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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 computationSat, 14 Mar 2009 09:46:56 -0600
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2009/Mar/14/t1237045791sprzpiooizwhgou.htm/, Retrieved Wed, 24 Apr 2024 15:46:07 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=39072, Retrieved Wed, 24 Apr 2024 15:46:07 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact230
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [centrummaten prij...] [2009-03-14 15:46:56] [16e291b2db388e9b7dc52bb84b5ee0ff] [Current]
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Dataseries X:
106,8
114,3
105,7
90,1
91,6
97,7
100,8
104,6
95,9
102,7
104
107,9
113,8
113,8
123,1
125,1
137,6
134
140,3
152,1
150,6
167,3
153,2
142
154,4
158,5
180,9
181,3
172,4
192
199,3
215,4
214,3
201,5
190,5
196
215,7
209,4
214,1
237,8
239
237,8
251,5
248,8
215,4
201,2
203,1
214,2
188,9
203
213,3
228,5
228,2
240,9
258,8
248,5
269,2
289,6
323,4
317,2
322,8
340,9
368,2
388,5
441,2
474,3
483,9
417,9
365,9
263
199,4
157,2




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

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 3 seconds \tabularnewline
R Server & 'Herman Ole Andreas Wold' @ 193.190.124.10:1001 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=39072&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]3 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Herman Ole Andreas Wold' @ 193.190.124.10:1001[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=39072&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=39072&T=0

As an alternative you can also use a QR Code:  

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

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







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean209.05833333333311.020463741950118.9700123541570
Geometric Mean190.764799868453
Harmonic Mean174.670063085927
Quadratic Mean228.753974464562
Winsorized Mean ( 1 / 24 )208.94583333333310.97118182974819.0449704121012
Winsorized Mean ( 2 / 24 )208.14583333333310.654869124593119.5352782750659
Winsorized Mean ( 3 / 24 )207.2510.354943894937020.0145941979786
Winsorized Mean ( 4 / 24 )205.7888888888899.8820701905125820.8244714843717
Winsorized Mean ( 5 / 24 )204.5111111111119.5075308992965221.5104334950143
Winsorized Mean ( 6 / 24 )204.4277777777789.4449341445353521.6441718543962
Winsorized Mean ( 7 / 24 )202.0555555555568.8748750545303222.7671436852976
Winsorized Mean ( 8 / 24 )200.2333333333338.4414057933728123.7203776520888
Winsorized Mean ( 9 / 24 )200.2958333333338.4043845302878723.8323023668781
Winsorized Mean ( 10 / 24 )199.6708333333338.2222593879351824.2841807722969
Winsorized Mean ( 11 / 24 )196.3555555555567.2714917781383827.0034762530978
Winsorized Mean ( 12 / 24 )192.9555555555566.6901586941163428.8417008291971
Winsorized Mean ( 13 / 24 )191.9263888888896.4989333400274529.5319829958555
Winsorized Mean ( 14 / 24 )192.8208333333336.0916840675589531.6531243568907
Winsorized Mean ( 15 / 24 )191.7166666666675.7978147359199133.0670563650302
Winsorized Mean ( 16 / 24 )193.0944444444445.3978589655462835.7724137805262
Winsorized Mean ( 17 / 24 )193.8736111111115.2579122853442436.8727359053724
Winsorized Mean ( 18 / 24 )192.6486111111114.8846594816211239.4395170914094
Winsorized Mean ( 19 / 24 )192.5958333333334.7477370597967140.5658171266923
Winsorized Mean ( 20 / 24 )194.6513888888894.3515561195285944.7314440035248
Winsorized Mean ( 21 / 24 )195.0888888888894.2894872562555645.4807013599077
Winsorized Mean ( 22 / 24 )192.5833333333333.8552298685802349.9537874259768
Winsorized Mean ( 23 / 24 )192.8708333333333.7876500355063250.9209751495827
Winsorized Mean ( 24 / 24 )189.63753.1323101899986460.5423755940602
Trimmed Mean ( 1 / 24 )206.83142857142910.483343891252719.7295281655320
Trimmed Mean ( 2 / 24 )204.5926470588249.8903211162752320.686148068757
Trimmed Mean ( 3 / 24 )202.6545454545459.382021984197921.6003059677195
Trimmed Mean ( 4 / 24 )200.931258.9098173724335722.5516687493134
Trimmed Mean ( 5 / 24 )199.5209677419358.5232764128360623.4089519191771
Trimmed Mean ( 6 / 24 )198.3233333333338.179399286807824.2466868750619
Trimmed Mean ( 7 / 24 )197.0603448275867.773326793291325.3508375587216
Trimmed Mean ( 8 / 24 )196.1428571428577.4397549433977226.3641556254377
Trimmed Mean ( 9 / 24 )195.4611111111117.1442770617898227.3591168736313
Trimmed Mean ( 10 / 24 )194.7173076923086.7818216569058528.7116526418870
Trimmed Mean ( 11 / 24 )194.0046.3698594864840630.4565588003391
Trimmed Mean ( 12 / 24 )193.6833333333336.0958946868443331.7727492489864
Trimmed Mean ( 13 / 24 )193.7782608695655.8873596790716232.9142895003355
Trimmed Mean ( 14 / 24 )194.0113636363645.6612179939050834.2702513567289
Trimmed Mean ( 15 / 24 )194.1571428571435.4639863505707535.5339728908477
Trimmed Mean ( 16 / 24 )194.455.2714786520944236.8871834324403
Trimmed Mean ( 17 / 24 )194.6105263157895.1119011413006438.0700880037508
Trimmed Mean ( 18 / 24 )194.6972222222224.9269577304817839.5167226659328
Trimmed Mean ( 19 / 24 )194.9382352941184.7664398211592240.8980796167291
Trimmed Mean ( 20 / 24 )195.2156254.5729197398463742.6894929510742
Trimmed Mean ( 21 / 24 )195.2833333333334.4126492246808644.2553494261617
Trimmed Mean ( 22 / 24 )195.3071428571434.1892560002013546.6209615377422
Trimmed Mean ( 23 / 24 )195.653.9980504864630848.9363505194463
Trimmed Mean ( 24 / 24 )196.01253.7167965427038252.736946385935
Median200.3
Midrange287
Midmean - Weighted Average at Xnp193.154054054054
Midmean - Weighted Average at X(n+1)p194.697222222222
Midmean - Empirical Distribution Function193.154054054054
Midmean - Empirical Distribution Function - Averaging194.697222222222
Midmean - Empirical Distribution Function - Interpolation194.697222222222
Midmean - Closest Observation193.154054054054
Midmean - True Basic - Statistics Graphics Toolkit194.697222222222
Midmean - MS Excel (old versions)194.610526315789
Number of observations72

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 209.058333333333 & 11.0204637419501 & 18.9700123541570 \tabularnewline
Geometric Mean & 190.764799868453 &  &  \tabularnewline
Harmonic Mean & 174.670063085927 &  &  \tabularnewline
Quadratic Mean & 228.753974464562 &  &  \tabularnewline
Winsorized Mean ( 1 / 24 ) & 208.945833333333 & 10.971181829748 & 19.0449704121012 \tabularnewline
Winsorized Mean ( 2 / 24 ) & 208.145833333333 & 10.6548691245931 & 19.5352782750659 \tabularnewline
Winsorized Mean ( 3 / 24 ) & 207.25 & 10.3549438949370 & 20.0145941979786 \tabularnewline
Winsorized Mean ( 4 / 24 ) & 205.788888888889 & 9.88207019051258 & 20.8244714843717 \tabularnewline
Winsorized Mean ( 5 / 24 ) & 204.511111111111 & 9.50753089929652 & 21.5104334950143 \tabularnewline
Winsorized Mean ( 6 / 24 ) & 204.427777777778 & 9.44493414453535 & 21.6441718543962 \tabularnewline
Winsorized Mean ( 7 / 24 ) & 202.055555555556 & 8.87487505453032 & 22.7671436852976 \tabularnewline
Winsorized Mean ( 8 / 24 ) & 200.233333333333 & 8.44140579337281 & 23.7203776520888 \tabularnewline
Winsorized Mean ( 9 / 24 ) & 200.295833333333 & 8.40438453028787 & 23.8323023668781 \tabularnewline
Winsorized Mean ( 10 / 24 ) & 199.670833333333 & 8.22225938793518 & 24.2841807722969 \tabularnewline
Winsorized Mean ( 11 / 24 ) & 196.355555555556 & 7.27149177813838 & 27.0034762530978 \tabularnewline
Winsorized Mean ( 12 / 24 ) & 192.955555555556 & 6.69015869411634 & 28.8417008291971 \tabularnewline
Winsorized Mean ( 13 / 24 ) & 191.926388888889 & 6.49893334002745 & 29.5319829958555 \tabularnewline
Winsorized Mean ( 14 / 24 ) & 192.820833333333 & 6.09168406755895 & 31.6531243568907 \tabularnewline
Winsorized Mean ( 15 / 24 ) & 191.716666666667 & 5.79781473591991 & 33.0670563650302 \tabularnewline
Winsorized Mean ( 16 / 24 ) & 193.094444444444 & 5.39785896554628 & 35.7724137805262 \tabularnewline
Winsorized Mean ( 17 / 24 ) & 193.873611111111 & 5.25791228534424 & 36.8727359053724 \tabularnewline
Winsorized Mean ( 18 / 24 ) & 192.648611111111 & 4.88465948162112 & 39.4395170914094 \tabularnewline
Winsorized Mean ( 19 / 24 ) & 192.595833333333 & 4.74773705979671 & 40.5658171266923 \tabularnewline
Winsorized Mean ( 20 / 24 ) & 194.651388888889 & 4.35155611952859 & 44.7314440035248 \tabularnewline
Winsorized Mean ( 21 / 24 ) & 195.088888888889 & 4.28948725625556 & 45.4807013599077 \tabularnewline
Winsorized Mean ( 22 / 24 ) & 192.583333333333 & 3.85522986858023 & 49.9537874259768 \tabularnewline
Winsorized Mean ( 23 / 24 ) & 192.870833333333 & 3.78765003550632 & 50.9209751495827 \tabularnewline
Winsorized Mean ( 24 / 24 ) & 189.6375 & 3.13231018999864 & 60.5423755940602 \tabularnewline
Trimmed Mean ( 1 / 24 ) & 206.831428571429 & 10.4833438912527 & 19.7295281655320 \tabularnewline
Trimmed Mean ( 2 / 24 ) & 204.592647058824 & 9.89032111627523 & 20.686148068757 \tabularnewline
Trimmed Mean ( 3 / 24 ) & 202.654545454545 & 9.3820219841979 & 21.6003059677195 \tabularnewline
Trimmed Mean ( 4 / 24 ) & 200.93125 & 8.90981737243357 & 22.5516687493134 \tabularnewline
Trimmed Mean ( 5 / 24 ) & 199.520967741935 & 8.52327641283606 & 23.4089519191771 \tabularnewline
Trimmed Mean ( 6 / 24 ) & 198.323333333333 & 8.1793992868078 & 24.2466868750619 \tabularnewline
Trimmed Mean ( 7 / 24 ) & 197.060344827586 & 7.7733267932913 & 25.3508375587216 \tabularnewline
Trimmed Mean ( 8 / 24 ) & 196.142857142857 & 7.43975494339772 & 26.3641556254377 \tabularnewline
Trimmed Mean ( 9 / 24 ) & 195.461111111111 & 7.14427706178982 & 27.3591168736313 \tabularnewline
Trimmed Mean ( 10 / 24 ) & 194.717307692308 & 6.78182165690585 & 28.7116526418870 \tabularnewline
Trimmed Mean ( 11 / 24 ) & 194.004 & 6.36985948648406 & 30.4565588003391 \tabularnewline
Trimmed Mean ( 12 / 24 ) & 193.683333333333 & 6.09589468684433 & 31.7727492489864 \tabularnewline
Trimmed Mean ( 13 / 24 ) & 193.778260869565 & 5.88735967907162 & 32.9142895003355 \tabularnewline
Trimmed Mean ( 14 / 24 ) & 194.011363636364 & 5.66121799390508 & 34.2702513567289 \tabularnewline
Trimmed Mean ( 15 / 24 ) & 194.157142857143 & 5.46398635057075 & 35.5339728908477 \tabularnewline
Trimmed Mean ( 16 / 24 ) & 194.45 & 5.27147865209442 & 36.8871834324403 \tabularnewline
Trimmed Mean ( 17 / 24 ) & 194.610526315789 & 5.11190114130064 & 38.0700880037508 \tabularnewline
Trimmed Mean ( 18 / 24 ) & 194.697222222222 & 4.92695773048178 & 39.5167226659328 \tabularnewline
Trimmed Mean ( 19 / 24 ) & 194.938235294118 & 4.76643982115922 & 40.8980796167291 \tabularnewline
Trimmed Mean ( 20 / 24 ) & 195.215625 & 4.57291973984637 & 42.6894929510742 \tabularnewline
Trimmed Mean ( 21 / 24 ) & 195.283333333333 & 4.41264922468086 & 44.2553494261617 \tabularnewline
Trimmed Mean ( 22 / 24 ) & 195.307142857143 & 4.18925600020135 & 46.6209615377422 \tabularnewline
Trimmed Mean ( 23 / 24 ) & 195.65 & 3.99805048646308 & 48.9363505194463 \tabularnewline
Trimmed Mean ( 24 / 24 ) & 196.0125 & 3.71679654270382 & 52.736946385935 \tabularnewline
Median & 200.3 &  &  \tabularnewline
Midrange & 287 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 193.154054054054 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 194.697222222222 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 193.154054054054 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 194.697222222222 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 194.697222222222 &  &  \tabularnewline
Midmean - Closest Observation & 193.154054054054 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 194.697222222222 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 194.610526315789 &  &  \tabularnewline
Number of observations & 72 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=39072&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]209.058333333333[/C][C]11.0204637419501[/C][C]18.9700123541570[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]190.764799868453[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]174.670063085927[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]228.753974464562[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 24 )[/C][C]208.945833333333[/C][C]10.971181829748[/C][C]19.0449704121012[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 24 )[/C][C]208.145833333333[/C][C]10.6548691245931[/C][C]19.5352782750659[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 24 )[/C][C]207.25[/C][C]10.3549438949370[/C][C]20.0145941979786[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 24 )[/C][C]205.788888888889[/C][C]9.88207019051258[/C][C]20.8244714843717[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 24 )[/C][C]204.511111111111[/C][C]9.50753089929652[/C][C]21.5104334950143[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 24 )[/C][C]204.427777777778[/C][C]9.44493414453535[/C][C]21.6441718543962[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 24 )[/C][C]202.055555555556[/C][C]8.87487505453032[/C][C]22.7671436852976[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 24 )[/C][C]200.233333333333[/C][C]8.44140579337281[/C][C]23.7203776520888[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 24 )[/C][C]200.295833333333[/C][C]8.40438453028787[/C][C]23.8323023668781[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 24 )[/C][C]199.670833333333[/C][C]8.22225938793518[/C][C]24.2841807722969[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 24 )[/C][C]196.355555555556[/C][C]7.27149177813838[/C][C]27.0034762530978[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 24 )[/C][C]192.955555555556[/C][C]6.69015869411634[/C][C]28.8417008291971[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 24 )[/C][C]191.926388888889[/C][C]6.49893334002745[/C][C]29.5319829958555[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 24 )[/C][C]192.820833333333[/C][C]6.09168406755895[/C][C]31.6531243568907[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 24 )[/C][C]191.716666666667[/C][C]5.79781473591991[/C][C]33.0670563650302[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 24 )[/C][C]193.094444444444[/C][C]5.39785896554628[/C][C]35.7724137805262[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 24 )[/C][C]193.873611111111[/C][C]5.25791228534424[/C][C]36.8727359053724[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 24 )[/C][C]192.648611111111[/C][C]4.88465948162112[/C][C]39.4395170914094[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 24 )[/C][C]192.595833333333[/C][C]4.74773705979671[/C][C]40.5658171266923[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 24 )[/C][C]194.651388888889[/C][C]4.35155611952859[/C][C]44.7314440035248[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 24 )[/C][C]195.088888888889[/C][C]4.28948725625556[/C][C]45.4807013599077[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 24 )[/C][C]192.583333333333[/C][C]3.85522986858023[/C][C]49.9537874259768[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 24 )[/C][C]192.870833333333[/C][C]3.78765003550632[/C][C]50.9209751495827[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 24 )[/C][C]189.6375[/C][C]3.13231018999864[/C][C]60.5423755940602[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 24 )[/C][C]206.831428571429[/C][C]10.4833438912527[/C][C]19.7295281655320[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 24 )[/C][C]204.592647058824[/C][C]9.89032111627523[/C][C]20.686148068757[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 24 )[/C][C]202.654545454545[/C][C]9.3820219841979[/C][C]21.6003059677195[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 24 )[/C][C]200.93125[/C][C]8.90981737243357[/C][C]22.5516687493134[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 24 )[/C][C]199.520967741935[/C][C]8.52327641283606[/C][C]23.4089519191771[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 24 )[/C][C]198.323333333333[/C][C]8.1793992868078[/C][C]24.2466868750619[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 24 )[/C][C]197.060344827586[/C][C]7.7733267932913[/C][C]25.3508375587216[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 24 )[/C][C]196.142857142857[/C][C]7.43975494339772[/C][C]26.3641556254377[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 24 )[/C][C]195.461111111111[/C][C]7.14427706178982[/C][C]27.3591168736313[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 24 )[/C][C]194.717307692308[/C][C]6.78182165690585[/C][C]28.7116526418870[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 24 )[/C][C]194.004[/C][C]6.36985948648406[/C][C]30.4565588003391[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 24 )[/C][C]193.683333333333[/C][C]6.09589468684433[/C][C]31.7727492489864[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 24 )[/C][C]193.778260869565[/C][C]5.88735967907162[/C][C]32.9142895003355[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 24 )[/C][C]194.011363636364[/C][C]5.66121799390508[/C][C]34.2702513567289[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 24 )[/C][C]194.157142857143[/C][C]5.46398635057075[/C][C]35.5339728908477[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 24 )[/C][C]194.45[/C][C]5.27147865209442[/C][C]36.8871834324403[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 24 )[/C][C]194.610526315789[/C][C]5.11190114130064[/C][C]38.0700880037508[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 24 )[/C][C]194.697222222222[/C][C]4.92695773048178[/C][C]39.5167226659328[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 24 )[/C][C]194.938235294118[/C][C]4.76643982115922[/C][C]40.8980796167291[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 24 )[/C][C]195.215625[/C][C]4.57291973984637[/C][C]42.6894929510742[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 24 )[/C][C]195.283333333333[/C][C]4.41264922468086[/C][C]44.2553494261617[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 24 )[/C][C]195.307142857143[/C][C]4.18925600020135[/C][C]46.6209615377422[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 24 )[/C][C]195.65[/C][C]3.99805048646308[/C][C]48.9363505194463[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 24 )[/C][C]196.0125[/C][C]3.71679654270382[/C][C]52.736946385935[/C][/ROW]
[ROW][C]Median[/C][C]200.3[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]287[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]193.154054054054[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]194.697222222222[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]193.154054054054[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]194.697222222222[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]194.697222222222[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]193.154054054054[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]194.697222222222[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]194.610526315789[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]72[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=39072&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=39072&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 Mean209.05833333333311.020463741950118.9700123541570
Geometric Mean190.764799868453
Harmonic Mean174.670063085927
Quadratic Mean228.753974464562
Winsorized Mean ( 1 / 24 )208.94583333333310.97118182974819.0449704121012
Winsorized Mean ( 2 / 24 )208.14583333333310.654869124593119.5352782750659
Winsorized Mean ( 3 / 24 )207.2510.354943894937020.0145941979786
Winsorized Mean ( 4 / 24 )205.7888888888899.8820701905125820.8244714843717
Winsorized Mean ( 5 / 24 )204.5111111111119.5075308992965221.5104334950143
Winsorized Mean ( 6 / 24 )204.4277777777789.4449341445353521.6441718543962
Winsorized Mean ( 7 / 24 )202.0555555555568.8748750545303222.7671436852976
Winsorized Mean ( 8 / 24 )200.2333333333338.4414057933728123.7203776520888
Winsorized Mean ( 9 / 24 )200.2958333333338.4043845302878723.8323023668781
Winsorized Mean ( 10 / 24 )199.6708333333338.2222593879351824.2841807722969
Winsorized Mean ( 11 / 24 )196.3555555555567.2714917781383827.0034762530978
Winsorized Mean ( 12 / 24 )192.9555555555566.6901586941163428.8417008291971
Winsorized Mean ( 13 / 24 )191.9263888888896.4989333400274529.5319829958555
Winsorized Mean ( 14 / 24 )192.8208333333336.0916840675589531.6531243568907
Winsorized Mean ( 15 / 24 )191.7166666666675.7978147359199133.0670563650302
Winsorized Mean ( 16 / 24 )193.0944444444445.3978589655462835.7724137805262
Winsorized Mean ( 17 / 24 )193.8736111111115.2579122853442436.8727359053724
Winsorized Mean ( 18 / 24 )192.6486111111114.8846594816211239.4395170914094
Winsorized Mean ( 19 / 24 )192.5958333333334.7477370597967140.5658171266923
Winsorized Mean ( 20 / 24 )194.6513888888894.3515561195285944.7314440035248
Winsorized Mean ( 21 / 24 )195.0888888888894.2894872562555645.4807013599077
Winsorized Mean ( 22 / 24 )192.5833333333333.8552298685802349.9537874259768
Winsorized Mean ( 23 / 24 )192.8708333333333.7876500355063250.9209751495827
Winsorized Mean ( 24 / 24 )189.63753.1323101899986460.5423755940602
Trimmed Mean ( 1 / 24 )206.83142857142910.483343891252719.7295281655320
Trimmed Mean ( 2 / 24 )204.5926470588249.8903211162752320.686148068757
Trimmed Mean ( 3 / 24 )202.6545454545459.382021984197921.6003059677195
Trimmed Mean ( 4 / 24 )200.931258.9098173724335722.5516687493134
Trimmed Mean ( 5 / 24 )199.5209677419358.5232764128360623.4089519191771
Trimmed Mean ( 6 / 24 )198.3233333333338.179399286807824.2466868750619
Trimmed Mean ( 7 / 24 )197.0603448275867.773326793291325.3508375587216
Trimmed Mean ( 8 / 24 )196.1428571428577.4397549433977226.3641556254377
Trimmed Mean ( 9 / 24 )195.4611111111117.1442770617898227.3591168736313
Trimmed Mean ( 10 / 24 )194.7173076923086.7818216569058528.7116526418870
Trimmed Mean ( 11 / 24 )194.0046.3698594864840630.4565588003391
Trimmed Mean ( 12 / 24 )193.6833333333336.0958946868443331.7727492489864
Trimmed Mean ( 13 / 24 )193.7782608695655.8873596790716232.9142895003355
Trimmed Mean ( 14 / 24 )194.0113636363645.6612179939050834.2702513567289
Trimmed Mean ( 15 / 24 )194.1571428571435.4639863505707535.5339728908477
Trimmed Mean ( 16 / 24 )194.455.2714786520944236.8871834324403
Trimmed Mean ( 17 / 24 )194.6105263157895.1119011413006438.0700880037508
Trimmed Mean ( 18 / 24 )194.6972222222224.9269577304817839.5167226659328
Trimmed Mean ( 19 / 24 )194.9382352941184.7664398211592240.8980796167291
Trimmed Mean ( 20 / 24 )195.2156254.5729197398463742.6894929510742
Trimmed Mean ( 21 / 24 )195.2833333333334.4126492246808644.2553494261617
Trimmed Mean ( 22 / 24 )195.3071428571434.1892560002013546.6209615377422
Trimmed Mean ( 23 / 24 )195.653.9980504864630848.9363505194463
Trimmed Mean ( 24 / 24 )196.01253.7167965427038252.736946385935
Median200.3
Midrange287
Midmean - Weighted Average at Xnp193.154054054054
Midmean - Weighted Average at X(n+1)p194.697222222222
Midmean - Empirical Distribution Function193.154054054054
Midmean - Empirical Distribution Function - Averaging194.697222222222
Midmean - Empirical Distribution Function - Interpolation194.697222222222
Midmean - Closest Observation193.154054054054
Midmean - True Basic - Statistics Graphics Toolkit194.697222222222
Midmean - MS Excel (old versions)194.610526315789
Number of observations72



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')