basic - Statistics Graphics Toolkit22533.8056451613
Midmean - MS Excel (old versions)22533.8056451613
Number of observations61

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 22603.2086065574 & 735.932664823346 & 30.7136911934505 \tabularnewline
Geometric Mean & 21809.2175706781 &  &  \tabularnewline
Harmonic Mean & 20918.4698488398 &  &  \tabularnewline
Quadratic Mean & 23310.9599231947 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 22583.225 & 719.506217671369 & 31.3871158377047 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 22609.093852459 & 712.188053646686 & 31.7459605460826 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 22651.4381147541 & 693.13286369164 & 32.6797924341836 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 22692.5528688525 & 670.809815107406 & 33.8285939737168 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 22798.4545081967 & 632.726776725537 & 36.0320684169277 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 22882.9463114754 & 597.197403144916 & 38.3172234021296 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 22913.3561475410 & 588.383041047265 & 38.9429241651109 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 22884.2413934426 & 580.117217518231 & 39.4476162789005 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 22872.1430327869 & 569.713073356753 & 40.1467758112414 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 22846.2413934426 & 550.501039784907 & 41.5008142443639 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 22642.6512295082 & 503.411354170384 & 44.9784277647512 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 22557.2741803279 & 477.728912558278 & 47.2177286895445 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 22541.7168032787 & 472.080321395212 & 47.749748891582 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 22556.6348360656 & 454.953794793817 & 49.5800564676862 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 22583.6840163934 & 443.467565594487 & 50.9252215235156 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 22546.1758196721 & 434.449642693133 & 51.8959474334227 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 22609.9954918033 & 419.30717472084 & 53.9222719164207 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 22566.9135245902 & 400.627508161409 & 56.3289166741346 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 22622.6676229508 & 362.554184776129 & 62.3980319987755 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 22644.9627049180 & 356.413962289017 & 63.5355656649477 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 22628.4114406780 & 697.561280602317 & 32.4393169029382 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 22676.7688596491 & 670.547966858826 & 33.8182650316250 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 22714.2977272727 & 642.080887346226 & 35.3760689266937 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 22738.4136792453 & 616.165019845443 & 36.9031232654994 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 22752.1269607843 & 592.815719972895 & 38.3797632117863 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 22740.5923469388 & 576.721526499095 & 39.4308020458023 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 22709.7994680851 & 566.923510809759 & 40.0579602628365 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 22670.3805555556 & 556.276293856409 & 40.7538138977525 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 22632.4575581395 & 544.228343994187 & 41.5863264159231 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 22592.8347560976 & 530.701780983524 & 42.5716203820296 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 22553.1993589744 & 517.387729595257 & 43.5905184234217 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 22539.7925675676 & 511.438280661251 & 44.0713834295417 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 22537.2535714286 & 508.609783371001 & 44.3114826106068 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 22536.6189393939 & 504.496506691576 & 44.6715064236742 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 22533.8056451613 & 501.454063707752 & 44.9369289752012 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 22526.8112068965 & 498.083893850627 & 45.2269416558413 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 22524.0768518518 & 493.346262546284 & 45.6557159987378 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 22511.745 & 488.241354659763 & 46.1078210298012 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 22503.6163043478 & 483.576999436403 & 46.5357457666002 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 22485.4154761905 & 485.948074920844 & 46.2712306862274 \tabularnewline
Median & 22441.225 &  &  \tabularnewline
Midrange & 21859.725 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 22396.2916666667 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 22533.8056451613 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 22533.8056451613 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 22533.8056451613 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 22533.8056451613 &  &  \tabularnewline
Midmean - Closest Observation & 22404.69375 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 22533.8056451613 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 22533.8056451613 &  &  \tabularnewline
Number of observations & 61 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=47472&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]22603.2086065574[/C][C]735.932664823346[/C][C]30.7136911934505[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]21809.2175706781[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]20918.4698488398[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]23310.9599231947[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]22583.225[/C][C]719.506217671369[/C][C]31.3871158377047[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]22609.093852459[/C][C]712.188053646686[/C][C]31.7459605460826[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]22651.4381147541[/C][C]693.13286369164[/C][C]32.6797924341836[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]22692.5528688525[/C][C]670.809815107406[/C][C]33.8285939737168[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]22798.4545081967[/C][C]632.726776725537[/C][C]36.0320684169277[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]22882.9463114754[/C][C]597.197403144916[/C][C]38.3172234021296[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]22913.3561475410[/C][C]588.383041047265[/C][C]38.9429241651109[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]22884.2413934426[/C][C]580.117217518231[/C][C]39.4476162789005[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]22872.1430327869[/C][C]569.713073356753[/C][C]40.1467758112414[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]22846.2413934426[/C][C]550.501039784907[/C][C]41.5008142443639[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]22642.6512295082[/C][C]503.411354170384[/C][C]44.9784277647512[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]22557.2741803279[/C][C]477.728912558278[/C][C]47.2177286895445[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]22541.7168032787[/C][C]472.080321395212[/C][C]47.749748891582[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]22556.6348360656[/C][C]454.953794793817[/C][C]49.5800564676862[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]22583.6840163934[/C][C]443.467565594487[/C][C]50.9252215235156[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]22546.1758196721[/C][C]434.449642693133[/C][C]51.8959474334227[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]22609.9954918033[/C][C]419.30717472084[/C][C]53.9222719164207[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]22566.9135245902[/C][C]400.627508161409[/C][C]56.3289166741346[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]22622.6676229508[/C][C]362.554184776129[/C][C]62.3980319987755[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]22644.9627049180[/C][C]356.413962289017[/C][C]63.5355656649477[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]22628.4114406780[/C][C]697.561280602317[/C][C]32.4393169029382[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]22676.7688596491[/C][C]670.547966858826[/C][C]33.8182650316250[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]22714.2977272727[/C][C]642.080887346226[/C][C]35.3760689266937[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]22738.4136792453[/C][C]616.165019845443[/C][C]36.9031232654994[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]22752.1269607843[/C][C]592.815719972895[/C][C]38.3797632117863[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]22740.5923469388[/C][C]576.721526499095[/C][C]39.4308020458023[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]22709.7994680851[/C][C]566.923510809759[/C][C]40.0579602628365[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]22670.3805555556[/C][C]556.276293856409[/C][C]40.7538138977525[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]22632.4575581395[/C][C]544.228343994187[/C][C]41.5863264159231[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]22592.8347560976[/C][C]530.701780983524[/C][C]42.5716203820296[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]22553.1993589744[/C][C]517.387729595257[/C][C]43.5905184234217[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]22539.7925675676[/C][C]511.438280661251[/C][C]44.0713834295417[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]22537.2535714286[/C][C]508.609783371001[/C][C]44.3114826106068[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]22536.6189393939[/C][C]504.496506691576[/C][C]44.6715064236742[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]22533.8056451613[/C][C]501.454063707752[/C][C]44.9369289752012[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]22526.8112068965[/C][C]498.083893850627[/C][C]45.2269416558413[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]22524.0768518518[/C][C]493.346262546284[/C][C]45.6557159987378[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]22511.745[/C][C]488.241354659763[/C][C]46.1078210298012[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]22503.6163043478[/C][C]483.576999436403[/C][C]46.5357457666002[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]22485.4154761905[/C][C]485.948074920844[/C][C]46.2712306862274[/C][/ROW]
[ROW][C]Median[/C][C]22441.225[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]21859.725[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]22396.2916666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]22533.8056451613[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]22533.8056451613[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]22533.8056451613[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]22533.8056451613[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]22404.69375[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]22533.8056451613[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]22533.8056451613[/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=47472&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=47472&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 Mean22603.2086065574735.93266482334630.7136911934505
Geometric Mean21809.2175706781
Harmonic Mean20918.4698488398
Quadratic Mean23310.9599231947
Winsorized Mean ( 1 / 20 )22583.225719.50621767136931.3871158377047
Winsorized Mean ( 2 / 20 )22609.093852459712.18805364668631.7459605460826
Winsorized Mean ( 3 / 20 )22651.4381147541693.1328636916432.6797924341836
Winsorized Mean ( 4 / 20 )22692.5528688525670.80981510740633.8285939737168
Winsorized Mean ( 5 / 20 )22798.4545081967632.72677672553736.0320684169277
Winsorized Mean ( 6 / 20 )22882.9463114754597.19740314491638.3172234021296
Winsorized Mean ( 7 / 20 )22913.3561475410588.38304104726538.9429241651109
Winsorized Mean ( 8 / 20 )22884.2413934426580.11721751823139.4476162789005
Winsorized Mean ( 9 / 20 )22872.1430327869569.71307335675340.1467758112414
Winsorized Mean ( 10 / 20 )22846.2413934426550.50103978490741.5008142443639
Winsorized Mean ( 11 / 20 )22642.6512295082503.41135417038444.9784277647512
Winsorized Mean ( 12 / 20 )22557.2741803279477.72891255827847.2177286895445
Winsorized Mean ( 13 / 20 )22541.7168032787472.08032139521247.749748891582
Winsorized Mean ( 14 / 20 )22556.6348360656454.95379479381749.5800564676862
Winsorized Mean ( 15 / 20 )22583.6840163934443.46756559448750.9252215235156
Winsorized Mean ( 16 / 20 )22546.1758196721434.44964269313351.8959474334227
Winsorized Mean ( 17 / 20 )22609.9954918033419.3071747208453.9222719164207
Winsorized Mean ( 18 / 20 )22566.9135245902400.62750816140956.3289166741346
Winsorized Mean ( 19 / 20 )22622.6676229508362.55418477612962.3980319987755
Winsorized Mean ( 20 / 20 )22644.9627049180356.41396228901763.5355656649477
Trimmed Mean ( 1 / 20 )22628.4114406780697.56128060231732.4393169029382
Trimmed Mean ( 2 / 20 )22676.7688596491670.54796685882633.8182650316250
Trimmed Mean ( 3 / 20 )22714.2977272727642.08088734622635.3760689266937
Trimmed Mean ( 4 / 20 )22738.4136792453616.16501984544336.9031232654994
Trimmed Mean ( 5 / 20 )22752.1269607843592.81571997289538.3797632117863
Trimmed Mean ( 6 / 20 )22740.5923469388576.72152649909539.4308020458023
Trimmed Mean ( 7 / 20 )22709.7994680851566.92351080975940.0579602628365
Trimmed Mean ( 8 / 20 )22670.3805555556556.27629385640940.7538138977525
Trimmed Mean ( 9 / 20 )22632.4575581395544.22834399418741.5863264159231
Trimmed Mean ( 10 / 20 )22592.8347560976530.70178098352442.5716203820296
Trimmed Mean ( 11 / 20 )22553.1993589744517.38772959525743.5905184234217
Trimmed Mean ( 12 / 20 )22539.7925675676511.43828066125144.0713834295417
Trimmed Mean ( 13 / 20 )22537.2535714286508.60978337100144.3114826106068
Trimmed Mean ( 14 / 20 )22536.6189393939504.49650669157644.6715064236742
Trimmed Mean ( 15 / 20 )22533.8056451613501.45406370775244.9369289752012
Trimmed Mean ( 16 / 20 )22526.8112068965498.08389385062745.2269416558413
Trimmed Mean ( 17 / 20 )22524.0768518518493.34626254628445.6557159987378
Trimmed Mean ( 18 / 20 )22511.745488.24135465976346.1078210298012
Trimmed Mean ( 19 / 20 )22503.6163043478483.57699943640346.5357457666002
Trimmed Mean ( 20 / 20 )22485.4154761905485.94807492084446.2712306862274
Median22441.225
Midrange21859.725
Midmean - Weighted Average at Xnp22396.2916666667
Midmean - Weighted Average at X(n+1)p22533.8056451613
Midmean - Empirical Distribution Function22533.8056451613
Midmean - Empirical Distribution Function - Averaging22533.8056451613
Midmean - Empirical Distribution Function - Interpolation22533.8056451613
Midmean - Closest Observation22404.69375
Midmean - True Basic - Statistics Graphics Toolkit22533.8056451613
Midmean - MS Excel (old versions)22533.8056451613
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')