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Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationSun, 21 Oct 2012 07:29:29 -0400
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2012/Oct/21/t1350819013pgrqsmns4m5ivkh.htm/, Retrieved Mon, 29 Apr 2024 02:41:31 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=180791, Retrieved Mon, 29 Apr 2024 02:41:31 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact61
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [centrummaten trei...] [2012-10-21 11:29:29] [e9693728cfb785c84158f00c620f24e3] [Current]
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Dataseries X:
2.9
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3.1
3.1
3.1
3.1
3.1
3.1
3.1
3.1
3.1
3.1
3.1
3.1
3.3
3.3
3.3
3.3
3.3
3.3
3.3
3.3
3.3
3.3
3.3
3.3
3.3
3.3
3.3
3.3
3.3
3.3
3.3
3.3
3.3
3.3
3.3
3.3
3.3
3.3
3.3
3.3
3.3
3.3
3.3
3.3
3.3
3.3
3.3




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Gertrude Mary Cox' @ cox.wessa.net

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 2 seconds \tabularnewline
R Server & 'Gertrude Mary Cox' @ cox.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=180791&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]'Gertrude Mary Cox' @ cox.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=180791&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=180791&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'Gertrude Mary Cox' @ cox.wessa.net







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean3.161111111111110.0166144199341376190.263104197576
Geometric Mean3.15799629195959
Harmonic Mean3.15487049815673
Quadratic Mean3.16420957305647
Winsorized Mean ( 1 / 24 )3.16250.0163631399009432193.26975257467
Winsorized Mean ( 2 / 24 )3.16250.0163631399009432193.26975257467
Winsorized Mean ( 3 / 24 )3.16250.0163631399009432193.26975257467
Winsorized Mean ( 4 / 24 )3.16250.0163631399009432193.26975257467
Winsorized Mean ( 5 / 24 )3.16250.0163631399009432193.26975257467
Winsorized Mean ( 6 / 24 )3.16250.0163631399009432193.26975257467
Winsorized Mean ( 7 / 24 )3.16250.0163631399009432193.26975257467
Winsorized Mean ( 8 / 24 )3.16250.0163631399009432193.26975257467
Winsorized Mean ( 9 / 24 )3.16250.0163631399009432193.26975257467
Winsorized Mean ( 10 / 24 )3.16250.0163631399009432193.26975257467
Winsorized Mean ( 11 / 24 )3.16250.0163631399009432193.26975257467
Winsorized Mean ( 12 / 24 )3.16250.0163631399009432193.26975257467
Winsorized Mean ( 13 / 24 )3.16250.0163631399009432193.26975257467
Winsorized Mean ( 14 / 24 )3.16250.0163631399009432193.26975257467
Winsorized Mean ( 15 / 24 )3.16250.0163631399009432193.26975257467
Winsorized Mean ( 16 / 24 )3.16250.0163631399009432193.26975257467
Winsorized Mean ( 17 / 24 )3.16250.0163631399009432193.26975257467
Winsorized Mean ( 18 / 24 )3.16250.0163631399009432193.26975257467
Winsorized Mean ( 19 / 24 )3.16250.0163631399009432193.26975257467
Winsorized Mean ( 20 / 24 )3.16250.0163631399009432193.26975257467
Winsorized Mean ( 21 / 24 )3.16250.0163631399009432193.26975257467
Winsorized Mean ( 22 / 24 )3.16250.0163631399009432193.26975257467
Winsorized Mean ( 23 / 24 )3.16250.0163631399009432193.26975257467
Winsorized Mean ( 24 / 24 )3.16250.0163631399009432193.26975257467
Trimmed Mean ( 1 / 24 )3.162857142857140.0165529989616049191.074569036914
Trimmed Mean ( 2 / 24 )3.163235294117650.0167489875946718188.861283479841
Trimmed Mean ( 3 / 24 )3.163636363636360.0169513720572036186.630105985548
Trimmed Mean ( 4 / 24 )3.16406250.0171604223935832184.381388023592
Trimmed Mean ( 5 / 24 )3.164516129032260.0173764086613702182.115659840998
Trimmed Mean ( 6 / 24 )3.1650.0175995955269394179.833678288538
Trimmed Mean ( 7 / 24 )3.165517241379310.0178302346146136177.536488430997
Trimmed Mean ( 8 / 24 )3.166071428571430.0180685537470033175.225503540731
Trimmed Mean ( 9 / 24 )3.166666666666670.0183147418598252172.902609870412
Trimmed Mean ( 10 / 24 )3.167307692307690.0185689278580114170.570305217767
Trimmed Mean ( 11 / 24 )3.1680.0188311509180389168.231884168337
Trimmed Mean ( 12 / 24 )3.168750.0191013186021391165.891688736355
Trimmed Mean ( 13 / 24 )3.16956521739130.0193791474208078163.555452082895
Trimmed Mean ( 14 / 24 )3.170454545454550.019664077811561161.230777046181
Trimmed Mean ( 15 / 24 )3.171428571428570.0199551513077022158.927813802368
Trimmed Mean ( 16 / 24 )3.17250.0202508309421158156.660238242478
Trimmed Mean ( 17 / 24 )3.173684210526320.0205487348844886154.446696031005
Trimmed Mean ( 18 / 24 )3.1750.0208452346958198152.312988859593
Trimmed Mean ( 19 / 24 )3.176470588235290.0211348372677749150.29548361267
Trimmed Mean ( 20 / 24 )3.1781250.0214092114445492148.446616459064
Trimmed Mean ( 21 / 24 )3.180.0216556116801484146.844155084065
Trimmed Mean ( 22 / 24 )3.182142857142860.0218542377984355145.60758817087
Trimmed Mean ( 23 / 24 )3.184615384615380.021973625933978144.928988696899
Trimmed Mean ( 24 / 24 )3.18750.0219621710338877145.135924635213
Median3.1
Midrange3.1
Midmean - Weighted Average at Xnp3.16478873239437
Midmean - Weighted Average at X(n+1)p3.16478873239437
Midmean - Empirical Distribution Function3.16478873239437
Midmean - Empirical Distribution Function - Averaging3.16478873239437
Midmean - Empirical Distribution Function - Interpolation3.16478873239437
Midmean - Closest Observation3.16478873239437
Midmean - True Basic - Statistics Graphics Toolkit3.16478873239437
Midmean - MS Excel (old versions)3.16478873239437
Number of observations72

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 3.16111111111111 & 0.0166144199341376 & 190.263104197576 \tabularnewline
Geometric Mean & 3.15799629195959 &  &  \tabularnewline
Harmonic Mean & 3.15487049815673 &  &  \tabularnewline
Quadratic Mean & 3.16420957305647 &  &  \tabularnewline
Winsorized Mean ( 1 / 24 ) & 3.1625 & 0.0163631399009432 & 193.26975257467 \tabularnewline
Winsorized Mean ( 2 / 24 ) & 3.1625 & 0.0163631399009432 & 193.26975257467 \tabularnewline
Winsorized Mean ( 3 / 24 ) & 3.1625 & 0.0163631399009432 & 193.26975257467 \tabularnewline
Winsorized Mean ( 4 / 24 ) & 3.1625 & 0.0163631399009432 & 193.26975257467 \tabularnewline
Winsorized Mean ( 5 / 24 ) & 3.1625 & 0.0163631399009432 & 193.26975257467 \tabularnewline
Winsorized Mean ( 6 / 24 ) & 3.1625 & 0.0163631399009432 & 193.26975257467 \tabularnewline
Winsorized Mean ( 7 / 24 ) & 3.1625 & 0.0163631399009432 & 193.26975257467 \tabularnewline
Winsorized Mean ( 8 / 24 ) & 3.1625 & 0.0163631399009432 & 193.26975257467 \tabularnewline
Winsorized Mean ( 9 / 24 ) & 3.1625 & 0.0163631399009432 & 193.26975257467 \tabularnewline
Winsorized Mean ( 10 / 24 ) & 3.1625 & 0.0163631399009432 & 193.26975257467 \tabularnewline
Winsorized Mean ( 11 / 24 ) & 3.1625 & 0.0163631399009432 & 193.26975257467 \tabularnewline
Winsorized Mean ( 12 / 24 ) & 3.1625 & 0.0163631399009432 & 193.26975257467 \tabularnewline
Winsorized Mean ( 13 / 24 ) & 3.1625 & 0.0163631399009432 & 193.26975257467 \tabularnewline
Winsorized Mean ( 14 / 24 ) & 3.1625 & 0.0163631399009432 & 193.26975257467 \tabularnewline
Winsorized Mean ( 15 / 24 ) & 3.1625 & 0.0163631399009432 & 193.26975257467 \tabularnewline
Winsorized Mean ( 16 / 24 ) & 3.1625 & 0.0163631399009432 & 193.26975257467 \tabularnewline
Winsorized Mean ( 17 / 24 ) & 3.1625 & 0.0163631399009432 & 193.26975257467 \tabularnewline
Winsorized Mean ( 18 / 24 ) & 3.1625 & 0.0163631399009432 & 193.26975257467 \tabularnewline
Winsorized Mean ( 19 / 24 ) & 3.1625 & 0.0163631399009432 & 193.26975257467 \tabularnewline
Winsorized Mean ( 20 / 24 ) & 3.1625 & 0.0163631399009432 & 193.26975257467 \tabularnewline
Winsorized Mean ( 21 / 24 ) & 3.1625 & 0.0163631399009432 & 193.26975257467 \tabularnewline
Winsorized Mean ( 22 / 24 ) & 3.1625 & 0.0163631399009432 & 193.26975257467 \tabularnewline
Winsorized Mean ( 23 / 24 ) & 3.1625 & 0.0163631399009432 & 193.26975257467 \tabularnewline
Winsorized Mean ( 24 / 24 ) & 3.1625 & 0.0163631399009432 & 193.26975257467 \tabularnewline
Trimmed Mean ( 1 / 24 ) & 3.16285714285714 & 0.0165529989616049 & 191.074569036914 \tabularnewline
Trimmed Mean ( 2 / 24 ) & 3.16323529411765 & 0.0167489875946718 & 188.861283479841 \tabularnewline
Trimmed Mean ( 3 / 24 ) & 3.16363636363636 & 0.0169513720572036 & 186.630105985548 \tabularnewline
Trimmed Mean ( 4 / 24 ) & 3.1640625 & 0.0171604223935832 & 184.381388023592 \tabularnewline
Trimmed Mean ( 5 / 24 ) & 3.16451612903226 & 0.0173764086613702 & 182.115659840998 \tabularnewline
Trimmed Mean ( 6 / 24 ) & 3.165 & 0.0175995955269394 & 179.833678288538 \tabularnewline
Trimmed Mean ( 7 / 24 ) & 3.16551724137931 & 0.0178302346146136 & 177.536488430997 \tabularnewline
Trimmed Mean ( 8 / 24 ) & 3.16607142857143 & 0.0180685537470033 & 175.225503540731 \tabularnewline
Trimmed Mean ( 9 / 24 ) & 3.16666666666667 & 0.0183147418598252 & 172.902609870412 \tabularnewline
Trimmed Mean ( 10 / 24 ) & 3.16730769230769 & 0.0185689278580114 & 170.570305217767 \tabularnewline
Trimmed Mean ( 11 / 24 ) & 3.168 & 0.0188311509180389 & 168.231884168337 \tabularnewline
Trimmed Mean ( 12 / 24 ) & 3.16875 & 0.0191013186021391 & 165.891688736355 \tabularnewline
Trimmed Mean ( 13 / 24 ) & 3.1695652173913 & 0.0193791474208078 & 163.555452082895 \tabularnewline
Trimmed Mean ( 14 / 24 ) & 3.17045454545455 & 0.019664077811561 & 161.230777046181 \tabularnewline
Trimmed Mean ( 15 / 24 ) & 3.17142857142857 & 0.0199551513077022 & 158.927813802368 \tabularnewline
Trimmed Mean ( 16 / 24 ) & 3.1725 & 0.0202508309421158 & 156.660238242478 \tabularnewline
Trimmed Mean ( 17 / 24 ) & 3.17368421052632 & 0.0205487348844886 & 154.446696031005 \tabularnewline
Trimmed Mean ( 18 / 24 ) & 3.175 & 0.0208452346958198 & 152.312988859593 \tabularnewline
Trimmed Mean ( 19 / 24 ) & 3.17647058823529 & 0.0211348372677749 & 150.29548361267 \tabularnewline
Trimmed Mean ( 20 / 24 ) & 3.178125 & 0.0214092114445492 & 148.446616459064 \tabularnewline
Trimmed Mean ( 21 / 24 ) & 3.18 & 0.0216556116801484 & 146.844155084065 \tabularnewline
Trimmed Mean ( 22 / 24 ) & 3.18214285714286 & 0.0218542377984355 & 145.60758817087 \tabularnewline
Trimmed Mean ( 23 / 24 ) & 3.18461538461538 & 0.021973625933978 & 144.928988696899 \tabularnewline
Trimmed Mean ( 24 / 24 ) & 3.1875 & 0.0219621710338877 & 145.135924635213 \tabularnewline
Median & 3.1 &  &  \tabularnewline
Midrange & 3.1 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 3.16478873239437 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 3.16478873239437 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 3.16478873239437 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 3.16478873239437 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 3.16478873239437 &  &  \tabularnewline
Midmean - Closest Observation & 3.16478873239437 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 3.16478873239437 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 3.16478873239437 &  &  \tabularnewline
Number of observations & 72 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=180791&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]3.16111111111111[/C][C]0.0166144199341376[/C][C]190.263104197576[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]3.15799629195959[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]3.15487049815673[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]3.16420957305647[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 24 )[/C][C]3.1625[/C][C]0.0163631399009432[/C][C]193.26975257467[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 24 )[/C][C]3.1625[/C][C]0.0163631399009432[/C][C]193.26975257467[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 24 )[/C][C]3.1625[/C][C]0.0163631399009432[/C][C]193.26975257467[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 24 )[/C][C]3.1625[/C][C]0.0163631399009432[/C][C]193.26975257467[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 24 )[/C][C]3.1625[/C][C]0.0163631399009432[/C][C]193.26975257467[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 24 )[/C][C]3.1625[/C][C]0.0163631399009432[/C][C]193.26975257467[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 24 )[/C][C]3.1625[/C][C]0.0163631399009432[/C][C]193.26975257467[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 24 )[/C][C]3.1625[/C][C]0.0163631399009432[/C][C]193.26975257467[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 24 )[/C][C]3.1625[/C][C]0.0163631399009432[/C][C]193.26975257467[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 24 )[/C][C]3.1625[/C][C]0.0163631399009432[/C][C]193.26975257467[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 24 )[/C][C]3.1625[/C][C]0.0163631399009432[/C][C]193.26975257467[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 24 )[/C][C]3.1625[/C][C]0.0163631399009432[/C][C]193.26975257467[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 24 )[/C][C]3.1625[/C][C]0.0163631399009432[/C][C]193.26975257467[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 24 )[/C][C]3.1625[/C][C]0.0163631399009432[/C][C]193.26975257467[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 24 )[/C][C]3.1625[/C][C]0.0163631399009432[/C][C]193.26975257467[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 24 )[/C][C]3.1625[/C][C]0.0163631399009432[/C][C]193.26975257467[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 24 )[/C][C]3.1625[/C][C]0.0163631399009432[/C][C]193.26975257467[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 24 )[/C][C]3.1625[/C][C]0.0163631399009432[/C][C]193.26975257467[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 24 )[/C][C]3.1625[/C][C]0.0163631399009432[/C][C]193.26975257467[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 24 )[/C][C]3.1625[/C][C]0.0163631399009432[/C][C]193.26975257467[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 24 )[/C][C]3.1625[/C][C]0.0163631399009432[/C][C]193.26975257467[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 24 )[/C][C]3.1625[/C][C]0.0163631399009432[/C][C]193.26975257467[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 24 )[/C][C]3.1625[/C][C]0.0163631399009432[/C][C]193.26975257467[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 24 )[/C][C]3.1625[/C][C]0.0163631399009432[/C][C]193.26975257467[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 24 )[/C][C]3.16285714285714[/C][C]0.0165529989616049[/C][C]191.074569036914[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 24 )[/C][C]3.16323529411765[/C][C]0.0167489875946718[/C][C]188.861283479841[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 24 )[/C][C]3.16363636363636[/C][C]0.0169513720572036[/C][C]186.630105985548[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 24 )[/C][C]3.1640625[/C][C]0.0171604223935832[/C][C]184.381388023592[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 24 )[/C][C]3.16451612903226[/C][C]0.0173764086613702[/C][C]182.115659840998[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 24 )[/C][C]3.165[/C][C]0.0175995955269394[/C][C]179.833678288538[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 24 )[/C][C]3.16551724137931[/C][C]0.0178302346146136[/C][C]177.536488430997[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 24 )[/C][C]3.16607142857143[/C][C]0.0180685537470033[/C][C]175.225503540731[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 24 )[/C][C]3.16666666666667[/C][C]0.0183147418598252[/C][C]172.902609870412[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 24 )[/C][C]3.16730769230769[/C][C]0.0185689278580114[/C][C]170.570305217767[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 24 )[/C][C]3.168[/C][C]0.0188311509180389[/C][C]168.231884168337[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 24 )[/C][C]3.16875[/C][C]0.0191013186021391[/C][C]165.891688736355[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 24 )[/C][C]3.1695652173913[/C][C]0.0193791474208078[/C][C]163.555452082895[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 24 )[/C][C]3.17045454545455[/C][C]0.019664077811561[/C][C]161.230777046181[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 24 )[/C][C]3.17142857142857[/C][C]0.0199551513077022[/C][C]158.927813802368[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 24 )[/C][C]3.1725[/C][C]0.0202508309421158[/C][C]156.660238242478[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 24 )[/C][C]3.17368421052632[/C][C]0.0205487348844886[/C][C]154.446696031005[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 24 )[/C][C]3.175[/C][C]0.0208452346958198[/C][C]152.312988859593[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 24 )[/C][C]3.17647058823529[/C][C]0.0211348372677749[/C][C]150.29548361267[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 24 )[/C][C]3.178125[/C][C]0.0214092114445492[/C][C]148.446616459064[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 24 )[/C][C]3.18[/C][C]0.0216556116801484[/C][C]146.844155084065[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 24 )[/C][C]3.18214285714286[/C][C]0.0218542377984355[/C][C]145.60758817087[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 24 )[/C][C]3.18461538461538[/C][C]0.021973625933978[/C][C]144.928988696899[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 24 )[/C][C]3.1875[/C][C]0.0219621710338877[/C][C]145.135924635213[/C][/ROW]
[ROW][C]Median[/C][C]3.1[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]3.1[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]3.16478873239437[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]3.16478873239437[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]3.16478873239437[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]3.16478873239437[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]3.16478873239437[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]3.16478873239437[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]3.16478873239437[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]3.16478873239437[/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=180791&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=180791&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 Mean3.161111111111110.0166144199341376190.263104197576
Geometric Mean3.15799629195959
Harmonic Mean3.15487049815673
Quadratic Mean3.16420957305647
Winsorized Mean ( 1 / 24 )3.16250.0163631399009432193.26975257467
Winsorized Mean ( 2 / 24 )3.16250.0163631399009432193.26975257467
Winsorized Mean ( 3 / 24 )3.16250.0163631399009432193.26975257467
Winsorized Mean ( 4 / 24 )3.16250.0163631399009432193.26975257467
Winsorized Mean ( 5 / 24 )3.16250.0163631399009432193.26975257467
Winsorized Mean ( 6 / 24 )3.16250.0163631399009432193.26975257467
Winsorized Mean ( 7 / 24 )3.16250.0163631399009432193.26975257467
Winsorized Mean ( 8 / 24 )3.16250.0163631399009432193.26975257467
Winsorized Mean ( 9 / 24 )3.16250.0163631399009432193.26975257467
Winsorized Mean ( 10 / 24 )3.16250.0163631399009432193.26975257467
Winsorized Mean ( 11 / 24 )3.16250.0163631399009432193.26975257467
Winsorized Mean ( 12 / 24 )3.16250.0163631399009432193.26975257467
Winsorized Mean ( 13 / 24 )3.16250.0163631399009432193.26975257467
Winsorized Mean ( 14 / 24 )3.16250.0163631399009432193.26975257467
Winsorized Mean ( 15 / 24 )3.16250.0163631399009432193.26975257467
Winsorized Mean ( 16 / 24 )3.16250.0163631399009432193.26975257467
Winsorized Mean ( 17 / 24 )3.16250.0163631399009432193.26975257467
Winsorized Mean ( 18 / 24 )3.16250.0163631399009432193.26975257467
Winsorized Mean ( 19 / 24 )3.16250.0163631399009432193.26975257467
Winsorized Mean ( 20 / 24 )3.16250.0163631399009432193.26975257467
Winsorized Mean ( 21 / 24 )3.16250.0163631399009432193.26975257467
Winsorized Mean ( 22 / 24 )3.16250.0163631399009432193.26975257467
Winsorized Mean ( 23 / 24 )3.16250.0163631399009432193.26975257467
Winsorized Mean ( 24 / 24 )3.16250.0163631399009432193.26975257467
Trimmed Mean ( 1 / 24 )3.162857142857140.0165529989616049191.074569036914
Trimmed Mean ( 2 / 24 )3.163235294117650.0167489875946718188.861283479841
Trimmed Mean ( 3 / 24 )3.163636363636360.0169513720572036186.630105985548
Trimmed Mean ( 4 / 24 )3.16406250.0171604223935832184.381388023592
Trimmed Mean ( 5 / 24 )3.164516129032260.0173764086613702182.115659840998
Trimmed Mean ( 6 / 24 )3.1650.0175995955269394179.833678288538
Trimmed Mean ( 7 / 24 )3.165517241379310.0178302346146136177.536488430997
Trimmed Mean ( 8 / 24 )3.166071428571430.0180685537470033175.225503540731
Trimmed Mean ( 9 / 24 )3.166666666666670.0183147418598252172.902609870412
Trimmed Mean ( 10 / 24 )3.167307692307690.0185689278580114170.570305217767
Trimmed Mean ( 11 / 24 )3.1680.0188311509180389168.231884168337
Trimmed Mean ( 12 / 24 )3.168750.0191013186021391165.891688736355
Trimmed Mean ( 13 / 24 )3.16956521739130.0193791474208078163.555452082895
Trimmed Mean ( 14 / 24 )3.170454545454550.019664077811561161.230777046181
Trimmed Mean ( 15 / 24 )3.171428571428570.0199551513077022158.927813802368
Trimmed Mean ( 16 / 24 )3.17250.0202508309421158156.660238242478
Trimmed Mean ( 17 / 24 )3.173684210526320.0205487348844886154.446696031005
Trimmed Mean ( 18 / 24 )3.1750.0208452346958198152.312988859593
Trimmed Mean ( 19 / 24 )3.176470588235290.0211348372677749150.29548361267
Trimmed Mean ( 20 / 24 )3.1781250.0214092114445492148.446616459064
Trimmed Mean ( 21 / 24 )3.180.0216556116801484146.844155084065
Trimmed Mean ( 22 / 24 )3.182142857142860.0218542377984355145.60758817087
Trimmed Mean ( 23 / 24 )3.184615384615380.021973625933978144.928988696899
Trimmed Mean ( 24 / 24 )3.18750.0219621710338877145.135924635213
Median3.1
Midrange3.1
Midmean - Weighted Average at Xnp3.16478873239437
Midmean - Weighted Average at X(n+1)p3.16478873239437
Midmean - Empirical Distribution Function3.16478873239437
Midmean - Empirical Distribution Function - Averaging3.16478873239437
Midmean - Empirical Distribution Function - Interpolation3.16478873239437
Midmean - Closest Observation3.16478873239437
Midmean - True Basic - Statistics Graphics Toolkit3.16478873239437
Midmean - MS Excel (old versions)3.16478873239437
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')