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of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationFri, 19 Oct 2012 08:14:19 -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/19/t1350649159smr177km6whmvfk.htm/, Retrieved Mon, 29 Apr 2024 08:41:01 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=180082, Retrieved Mon, 29 Apr 2024 08:41:01 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact56
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [] [2012-10-19 12:14:19] [0769c782addd77dfcec38b8d0e028078] [Current]
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Dataseries X:
-1
-2
-5
-4
-6
-2
-2
-2
-2
2
1
-8
-1
1
-1
2
2
1
-1
-2
-2
-1
-8
-4
-6
-3
-3
-7
-9
-11
-13
-11
-9
-17
-22
-25
-20
-24
-24
-22
-19
-18
-17
-11
-11
-12
-10
-15
-15
-15
-13
-8
-13
-9
-7
-4
-4
-2
0
-2
-3
1
-2
-1
1
-3
-4
-9
-9
-7
-14
-12




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 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 & 2 seconds \tabularnewline
R Server & 'Herman Ole Andreas Wold' @ wold.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=180082&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]'Herman Ole Andreas Wold' @ wold.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=180082&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=180082&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'Herman Ole Andreas Wold' @ wold.wessa.net







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean-7.472222222222220.845907995784789-8.83337462165716
Geometric MeanNaN
Harmonic Mean0
Quadratic Mean10.3266107164398
Winsorized Mean ( 1 / 24 )-7.458333333333330.841959461924538-8.85830455101151
Winsorized Mean ( 2 / 24 )-7.458333333333330.841959461924538-8.85830455101151
Winsorized Mean ( 3 / 24 )-7.416666666666670.813556403643431-9.11635214651604
Winsorized Mean ( 4 / 24 )-7.416666666666670.813556403643431-9.11635214651604
Winsorized Mean ( 5 / 24 )-7.277777777777780.780038074946026-9.33002889414258
Winsorized Mean ( 6 / 24 )-7.194444444444440.761361232789889-9.4494494000982
Winsorized Mean ( 7 / 24 )-7.097222222222220.740659024900631-9.58230708546947
Winsorized Mean ( 8 / 24 )-7.097222222222220.701596581375465-10.1158164258843
Winsorized Mean ( 9 / 24 )-7.222222222222220.684680974515251-10.5483027731791
Winsorized Mean ( 10 / 24 )-6.944444444444440.631678369237939-10.9936397740234
Winsorized Mean ( 11 / 24 )-6.944444444444440.631678369237939-10.9936397740234
Winsorized Mean ( 12 / 24 )-6.944444444444440.631678369237939-10.9936397740234
Winsorized Mean ( 13 / 24 )-6.763888888888890.600108576363887-11.2711085215144
Winsorized Mean ( 14 / 24 )-6.569444444444440.568068684299465-11.5645248999173
Winsorized Mean ( 15 / 24 )-6.777777777777780.540685178757709-12.5355346217378
Winsorized Mean ( 16 / 24 )-6.777777777777780.540685178757709-12.5355346217378
Winsorized Mean ( 17 / 24 )-6.541666666666670.503484532524479-12.9927857641756
Winsorized Mean ( 18 / 24 )-6.541666666666670.503484532524479-12.9927857641756
Winsorized Mean ( 19 / 24 )-6.277777777777780.464390080007444-13.5183287672233
Winsorized Mean ( 20 / 24 )-6.277777777777780.464390080007444-13.5183287672233
Winsorized Mean ( 21 / 24 )-6.277777777777780.464390080007444-13.5183287672233
Winsorized Mean ( 22 / 24 )-6.277777777777780.464390080007444-13.5183287672233
Winsorized Mean ( 23 / 24 )-5.958333333333330.419794597288201-14.1934493007369
Winsorized Mean ( 24 / 24 )-5.6250.37604184955063-14.9584414785798
Trimmed Mean ( 1 / 24 )-7.357142857142860.821561335926744-8.95507436318652
Trimmed Mean ( 2 / 24 )-7.250.797101586637829-9.09545297805825
Trimmed Mean ( 3 / 24 )-7.136363636363640.767609543942547-9.29686673736533
Trimmed Mean ( 4 / 24 )-7.031250.745345594045804-9.43354338734832
Trimmed Mean ( 5 / 24 )-6.919354838709680.718162937508309-9.63479800658695
Trimmed Mean ( 6 / 24 )-6.833333333333330.696304476985775-9.81371448725144
Trimmed Mean ( 7 / 24 )-6.758620689655170.67507268987629-10.0116932457951
Trimmed Mean ( 8 / 24 )-6.696428571428570.654613816389888-10.2295863664451
Trimmed Mean ( 9 / 24 )-6.629629629629630.638993955245415-10.3751053906033
Trimmed Mean ( 10 / 24 )-6.538461538461540.622880441247469-10.4971373404609
Trimmed Mean ( 11 / 24 )-6.480.614943169765155-10.5375591088762
Trimmed Mean ( 12 / 24 )-6.416666666666670.604235444850134-10.6194807361196
Trimmed Mean ( 13 / 24 )-6.347826086956520.589945867740511-10.7600144929715
Trimmed Mean ( 14 / 24 )-6.295454545454550.578490001900356-10.8825641320918
Trimmed Mean ( 15 / 24 )-6.261904761904760.570326560294113-10.9795075275392
Trimmed Mean ( 16 / 24 )-6.20.564096736566636-10.9910226351178
Trimmed Mean ( 17 / 24 )-6.131578947368420.554524968918849-11.0573541157634
Trimmed Mean ( 18 / 24 )-6.083333333333330.549711323953345-11.0664144401901
Trimmed Mean ( 19 / 24 )-6.029411764705880.541479609743194-11.1350670574012
Trimmed Mean ( 20 / 24 )-60.538815906080325-11.13552872566
Trimmed Mean ( 21 / 24 )-5.966666666666670.532794267800214-11.1988191826869
Trimmed Mean ( 22 / 24 )-5.928571428571430.52182162470723-11.3612988574356
Trimmed Mean ( 23 / 24 )-5.884615384615390.503302701629403-11.6920003917412
Trimmed Mean ( 24 / 24 )-5.8750.490165973073836-11.9857361031363
Median-6
Midrange-11.5
Midmean - Weighted Average at Xnp-5.925
Midmean - Weighted Average at X(n+1)p-5.925
Midmean - Empirical Distribution Function-5.925
Midmean - Empirical Distribution Function - Averaging-5.925
Midmean - Empirical Distribution Function - Interpolation-5.925
Midmean - Closest Observation-5.925
Midmean - True Basic - Statistics Graphics Toolkit-5.925
Midmean - MS Excel (old versions)-5.925
Number of observations72

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & -7.47222222222222 & 0.845907995784789 & -8.83337462165716 \tabularnewline
Geometric Mean & NaN &  &  \tabularnewline
Harmonic Mean & 0 &  &  \tabularnewline
Quadratic Mean & 10.3266107164398 &  &  \tabularnewline
Winsorized Mean ( 1 / 24 ) & -7.45833333333333 & 0.841959461924538 & -8.85830455101151 \tabularnewline
Winsorized Mean ( 2 / 24 ) & -7.45833333333333 & 0.841959461924538 & -8.85830455101151 \tabularnewline
Winsorized Mean ( 3 / 24 ) & -7.41666666666667 & 0.813556403643431 & -9.11635214651604 \tabularnewline
Winsorized Mean ( 4 / 24 ) & -7.41666666666667 & 0.813556403643431 & -9.11635214651604 \tabularnewline
Winsorized Mean ( 5 / 24 ) & -7.27777777777778 & 0.780038074946026 & -9.33002889414258 \tabularnewline
Winsorized Mean ( 6 / 24 ) & -7.19444444444444 & 0.761361232789889 & -9.4494494000982 \tabularnewline
Winsorized Mean ( 7 / 24 ) & -7.09722222222222 & 0.740659024900631 & -9.58230708546947 \tabularnewline
Winsorized Mean ( 8 / 24 ) & -7.09722222222222 & 0.701596581375465 & -10.1158164258843 \tabularnewline
Winsorized Mean ( 9 / 24 ) & -7.22222222222222 & 0.684680974515251 & -10.5483027731791 \tabularnewline
Winsorized Mean ( 10 / 24 ) & -6.94444444444444 & 0.631678369237939 & -10.9936397740234 \tabularnewline
Winsorized Mean ( 11 / 24 ) & -6.94444444444444 & 0.631678369237939 & -10.9936397740234 \tabularnewline
Winsorized Mean ( 12 / 24 ) & -6.94444444444444 & 0.631678369237939 & -10.9936397740234 \tabularnewline
Winsorized Mean ( 13 / 24 ) & -6.76388888888889 & 0.600108576363887 & -11.2711085215144 \tabularnewline
Winsorized Mean ( 14 / 24 ) & -6.56944444444444 & 0.568068684299465 & -11.5645248999173 \tabularnewline
Winsorized Mean ( 15 / 24 ) & -6.77777777777778 & 0.540685178757709 & -12.5355346217378 \tabularnewline
Winsorized Mean ( 16 / 24 ) & -6.77777777777778 & 0.540685178757709 & -12.5355346217378 \tabularnewline
Winsorized Mean ( 17 / 24 ) & -6.54166666666667 & 0.503484532524479 & -12.9927857641756 \tabularnewline
Winsorized Mean ( 18 / 24 ) & -6.54166666666667 & 0.503484532524479 & -12.9927857641756 \tabularnewline
Winsorized Mean ( 19 / 24 ) & -6.27777777777778 & 0.464390080007444 & -13.5183287672233 \tabularnewline
Winsorized Mean ( 20 / 24 ) & -6.27777777777778 & 0.464390080007444 & -13.5183287672233 \tabularnewline
Winsorized Mean ( 21 / 24 ) & -6.27777777777778 & 0.464390080007444 & -13.5183287672233 \tabularnewline
Winsorized Mean ( 22 / 24 ) & -6.27777777777778 & 0.464390080007444 & -13.5183287672233 \tabularnewline
Winsorized Mean ( 23 / 24 ) & -5.95833333333333 & 0.419794597288201 & -14.1934493007369 \tabularnewline
Winsorized Mean ( 24 / 24 ) & -5.625 & 0.37604184955063 & -14.9584414785798 \tabularnewline
Trimmed Mean ( 1 / 24 ) & -7.35714285714286 & 0.821561335926744 & -8.95507436318652 \tabularnewline
Trimmed Mean ( 2 / 24 ) & -7.25 & 0.797101586637829 & -9.09545297805825 \tabularnewline
Trimmed Mean ( 3 / 24 ) & -7.13636363636364 & 0.767609543942547 & -9.29686673736533 \tabularnewline
Trimmed Mean ( 4 / 24 ) & -7.03125 & 0.745345594045804 & -9.43354338734832 \tabularnewline
Trimmed Mean ( 5 / 24 ) & -6.91935483870968 & 0.718162937508309 & -9.63479800658695 \tabularnewline
Trimmed Mean ( 6 / 24 ) & -6.83333333333333 & 0.696304476985775 & -9.81371448725144 \tabularnewline
Trimmed Mean ( 7 / 24 ) & -6.75862068965517 & 0.67507268987629 & -10.0116932457951 \tabularnewline
Trimmed Mean ( 8 / 24 ) & -6.69642857142857 & 0.654613816389888 & -10.2295863664451 \tabularnewline
Trimmed Mean ( 9 / 24 ) & -6.62962962962963 & 0.638993955245415 & -10.3751053906033 \tabularnewline
Trimmed Mean ( 10 / 24 ) & -6.53846153846154 & 0.622880441247469 & -10.4971373404609 \tabularnewline
Trimmed Mean ( 11 / 24 ) & -6.48 & 0.614943169765155 & -10.5375591088762 \tabularnewline
Trimmed Mean ( 12 / 24 ) & -6.41666666666667 & 0.604235444850134 & -10.6194807361196 \tabularnewline
Trimmed Mean ( 13 / 24 ) & -6.34782608695652 & 0.589945867740511 & -10.7600144929715 \tabularnewline
Trimmed Mean ( 14 / 24 ) & -6.29545454545455 & 0.578490001900356 & -10.8825641320918 \tabularnewline
Trimmed Mean ( 15 / 24 ) & -6.26190476190476 & 0.570326560294113 & -10.9795075275392 \tabularnewline
Trimmed Mean ( 16 / 24 ) & -6.2 & 0.564096736566636 & -10.9910226351178 \tabularnewline
Trimmed Mean ( 17 / 24 ) & -6.13157894736842 & 0.554524968918849 & -11.0573541157634 \tabularnewline
Trimmed Mean ( 18 / 24 ) & -6.08333333333333 & 0.549711323953345 & -11.0664144401901 \tabularnewline
Trimmed Mean ( 19 / 24 ) & -6.02941176470588 & 0.541479609743194 & -11.1350670574012 \tabularnewline
Trimmed Mean ( 20 / 24 ) & -6 & 0.538815906080325 & -11.13552872566 \tabularnewline
Trimmed Mean ( 21 / 24 ) & -5.96666666666667 & 0.532794267800214 & -11.1988191826869 \tabularnewline
Trimmed Mean ( 22 / 24 ) & -5.92857142857143 & 0.52182162470723 & -11.3612988574356 \tabularnewline
Trimmed Mean ( 23 / 24 ) & -5.88461538461539 & 0.503302701629403 & -11.6920003917412 \tabularnewline
Trimmed Mean ( 24 / 24 ) & -5.875 & 0.490165973073836 & -11.9857361031363 \tabularnewline
Median & -6 &  &  \tabularnewline
Midrange & -11.5 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & -5.925 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & -5.925 &  &  \tabularnewline
Midmean - Empirical Distribution Function & -5.925 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & -5.925 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & -5.925 &  &  \tabularnewline
Midmean - Closest Observation & -5.925 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & -5.925 &  &  \tabularnewline
Midmean - MS Excel (old versions) & -5.925 &  &  \tabularnewline
Number of observations & 72 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=180082&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]-7.47222222222222[/C][C]0.845907995784789[/C][C]-8.83337462165716[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]NaN[/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]10.3266107164398[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 24 )[/C][C]-7.45833333333333[/C][C]0.841959461924538[/C][C]-8.85830455101151[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 24 )[/C][C]-7.45833333333333[/C][C]0.841959461924538[/C][C]-8.85830455101151[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 24 )[/C][C]-7.41666666666667[/C][C]0.813556403643431[/C][C]-9.11635214651604[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 24 )[/C][C]-7.41666666666667[/C][C]0.813556403643431[/C][C]-9.11635214651604[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 24 )[/C][C]-7.27777777777778[/C][C]0.780038074946026[/C][C]-9.33002889414258[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 24 )[/C][C]-7.19444444444444[/C][C]0.761361232789889[/C][C]-9.4494494000982[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 24 )[/C][C]-7.09722222222222[/C][C]0.740659024900631[/C][C]-9.58230708546947[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 24 )[/C][C]-7.09722222222222[/C][C]0.701596581375465[/C][C]-10.1158164258843[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 24 )[/C][C]-7.22222222222222[/C][C]0.684680974515251[/C][C]-10.5483027731791[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 24 )[/C][C]-6.94444444444444[/C][C]0.631678369237939[/C][C]-10.9936397740234[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 24 )[/C][C]-6.94444444444444[/C][C]0.631678369237939[/C][C]-10.9936397740234[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 24 )[/C][C]-6.94444444444444[/C][C]0.631678369237939[/C][C]-10.9936397740234[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 24 )[/C][C]-6.76388888888889[/C][C]0.600108576363887[/C][C]-11.2711085215144[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 24 )[/C][C]-6.56944444444444[/C][C]0.568068684299465[/C][C]-11.5645248999173[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 24 )[/C][C]-6.77777777777778[/C][C]0.540685178757709[/C][C]-12.5355346217378[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 24 )[/C][C]-6.77777777777778[/C][C]0.540685178757709[/C][C]-12.5355346217378[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 24 )[/C][C]-6.54166666666667[/C][C]0.503484532524479[/C][C]-12.9927857641756[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 24 )[/C][C]-6.54166666666667[/C][C]0.503484532524479[/C][C]-12.9927857641756[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 24 )[/C][C]-6.27777777777778[/C][C]0.464390080007444[/C][C]-13.5183287672233[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 24 )[/C][C]-6.27777777777778[/C][C]0.464390080007444[/C][C]-13.5183287672233[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 24 )[/C][C]-6.27777777777778[/C][C]0.464390080007444[/C][C]-13.5183287672233[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 24 )[/C][C]-6.27777777777778[/C][C]0.464390080007444[/C][C]-13.5183287672233[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 24 )[/C][C]-5.95833333333333[/C][C]0.419794597288201[/C][C]-14.1934493007369[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 24 )[/C][C]-5.625[/C][C]0.37604184955063[/C][C]-14.9584414785798[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 24 )[/C][C]-7.35714285714286[/C][C]0.821561335926744[/C][C]-8.95507436318652[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 24 )[/C][C]-7.25[/C][C]0.797101586637829[/C][C]-9.09545297805825[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 24 )[/C][C]-7.13636363636364[/C][C]0.767609543942547[/C][C]-9.29686673736533[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 24 )[/C][C]-7.03125[/C][C]0.745345594045804[/C][C]-9.43354338734832[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 24 )[/C][C]-6.91935483870968[/C][C]0.718162937508309[/C][C]-9.63479800658695[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 24 )[/C][C]-6.83333333333333[/C][C]0.696304476985775[/C][C]-9.81371448725144[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 24 )[/C][C]-6.75862068965517[/C][C]0.67507268987629[/C][C]-10.0116932457951[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 24 )[/C][C]-6.69642857142857[/C][C]0.654613816389888[/C][C]-10.2295863664451[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 24 )[/C][C]-6.62962962962963[/C][C]0.638993955245415[/C][C]-10.3751053906033[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 24 )[/C][C]-6.53846153846154[/C][C]0.622880441247469[/C][C]-10.4971373404609[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 24 )[/C][C]-6.48[/C][C]0.614943169765155[/C][C]-10.5375591088762[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 24 )[/C][C]-6.41666666666667[/C][C]0.604235444850134[/C][C]-10.6194807361196[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 24 )[/C][C]-6.34782608695652[/C][C]0.589945867740511[/C][C]-10.7600144929715[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 24 )[/C][C]-6.29545454545455[/C][C]0.578490001900356[/C][C]-10.8825641320918[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 24 )[/C][C]-6.26190476190476[/C][C]0.570326560294113[/C][C]-10.9795075275392[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 24 )[/C][C]-6.2[/C][C]0.564096736566636[/C][C]-10.9910226351178[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 24 )[/C][C]-6.13157894736842[/C][C]0.554524968918849[/C][C]-11.0573541157634[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 24 )[/C][C]-6.08333333333333[/C][C]0.549711323953345[/C][C]-11.0664144401901[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 24 )[/C][C]-6.02941176470588[/C][C]0.541479609743194[/C][C]-11.1350670574012[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 24 )[/C][C]-6[/C][C]0.538815906080325[/C][C]-11.13552872566[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 24 )[/C][C]-5.96666666666667[/C][C]0.532794267800214[/C][C]-11.1988191826869[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 24 )[/C][C]-5.92857142857143[/C][C]0.52182162470723[/C][C]-11.3612988574356[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 24 )[/C][C]-5.88461538461539[/C][C]0.503302701629403[/C][C]-11.6920003917412[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 24 )[/C][C]-5.875[/C][C]0.490165973073836[/C][C]-11.9857361031363[/C][/ROW]
[ROW][C]Median[/C][C]-6[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]-11.5[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]-5.925[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]-5.925[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]-5.925[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]-5.925[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]-5.925[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]-5.925[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]-5.925[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]-5.925[/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=180082&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=180082&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-7.472222222222220.845907995784789-8.83337462165716
Geometric MeanNaN
Harmonic Mean0
Quadratic Mean10.3266107164398
Winsorized Mean ( 1 / 24 )-7.458333333333330.841959461924538-8.85830455101151
Winsorized Mean ( 2 / 24 )-7.458333333333330.841959461924538-8.85830455101151
Winsorized Mean ( 3 / 24 )-7.416666666666670.813556403643431-9.11635214651604
Winsorized Mean ( 4 / 24 )-7.416666666666670.813556403643431-9.11635214651604
Winsorized Mean ( 5 / 24 )-7.277777777777780.780038074946026-9.33002889414258
Winsorized Mean ( 6 / 24 )-7.194444444444440.761361232789889-9.4494494000982
Winsorized Mean ( 7 / 24 )-7.097222222222220.740659024900631-9.58230708546947
Winsorized Mean ( 8 / 24 )-7.097222222222220.701596581375465-10.1158164258843
Winsorized Mean ( 9 / 24 )-7.222222222222220.684680974515251-10.5483027731791
Winsorized Mean ( 10 / 24 )-6.944444444444440.631678369237939-10.9936397740234
Winsorized Mean ( 11 / 24 )-6.944444444444440.631678369237939-10.9936397740234
Winsorized Mean ( 12 / 24 )-6.944444444444440.631678369237939-10.9936397740234
Winsorized Mean ( 13 / 24 )-6.763888888888890.600108576363887-11.2711085215144
Winsorized Mean ( 14 / 24 )-6.569444444444440.568068684299465-11.5645248999173
Winsorized Mean ( 15 / 24 )-6.777777777777780.540685178757709-12.5355346217378
Winsorized Mean ( 16 / 24 )-6.777777777777780.540685178757709-12.5355346217378
Winsorized Mean ( 17 / 24 )-6.541666666666670.503484532524479-12.9927857641756
Winsorized Mean ( 18 / 24 )-6.541666666666670.503484532524479-12.9927857641756
Winsorized Mean ( 19 / 24 )-6.277777777777780.464390080007444-13.5183287672233
Winsorized Mean ( 20 / 24 )-6.277777777777780.464390080007444-13.5183287672233
Winsorized Mean ( 21 / 24 )-6.277777777777780.464390080007444-13.5183287672233
Winsorized Mean ( 22 / 24 )-6.277777777777780.464390080007444-13.5183287672233
Winsorized Mean ( 23 / 24 )-5.958333333333330.419794597288201-14.1934493007369
Winsorized Mean ( 24 / 24 )-5.6250.37604184955063-14.9584414785798
Trimmed Mean ( 1 / 24 )-7.357142857142860.821561335926744-8.95507436318652
Trimmed Mean ( 2 / 24 )-7.250.797101586637829-9.09545297805825
Trimmed Mean ( 3 / 24 )-7.136363636363640.767609543942547-9.29686673736533
Trimmed Mean ( 4 / 24 )-7.031250.745345594045804-9.43354338734832
Trimmed Mean ( 5 / 24 )-6.919354838709680.718162937508309-9.63479800658695
Trimmed Mean ( 6 / 24 )-6.833333333333330.696304476985775-9.81371448725144
Trimmed Mean ( 7 / 24 )-6.758620689655170.67507268987629-10.0116932457951
Trimmed Mean ( 8 / 24 )-6.696428571428570.654613816389888-10.2295863664451
Trimmed Mean ( 9 / 24 )-6.629629629629630.638993955245415-10.3751053906033
Trimmed Mean ( 10 / 24 )-6.538461538461540.622880441247469-10.4971373404609
Trimmed Mean ( 11 / 24 )-6.480.614943169765155-10.5375591088762
Trimmed Mean ( 12 / 24 )-6.416666666666670.604235444850134-10.6194807361196
Trimmed Mean ( 13 / 24 )-6.347826086956520.589945867740511-10.7600144929715
Trimmed Mean ( 14 / 24 )-6.295454545454550.578490001900356-10.8825641320918
Trimmed Mean ( 15 / 24 )-6.261904761904760.570326560294113-10.9795075275392
Trimmed Mean ( 16 / 24 )-6.20.564096736566636-10.9910226351178
Trimmed Mean ( 17 / 24 )-6.131578947368420.554524968918849-11.0573541157634
Trimmed Mean ( 18 / 24 )-6.083333333333330.549711323953345-11.0664144401901
Trimmed Mean ( 19 / 24 )-6.029411764705880.541479609743194-11.1350670574012
Trimmed Mean ( 20 / 24 )-60.538815906080325-11.13552872566
Trimmed Mean ( 21 / 24 )-5.966666666666670.532794267800214-11.1988191826869
Trimmed Mean ( 22 / 24 )-5.928571428571430.52182162470723-11.3612988574356
Trimmed Mean ( 23 / 24 )-5.884615384615390.503302701629403-11.6920003917412
Trimmed Mean ( 24 / 24 )-5.8750.490165973073836-11.9857361031363
Median-6
Midrange-11.5
Midmean - Weighted Average at Xnp-5.925
Midmean - Weighted Average at X(n+1)p-5.925
Midmean - Empirical Distribution Function-5.925
Midmean - Empirical Distribution Function - Averaging-5.925
Midmean - Empirical Distribution Function - Interpolation-5.925
Midmean - Closest Observation-5.925
Midmean - True Basic - Statistics Graphics Toolkit-5.925
Midmean - MS Excel (old versions)-5.925
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')