Free Statistics

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 computationTue, 29 Nov 2011 11:15:54 -0500
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2011/Nov/29/t13225834096b9qkc3w9eymxwh.htm/, Retrieved Tue, 30 Apr 2024 10:02:03 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=148590, Retrieved Tue, 30 Apr 2024 10:02:03 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact95
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Classical Decomposition] [HPC Retail Sales] [2008-03-02 16:19:32] [74be16979710d4c4e7c6647856088456]
- RMPD    [Central Tendency] [Central Tendency ...] [2011-11-29 16:15:54] [5959e8d69ed0f77745135d9c4c7e0d16] [Current]
Feedback Forum

Post a new message
Dataseries X:
250.782608695645
363.92546583851
8.21118012422378
359.628364389234
81.128364389234
258.628364389234
464.961697722568
720.628364389234
204.295031055901
230.128364389234
231.795031055901
-210.704968944099
155.664596273294
185.807453416149
-74.9068322981364
-28.4896480331261
62.010351966874
22.510351966874
-283.156314699793
-126.489648033126
-535.82298136646
7.01035196687387
-190.32298136646
-276.82298136646
-108.453416149067
-341.310559006211
-126.024844720497
-80.6076604554865
-223.107660455486
-551.607660455487
107.725672877847
-418.607660455486
-218.94099378882
97.8923395445136
-516.44099378882
-71.9409937888199
-416.571428571427
-374.428571428571
79.857142857143
-92.7256728778469
116.774327122153
-196.725672877847
-288.392339544514
-604.725672877847
158.94099378882
107.774327122153
22.4409937888197
3.94099378881965
-321.689440993788
49.4534161490682
341.739130434783
-210.843685300207
14.6563146997928
189.156314699793
79.489648033126
-40.8436853002073
131.822981366459
-342.343685300207
218.32298136646
81.8229813664593
2.19254658385198
-111.664596273292
83.6211180124221
53.0383022774324
-51.4616977225677
278.038302277433
-80.6283643892342
470.038302277433
259.704968944099
-100.461697722567
234.204968944099
473.704968944099
438.074534161492
228.217391304347
-312.496894409938




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

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 1 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=148590&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' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=148590&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=148590&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' @ jenkins.wessa.net







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean1.72750702631674e-1530.92756845462255.5856541999135e-17
Geometric MeanNaN
Harmonic Mean66.6668169741723
Quadratic Mean266.049003565389
Winsorized Mean ( 1 / 25 )-2.58407177363729.8700598690305-0.0865104316819995
Winsorized Mean ( 2 / 25 )-2.2609247757073729.7457417561426-0.0760083508504366
Winsorized Mean ( 3 / 25 )-1.6887094547963729.5169382506329-0.0572115386920311
Winsorized Mean ( 4 / 25 )2.0950862663907328.06775637441330.0746438809872462
Winsorized Mean ( 5 / 25 )-2.7124361628708127.0675521682789-0.100209880302718
Winsorized Mean ( 6 / 25 )0.31522429261559726.3315655180930.0119713464206676
Winsorized Mean ( 7 / 25 )1.6401518288474725.4653775297310.0644071279498048
Winsorized Mean ( 8 / 25 )-5.0444030365769624.2950870893191-0.207630580538015
Winsorized Mean ( 9 / 25 )-4.8898688750862823.5199848411787-0.207902722221364
Winsorized Mean ( 10 / 25 )-3.8077432712216223.2767539803426-0.163585664669451
Winsorized Mean ( 11 / 25 )-1.4231193926858222.4799258077142-0.063306231740207
Winsorized Mean ( 12 / 25 )-3.237777777777821.9403398849058-0.147571906121895
Winsorized Mean ( 13 / 25 )-2.5577225672877421.69087483197-0.117916985234636
Winsorized Mean ( 14 / 25 )7.158026224982920.00520890606420.35780812180437
Winsorized Mean ( 15 / 25 )7.6091649413386919.81850321584760.383942463185318
Winsorized Mean ( 16 / 25 )7.2257832988269119.23746089020990.375610031909365
Winsorized Mean ( 17 / 25 )4.0775569358180218.76758937586710.217265886105824
Winsorized Mean ( 18 / 25 )3.7992960662525817.73307498316610.214249140087618
Winsorized Mean ( 19 / 25 )4.5729330572808117.36640016031390.2633207236426
Winsorized Mean ( 20 / 25 )14.430766045548813.88548478902591.03926987532721
Winsorized Mean ( 21 / 25 )13.643519668737613.73903315270870.993048019980054
Winsorized Mean ( 22 / 25 )10.862318840579512.20582903046570.889928804792135
Winsorized Mean ( 23 / 25 )7.2321601104213411.46460626294790.630824988189498
Winsorized Mean ( 24 / 25 )6.9095100069013410.74894476457430.642808215897925
Winsorized Mean ( 25 / 25 )9.4719668737060410.40160262176640.910625719721783
Trimmed Mean ( 1 / 25 )-1.5877081028957129.0104197930215-0.0547288910061768
Trimmed Mean ( 2 / 25 )-0.53521126760561727.9945715370785-0.0191183946822238
Trimmed Mean ( 3 / 25 )0.40267650853664126.86732968508950.0149875895095043
Trimmed Mean ( 4 / 25 )1.1830444053026925.62627106200890.046165296637971
Trimmed Mean ( 5 / 25 )0.91995540691191224.69452796635980.0372534112887326
Trimmed Mean ( 6 / 25 )1.7848105425744623.89777480913630.0746852188887526
Trimmed Mean ( 7 / 25 )2.0859552659266923.14799600252420.0901138597785842
Trimmed Mean ( 8 / 25 )2.1669123065585122.46589940013770.0964533966775098
Trimmed Mean ( 9 / 25 )3.352983909047921.91475242371170.153001222382963
Trimmed Mean ( 10 / 25 )4.6019009975530821.41087264519660.214932902260081
Trimmed Mean ( 11 / 25 )5.7919449978513820.83496113945420.277991639105266
Trimmed Mean ( 12 / 25 )6.7565257987253420.28962083226120.333004044510394
Trimmed Mean ( 13 / 25 )8.0313094181772719.71192771334690.407433993010197
Trimmed Mean ( 14 / 25 )9.3311087617286319.02578422229810.490445421471385
Trimmed Mean ( 15 / 25 )9.5898090637221618.52952250893750.517542157877874
Trimmed Mean ( 16 / 25 )9.8201165198132617.91750686498740.548073824880334
Trimmed Mean ( 17 / 25 )10.11672473867617.24329758901610.586704757976242
Trimmed Mean ( 18 / 25 )10.799888517279916.45214945238970.656442402771339
Trimmed Mean ( 19 / 25 )11.588243523026215.65000180827940.740462759365027
Trimmed Mean ( 20 / 25 )12.379443951493714.64121211241820.845520429349827
Trimmed Mean ( 21 / 25 )12.146339168078414.24646932190120.852585921018743
Trimmed Mean ( 22 / 25 )11.973852935283513.70338885170260.873787722501637
Trimmed Mean ( 23 / 25 )12.10451916898713.36247643759690.905858971988863
Trimmed Mean ( 24 / 25 )12.692968330649513.04648475946790.972903319527365
Trimmed Mean ( 25 / 25 )13.41590062111812.75607356763891.051726501104
Median14.6563146997928
Midrange57.9513457556935
Midmean - Weighted Average at Xnp6.10629835458218
Midmean - Weighted Average at X(n+1)p10.7998885172799
Midmean - Empirical Distribution Function10.7998885172799
Midmean - Empirical Distribution Function - Averaging10.7998885172799
Midmean - Empirical Distribution Function - Interpolation11.5882435230262
Midmean - Closest Observation6.10629835458218
Midmean - True Basic - Statistics Graphics Toolkit10.7998885172799
Midmean - MS Excel (old versions)10.7998885172799
Number of observations75

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 1.72750702631674e-15 & 30.9275684546225 & 5.5856541999135e-17 \tabularnewline
Geometric Mean & NaN &  &  \tabularnewline
Harmonic Mean & 66.6668169741723 &  &  \tabularnewline
Quadratic Mean & 266.049003565389 &  &  \tabularnewline
Winsorized Mean ( 1 / 25 ) & -2.584071773637 & 29.8700598690305 & -0.0865104316819995 \tabularnewline
Winsorized Mean ( 2 / 25 ) & -2.26092477570737 & 29.7457417561426 & -0.0760083508504366 \tabularnewline
Winsorized Mean ( 3 / 25 ) & -1.68870945479637 & 29.5169382506329 & -0.0572115386920311 \tabularnewline
Winsorized Mean ( 4 / 25 ) & 2.09508626639073 & 28.0677563744133 & 0.0746438809872462 \tabularnewline
Winsorized Mean ( 5 / 25 ) & -2.71243616287081 & 27.0675521682789 & -0.100209880302718 \tabularnewline
Winsorized Mean ( 6 / 25 ) & 0.315224292615597 & 26.331565518093 & 0.0119713464206676 \tabularnewline
Winsorized Mean ( 7 / 25 ) & 1.64015182884747 & 25.465377529731 & 0.0644071279498048 \tabularnewline
Winsorized Mean ( 8 / 25 ) & -5.04440303657696 & 24.2950870893191 & -0.207630580538015 \tabularnewline
Winsorized Mean ( 9 / 25 ) & -4.88986887508628 & 23.5199848411787 & -0.207902722221364 \tabularnewline
Winsorized Mean ( 10 / 25 ) & -3.80774327122162 & 23.2767539803426 & -0.163585664669451 \tabularnewline
Winsorized Mean ( 11 / 25 ) & -1.42311939268582 & 22.4799258077142 & -0.063306231740207 \tabularnewline
Winsorized Mean ( 12 / 25 ) & -3.2377777777778 & 21.9403398849058 & -0.147571906121895 \tabularnewline
Winsorized Mean ( 13 / 25 ) & -2.55772256728774 & 21.69087483197 & -0.117916985234636 \tabularnewline
Winsorized Mean ( 14 / 25 ) & 7.1580262249829 & 20.0052089060642 & 0.35780812180437 \tabularnewline
Winsorized Mean ( 15 / 25 ) & 7.60916494133869 & 19.8185032158476 & 0.383942463185318 \tabularnewline
Winsorized Mean ( 16 / 25 ) & 7.22578329882691 & 19.2374608902099 & 0.375610031909365 \tabularnewline
Winsorized Mean ( 17 / 25 ) & 4.07755693581802 & 18.7675893758671 & 0.217265886105824 \tabularnewline
Winsorized Mean ( 18 / 25 ) & 3.79929606625258 & 17.7330749831661 & 0.214249140087618 \tabularnewline
Winsorized Mean ( 19 / 25 ) & 4.57293305728081 & 17.3664001603139 & 0.2633207236426 \tabularnewline
Winsorized Mean ( 20 / 25 ) & 14.4307660455488 & 13.8854847890259 & 1.03926987532721 \tabularnewline
Winsorized Mean ( 21 / 25 ) & 13.6435196687376 & 13.7390331527087 & 0.993048019980054 \tabularnewline
Winsorized Mean ( 22 / 25 ) & 10.8623188405795 & 12.2058290304657 & 0.889928804792135 \tabularnewline
Winsorized Mean ( 23 / 25 ) & 7.23216011042134 & 11.4646062629479 & 0.630824988189498 \tabularnewline
Winsorized Mean ( 24 / 25 ) & 6.90951000690134 & 10.7489447645743 & 0.642808215897925 \tabularnewline
Winsorized Mean ( 25 / 25 ) & 9.47196687370604 & 10.4016026217664 & 0.910625719721783 \tabularnewline
Trimmed Mean ( 1 / 25 ) & -1.58770810289571 & 29.0104197930215 & -0.0547288910061768 \tabularnewline
Trimmed Mean ( 2 / 25 ) & -0.535211267605617 & 27.9945715370785 & -0.0191183946822238 \tabularnewline
Trimmed Mean ( 3 / 25 ) & 0.402676508536641 & 26.8673296850895 & 0.0149875895095043 \tabularnewline
Trimmed Mean ( 4 / 25 ) & 1.18304440530269 & 25.6262710620089 & 0.046165296637971 \tabularnewline
Trimmed Mean ( 5 / 25 ) & 0.919955406911912 & 24.6945279663598 & 0.0372534112887326 \tabularnewline
Trimmed Mean ( 6 / 25 ) & 1.78481054257446 & 23.8977748091363 & 0.0746852188887526 \tabularnewline
Trimmed Mean ( 7 / 25 ) & 2.08595526592669 & 23.1479960025242 & 0.0901138597785842 \tabularnewline
Trimmed Mean ( 8 / 25 ) & 2.16691230655851 & 22.4658994001377 & 0.0964533966775098 \tabularnewline
Trimmed Mean ( 9 / 25 ) & 3.3529839090479 & 21.9147524237117 & 0.153001222382963 \tabularnewline
Trimmed Mean ( 10 / 25 ) & 4.60190099755308 & 21.4108726451966 & 0.214932902260081 \tabularnewline
Trimmed Mean ( 11 / 25 ) & 5.79194499785138 & 20.8349611394542 & 0.277991639105266 \tabularnewline
Trimmed Mean ( 12 / 25 ) & 6.75652579872534 & 20.2896208322612 & 0.333004044510394 \tabularnewline
Trimmed Mean ( 13 / 25 ) & 8.03130941817727 & 19.7119277133469 & 0.407433993010197 \tabularnewline
Trimmed Mean ( 14 / 25 ) & 9.33110876172863 & 19.0257842222981 & 0.490445421471385 \tabularnewline
Trimmed Mean ( 15 / 25 ) & 9.58980906372216 & 18.5295225089375 & 0.517542157877874 \tabularnewline
Trimmed Mean ( 16 / 25 ) & 9.82011651981326 & 17.9175068649874 & 0.548073824880334 \tabularnewline
Trimmed Mean ( 17 / 25 ) & 10.116724738676 & 17.2432975890161 & 0.586704757976242 \tabularnewline
Trimmed Mean ( 18 / 25 ) & 10.7998885172799 & 16.4521494523897 & 0.656442402771339 \tabularnewline
Trimmed Mean ( 19 / 25 ) & 11.5882435230262 & 15.6500018082794 & 0.740462759365027 \tabularnewline
Trimmed Mean ( 20 / 25 ) & 12.3794439514937 & 14.6412121124182 & 0.845520429349827 \tabularnewline
Trimmed Mean ( 21 / 25 ) & 12.1463391680784 & 14.2464693219012 & 0.852585921018743 \tabularnewline
Trimmed Mean ( 22 / 25 ) & 11.9738529352835 & 13.7033888517026 & 0.873787722501637 \tabularnewline
Trimmed Mean ( 23 / 25 ) & 12.104519168987 & 13.3624764375969 & 0.905858971988863 \tabularnewline
Trimmed Mean ( 24 / 25 ) & 12.6929683306495 & 13.0464847594679 & 0.972903319527365 \tabularnewline
Trimmed Mean ( 25 / 25 ) & 13.415900621118 & 12.7560735676389 & 1.051726501104 \tabularnewline
Median & 14.6563146997928 &  &  \tabularnewline
Midrange & 57.9513457556935 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 6.10629835458218 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 10.7998885172799 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 10.7998885172799 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 10.7998885172799 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 11.5882435230262 &  &  \tabularnewline
Midmean - Closest Observation & 6.10629835458218 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 10.7998885172799 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 10.7998885172799 &  &  \tabularnewline
Number of observations & 75 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=148590&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]1.72750702631674e-15[/C][C]30.9275684546225[/C][C]5.5856541999135e-17[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]NaN[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]66.6668169741723[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]266.049003565389[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 25 )[/C][C]-2.584071773637[/C][C]29.8700598690305[/C][C]-0.0865104316819995[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 25 )[/C][C]-2.26092477570737[/C][C]29.7457417561426[/C][C]-0.0760083508504366[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 25 )[/C][C]-1.68870945479637[/C][C]29.5169382506329[/C][C]-0.0572115386920311[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 25 )[/C][C]2.09508626639073[/C][C]28.0677563744133[/C][C]0.0746438809872462[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 25 )[/C][C]-2.71243616287081[/C][C]27.0675521682789[/C][C]-0.100209880302718[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 25 )[/C][C]0.315224292615597[/C][C]26.331565518093[/C][C]0.0119713464206676[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 25 )[/C][C]1.64015182884747[/C][C]25.465377529731[/C][C]0.0644071279498048[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 25 )[/C][C]-5.04440303657696[/C][C]24.2950870893191[/C][C]-0.207630580538015[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 25 )[/C][C]-4.88986887508628[/C][C]23.5199848411787[/C][C]-0.207902722221364[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 25 )[/C][C]-3.80774327122162[/C][C]23.2767539803426[/C][C]-0.163585664669451[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 25 )[/C][C]-1.42311939268582[/C][C]22.4799258077142[/C][C]-0.063306231740207[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 25 )[/C][C]-3.2377777777778[/C][C]21.9403398849058[/C][C]-0.147571906121895[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 25 )[/C][C]-2.55772256728774[/C][C]21.69087483197[/C][C]-0.117916985234636[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 25 )[/C][C]7.1580262249829[/C][C]20.0052089060642[/C][C]0.35780812180437[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 25 )[/C][C]7.60916494133869[/C][C]19.8185032158476[/C][C]0.383942463185318[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 25 )[/C][C]7.22578329882691[/C][C]19.2374608902099[/C][C]0.375610031909365[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 25 )[/C][C]4.07755693581802[/C][C]18.7675893758671[/C][C]0.217265886105824[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 25 )[/C][C]3.79929606625258[/C][C]17.7330749831661[/C][C]0.214249140087618[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 25 )[/C][C]4.57293305728081[/C][C]17.3664001603139[/C][C]0.2633207236426[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 25 )[/C][C]14.4307660455488[/C][C]13.8854847890259[/C][C]1.03926987532721[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 25 )[/C][C]13.6435196687376[/C][C]13.7390331527087[/C][C]0.993048019980054[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 25 )[/C][C]10.8623188405795[/C][C]12.2058290304657[/C][C]0.889928804792135[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 25 )[/C][C]7.23216011042134[/C][C]11.4646062629479[/C][C]0.630824988189498[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 25 )[/C][C]6.90951000690134[/C][C]10.7489447645743[/C][C]0.642808215897925[/C][/ROW]
[ROW][C]Winsorized Mean ( 25 / 25 )[/C][C]9.47196687370604[/C][C]10.4016026217664[/C][C]0.910625719721783[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 25 )[/C][C]-1.58770810289571[/C][C]29.0104197930215[/C][C]-0.0547288910061768[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 25 )[/C][C]-0.535211267605617[/C][C]27.9945715370785[/C][C]-0.0191183946822238[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 25 )[/C][C]0.402676508536641[/C][C]26.8673296850895[/C][C]0.0149875895095043[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 25 )[/C][C]1.18304440530269[/C][C]25.6262710620089[/C][C]0.046165296637971[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 25 )[/C][C]0.919955406911912[/C][C]24.6945279663598[/C][C]0.0372534112887326[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 25 )[/C][C]1.78481054257446[/C][C]23.8977748091363[/C][C]0.0746852188887526[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 25 )[/C][C]2.08595526592669[/C][C]23.1479960025242[/C][C]0.0901138597785842[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 25 )[/C][C]2.16691230655851[/C][C]22.4658994001377[/C][C]0.0964533966775098[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 25 )[/C][C]3.3529839090479[/C][C]21.9147524237117[/C][C]0.153001222382963[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 25 )[/C][C]4.60190099755308[/C][C]21.4108726451966[/C][C]0.214932902260081[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 25 )[/C][C]5.79194499785138[/C][C]20.8349611394542[/C][C]0.277991639105266[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 25 )[/C][C]6.75652579872534[/C][C]20.2896208322612[/C][C]0.333004044510394[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 25 )[/C][C]8.03130941817727[/C][C]19.7119277133469[/C][C]0.407433993010197[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 25 )[/C][C]9.33110876172863[/C][C]19.0257842222981[/C][C]0.490445421471385[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 25 )[/C][C]9.58980906372216[/C][C]18.5295225089375[/C][C]0.517542157877874[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 25 )[/C][C]9.82011651981326[/C][C]17.9175068649874[/C][C]0.548073824880334[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 25 )[/C][C]10.116724738676[/C][C]17.2432975890161[/C][C]0.586704757976242[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 25 )[/C][C]10.7998885172799[/C][C]16.4521494523897[/C][C]0.656442402771339[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 25 )[/C][C]11.5882435230262[/C][C]15.6500018082794[/C][C]0.740462759365027[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 25 )[/C][C]12.3794439514937[/C][C]14.6412121124182[/C][C]0.845520429349827[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 25 )[/C][C]12.1463391680784[/C][C]14.2464693219012[/C][C]0.852585921018743[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 25 )[/C][C]11.9738529352835[/C][C]13.7033888517026[/C][C]0.873787722501637[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 25 )[/C][C]12.104519168987[/C][C]13.3624764375969[/C][C]0.905858971988863[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 25 )[/C][C]12.6929683306495[/C][C]13.0464847594679[/C][C]0.972903319527365[/C][/ROW]
[ROW][C]Trimmed Mean ( 25 / 25 )[/C][C]13.415900621118[/C][C]12.7560735676389[/C][C]1.051726501104[/C][/ROW]
[ROW][C]Median[/C][C]14.6563146997928[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]57.9513457556935[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]6.10629835458218[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]10.7998885172799[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]10.7998885172799[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]10.7998885172799[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]11.5882435230262[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]6.10629835458218[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]10.7998885172799[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]10.7998885172799[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]75[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=148590&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=148590&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 Mean1.72750702631674e-1530.92756845462255.5856541999135e-17
Geometric MeanNaN
Harmonic Mean66.6668169741723
Quadratic Mean266.049003565389
Winsorized Mean ( 1 / 25 )-2.58407177363729.8700598690305-0.0865104316819995
Winsorized Mean ( 2 / 25 )-2.2609247757073729.7457417561426-0.0760083508504366
Winsorized Mean ( 3 / 25 )-1.6887094547963729.5169382506329-0.0572115386920311
Winsorized Mean ( 4 / 25 )2.0950862663907328.06775637441330.0746438809872462
Winsorized Mean ( 5 / 25 )-2.7124361628708127.0675521682789-0.100209880302718
Winsorized Mean ( 6 / 25 )0.31522429261559726.3315655180930.0119713464206676
Winsorized Mean ( 7 / 25 )1.6401518288474725.4653775297310.0644071279498048
Winsorized Mean ( 8 / 25 )-5.0444030365769624.2950870893191-0.207630580538015
Winsorized Mean ( 9 / 25 )-4.8898688750862823.5199848411787-0.207902722221364
Winsorized Mean ( 10 / 25 )-3.8077432712216223.2767539803426-0.163585664669451
Winsorized Mean ( 11 / 25 )-1.4231193926858222.4799258077142-0.063306231740207
Winsorized Mean ( 12 / 25 )-3.237777777777821.9403398849058-0.147571906121895
Winsorized Mean ( 13 / 25 )-2.5577225672877421.69087483197-0.117916985234636
Winsorized Mean ( 14 / 25 )7.158026224982920.00520890606420.35780812180437
Winsorized Mean ( 15 / 25 )7.6091649413386919.81850321584760.383942463185318
Winsorized Mean ( 16 / 25 )7.2257832988269119.23746089020990.375610031909365
Winsorized Mean ( 17 / 25 )4.0775569358180218.76758937586710.217265886105824
Winsorized Mean ( 18 / 25 )3.7992960662525817.73307498316610.214249140087618
Winsorized Mean ( 19 / 25 )4.5729330572808117.36640016031390.2633207236426
Winsorized Mean ( 20 / 25 )14.430766045548813.88548478902591.03926987532721
Winsorized Mean ( 21 / 25 )13.643519668737613.73903315270870.993048019980054
Winsorized Mean ( 22 / 25 )10.862318840579512.20582903046570.889928804792135
Winsorized Mean ( 23 / 25 )7.2321601104213411.46460626294790.630824988189498
Winsorized Mean ( 24 / 25 )6.9095100069013410.74894476457430.642808215897925
Winsorized Mean ( 25 / 25 )9.4719668737060410.40160262176640.910625719721783
Trimmed Mean ( 1 / 25 )-1.5877081028957129.0104197930215-0.0547288910061768
Trimmed Mean ( 2 / 25 )-0.53521126760561727.9945715370785-0.0191183946822238
Trimmed Mean ( 3 / 25 )0.40267650853664126.86732968508950.0149875895095043
Trimmed Mean ( 4 / 25 )1.1830444053026925.62627106200890.046165296637971
Trimmed Mean ( 5 / 25 )0.91995540691191224.69452796635980.0372534112887326
Trimmed Mean ( 6 / 25 )1.7848105425744623.89777480913630.0746852188887526
Trimmed Mean ( 7 / 25 )2.0859552659266923.14799600252420.0901138597785842
Trimmed Mean ( 8 / 25 )2.1669123065585122.46589940013770.0964533966775098
Trimmed Mean ( 9 / 25 )3.352983909047921.91475242371170.153001222382963
Trimmed Mean ( 10 / 25 )4.6019009975530821.41087264519660.214932902260081
Trimmed Mean ( 11 / 25 )5.7919449978513820.83496113945420.277991639105266
Trimmed Mean ( 12 / 25 )6.7565257987253420.28962083226120.333004044510394
Trimmed Mean ( 13 / 25 )8.0313094181772719.71192771334690.407433993010197
Trimmed Mean ( 14 / 25 )9.3311087617286319.02578422229810.490445421471385
Trimmed Mean ( 15 / 25 )9.5898090637221618.52952250893750.517542157877874
Trimmed Mean ( 16 / 25 )9.8201165198132617.91750686498740.548073824880334
Trimmed Mean ( 17 / 25 )10.11672473867617.24329758901610.586704757976242
Trimmed Mean ( 18 / 25 )10.799888517279916.45214945238970.656442402771339
Trimmed Mean ( 19 / 25 )11.588243523026215.65000180827940.740462759365027
Trimmed Mean ( 20 / 25 )12.379443951493714.64121211241820.845520429349827
Trimmed Mean ( 21 / 25 )12.146339168078414.24646932190120.852585921018743
Trimmed Mean ( 22 / 25 )11.973852935283513.70338885170260.873787722501637
Trimmed Mean ( 23 / 25 )12.10451916898713.36247643759690.905858971988863
Trimmed Mean ( 24 / 25 )12.692968330649513.04648475946790.972903319527365
Trimmed Mean ( 25 / 25 )13.41590062111812.75607356763891.051726501104
Median14.6563146997928
Midrange57.9513457556935
Midmean - Weighted Average at Xnp6.10629835458218
Midmean - Weighted Average at X(n+1)p10.7998885172799
Midmean - Empirical Distribution Function10.7998885172799
Midmean - Empirical Distribution Function - Averaging10.7998885172799
Midmean - Empirical Distribution Function - Interpolation11.5882435230262
Midmean - Closest Observation6.10629835458218
Midmean - True Basic - Statistics Graphics Toolkit10.7998885172799
Midmean - MS Excel (old versions)10.7998885172799
Number of observations75



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')