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of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationFri, 17 Oct 2008 04:09:49 -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/17/t1224238254lqw2gwljfapcd2v.htm/, Retrieved Wed, 15 May 2024 01:38:44 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=16407, Retrieved Wed, 15 May 2024 01:38:44 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact200
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
F     [Central Tendency] [Q1 central tenden...] [2007-10-18 09:35:57] [b731da8b544846036771bbf9bf2f34ce]
-    D    [Central Tendency] [Prijsindexcijfers...] [2008-10-17 10:09:49] [5338a3370b0f0a39c3af1ba0be9c6dab] [Current]
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Dataseries X:
95,4
101,2
101,5
101,9
101,7
100,1
97,4
96,5
99,2
102,2
105,3
111,1
114,9
124,5
142,2
159,7
165,2
198,6
207,8
219,6
239,6
235,3
218,5
213,8
205,5
198,4
198,5
190,2
180,7
193,6
192,8
195,5
197,2
196,9
178,9
172,4
156,4
143,7
153,6
168,8
185,8
199,9
205,4
197,5
199,6
200,5
193,7
179,6
169,1
169,8
195,5
194,8
204,5
203,8
204,8
204,9
240,0
248,3
258,4
254,9




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'Sir Ronald Aylmer Fisher' @ 193.190.124.24

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 3 seconds \tabularnewline
R Server & 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=16407&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]3 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Sir Ronald Aylmer Fisher' @ 193.190.124.24[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=16407&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=16407&T=0

As an alternative you can also use a QR Code:  

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

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'Sir Ronald Aylmer Fisher' @ 193.190.124.24







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean174.7855.9507459652024229.3719478233608
Geometric Mean167.946240539417
Harmonic Mean160.350726852889
Quadratic Mean180.662855894619
Winsorized Mean ( 1 / 20 )174.7455.9329989868026429.4530641904209
Winsorized Mean ( 2 / 20 )174.5555.877720274176829.6977385546724
Winsorized Mean ( 3 / 20 )174.235.7735703589083930.1771675357121
Winsorized Mean ( 4 / 20 )174.2633333333335.7552702286596830.2789141794853
Winsorized Mean ( 5 / 20 )173.9966666666675.6679508182713430.6983374142498
Winsorized Mean ( 6 / 20 )172.4566666666675.400628424757431.9327035861412
Winsorized Mean ( 7 / 20 )172.3516666666675.3766031595087932.055865302585
Winsorized Mean ( 8 / 20 )171.7516666666675.2827624448733532.5117149330353
Winsorized Mean ( 9 / 20 )170.8966666666675.1572821460251733.1369628086725
Winsorized Mean ( 10 / 20 )171.034.99566326051234.2356942574371
Winsorized Mean ( 11 / 20 )172.0754.7594150669657936.1546529518596
Winsorized Mean ( 12 / 20 )172.7354.5837318727637.6843595556978
Winsorized Mean ( 13 / 20 )174.7933333333334.1443678115532642.1761149785165
Winsorized Mean ( 14 / 20 )178.8533333333333.3201639285193553.8688261133823
Winsorized Mean ( 15 / 20 )179.0533333333333.2274366406334355.4784967980631
Winsorized Mean ( 16 / 20 )180.8133333333332.6370475129749568.5665815438232
Winsorized Mean ( 17 / 20 )181.4366666666672.4782100870194473.2127867677602
Winsorized Mean ( 18 / 20 )182.3366666666672.2993661207904279.2986662793775
Winsorized Mean ( 19 / 20 )183.7616666666671.97449284293993.0677805816407
Winsorized Mean ( 20 / 20 )184.9283333333331.78241740827613103.751417863556
Trimmed Mean ( 1 / 20 )174.7120689655175.8220880690075630.0084895478572
Trimmed Mean ( 2 / 20 )174.6767857142865.6842005863321430.7302290025272
Trimmed Mean ( 3 / 20 )174.7444444444445.5489339994421831.4915341328643
Trimmed Mean ( 4 / 20 )174.9423076923085.4286683464955932.2256392408351
Trimmed Mean ( 5 / 20 )175.1465.2826842357549533.154735771363
Trimmed Mean ( 6 / 20 )175.4333333333335.1261163230968234.2234397886916
Trimmed Mean ( 7 / 20 )176.0804347826095.0045859351471535.1838168160922
Trimmed Mean ( 8 / 20 )176.8068181818184.8491999271727436.4610287959200
Trimmed Mean ( 9 / 20 )177.7095238095244.665098636753238.0934118754680
Trimmed Mean ( 10 / 20 )178.8454.4446336845395540.2384116878077
Trimmed Mean ( 11 / 20 )180.0789473684214.1862933524350743.0163230829663
Trimmed Mean ( 12 / 20 )181.2916666666673.9023830224579846.4566562593534
Trimmed Mean ( 13 / 20 )182.553.5536360079509251.3699207210761
Trimmed Mean ( 14 / 20 )183.668753.2166509754687257.0993718002732
Trimmed Mean ( 15 / 20 )184.3566666666673.0505838270442260.4332406906169
Trimmed Mean ( 16 / 20 )185.1142857142862.8287063727096765.4413224010102
Trimmed Mean ( 17 / 20 )185.7346153846152.7201014817476868.2822374940511
Trimmed Mean ( 18 / 20 )186.3666666666672.6024491437670271.6120301958725
Trimmed Mean ( 19 / 20 )186.9772727272732.4811491177496875.3591436281164
Trimmed Mean ( 20 / 20 )187.4852.4222789943183277.4002501114707
Median193.2
Midrange176.9
Midmean - Weighted Average at Xnp182.996774193548
Midmean - Weighted Average at X(n+1)p184.356666666667
Midmean - Empirical Distribution Function182.996774193548
Midmean - Empirical Distribution Function - Averaging184.356666666667
Midmean - Empirical Distribution Function - Interpolation184.356666666667
Midmean - Closest Observation182.996774193548
Midmean - True Basic - Statistics Graphics Toolkit184.356666666667
Midmean - MS Excel (old versions)183.66875
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 174.785 & 5.95074596520242 & 29.3719478233608 \tabularnewline
Geometric Mean & 167.946240539417 &  &  \tabularnewline
Harmonic Mean & 160.350726852889 &  &  \tabularnewline
Quadratic Mean & 180.662855894619 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 174.745 & 5.93299898680264 & 29.4530641904209 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 174.555 & 5.8777202741768 & 29.6977385546724 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 174.23 & 5.77357035890839 & 30.1771675357121 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 174.263333333333 & 5.75527022865968 & 30.2789141794853 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 173.996666666667 & 5.66795081827134 & 30.6983374142498 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 172.456666666667 & 5.4006284247574 & 31.9327035861412 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 172.351666666667 & 5.37660315950879 & 32.055865302585 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 171.751666666667 & 5.28276244487335 & 32.5117149330353 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 170.896666666667 & 5.15728214602517 & 33.1369628086725 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 171.03 & 4.995663260512 & 34.2356942574371 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 172.075 & 4.75941506696579 & 36.1546529518596 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 172.735 & 4.58373187276 & 37.6843595556978 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 174.793333333333 & 4.14436781155326 & 42.1761149785165 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 178.853333333333 & 3.32016392851935 & 53.8688261133823 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 179.053333333333 & 3.22743664063343 & 55.4784967980631 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 180.813333333333 & 2.63704751297495 & 68.5665815438232 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 181.436666666667 & 2.47821008701944 & 73.2127867677602 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 182.336666666667 & 2.29936612079042 & 79.2986662793775 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 183.761666666667 & 1.974492842939 & 93.0677805816407 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 184.928333333333 & 1.78241740827613 & 103.751417863556 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 174.712068965517 & 5.82208806900756 & 30.0084895478572 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 174.676785714286 & 5.68420058633214 & 30.7302290025272 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 174.744444444444 & 5.54893399944218 & 31.4915341328643 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 174.942307692308 & 5.42866834649559 & 32.2256392408351 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 175.146 & 5.28268423575495 & 33.154735771363 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 175.433333333333 & 5.12611632309682 & 34.2234397886916 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 176.080434782609 & 5.00458593514715 & 35.1838168160922 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 176.806818181818 & 4.84919992717274 & 36.4610287959200 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 177.709523809524 & 4.6650986367532 & 38.0934118754680 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 178.845 & 4.44463368453955 & 40.2384116878077 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 180.078947368421 & 4.18629335243507 & 43.0163230829663 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 181.291666666667 & 3.90238302245798 & 46.4566562593534 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 182.55 & 3.55363600795092 & 51.3699207210761 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 183.66875 & 3.21665097546872 & 57.0993718002732 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 184.356666666667 & 3.05058382704422 & 60.4332406906169 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 185.114285714286 & 2.82870637270967 & 65.4413224010102 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 185.734615384615 & 2.72010148174768 & 68.2822374940511 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 186.366666666667 & 2.60244914376702 & 71.6120301958725 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 186.977272727273 & 2.48114911774968 & 75.3591436281164 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 187.485 & 2.42227899431832 & 77.4002501114707 \tabularnewline
Median & 193.2 &  &  \tabularnewline
Midrange & 176.9 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 182.996774193548 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 184.356666666667 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 182.996774193548 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 184.356666666667 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 184.356666666667 &  &  \tabularnewline
Midmean - Closest Observation & 182.996774193548 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 184.356666666667 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 183.66875 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=16407&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]174.785[/C][C]5.95074596520242[/C][C]29.3719478233608[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]167.946240539417[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]160.350726852889[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]180.662855894619[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]174.745[/C][C]5.93299898680264[/C][C]29.4530641904209[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]174.555[/C][C]5.8777202741768[/C][C]29.6977385546724[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]174.23[/C][C]5.77357035890839[/C][C]30.1771675357121[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]174.263333333333[/C][C]5.75527022865968[/C][C]30.2789141794853[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]173.996666666667[/C][C]5.66795081827134[/C][C]30.6983374142498[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]172.456666666667[/C][C]5.4006284247574[/C][C]31.9327035861412[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]172.351666666667[/C][C]5.37660315950879[/C][C]32.055865302585[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]171.751666666667[/C][C]5.28276244487335[/C][C]32.5117149330353[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]170.896666666667[/C][C]5.15728214602517[/C][C]33.1369628086725[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]171.03[/C][C]4.995663260512[/C][C]34.2356942574371[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]172.075[/C][C]4.75941506696579[/C][C]36.1546529518596[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]172.735[/C][C]4.58373187276[/C][C]37.6843595556978[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]174.793333333333[/C][C]4.14436781155326[/C][C]42.1761149785165[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]178.853333333333[/C][C]3.32016392851935[/C][C]53.8688261133823[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]179.053333333333[/C][C]3.22743664063343[/C][C]55.4784967980631[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]180.813333333333[/C][C]2.63704751297495[/C][C]68.5665815438232[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]181.436666666667[/C][C]2.47821008701944[/C][C]73.2127867677602[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]182.336666666667[/C][C]2.29936612079042[/C][C]79.2986662793775[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]183.761666666667[/C][C]1.974492842939[/C][C]93.0677805816407[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]184.928333333333[/C][C]1.78241740827613[/C][C]103.751417863556[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]174.712068965517[/C][C]5.82208806900756[/C][C]30.0084895478572[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]174.676785714286[/C][C]5.68420058633214[/C][C]30.7302290025272[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]174.744444444444[/C][C]5.54893399944218[/C][C]31.4915341328643[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]174.942307692308[/C][C]5.42866834649559[/C][C]32.2256392408351[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]175.146[/C][C]5.28268423575495[/C][C]33.154735771363[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]175.433333333333[/C][C]5.12611632309682[/C][C]34.2234397886916[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]176.080434782609[/C][C]5.00458593514715[/C][C]35.1838168160922[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]176.806818181818[/C][C]4.84919992717274[/C][C]36.4610287959200[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]177.709523809524[/C][C]4.6650986367532[/C][C]38.0934118754680[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]178.845[/C][C]4.44463368453955[/C][C]40.2384116878077[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]180.078947368421[/C][C]4.18629335243507[/C][C]43.0163230829663[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]181.291666666667[/C][C]3.90238302245798[/C][C]46.4566562593534[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]182.55[/C][C]3.55363600795092[/C][C]51.3699207210761[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]183.66875[/C][C]3.21665097546872[/C][C]57.0993718002732[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]184.356666666667[/C][C]3.05058382704422[/C][C]60.4332406906169[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]185.114285714286[/C][C]2.82870637270967[/C][C]65.4413224010102[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]185.734615384615[/C][C]2.72010148174768[/C][C]68.2822374940511[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]186.366666666667[/C][C]2.60244914376702[/C][C]71.6120301958725[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]186.977272727273[/C][C]2.48114911774968[/C][C]75.3591436281164[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]187.485[/C][C]2.42227899431832[/C][C]77.4002501114707[/C][/ROW]
[ROW][C]Median[/C][C]193.2[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]176.9[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]182.996774193548[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]184.356666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]182.996774193548[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]184.356666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]184.356666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]182.996774193548[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]184.356666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]183.66875[/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=16407&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=16407&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 Mean174.7855.9507459652024229.3719478233608
Geometric Mean167.946240539417
Harmonic Mean160.350726852889
Quadratic Mean180.662855894619
Winsorized Mean ( 1 / 20 )174.7455.9329989868026429.4530641904209
Winsorized Mean ( 2 / 20 )174.5555.877720274176829.6977385546724
Winsorized Mean ( 3 / 20 )174.235.7735703589083930.1771675357121
Winsorized Mean ( 4 / 20 )174.2633333333335.7552702286596830.2789141794853
Winsorized Mean ( 5 / 20 )173.9966666666675.6679508182713430.6983374142498
Winsorized Mean ( 6 / 20 )172.4566666666675.400628424757431.9327035861412
Winsorized Mean ( 7 / 20 )172.3516666666675.3766031595087932.055865302585
Winsorized Mean ( 8 / 20 )171.7516666666675.2827624448733532.5117149330353
Winsorized Mean ( 9 / 20 )170.8966666666675.1572821460251733.1369628086725
Winsorized Mean ( 10 / 20 )171.034.99566326051234.2356942574371
Winsorized Mean ( 11 / 20 )172.0754.7594150669657936.1546529518596
Winsorized Mean ( 12 / 20 )172.7354.5837318727637.6843595556978
Winsorized Mean ( 13 / 20 )174.7933333333334.1443678115532642.1761149785165
Winsorized Mean ( 14 / 20 )178.8533333333333.3201639285193553.8688261133823
Winsorized Mean ( 15 / 20 )179.0533333333333.2274366406334355.4784967980631
Winsorized Mean ( 16 / 20 )180.8133333333332.6370475129749568.5665815438232
Winsorized Mean ( 17 / 20 )181.4366666666672.4782100870194473.2127867677602
Winsorized Mean ( 18 / 20 )182.3366666666672.2993661207904279.2986662793775
Winsorized Mean ( 19 / 20 )183.7616666666671.97449284293993.0677805816407
Winsorized Mean ( 20 / 20 )184.9283333333331.78241740827613103.751417863556
Trimmed Mean ( 1 / 20 )174.7120689655175.8220880690075630.0084895478572
Trimmed Mean ( 2 / 20 )174.6767857142865.6842005863321430.7302290025272
Trimmed Mean ( 3 / 20 )174.7444444444445.5489339994421831.4915341328643
Trimmed Mean ( 4 / 20 )174.9423076923085.4286683464955932.2256392408351
Trimmed Mean ( 5 / 20 )175.1465.2826842357549533.154735771363
Trimmed Mean ( 6 / 20 )175.4333333333335.1261163230968234.2234397886916
Trimmed Mean ( 7 / 20 )176.0804347826095.0045859351471535.1838168160922
Trimmed Mean ( 8 / 20 )176.8068181818184.8491999271727436.4610287959200
Trimmed Mean ( 9 / 20 )177.7095238095244.665098636753238.0934118754680
Trimmed Mean ( 10 / 20 )178.8454.4446336845395540.2384116878077
Trimmed Mean ( 11 / 20 )180.0789473684214.1862933524350743.0163230829663
Trimmed Mean ( 12 / 20 )181.2916666666673.9023830224579846.4566562593534
Trimmed Mean ( 13 / 20 )182.553.5536360079509251.3699207210761
Trimmed Mean ( 14 / 20 )183.668753.2166509754687257.0993718002732
Trimmed Mean ( 15 / 20 )184.3566666666673.0505838270442260.4332406906169
Trimmed Mean ( 16 / 20 )185.1142857142862.8287063727096765.4413224010102
Trimmed Mean ( 17 / 20 )185.7346153846152.7201014817476868.2822374940511
Trimmed Mean ( 18 / 20 )186.3666666666672.6024491437670271.6120301958725
Trimmed Mean ( 19 / 20 )186.9772727272732.4811491177496875.3591436281164
Trimmed Mean ( 20 / 20 )187.4852.4222789943183277.4002501114707
Median193.2
Midrange176.9
Midmean - Weighted Average at Xnp182.996774193548
Midmean - Weighted Average at X(n+1)p184.356666666667
Midmean - Empirical Distribution Function182.996774193548
Midmean - Empirical Distribution Function - Averaging184.356666666667
Midmean - Empirical Distribution Function - Interpolation184.356666666667
Midmean - Closest Observation182.996774193548
Midmean - True Basic - Statistics Graphics Toolkit184.356666666667
Midmean - MS Excel (old versions)183.66875
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')