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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 computationFri, 21 Dec 2012 12:45:37 -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/21/t1356111972xpaq1frrvkjnte3.htm/, Retrieved Fri, 29 Mar 2024 05:11:25 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=204026, Retrieved Fri, 29 Mar 2024 05:11:25 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact59
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
F     [Univariate Data Series] [HPC Retail Sales] [2008-03-02 15:42:48] [74be16979710d4c4e7c6647856088456]
- RMPD  [Classical Decomposition] [Classical Decompo...] [2011-12-19 14:36:02] [920204e71d7e82687d0571379c55a021]
- RMPD    [Exponential Smoothing] [] [2012-12-21 12:33:31] [63daa42bab46576bcb233b0e49169cb8]
- RMPD        [Central Tendency] [] [2012-12-21 17:45:37] [7f1e2e1b7f66b13ad70fccbed4479dd6] [Current]
- RM            [Skewness and Kurtosis Test] [] [2012-12-21 17:51:01] [63daa42bab46576bcb233b0e49169cb8]
- RM D          [ARIMA Forecasting] [] [2012-12-21 18:05:13] [63daa42bab46576bcb233b0e49169cb8]
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Dataseries X:
9.25191650214777
22.2914871230951
-37.1571787649763
34.224161696956
-175.791407723369
104.976083788091
-61.2440566193924
-396.729670519991
-396.44439811595
-260.009316250619
127.969010838924
-36.029843990865
204.138369304772
44.2385868220351
-159.706287586558
203.135138014012
121.756524240195
-16.2019122127222
-243.900810016438
391.694842810854
-164.230167509228
293.821184035543
150.197655607195
-191.027489037513
251.842321753037
-153.374881204494
8.18402596025766
276.1970369319
7.49356404167146
290.310133584017
154.709015298645
-344.563215952582
-268.812624669854
308.788007352866
53.4487117440643
309.745158451437
86.3072721974973
-34.8646306292142
196.561770310134
226.513512286837
-188.002590164262
-58.5622808860067
209.148059687373
145.969099713114
129.401752384417
-33.0299340425404
-386.049808213019
144.248501280284
117.138964770494
129.897118044286
-152.218688906803
-55.0236881931042
144.022136076712
-16.856654827111
144.68580457337
-160.202973634943
329.620650920572
138.317376113197
9.00038368421579
50.5918463806914
313.875297519637
236.907637607489
110.051329051183
-383.848947462751




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Gertrude Mary Cox' @ cox.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 & 'Gertrude Mary Cox' @ cox.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=204026&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]'Gertrude Mary Cox' @ cox.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=204026&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=204026&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'Gertrude Mary Cox' @ cox.wessa.net







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean29.012312365139325.0063616253571.16019726499197
Geometric MeanNaN
Harmonic Mean149.81499704452
Quadratic Mean200.59101659415
Winsorized Mean ( 1 / 21 )28.046860498166724.79982831062481.13092962365997
Winsorized Mean ( 2 / 21 )27.879649138854124.61949463326391.1324216664133
Winsorized Mean ( 3 / 21 )27.789214217701124.55651206954931.13164337585875
Winsorized Mean ( 4 / 21 )30.184750493425923.91320634404421.26226278731307
Winsorized Mean ( 5 / 21 )34.933482365723222.3188273525991.56520241022678
Winsorized Mean ( 6 / 21 )35.429631550195922.08158302695261.60448784432488
Winsorized Mean ( 7 / 21 )35.647879473234221.43308528245841.66321735781128
Winsorized Mean ( 8 / 21 )39.212705198241919.59585768173622.00107113631414
Winsorized Mean ( 9 / 21 )37.537891644325119.16208887069051.95896657705943
Winsorized Mean ( 10 / 21 )37.821806819362818.54404805272672.0395658332972
Winsorized Mean ( 11 / 21 )36.824207815635417.71155514041672.07910640955547
Winsorized Mean ( 12 / 21 )36.639989720326217.43167891707712.10191972297237
Winsorized Mean ( 13 / 21 )36.537097717968717.38255613137952.10194044200501
Winsorized Mean ( 14 / 21 )36.484168678821916.91771421937932.15656608249294
Winsorized Mean ( 15 / 21 )26.945911792775515.48561700764891.74006058521698
Winsorized Mean ( 16 / 21 )48.561729941765711.46194807721694.23677804284357
Winsorized Mean ( 17 / 21 )48.15086646158111.19696564869014.30034957437008
Winsorized Mean ( 18 / 21 )48.785168898406810.99711544803234.43617866239059
Winsorized Mean ( 19 / 21 )53.959464469747410.20498036494725.28756181198457
Winsorized Mean ( 20 / 21 )54.241017460540910.14520211431825.34646987308309
Winsorized Mean ( 21 / 21 )52.75147873180429.830340805784455.36619022412364
Trimmed Mean ( 1 / 21 )30.029400307710524.16464586919461.24269978837109
Trimmed Mean ( 2 / 21 )32.144109437890523.38887983690971.3743330019236
Trimmed Mean ( 3 / 21 )34.496915120117422.55557667032921.52941845044895
Trimmed Mean ( 4 / 21 )37.052229749609321.5533190943641.71909623698274
Trimmed Mean ( 5 / 21 )39.087038418108120.57104129476741.90010013873486
Trimmed Mean ( 6 / 21 )40.109452215618319.91081195091082.01445588027783
Trimmed Mean ( 7 / 21 )41.107813957575119.15179465834552.14642098513008
Trimmed Mean ( 8 / 21 )42.147801478401918.37949251064342.29319723893325
Trimmed Mean ( 9 / 21 )42.658253005386217.90656461911362.38226895626047
Trimmed Mean ( 10 / 21 )43.485786154648617.39917933215192.49930099141465
Trimmed Mean ( 11 / 21 )44.348868720025516.88856289590432.62597054547374
Trimmed Mean ( 12 / 21 )45.443364851573216.41690537472982.76808349772931
Trimmed Mean ( 13 / 21 )46.678926273502615.84308115097052.94632879985237
Trimmed Mean ( 14 / 21 )48.065842999045615.05987725662173.19164905397297
Trimmed Mean ( 15 / 21 )49.623042907647214.09972207194943.51943411752558
Trimmed Mean ( 16 / 21 )52.6466603896313.12856432520374.01008511559495
Trimmed Mean ( 17 / 21 )53.191317782678613.06412724526624.07155539624374
Trimmed Mean ( 18 / 21 )53.869025523330412.98017884018964.15009886894158
Trimmed Mean ( 19 / 21 )54.564253779730212.8456406817334.24768644333348
Trimmed Mean ( 20 / 21 )54.649136489903312.82551215048994.26097109017326
Trimmed Mean ( 21 / 21 )54.708499257810512.70632903774454.30561014871387
Median47.4152166013633
Midrange-2.51741385456847
Midmean - Weighted Average at Xnp46.4386195018593
Midmean - Weighted Average at X(n+1)p52.64666038963
Midmean - Empirical Distribution Function46.4386195018593
Midmean - Empirical Distribution Function - Averaging52.64666038963
Midmean - Empirical Distribution Function - Interpolation52.64666038963
Midmean - Closest Observation46.4386195018593
Midmean - True Basic - Statistics Graphics Toolkit52.64666038963
Midmean - MS Excel (old versions)49.6230429076472
Number of observations64

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 29.0123123651393 & 25.006361625357 & 1.16019726499197 \tabularnewline
Geometric Mean & NaN &  &  \tabularnewline
Harmonic Mean & 149.81499704452 &  &  \tabularnewline
Quadratic Mean & 200.59101659415 &  &  \tabularnewline
Winsorized Mean ( 1 / 21 ) & 28.0468604981667 & 24.7998283106248 & 1.13092962365997 \tabularnewline
Winsorized Mean ( 2 / 21 ) & 27.8796491388541 & 24.6194946332639 & 1.1324216664133 \tabularnewline
Winsorized Mean ( 3 / 21 ) & 27.7892142177011 & 24.5565120695493 & 1.13164337585875 \tabularnewline
Winsorized Mean ( 4 / 21 ) & 30.1847504934259 & 23.9132063440442 & 1.26226278731307 \tabularnewline
Winsorized Mean ( 5 / 21 ) & 34.9334823657232 & 22.318827352599 & 1.56520241022678 \tabularnewline
Winsorized Mean ( 6 / 21 ) & 35.4296315501959 & 22.0815830269526 & 1.60448784432488 \tabularnewline
Winsorized Mean ( 7 / 21 ) & 35.6478794732342 & 21.4330852824584 & 1.66321735781128 \tabularnewline
Winsorized Mean ( 8 / 21 ) & 39.2127051982419 & 19.5958576817362 & 2.00107113631414 \tabularnewline
Winsorized Mean ( 9 / 21 ) & 37.5378916443251 & 19.1620888706905 & 1.95896657705943 \tabularnewline
Winsorized Mean ( 10 / 21 ) & 37.8218068193628 & 18.5440480527267 & 2.0395658332972 \tabularnewline
Winsorized Mean ( 11 / 21 ) & 36.8242078156354 & 17.7115551404167 & 2.07910640955547 \tabularnewline
Winsorized Mean ( 12 / 21 ) & 36.6399897203262 & 17.4316789170771 & 2.10191972297237 \tabularnewline
Winsorized Mean ( 13 / 21 ) & 36.5370977179687 & 17.3825561313795 & 2.10194044200501 \tabularnewline
Winsorized Mean ( 14 / 21 ) & 36.4841686788219 & 16.9177142193793 & 2.15656608249294 \tabularnewline
Winsorized Mean ( 15 / 21 ) & 26.9459117927755 & 15.4856170076489 & 1.74006058521698 \tabularnewline
Winsorized Mean ( 16 / 21 ) & 48.5617299417657 & 11.4619480772169 & 4.23677804284357 \tabularnewline
Winsorized Mean ( 17 / 21 ) & 48.150866461581 & 11.1969656486901 & 4.30034957437008 \tabularnewline
Winsorized Mean ( 18 / 21 ) & 48.7851688984068 & 10.9971154480323 & 4.43617866239059 \tabularnewline
Winsorized Mean ( 19 / 21 ) & 53.9594644697474 & 10.2049803649472 & 5.28756181198457 \tabularnewline
Winsorized Mean ( 20 / 21 ) & 54.2410174605409 & 10.1452021143182 & 5.34646987308309 \tabularnewline
Winsorized Mean ( 21 / 21 ) & 52.7514787318042 & 9.83034080578445 & 5.36619022412364 \tabularnewline
Trimmed Mean ( 1 / 21 ) & 30.0294003077105 & 24.1646458691946 & 1.24269978837109 \tabularnewline
Trimmed Mean ( 2 / 21 ) & 32.1441094378905 & 23.3888798369097 & 1.3743330019236 \tabularnewline
Trimmed Mean ( 3 / 21 ) & 34.4969151201174 & 22.5555766703292 & 1.52941845044895 \tabularnewline
Trimmed Mean ( 4 / 21 ) & 37.0522297496093 & 21.553319094364 & 1.71909623698274 \tabularnewline
Trimmed Mean ( 5 / 21 ) & 39.0870384181081 & 20.5710412947674 & 1.90010013873486 \tabularnewline
Trimmed Mean ( 6 / 21 ) & 40.1094522156183 & 19.9108119509108 & 2.01445588027783 \tabularnewline
Trimmed Mean ( 7 / 21 ) & 41.1078139575751 & 19.1517946583455 & 2.14642098513008 \tabularnewline
Trimmed Mean ( 8 / 21 ) & 42.1478014784019 & 18.3794925106434 & 2.29319723893325 \tabularnewline
Trimmed Mean ( 9 / 21 ) & 42.6582530053862 & 17.9065646191136 & 2.38226895626047 \tabularnewline
Trimmed Mean ( 10 / 21 ) & 43.4857861546486 & 17.3991793321519 & 2.49930099141465 \tabularnewline
Trimmed Mean ( 11 / 21 ) & 44.3488687200255 & 16.8885628959043 & 2.62597054547374 \tabularnewline
Trimmed Mean ( 12 / 21 ) & 45.4433648515732 & 16.4169053747298 & 2.76808349772931 \tabularnewline
Trimmed Mean ( 13 / 21 ) & 46.6789262735026 & 15.8430811509705 & 2.94632879985237 \tabularnewline
Trimmed Mean ( 14 / 21 ) & 48.0658429990456 & 15.0598772566217 & 3.19164905397297 \tabularnewline
Trimmed Mean ( 15 / 21 ) & 49.6230429076472 & 14.0997220719494 & 3.51943411752558 \tabularnewline
Trimmed Mean ( 16 / 21 ) & 52.64666038963 & 13.1285643252037 & 4.01008511559495 \tabularnewline
Trimmed Mean ( 17 / 21 ) & 53.1913177826786 & 13.0641272452662 & 4.07155539624374 \tabularnewline
Trimmed Mean ( 18 / 21 ) & 53.8690255233304 & 12.9801788401896 & 4.15009886894158 \tabularnewline
Trimmed Mean ( 19 / 21 ) & 54.5642537797302 & 12.845640681733 & 4.24768644333348 \tabularnewline
Trimmed Mean ( 20 / 21 ) & 54.6491364899033 & 12.8255121504899 & 4.26097109017326 \tabularnewline
Trimmed Mean ( 21 / 21 ) & 54.7084992578105 & 12.7063290377445 & 4.30561014871387 \tabularnewline
Median & 47.4152166013633 &  &  \tabularnewline
Midrange & -2.51741385456847 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 46.4386195018593 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 52.64666038963 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 46.4386195018593 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 52.64666038963 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 52.64666038963 &  &  \tabularnewline
Midmean - Closest Observation & 46.4386195018593 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 52.64666038963 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 49.6230429076472 &  &  \tabularnewline
Number of observations & 64 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=204026&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]29.0123123651393[/C][C]25.006361625357[/C][C]1.16019726499197[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]NaN[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]149.81499704452[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]200.59101659415[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 21 )[/C][C]28.0468604981667[/C][C]24.7998283106248[/C][C]1.13092962365997[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 21 )[/C][C]27.8796491388541[/C][C]24.6194946332639[/C][C]1.1324216664133[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 21 )[/C][C]27.7892142177011[/C][C]24.5565120695493[/C][C]1.13164337585875[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 21 )[/C][C]30.1847504934259[/C][C]23.9132063440442[/C][C]1.26226278731307[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 21 )[/C][C]34.9334823657232[/C][C]22.318827352599[/C][C]1.56520241022678[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 21 )[/C][C]35.4296315501959[/C][C]22.0815830269526[/C][C]1.60448784432488[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 21 )[/C][C]35.6478794732342[/C][C]21.4330852824584[/C][C]1.66321735781128[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 21 )[/C][C]39.2127051982419[/C][C]19.5958576817362[/C][C]2.00107113631414[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 21 )[/C][C]37.5378916443251[/C][C]19.1620888706905[/C][C]1.95896657705943[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 21 )[/C][C]37.8218068193628[/C][C]18.5440480527267[/C][C]2.0395658332972[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 21 )[/C][C]36.8242078156354[/C][C]17.7115551404167[/C][C]2.07910640955547[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 21 )[/C][C]36.6399897203262[/C][C]17.4316789170771[/C][C]2.10191972297237[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 21 )[/C][C]36.5370977179687[/C][C]17.3825561313795[/C][C]2.10194044200501[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 21 )[/C][C]36.4841686788219[/C][C]16.9177142193793[/C][C]2.15656608249294[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 21 )[/C][C]26.9459117927755[/C][C]15.4856170076489[/C][C]1.74006058521698[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 21 )[/C][C]48.5617299417657[/C][C]11.4619480772169[/C][C]4.23677804284357[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 21 )[/C][C]48.150866461581[/C][C]11.1969656486901[/C][C]4.30034957437008[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 21 )[/C][C]48.7851688984068[/C][C]10.9971154480323[/C][C]4.43617866239059[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 21 )[/C][C]53.9594644697474[/C][C]10.2049803649472[/C][C]5.28756181198457[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 21 )[/C][C]54.2410174605409[/C][C]10.1452021143182[/C][C]5.34646987308309[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 21 )[/C][C]52.7514787318042[/C][C]9.83034080578445[/C][C]5.36619022412364[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 21 )[/C][C]30.0294003077105[/C][C]24.1646458691946[/C][C]1.24269978837109[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 21 )[/C][C]32.1441094378905[/C][C]23.3888798369097[/C][C]1.3743330019236[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 21 )[/C][C]34.4969151201174[/C][C]22.5555766703292[/C][C]1.52941845044895[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 21 )[/C][C]37.0522297496093[/C][C]21.553319094364[/C][C]1.71909623698274[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 21 )[/C][C]39.0870384181081[/C][C]20.5710412947674[/C][C]1.90010013873486[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 21 )[/C][C]40.1094522156183[/C][C]19.9108119509108[/C][C]2.01445588027783[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 21 )[/C][C]41.1078139575751[/C][C]19.1517946583455[/C][C]2.14642098513008[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 21 )[/C][C]42.1478014784019[/C][C]18.3794925106434[/C][C]2.29319723893325[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 21 )[/C][C]42.6582530053862[/C][C]17.9065646191136[/C][C]2.38226895626047[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 21 )[/C][C]43.4857861546486[/C][C]17.3991793321519[/C][C]2.49930099141465[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 21 )[/C][C]44.3488687200255[/C][C]16.8885628959043[/C][C]2.62597054547374[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 21 )[/C][C]45.4433648515732[/C][C]16.4169053747298[/C][C]2.76808349772931[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 21 )[/C][C]46.6789262735026[/C][C]15.8430811509705[/C][C]2.94632879985237[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 21 )[/C][C]48.0658429990456[/C][C]15.0598772566217[/C][C]3.19164905397297[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 21 )[/C][C]49.6230429076472[/C][C]14.0997220719494[/C][C]3.51943411752558[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 21 )[/C][C]52.64666038963[/C][C]13.1285643252037[/C][C]4.01008511559495[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 21 )[/C][C]53.1913177826786[/C][C]13.0641272452662[/C][C]4.07155539624374[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 21 )[/C][C]53.8690255233304[/C][C]12.9801788401896[/C][C]4.15009886894158[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 21 )[/C][C]54.5642537797302[/C][C]12.845640681733[/C][C]4.24768644333348[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 21 )[/C][C]54.6491364899033[/C][C]12.8255121504899[/C][C]4.26097109017326[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 21 )[/C][C]54.7084992578105[/C][C]12.7063290377445[/C][C]4.30561014871387[/C][/ROW]
[ROW][C]Median[/C][C]47.4152166013633[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]-2.51741385456847[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]46.4386195018593[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]52.64666038963[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]46.4386195018593[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]52.64666038963[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]52.64666038963[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]46.4386195018593[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]52.64666038963[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]49.6230429076472[/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=204026&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=204026&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 Mean29.012312365139325.0063616253571.16019726499197
Geometric MeanNaN
Harmonic Mean149.81499704452
Quadratic Mean200.59101659415
Winsorized Mean ( 1 / 21 )28.046860498166724.79982831062481.13092962365997
Winsorized Mean ( 2 / 21 )27.879649138854124.61949463326391.1324216664133
Winsorized Mean ( 3 / 21 )27.789214217701124.55651206954931.13164337585875
Winsorized Mean ( 4 / 21 )30.184750493425923.91320634404421.26226278731307
Winsorized Mean ( 5 / 21 )34.933482365723222.3188273525991.56520241022678
Winsorized Mean ( 6 / 21 )35.429631550195922.08158302695261.60448784432488
Winsorized Mean ( 7 / 21 )35.647879473234221.43308528245841.66321735781128
Winsorized Mean ( 8 / 21 )39.212705198241919.59585768173622.00107113631414
Winsorized Mean ( 9 / 21 )37.537891644325119.16208887069051.95896657705943
Winsorized Mean ( 10 / 21 )37.821806819362818.54404805272672.0395658332972
Winsorized Mean ( 11 / 21 )36.824207815635417.71155514041672.07910640955547
Winsorized Mean ( 12 / 21 )36.639989720326217.43167891707712.10191972297237
Winsorized Mean ( 13 / 21 )36.537097717968717.38255613137952.10194044200501
Winsorized Mean ( 14 / 21 )36.484168678821916.91771421937932.15656608249294
Winsorized Mean ( 15 / 21 )26.945911792775515.48561700764891.74006058521698
Winsorized Mean ( 16 / 21 )48.561729941765711.46194807721694.23677804284357
Winsorized Mean ( 17 / 21 )48.15086646158111.19696564869014.30034957437008
Winsorized Mean ( 18 / 21 )48.785168898406810.99711544803234.43617866239059
Winsorized Mean ( 19 / 21 )53.959464469747410.20498036494725.28756181198457
Winsorized Mean ( 20 / 21 )54.241017460540910.14520211431825.34646987308309
Winsorized Mean ( 21 / 21 )52.75147873180429.830340805784455.36619022412364
Trimmed Mean ( 1 / 21 )30.029400307710524.16464586919461.24269978837109
Trimmed Mean ( 2 / 21 )32.144109437890523.38887983690971.3743330019236
Trimmed Mean ( 3 / 21 )34.496915120117422.55557667032921.52941845044895
Trimmed Mean ( 4 / 21 )37.052229749609321.5533190943641.71909623698274
Trimmed Mean ( 5 / 21 )39.087038418108120.57104129476741.90010013873486
Trimmed Mean ( 6 / 21 )40.109452215618319.91081195091082.01445588027783
Trimmed Mean ( 7 / 21 )41.107813957575119.15179465834552.14642098513008
Trimmed Mean ( 8 / 21 )42.147801478401918.37949251064342.29319723893325
Trimmed Mean ( 9 / 21 )42.658253005386217.90656461911362.38226895626047
Trimmed Mean ( 10 / 21 )43.485786154648617.39917933215192.49930099141465
Trimmed Mean ( 11 / 21 )44.348868720025516.88856289590432.62597054547374
Trimmed Mean ( 12 / 21 )45.443364851573216.41690537472982.76808349772931
Trimmed Mean ( 13 / 21 )46.678926273502615.84308115097052.94632879985237
Trimmed Mean ( 14 / 21 )48.065842999045615.05987725662173.19164905397297
Trimmed Mean ( 15 / 21 )49.623042907647214.09972207194943.51943411752558
Trimmed Mean ( 16 / 21 )52.6466603896313.12856432520374.01008511559495
Trimmed Mean ( 17 / 21 )53.191317782678613.06412724526624.07155539624374
Trimmed Mean ( 18 / 21 )53.869025523330412.98017884018964.15009886894158
Trimmed Mean ( 19 / 21 )54.564253779730212.8456406817334.24768644333348
Trimmed Mean ( 20 / 21 )54.649136489903312.82551215048994.26097109017326
Trimmed Mean ( 21 / 21 )54.708499257810512.70632903774454.30561014871387
Median47.4152166013633
Midrange-2.51741385456847
Midmean - Weighted Average at Xnp46.4386195018593
Midmean - Weighted Average at X(n+1)p52.64666038963
Midmean - Empirical Distribution Function46.4386195018593
Midmean - Empirical Distribution Function - Averaging52.64666038963
Midmean - Empirical Distribution Function - Interpolation52.64666038963
Midmean - Closest Observation46.4386195018593
Midmean - True Basic - Statistics Graphics Toolkit52.64666038963
Midmean - MS Excel (old versions)49.6230429076472
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')