Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationFri, 12 Mar 2010 04:58:27 -0700
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/12/t1268395491qvoomprx79np9lg.htm/, Retrieved Fri, 21 Jan 2022 10:25:22 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=74337, Retrieved Fri, 21 Jan 2022 10:25:22 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords KDGP1W52
Estimated Impact148
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Central Tendency] [] [2010-03-12 11:35:52] [2b5a188751227050025c4bb07404e527]
-    D    [Central Tendency] [] [2010-03-12 11:58:27] [589929edeb20bd59f78e9be1ffd92c80] [Current]
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Dataseries X:
2
2.4
1.5
1.2
1.5
0.6
2.7
3.7
4.9
6.6
7.4
7.2
5.3
4.7
6.1
6.6
7
7.5
6.6
7.8
4.7
5.4
4.3
4.5
5.8
4.6
5.2
3.6
4.8
6.7
6.3
4.8
8.7
6.8
7.4
9
7.9
9.1
8.7
9.8
6.4
6.1
4.7
4.8
4.2
2.8
6.1
5.8
4.9
4.6
4.1
3.6
5.9
4.5
4.8
5.7
5
7
4.6
2.6
5
4.1
3.2
0
2.3
3.8
4.5
5.9
5
4.2
4.5
6




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 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 & 1 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=74337&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]1 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=74337&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=74337&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 time1 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean5.11250.23932561664492321.3621093791443
Geometric Mean0
Harmonic Mean0
Quadratic Mean5.49584438967804
Winsorized Mean ( 1 / 24 )5.111111111111110.23443365274912521.8019514313531
Winsorized Mean ( 2 / 24 )5.1250.22950199538172722.3309605281456
Winsorized Mean ( 3 / 24 )5.1250.22367458687515622.9127504898915
Winsorized Mean ( 4 / 24 )5.1250.22367458687515622.9127504898915
Winsorized Mean ( 5 / 24 )5.104166666666670.20433905723818224.9789087590687
Winsorized Mean ( 6 / 24 )5.120833333333330.19754892324068125.9218488733266
Winsorized Mean ( 7 / 24 )5.101388888888890.19021951177171126.8184311975905
Winsorized Mean ( 8 / 24 )5.11250.18389731327832427.8008411806559
Winsorized Mean ( 9 / 24 )5.1250.18151843890352328.2340462542428
Winsorized Mean ( 10 / 24 )5.111111111111110.17411249978224129.3552221552357
Winsorized Mean ( 11 / 24 )5.141666666666670.15797463693736732.5474187904303
Winsorized Mean ( 12 / 24 )5.208333333333330.14704643002181235.4196516879788
Winsorized Mean ( 13 / 24 )5.172222222222220.14100885972872836.6801223141049
Winsorized Mean ( 14 / 24 )5.172222222222220.13485374652115238.3543086910896
Winsorized Mean ( 15 / 24 )5.172222222222220.12838868726067340.2856539199661
Winsorized Mean ( 16 / 24 )5.238888888888890.11885202652022344.0790876039246
Winsorized Mean ( 17 / 24 )5.238888888888890.11885202652022344.0790876039246
Winsorized Mean ( 18 / 24 )5.213888888888890.10758236564289848.4641591373398
Winsorized Mean ( 19 / 24 )5.18750.10353564739591050.1035163296322
Winsorized Mean ( 20 / 24 )5.159722222222220.091600695898733956.328417285458
Winsorized Mean ( 21 / 24 )5.218055555555560.084228209008835261.9514010443722
Winsorized Mean ( 22 / 24 )5.218055555555560.084228209008835261.9514010443722
Winsorized Mean ( 23 / 24 )5.186111111111110.079570087892059465.1766417318316
Winsorized Mean ( 24 / 24 )5.152777777777780.074823010314634668.8662185083183
Trimmed Mean ( 1 / 24 )5.118571428571430.22507687076228922.7414367866226
Trimmed Mean ( 2 / 24 )5.126470588235290.21387984991064523.9689273691610
Trimmed Mean ( 3 / 24 )5.127272727272730.20369026093265625.1719090730995
Trimmed Mean ( 4 / 24 )5.1281250.19420509467983426.4057181839345
Trimmed Mean ( 5 / 24 )5.129032258064520.18263288442869428.0838375526346
Trimmed Mean ( 6 / 24 )5.1350.17521294550114329.3071952264310
Trimmed Mean ( 7 / 24 )5.137931034482760.16820513622847930.5456251199352
Trimmed Mean ( 8 / 24 )5.144642857142860.16162566263977931.8306064341336
Trimmed Mean ( 9 / 24 )5.150.15515259277248733.1931288286743
Trimmed Mean ( 10 / 24 )5.153846153846150.14766818870432234.9015329507818
Trimmed Mean ( 11 / 24 )5.160.14011656954559136.8264796714213
Trimmed Mean ( 12 / 24 )5.16250.13460030797810838.3542955996777
Trimmed Mean ( 13 / 24 )5.156521739130430.13013007887921839.6259018940312
Trimmed Mean ( 14 / 24 )5.154545454545450.12577264570887640.9830406722667
Trimmed Mean ( 15 / 24 )5.152380952380950.12150995883334242.4029520036932
Trimmed Mean ( 16 / 24 )5.150.11739698157129643.8682488345951
Trimmed Mean ( 17 / 24 )5.139473684210530.11405742568536145.0604040318101
Trimmed Mean ( 18 / 24 )5.127777777777780.10937129938310046.8841259699809
Trimmed Mean ( 19 / 24 )5.117647058823530.10592690684718448.3130038546913
Trimmed Mean ( 20 / 24 )5.1093750.10213046832597950.0279209891796
Trimmed Mean ( 21 / 24 )5.103333333333330.10005554013202451.0050050861695
Trimmed Mean ( 22 / 24 )5.089285714285710.098579767303143651.6260674326366
Trimmed Mean ( 23 / 24 )5.073076923076920.09584565995674752.9296467400432
Trimmed Mean ( 24 / 24 )5.058333333333330.093039781632286654.3674248218355
Median4.9
Midrange4.9
Midmean - Weighted Average at Xnp5.07368421052632
Midmean - Weighted Average at X(n+1)p5.12777777777778
Midmean - Empirical Distribution Function5.07368421052632
Midmean - Empirical Distribution Function - Averaging5.12777777777778
Midmean - Empirical Distribution Function - Interpolation5.12777777777778
Midmean - Closest Observation5.07368421052632
Midmean - True Basic - Statistics Graphics Toolkit5.12777777777778
Midmean - MS Excel (old versions)5.18536585365854
Number of observations72

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 5.1125 & 0.239325616644923 & 21.3621093791443 \tabularnewline
Geometric Mean & 0 &  &  \tabularnewline
Harmonic Mean & 0 &  &  \tabularnewline
Quadratic Mean & 5.49584438967804 &  &  \tabularnewline
Winsorized Mean ( 1 / 24 ) & 5.11111111111111 & 0.234433652749125 & 21.8019514313531 \tabularnewline
Winsorized Mean ( 2 / 24 ) & 5.125 & 0.229501995381727 & 22.3309605281456 \tabularnewline
Winsorized Mean ( 3 / 24 ) & 5.125 & 0.223674586875156 & 22.9127504898915 \tabularnewline
Winsorized Mean ( 4 / 24 ) & 5.125 & 0.223674586875156 & 22.9127504898915 \tabularnewline
Winsorized Mean ( 5 / 24 ) & 5.10416666666667 & 0.204339057238182 & 24.9789087590687 \tabularnewline
Winsorized Mean ( 6 / 24 ) & 5.12083333333333 & 0.197548923240681 & 25.9218488733266 \tabularnewline
Winsorized Mean ( 7 / 24 ) & 5.10138888888889 & 0.190219511771711 & 26.8184311975905 \tabularnewline
Winsorized Mean ( 8 / 24 ) & 5.1125 & 0.183897313278324 & 27.8008411806559 \tabularnewline
Winsorized Mean ( 9 / 24 ) & 5.125 & 0.181518438903523 & 28.2340462542428 \tabularnewline
Winsorized Mean ( 10 / 24 ) & 5.11111111111111 & 0.174112499782241 & 29.3552221552357 \tabularnewline
Winsorized Mean ( 11 / 24 ) & 5.14166666666667 & 0.157974636937367 & 32.5474187904303 \tabularnewline
Winsorized Mean ( 12 / 24 ) & 5.20833333333333 & 0.147046430021812 & 35.4196516879788 \tabularnewline
Winsorized Mean ( 13 / 24 ) & 5.17222222222222 & 0.141008859728728 & 36.6801223141049 \tabularnewline
Winsorized Mean ( 14 / 24 ) & 5.17222222222222 & 0.134853746521152 & 38.3543086910896 \tabularnewline
Winsorized Mean ( 15 / 24 ) & 5.17222222222222 & 0.128388687260673 & 40.2856539199661 \tabularnewline
Winsorized Mean ( 16 / 24 ) & 5.23888888888889 & 0.118852026520223 & 44.0790876039246 \tabularnewline
Winsorized Mean ( 17 / 24 ) & 5.23888888888889 & 0.118852026520223 & 44.0790876039246 \tabularnewline
Winsorized Mean ( 18 / 24 ) & 5.21388888888889 & 0.107582365642898 & 48.4641591373398 \tabularnewline
Winsorized Mean ( 19 / 24 ) & 5.1875 & 0.103535647395910 & 50.1035163296322 \tabularnewline
Winsorized Mean ( 20 / 24 ) & 5.15972222222222 & 0.0916006958987339 & 56.328417285458 \tabularnewline
Winsorized Mean ( 21 / 24 ) & 5.21805555555556 & 0.0842282090088352 & 61.9514010443722 \tabularnewline
Winsorized Mean ( 22 / 24 ) & 5.21805555555556 & 0.0842282090088352 & 61.9514010443722 \tabularnewline
Winsorized Mean ( 23 / 24 ) & 5.18611111111111 & 0.0795700878920594 & 65.1766417318316 \tabularnewline
Winsorized Mean ( 24 / 24 ) & 5.15277777777778 & 0.0748230103146346 & 68.8662185083183 \tabularnewline
Trimmed Mean ( 1 / 24 ) & 5.11857142857143 & 0.225076870762289 & 22.7414367866226 \tabularnewline
Trimmed Mean ( 2 / 24 ) & 5.12647058823529 & 0.213879849910645 & 23.9689273691610 \tabularnewline
Trimmed Mean ( 3 / 24 ) & 5.12727272727273 & 0.203690260932656 & 25.1719090730995 \tabularnewline
Trimmed Mean ( 4 / 24 ) & 5.128125 & 0.194205094679834 & 26.4057181839345 \tabularnewline
Trimmed Mean ( 5 / 24 ) & 5.12903225806452 & 0.182632884428694 & 28.0838375526346 \tabularnewline
Trimmed Mean ( 6 / 24 ) & 5.135 & 0.175212945501143 & 29.3071952264310 \tabularnewline
Trimmed Mean ( 7 / 24 ) & 5.13793103448276 & 0.168205136228479 & 30.5456251199352 \tabularnewline
Trimmed Mean ( 8 / 24 ) & 5.14464285714286 & 0.161625662639779 & 31.8306064341336 \tabularnewline
Trimmed Mean ( 9 / 24 ) & 5.15 & 0.155152592772487 & 33.1931288286743 \tabularnewline
Trimmed Mean ( 10 / 24 ) & 5.15384615384615 & 0.147668188704322 & 34.9015329507818 \tabularnewline
Trimmed Mean ( 11 / 24 ) & 5.16 & 0.140116569545591 & 36.8264796714213 \tabularnewline
Trimmed Mean ( 12 / 24 ) & 5.1625 & 0.134600307978108 & 38.3542955996777 \tabularnewline
Trimmed Mean ( 13 / 24 ) & 5.15652173913043 & 0.130130078879218 & 39.6259018940312 \tabularnewline
Trimmed Mean ( 14 / 24 ) & 5.15454545454545 & 0.125772645708876 & 40.9830406722667 \tabularnewline
Trimmed Mean ( 15 / 24 ) & 5.15238095238095 & 0.121509958833342 & 42.4029520036932 \tabularnewline
Trimmed Mean ( 16 / 24 ) & 5.15 & 0.117396981571296 & 43.8682488345951 \tabularnewline
Trimmed Mean ( 17 / 24 ) & 5.13947368421053 & 0.114057425685361 & 45.0604040318101 \tabularnewline
Trimmed Mean ( 18 / 24 ) & 5.12777777777778 & 0.109371299383100 & 46.8841259699809 \tabularnewline
Trimmed Mean ( 19 / 24 ) & 5.11764705882353 & 0.105926906847184 & 48.3130038546913 \tabularnewline
Trimmed Mean ( 20 / 24 ) & 5.109375 & 0.102130468325979 & 50.0279209891796 \tabularnewline
Trimmed Mean ( 21 / 24 ) & 5.10333333333333 & 0.100055540132024 & 51.0050050861695 \tabularnewline
Trimmed Mean ( 22 / 24 ) & 5.08928571428571 & 0.0985797673031436 & 51.6260674326366 \tabularnewline
Trimmed Mean ( 23 / 24 ) & 5.07307692307692 & 0.095845659956747 & 52.9296467400432 \tabularnewline
Trimmed Mean ( 24 / 24 ) & 5.05833333333333 & 0.0930397816322866 & 54.3674248218355 \tabularnewline
Median & 4.9 &  &  \tabularnewline
Midrange & 4.9 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 5.07368421052632 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 5.12777777777778 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 5.07368421052632 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 5.12777777777778 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 5.12777777777778 &  &  \tabularnewline
Midmean - Closest Observation & 5.07368421052632 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 5.12777777777778 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 5.18536585365854 &  &  \tabularnewline
Number of observations & 72 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=74337&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]5.1125[/C][C]0.239325616644923[/C][C]21.3621093791443[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]0[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]0[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]5.49584438967804[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 24 )[/C][C]5.11111111111111[/C][C]0.234433652749125[/C][C]21.8019514313531[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 24 )[/C][C]5.125[/C][C]0.229501995381727[/C][C]22.3309605281456[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 24 )[/C][C]5.125[/C][C]0.223674586875156[/C][C]22.9127504898915[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 24 )[/C][C]5.125[/C][C]0.223674586875156[/C][C]22.9127504898915[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 24 )[/C][C]5.10416666666667[/C][C]0.204339057238182[/C][C]24.9789087590687[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 24 )[/C][C]5.12083333333333[/C][C]0.197548923240681[/C][C]25.9218488733266[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 24 )[/C][C]5.10138888888889[/C][C]0.190219511771711[/C][C]26.8184311975905[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 24 )[/C][C]5.1125[/C][C]0.183897313278324[/C][C]27.8008411806559[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 24 )[/C][C]5.125[/C][C]0.181518438903523[/C][C]28.2340462542428[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 24 )[/C][C]5.11111111111111[/C][C]0.174112499782241[/C][C]29.3552221552357[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 24 )[/C][C]5.14166666666667[/C][C]0.157974636937367[/C][C]32.5474187904303[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 24 )[/C][C]5.20833333333333[/C][C]0.147046430021812[/C][C]35.4196516879788[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 24 )[/C][C]5.17222222222222[/C][C]0.141008859728728[/C][C]36.6801223141049[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 24 )[/C][C]5.17222222222222[/C][C]0.134853746521152[/C][C]38.3543086910896[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 24 )[/C][C]5.17222222222222[/C][C]0.128388687260673[/C][C]40.2856539199661[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 24 )[/C][C]5.23888888888889[/C][C]0.118852026520223[/C][C]44.0790876039246[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 24 )[/C][C]5.23888888888889[/C][C]0.118852026520223[/C][C]44.0790876039246[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 24 )[/C][C]5.21388888888889[/C][C]0.107582365642898[/C][C]48.4641591373398[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 24 )[/C][C]5.1875[/C][C]0.103535647395910[/C][C]50.1035163296322[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 24 )[/C][C]5.15972222222222[/C][C]0.0916006958987339[/C][C]56.328417285458[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 24 )[/C][C]5.21805555555556[/C][C]0.0842282090088352[/C][C]61.9514010443722[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 24 )[/C][C]5.21805555555556[/C][C]0.0842282090088352[/C][C]61.9514010443722[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 24 )[/C][C]5.18611111111111[/C][C]0.0795700878920594[/C][C]65.1766417318316[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 24 )[/C][C]5.15277777777778[/C][C]0.0748230103146346[/C][C]68.8662185083183[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 24 )[/C][C]5.11857142857143[/C][C]0.225076870762289[/C][C]22.7414367866226[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 24 )[/C][C]5.12647058823529[/C][C]0.213879849910645[/C][C]23.9689273691610[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 24 )[/C][C]5.12727272727273[/C][C]0.203690260932656[/C][C]25.1719090730995[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 24 )[/C][C]5.128125[/C][C]0.194205094679834[/C][C]26.4057181839345[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 24 )[/C][C]5.12903225806452[/C][C]0.182632884428694[/C][C]28.0838375526346[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 24 )[/C][C]5.135[/C][C]0.175212945501143[/C][C]29.3071952264310[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 24 )[/C][C]5.13793103448276[/C][C]0.168205136228479[/C][C]30.5456251199352[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 24 )[/C][C]5.14464285714286[/C][C]0.161625662639779[/C][C]31.8306064341336[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 24 )[/C][C]5.15[/C][C]0.155152592772487[/C][C]33.1931288286743[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 24 )[/C][C]5.15384615384615[/C][C]0.147668188704322[/C][C]34.9015329507818[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 24 )[/C][C]5.16[/C][C]0.140116569545591[/C][C]36.8264796714213[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 24 )[/C][C]5.1625[/C][C]0.134600307978108[/C][C]38.3542955996777[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 24 )[/C][C]5.15652173913043[/C][C]0.130130078879218[/C][C]39.6259018940312[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 24 )[/C][C]5.15454545454545[/C][C]0.125772645708876[/C][C]40.9830406722667[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 24 )[/C][C]5.15238095238095[/C][C]0.121509958833342[/C][C]42.4029520036932[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 24 )[/C][C]5.15[/C][C]0.117396981571296[/C][C]43.8682488345951[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 24 )[/C][C]5.13947368421053[/C][C]0.114057425685361[/C][C]45.0604040318101[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 24 )[/C][C]5.12777777777778[/C][C]0.109371299383100[/C][C]46.8841259699809[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 24 )[/C][C]5.11764705882353[/C][C]0.105926906847184[/C][C]48.3130038546913[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 24 )[/C][C]5.109375[/C][C]0.102130468325979[/C][C]50.0279209891796[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 24 )[/C][C]5.10333333333333[/C][C]0.100055540132024[/C][C]51.0050050861695[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 24 )[/C][C]5.08928571428571[/C][C]0.0985797673031436[/C][C]51.6260674326366[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 24 )[/C][C]5.07307692307692[/C][C]0.095845659956747[/C][C]52.9296467400432[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 24 )[/C][C]5.05833333333333[/C][C]0.0930397816322866[/C][C]54.3674248218355[/C][/ROW]
[ROW][C]Median[/C][C]4.9[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]4.9[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]5.07368421052632[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]5.12777777777778[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]5.07368421052632[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]5.12777777777778[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]5.12777777777778[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]5.07368421052632[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]5.12777777777778[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]5.18536585365854[/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=74337&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=74337&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 Mean5.11250.23932561664492321.3621093791443
Geometric Mean0
Harmonic Mean0
Quadratic Mean5.49584438967804
Winsorized Mean ( 1 / 24 )5.111111111111110.23443365274912521.8019514313531
Winsorized Mean ( 2 / 24 )5.1250.22950199538172722.3309605281456
Winsorized Mean ( 3 / 24 )5.1250.22367458687515622.9127504898915
Winsorized Mean ( 4 / 24 )5.1250.22367458687515622.9127504898915
Winsorized Mean ( 5 / 24 )5.104166666666670.20433905723818224.9789087590687
Winsorized Mean ( 6 / 24 )5.120833333333330.19754892324068125.9218488733266
Winsorized Mean ( 7 / 24 )5.101388888888890.19021951177171126.8184311975905
Winsorized Mean ( 8 / 24 )5.11250.18389731327832427.8008411806559
Winsorized Mean ( 9 / 24 )5.1250.18151843890352328.2340462542428
Winsorized Mean ( 10 / 24 )5.111111111111110.17411249978224129.3552221552357
Winsorized Mean ( 11 / 24 )5.141666666666670.15797463693736732.5474187904303
Winsorized Mean ( 12 / 24 )5.208333333333330.14704643002181235.4196516879788
Winsorized Mean ( 13 / 24 )5.172222222222220.14100885972872836.6801223141049
Winsorized Mean ( 14 / 24 )5.172222222222220.13485374652115238.3543086910896
Winsorized Mean ( 15 / 24 )5.172222222222220.12838868726067340.2856539199661
Winsorized Mean ( 16 / 24 )5.238888888888890.11885202652022344.0790876039246
Winsorized Mean ( 17 / 24 )5.238888888888890.11885202652022344.0790876039246
Winsorized Mean ( 18 / 24 )5.213888888888890.10758236564289848.4641591373398
Winsorized Mean ( 19 / 24 )5.18750.10353564739591050.1035163296322
Winsorized Mean ( 20 / 24 )5.159722222222220.091600695898733956.328417285458
Winsorized Mean ( 21 / 24 )5.218055555555560.084228209008835261.9514010443722
Winsorized Mean ( 22 / 24 )5.218055555555560.084228209008835261.9514010443722
Winsorized Mean ( 23 / 24 )5.186111111111110.079570087892059465.1766417318316
Winsorized Mean ( 24 / 24 )5.152777777777780.074823010314634668.8662185083183
Trimmed Mean ( 1 / 24 )5.118571428571430.22507687076228922.7414367866226
Trimmed Mean ( 2 / 24 )5.126470588235290.21387984991064523.9689273691610
Trimmed Mean ( 3 / 24 )5.127272727272730.20369026093265625.1719090730995
Trimmed Mean ( 4 / 24 )5.1281250.19420509467983426.4057181839345
Trimmed Mean ( 5 / 24 )5.129032258064520.18263288442869428.0838375526346
Trimmed Mean ( 6 / 24 )5.1350.17521294550114329.3071952264310
Trimmed Mean ( 7 / 24 )5.137931034482760.16820513622847930.5456251199352
Trimmed Mean ( 8 / 24 )5.144642857142860.16162566263977931.8306064341336
Trimmed Mean ( 9 / 24 )5.150.15515259277248733.1931288286743
Trimmed Mean ( 10 / 24 )5.153846153846150.14766818870432234.9015329507818
Trimmed Mean ( 11 / 24 )5.160.14011656954559136.8264796714213
Trimmed Mean ( 12 / 24 )5.16250.13460030797810838.3542955996777
Trimmed Mean ( 13 / 24 )5.156521739130430.13013007887921839.6259018940312
Trimmed Mean ( 14 / 24 )5.154545454545450.12577264570887640.9830406722667
Trimmed Mean ( 15 / 24 )5.152380952380950.12150995883334242.4029520036932
Trimmed Mean ( 16 / 24 )5.150.11739698157129643.8682488345951
Trimmed Mean ( 17 / 24 )5.139473684210530.11405742568536145.0604040318101
Trimmed Mean ( 18 / 24 )5.127777777777780.10937129938310046.8841259699809
Trimmed Mean ( 19 / 24 )5.117647058823530.10592690684718448.3130038546913
Trimmed Mean ( 20 / 24 )5.1093750.10213046832597950.0279209891796
Trimmed Mean ( 21 / 24 )5.103333333333330.10005554013202451.0050050861695
Trimmed Mean ( 22 / 24 )5.089285714285710.098579767303143651.6260674326366
Trimmed Mean ( 23 / 24 )5.073076923076920.09584565995674752.9296467400432
Trimmed Mean ( 24 / 24 )5.058333333333330.093039781632286654.3674248218355
Median4.9
Midrange4.9
Midmean - Weighted Average at Xnp5.07368421052632
Midmean - Weighted Average at X(n+1)p5.12777777777778
Midmean - Empirical Distribution Function5.07368421052632
Midmean - Empirical Distribution Function - Averaging5.12777777777778
Midmean - Empirical Distribution Function - Interpolation5.12777777777778
Midmean - Closest Observation5.07368421052632
Midmean - True Basic - Statistics Graphics Toolkit5.12777777777778
Midmean - MS Excel (old versions)5.18536585365854
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')