Free Statistics

of Irreproducible Research!

Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationMon, 20 Oct 2008 15:35:54 -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/t1224538623m3vjywiaxlce3yp.htm/, Retrieved Sun, 19 May 2024 14:56:02 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=18190, Retrieved Sun, 19 May 2024 14:56:02 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact117
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
F       [Central Tendency] [Q9] [2008-10-20 21:35:54] [d96f761aa3e94002e7c05c3c847d2c79] [Current]
Feedback Forum
2008-10-27 21:11:07 [Jan Helsen] [reply
Zowel je gemiddelde, als mediaan, als midrange liggen dicht bij elkaar. Je grafiek is dus stabiel en ondervindt weinig tot geen invloed van outliners. Je maakt een correct voorspelling met de lichte daling.
Hou er wel rekening mee dat er zich altijd omstandigheden kunnen voordoen diet het verloop van je grafiek serieus zullen beïnvloeden al is dat hoogst onwaarschijnlijk.

Post a new message
Dataseries X:
157928
147768
137507
136919
136151
133001
125554
119647
114158
116193
152803
161761
160942
149470
139208
134588
130322
126611
122401
117352
112135
112879
148729
157230
157221
146681
136524
132111
125326
122716
116615
113719
110737
112093
143565
149946
149147
134339
122683
115614
116566
111272
104609
101802
94542
93051
124129
130374
123946
114971
105531
104919
104782
101281
94545
93248
84031
87486
115867
120327




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'George Udny Yule' @ 72.249.76.132

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 2 seconds \tabularnewline
R Server & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=18190&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'George Udny Yule' @ 72.249.76.132[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=18190&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=18190&T=0

As an alternative you can also use a QR Code:  

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

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'George Udny Yule' @ 72.249.76.132







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean124459.552536.9669193660449.0584047627633
Geometric Mean122911.931074325
Harmonic Mean121344.291428492
Quadratic Mean125975.852662524
Winsorized Mean ( 1 / 20 )124503.4833333332518.6414031759149.432794671103
Winsorized Mean ( 2 / 20 )124588.5166666672451.3655861582450.8241273232201
Winsorized Mean ( 3 / 20 )124563.4666666672441.2406165147451.0246576367801
Winsorized Mean ( 4 / 20 )124649.1333333332422.6397674100351.4517820644015
Winsorized Mean ( 5 / 20 )124281.2166666672342.5837423414153.0530518163878
Winsorized Mean ( 6 / 20 )124669.1166666672149.5738119295157.9971322570035
Winsorized Mean ( 7 / 20 )124674.3666666672127.411200981258.603793478743
Winsorized Mean ( 8 / 20 )125005.5666666672053.2122450859860.8829247759684
Winsorized Mean ( 9 / 20 )124968.8166666672036.4000336102861.3675184659631
Winsorized Mean ( 10 / 20 )124831.4833333332001.1595166333562.3795765883488
Winsorized Mean ( 11 / 20 )124744.41943.8792983790664.1729144932098
Winsorized Mean ( 12 / 20 )125162.41661.0045402101975.3534364115352
Winsorized Mean ( 13 / 20 )124334.31473.9406682054284.3550237007722
Winsorized Mean ( 14 / 20 )124128.9666666671378.7519550860190.0299478878516
Winsorized Mean ( 15 / 20 )123992.4666666671353.2059103687391.6286765499569
Winsorized Mean ( 16 / 20 )124085.5333333331307.0287841652794.9371083763702
Winsorized Mean ( 17 / 20 )124217.851255.8309788179198.9128729066101
Winsorized Mean ( 18 / 20 )123880.651162.77191749049106.539079708220
Winsorized Mean ( 19 / 20 )124059.251114.40927845255111.322879662548
Winsorized Mean ( 20 / 20 )123827.5833333331015.87486225322121.892555800310
Trimmed Mean ( 1 / 20 )124513.4655172412444.6762809629250.9324962518954
Trimmed Mean ( 2 / 20 )124524.1607142862353.502495698252.9101460235945
Trimmed Mean ( 3 / 20 )124488.4074074072285.7987240331154.4616663306895
Trimmed Mean ( 4 / 20 )124459.5384615382205.9818819964256.4191118146909
Trimmed Mean ( 5 / 20 )124402.662112.8414037103358.8793175775229
Trimmed Mean ( 6 / 20 )124433.0208333332023.6783878948361.4885357167733
Trimmed Mean ( 7 / 20 )124381.6956521741972.2579918325663.0656314575774
Trimmed Mean ( 8 / 20 )124324.6818181821911.4211900921065.043059301959
Trimmed Mean ( 9 / 20 )124203.0952380951852.1112195495567.0602790626701
Trimmed Mean ( 10 / 20 )124075.4751777.2879219969669.8116908714423
Trimmed Mean ( 11 / 20 )123956.1052631581686.4462487473273.5013673606447
Trimmed Mean ( 12 / 20 )123836.6666666671579.2270135472878.4160007423525
Trimmed Mean ( 13 / 20 )123641.7058823531516.4829070453881.5318822968132
Trimmed Mean ( 14 / 20 )123541.81251484.0033593762983.2490113445047
Trimmed Mean ( 15 / 20 )123457.9333333331461.5119717350684.4727485788351
Trimmed Mean ( 16 / 20 )123381.5714285711431.3028229466586.2022832977883
Trimmed Mean ( 17 / 20 )123280.0384615381395.3037314569788.3535503290096
Trimmed Mean ( 18 / 20 )123142.1251351.2846387957291.129671325018
Trimmed Mean ( 19 / 20 )123030.2272727271312.5579895362093.7331746509734
Trimmed Mean ( 20 / 20 )122867.751259.2500417959797.572162733275
Median122699.5
Midrange122896
Midmean - Weighted Average at Xnp123091.322580645
Midmean - Weighted Average at X(n+1)p123457.933333333
Midmean - Empirical Distribution Function123091.322580645
Midmean - Empirical Distribution Function - Averaging123457.933333333
Midmean - Empirical Distribution Function - Interpolation123457.933333333
Midmean - Closest Observation123091.322580645
Midmean - True Basic - Statistics Graphics Toolkit123457.933333333
Midmean - MS Excel (old versions)123541.8125
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 124459.55 & 2536.96691936604 & 49.0584047627633 \tabularnewline
Geometric Mean & 122911.931074325 &  &  \tabularnewline
Harmonic Mean & 121344.291428492 &  &  \tabularnewline
Quadratic Mean & 125975.852662524 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 124503.483333333 & 2518.64140317591 & 49.432794671103 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 124588.516666667 & 2451.36558615824 & 50.8241273232201 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 124563.466666667 & 2441.24061651474 & 51.0246576367801 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 124649.133333333 & 2422.63976741003 & 51.4517820644015 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 124281.216666667 & 2342.58374234141 & 53.0530518163878 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 124669.116666667 & 2149.57381192951 & 57.9971322570035 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 124674.366666667 & 2127.4112009812 & 58.603793478743 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 125005.566666667 & 2053.21224508598 & 60.8829247759684 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 124968.816666667 & 2036.40003361028 & 61.3675184659631 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 124831.483333333 & 2001.15951663335 & 62.3795765883488 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 124744.4 & 1943.87929837906 & 64.1729144932098 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 125162.4 & 1661.00454021019 & 75.3534364115352 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 124334.3 & 1473.94066820542 & 84.3550237007722 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 124128.966666667 & 1378.75195508601 & 90.0299478878516 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 123992.466666667 & 1353.20591036873 & 91.6286765499569 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 124085.533333333 & 1307.02878416527 & 94.9371083763702 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 124217.85 & 1255.83097881791 & 98.9128729066101 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 123880.65 & 1162.77191749049 & 106.539079708220 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 124059.25 & 1114.40927845255 & 111.322879662548 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 123827.583333333 & 1015.87486225322 & 121.892555800310 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 124513.465517241 & 2444.67628096292 & 50.9324962518954 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 124524.160714286 & 2353.5024956982 & 52.9101460235945 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 124488.407407407 & 2285.79872403311 & 54.4616663306895 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 124459.538461538 & 2205.98188199642 & 56.4191118146909 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 124402.66 & 2112.84140371033 & 58.8793175775229 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 124433.020833333 & 2023.67838789483 & 61.4885357167733 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 124381.695652174 & 1972.25799183256 & 63.0656314575774 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 124324.681818182 & 1911.42119009210 & 65.043059301959 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 124203.095238095 & 1852.11121954955 & 67.0602790626701 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 124075.475 & 1777.28792199696 & 69.8116908714423 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 123956.105263158 & 1686.44624874732 & 73.5013673606447 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 123836.666666667 & 1579.22701354728 & 78.4160007423525 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 123641.705882353 & 1516.48290704538 & 81.5318822968132 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 123541.8125 & 1484.00335937629 & 83.2490113445047 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 123457.933333333 & 1461.51197173506 & 84.4727485788351 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 123381.571428571 & 1431.30282294665 & 86.2022832977883 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 123280.038461538 & 1395.30373145697 & 88.3535503290096 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 123142.125 & 1351.28463879572 & 91.129671325018 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 123030.227272727 & 1312.55798953620 & 93.7331746509734 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 122867.75 & 1259.25004179597 & 97.572162733275 \tabularnewline
Median & 122699.5 &  &  \tabularnewline
Midrange & 122896 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 123091.322580645 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 123457.933333333 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 123091.322580645 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 123457.933333333 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 123457.933333333 &  &  \tabularnewline
Midmean - Closest Observation & 123091.322580645 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 123457.933333333 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 123541.8125 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=18190&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]124459.55[/C][C]2536.96691936604[/C][C]49.0584047627633[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]122911.931074325[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]121344.291428492[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]125975.852662524[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]124503.483333333[/C][C]2518.64140317591[/C][C]49.432794671103[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]124588.516666667[/C][C]2451.36558615824[/C][C]50.8241273232201[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]124563.466666667[/C][C]2441.24061651474[/C][C]51.0246576367801[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]124649.133333333[/C][C]2422.63976741003[/C][C]51.4517820644015[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]124281.216666667[/C][C]2342.58374234141[/C][C]53.0530518163878[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]124669.116666667[/C][C]2149.57381192951[/C][C]57.9971322570035[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]124674.366666667[/C][C]2127.4112009812[/C][C]58.603793478743[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]125005.566666667[/C][C]2053.21224508598[/C][C]60.8829247759684[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]124968.816666667[/C][C]2036.40003361028[/C][C]61.3675184659631[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]124831.483333333[/C][C]2001.15951663335[/C][C]62.3795765883488[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]124744.4[/C][C]1943.87929837906[/C][C]64.1729144932098[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]125162.4[/C][C]1661.00454021019[/C][C]75.3534364115352[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]124334.3[/C][C]1473.94066820542[/C][C]84.3550237007722[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]124128.966666667[/C][C]1378.75195508601[/C][C]90.0299478878516[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]123992.466666667[/C][C]1353.20591036873[/C][C]91.6286765499569[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]124085.533333333[/C][C]1307.02878416527[/C][C]94.9371083763702[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]124217.85[/C][C]1255.83097881791[/C][C]98.9128729066101[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]123880.65[/C][C]1162.77191749049[/C][C]106.539079708220[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]124059.25[/C][C]1114.40927845255[/C][C]111.322879662548[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]123827.583333333[/C][C]1015.87486225322[/C][C]121.892555800310[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]124513.465517241[/C][C]2444.67628096292[/C][C]50.9324962518954[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]124524.160714286[/C][C]2353.5024956982[/C][C]52.9101460235945[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]124488.407407407[/C][C]2285.79872403311[/C][C]54.4616663306895[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]124459.538461538[/C][C]2205.98188199642[/C][C]56.4191118146909[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]124402.66[/C][C]2112.84140371033[/C][C]58.8793175775229[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]124433.020833333[/C][C]2023.67838789483[/C][C]61.4885357167733[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]124381.695652174[/C][C]1972.25799183256[/C][C]63.0656314575774[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]124324.681818182[/C][C]1911.42119009210[/C][C]65.043059301959[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]124203.095238095[/C][C]1852.11121954955[/C][C]67.0602790626701[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]124075.475[/C][C]1777.28792199696[/C][C]69.8116908714423[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]123956.105263158[/C][C]1686.44624874732[/C][C]73.5013673606447[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]123836.666666667[/C][C]1579.22701354728[/C][C]78.4160007423525[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]123641.705882353[/C][C]1516.48290704538[/C][C]81.5318822968132[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]123541.8125[/C][C]1484.00335937629[/C][C]83.2490113445047[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]123457.933333333[/C][C]1461.51197173506[/C][C]84.4727485788351[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]123381.571428571[/C][C]1431.30282294665[/C][C]86.2022832977883[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]123280.038461538[/C][C]1395.30373145697[/C][C]88.3535503290096[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]123142.125[/C][C]1351.28463879572[/C][C]91.129671325018[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]123030.227272727[/C][C]1312.55798953620[/C][C]93.7331746509734[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]122867.75[/C][C]1259.25004179597[/C][C]97.572162733275[/C][/ROW]
[ROW][C]Median[/C][C]122699.5[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]122896[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]123091.322580645[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]123457.933333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]123091.322580645[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]123457.933333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]123457.933333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]123091.322580645[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]123457.933333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]123541.8125[/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=18190&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=18190&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 Mean124459.552536.9669193660449.0584047627633
Geometric Mean122911.931074325
Harmonic Mean121344.291428492
Quadratic Mean125975.852662524
Winsorized Mean ( 1 / 20 )124503.4833333332518.6414031759149.432794671103
Winsorized Mean ( 2 / 20 )124588.5166666672451.3655861582450.8241273232201
Winsorized Mean ( 3 / 20 )124563.4666666672441.2406165147451.0246576367801
Winsorized Mean ( 4 / 20 )124649.1333333332422.6397674100351.4517820644015
Winsorized Mean ( 5 / 20 )124281.2166666672342.5837423414153.0530518163878
Winsorized Mean ( 6 / 20 )124669.1166666672149.5738119295157.9971322570035
Winsorized Mean ( 7 / 20 )124674.3666666672127.411200981258.603793478743
Winsorized Mean ( 8 / 20 )125005.5666666672053.2122450859860.8829247759684
Winsorized Mean ( 9 / 20 )124968.8166666672036.4000336102861.3675184659631
Winsorized Mean ( 10 / 20 )124831.4833333332001.1595166333562.3795765883488
Winsorized Mean ( 11 / 20 )124744.41943.8792983790664.1729144932098
Winsorized Mean ( 12 / 20 )125162.41661.0045402101975.3534364115352
Winsorized Mean ( 13 / 20 )124334.31473.9406682054284.3550237007722
Winsorized Mean ( 14 / 20 )124128.9666666671378.7519550860190.0299478878516
Winsorized Mean ( 15 / 20 )123992.4666666671353.2059103687391.6286765499569
Winsorized Mean ( 16 / 20 )124085.5333333331307.0287841652794.9371083763702
Winsorized Mean ( 17 / 20 )124217.851255.8309788179198.9128729066101
Winsorized Mean ( 18 / 20 )123880.651162.77191749049106.539079708220
Winsorized Mean ( 19 / 20 )124059.251114.40927845255111.322879662548
Winsorized Mean ( 20 / 20 )123827.5833333331015.87486225322121.892555800310
Trimmed Mean ( 1 / 20 )124513.4655172412444.6762809629250.9324962518954
Trimmed Mean ( 2 / 20 )124524.1607142862353.502495698252.9101460235945
Trimmed Mean ( 3 / 20 )124488.4074074072285.7987240331154.4616663306895
Trimmed Mean ( 4 / 20 )124459.5384615382205.9818819964256.4191118146909
Trimmed Mean ( 5 / 20 )124402.662112.8414037103358.8793175775229
Trimmed Mean ( 6 / 20 )124433.0208333332023.6783878948361.4885357167733
Trimmed Mean ( 7 / 20 )124381.6956521741972.2579918325663.0656314575774
Trimmed Mean ( 8 / 20 )124324.6818181821911.4211900921065.043059301959
Trimmed Mean ( 9 / 20 )124203.0952380951852.1112195495567.0602790626701
Trimmed Mean ( 10 / 20 )124075.4751777.2879219969669.8116908714423
Trimmed Mean ( 11 / 20 )123956.1052631581686.4462487473273.5013673606447
Trimmed Mean ( 12 / 20 )123836.6666666671579.2270135472878.4160007423525
Trimmed Mean ( 13 / 20 )123641.7058823531516.4829070453881.5318822968132
Trimmed Mean ( 14 / 20 )123541.81251484.0033593762983.2490113445047
Trimmed Mean ( 15 / 20 )123457.9333333331461.5119717350684.4727485788351
Trimmed Mean ( 16 / 20 )123381.5714285711431.3028229466586.2022832977883
Trimmed Mean ( 17 / 20 )123280.0384615381395.3037314569788.3535503290096
Trimmed Mean ( 18 / 20 )123142.1251351.2846387957291.129671325018
Trimmed Mean ( 19 / 20 )123030.2272727271312.5579895362093.7331746509734
Trimmed Mean ( 20 / 20 )122867.751259.2500417959797.572162733275
Median122699.5
Midrange122896
Midmean - Weighted Average at Xnp123091.322580645
Midmean - Weighted Average at X(n+1)p123457.933333333
Midmean - Empirical Distribution Function123091.322580645
Midmean - Empirical Distribution Function - Averaging123457.933333333
Midmean - Empirical Distribution Function - Interpolation123457.933333333
Midmean - Closest Observation123091.322580645
Midmean - True Basic - Statistics Graphics Toolkit123457.933333333
Midmean - MS Excel (old versions)123541.8125
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')