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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 computationThu, 22 Oct 2009 09:41:14 -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/2009/Oct/22/t12562261254pt0gvqb442o99h.htm/, Retrieved Fri, 03 May 2024 03:48:51 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=49768, Retrieved Fri, 03 May 2024 03:48:51 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact128
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [] [2009-10-22 15:41:14] [60d430b39377ac0bf942b21543df0c0d] [Current]
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Dataseries X:
17316
14553
11941
10497
8800
7390
6301
5306
4122
3867
11940
14137
15645
13264
11158
9645
7466
7004
5319
4663
3557
3368
9916
11745
13258
10455
7959
6002
5990
4793
3586
3180
1555
1571
7803
9239
10035
8032
5866
5523
4995
4529
3269
3188
1230
1273
6598
7740
9016
6774
5663
5452
5758
5312
5067
4395
2620
3020
8477
10289




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time4 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 4 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=49768&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]4 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=49768&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=49768&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 time4 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean7140.53333333333487.76987399917114.6391438134317
Geometric Mean6094.15955540009
Harmonic Mean4954.47403369328
Quadratic Mean8063.77478810844
Winsorized Mean ( 1 / 20 )7113.4478.48337802984114.8665561367868
Winsorized Mean ( 2 / 20 )7086.4466.11638977143815.2030697815085
Winsorized Mean ( 3 / 20 )7066.4460.4237112685515.3476022781946
Winsorized Mean ( 4 / 20 )7078.13333333333432.56819812182816.3630460215659
Winsorized Mean ( 5 / 20 )7110.96666666667426.82634633381116.6600930981551
Winsorized Mean ( 6 / 20 )6995.26666666667394.04994009884317.7522338029336
Winsorized Mean ( 7 / 20 )6996.08333333333393.87206567562717.7623242240666
Winsorized Mean ( 8 / 20 )6980.88333333333386.62714786240618.0558539976549
Winsorized Mean ( 9 / 20 )6907.68333333333366.33655722454718.8561124930244
Winsorized Mean ( 10 / 20 )6829.01666666667340.26521684107220.0696877866782
Winsorized Mean ( 11 / 20 )6826.63333333333337.99601756643820.1973780119804
Winsorized Mean ( 12 / 20 )6849.63333333333323.01127734477321.2055547708392
Winsorized Mean ( 13 / 20 )6849.85304.64670825446722.4845692219934
Winsorized Mean ( 14 / 20 )6885.78333333333290.25881018144323.7229089757137
Winsorized Mean ( 15 / 20 )6851.53333333333273.55041001125525.0466937083056
Winsorized Mean ( 16 / 20 )6779250.00274122790927.1157026787162
Winsorized Mean ( 17 / 20 )6752.65234.30474485262128.8199455979752
Winsorized Mean ( 18 / 20 )6748.45215.28084590365831.347191951392
Winsorized Mean ( 19 / 20 )6668.96666666667195.85233825320234.0509933460426
Winsorized Mean ( 20 / 20 )6600.3162.17973969057240.6974386109691
Trimmed Mean ( 1 / 20 )7067461.27952453801315.3204285559344
Trimmed Mean ( 2 / 20 )7017.28571428571439.95121756915.9501450025767
Trimmed Mean ( 3 / 20 )6978.88888888889421.90734396896316.5412832666934
Trimmed Mean ( 4 / 20 )6945.23076923077402.15759220842617.2699232932330
Trimmed Mean ( 5 / 20 )6905.36388.71632987334617.7645225304786
Trimmed Mean ( 6 / 20 )6853.95833333333373.44064910341218.3535411846271
Trimmed Mean ( 7 / 20 )6823.23913043478364.61725837660318.7134288728244
Trimmed Mean ( 8 / 20 )6789.56818181818352.99354275087419.23425604023
Trimmed Mean ( 9 / 20 )6755.40476190476339.73402703934019.8843925666666
Trimmed Mean ( 10 / 20 )6730.025328.03685394796320.5160637257776
Trimmed Mean ( 11 / 20 )6714.3947368421319.58508515954721.0097249484908
Trimmed Mean ( 12 / 20 )6697.38888888889308.36472498572221.7190500281736
Trimmed Mean ( 13 / 20 )6675296.87030304005622.4845662622555
Trimmed Mean ( 14 / 20 )6649.78125285.84960634630423.2632163989894
Trimmed Mean ( 15 / 20 )6616.06666666667273.90323374494624.1547592418256
Trimmed Mean ( 16 / 20 )6582.42857142857261.52793526150625.1691222386881
Trimmed Mean ( 17 / 20 )6554.07692307692250.98436925328126.1134864397187
Trimmed Mean ( 18 / 20 )6524.875239.87703154466727.2009160609652
Trimmed Mean ( 19 / 20 )6491228.96657537879328.3491159758211
Trimmed Mean ( 20 / 20 )6462.9219.04641301019229.5047059259505
Median6151.5
Midrange9273
Midmean - Weighted Average at Xnp6544.41935483871
Midmean - Weighted Average at X(n+1)p6616.06666666667
Midmean - Empirical Distribution Function6544.41935483871
Midmean - Empirical Distribution Function - Averaging6616.06666666667
Midmean - Empirical Distribution Function - Interpolation6616.06666666667
Midmean - Closest Observation6544.41935483871
Midmean - True Basic - Statistics Graphics Toolkit6616.06666666667
Midmean - MS Excel (old versions)6649.78125
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 7140.53333333333 & 487.769873999171 & 14.6391438134317 \tabularnewline
Geometric Mean & 6094.15955540009 &  &  \tabularnewline
Harmonic Mean & 4954.47403369328 &  &  \tabularnewline
Quadratic Mean & 8063.77478810844 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 7113.4 & 478.483378029841 & 14.8665561367868 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 7086.4 & 466.116389771438 & 15.2030697815085 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 7066.4 & 460.42371126855 & 15.3476022781946 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 7078.13333333333 & 432.568198121828 & 16.3630460215659 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 7110.96666666667 & 426.826346333811 & 16.6600930981551 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 6995.26666666667 & 394.049940098843 & 17.7522338029336 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 6996.08333333333 & 393.872065675627 & 17.7623242240666 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 6980.88333333333 & 386.627147862406 & 18.0558539976549 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 6907.68333333333 & 366.336557224547 & 18.8561124930244 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 6829.01666666667 & 340.265216841072 & 20.0696877866782 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 6826.63333333333 & 337.996017566438 & 20.1973780119804 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 6849.63333333333 & 323.011277344773 & 21.2055547708392 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 6849.85 & 304.646708254467 & 22.4845692219934 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 6885.78333333333 & 290.258810181443 & 23.7229089757137 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 6851.53333333333 & 273.550410011255 & 25.0466937083056 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 6779 & 250.002741227909 & 27.1157026787162 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 6752.65 & 234.304744852621 & 28.8199455979752 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 6748.45 & 215.280845903658 & 31.347191951392 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 6668.96666666667 & 195.852338253202 & 34.0509933460426 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 6600.3 & 162.179739690572 & 40.6974386109691 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 7067 & 461.279524538013 & 15.3204285559344 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 7017.28571428571 & 439.951217569 & 15.9501450025767 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 6978.88888888889 & 421.907343968963 & 16.5412832666934 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 6945.23076923077 & 402.157592208426 & 17.2699232932330 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 6905.36 & 388.716329873346 & 17.7645225304786 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 6853.95833333333 & 373.440649103412 & 18.3535411846271 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 6823.23913043478 & 364.617258376603 & 18.7134288728244 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 6789.56818181818 & 352.993542750874 & 19.23425604023 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 6755.40476190476 & 339.734027039340 & 19.8843925666666 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 6730.025 & 328.036853947963 & 20.5160637257776 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 6714.3947368421 & 319.585085159547 & 21.0097249484908 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 6697.38888888889 & 308.364724985722 & 21.7190500281736 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 6675 & 296.870303040056 & 22.4845662622555 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 6649.78125 & 285.849606346304 & 23.2632163989894 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 6616.06666666667 & 273.903233744946 & 24.1547592418256 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 6582.42857142857 & 261.527935261506 & 25.1691222386881 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 6554.07692307692 & 250.984369253281 & 26.1134864397187 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 6524.875 & 239.877031544667 & 27.2009160609652 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 6491 & 228.966575378793 & 28.3491159758211 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 6462.9 & 219.046413010192 & 29.5047059259505 \tabularnewline
Median & 6151.5 &  &  \tabularnewline
Midrange & 9273 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 6544.41935483871 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 6616.06666666667 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 6544.41935483871 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 6616.06666666667 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 6616.06666666667 &  &  \tabularnewline
Midmean - Closest Observation & 6544.41935483871 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 6616.06666666667 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 6649.78125 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=49768&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]7140.53333333333[/C][C]487.769873999171[/C][C]14.6391438134317[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]6094.15955540009[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]4954.47403369328[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]8063.77478810844[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]7113.4[/C][C]478.483378029841[/C][C]14.8665561367868[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]7086.4[/C][C]466.116389771438[/C][C]15.2030697815085[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]7066.4[/C][C]460.42371126855[/C][C]15.3476022781946[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]7078.13333333333[/C][C]432.568198121828[/C][C]16.3630460215659[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]7110.96666666667[/C][C]426.826346333811[/C][C]16.6600930981551[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]6995.26666666667[/C][C]394.049940098843[/C][C]17.7522338029336[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]6996.08333333333[/C][C]393.872065675627[/C][C]17.7623242240666[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]6980.88333333333[/C][C]386.627147862406[/C][C]18.0558539976549[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]6907.68333333333[/C][C]366.336557224547[/C][C]18.8561124930244[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]6829.01666666667[/C][C]340.265216841072[/C][C]20.0696877866782[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]6826.63333333333[/C][C]337.996017566438[/C][C]20.1973780119804[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]6849.63333333333[/C][C]323.011277344773[/C][C]21.2055547708392[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]6849.85[/C][C]304.646708254467[/C][C]22.4845692219934[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]6885.78333333333[/C][C]290.258810181443[/C][C]23.7229089757137[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]6851.53333333333[/C][C]273.550410011255[/C][C]25.0466937083056[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]6779[/C][C]250.002741227909[/C][C]27.1157026787162[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]6752.65[/C][C]234.304744852621[/C][C]28.8199455979752[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]6748.45[/C][C]215.280845903658[/C][C]31.347191951392[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]6668.96666666667[/C][C]195.852338253202[/C][C]34.0509933460426[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]6600.3[/C][C]162.179739690572[/C][C]40.6974386109691[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]7067[/C][C]461.279524538013[/C][C]15.3204285559344[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]7017.28571428571[/C][C]439.951217569[/C][C]15.9501450025767[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]6978.88888888889[/C][C]421.907343968963[/C][C]16.5412832666934[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]6945.23076923077[/C][C]402.157592208426[/C][C]17.2699232932330[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]6905.36[/C][C]388.716329873346[/C][C]17.7645225304786[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]6853.95833333333[/C][C]373.440649103412[/C][C]18.3535411846271[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]6823.23913043478[/C][C]364.617258376603[/C][C]18.7134288728244[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]6789.56818181818[/C][C]352.993542750874[/C][C]19.23425604023[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]6755.40476190476[/C][C]339.734027039340[/C][C]19.8843925666666[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]6730.025[/C][C]328.036853947963[/C][C]20.5160637257776[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]6714.3947368421[/C][C]319.585085159547[/C][C]21.0097249484908[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]6697.38888888889[/C][C]308.364724985722[/C][C]21.7190500281736[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]6675[/C][C]296.870303040056[/C][C]22.4845662622555[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]6649.78125[/C][C]285.849606346304[/C][C]23.2632163989894[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]6616.06666666667[/C][C]273.903233744946[/C][C]24.1547592418256[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]6582.42857142857[/C][C]261.527935261506[/C][C]25.1691222386881[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]6554.07692307692[/C][C]250.984369253281[/C][C]26.1134864397187[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]6524.875[/C][C]239.877031544667[/C][C]27.2009160609652[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]6491[/C][C]228.966575378793[/C][C]28.3491159758211[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]6462.9[/C][C]219.046413010192[/C][C]29.5047059259505[/C][/ROW]
[ROW][C]Median[/C][C]6151.5[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]9273[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]6544.41935483871[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]6616.06666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]6544.41935483871[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]6616.06666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]6616.06666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]6544.41935483871[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]6616.06666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]6649.78125[/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=49768&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=49768&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 Mean7140.53333333333487.76987399917114.6391438134317
Geometric Mean6094.15955540009
Harmonic Mean4954.47403369328
Quadratic Mean8063.77478810844
Winsorized Mean ( 1 / 20 )7113.4478.48337802984114.8665561367868
Winsorized Mean ( 2 / 20 )7086.4466.11638977143815.2030697815085
Winsorized Mean ( 3 / 20 )7066.4460.4237112685515.3476022781946
Winsorized Mean ( 4 / 20 )7078.13333333333432.56819812182816.3630460215659
Winsorized Mean ( 5 / 20 )7110.96666666667426.82634633381116.6600930981551
Winsorized Mean ( 6 / 20 )6995.26666666667394.04994009884317.7522338029336
Winsorized Mean ( 7 / 20 )6996.08333333333393.87206567562717.7623242240666
Winsorized Mean ( 8 / 20 )6980.88333333333386.62714786240618.0558539976549
Winsorized Mean ( 9 / 20 )6907.68333333333366.33655722454718.8561124930244
Winsorized Mean ( 10 / 20 )6829.01666666667340.26521684107220.0696877866782
Winsorized Mean ( 11 / 20 )6826.63333333333337.99601756643820.1973780119804
Winsorized Mean ( 12 / 20 )6849.63333333333323.01127734477321.2055547708392
Winsorized Mean ( 13 / 20 )6849.85304.64670825446722.4845692219934
Winsorized Mean ( 14 / 20 )6885.78333333333290.25881018144323.7229089757137
Winsorized Mean ( 15 / 20 )6851.53333333333273.55041001125525.0466937083056
Winsorized Mean ( 16 / 20 )6779250.00274122790927.1157026787162
Winsorized Mean ( 17 / 20 )6752.65234.30474485262128.8199455979752
Winsorized Mean ( 18 / 20 )6748.45215.28084590365831.347191951392
Winsorized Mean ( 19 / 20 )6668.96666666667195.85233825320234.0509933460426
Winsorized Mean ( 20 / 20 )6600.3162.17973969057240.6974386109691
Trimmed Mean ( 1 / 20 )7067461.27952453801315.3204285559344
Trimmed Mean ( 2 / 20 )7017.28571428571439.95121756915.9501450025767
Trimmed Mean ( 3 / 20 )6978.88888888889421.90734396896316.5412832666934
Trimmed Mean ( 4 / 20 )6945.23076923077402.15759220842617.2699232932330
Trimmed Mean ( 5 / 20 )6905.36388.71632987334617.7645225304786
Trimmed Mean ( 6 / 20 )6853.95833333333373.44064910341218.3535411846271
Trimmed Mean ( 7 / 20 )6823.23913043478364.61725837660318.7134288728244
Trimmed Mean ( 8 / 20 )6789.56818181818352.99354275087419.23425604023
Trimmed Mean ( 9 / 20 )6755.40476190476339.73402703934019.8843925666666
Trimmed Mean ( 10 / 20 )6730.025328.03685394796320.5160637257776
Trimmed Mean ( 11 / 20 )6714.3947368421319.58508515954721.0097249484908
Trimmed Mean ( 12 / 20 )6697.38888888889308.36472498572221.7190500281736
Trimmed Mean ( 13 / 20 )6675296.87030304005622.4845662622555
Trimmed Mean ( 14 / 20 )6649.78125285.84960634630423.2632163989894
Trimmed Mean ( 15 / 20 )6616.06666666667273.90323374494624.1547592418256
Trimmed Mean ( 16 / 20 )6582.42857142857261.52793526150625.1691222386881
Trimmed Mean ( 17 / 20 )6554.07692307692250.98436925328126.1134864397187
Trimmed Mean ( 18 / 20 )6524.875239.87703154466727.2009160609652
Trimmed Mean ( 19 / 20 )6491228.96657537879328.3491159758211
Trimmed Mean ( 20 / 20 )6462.9219.04641301019229.5047059259505
Median6151.5
Midrange9273
Midmean - Weighted Average at Xnp6544.41935483871
Midmean - Weighted Average at X(n+1)p6616.06666666667
Midmean - Empirical Distribution Function6544.41935483871
Midmean - Empirical Distribution Function - Averaging6616.06666666667
Midmean - Empirical Distribution Function - Interpolation6616.06666666667
Midmean - Closest Observation6544.41935483871
Midmean - True Basic - Statistics Graphics Toolkit6616.06666666667
Midmean - MS Excel (old versions)6649.78125
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')