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Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationSun, 14 Mar 2010 13:59:47 -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/2010/Mar/14/t1268596997wbhz2swmzfvilzy.htm/, Retrieved Wed, 19 Jan 2022 11:39:18 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=74417, Retrieved Wed, 19 Jan 2022 11:39:18 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact110
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [OPGAVE5- o2] [2010-03-14 19:59:47] [bf0252597522c891d765285c82c7204e] [Current]
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Dataseries X:
278,1
283,3
287
287,9
279,7
273,2
272,6
274,8
277,2
277,5
278,7
279
280,1
280,8
280,1
270,5
260
258,2
260,1
262,2
263,4
264,7
267,4
266,8
265,2
262,5
255
252,8
249,6
254,2
259,4
260,8
261,6
257,2
249,8
235,2
227,4
223,1
221,6
218,5
220,1
222,1
222,9
222,8
222,1
209
201,7
204,5
208,7
213
218,6
221,9
224,6
226,8
229,6
231,4
229,1
232,7
236,6
242,2
251,5
261,5
266,4
280,9
294,4
308,8
328,8
348,2
365,9
387,5
395,9
395,8




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 2 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=74417&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]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=74417&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=74417&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'Gwilym Jenkins' @ 72.249.127.135







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean261.7111111111114.935063677779553.0309491829833
Geometric Mean258.748664300609
Harmonic Mean256.065971032172
Quadratic Mean264.994151402965
Winsorized Mean ( 1 / 24 )261.7486111111114.928019832757253.114358300921
Winsorized Mean ( 2 / 24 )261.6347222222224.8228943282611654.2484874049794
Winsorized Mean ( 3 / 24 )260.7472222222224.5070480244227657.8532158542103
Winsorized Mean ( 4 / 24 )259.9861111111114.1624961783623262.4591831369319
Winsorized Mean ( 5 / 24 )259.0208333333333.7225957137203469.580704769702
Winsorized Mean ( 6 / 24 )257.36253.3170697359886277.5873046043441
Winsorized Mean ( 7 / 24 )256.1083333333333.0133147084367784.992228862214
Winsorized Mean ( 8 / 24 )255.5527777777782.8630907466787789.2576590784706
Winsorized Mean ( 9 / 24 )255.4777777777782.8390877922780489.9858674580775
Winsorized Mean ( 10 / 24 )254.9916666666672.7570579154204992.486873503989
Winsorized Mean ( 11 / 24 )254.6252.7054542298816294.115434365024
Winsorized Mean ( 12 / 24 )254.7252.6835219584943794.921898885045
Winsorized Mean ( 13 / 24 )254.6166666666672.6633297784178495.6008785430706
Winsorized Mean ( 14 / 24 )254.6555555555562.6568156431807895.849915747514
Winsorized Mean ( 15 / 24 )254.8847222222222.5937414590407398.2691321580252
Winsorized Mean ( 16 / 24 )255.2180555555562.49335292100595102.359378572283
Winsorized Mean ( 17 / 24 )255.2888888888892.46117390241260103.726473224276
Winsorized Mean ( 18 / 24 )255.5638888888892.37380585707582107.659979069942
Winsorized Mean ( 19 / 24 )255.53752.33202464767319109.577529660746
Winsorized Mean ( 20 / 24 )255.9541666666672.24322309049380114.101075256997
Winsorized Mean ( 21 / 24 )255.6333333333332.09284869244106122.14611321718
Winsorized Mean ( 22 / 24 )255.9083333333331.91296412126952133.775814448366
Winsorized Mean ( 23 / 24 )256.1638888888891.82063496631733140.700301613476
Winsorized Mean ( 24 / 24 )257.3305555555561.45281503077639177.125477162800
Trimmed Mean ( 1 / 24 )260.6514285714294.6137658560171556.4942905005667
Trimmed Mean ( 2 / 24 )259.4897058823534.224430462106661.4259622001099
Trimmed Mean ( 3 / 24 )258.3196969696973.8092313461472467.8141266560164
Trimmed Mean ( 4 / 24 )257.4093753.4571481896081274.4571423850877
Trimmed Mean ( 5 / 24 )256.6612903225813.1672958260148081.0348336314137
Trimmed Mean ( 6 / 24 )256.0952.971646070317286.179509248443
Trimmed Mean ( 7 / 24 )255.8327586206902.8616478399934889.4005038094668
Trimmed Mean ( 8 / 24 )255.7821428571432.8093375231732991.0471386037743
Trimmed Mean ( 9 / 24 )255.8203703703702.7793580992654992.0429686401247
Trimmed Mean ( 10 / 24 )255.8730769230772.7451837921484193.2079949090869
Trimmed Mean ( 11 / 24 )2562.7174342640792394.2065106722066
Trimmed Mean ( 12 / 24 )256.18752.6896993309912595.2476349486938
Trimmed Mean ( 13 / 24 )256.3782608695652.6556673752843396.54004987809
Trimmed Mean ( 14 / 24 )256.62.6124943731794598.2203072413562
Trimmed Mean ( 15 / 24 )256.8380952380952.55443171726174100.546079780679
Trimmed Mean ( 16 / 24 )257.07252.48999275948901103.242268083043
Trimmed Mean ( 17 / 24 )257.2921052631582.42571390139516106.068611436483
Trimmed Mean ( 18 / 24 )257.5277777777782.34337841557634109.895941716456
Trimmed Mean ( 19 / 24 )257.7588235294122.25116772093745114.500053075598
Trimmed Mean ( 20 / 24 )258.0218752.13013485098173121.129361777769
Trimmed Mean ( 21 / 24 )258.271.98349598483059130.209489696577
Trimmed Mean ( 22 / 24 )258.5928571428571.81586867992600142.407245634852
Trimmed Mean ( 23 / 24 )258.9307692307691.63107108962433158.748917124395
Trimmed Mean ( 24 / 24 )259.2916666666671.37301789503874188.847987781944
Median260.45
Midrange298.8
Midmean - Weighted Average at Xnp256.713513513513
Midmean - Weighted Average at X(n+1)p257.527777777778
Midmean - Empirical Distribution Function256.713513513513
Midmean - Empirical Distribution Function - Averaging257.527777777778
Midmean - Empirical Distribution Function - Interpolation257.527777777778
Midmean - Closest Observation256.713513513513
Midmean - True Basic - Statistics Graphics Toolkit257.527777777778
Midmean - MS Excel (old versions)257.292105263158
Number of observations72

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 261.711111111111 & 4.9350636777795 & 53.0309491829833 \tabularnewline
Geometric Mean & 258.748664300609 &  &  \tabularnewline
Harmonic Mean & 256.065971032172 &  &  \tabularnewline
Quadratic Mean & 264.994151402965 &  &  \tabularnewline
Winsorized Mean ( 1 / 24 ) & 261.748611111111 & 4.9280198327572 & 53.114358300921 \tabularnewline
Winsorized Mean ( 2 / 24 ) & 261.634722222222 & 4.82289432826116 & 54.2484874049794 \tabularnewline
Winsorized Mean ( 3 / 24 ) & 260.747222222222 & 4.50704802442276 & 57.8532158542103 \tabularnewline
Winsorized Mean ( 4 / 24 ) & 259.986111111111 & 4.16249617836232 & 62.4591831369319 \tabularnewline
Winsorized Mean ( 5 / 24 ) & 259.020833333333 & 3.72259571372034 & 69.580704769702 \tabularnewline
Winsorized Mean ( 6 / 24 ) & 257.3625 & 3.31706973598862 & 77.5873046043441 \tabularnewline
Winsorized Mean ( 7 / 24 ) & 256.108333333333 & 3.01331470843677 & 84.992228862214 \tabularnewline
Winsorized Mean ( 8 / 24 ) & 255.552777777778 & 2.86309074667877 & 89.2576590784706 \tabularnewline
Winsorized Mean ( 9 / 24 ) & 255.477777777778 & 2.83908779227804 & 89.9858674580775 \tabularnewline
Winsorized Mean ( 10 / 24 ) & 254.991666666667 & 2.75705791542049 & 92.486873503989 \tabularnewline
Winsorized Mean ( 11 / 24 ) & 254.625 & 2.70545422988162 & 94.115434365024 \tabularnewline
Winsorized Mean ( 12 / 24 ) & 254.725 & 2.68352195849437 & 94.921898885045 \tabularnewline
Winsorized Mean ( 13 / 24 ) & 254.616666666667 & 2.66332977841784 & 95.6008785430706 \tabularnewline
Winsorized Mean ( 14 / 24 ) & 254.655555555556 & 2.65681564318078 & 95.849915747514 \tabularnewline
Winsorized Mean ( 15 / 24 ) & 254.884722222222 & 2.59374145904073 & 98.2691321580252 \tabularnewline
Winsorized Mean ( 16 / 24 ) & 255.218055555556 & 2.49335292100595 & 102.359378572283 \tabularnewline
Winsorized Mean ( 17 / 24 ) & 255.288888888889 & 2.46117390241260 & 103.726473224276 \tabularnewline
Winsorized Mean ( 18 / 24 ) & 255.563888888889 & 2.37380585707582 & 107.659979069942 \tabularnewline
Winsorized Mean ( 19 / 24 ) & 255.5375 & 2.33202464767319 & 109.577529660746 \tabularnewline
Winsorized Mean ( 20 / 24 ) & 255.954166666667 & 2.24322309049380 & 114.101075256997 \tabularnewline
Winsorized Mean ( 21 / 24 ) & 255.633333333333 & 2.09284869244106 & 122.14611321718 \tabularnewline
Winsorized Mean ( 22 / 24 ) & 255.908333333333 & 1.91296412126952 & 133.775814448366 \tabularnewline
Winsorized Mean ( 23 / 24 ) & 256.163888888889 & 1.82063496631733 & 140.700301613476 \tabularnewline
Winsorized Mean ( 24 / 24 ) & 257.330555555556 & 1.45281503077639 & 177.125477162800 \tabularnewline
Trimmed Mean ( 1 / 24 ) & 260.651428571429 & 4.61376585601715 & 56.4942905005667 \tabularnewline
Trimmed Mean ( 2 / 24 ) & 259.489705882353 & 4.2244304621066 & 61.4259622001099 \tabularnewline
Trimmed Mean ( 3 / 24 ) & 258.319696969697 & 3.80923134614724 & 67.8141266560164 \tabularnewline
Trimmed Mean ( 4 / 24 ) & 257.409375 & 3.45714818960812 & 74.4571423850877 \tabularnewline
Trimmed Mean ( 5 / 24 ) & 256.661290322581 & 3.16729582601480 & 81.0348336314137 \tabularnewline
Trimmed Mean ( 6 / 24 ) & 256.095 & 2.9716460703172 & 86.179509248443 \tabularnewline
Trimmed Mean ( 7 / 24 ) & 255.832758620690 & 2.86164783999348 & 89.4005038094668 \tabularnewline
Trimmed Mean ( 8 / 24 ) & 255.782142857143 & 2.80933752317329 & 91.0471386037743 \tabularnewline
Trimmed Mean ( 9 / 24 ) & 255.820370370370 & 2.77935809926549 & 92.0429686401247 \tabularnewline
Trimmed Mean ( 10 / 24 ) & 255.873076923077 & 2.74518379214841 & 93.2079949090869 \tabularnewline
Trimmed Mean ( 11 / 24 ) & 256 & 2.71743426407923 & 94.2065106722066 \tabularnewline
Trimmed Mean ( 12 / 24 ) & 256.1875 & 2.68969933099125 & 95.2476349486938 \tabularnewline
Trimmed Mean ( 13 / 24 ) & 256.378260869565 & 2.65566737528433 & 96.54004987809 \tabularnewline
Trimmed Mean ( 14 / 24 ) & 256.6 & 2.61249437317945 & 98.2203072413562 \tabularnewline
Trimmed Mean ( 15 / 24 ) & 256.838095238095 & 2.55443171726174 & 100.546079780679 \tabularnewline
Trimmed Mean ( 16 / 24 ) & 257.0725 & 2.48999275948901 & 103.242268083043 \tabularnewline
Trimmed Mean ( 17 / 24 ) & 257.292105263158 & 2.42571390139516 & 106.068611436483 \tabularnewline
Trimmed Mean ( 18 / 24 ) & 257.527777777778 & 2.34337841557634 & 109.895941716456 \tabularnewline
Trimmed Mean ( 19 / 24 ) & 257.758823529412 & 2.25116772093745 & 114.500053075598 \tabularnewline
Trimmed Mean ( 20 / 24 ) & 258.021875 & 2.13013485098173 & 121.129361777769 \tabularnewline
Trimmed Mean ( 21 / 24 ) & 258.27 & 1.98349598483059 & 130.209489696577 \tabularnewline
Trimmed Mean ( 22 / 24 ) & 258.592857142857 & 1.81586867992600 & 142.407245634852 \tabularnewline
Trimmed Mean ( 23 / 24 ) & 258.930769230769 & 1.63107108962433 & 158.748917124395 \tabularnewline
Trimmed Mean ( 24 / 24 ) & 259.291666666667 & 1.37301789503874 & 188.847987781944 \tabularnewline
Median & 260.45 &  &  \tabularnewline
Midrange & 298.8 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 256.713513513513 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 257.527777777778 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 256.713513513513 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 257.527777777778 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 257.527777777778 &  &  \tabularnewline
Midmean - Closest Observation & 256.713513513513 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 257.527777777778 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 257.292105263158 &  &  \tabularnewline
Number of observations & 72 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=74417&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]261.711111111111[/C][C]4.9350636777795[/C][C]53.0309491829833[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]258.748664300609[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]256.065971032172[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]264.994151402965[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 24 )[/C][C]261.748611111111[/C][C]4.9280198327572[/C][C]53.114358300921[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 24 )[/C][C]261.634722222222[/C][C]4.82289432826116[/C][C]54.2484874049794[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 24 )[/C][C]260.747222222222[/C][C]4.50704802442276[/C][C]57.8532158542103[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 24 )[/C][C]259.986111111111[/C][C]4.16249617836232[/C][C]62.4591831369319[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 24 )[/C][C]259.020833333333[/C][C]3.72259571372034[/C][C]69.580704769702[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 24 )[/C][C]257.3625[/C][C]3.31706973598862[/C][C]77.5873046043441[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 24 )[/C][C]256.108333333333[/C][C]3.01331470843677[/C][C]84.992228862214[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 24 )[/C][C]255.552777777778[/C][C]2.86309074667877[/C][C]89.2576590784706[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 24 )[/C][C]255.477777777778[/C][C]2.83908779227804[/C][C]89.9858674580775[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 24 )[/C][C]254.991666666667[/C][C]2.75705791542049[/C][C]92.486873503989[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 24 )[/C][C]254.625[/C][C]2.70545422988162[/C][C]94.115434365024[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 24 )[/C][C]254.725[/C][C]2.68352195849437[/C][C]94.921898885045[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 24 )[/C][C]254.616666666667[/C][C]2.66332977841784[/C][C]95.6008785430706[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 24 )[/C][C]254.655555555556[/C][C]2.65681564318078[/C][C]95.849915747514[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 24 )[/C][C]254.884722222222[/C][C]2.59374145904073[/C][C]98.2691321580252[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 24 )[/C][C]255.218055555556[/C][C]2.49335292100595[/C][C]102.359378572283[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 24 )[/C][C]255.288888888889[/C][C]2.46117390241260[/C][C]103.726473224276[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 24 )[/C][C]255.563888888889[/C][C]2.37380585707582[/C][C]107.659979069942[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 24 )[/C][C]255.5375[/C][C]2.33202464767319[/C][C]109.577529660746[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 24 )[/C][C]255.954166666667[/C][C]2.24322309049380[/C][C]114.101075256997[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 24 )[/C][C]255.633333333333[/C][C]2.09284869244106[/C][C]122.14611321718[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 24 )[/C][C]255.908333333333[/C][C]1.91296412126952[/C][C]133.775814448366[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 24 )[/C][C]256.163888888889[/C][C]1.82063496631733[/C][C]140.700301613476[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 24 )[/C][C]257.330555555556[/C][C]1.45281503077639[/C][C]177.125477162800[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 24 )[/C][C]260.651428571429[/C][C]4.61376585601715[/C][C]56.4942905005667[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 24 )[/C][C]259.489705882353[/C][C]4.2244304621066[/C][C]61.4259622001099[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 24 )[/C][C]258.319696969697[/C][C]3.80923134614724[/C][C]67.8141266560164[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 24 )[/C][C]257.409375[/C][C]3.45714818960812[/C][C]74.4571423850877[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 24 )[/C][C]256.661290322581[/C][C]3.16729582601480[/C][C]81.0348336314137[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 24 )[/C][C]256.095[/C][C]2.9716460703172[/C][C]86.179509248443[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 24 )[/C][C]255.832758620690[/C][C]2.86164783999348[/C][C]89.4005038094668[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 24 )[/C][C]255.782142857143[/C][C]2.80933752317329[/C][C]91.0471386037743[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 24 )[/C][C]255.820370370370[/C][C]2.77935809926549[/C][C]92.0429686401247[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 24 )[/C][C]255.873076923077[/C][C]2.74518379214841[/C][C]93.2079949090869[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 24 )[/C][C]256[/C][C]2.71743426407923[/C][C]94.2065106722066[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 24 )[/C][C]256.1875[/C][C]2.68969933099125[/C][C]95.2476349486938[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 24 )[/C][C]256.378260869565[/C][C]2.65566737528433[/C][C]96.54004987809[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 24 )[/C][C]256.6[/C][C]2.61249437317945[/C][C]98.2203072413562[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 24 )[/C][C]256.838095238095[/C][C]2.55443171726174[/C][C]100.546079780679[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 24 )[/C][C]257.0725[/C][C]2.48999275948901[/C][C]103.242268083043[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 24 )[/C][C]257.292105263158[/C][C]2.42571390139516[/C][C]106.068611436483[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 24 )[/C][C]257.527777777778[/C][C]2.34337841557634[/C][C]109.895941716456[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 24 )[/C][C]257.758823529412[/C][C]2.25116772093745[/C][C]114.500053075598[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 24 )[/C][C]258.021875[/C][C]2.13013485098173[/C][C]121.129361777769[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 24 )[/C][C]258.27[/C][C]1.98349598483059[/C][C]130.209489696577[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 24 )[/C][C]258.592857142857[/C][C]1.81586867992600[/C][C]142.407245634852[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 24 )[/C][C]258.930769230769[/C][C]1.63107108962433[/C][C]158.748917124395[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 24 )[/C][C]259.291666666667[/C][C]1.37301789503874[/C][C]188.847987781944[/C][/ROW]
[ROW][C]Median[/C][C]260.45[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]298.8[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]256.713513513513[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]257.527777777778[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]256.713513513513[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]257.527777777778[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]257.527777777778[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]256.713513513513[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]257.527777777778[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]257.292105263158[/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=74417&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=74417&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 Mean261.7111111111114.935063677779553.0309491829833
Geometric Mean258.748664300609
Harmonic Mean256.065971032172
Quadratic Mean264.994151402965
Winsorized Mean ( 1 / 24 )261.7486111111114.928019832757253.114358300921
Winsorized Mean ( 2 / 24 )261.6347222222224.8228943282611654.2484874049794
Winsorized Mean ( 3 / 24 )260.7472222222224.5070480244227657.8532158542103
Winsorized Mean ( 4 / 24 )259.9861111111114.1624961783623262.4591831369319
Winsorized Mean ( 5 / 24 )259.0208333333333.7225957137203469.580704769702
Winsorized Mean ( 6 / 24 )257.36253.3170697359886277.5873046043441
Winsorized Mean ( 7 / 24 )256.1083333333333.0133147084367784.992228862214
Winsorized Mean ( 8 / 24 )255.5527777777782.8630907466787789.2576590784706
Winsorized Mean ( 9 / 24 )255.4777777777782.8390877922780489.9858674580775
Winsorized Mean ( 10 / 24 )254.9916666666672.7570579154204992.486873503989
Winsorized Mean ( 11 / 24 )254.6252.7054542298816294.115434365024
Winsorized Mean ( 12 / 24 )254.7252.6835219584943794.921898885045
Winsorized Mean ( 13 / 24 )254.6166666666672.6633297784178495.6008785430706
Winsorized Mean ( 14 / 24 )254.6555555555562.6568156431807895.849915747514
Winsorized Mean ( 15 / 24 )254.8847222222222.5937414590407398.2691321580252
Winsorized Mean ( 16 / 24 )255.2180555555562.49335292100595102.359378572283
Winsorized Mean ( 17 / 24 )255.2888888888892.46117390241260103.726473224276
Winsorized Mean ( 18 / 24 )255.5638888888892.37380585707582107.659979069942
Winsorized Mean ( 19 / 24 )255.53752.33202464767319109.577529660746
Winsorized Mean ( 20 / 24 )255.9541666666672.24322309049380114.101075256997
Winsorized Mean ( 21 / 24 )255.6333333333332.09284869244106122.14611321718
Winsorized Mean ( 22 / 24 )255.9083333333331.91296412126952133.775814448366
Winsorized Mean ( 23 / 24 )256.1638888888891.82063496631733140.700301613476
Winsorized Mean ( 24 / 24 )257.3305555555561.45281503077639177.125477162800
Trimmed Mean ( 1 / 24 )260.6514285714294.6137658560171556.4942905005667
Trimmed Mean ( 2 / 24 )259.4897058823534.224430462106661.4259622001099
Trimmed Mean ( 3 / 24 )258.3196969696973.8092313461472467.8141266560164
Trimmed Mean ( 4 / 24 )257.4093753.4571481896081274.4571423850877
Trimmed Mean ( 5 / 24 )256.6612903225813.1672958260148081.0348336314137
Trimmed Mean ( 6 / 24 )256.0952.971646070317286.179509248443
Trimmed Mean ( 7 / 24 )255.8327586206902.8616478399934889.4005038094668
Trimmed Mean ( 8 / 24 )255.7821428571432.8093375231732991.0471386037743
Trimmed Mean ( 9 / 24 )255.8203703703702.7793580992654992.0429686401247
Trimmed Mean ( 10 / 24 )255.8730769230772.7451837921484193.2079949090869
Trimmed Mean ( 11 / 24 )2562.7174342640792394.2065106722066
Trimmed Mean ( 12 / 24 )256.18752.6896993309912595.2476349486938
Trimmed Mean ( 13 / 24 )256.3782608695652.6556673752843396.54004987809
Trimmed Mean ( 14 / 24 )256.62.6124943731794598.2203072413562
Trimmed Mean ( 15 / 24 )256.8380952380952.55443171726174100.546079780679
Trimmed Mean ( 16 / 24 )257.07252.48999275948901103.242268083043
Trimmed Mean ( 17 / 24 )257.2921052631582.42571390139516106.068611436483
Trimmed Mean ( 18 / 24 )257.5277777777782.34337841557634109.895941716456
Trimmed Mean ( 19 / 24 )257.7588235294122.25116772093745114.500053075598
Trimmed Mean ( 20 / 24 )258.0218752.13013485098173121.129361777769
Trimmed Mean ( 21 / 24 )258.271.98349598483059130.209489696577
Trimmed Mean ( 22 / 24 )258.5928571428571.81586867992600142.407245634852
Trimmed Mean ( 23 / 24 )258.9307692307691.63107108962433158.748917124395
Trimmed Mean ( 24 / 24 )259.2916666666671.37301789503874188.847987781944
Median260.45
Midrange298.8
Midmean - Weighted Average at Xnp256.713513513513
Midmean - Weighted Average at X(n+1)p257.527777777778
Midmean - Empirical Distribution Function256.713513513513
Midmean - Empirical Distribution Function - Averaging257.527777777778
Midmean - Empirical Distribution Function - Interpolation257.527777777778
Midmean - Closest Observation256.713513513513
Midmean - True Basic - Statistics Graphics Toolkit257.527777777778
Midmean - MS Excel (old versions)257.292105263158
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')