Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationWed, 12 Oct 2016 10:03:34 +0100
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2016/Oct/12/t14762632004t1wb3qsjpjxhu1.htm/, Retrieved Sun, 05 May 2024 16:34:50 +0200
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=, Retrieved Sun, 05 May 2024 16:34:50 +0200
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact0
Dataseries X:
12347
12624
11918
10028
10228
11026
13878
22165
23533
13445
12164
9606
12177
13142
11210
9485
10082
10680
13579
21709
22205
14687
11222
8196
12794
12627
11080
10425
10865
10771
14771
20993
23882
14825
11648
10091
14976
14472
12254
12257
10767
12275
14845
21939
26740
16974
12956
12494
16024
15306
13989
12792
10697
14257
17251
25795
29016
18968
16009
14511




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Herman Ole Andreas Wold' @ wold.wessa.net

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 1 seconds \tabularnewline
R Server & 'Herman Ole Andreas Wold' @ wold.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Herman Ole Andreas Wold' @ wold.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&T=0

As an alternative you can also use a QR Code:  

The GUIDs for individual cells are displayed in the table below:

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Herman Ole Andreas Wold' @ wold.wessa.net







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean14561.2613.34924190250123.740471178922
Geometric Mean13926.7797686408
Harmonic Mean13403.3181939073
Quadratic Mean15304.3845253574
Winsorized Mean ( 1 / 20 )14544.75595.73724473117124.4147065315068
Winsorized Mean ( 2 / 20 )14517.2833333333584.54174532636324.8353234810082
Winsorized Mean ( 3 / 20 )14442.7333333333552.05771717141326.1616365175254
Winsorized Mean ( 4 / 20 )14423.0666666667544.90236614024326.4690843037275
Winsorized Mean ( 5 / 20 )14313.15514.70319944308627.8085506666502
Winsorized Mean ( 6 / 20 )14322.85511.78260624929627.9861992672396
Winsorized Mean ( 7 / 20 )14319.4666666667501.8959063676728.530750071862
Winsorized Mean ( 8 / 20 )14322.8489.64926326601329.2511417345252
Winsorized Mean ( 9 / 20 )14217.95462.24290788483830.7586114518435
Winsorized Mean ( 10 / 20 )13892.1166666667380.21435531025536.537591157837
Winsorized Mean ( 11 / 20 )13578.0666666667312.74840871906743.4153021666161
Winsorized Mean ( 12 / 20 )13541.4666666667298.9855498526945.2913750291227
Winsorized Mean ( 13 / 20 )13370.5166666667255.3261606267152.3664188340438
Winsorized Mean ( 14 / 20 )13379.6166666667252.75731431314652.9346369383019
Winsorized Mean ( 15 / 20 )13236.3666666667217.95827228105860.7289025011095
Winsorized Mean ( 16 / 20 )13151.5666666667203.67412679245864.571611887002
Winsorized Mean ( 17 / 20 )13235.15179.2436554992273.8388757088118
Winsorized Mean ( 18 / 20 )13310.15166.49413356421779.9436575635635
Winsorized Mean ( 19 / 20 )13370.95153.113606551887.3269874645429
Winsorized Mean ( 20 / 20 )13347.2833333333148.21926057139690.0509372525444
Trimmed Mean ( 1 / 20 )14421.724137931571.86323122643425.2188344178062
Trimmed Mean ( 2 / 20 )14289.9107142857541.78305446166326.3757062842889
Trimmed Mean ( 3 / 20 )14163.5925925926511.53746927547727.688279829537
Trimmed Mean ( 4 / 20 )14056.2307692308490.00233063085428.6860488013068
Trimmed Mean ( 5 / 20 )13946.18465.34693372421729.9694249371912
Trimmed Mean ( 6 / 20 )13854.4375445.16089599283531.1223147062382
Trimmed Mean ( 7 / 20 )13752.6086956522419.55464941260132.7790639786892
Trimmed Mean ( 8 / 20 )13642.1818181818388.62493572703935.1037222885867
Trimmed Mean ( 9 / 20 )13520.6428571429350.27699644840538.5998595232742
Trimmed Mean ( 10 / 20 )13404.425306.89687545405543.6772938146344
Trimmed Mean ( 11 / 20 )13327.4210526316278.17094284744447.9109029728554
Trimmed Mean ( 12 / 20 )13289.4444444444262.487032013650.6289561907039
Trimmed Mean ( 13 / 20 )13252.3823529412244.93571863873454.1055523734686
Trimmed Mean ( 14 / 20 )13235.34375234.74587584998956.3815815808318
Trimmed Mean ( 15 / 20 )13214.7333333333220.53582049772659.9210291711753
Trimmed Mean ( 16 / 20 )13211.6428571429211.82234753703362.371336220004
Trimmed Mean ( 17 / 20 )13220.3076923077203.23217317397865.0502697768743
Trimmed Mean ( 18 / 20 )13218.125198.43255628327766.6126831583531
Trimmed Mean ( 19 / 20 )13204.1818181818194.39447149296467.9246776761331
Trimmed Mean ( 20 / 20 )13177.85191.31023681582368.8820954870622
Median12875
Midrange18606
Midmean - Weighted Average at Xnp13145.8709677419
Midmean - Weighted Average at X(n+1)p13214.7333333333
Midmean - Empirical Distribution Function13145.8709677419
Midmean - Empirical Distribution Function - Averaging13214.7333333333
Midmean - Empirical Distribution Function - Interpolation13214.7333333333
Midmean - Closest Observation13145.8709677419
Midmean - True Basic - Statistics Graphics Toolkit13214.7333333333
Midmean - MS Excel (old versions)13235.34375
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 14561.2 & 613.349241902501 & 23.740471178922 \tabularnewline
Geometric Mean & 13926.7797686408 &  &  \tabularnewline
Harmonic Mean & 13403.3181939073 &  &  \tabularnewline
Quadratic Mean & 15304.3845253574 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 14544.75 & 595.737244731171 & 24.4147065315068 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 14517.2833333333 & 584.541745326363 & 24.8353234810082 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 14442.7333333333 & 552.057717171413 & 26.1616365175254 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 14423.0666666667 & 544.902366140243 & 26.4690843037275 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 14313.15 & 514.703199443086 & 27.8085506666502 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 14322.85 & 511.782606249296 & 27.9861992672396 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 14319.4666666667 & 501.89590636767 & 28.530750071862 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 14322.8 & 489.649263266013 & 29.2511417345252 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 14217.95 & 462.242907884838 & 30.7586114518435 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 13892.1166666667 & 380.214355310255 & 36.537591157837 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 13578.0666666667 & 312.748408719067 & 43.4153021666161 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 13541.4666666667 & 298.98554985269 & 45.2913750291227 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 13370.5166666667 & 255.32616062671 & 52.3664188340438 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 13379.6166666667 & 252.757314313146 & 52.9346369383019 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 13236.3666666667 & 217.958272281058 & 60.7289025011095 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 13151.5666666667 & 203.674126792458 & 64.571611887002 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 13235.15 & 179.24365549922 & 73.8388757088118 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 13310.15 & 166.494133564217 & 79.9436575635635 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 13370.95 & 153.1136065518 & 87.3269874645429 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 13347.2833333333 & 148.219260571396 & 90.0509372525444 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 14421.724137931 & 571.863231226434 & 25.2188344178062 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 14289.9107142857 & 541.783054461663 & 26.3757062842889 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 14163.5925925926 & 511.537469275477 & 27.688279829537 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 14056.2307692308 & 490.002330630854 & 28.6860488013068 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 13946.18 & 465.346933724217 & 29.9694249371912 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 13854.4375 & 445.160895992835 & 31.1223147062382 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 13752.6086956522 & 419.554649412601 & 32.7790639786892 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 13642.1818181818 & 388.624935727039 & 35.1037222885867 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 13520.6428571429 & 350.276996448405 & 38.5998595232742 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 13404.425 & 306.896875454055 & 43.6772938146344 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 13327.4210526316 & 278.170942847444 & 47.9109029728554 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 13289.4444444444 & 262.4870320136 & 50.6289561907039 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 13252.3823529412 & 244.935718638734 & 54.1055523734686 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 13235.34375 & 234.745875849989 & 56.3815815808318 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 13214.7333333333 & 220.535820497726 & 59.9210291711753 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 13211.6428571429 & 211.822347537033 & 62.371336220004 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 13220.3076923077 & 203.232173173978 & 65.0502697768743 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 13218.125 & 198.432556283277 & 66.6126831583531 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 13204.1818181818 & 194.394471492964 & 67.9246776761331 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 13177.85 & 191.310236815823 & 68.8820954870622 \tabularnewline
Median & 12875 &  &  \tabularnewline
Midrange & 18606 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 13145.8709677419 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 13214.7333333333 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 13145.8709677419 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 13214.7333333333 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 13214.7333333333 &  &  \tabularnewline
Midmean - Closest Observation & 13145.8709677419 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 13214.7333333333 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 13235.34375 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&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]14561.2[/C][C]613.349241902501[/C][C]23.740471178922[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]13926.7797686408[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]13403.3181939073[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]15304.3845253574[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]14544.75[/C][C]595.737244731171[/C][C]24.4147065315068[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]14517.2833333333[/C][C]584.541745326363[/C][C]24.8353234810082[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]14442.7333333333[/C][C]552.057717171413[/C][C]26.1616365175254[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]14423.0666666667[/C][C]544.902366140243[/C][C]26.4690843037275[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]14313.15[/C][C]514.703199443086[/C][C]27.8085506666502[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]14322.85[/C][C]511.782606249296[/C][C]27.9861992672396[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]14319.4666666667[/C][C]501.89590636767[/C][C]28.530750071862[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]14322.8[/C][C]489.649263266013[/C][C]29.2511417345252[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]14217.95[/C][C]462.242907884838[/C][C]30.7586114518435[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]13892.1166666667[/C][C]380.214355310255[/C][C]36.537591157837[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]13578.0666666667[/C][C]312.748408719067[/C][C]43.4153021666161[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]13541.4666666667[/C][C]298.98554985269[/C][C]45.2913750291227[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]13370.5166666667[/C][C]255.32616062671[/C][C]52.3664188340438[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]13379.6166666667[/C][C]252.757314313146[/C][C]52.9346369383019[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]13236.3666666667[/C][C]217.958272281058[/C][C]60.7289025011095[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]13151.5666666667[/C][C]203.674126792458[/C][C]64.571611887002[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]13235.15[/C][C]179.24365549922[/C][C]73.8388757088118[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]13310.15[/C][C]166.494133564217[/C][C]79.9436575635635[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]13370.95[/C][C]153.1136065518[/C][C]87.3269874645429[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]13347.2833333333[/C][C]148.219260571396[/C][C]90.0509372525444[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]14421.724137931[/C][C]571.863231226434[/C][C]25.2188344178062[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]14289.9107142857[/C][C]541.783054461663[/C][C]26.3757062842889[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]14163.5925925926[/C][C]511.537469275477[/C][C]27.688279829537[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]14056.2307692308[/C][C]490.002330630854[/C][C]28.6860488013068[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]13946.18[/C][C]465.346933724217[/C][C]29.9694249371912[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]13854.4375[/C][C]445.160895992835[/C][C]31.1223147062382[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]13752.6086956522[/C][C]419.554649412601[/C][C]32.7790639786892[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]13642.1818181818[/C][C]388.624935727039[/C][C]35.1037222885867[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]13520.6428571429[/C][C]350.276996448405[/C][C]38.5998595232742[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]13404.425[/C][C]306.896875454055[/C][C]43.6772938146344[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]13327.4210526316[/C][C]278.170942847444[/C][C]47.9109029728554[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]13289.4444444444[/C][C]262.4870320136[/C][C]50.6289561907039[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]13252.3823529412[/C][C]244.935718638734[/C][C]54.1055523734686[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]13235.34375[/C][C]234.745875849989[/C][C]56.3815815808318[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]13214.7333333333[/C][C]220.535820497726[/C][C]59.9210291711753[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]13211.6428571429[/C][C]211.822347537033[/C][C]62.371336220004[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]13220.3076923077[/C][C]203.232173173978[/C][C]65.0502697768743[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]13218.125[/C][C]198.432556283277[/C][C]66.6126831583531[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]13204.1818181818[/C][C]194.394471492964[/C][C]67.9246776761331[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]13177.85[/C][C]191.310236815823[/C][C]68.8820954870622[/C][/ROW]
[ROW][C]Median[/C][C]12875[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]18606[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]13145.8709677419[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]13214.7333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]13145.8709677419[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]13214.7333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]13214.7333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]13145.8709677419[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]13214.7333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]13235.34375[/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=&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&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 Mean14561.2613.34924190250123.740471178922
Geometric Mean13926.7797686408
Harmonic Mean13403.3181939073
Quadratic Mean15304.3845253574
Winsorized Mean ( 1 / 20 )14544.75595.73724473117124.4147065315068
Winsorized Mean ( 2 / 20 )14517.2833333333584.54174532636324.8353234810082
Winsorized Mean ( 3 / 20 )14442.7333333333552.05771717141326.1616365175254
Winsorized Mean ( 4 / 20 )14423.0666666667544.90236614024326.4690843037275
Winsorized Mean ( 5 / 20 )14313.15514.70319944308627.8085506666502
Winsorized Mean ( 6 / 20 )14322.85511.78260624929627.9861992672396
Winsorized Mean ( 7 / 20 )14319.4666666667501.8959063676728.530750071862
Winsorized Mean ( 8 / 20 )14322.8489.64926326601329.2511417345252
Winsorized Mean ( 9 / 20 )14217.95462.24290788483830.7586114518435
Winsorized Mean ( 10 / 20 )13892.1166666667380.21435531025536.537591157837
Winsorized Mean ( 11 / 20 )13578.0666666667312.74840871906743.4153021666161
Winsorized Mean ( 12 / 20 )13541.4666666667298.9855498526945.2913750291227
Winsorized Mean ( 13 / 20 )13370.5166666667255.3261606267152.3664188340438
Winsorized Mean ( 14 / 20 )13379.6166666667252.75731431314652.9346369383019
Winsorized Mean ( 15 / 20 )13236.3666666667217.95827228105860.7289025011095
Winsorized Mean ( 16 / 20 )13151.5666666667203.67412679245864.571611887002
Winsorized Mean ( 17 / 20 )13235.15179.2436554992273.8388757088118
Winsorized Mean ( 18 / 20 )13310.15166.49413356421779.9436575635635
Winsorized Mean ( 19 / 20 )13370.95153.113606551887.3269874645429
Winsorized Mean ( 20 / 20 )13347.2833333333148.21926057139690.0509372525444
Trimmed Mean ( 1 / 20 )14421.724137931571.86323122643425.2188344178062
Trimmed Mean ( 2 / 20 )14289.9107142857541.78305446166326.3757062842889
Trimmed Mean ( 3 / 20 )14163.5925925926511.53746927547727.688279829537
Trimmed Mean ( 4 / 20 )14056.2307692308490.00233063085428.6860488013068
Trimmed Mean ( 5 / 20 )13946.18465.34693372421729.9694249371912
Trimmed Mean ( 6 / 20 )13854.4375445.16089599283531.1223147062382
Trimmed Mean ( 7 / 20 )13752.6086956522419.55464941260132.7790639786892
Trimmed Mean ( 8 / 20 )13642.1818181818388.62493572703935.1037222885867
Trimmed Mean ( 9 / 20 )13520.6428571429350.27699644840538.5998595232742
Trimmed Mean ( 10 / 20 )13404.425306.89687545405543.6772938146344
Trimmed Mean ( 11 / 20 )13327.4210526316278.17094284744447.9109029728554
Trimmed Mean ( 12 / 20 )13289.4444444444262.487032013650.6289561907039
Trimmed Mean ( 13 / 20 )13252.3823529412244.93571863873454.1055523734686
Trimmed Mean ( 14 / 20 )13235.34375234.74587584998956.3815815808318
Trimmed Mean ( 15 / 20 )13214.7333333333220.53582049772659.9210291711753
Trimmed Mean ( 16 / 20 )13211.6428571429211.82234753703362.371336220004
Trimmed Mean ( 17 / 20 )13220.3076923077203.23217317397865.0502697768743
Trimmed Mean ( 18 / 20 )13218.125198.43255628327766.6126831583531
Trimmed Mean ( 19 / 20 )13204.1818181818194.39447149296467.9246776761331
Trimmed Mean ( 20 / 20 )13177.85191.31023681582368.8820954870622
Median12875
Midrange18606
Midmean - Weighted Average at Xnp13145.8709677419
Midmean - Weighted Average at X(n+1)p13214.7333333333
Midmean - Empirical Distribution Function13145.8709677419
Midmean - Empirical Distribution Function - Averaging13214.7333333333
Midmean - Empirical Distribution Function - Interpolation13214.7333333333
Midmean - Closest Observation13145.8709677419
Midmean - True Basic - Statistics Graphics Toolkit13214.7333333333
Midmean - MS Excel (old versions)13235.34375
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')