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Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationSun, 21 Dec 2008 05:10:15 -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/21/t1229861717jqv4iedhyegnv0p.htm/, Retrieved Sun, 19 May 2024 10:41:09 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=35526, Retrieved Sun, 19 May 2024 10:41:09 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact146
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [Central Tendency V2] [2008-12-21 12:10:15] [d41d8cd98f00b204e9800998ecf8427e] [Current]
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Dataseries X:
118,4
121,4
128,8
131,7
141,7
142,9
139,4
134,7
125
113,6
111,5
108,5
112,3
116,6
115,5
120,1
132,9
128,1
129,3
132,5
131
124,9
120,8
122
122,1
127,4
135,2
137,3
135
136
138,4
134,7
138,4
133,9
133,6
141,2
151,8
155,4
156,6
161,6
160,7
156
159,5
168,7
169,9
169,9
185,9
190,8
195,8
211,9
227,1
251,3
256,7
251,9
251,2
270,3
267,2
243
229,9
187,2
178,2




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135

\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 & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=35526&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]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=35526&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=35526&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'Gwilym Jenkins' @ 72.249.127.135







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean157.7918032786895.7399040828422727.4903205700527
Geometric Mean152.481238927626
Harmonic Mean148.059180829490
Quadratic Mean163.936094606264
Winsorized Mean ( 1 / 20 )157.7901639344265.7166589581993527.601815166551
Winsorized Mean ( 2 / 20 )157.4721311475415.6074151390627328.0828380353987
Winsorized Mean ( 3 / 20 )157.35.5304433166508928.4425661730238
Winsorized Mean ( 4 / 20 )157.3852459016395.503132657817628.5992098842215
Winsorized Mean ( 5 / 20 )157.4672131147545.4894880773555628.6852272736168
Winsorized Mean ( 6 / 20 )156.8377049180335.2423470966361029.9174591126696
Winsorized Mean ( 7 / 20 )155.5295081967214.8187074793895832.2761879325414
Winsorized Mean ( 8 / 20 )155.2540983606564.7136121761744232.9373933531079
Winsorized Mean ( 9 / 20 )153.14.1517920286522536.8756428413153
Winsorized Mean ( 10 / 20 )150.5590163934433.5442806826838442.4794280907332
Winsorized Mean ( 11 / 20 )149.6754098360663.3536862157243344.6301174911019
Winsorized Mean ( 12 / 20 )149.5180327868853.1365399022572747.6697371773533
Winsorized Mean ( 13 / 20 )149.2622950819673.0785305947143848.4849152833627
Winsorized Mean ( 14 / 20 )148.0459016393442.6641739446757355.5691575376336
Winsorized Mean ( 15 / 20 )146.1770491803282.2702487688277864.3881195697354
Winsorized Mean ( 16 / 20 )146.3606557377052.246102001353465.1620699547548
Winsorized Mean ( 17 / 20 )146.1655737704922.1698428404295567.3622858978838
Winsorized Mean ( 18 / 20 )144.5721311475411.7527981238868782.4807655698246
Winsorized Mean ( 19 / 20 )144.5098360655741.6796527498884586.0355428079828
Winsorized Mean ( 20 / 20 )144.378688524591.5836616537723491.167635574603
Trimmed Mean ( 1 / 20 )156.7203389830515.5505928620436228.2348828095004
Trimmed Mean ( 2 / 20 )155.5754385964915.3423910479915429.1209380217458
Trimmed Mean ( 3 / 20 )154.5236363636365.1556101727577829.9719395349436
Trimmed Mean ( 4 / 20 )153.4584905660384.957237627033130.9564523857378
Trimmed Mean ( 5 / 20 )152.284313725494.7130352174759732.3113040108036
Trimmed Mean ( 6 / 20 )150.9938775510204.3984724158763434.3287085320818
Trimmed Mean ( 7 / 20 )149.7297872340434.0749521598908236.7439374400052
Trimmed Mean ( 8 / 20 )148.6066666666673.7965007812218639.1430623172003
Trimmed Mean ( 9 / 20 )147.4279069767443.4538891452857142.684608791794
Trimmed Mean ( 10 / 20 )146.4902439024393.1886093093668745.9417349977963
Trimmed Mean ( 11 / 20 )145.8538461538463.0323533129834648.0992256177246
Trimmed Mean ( 12 / 20 )145.2810810810812.8777254683932350.4846910091805
Trimmed Mean ( 13 / 20 )144.6657142857142.7262895117358253.063225186824
Trimmed Mean ( 14 / 20 )144.0121212121212.527079692504456.9875661773854
Trimmed Mean ( 15 / 20 )143.4451612903232.3847672446091760.1505918930178
Trimmed Mean ( 16 / 20 )143.0620689655172.3143981427958661.8139404453091
Trimmed Mean ( 17 / 20 )142.5962962962962.207178662692564.6056881151367
Trimmed Mean ( 18 / 20 )142.0842.0636269042634668.8515931375259
Trimmed Mean ( 19 / 20 )141.7173913043482.0119765140378970.4369013830741
Trimmed Mean ( 20 / 20 )141.2904761904761.941892851267872.7591515145813
Median138.4
Midrange189.4
Midmean - Weighted Average at Xnp143.445161290323
Midmean - Weighted Average at X(n+1)p143.445161290323
Midmean - Empirical Distribution Function143.445161290323
Midmean - Empirical Distribution Function - Averaging143.445161290323
Midmean - Empirical Distribution Function - Interpolation143.445161290323
Midmean - Closest Observation142.94375
Midmean - True Basic - Statistics Graphics Toolkit143.445161290323
Midmean - MS Excel (old versions)143.445161290323
Number of observations61

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 157.791803278689 & 5.73990408284227 & 27.4903205700527 \tabularnewline
Geometric Mean & 152.481238927626 &  &  \tabularnewline
Harmonic Mean & 148.059180829490 &  &  \tabularnewline
Quadratic Mean & 163.936094606264 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 157.790163934426 & 5.71665895819935 & 27.601815166551 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 157.472131147541 & 5.60741513906273 & 28.0828380353987 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 157.3 & 5.53044331665089 & 28.4425661730238 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 157.385245901639 & 5.5031326578176 & 28.5992098842215 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 157.467213114754 & 5.48948807735556 & 28.6852272736168 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 156.837704918033 & 5.24234709663610 & 29.9174591126696 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 155.529508196721 & 4.81870747938958 & 32.2761879325414 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 155.254098360656 & 4.71361217617442 & 32.9373933531079 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 153.1 & 4.15179202865225 & 36.8756428413153 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 150.559016393443 & 3.54428068268384 & 42.4794280907332 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 149.675409836066 & 3.35368621572433 & 44.6301174911019 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 149.518032786885 & 3.13653990225727 & 47.6697371773533 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 149.262295081967 & 3.07853059471438 & 48.4849152833627 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 148.045901639344 & 2.66417394467573 & 55.5691575376336 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 146.177049180328 & 2.27024876882778 & 64.3881195697354 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 146.360655737705 & 2.2461020013534 & 65.1620699547548 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 146.165573770492 & 2.16984284042955 & 67.3622858978838 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 144.572131147541 & 1.75279812388687 & 82.4807655698246 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 144.509836065574 & 1.67965274988845 & 86.0355428079828 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 144.37868852459 & 1.58366165377234 & 91.167635574603 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 156.720338983051 & 5.55059286204362 & 28.2348828095004 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 155.575438596491 & 5.34239104799154 & 29.1209380217458 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 154.523636363636 & 5.15561017275778 & 29.9719395349436 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 153.458490566038 & 4.9572376270331 & 30.9564523857378 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 152.28431372549 & 4.71303521747597 & 32.3113040108036 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 150.993877551020 & 4.39847241587634 & 34.3287085320818 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 149.729787234043 & 4.07495215989082 & 36.7439374400052 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 148.606666666667 & 3.79650078122186 & 39.1430623172003 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 147.427906976744 & 3.45388914528571 & 42.684608791794 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 146.490243902439 & 3.18860930936687 & 45.9417349977963 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 145.853846153846 & 3.03235331298346 & 48.0992256177246 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 145.281081081081 & 2.87772546839323 & 50.4846910091805 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 144.665714285714 & 2.72628951173582 & 53.063225186824 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 144.012121212121 & 2.5270796925044 & 56.9875661773854 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 143.445161290323 & 2.38476724460917 & 60.1505918930178 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 143.062068965517 & 2.31439814279586 & 61.8139404453091 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 142.596296296296 & 2.2071786626925 & 64.6056881151367 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 142.084 & 2.06362690426346 & 68.8515931375259 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 141.717391304348 & 2.01197651403789 & 70.4369013830741 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 141.290476190476 & 1.9418928512678 & 72.7591515145813 \tabularnewline
Median & 138.4 &  &  \tabularnewline
Midrange & 189.4 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 143.445161290323 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 143.445161290323 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 143.445161290323 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 143.445161290323 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 143.445161290323 &  &  \tabularnewline
Midmean - Closest Observation & 142.94375 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 143.445161290323 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 143.445161290323 &  &  \tabularnewline
Number of observations & 61 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=35526&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]157.791803278689[/C][C]5.73990408284227[/C][C]27.4903205700527[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]152.481238927626[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]148.059180829490[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]163.936094606264[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]157.790163934426[/C][C]5.71665895819935[/C][C]27.601815166551[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]157.472131147541[/C][C]5.60741513906273[/C][C]28.0828380353987[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]157.3[/C][C]5.53044331665089[/C][C]28.4425661730238[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]157.385245901639[/C][C]5.5031326578176[/C][C]28.5992098842215[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]157.467213114754[/C][C]5.48948807735556[/C][C]28.6852272736168[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]156.837704918033[/C][C]5.24234709663610[/C][C]29.9174591126696[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]155.529508196721[/C][C]4.81870747938958[/C][C]32.2761879325414[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]155.254098360656[/C][C]4.71361217617442[/C][C]32.9373933531079[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]153.1[/C][C]4.15179202865225[/C][C]36.8756428413153[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]150.559016393443[/C][C]3.54428068268384[/C][C]42.4794280907332[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]149.675409836066[/C][C]3.35368621572433[/C][C]44.6301174911019[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]149.518032786885[/C][C]3.13653990225727[/C][C]47.6697371773533[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]149.262295081967[/C][C]3.07853059471438[/C][C]48.4849152833627[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]148.045901639344[/C][C]2.66417394467573[/C][C]55.5691575376336[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]146.177049180328[/C][C]2.27024876882778[/C][C]64.3881195697354[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]146.360655737705[/C][C]2.2461020013534[/C][C]65.1620699547548[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]146.165573770492[/C][C]2.16984284042955[/C][C]67.3622858978838[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]144.572131147541[/C][C]1.75279812388687[/C][C]82.4807655698246[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]144.509836065574[/C][C]1.67965274988845[/C][C]86.0355428079828[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]144.37868852459[/C][C]1.58366165377234[/C][C]91.167635574603[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]156.720338983051[/C][C]5.55059286204362[/C][C]28.2348828095004[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]155.575438596491[/C][C]5.34239104799154[/C][C]29.1209380217458[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]154.523636363636[/C][C]5.15561017275778[/C][C]29.9719395349436[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]153.458490566038[/C][C]4.9572376270331[/C][C]30.9564523857378[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]152.28431372549[/C][C]4.71303521747597[/C][C]32.3113040108036[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]150.993877551020[/C][C]4.39847241587634[/C][C]34.3287085320818[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]149.729787234043[/C][C]4.07495215989082[/C][C]36.7439374400052[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]148.606666666667[/C][C]3.79650078122186[/C][C]39.1430623172003[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]147.427906976744[/C][C]3.45388914528571[/C][C]42.684608791794[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]146.490243902439[/C][C]3.18860930936687[/C][C]45.9417349977963[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]145.853846153846[/C][C]3.03235331298346[/C][C]48.0992256177246[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]145.281081081081[/C][C]2.87772546839323[/C][C]50.4846910091805[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]144.665714285714[/C][C]2.72628951173582[/C][C]53.063225186824[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]144.012121212121[/C][C]2.5270796925044[/C][C]56.9875661773854[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]143.445161290323[/C][C]2.38476724460917[/C][C]60.1505918930178[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]143.062068965517[/C][C]2.31439814279586[/C][C]61.8139404453091[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]142.596296296296[/C][C]2.2071786626925[/C][C]64.6056881151367[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]142.084[/C][C]2.06362690426346[/C][C]68.8515931375259[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]141.717391304348[/C][C]2.01197651403789[/C][C]70.4369013830741[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]141.290476190476[/C][C]1.9418928512678[/C][C]72.7591515145813[/C][/ROW]
[ROW][C]Median[/C][C]138.4[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]189.4[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]143.445161290323[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]143.445161290323[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]143.445161290323[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]143.445161290323[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]143.445161290323[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]142.94375[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]143.445161290323[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]143.445161290323[/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=35526&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=35526&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 Mean157.7918032786895.7399040828422727.4903205700527
Geometric Mean152.481238927626
Harmonic Mean148.059180829490
Quadratic Mean163.936094606264
Winsorized Mean ( 1 / 20 )157.7901639344265.7166589581993527.601815166551
Winsorized Mean ( 2 / 20 )157.4721311475415.6074151390627328.0828380353987
Winsorized Mean ( 3 / 20 )157.35.5304433166508928.4425661730238
Winsorized Mean ( 4 / 20 )157.3852459016395.503132657817628.5992098842215
Winsorized Mean ( 5 / 20 )157.4672131147545.4894880773555628.6852272736168
Winsorized Mean ( 6 / 20 )156.8377049180335.2423470966361029.9174591126696
Winsorized Mean ( 7 / 20 )155.5295081967214.8187074793895832.2761879325414
Winsorized Mean ( 8 / 20 )155.2540983606564.7136121761744232.9373933531079
Winsorized Mean ( 9 / 20 )153.14.1517920286522536.8756428413153
Winsorized Mean ( 10 / 20 )150.5590163934433.5442806826838442.4794280907332
Winsorized Mean ( 11 / 20 )149.6754098360663.3536862157243344.6301174911019
Winsorized Mean ( 12 / 20 )149.5180327868853.1365399022572747.6697371773533
Winsorized Mean ( 13 / 20 )149.2622950819673.0785305947143848.4849152833627
Winsorized Mean ( 14 / 20 )148.0459016393442.6641739446757355.5691575376336
Winsorized Mean ( 15 / 20 )146.1770491803282.2702487688277864.3881195697354
Winsorized Mean ( 16 / 20 )146.3606557377052.246102001353465.1620699547548
Winsorized Mean ( 17 / 20 )146.1655737704922.1698428404295567.3622858978838
Winsorized Mean ( 18 / 20 )144.5721311475411.7527981238868782.4807655698246
Winsorized Mean ( 19 / 20 )144.5098360655741.6796527498884586.0355428079828
Winsorized Mean ( 20 / 20 )144.378688524591.5836616537723491.167635574603
Trimmed Mean ( 1 / 20 )156.7203389830515.5505928620436228.2348828095004
Trimmed Mean ( 2 / 20 )155.5754385964915.3423910479915429.1209380217458
Trimmed Mean ( 3 / 20 )154.5236363636365.1556101727577829.9719395349436
Trimmed Mean ( 4 / 20 )153.4584905660384.957237627033130.9564523857378
Trimmed Mean ( 5 / 20 )152.284313725494.7130352174759732.3113040108036
Trimmed Mean ( 6 / 20 )150.9938775510204.3984724158763434.3287085320818
Trimmed Mean ( 7 / 20 )149.7297872340434.0749521598908236.7439374400052
Trimmed Mean ( 8 / 20 )148.6066666666673.7965007812218639.1430623172003
Trimmed Mean ( 9 / 20 )147.4279069767443.4538891452857142.684608791794
Trimmed Mean ( 10 / 20 )146.4902439024393.1886093093668745.9417349977963
Trimmed Mean ( 11 / 20 )145.8538461538463.0323533129834648.0992256177246
Trimmed Mean ( 12 / 20 )145.2810810810812.8777254683932350.4846910091805
Trimmed Mean ( 13 / 20 )144.6657142857142.7262895117358253.063225186824
Trimmed Mean ( 14 / 20 )144.0121212121212.527079692504456.9875661773854
Trimmed Mean ( 15 / 20 )143.4451612903232.3847672446091760.1505918930178
Trimmed Mean ( 16 / 20 )143.0620689655172.3143981427958661.8139404453091
Trimmed Mean ( 17 / 20 )142.5962962962962.207178662692564.6056881151367
Trimmed Mean ( 18 / 20 )142.0842.0636269042634668.8515931375259
Trimmed Mean ( 19 / 20 )141.7173913043482.0119765140378970.4369013830741
Trimmed Mean ( 20 / 20 )141.2904761904761.941892851267872.7591515145813
Median138.4
Midrange189.4
Midmean - Weighted Average at Xnp143.445161290323
Midmean - Weighted Average at X(n+1)p143.445161290323
Midmean - Empirical Distribution Function143.445161290323
Midmean - Empirical Distribution Function - Averaging143.445161290323
Midmean - Empirical Distribution Function - Interpolation143.445161290323
Midmean - Closest Observation142.94375
Midmean - True Basic - Statistics Graphics Toolkit143.445161290323
Midmean - MS Excel (old versions)143.445161290323
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')