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Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationTue, 18 Dec 2012 06:28:06 -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/2012/Dec/18/t13558300936ucigtvc3dm19ie.htm/, Retrieved Sat, 20 Apr 2024 07:36:36 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=201379, Retrieved Sat, 20 Apr 2024 07:36:36 +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] [2011-12-21 10:56:31] [8e7c659e1b71a02d35eacc5210237549]
- R       [Central Tendency] [] [2012-12-18 11:28:06] [68acb5451e1b1259a9abdc7e099f7f6d] [Current]
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Dataseries X:
9.25191650214777
22.2914871231093
-37.1571787652725
34.2241616971526
-175.791407724228
104.976083789095
-61.2440566196127
-396.729670521475
-396.444398116046
-260.009316249011
127.969010842559
-36.0298439891068
204.138369307228
44.2385868225793
-159.706287587307
203.135138015573
121.756524240115
-16.201912213436
-243.900810018248
391.694842812422
-164.230167511809
293.821184036089
150.197655606598
-191.027489040204
251.842321753795
-153.374881206835
8.18402595915808
276.197036933044
7.49356404026701
290.310133584149
154.709015296672
-344.563215955918
-268.812624672229
308.788007355503
53.4487117440732
309.745158451771
86.3072721968555
-34.8646306315522
196.561770309702
226.513512287148
-188.002590167187
-58.5622808865756
209.148059688065
145.969099712344
129.401752382899
-33.029934043082
-386.049808215712
144.248501282334
117.138964771591
129.897118044206
-152.218688907773
-55.0236881924031
144.022136077333
-16.8566548273021
144.685804574834
-160.202973636103
329.620650922733
138.317376113334
9.00038368194928
50.5918463808212
313.87529752068
236.907637607133
110.05132904939
-383.848947466715




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Herman Ole Andreas Wold' @ wold.wessa.net

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 2 seconds \tabularnewline
R Server & 'Herman Ole Andreas Wold' @ wold.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=201379&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]'Herman Ole Andreas Wold' @ wold.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=201379&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=201379&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'Herman Ole Andreas Wold' @ wold.wessa.net







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean29.012312364864225.00636162548111.16019726497521
Geometric MeanNaN
Harmonic Mean149.814997018626
Quadratic Mean200.591016595084
Winsorized Mean ( 1 / 21 )28.046860497922624.79982831074461.13092962364466
Winsorized Mean ( 2 / 21 )27.879649138493924.61949463339921.13242166639245
Winsorized Mean ( 3 / 21 )27.78921421724824.55651206969441.13164337583362
Winsorized Mean ( 4 / 21 )30.184750493156123.91320634420421.26226278729334
Winsorized Mean ( 5 / 21 )34.933482365365122.31882735270881.56520241020303
Winsorized Mean ( 6 / 21 )35.429631550172422.08158302697581.60448784432213
Winsorized Mean ( 7 / 21 )35.647879472947521.43308528258141.66321735778836
Winsorized Mean ( 8 / 21 )39.212705197796919.59585768187122.00107113627763
Winsorized Mean ( 9 / 21 )37.537891643690619.1620888708061.9589665770145
Winsorized Mean ( 10 / 21 )37.821806819155218.54404805279972.03956583327798
Winsorized Mean ( 11 / 21 )36.824207815197417.7115551405542.07910640951461
Winsorized Mean ( 12 / 21 )36.639989720485317.43167891721692.10191972296465
Winsorized Mean ( 13 / 21 )36.537097718029617.38255613147662.10194044199677
Winsorized Mean ( 14 / 21 )36.484168678098516.91771421947252.1565660824383
Winsorized Mean ( 15 / 21 )26.945911792012315.4856170076411.74006058516858
Winsorized Mean ( 16 / 21 )48.561729941533911.46194807722154.23677804282164
Winsorized Mean ( 17 / 21 )48.150866461210611.19696564870314.30034957433203
Winsorized Mean ( 18 / 21 )48.78516889902210.99711544807894.43617866242774
Winsorized Mean ( 19 / 21 )53.959464470240410.20498036506435.28756181197221
Winsorized Mean ( 20 / 21 )54.241017461229410.14520211428195.34646987317004
Winsorized Mean ( 21 / 21 )52.75147873098989.830340805916165.36619022396889
Trimmed Mean ( 1 / 21 )30.029400307425224.16464586931861.24269978835291
Trimmed Mean ( 2 / 21 )32.144109437561323.38887983703871.37433300190195
Trimmed Mean ( 3 / 21 )34.496915119805322.55557667045391.52941845042666
Trimmed Mean ( 4 / 21 )37.052229749350921.55331909447831.71909623696163
Trimmed Mean ( 5 / 21 )39.087038417853120.5710412948631.90010013871363
Trimmed Mean ( 6 / 21 )40.109452215388619.91081195100112.01445588025715
Trimmed Mean ( 7 / 21 )41.107813957301419.1517946584572.14642098510329
Trimmed Mean ( 8 / 21 )42.147801478130718.3794925107512.29319723890507
Trimmed Mean ( 9 / 21 )42.658253005145217.90656461921292.3822689562338
Trimmed Mean ( 10 / 21 )43.485786154471317.39917933224552.49930099139101
Trimmed Mean ( 11 / 21 )44.348868719852716.88856289600212.62597054544831
Trimmed Mean ( 12 / 21 )45.44336485143916.41690537481562.76808349770668
Trimmed Mean ( 13 / 21 )46.678926273327215.84308115104122.94632879982815
Trimmed Mean ( 14 / 21 )48.06584299883815.05987725668433.19164905394592
Trimmed Mean ( 15 / 21 )49.623042907508914.09972207199923.51943411750334
Trimmed Mean ( 16 / 21 )52.646660389575113.12856432526544.01008511557189
Trimmed Mean ( 17 / 21 )53.191317782647213.064127245344.07155539621835
Trimmed Mean ( 18 / 21 )53.869025523344612.98017884027584.15009886891511
Trimmed Mean ( 19 / 21 )54.564253779662212.84564068182774.24768644329688
Trimmed Mean ( 20 / 21 )54.649136489756512.82551215057174.26097109013462
Trimmed Mean ( 21 / 21 )54.708499257542312.7063290378614.30561014865327
Median47.4152166017003
Midrange-2.5174138545265
Midmean - Weighted Average at Xnp46.4386195017766
Midmean - Weighted Average at X(n+1)p52.6466603895751
Midmean - Empirical Distribution Function46.4386195017766
Midmean - Empirical Distribution Function - Averaging52.6466603895751
Midmean - Empirical Distribution Function - Interpolation52.6466603895751
Midmean - Closest Observation46.4386195017766
Midmean - True Basic - Statistics Graphics Toolkit52.6466603895751
Midmean - MS Excel (old versions)49.6230429075089
Number of observations64

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 29.0123123648642 & 25.0063616254811 & 1.16019726497521 \tabularnewline
Geometric Mean & NaN &  &  \tabularnewline
Harmonic Mean & 149.814997018626 &  &  \tabularnewline
Quadratic Mean & 200.591016595084 &  &  \tabularnewline
Winsorized Mean ( 1 / 21 ) & 28.0468604979226 & 24.7998283107446 & 1.13092962364466 \tabularnewline
Winsorized Mean ( 2 / 21 ) & 27.8796491384939 & 24.6194946333992 & 1.13242166639245 \tabularnewline
Winsorized Mean ( 3 / 21 ) & 27.789214217248 & 24.5565120696944 & 1.13164337583362 \tabularnewline
Winsorized Mean ( 4 / 21 ) & 30.1847504931561 & 23.9132063442042 & 1.26226278729334 \tabularnewline
Winsorized Mean ( 5 / 21 ) & 34.9334823653651 & 22.3188273527088 & 1.56520241020303 \tabularnewline
Winsorized Mean ( 6 / 21 ) & 35.4296315501724 & 22.0815830269758 & 1.60448784432213 \tabularnewline
Winsorized Mean ( 7 / 21 ) & 35.6478794729475 & 21.4330852825814 & 1.66321735778836 \tabularnewline
Winsorized Mean ( 8 / 21 ) & 39.2127051977969 & 19.5958576818712 & 2.00107113627763 \tabularnewline
Winsorized Mean ( 9 / 21 ) & 37.5378916436906 & 19.162088870806 & 1.9589665770145 \tabularnewline
Winsorized Mean ( 10 / 21 ) & 37.8218068191552 & 18.5440480527997 & 2.03956583327798 \tabularnewline
Winsorized Mean ( 11 / 21 ) & 36.8242078151974 & 17.711555140554 & 2.07910640951461 \tabularnewline
Winsorized Mean ( 12 / 21 ) & 36.6399897204853 & 17.4316789172169 & 2.10191972296465 \tabularnewline
Winsorized Mean ( 13 / 21 ) & 36.5370977180296 & 17.3825561314766 & 2.10194044199677 \tabularnewline
Winsorized Mean ( 14 / 21 ) & 36.4841686780985 & 16.9177142194725 & 2.1565660824383 \tabularnewline
Winsorized Mean ( 15 / 21 ) & 26.9459117920123 & 15.485617007641 & 1.74006058516858 \tabularnewline
Winsorized Mean ( 16 / 21 ) & 48.5617299415339 & 11.4619480772215 & 4.23677804282164 \tabularnewline
Winsorized Mean ( 17 / 21 ) & 48.1508664612106 & 11.1969656487031 & 4.30034957433203 \tabularnewline
Winsorized Mean ( 18 / 21 ) & 48.785168899022 & 10.9971154480789 & 4.43617866242774 \tabularnewline
Winsorized Mean ( 19 / 21 ) & 53.9594644702404 & 10.2049803650643 & 5.28756181197221 \tabularnewline
Winsorized Mean ( 20 / 21 ) & 54.2410174612294 & 10.1452021142819 & 5.34646987317004 \tabularnewline
Winsorized Mean ( 21 / 21 ) & 52.7514787309898 & 9.83034080591616 & 5.36619022396889 \tabularnewline
Trimmed Mean ( 1 / 21 ) & 30.0294003074252 & 24.1646458693186 & 1.24269978835291 \tabularnewline
Trimmed Mean ( 2 / 21 ) & 32.1441094375613 & 23.3888798370387 & 1.37433300190195 \tabularnewline
Trimmed Mean ( 3 / 21 ) & 34.4969151198053 & 22.5555766704539 & 1.52941845042666 \tabularnewline
Trimmed Mean ( 4 / 21 ) & 37.0522297493509 & 21.5533190944783 & 1.71909623696163 \tabularnewline
Trimmed Mean ( 5 / 21 ) & 39.0870384178531 & 20.571041294863 & 1.90010013871363 \tabularnewline
Trimmed Mean ( 6 / 21 ) & 40.1094522153886 & 19.9108119510011 & 2.01445588025715 \tabularnewline
Trimmed Mean ( 7 / 21 ) & 41.1078139573014 & 19.151794658457 & 2.14642098510329 \tabularnewline
Trimmed Mean ( 8 / 21 ) & 42.1478014781307 & 18.379492510751 & 2.29319723890507 \tabularnewline
Trimmed Mean ( 9 / 21 ) & 42.6582530051452 & 17.9065646192129 & 2.3822689562338 \tabularnewline
Trimmed Mean ( 10 / 21 ) & 43.4857861544713 & 17.3991793322455 & 2.49930099139101 \tabularnewline
Trimmed Mean ( 11 / 21 ) & 44.3488687198527 & 16.8885628960021 & 2.62597054544831 \tabularnewline
Trimmed Mean ( 12 / 21 ) & 45.443364851439 & 16.4169053748156 & 2.76808349770668 \tabularnewline
Trimmed Mean ( 13 / 21 ) & 46.6789262733272 & 15.8430811510412 & 2.94632879982815 \tabularnewline
Trimmed Mean ( 14 / 21 ) & 48.065842998838 & 15.0598772566843 & 3.19164905394592 \tabularnewline
Trimmed Mean ( 15 / 21 ) & 49.6230429075089 & 14.0997220719992 & 3.51943411750334 \tabularnewline
Trimmed Mean ( 16 / 21 ) & 52.6466603895751 & 13.1285643252654 & 4.01008511557189 \tabularnewline
Trimmed Mean ( 17 / 21 ) & 53.1913177826472 & 13.06412724534 & 4.07155539621835 \tabularnewline
Trimmed Mean ( 18 / 21 ) & 53.8690255233446 & 12.9801788402758 & 4.15009886891511 \tabularnewline
Trimmed Mean ( 19 / 21 ) & 54.5642537796622 & 12.8456406818277 & 4.24768644329688 \tabularnewline
Trimmed Mean ( 20 / 21 ) & 54.6491364897565 & 12.8255121505717 & 4.26097109013462 \tabularnewline
Trimmed Mean ( 21 / 21 ) & 54.7084992575423 & 12.706329037861 & 4.30561014865327 \tabularnewline
Median & 47.4152166017003 &  &  \tabularnewline
Midrange & -2.5174138545265 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 46.4386195017766 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 52.6466603895751 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 46.4386195017766 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 52.6466603895751 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 52.6466603895751 &  &  \tabularnewline
Midmean - Closest Observation & 46.4386195017766 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 52.6466603895751 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 49.6230429075089 &  &  \tabularnewline
Number of observations & 64 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=201379&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]29.0123123648642[/C][C]25.0063616254811[/C][C]1.16019726497521[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]NaN[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]149.814997018626[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]200.591016595084[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 21 )[/C][C]28.0468604979226[/C][C]24.7998283107446[/C][C]1.13092962364466[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 21 )[/C][C]27.8796491384939[/C][C]24.6194946333992[/C][C]1.13242166639245[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 21 )[/C][C]27.789214217248[/C][C]24.5565120696944[/C][C]1.13164337583362[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 21 )[/C][C]30.1847504931561[/C][C]23.9132063442042[/C][C]1.26226278729334[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 21 )[/C][C]34.9334823653651[/C][C]22.3188273527088[/C][C]1.56520241020303[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 21 )[/C][C]35.4296315501724[/C][C]22.0815830269758[/C][C]1.60448784432213[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 21 )[/C][C]35.6478794729475[/C][C]21.4330852825814[/C][C]1.66321735778836[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 21 )[/C][C]39.2127051977969[/C][C]19.5958576818712[/C][C]2.00107113627763[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 21 )[/C][C]37.5378916436906[/C][C]19.162088870806[/C][C]1.9589665770145[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 21 )[/C][C]37.8218068191552[/C][C]18.5440480527997[/C][C]2.03956583327798[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 21 )[/C][C]36.8242078151974[/C][C]17.711555140554[/C][C]2.07910640951461[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 21 )[/C][C]36.6399897204853[/C][C]17.4316789172169[/C][C]2.10191972296465[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 21 )[/C][C]36.5370977180296[/C][C]17.3825561314766[/C][C]2.10194044199677[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 21 )[/C][C]36.4841686780985[/C][C]16.9177142194725[/C][C]2.1565660824383[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 21 )[/C][C]26.9459117920123[/C][C]15.485617007641[/C][C]1.74006058516858[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 21 )[/C][C]48.5617299415339[/C][C]11.4619480772215[/C][C]4.23677804282164[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 21 )[/C][C]48.1508664612106[/C][C]11.1969656487031[/C][C]4.30034957433203[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 21 )[/C][C]48.785168899022[/C][C]10.9971154480789[/C][C]4.43617866242774[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 21 )[/C][C]53.9594644702404[/C][C]10.2049803650643[/C][C]5.28756181197221[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 21 )[/C][C]54.2410174612294[/C][C]10.1452021142819[/C][C]5.34646987317004[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 21 )[/C][C]52.7514787309898[/C][C]9.83034080591616[/C][C]5.36619022396889[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 21 )[/C][C]30.0294003074252[/C][C]24.1646458693186[/C][C]1.24269978835291[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 21 )[/C][C]32.1441094375613[/C][C]23.3888798370387[/C][C]1.37433300190195[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 21 )[/C][C]34.4969151198053[/C][C]22.5555766704539[/C][C]1.52941845042666[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 21 )[/C][C]37.0522297493509[/C][C]21.5533190944783[/C][C]1.71909623696163[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 21 )[/C][C]39.0870384178531[/C][C]20.571041294863[/C][C]1.90010013871363[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 21 )[/C][C]40.1094522153886[/C][C]19.9108119510011[/C][C]2.01445588025715[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 21 )[/C][C]41.1078139573014[/C][C]19.151794658457[/C][C]2.14642098510329[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 21 )[/C][C]42.1478014781307[/C][C]18.379492510751[/C][C]2.29319723890507[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 21 )[/C][C]42.6582530051452[/C][C]17.9065646192129[/C][C]2.3822689562338[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 21 )[/C][C]43.4857861544713[/C][C]17.3991793322455[/C][C]2.49930099139101[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 21 )[/C][C]44.3488687198527[/C][C]16.8885628960021[/C][C]2.62597054544831[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 21 )[/C][C]45.443364851439[/C][C]16.4169053748156[/C][C]2.76808349770668[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 21 )[/C][C]46.6789262733272[/C][C]15.8430811510412[/C][C]2.94632879982815[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 21 )[/C][C]48.065842998838[/C][C]15.0598772566843[/C][C]3.19164905394592[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 21 )[/C][C]49.6230429075089[/C][C]14.0997220719992[/C][C]3.51943411750334[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 21 )[/C][C]52.6466603895751[/C][C]13.1285643252654[/C][C]4.01008511557189[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 21 )[/C][C]53.1913177826472[/C][C]13.06412724534[/C][C]4.07155539621835[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 21 )[/C][C]53.8690255233446[/C][C]12.9801788402758[/C][C]4.15009886891511[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 21 )[/C][C]54.5642537796622[/C][C]12.8456406818277[/C][C]4.24768644329688[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 21 )[/C][C]54.6491364897565[/C][C]12.8255121505717[/C][C]4.26097109013462[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 21 )[/C][C]54.7084992575423[/C][C]12.706329037861[/C][C]4.30561014865327[/C][/ROW]
[ROW][C]Median[/C][C]47.4152166017003[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]-2.5174138545265[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]46.4386195017766[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]52.6466603895751[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]46.4386195017766[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]52.6466603895751[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]52.6466603895751[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]46.4386195017766[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]52.6466603895751[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]49.6230429075089[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]64[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=201379&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=201379&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 Mean29.012312364864225.00636162548111.16019726497521
Geometric MeanNaN
Harmonic Mean149.814997018626
Quadratic Mean200.591016595084
Winsorized Mean ( 1 / 21 )28.046860497922624.79982831074461.13092962364466
Winsorized Mean ( 2 / 21 )27.879649138493924.61949463339921.13242166639245
Winsorized Mean ( 3 / 21 )27.78921421724824.55651206969441.13164337583362
Winsorized Mean ( 4 / 21 )30.184750493156123.91320634420421.26226278729334
Winsorized Mean ( 5 / 21 )34.933482365365122.31882735270881.56520241020303
Winsorized Mean ( 6 / 21 )35.429631550172422.08158302697581.60448784432213
Winsorized Mean ( 7 / 21 )35.647879472947521.43308528258141.66321735778836
Winsorized Mean ( 8 / 21 )39.212705197796919.59585768187122.00107113627763
Winsorized Mean ( 9 / 21 )37.537891643690619.1620888708061.9589665770145
Winsorized Mean ( 10 / 21 )37.821806819155218.54404805279972.03956583327798
Winsorized Mean ( 11 / 21 )36.824207815197417.7115551405542.07910640951461
Winsorized Mean ( 12 / 21 )36.639989720485317.43167891721692.10191972296465
Winsorized Mean ( 13 / 21 )36.537097718029617.38255613147662.10194044199677
Winsorized Mean ( 14 / 21 )36.484168678098516.91771421947252.1565660824383
Winsorized Mean ( 15 / 21 )26.945911792012315.4856170076411.74006058516858
Winsorized Mean ( 16 / 21 )48.561729941533911.46194807722154.23677804282164
Winsorized Mean ( 17 / 21 )48.150866461210611.19696564870314.30034957433203
Winsorized Mean ( 18 / 21 )48.78516889902210.99711544807894.43617866242774
Winsorized Mean ( 19 / 21 )53.959464470240410.20498036506435.28756181197221
Winsorized Mean ( 20 / 21 )54.241017461229410.14520211428195.34646987317004
Winsorized Mean ( 21 / 21 )52.75147873098989.830340805916165.36619022396889
Trimmed Mean ( 1 / 21 )30.029400307425224.16464586931861.24269978835291
Trimmed Mean ( 2 / 21 )32.144109437561323.38887983703871.37433300190195
Trimmed Mean ( 3 / 21 )34.496915119805322.55557667045391.52941845042666
Trimmed Mean ( 4 / 21 )37.052229749350921.55331909447831.71909623696163
Trimmed Mean ( 5 / 21 )39.087038417853120.5710412948631.90010013871363
Trimmed Mean ( 6 / 21 )40.109452215388619.91081195100112.01445588025715
Trimmed Mean ( 7 / 21 )41.107813957301419.1517946584572.14642098510329
Trimmed Mean ( 8 / 21 )42.147801478130718.3794925107512.29319723890507
Trimmed Mean ( 9 / 21 )42.658253005145217.90656461921292.3822689562338
Trimmed Mean ( 10 / 21 )43.485786154471317.39917933224552.49930099139101
Trimmed Mean ( 11 / 21 )44.348868719852716.88856289600212.62597054544831
Trimmed Mean ( 12 / 21 )45.44336485143916.41690537481562.76808349770668
Trimmed Mean ( 13 / 21 )46.678926273327215.84308115104122.94632879982815
Trimmed Mean ( 14 / 21 )48.06584299883815.05987725668433.19164905394592
Trimmed Mean ( 15 / 21 )49.623042907508914.09972207199923.51943411750334
Trimmed Mean ( 16 / 21 )52.646660389575113.12856432526544.01008511557189
Trimmed Mean ( 17 / 21 )53.191317782647213.064127245344.07155539621835
Trimmed Mean ( 18 / 21 )53.869025523344612.98017884027584.15009886891511
Trimmed Mean ( 19 / 21 )54.564253779662212.84564068182774.24768644329688
Trimmed Mean ( 20 / 21 )54.649136489756512.82551215057174.26097109013462
Trimmed Mean ( 21 / 21 )54.708499257542312.7063290378614.30561014865327
Median47.4152166017003
Midrange-2.5174138545265
Midmean - Weighted Average at Xnp46.4386195017766
Midmean - Weighted Average at X(n+1)p52.6466603895751
Midmean - Empirical Distribution Function46.4386195017766
Midmean - Empirical Distribution Function - Averaging52.6466603895751
Midmean - Empirical Distribution Function - Interpolation52.6466603895751
Midmean - Closest Observation46.4386195017766
Midmean - True Basic - Statistics Graphics Toolkit52.6466603895751
Midmean - MS Excel (old versions)49.6230429075089
Number of observations64



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')