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of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationMon, 20 Oct 2008 15:22:05 -0600
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2008/Oct/20/t1224538075dewbo46y44jef7g.htm/, Retrieved Sun, 19 May 2024 15:54:37 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=18181, Retrieved Sun, 19 May 2024 15:54:37 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact106
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
F       [Central Tendency] [Central tendency ...] [2008-10-20 21:22:05] [14a75ec03b2c0d8ddd8b141a7b1594fd] [Current]
Feedback Forum
2008-10-23 20:25:25 [Kenny Simons] [reply
Als we naar de trimmed en winsorized mean kijken, zien we dat deze tijdreeks perfect tussen het betrouwbaarheidsinterval ligt. De trimmed mean loopt ook vrij horizontaal, en de laatst waargenomen waarden van de winsorized mean lopen ook vrij horizontaal. Hierdoor kunnen we dus besluiten dan de volgende observaties niet zo ver hieraf gaan liggen.
2008-10-27 11:04:17 [Joris Deboel] [reply
Inderdaad de veronderstelling dat de volgende observaties in de lijn gaan liggen van de laatste observatie zou een correcte veronderstelling zijn.

Post a new message
Dataseries X:
14433,5
13691,5
14194,1
13519,2
11857,9
14616
15643,4
14077,3
14887,5
14159,9
14643
17192,4
15386,1
14287,1
17526,6
14497
14398,3
16629,6
16670,7
16614,8
16869,2
15663,9
16359,9
18447,7
16889
16505
18320,9
15052,1
15699,8
18135,3
16768,7
18883
19021
18101,9
17776,1
21489,9
17065,3
18690
18953,1
16398,9
16895,6
18553
19270
19422,1
17579,4
18637,3
18076,7
20438,6
18075,2
19563
19899,2
19227,5
17789,6
19220,8
22058,6
21230,8
19504,4
23913,1
23165,7
23574,3




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'Herman Ole Andreas Wold' @ 193.190.124.10:1001

\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 & 3 seconds \tabularnewline
R Server & 'Herman Ole Andreas Wold' @ 193.190.124.10:1001 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=18181&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]3 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Herman Ole Andreas Wold' @ 193.190.124.10:1001[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=18181&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=18181&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 time3 seconds
R Server'Herman Ole Andreas Wold' @ 193.190.124.10:1001







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean17435.1916666667334.08738549747852.1875186658261
Geometric Mean17249.0815032542
Harmonic Mean17065.1298436409
Quadratic Mean17623.0291647369
Winsorized Mean ( 1 / 20 )17457.2333333333325.48960179930953.6337665990853
Winsorized Mean ( 2 / 20 )17449.3566666667320.09782048623554.5125756875219
Winsorized Mean ( 3 / 20 )17413.2916666667300.70213607499757.9087727608416
Winsorized Mean ( 4 / 20 )17380.885290.14525994589059.9040804707319
Winsorized Mean ( 5 / 20 )17362.1433333333284.52791951779161.0208775390414
Winsorized Mean ( 6 / 20 )17292.2233333333265.63868322341665.0967815511631
Winsorized Mean ( 7 / 20 )17242.2666666667251.17305125367868.6469610517747
Winsorized Mean ( 8 / 20 )17202.1333333333242.5469777394670.9228929325666
Winsorized Mean ( 9 / 20 )17202.8683333333239.2709987064671.897005597565
Winsorized Mean ( 10 / 20 )17208.985233.28044556176873.7695135936432
Winsorized Mean ( 11 / 20 )17186.05227.942870475475.3963041886618
Winsorized Mean ( 12 / 20 )17226.45217.53888722433679.1879108135518
Winsorized Mean ( 13 / 20 )17260.6616666667210.89547295909981.8446286422382
Winsorized Mean ( 14 / 20 )17291.975190.07119859306590.9763032379324
Winsorized Mean ( 15 / 20 )17339.325176.74393795092798.1042133666518
Winsorized Mean ( 16 / 20 )17326.0983333333172.981751747998100.161422567706
Winsorized Mean ( 17 / 20 )17281.5866666667163.141222858776105.930226363612
Winsorized Mean ( 18 / 20 )17463.8066666667130.033937027638134.301914299148
Winsorized Mean ( 19 / 20 )17449.4616666667124.207836872843140.485995940259
Winsorized Mean ( 20 / 20 )17449.7283333333113.935594382022153.154318700660
Trimmed Mean ( 1 / 20 )17419.6637931034312.10283698032855.8138591806566
Trimmed Mean ( 2 / 20 )17379.4107142857295.44570329472658.8243813346259
Trimmed Mean ( 3 / 20 )17340.5518518519278.3123833331362.3060736434995
Trimmed Mean ( 4 / 20 )17312.575266.77129537067564.8966935364781
Trimmed Mean ( 5 / 20 )17292.082256.60601148874867.3876730310282
Trimmed Mean ( 6 / 20 )17274.5666666667245.70653916711370.3056854946693
Trimmed Mean ( 7 / 20 )17270.7282608696238.00887115897172.5633804184303
Trimmed Mean ( 8 / 20 )17276.2727272727232.30252097470174.3697169311143
Trimmed Mean ( 9 / 20 )17289.5119047619227.06392483293976.1438080376817
Trimmed Mean ( 10 / 20 )17303.9525220.82410836041778.3607941563946
Trimmed Mean ( 11 / 20 )17318.9473684211213.93579591964780.9539483281513
Trimmed Mean ( 12 / 20 )17339.0833333333205.80590465020484.2496883789779
Trimmed Mean ( 13 / 20 )17355.6470588235197.54045188004287.8586987811633
Trimmed Mean ( 14 / 20 )17369.346875187.81374755285292.481765053499
Trimmed Mean ( 15 / 20 )17380.4180.44300650815296.3207183051162
Trimmed Mean ( 16 / 20 )17386.2678571429173.797463164672100.037523796705
Trimmed Mean ( 17 / 20 )17394.9461538462164.675371679768105.631740656841
Trimmed Mean ( 18 / 20 )17411.6166666667153.871128987048113.157138582718
Trimmed Mean ( 19 / 20 )17403.7090909091150.464992104072115.666168239796
Trimmed Mean ( 20 / 20 )17396.485146.251344082893118.949231605967
Median17359.5
Midrange17885.5
Midmean - Weighted Average at Xnp17316.0677419355
Midmean - Weighted Average at X(n+1)p17380.4
Midmean - Empirical Distribution Function17316.0677419355
Midmean - Empirical Distribution Function - Averaging17380.4
Midmean - Empirical Distribution Function - Interpolation17380.4
Midmean - Closest Observation17316.0677419355
Midmean - True Basic - Statistics Graphics Toolkit17380.4
Midmean - MS Excel (old versions)17369.346875
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 17435.1916666667 & 334.087385497478 & 52.1875186658261 \tabularnewline
Geometric Mean & 17249.0815032542 &  &  \tabularnewline
Harmonic Mean & 17065.1298436409 &  &  \tabularnewline
Quadratic Mean & 17623.0291647369 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 17457.2333333333 & 325.489601799309 & 53.6337665990853 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 17449.3566666667 & 320.097820486235 & 54.5125756875219 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 17413.2916666667 & 300.702136074997 & 57.9087727608416 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 17380.885 & 290.145259945890 & 59.9040804707319 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 17362.1433333333 & 284.527919517791 & 61.0208775390414 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 17292.2233333333 & 265.638683223416 & 65.0967815511631 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 17242.2666666667 & 251.173051253678 & 68.6469610517747 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 17202.1333333333 & 242.54697773946 & 70.9228929325666 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 17202.8683333333 & 239.27099870646 & 71.897005597565 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 17208.985 & 233.280445561768 & 73.7695135936432 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 17186.05 & 227.9428704754 & 75.3963041886618 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 17226.45 & 217.538887224336 & 79.1879108135518 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 17260.6616666667 & 210.895472959099 & 81.8446286422382 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 17291.975 & 190.071198593065 & 90.9763032379324 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 17339.325 & 176.743937950927 & 98.1042133666518 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 17326.0983333333 & 172.981751747998 & 100.161422567706 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 17281.5866666667 & 163.141222858776 & 105.930226363612 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 17463.8066666667 & 130.033937027638 & 134.301914299148 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 17449.4616666667 & 124.207836872843 & 140.485995940259 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 17449.7283333333 & 113.935594382022 & 153.154318700660 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 17419.6637931034 & 312.102836980328 & 55.8138591806566 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 17379.4107142857 & 295.445703294726 & 58.8243813346259 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 17340.5518518519 & 278.31238333313 & 62.3060736434995 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 17312.575 & 266.771295370675 & 64.8966935364781 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 17292.082 & 256.606011488748 & 67.3876730310282 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 17274.5666666667 & 245.706539167113 & 70.3056854946693 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 17270.7282608696 & 238.008871158971 & 72.5633804184303 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 17276.2727272727 & 232.302520974701 & 74.3697169311143 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 17289.5119047619 & 227.063924832939 & 76.1438080376817 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 17303.9525 & 220.824108360417 & 78.3607941563946 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 17318.9473684211 & 213.935795919647 & 80.9539483281513 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 17339.0833333333 & 205.805904650204 & 84.2496883789779 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 17355.6470588235 & 197.540451880042 & 87.8586987811633 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 17369.346875 & 187.813747552852 & 92.481765053499 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 17380.4 & 180.443006508152 & 96.3207183051162 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 17386.2678571429 & 173.797463164672 & 100.037523796705 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 17394.9461538462 & 164.675371679768 & 105.631740656841 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 17411.6166666667 & 153.871128987048 & 113.157138582718 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 17403.7090909091 & 150.464992104072 & 115.666168239796 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 17396.485 & 146.251344082893 & 118.949231605967 \tabularnewline
Median & 17359.5 &  &  \tabularnewline
Midrange & 17885.5 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 17316.0677419355 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 17380.4 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 17316.0677419355 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 17380.4 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 17380.4 &  &  \tabularnewline
Midmean - Closest Observation & 17316.0677419355 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 17380.4 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 17369.346875 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=18181&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]17435.1916666667[/C][C]334.087385497478[/C][C]52.1875186658261[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]17249.0815032542[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]17065.1298436409[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]17623.0291647369[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]17457.2333333333[/C][C]325.489601799309[/C][C]53.6337665990853[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]17449.3566666667[/C][C]320.097820486235[/C][C]54.5125756875219[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]17413.2916666667[/C][C]300.702136074997[/C][C]57.9087727608416[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]17380.885[/C][C]290.145259945890[/C][C]59.9040804707319[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]17362.1433333333[/C][C]284.527919517791[/C][C]61.0208775390414[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]17292.2233333333[/C][C]265.638683223416[/C][C]65.0967815511631[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]17242.2666666667[/C][C]251.173051253678[/C][C]68.6469610517747[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]17202.1333333333[/C][C]242.54697773946[/C][C]70.9228929325666[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]17202.8683333333[/C][C]239.27099870646[/C][C]71.897005597565[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]17208.985[/C][C]233.280445561768[/C][C]73.7695135936432[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]17186.05[/C][C]227.9428704754[/C][C]75.3963041886618[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]17226.45[/C][C]217.538887224336[/C][C]79.1879108135518[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]17260.6616666667[/C][C]210.895472959099[/C][C]81.8446286422382[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]17291.975[/C][C]190.071198593065[/C][C]90.9763032379324[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]17339.325[/C][C]176.743937950927[/C][C]98.1042133666518[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]17326.0983333333[/C][C]172.981751747998[/C][C]100.161422567706[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]17281.5866666667[/C][C]163.141222858776[/C][C]105.930226363612[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]17463.8066666667[/C][C]130.033937027638[/C][C]134.301914299148[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]17449.4616666667[/C][C]124.207836872843[/C][C]140.485995940259[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]17449.7283333333[/C][C]113.935594382022[/C][C]153.154318700660[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]17419.6637931034[/C][C]312.102836980328[/C][C]55.8138591806566[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]17379.4107142857[/C][C]295.445703294726[/C][C]58.8243813346259[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]17340.5518518519[/C][C]278.31238333313[/C][C]62.3060736434995[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]17312.575[/C][C]266.771295370675[/C][C]64.8966935364781[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]17292.082[/C][C]256.606011488748[/C][C]67.3876730310282[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]17274.5666666667[/C][C]245.706539167113[/C][C]70.3056854946693[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]17270.7282608696[/C][C]238.008871158971[/C][C]72.5633804184303[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]17276.2727272727[/C][C]232.302520974701[/C][C]74.3697169311143[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]17289.5119047619[/C][C]227.063924832939[/C][C]76.1438080376817[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]17303.9525[/C][C]220.824108360417[/C][C]78.3607941563946[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]17318.9473684211[/C][C]213.935795919647[/C][C]80.9539483281513[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]17339.0833333333[/C][C]205.805904650204[/C][C]84.2496883789779[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]17355.6470588235[/C][C]197.540451880042[/C][C]87.8586987811633[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]17369.346875[/C][C]187.813747552852[/C][C]92.481765053499[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]17380.4[/C][C]180.443006508152[/C][C]96.3207183051162[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]17386.2678571429[/C][C]173.797463164672[/C][C]100.037523796705[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]17394.9461538462[/C][C]164.675371679768[/C][C]105.631740656841[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]17411.6166666667[/C][C]153.871128987048[/C][C]113.157138582718[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]17403.7090909091[/C][C]150.464992104072[/C][C]115.666168239796[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]17396.485[/C][C]146.251344082893[/C][C]118.949231605967[/C][/ROW]
[ROW][C]Median[/C][C]17359.5[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]17885.5[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]17316.0677419355[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]17380.4[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]17316.0677419355[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]17380.4[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]17380.4[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]17316.0677419355[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]17380.4[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]17369.346875[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]60[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=18181&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=18181&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 Mean17435.1916666667334.08738549747852.1875186658261
Geometric Mean17249.0815032542
Harmonic Mean17065.1298436409
Quadratic Mean17623.0291647369
Winsorized Mean ( 1 / 20 )17457.2333333333325.48960179930953.6337665990853
Winsorized Mean ( 2 / 20 )17449.3566666667320.09782048623554.5125756875219
Winsorized Mean ( 3 / 20 )17413.2916666667300.70213607499757.9087727608416
Winsorized Mean ( 4 / 20 )17380.885290.14525994589059.9040804707319
Winsorized Mean ( 5 / 20 )17362.1433333333284.52791951779161.0208775390414
Winsorized Mean ( 6 / 20 )17292.2233333333265.63868322341665.0967815511631
Winsorized Mean ( 7 / 20 )17242.2666666667251.17305125367868.6469610517747
Winsorized Mean ( 8 / 20 )17202.1333333333242.5469777394670.9228929325666
Winsorized Mean ( 9 / 20 )17202.8683333333239.2709987064671.897005597565
Winsorized Mean ( 10 / 20 )17208.985233.28044556176873.7695135936432
Winsorized Mean ( 11 / 20 )17186.05227.942870475475.3963041886618
Winsorized Mean ( 12 / 20 )17226.45217.53888722433679.1879108135518
Winsorized Mean ( 13 / 20 )17260.6616666667210.89547295909981.8446286422382
Winsorized Mean ( 14 / 20 )17291.975190.07119859306590.9763032379324
Winsorized Mean ( 15 / 20 )17339.325176.74393795092798.1042133666518
Winsorized Mean ( 16 / 20 )17326.0983333333172.981751747998100.161422567706
Winsorized Mean ( 17 / 20 )17281.5866666667163.141222858776105.930226363612
Winsorized Mean ( 18 / 20 )17463.8066666667130.033937027638134.301914299148
Winsorized Mean ( 19 / 20 )17449.4616666667124.207836872843140.485995940259
Winsorized Mean ( 20 / 20 )17449.7283333333113.935594382022153.154318700660
Trimmed Mean ( 1 / 20 )17419.6637931034312.10283698032855.8138591806566
Trimmed Mean ( 2 / 20 )17379.4107142857295.44570329472658.8243813346259
Trimmed Mean ( 3 / 20 )17340.5518518519278.3123833331362.3060736434995
Trimmed Mean ( 4 / 20 )17312.575266.77129537067564.8966935364781
Trimmed Mean ( 5 / 20 )17292.082256.60601148874867.3876730310282
Trimmed Mean ( 6 / 20 )17274.5666666667245.70653916711370.3056854946693
Trimmed Mean ( 7 / 20 )17270.7282608696238.00887115897172.5633804184303
Trimmed Mean ( 8 / 20 )17276.2727272727232.30252097470174.3697169311143
Trimmed Mean ( 9 / 20 )17289.5119047619227.06392483293976.1438080376817
Trimmed Mean ( 10 / 20 )17303.9525220.82410836041778.3607941563946
Trimmed Mean ( 11 / 20 )17318.9473684211213.93579591964780.9539483281513
Trimmed Mean ( 12 / 20 )17339.0833333333205.80590465020484.2496883789779
Trimmed Mean ( 13 / 20 )17355.6470588235197.54045188004287.8586987811633
Trimmed Mean ( 14 / 20 )17369.346875187.81374755285292.481765053499
Trimmed Mean ( 15 / 20 )17380.4180.44300650815296.3207183051162
Trimmed Mean ( 16 / 20 )17386.2678571429173.797463164672100.037523796705
Trimmed Mean ( 17 / 20 )17394.9461538462164.675371679768105.631740656841
Trimmed Mean ( 18 / 20 )17411.6166666667153.871128987048113.157138582718
Trimmed Mean ( 19 / 20 )17403.7090909091150.464992104072115.666168239796
Trimmed Mean ( 20 / 20 )17396.485146.251344082893118.949231605967
Median17359.5
Midrange17885.5
Midmean - Weighted Average at Xnp17316.0677419355
Midmean - Weighted Average at X(n+1)p17380.4
Midmean - Empirical Distribution Function17316.0677419355
Midmean - Empirical Distribution Function - Averaging17380.4
Midmean - Empirical Distribution Function - Interpolation17380.4
Midmean - Closest Observation17316.0677419355
Midmean - True Basic - Statistics Graphics Toolkit17380.4
Midmean - MS Excel (old versions)17369.346875
Number of observations60



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')