Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationMon, 17 Oct 2016 20:03:31 +0100
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2016/Oct/17/t1476731031z5mm76tmxvgwsr8.htm/, Retrieved Sun, 05 May 2024 01:14:20 +0200
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=, Retrieved Sun, 05 May 2024 01:14:20 +0200
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact0
Dataseries X:
-5
-3
-7
-10
-10
-11
-11
-19
-30
-38
-36
-40
-34
-35
-38
-32
-37
-39
-31
-30
-29
-36
-41
-42
-33
-43
-41
-34
-32
-36
-37
-30
-32
-30
-21
-19
-9
-8
-6
-4
-1
-2
-1
-4
-8
-6
-11
-11
-3
-6
2
2
4
8
6
8
5
3
5
3




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Herman Ole Andreas Wold' @ wold.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 & 1 seconds \tabularnewline
R Server & 'Herman Ole Andreas Wold' @ wold.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&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]'Herman Ole Andreas Wold' @ wold.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&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'Herman Ole Andreas Wold' @ wold.wessa.net







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean-17.76666666666672.14717876475953-8.27442361030261
Geometric MeanNaN
Harmonic Mean-16.6581149514969
Quadratic Mean24.2418371141023
Winsorized Mean ( 1 / 20 )-17.752.14392124507519-8.2792220286886
Winsorized Mean ( 2 / 20 )-17.78333333333332.12452609094619-8.37049420532804
Winsorized Mean ( 3 / 20 )-17.83333333333332.11520813666022-8.43100639802334
Winsorized Mean ( 4 / 20 )-17.76666666666672.10304684359749-8.44806035621864
Winsorized Mean ( 5 / 20 )-17.76666666666672.0732853737618-8.56933005533655
Winsorized Mean ( 6 / 20 )-17.76666666666672.03866116843841-8.71486980853992
Winsorized Mean ( 7 / 20 )-17.76666666666672.03866116843841-8.71486980853992
Winsorized Mean ( 8 / 20 )-17.76666666666671.9938275751044-8.91083406033059
Winsorized Mean ( 9 / 20 )-17.76666666666671.9938275751044-8.91083406033059
Winsorized Mean ( 10 / 20 )-18.11.88627214337435-9.59564613387173
Winsorized Mean ( 11 / 20 )-18.11.88627214337435-9.59564613387173
Winsorized Mean ( 12 / 20 )-18.31.85601785009924-9.85981896619233
Winsorized Mean ( 13 / 20 )-18.31.78953328511405-10.2261299927896
Winsorized Mean ( 14 / 20 )-18.06666666666671.75310324799105-10.305534877863
Winsorized Mean ( 15 / 20 )-18.31666666666671.71722606211275-10.6664271354764
Winsorized Mean ( 16 / 20 )-18.051.67642763175741-10.7669425497825
Winsorized Mean ( 17 / 20 )-18.051.59420295158661-11.3222723506038
Winsorized Mean ( 18 / 20 )-18.351.55316789449002-11.8145630392554
Winsorized Mean ( 19 / 20 )-18.351.55316789449002-11.8145630392554
Winsorized Mean ( 20 / 20 )-18.01666666666671.50394803722793-11.9795805577664
Trimmed Mean ( 1 / 20 )-17.77586206896552.13149730573053-8.3396127319397
Trimmed Mean ( 2 / 20 )-17.80357142857142.11433260521888-8.42042135879013
Trimmed Mean ( 3 / 20 )-17.81481481481482.10355163277488-8.46892205413306
Trimmed Mean ( 4 / 20 )-17.80769230769232.09197245783921-8.51239328747465
Trimmed Mean ( 5 / 20 )-17.822.07938177625672-8.56985484987722
Trimmed Mean ( 6 / 20 )-17.83333333333332.07020687400608-8.61427597273109
Trimmed Mean ( 7 / 20 )-17.84782608695652.06511568526578-8.64253088303839
Trimmed Mean ( 8 / 20 )-17.86363636363642.05464227353306-8.6942805537233
Trimmed Mean ( 9 / 20 )-17.88095238095242.04854056459136-8.72862987925224
Trimmed Mean ( 10 / 20 )-17.92.03583284790657-8.79247037319709
Trimmed Mean ( 11 / 20 )-17.86842105263162.04019741208358-8.75818239293973
Trimmed Mean ( 12 / 20 )-17.83333333333332.03910188758103-8.745680361509
Trimmed Mean ( 13 / 20 )-17.76470588235292.03755245485639-8.71864959354141
Trimmed Mean ( 14 / 20 )-17.68752.04359616418168-8.65508573073813
Trimmed Mean ( 15 / 20 )-17.63333333333332.05134289255484-8.59599504175138
Trimmed Mean ( 16 / 20 )-17.53571428571432.05961555901698-8.51407157464076
Trimmed Mean ( 17 / 20 )-17.46153846153852.06973113767188-8.43662161897026
Trimmed Mean ( 18 / 20 )-17.3752.09278652393946-8.30232792558952
Trimmed Mean ( 19 / 20 )-17.22727272727272.11869826303592-8.13106473339317
Trimmed Mean ( 20 / 20 )-17.052.13304205796619-7.99327886495441
Median-11
Midrange-17.5
Midmean - Weighted Average at Xnp-18.1612903225806
Midmean - Weighted Average at X(n+1)p-18.1612903225806
Midmean - Empirical Distribution Function-18.1612903225806
Midmean - Empirical Distribution Function - Averaging-18.1612903225806
Midmean - Empirical Distribution Function - Interpolation-18.1612903225806
Midmean - Closest Observation-18.1612903225806
Midmean - True Basic - Statistics Graphics Toolkit-18.1612903225806
Midmean - MS Excel (old versions)-17.2424242424242
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & -17.7666666666667 & 2.14717876475953 & -8.27442361030261 \tabularnewline
Geometric Mean & NaN &  &  \tabularnewline
Harmonic Mean & -16.6581149514969 &  &  \tabularnewline
Quadratic Mean & 24.2418371141023 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & -17.75 & 2.14392124507519 & -8.2792220286886 \tabularnewline
Winsorized Mean ( 2 / 20 ) & -17.7833333333333 & 2.12452609094619 & -8.37049420532804 \tabularnewline
Winsorized Mean ( 3 / 20 ) & -17.8333333333333 & 2.11520813666022 & -8.43100639802334 \tabularnewline
Winsorized Mean ( 4 / 20 ) & -17.7666666666667 & 2.10304684359749 & -8.44806035621864 \tabularnewline
Winsorized Mean ( 5 / 20 ) & -17.7666666666667 & 2.0732853737618 & -8.56933005533655 \tabularnewline
Winsorized Mean ( 6 / 20 ) & -17.7666666666667 & 2.03866116843841 & -8.71486980853992 \tabularnewline
Winsorized Mean ( 7 / 20 ) & -17.7666666666667 & 2.03866116843841 & -8.71486980853992 \tabularnewline
Winsorized Mean ( 8 / 20 ) & -17.7666666666667 & 1.9938275751044 & -8.91083406033059 \tabularnewline
Winsorized Mean ( 9 / 20 ) & -17.7666666666667 & 1.9938275751044 & -8.91083406033059 \tabularnewline
Winsorized Mean ( 10 / 20 ) & -18.1 & 1.88627214337435 & -9.59564613387173 \tabularnewline
Winsorized Mean ( 11 / 20 ) & -18.1 & 1.88627214337435 & -9.59564613387173 \tabularnewline
Winsorized Mean ( 12 / 20 ) & -18.3 & 1.85601785009924 & -9.85981896619233 \tabularnewline
Winsorized Mean ( 13 / 20 ) & -18.3 & 1.78953328511405 & -10.2261299927896 \tabularnewline
Winsorized Mean ( 14 / 20 ) & -18.0666666666667 & 1.75310324799105 & -10.305534877863 \tabularnewline
Winsorized Mean ( 15 / 20 ) & -18.3166666666667 & 1.71722606211275 & -10.6664271354764 \tabularnewline
Winsorized Mean ( 16 / 20 ) & -18.05 & 1.67642763175741 & -10.7669425497825 \tabularnewline
Winsorized Mean ( 17 / 20 ) & -18.05 & 1.59420295158661 & -11.3222723506038 \tabularnewline
Winsorized Mean ( 18 / 20 ) & -18.35 & 1.55316789449002 & -11.8145630392554 \tabularnewline
Winsorized Mean ( 19 / 20 ) & -18.35 & 1.55316789449002 & -11.8145630392554 \tabularnewline
Winsorized Mean ( 20 / 20 ) & -18.0166666666667 & 1.50394803722793 & -11.9795805577664 \tabularnewline
Trimmed Mean ( 1 / 20 ) & -17.7758620689655 & 2.13149730573053 & -8.3396127319397 \tabularnewline
Trimmed Mean ( 2 / 20 ) & -17.8035714285714 & 2.11433260521888 & -8.42042135879013 \tabularnewline
Trimmed Mean ( 3 / 20 ) & -17.8148148148148 & 2.10355163277488 & -8.46892205413306 \tabularnewline
Trimmed Mean ( 4 / 20 ) & -17.8076923076923 & 2.09197245783921 & -8.51239328747465 \tabularnewline
Trimmed Mean ( 5 / 20 ) & -17.82 & 2.07938177625672 & -8.56985484987722 \tabularnewline
Trimmed Mean ( 6 / 20 ) & -17.8333333333333 & 2.07020687400608 & -8.61427597273109 \tabularnewline
Trimmed Mean ( 7 / 20 ) & -17.8478260869565 & 2.06511568526578 & -8.64253088303839 \tabularnewline
Trimmed Mean ( 8 / 20 ) & -17.8636363636364 & 2.05464227353306 & -8.6942805537233 \tabularnewline
Trimmed Mean ( 9 / 20 ) & -17.8809523809524 & 2.04854056459136 & -8.72862987925224 \tabularnewline
Trimmed Mean ( 10 / 20 ) & -17.9 & 2.03583284790657 & -8.79247037319709 \tabularnewline
Trimmed Mean ( 11 / 20 ) & -17.8684210526316 & 2.04019741208358 & -8.75818239293973 \tabularnewline
Trimmed Mean ( 12 / 20 ) & -17.8333333333333 & 2.03910188758103 & -8.745680361509 \tabularnewline
Trimmed Mean ( 13 / 20 ) & -17.7647058823529 & 2.03755245485639 & -8.71864959354141 \tabularnewline
Trimmed Mean ( 14 / 20 ) & -17.6875 & 2.04359616418168 & -8.65508573073813 \tabularnewline
Trimmed Mean ( 15 / 20 ) & -17.6333333333333 & 2.05134289255484 & -8.59599504175138 \tabularnewline
Trimmed Mean ( 16 / 20 ) & -17.5357142857143 & 2.05961555901698 & -8.51407157464076 \tabularnewline
Trimmed Mean ( 17 / 20 ) & -17.4615384615385 & 2.06973113767188 & -8.43662161897026 \tabularnewline
Trimmed Mean ( 18 / 20 ) & -17.375 & 2.09278652393946 & -8.30232792558952 \tabularnewline
Trimmed Mean ( 19 / 20 ) & -17.2272727272727 & 2.11869826303592 & -8.13106473339317 \tabularnewline
Trimmed Mean ( 20 / 20 ) & -17.05 & 2.13304205796619 & -7.99327886495441 \tabularnewline
Median & -11 &  &  \tabularnewline
Midrange & -17.5 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & -18.1612903225806 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & -18.1612903225806 &  &  \tabularnewline
Midmean - Empirical Distribution Function & -18.1612903225806 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & -18.1612903225806 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & -18.1612903225806 &  &  \tabularnewline
Midmean - Closest Observation & -18.1612903225806 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & -18.1612903225806 &  &  \tabularnewline
Midmean - MS Excel (old versions) & -17.2424242424242 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&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]-17.7666666666667[/C][C]2.14717876475953[/C][C]-8.27442361030261[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]NaN[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]-16.6581149514969[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]24.2418371141023[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]-17.75[/C][C]2.14392124507519[/C][C]-8.2792220286886[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]-17.7833333333333[/C][C]2.12452609094619[/C][C]-8.37049420532804[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]-17.8333333333333[/C][C]2.11520813666022[/C][C]-8.43100639802334[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]-17.7666666666667[/C][C]2.10304684359749[/C][C]-8.44806035621864[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]-17.7666666666667[/C][C]2.0732853737618[/C][C]-8.56933005533655[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]-17.7666666666667[/C][C]2.03866116843841[/C][C]-8.71486980853992[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]-17.7666666666667[/C][C]2.03866116843841[/C][C]-8.71486980853992[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]-17.7666666666667[/C][C]1.9938275751044[/C][C]-8.91083406033059[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]-17.7666666666667[/C][C]1.9938275751044[/C][C]-8.91083406033059[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]-18.1[/C][C]1.88627214337435[/C][C]-9.59564613387173[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]-18.1[/C][C]1.88627214337435[/C][C]-9.59564613387173[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]-18.3[/C][C]1.85601785009924[/C][C]-9.85981896619233[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]-18.3[/C][C]1.78953328511405[/C][C]-10.2261299927896[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]-18.0666666666667[/C][C]1.75310324799105[/C][C]-10.305534877863[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]-18.3166666666667[/C][C]1.71722606211275[/C][C]-10.6664271354764[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]-18.05[/C][C]1.67642763175741[/C][C]-10.7669425497825[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]-18.05[/C][C]1.59420295158661[/C][C]-11.3222723506038[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]-18.35[/C][C]1.55316789449002[/C][C]-11.8145630392554[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]-18.35[/C][C]1.55316789449002[/C][C]-11.8145630392554[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]-18.0166666666667[/C][C]1.50394803722793[/C][C]-11.9795805577664[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]-17.7758620689655[/C][C]2.13149730573053[/C][C]-8.3396127319397[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]-17.8035714285714[/C][C]2.11433260521888[/C][C]-8.42042135879013[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]-17.8148148148148[/C][C]2.10355163277488[/C][C]-8.46892205413306[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]-17.8076923076923[/C][C]2.09197245783921[/C][C]-8.51239328747465[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]-17.82[/C][C]2.07938177625672[/C][C]-8.56985484987722[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]-17.8333333333333[/C][C]2.07020687400608[/C][C]-8.61427597273109[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]-17.8478260869565[/C][C]2.06511568526578[/C][C]-8.64253088303839[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]-17.8636363636364[/C][C]2.05464227353306[/C][C]-8.6942805537233[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]-17.8809523809524[/C][C]2.04854056459136[/C][C]-8.72862987925224[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]-17.9[/C][C]2.03583284790657[/C][C]-8.79247037319709[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]-17.8684210526316[/C][C]2.04019741208358[/C][C]-8.75818239293973[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]-17.8333333333333[/C][C]2.03910188758103[/C][C]-8.745680361509[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]-17.7647058823529[/C][C]2.03755245485639[/C][C]-8.71864959354141[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]-17.6875[/C][C]2.04359616418168[/C][C]-8.65508573073813[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]-17.6333333333333[/C][C]2.05134289255484[/C][C]-8.59599504175138[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]-17.5357142857143[/C][C]2.05961555901698[/C][C]-8.51407157464076[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]-17.4615384615385[/C][C]2.06973113767188[/C][C]-8.43662161897026[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]-17.375[/C][C]2.09278652393946[/C][C]-8.30232792558952[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]-17.2272727272727[/C][C]2.11869826303592[/C][C]-8.13106473339317[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]-17.05[/C][C]2.13304205796619[/C][C]-7.99327886495441[/C][/ROW]
[ROW][C]Median[/C][C]-11[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]-17.5[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]-18.1612903225806[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]-18.1612903225806[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]-18.1612903225806[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]-18.1612903225806[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]-18.1612903225806[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]-18.1612903225806[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]-18.1612903225806[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]-17.2424242424242[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]60[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&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 Mean-17.76666666666672.14717876475953-8.27442361030261
Geometric MeanNaN
Harmonic Mean-16.6581149514969
Quadratic Mean24.2418371141023
Winsorized Mean ( 1 / 20 )-17.752.14392124507519-8.2792220286886
Winsorized Mean ( 2 / 20 )-17.78333333333332.12452609094619-8.37049420532804
Winsorized Mean ( 3 / 20 )-17.83333333333332.11520813666022-8.43100639802334
Winsorized Mean ( 4 / 20 )-17.76666666666672.10304684359749-8.44806035621864
Winsorized Mean ( 5 / 20 )-17.76666666666672.0732853737618-8.56933005533655
Winsorized Mean ( 6 / 20 )-17.76666666666672.03866116843841-8.71486980853992
Winsorized Mean ( 7 / 20 )-17.76666666666672.03866116843841-8.71486980853992
Winsorized Mean ( 8 / 20 )-17.76666666666671.9938275751044-8.91083406033059
Winsorized Mean ( 9 / 20 )-17.76666666666671.9938275751044-8.91083406033059
Winsorized Mean ( 10 / 20 )-18.11.88627214337435-9.59564613387173
Winsorized Mean ( 11 / 20 )-18.11.88627214337435-9.59564613387173
Winsorized Mean ( 12 / 20 )-18.31.85601785009924-9.85981896619233
Winsorized Mean ( 13 / 20 )-18.31.78953328511405-10.2261299927896
Winsorized Mean ( 14 / 20 )-18.06666666666671.75310324799105-10.305534877863
Winsorized Mean ( 15 / 20 )-18.31666666666671.71722606211275-10.6664271354764
Winsorized Mean ( 16 / 20 )-18.051.67642763175741-10.7669425497825
Winsorized Mean ( 17 / 20 )-18.051.59420295158661-11.3222723506038
Winsorized Mean ( 18 / 20 )-18.351.55316789449002-11.8145630392554
Winsorized Mean ( 19 / 20 )-18.351.55316789449002-11.8145630392554
Winsorized Mean ( 20 / 20 )-18.01666666666671.50394803722793-11.9795805577664
Trimmed Mean ( 1 / 20 )-17.77586206896552.13149730573053-8.3396127319397
Trimmed Mean ( 2 / 20 )-17.80357142857142.11433260521888-8.42042135879013
Trimmed Mean ( 3 / 20 )-17.81481481481482.10355163277488-8.46892205413306
Trimmed Mean ( 4 / 20 )-17.80769230769232.09197245783921-8.51239328747465
Trimmed Mean ( 5 / 20 )-17.822.07938177625672-8.56985484987722
Trimmed Mean ( 6 / 20 )-17.83333333333332.07020687400608-8.61427597273109
Trimmed Mean ( 7 / 20 )-17.84782608695652.06511568526578-8.64253088303839
Trimmed Mean ( 8 / 20 )-17.86363636363642.05464227353306-8.6942805537233
Trimmed Mean ( 9 / 20 )-17.88095238095242.04854056459136-8.72862987925224
Trimmed Mean ( 10 / 20 )-17.92.03583284790657-8.79247037319709
Trimmed Mean ( 11 / 20 )-17.86842105263162.04019741208358-8.75818239293973
Trimmed Mean ( 12 / 20 )-17.83333333333332.03910188758103-8.745680361509
Trimmed Mean ( 13 / 20 )-17.76470588235292.03755245485639-8.71864959354141
Trimmed Mean ( 14 / 20 )-17.68752.04359616418168-8.65508573073813
Trimmed Mean ( 15 / 20 )-17.63333333333332.05134289255484-8.59599504175138
Trimmed Mean ( 16 / 20 )-17.53571428571432.05961555901698-8.51407157464076
Trimmed Mean ( 17 / 20 )-17.46153846153852.06973113767188-8.43662161897026
Trimmed Mean ( 18 / 20 )-17.3752.09278652393946-8.30232792558952
Trimmed Mean ( 19 / 20 )-17.22727272727272.11869826303592-8.13106473339317
Trimmed Mean ( 20 / 20 )-17.052.13304205796619-7.99327886495441
Median-11
Midrange-17.5
Midmean - Weighted Average at Xnp-18.1612903225806
Midmean - Weighted Average at X(n+1)p-18.1612903225806
Midmean - Empirical Distribution Function-18.1612903225806
Midmean - Empirical Distribution Function - Averaging-18.1612903225806
Midmean - Empirical Distribution Function - Interpolation-18.1612903225806
Midmean - Closest Observation-18.1612903225806
Midmean - True Basic - Statistics Graphics Toolkit-18.1612903225806
Midmean - MS Excel (old versions)-17.2424242424242
Number of observations60



Parameters (Session):
Parameters (R input):
R code (references can be found in the software module):
geomean <- function(x) {
return(exp(mean(log(x))))
}
harmean <- function(x) {
return(1/mean(1/x))
}
quamean <- function(x) {
return(sqrt(mean(x*x)))
}
winmean <- function(x) {
x <-sort(x[!is.na(x)])
n<-length(x)
denom <- 3
nodenom <- n/denom
if (nodenom>40) denom <- n/40
sqrtn = sqrt(n)
roundnodenom = floor(nodenom)
win <- array(NA,dim=c(roundnodenom,2))
for (j in 1:roundnodenom) {
win[j,1] <- (j*x[j+1]+sum(x[(j+1):(n-j)])+j*x[n-j])/n
win[j,2] <- sd(c(rep(x[j+1],j),x[(j+1):(n-j)],rep(x[n-j],j)))/sqrtn
}
return(win)
}
trimean <- function(x) {
x <-sort(x[!is.na(x)])
n<-length(x)
denom <- 3
nodenom <- n/denom
if (nodenom>40) denom <- n/40
sqrtn = sqrt(n)
roundnodenom = floor(nodenom)
tri <- array(NA,dim=c(roundnodenom,2))
for (j in 1:roundnodenom) {
tri[j,1] <- mean(x,trim=j/n)
tri[j,2] <- sd(x[(j+1):(n-j)]) / sqrt(n-j*2)
}
return(tri)
}
midrange <- function(x) {
return((max(x)+min(x))/2)
}
q1 <- function(data,n,p,i,f) {
np <- n*p;
i <<- floor(np)
f <<- np - i
qvalue <- (1-f)*data[i] + f*data[i+1]
}
q2 <- function(data,n,p,i,f) {
np <- (n+1)*p
i <<- floor(np)
f <<- np - i
qvalue <- (1-f)*data[i] + f*data[i+1]
}
q3 <- function(data,n,p,i,f) {
np <- n*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- data[i]
} else {
qvalue <- data[i+1]
}
}
q4 <- function(data,n,p,i,f) {
np <- n*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- (data[i]+data[i+1])/2
} else {
qvalue <- data[i+1]
}
}
q5 <- function(data,n,p,i,f) {
np <- (n-1)*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- data[i+1]
} else {
qvalue <- data[i+1] + f*(data[i+2]-data[i+1])
}
}
q6 <- function(data,n,p,i,f) {
np <- n*p+0.5
i <<- floor(np)
f <<- np - i
qvalue <- data[i]
}
q7 <- function(data,n,p,i,f) {
np <- (n+1)*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- data[i]
} else {
qvalue <- f*data[i] + (1-f)*data[i+1]
}
}
q8 <- function(data,n,p,i,f) {
np <- (n+1)*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- data[i]
} else {
if (f == 0.5) {
qvalue <- (data[i]+data[i+1])/2
} else {
if (f < 0.5) {
qvalue <- data[i]
} else {
qvalue <- data[i+1]
}
}
}
}
midmean <- function(x,def) {
x <-sort(x[!is.na(x)])
n<-length(x)
if (def==1) {
qvalue1 <- q1(x,n,0.25,i,f)
qvalue3 <- q1(x,n,0.75,i,f)
}
if (def==2) {
qvalue1 <- q2(x,n,0.25,i,f)
qvalue3 <- q2(x,n,0.75,i,f)
}
if (def==3) {
qvalue1 <- q3(x,n,0.25,i,f)
qvalue3 <- q3(x,n,0.75,i,f)
}
if (def==4) {
qvalue1 <- q4(x,n,0.25,i,f)
qvalue3 <- q4(x,n,0.75,i,f)
}
if (def==5) {
qvalue1 <- q5(x,n,0.25,i,f)
qvalue3 <- q5(x,n,0.75,i,f)
}
if (def==6) {
qvalue1 <- q6(x,n,0.25,i,f)
qvalue3 <- q6(x,n,0.75,i,f)
}
if (def==7) {
qvalue1 <- q7(x,n,0.25,i,f)
qvalue3 <- q7(x,n,0.75,i,f)
}
if (def==8) {
qvalue1 <- q8(x,n,0.25,i,f)
qvalue3 <- q8(x,n,0.75,i,f)
}
midm <- 0
myn <- 0
roundno4 <- round(n/4)
round3no4 <- round(3*n/4)
for (i in 1:n) {
if ((x[i]>=qvalue1) & (x[i]<=qvalue3)){
midm = midm + x[i]
myn = myn + 1
}
}
midm = midm / myn
return(midm)
}
(arm <- mean(x))
sqrtn <- sqrt(length(x))
(armse <- sd(x) / sqrtn)
(armose <- arm / armse)
(geo <- geomean(x))
(har <- harmean(x))
(qua <- quamean(x))
(win <- winmean(x))
(tri <- trimean(x))
(midr <- midrange(x))
midm <- array(NA,dim=8)
for (j in 1:8) midm[j] <- midmean(x,j)
midm
bitmap(file='test1.png')
lb <- win[,1] - 2*win[,2]
ub <- win[,1] + 2*win[,2]
if ((ylimmin == '') | (ylimmax == '')) plot(win[,1],type='b',main=main, xlab='j', pch=19, ylab='Winsorized Mean(j/n)', ylim=c(min(lb),max(ub))) else plot(win[,1],type='l',main=main, xlab='j', pch=19, ylab='Winsorized Mean(j/n)', ylim=c(ylimmin,ylimmax))
lines(ub,lty=3)
lines(lb,lty=3)
grid()
dev.off()
bitmap(file='test2.png')
lb <- tri[,1] - 2*tri[,2]
ub <- tri[,1] + 2*tri[,2]
if ((ylimmin == '') | (ylimmax == '')) plot(tri[,1],type='b',main=main, xlab='j', pch=19, ylab='Trimmed Mean(j/n)', ylim=c(min(lb),max(ub))) else plot(tri[,1],type='l',main=main, xlab='j', pch=19, ylab='Trimmed Mean(j/n)', ylim=c(ylimmin,ylimmax))
lines(ub,lty=3)
lines(lb,lty=3)
grid()
dev.off()
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Central Tendency - Ungrouped Data',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Measure',header=TRUE)
a<-table.element(a,'Value',header=TRUE)
a<-table.element(a,'S.E.',header=TRUE)
a<-table.element(a,'Value/S.E.',header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('arithmetic_mean.htm', 'Arithmetic Mean', 'click to view the definition of the Arithmetic Mean'),header=TRUE)
a<-table.element(a,arm)
a<-table.element(a,hyperlink('arithmetic_mean_standard_error.htm', armse, 'click to view the definition of the Standard Error of the Arithmetic Mean'))
a<-table.element(a,armose)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('geometric_mean.htm', 'Geometric Mean', 'click to view the definition of the Geometric Mean'),header=TRUE)
a<-table.element(a,geo)
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('harmonic_mean.htm', 'Harmonic Mean', 'click to view the definition of the Harmonic Mean'),header=TRUE)
a<-table.element(a,har)
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('quadratic_mean.htm', 'Quadratic Mean', 'click to view the definition of the Quadratic Mean'),header=TRUE)
a<-table.element(a,qua)
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
for (j in 1:length(win[,1])) {
a<-table.row.start(a)
mylabel <- paste('Winsorized Mean (',j)
mylabel <- paste(mylabel,'/')
mylabel <- paste(mylabel,length(win[,1]))
mylabel <- paste(mylabel,')')
a<-table.element(a,hyperlink('winsorized_mean.htm', mylabel, 'click to view the definition of the Winsorized Mean'),header=TRUE)
a<-table.element(a,win[j,1])
a<-table.element(a,win[j,2])
a<-table.element(a,win[j,1]/win[j,2])
a<-table.row.end(a)
}
for (j in 1:length(tri[,1])) {
a<-table.row.start(a)
mylabel <- paste('Trimmed Mean (',j)
mylabel <- paste(mylabel,'/')
mylabel <- paste(mylabel,length(tri[,1]))
mylabel <- paste(mylabel,')')
a<-table.element(a,hyperlink('arithmetic_mean.htm', mylabel, 'click to view the definition of the Trimmed Mean'),header=TRUE)
a<-table.element(a,tri[j,1])
a<-table.element(a,tri[j,2])
a<-table.element(a,tri[j,1]/tri[j,2])
a<-table.row.end(a)
}
a<-table.row.start(a)
a<-table.element(a,hyperlink('median_1.htm', 'Median', 'click to view the definition of the Median'),header=TRUE)
a<-table.element(a,median(x))
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('midrange.htm', 'Midrange', 'click to view the definition of the Midrange'),header=TRUE)
a<-table.element(a,midr)
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_1.htm','Weighted Average at Xnp',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[1])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_2.htm','Weighted Average at X(n+1)p',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[2])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_3.htm','Empirical Distribution Function',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[3])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_4.htm','Empirical Distribution Function - Averaging',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[4])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_5.htm','Empirical Distribution Function - Interpolation',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[5])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_6.htm','Closest Observation',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[6])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_7.htm','True Basic - Statistics Graphics Toolkit',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[7])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_8.htm','MS Excel (old versions)',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[8])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Number of observations',header=TRUE)
a<-table.element(a,length(x))
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable.tab')