Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationSat, 05 Mar 2016 10:34:21 +0000
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/Mar/05/t1457174077bl9oy0xnu6qfclj.htm/, Retrieved Sat, 27 Apr 2024 06:50:48 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=293435, Retrieved Sat, 27 Apr 2024 06:50:48 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact90
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [] [2016-03-05 10:34:21] [52aea4735e848aa60c3226a1f3eea286] [Current]
Feedback Forum

Post a new message
Dataseries X:
-15
-15
-13
-8
-13
-9
-7
-4
-4
-2
0
-2
-3
1
-2
-1
1
-3
-4
-9
-9
-7
-14
-12
-16
-20
-12
-12
-10
-10
-13
-16
-14
-17
-24
-25
-23
-17
-24
-20
-19
-18
-16
-12
-7
-6
-6
-5
-4
-4
-8
-9
-6
-7
-10
-11
-11
-12
-14
-12
-9
-5
-6
-6
-3
-2
-6
-6
-10
-8
-4
-3




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Sir Maurice George Kendall' @ kendall.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 & 'Sir Maurice George Kendall' @ kendall.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=293435&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]'Sir Maurice George Kendall' @ kendall.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=293435&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=293435&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'Sir Maurice George Kendall' @ kendall.wessa.net







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean-9.611111111111110.73785300444204-13.0257802750007
Geometric MeanNaN
Harmonic Mean0
Quadratic Mean11.4467365557952
Winsorized Mean ( 1 / 24 )-9.597222222222220.733893224757633-13.0771369709697
Winsorized Mean ( 2 / 24 )-9.6250.728483079974461-13.212386484443
Winsorized Mean ( 3 / 24 )-9.6250.709712824066719-13.5618234215466
Winsorized Mean ( 4 / 24 )-9.513888888888890.659584760409264-14.4240580740308
Winsorized Mean ( 5 / 24 )-9.513888888888890.659584760409264-14.4240580740308
Winsorized Mean ( 6 / 24 )-9.430555555555560.641492534414289-14.700959168864
Winsorized Mean ( 7 / 24 )-9.333333333333330.621724594212352-15.012005991427
Winsorized Mean ( 8 / 24 )-9.333333333333330.582746183377465-16.0161209108903
Winsorized Mean ( 9 / 24 )-9.333333333333330.582746183377465-16.0161209108903
Winsorized Mean ( 10 / 24 )-9.194444444444440.557927253662218-16.4796474524096
Winsorized Mean ( 11 / 24 )-9.194444444444440.557927253662218-16.4796474524096
Winsorized Mean ( 12 / 24 )-9.361111111111110.533063882768756-17.5609554758974
Winsorized Mean ( 13 / 24 )-9.180555555555560.502469016978979-18.2708888415693
Winsorized Mean ( 14 / 24 )-9.180555555555560.502469016978979-18.2708888415693
Winsorized Mean ( 15 / 24 )-8.972222222222220.469730145211182-19.1008014147963
Winsorized Mean ( 16 / 24 )-8.972222222222220.469730145211182-19.1008014147963
Winsorized Mean ( 17 / 24 )-8.972222222222220.469730145211182-19.1008014147963
Winsorized Mean ( 18 / 24 )-8.972222222222220.396567935705823-22.6246789374265
Winsorized Mean ( 19 / 24 )-8.972222222222220.396567935705823-22.6246789374265
Winsorized Mean ( 20 / 24 )-9.250.359179860437602-25.7531142997004
Winsorized Mean ( 21 / 24 )-8.958333333333330.317978195825349-28.172791250925
Winsorized Mean ( 22 / 24 )-8.958333333333330.317978195825349-28.172791250925
Winsorized Mean ( 23 / 24 )-8.958333333333330.317978195825349-28.172791250925
Winsorized Mean ( 24 / 24 )-8.958333333333330.317978195825349-28.172791250925
Trimmed Mean ( 1 / 24 )-9.542857142857140.709791242831216-13.4445968997766
Trimmed Mean ( 2 / 24 )-9.485294117647060.681014532345314-13.9281816571243
Trimmed Mean ( 3 / 24 )-9.409090909090910.649897704960159-14.4778029484928
Trimmed Mean ( 4 / 24 )-9.3281250.621240553367864-15.0153188638933
Trimmed Mean ( 5 / 24 )-9.27419354838710.605880470729653-15.3069689426007
Trimmed Mean ( 6 / 24 )-9.216666666666670.587098422275852-15.6986738798221
Trimmed Mean ( 7 / 24 )-9.172413793103450.569510637321263-16.1057813357914
Trimmed Mean ( 8 / 24 )-9.142857142857140.553283335172488-16.5247289438183
Trimmed Mean ( 9 / 24 )-9.111111111111110.542831221391426-16.7844271885409
Trimmed Mean ( 10 / 24 )-9.076923076923080.529553551290974-17.140708536077
Trimmed Mean ( 11 / 24 )-9.060.518561589831892-17.4714058612345
Trimmed Mean ( 12 / 24 )-9.041666666666670.504376531550781-17.926422228383
Trimmed Mean ( 13 / 24 )-90.49147318718299-18.3122909544382
Trimmed Mean ( 14 / 24 )-8.977272727272730.481682038286744-18.6373416771015
Trimmed Mean ( 15 / 24 )-8.952380952380950.468462259361878-19.1101433967713
Trimmed Mean ( 16 / 24 )-8.950.458467346375189-19.521564776122
Trimmed Mean ( 17 / 24 )-8.947368421052630.444577521607228-20.1255528815454
Trimmed Mean ( 18 / 24 )-8.944444444444440.425281315755659-21.0318302569949
Trimmed Mean ( 19 / 24 )-8.941176470588240.417831547713744-21.3989980400279
Trimmed Mean ( 20 / 24 )-8.93750.40644381232914-21.9895093218011
Trimmed Mean ( 21 / 24 )-8.90.399280962927513-22.2900684639346
Trimmed Mean ( 22 / 24 )-8.892857142857140.399534404006567-22.2580510055674
Trimmed Mean ( 23 / 24 )-8.884615384615390.397402810864292-22.3566999068091
Trimmed Mean ( 24 / 24 )-8.8750.391543304655168-22.6667137312339
Median-9
Midrange-12
Midmean - Weighted Average at Xnp-9.33333333333333
Midmean - Weighted Average at X(n+1)p-8.94444444444444
Midmean - Empirical Distribution Function-9.33333333333333
Midmean - Empirical Distribution Function - Averaging-8.94444444444444
Midmean - Empirical Distribution Function - Interpolation-8.94444444444444
Midmean - Closest Observation-9.33333333333333
Midmean - True Basic - Statistics Graphics Toolkit-8.94444444444444
Midmean - MS Excel (old versions)-8.62222222222222
Number of observations72

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & -9.61111111111111 & 0.73785300444204 & -13.0257802750007 \tabularnewline
Geometric Mean & NaN &  &  \tabularnewline
Harmonic Mean & 0 &  &  \tabularnewline
Quadratic Mean & 11.4467365557952 &  &  \tabularnewline
Winsorized Mean ( 1 / 24 ) & -9.59722222222222 & 0.733893224757633 & -13.0771369709697 \tabularnewline
Winsorized Mean ( 2 / 24 ) & -9.625 & 0.728483079974461 & -13.212386484443 \tabularnewline
Winsorized Mean ( 3 / 24 ) & -9.625 & 0.709712824066719 & -13.5618234215466 \tabularnewline
Winsorized Mean ( 4 / 24 ) & -9.51388888888889 & 0.659584760409264 & -14.4240580740308 \tabularnewline
Winsorized Mean ( 5 / 24 ) & -9.51388888888889 & 0.659584760409264 & -14.4240580740308 \tabularnewline
Winsorized Mean ( 6 / 24 ) & -9.43055555555556 & 0.641492534414289 & -14.700959168864 \tabularnewline
Winsorized Mean ( 7 / 24 ) & -9.33333333333333 & 0.621724594212352 & -15.012005991427 \tabularnewline
Winsorized Mean ( 8 / 24 ) & -9.33333333333333 & 0.582746183377465 & -16.0161209108903 \tabularnewline
Winsorized Mean ( 9 / 24 ) & -9.33333333333333 & 0.582746183377465 & -16.0161209108903 \tabularnewline
Winsorized Mean ( 10 / 24 ) & -9.19444444444444 & 0.557927253662218 & -16.4796474524096 \tabularnewline
Winsorized Mean ( 11 / 24 ) & -9.19444444444444 & 0.557927253662218 & -16.4796474524096 \tabularnewline
Winsorized Mean ( 12 / 24 ) & -9.36111111111111 & 0.533063882768756 & -17.5609554758974 \tabularnewline
Winsorized Mean ( 13 / 24 ) & -9.18055555555556 & 0.502469016978979 & -18.2708888415693 \tabularnewline
Winsorized Mean ( 14 / 24 ) & -9.18055555555556 & 0.502469016978979 & -18.2708888415693 \tabularnewline
Winsorized Mean ( 15 / 24 ) & -8.97222222222222 & 0.469730145211182 & -19.1008014147963 \tabularnewline
Winsorized Mean ( 16 / 24 ) & -8.97222222222222 & 0.469730145211182 & -19.1008014147963 \tabularnewline
Winsorized Mean ( 17 / 24 ) & -8.97222222222222 & 0.469730145211182 & -19.1008014147963 \tabularnewline
Winsorized Mean ( 18 / 24 ) & -8.97222222222222 & 0.396567935705823 & -22.6246789374265 \tabularnewline
Winsorized Mean ( 19 / 24 ) & -8.97222222222222 & 0.396567935705823 & -22.6246789374265 \tabularnewline
Winsorized Mean ( 20 / 24 ) & -9.25 & 0.359179860437602 & -25.7531142997004 \tabularnewline
Winsorized Mean ( 21 / 24 ) & -8.95833333333333 & 0.317978195825349 & -28.172791250925 \tabularnewline
Winsorized Mean ( 22 / 24 ) & -8.95833333333333 & 0.317978195825349 & -28.172791250925 \tabularnewline
Winsorized Mean ( 23 / 24 ) & -8.95833333333333 & 0.317978195825349 & -28.172791250925 \tabularnewline
Winsorized Mean ( 24 / 24 ) & -8.95833333333333 & 0.317978195825349 & -28.172791250925 \tabularnewline
Trimmed Mean ( 1 / 24 ) & -9.54285714285714 & 0.709791242831216 & -13.4445968997766 \tabularnewline
Trimmed Mean ( 2 / 24 ) & -9.48529411764706 & 0.681014532345314 & -13.9281816571243 \tabularnewline
Trimmed Mean ( 3 / 24 ) & -9.40909090909091 & 0.649897704960159 & -14.4778029484928 \tabularnewline
Trimmed Mean ( 4 / 24 ) & -9.328125 & 0.621240553367864 & -15.0153188638933 \tabularnewline
Trimmed Mean ( 5 / 24 ) & -9.2741935483871 & 0.605880470729653 & -15.3069689426007 \tabularnewline
Trimmed Mean ( 6 / 24 ) & -9.21666666666667 & 0.587098422275852 & -15.6986738798221 \tabularnewline
Trimmed Mean ( 7 / 24 ) & -9.17241379310345 & 0.569510637321263 & -16.1057813357914 \tabularnewline
Trimmed Mean ( 8 / 24 ) & -9.14285714285714 & 0.553283335172488 & -16.5247289438183 \tabularnewline
Trimmed Mean ( 9 / 24 ) & -9.11111111111111 & 0.542831221391426 & -16.7844271885409 \tabularnewline
Trimmed Mean ( 10 / 24 ) & -9.07692307692308 & 0.529553551290974 & -17.140708536077 \tabularnewline
Trimmed Mean ( 11 / 24 ) & -9.06 & 0.518561589831892 & -17.4714058612345 \tabularnewline
Trimmed Mean ( 12 / 24 ) & -9.04166666666667 & 0.504376531550781 & -17.926422228383 \tabularnewline
Trimmed Mean ( 13 / 24 ) & -9 & 0.49147318718299 & -18.3122909544382 \tabularnewline
Trimmed Mean ( 14 / 24 ) & -8.97727272727273 & 0.481682038286744 & -18.6373416771015 \tabularnewline
Trimmed Mean ( 15 / 24 ) & -8.95238095238095 & 0.468462259361878 & -19.1101433967713 \tabularnewline
Trimmed Mean ( 16 / 24 ) & -8.95 & 0.458467346375189 & -19.521564776122 \tabularnewline
Trimmed Mean ( 17 / 24 ) & -8.94736842105263 & 0.444577521607228 & -20.1255528815454 \tabularnewline
Trimmed Mean ( 18 / 24 ) & -8.94444444444444 & 0.425281315755659 & -21.0318302569949 \tabularnewline
Trimmed Mean ( 19 / 24 ) & -8.94117647058824 & 0.417831547713744 & -21.3989980400279 \tabularnewline
Trimmed Mean ( 20 / 24 ) & -8.9375 & 0.40644381232914 & -21.9895093218011 \tabularnewline
Trimmed Mean ( 21 / 24 ) & -8.9 & 0.399280962927513 & -22.2900684639346 \tabularnewline
Trimmed Mean ( 22 / 24 ) & -8.89285714285714 & 0.399534404006567 & -22.2580510055674 \tabularnewline
Trimmed Mean ( 23 / 24 ) & -8.88461538461539 & 0.397402810864292 & -22.3566999068091 \tabularnewline
Trimmed Mean ( 24 / 24 ) & -8.875 & 0.391543304655168 & -22.6667137312339 \tabularnewline
Median & -9 &  &  \tabularnewline
Midrange & -12 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & -9.33333333333333 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & -8.94444444444444 &  &  \tabularnewline
Midmean - Empirical Distribution Function & -9.33333333333333 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & -8.94444444444444 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & -8.94444444444444 &  &  \tabularnewline
Midmean - Closest Observation & -9.33333333333333 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & -8.94444444444444 &  &  \tabularnewline
Midmean - MS Excel (old versions) & -8.62222222222222 &  &  \tabularnewline
Number of observations & 72 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=293435&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]-9.61111111111111[/C][C]0.73785300444204[/C][C]-13.0257802750007[/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]11.4467365557952[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 24 )[/C][C]-9.59722222222222[/C][C]0.733893224757633[/C][C]-13.0771369709697[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 24 )[/C][C]-9.625[/C][C]0.728483079974461[/C][C]-13.212386484443[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 24 )[/C][C]-9.625[/C][C]0.709712824066719[/C][C]-13.5618234215466[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 24 )[/C][C]-9.51388888888889[/C][C]0.659584760409264[/C][C]-14.4240580740308[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 24 )[/C][C]-9.51388888888889[/C][C]0.659584760409264[/C][C]-14.4240580740308[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 24 )[/C][C]-9.43055555555556[/C][C]0.641492534414289[/C][C]-14.700959168864[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 24 )[/C][C]-9.33333333333333[/C][C]0.621724594212352[/C][C]-15.012005991427[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 24 )[/C][C]-9.33333333333333[/C][C]0.582746183377465[/C][C]-16.0161209108903[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 24 )[/C][C]-9.33333333333333[/C][C]0.582746183377465[/C][C]-16.0161209108903[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 24 )[/C][C]-9.19444444444444[/C][C]0.557927253662218[/C][C]-16.4796474524096[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 24 )[/C][C]-9.19444444444444[/C][C]0.557927253662218[/C][C]-16.4796474524096[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 24 )[/C][C]-9.36111111111111[/C][C]0.533063882768756[/C][C]-17.5609554758974[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 24 )[/C][C]-9.18055555555556[/C][C]0.502469016978979[/C][C]-18.2708888415693[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 24 )[/C][C]-9.18055555555556[/C][C]0.502469016978979[/C][C]-18.2708888415693[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 24 )[/C][C]-8.97222222222222[/C][C]0.469730145211182[/C][C]-19.1008014147963[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 24 )[/C][C]-8.97222222222222[/C][C]0.469730145211182[/C][C]-19.1008014147963[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 24 )[/C][C]-8.97222222222222[/C][C]0.469730145211182[/C][C]-19.1008014147963[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 24 )[/C][C]-8.97222222222222[/C][C]0.396567935705823[/C][C]-22.6246789374265[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 24 )[/C][C]-8.97222222222222[/C][C]0.396567935705823[/C][C]-22.6246789374265[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 24 )[/C][C]-9.25[/C][C]0.359179860437602[/C][C]-25.7531142997004[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 24 )[/C][C]-8.95833333333333[/C][C]0.317978195825349[/C][C]-28.172791250925[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 24 )[/C][C]-8.95833333333333[/C][C]0.317978195825349[/C][C]-28.172791250925[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 24 )[/C][C]-8.95833333333333[/C][C]0.317978195825349[/C][C]-28.172791250925[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 24 )[/C][C]-8.95833333333333[/C][C]0.317978195825349[/C][C]-28.172791250925[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 24 )[/C][C]-9.54285714285714[/C][C]0.709791242831216[/C][C]-13.4445968997766[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 24 )[/C][C]-9.48529411764706[/C][C]0.681014532345314[/C][C]-13.9281816571243[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 24 )[/C][C]-9.40909090909091[/C][C]0.649897704960159[/C][C]-14.4778029484928[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 24 )[/C][C]-9.328125[/C][C]0.621240553367864[/C][C]-15.0153188638933[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 24 )[/C][C]-9.2741935483871[/C][C]0.605880470729653[/C][C]-15.3069689426007[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 24 )[/C][C]-9.21666666666667[/C][C]0.587098422275852[/C][C]-15.6986738798221[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 24 )[/C][C]-9.17241379310345[/C][C]0.569510637321263[/C][C]-16.1057813357914[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 24 )[/C][C]-9.14285714285714[/C][C]0.553283335172488[/C][C]-16.5247289438183[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 24 )[/C][C]-9.11111111111111[/C][C]0.542831221391426[/C][C]-16.7844271885409[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 24 )[/C][C]-9.07692307692308[/C][C]0.529553551290974[/C][C]-17.140708536077[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 24 )[/C][C]-9.06[/C][C]0.518561589831892[/C][C]-17.4714058612345[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 24 )[/C][C]-9.04166666666667[/C][C]0.504376531550781[/C][C]-17.926422228383[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 24 )[/C][C]-9[/C][C]0.49147318718299[/C][C]-18.3122909544382[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 24 )[/C][C]-8.97727272727273[/C][C]0.481682038286744[/C][C]-18.6373416771015[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 24 )[/C][C]-8.95238095238095[/C][C]0.468462259361878[/C][C]-19.1101433967713[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 24 )[/C][C]-8.95[/C][C]0.458467346375189[/C][C]-19.521564776122[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 24 )[/C][C]-8.94736842105263[/C][C]0.444577521607228[/C][C]-20.1255528815454[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 24 )[/C][C]-8.94444444444444[/C][C]0.425281315755659[/C][C]-21.0318302569949[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 24 )[/C][C]-8.94117647058824[/C][C]0.417831547713744[/C][C]-21.3989980400279[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 24 )[/C][C]-8.9375[/C][C]0.40644381232914[/C][C]-21.9895093218011[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 24 )[/C][C]-8.9[/C][C]0.399280962927513[/C][C]-22.2900684639346[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 24 )[/C][C]-8.89285714285714[/C][C]0.399534404006567[/C][C]-22.2580510055674[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 24 )[/C][C]-8.88461538461539[/C][C]0.397402810864292[/C][C]-22.3566999068091[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 24 )[/C][C]-8.875[/C][C]0.391543304655168[/C][C]-22.6667137312339[/C][/ROW]
[ROW][C]Median[/C][C]-9[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]-12[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]-9.33333333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]-8.94444444444444[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]-9.33333333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]-8.94444444444444[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]-8.94444444444444[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]-9.33333333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]-8.94444444444444[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]-8.62222222222222[/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=293435&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=293435&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-9.611111111111110.73785300444204-13.0257802750007
Geometric MeanNaN
Harmonic Mean0
Quadratic Mean11.4467365557952
Winsorized Mean ( 1 / 24 )-9.597222222222220.733893224757633-13.0771369709697
Winsorized Mean ( 2 / 24 )-9.6250.728483079974461-13.212386484443
Winsorized Mean ( 3 / 24 )-9.6250.709712824066719-13.5618234215466
Winsorized Mean ( 4 / 24 )-9.513888888888890.659584760409264-14.4240580740308
Winsorized Mean ( 5 / 24 )-9.513888888888890.659584760409264-14.4240580740308
Winsorized Mean ( 6 / 24 )-9.430555555555560.641492534414289-14.700959168864
Winsorized Mean ( 7 / 24 )-9.333333333333330.621724594212352-15.012005991427
Winsorized Mean ( 8 / 24 )-9.333333333333330.582746183377465-16.0161209108903
Winsorized Mean ( 9 / 24 )-9.333333333333330.582746183377465-16.0161209108903
Winsorized Mean ( 10 / 24 )-9.194444444444440.557927253662218-16.4796474524096
Winsorized Mean ( 11 / 24 )-9.194444444444440.557927253662218-16.4796474524096
Winsorized Mean ( 12 / 24 )-9.361111111111110.533063882768756-17.5609554758974
Winsorized Mean ( 13 / 24 )-9.180555555555560.502469016978979-18.2708888415693
Winsorized Mean ( 14 / 24 )-9.180555555555560.502469016978979-18.2708888415693
Winsorized Mean ( 15 / 24 )-8.972222222222220.469730145211182-19.1008014147963
Winsorized Mean ( 16 / 24 )-8.972222222222220.469730145211182-19.1008014147963
Winsorized Mean ( 17 / 24 )-8.972222222222220.469730145211182-19.1008014147963
Winsorized Mean ( 18 / 24 )-8.972222222222220.396567935705823-22.6246789374265
Winsorized Mean ( 19 / 24 )-8.972222222222220.396567935705823-22.6246789374265
Winsorized Mean ( 20 / 24 )-9.250.359179860437602-25.7531142997004
Winsorized Mean ( 21 / 24 )-8.958333333333330.317978195825349-28.172791250925
Winsorized Mean ( 22 / 24 )-8.958333333333330.317978195825349-28.172791250925
Winsorized Mean ( 23 / 24 )-8.958333333333330.317978195825349-28.172791250925
Winsorized Mean ( 24 / 24 )-8.958333333333330.317978195825349-28.172791250925
Trimmed Mean ( 1 / 24 )-9.542857142857140.709791242831216-13.4445968997766
Trimmed Mean ( 2 / 24 )-9.485294117647060.681014532345314-13.9281816571243
Trimmed Mean ( 3 / 24 )-9.409090909090910.649897704960159-14.4778029484928
Trimmed Mean ( 4 / 24 )-9.3281250.621240553367864-15.0153188638933
Trimmed Mean ( 5 / 24 )-9.27419354838710.605880470729653-15.3069689426007
Trimmed Mean ( 6 / 24 )-9.216666666666670.587098422275852-15.6986738798221
Trimmed Mean ( 7 / 24 )-9.172413793103450.569510637321263-16.1057813357914
Trimmed Mean ( 8 / 24 )-9.142857142857140.553283335172488-16.5247289438183
Trimmed Mean ( 9 / 24 )-9.111111111111110.542831221391426-16.7844271885409
Trimmed Mean ( 10 / 24 )-9.076923076923080.529553551290974-17.140708536077
Trimmed Mean ( 11 / 24 )-9.060.518561589831892-17.4714058612345
Trimmed Mean ( 12 / 24 )-9.041666666666670.504376531550781-17.926422228383
Trimmed Mean ( 13 / 24 )-90.49147318718299-18.3122909544382
Trimmed Mean ( 14 / 24 )-8.977272727272730.481682038286744-18.6373416771015
Trimmed Mean ( 15 / 24 )-8.952380952380950.468462259361878-19.1101433967713
Trimmed Mean ( 16 / 24 )-8.950.458467346375189-19.521564776122
Trimmed Mean ( 17 / 24 )-8.947368421052630.444577521607228-20.1255528815454
Trimmed Mean ( 18 / 24 )-8.944444444444440.425281315755659-21.0318302569949
Trimmed Mean ( 19 / 24 )-8.941176470588240.417831547713744-21.3989980400279
Trimmed Mean ( 20 / 24 )-8.93750.40644381232914-21.9895093218011
Trimmed Mean ( 21 / 24 )-8.90.399280962927513-22.2900684639346
Trimmed Mean ( 22 / 24 )-8.892857142857140.399534404006567-22.2580510055674
Trimmed Mean ( 23 / 24 )-8.884615384615390.397402810864292-22.3566999068091
Trimmed Mean ( 24 / 24 )-8.8750.391543304655168-22.6667137312339
Median-9
Midrange-12
Midmean - Weighted Average at Xnp-9.33333333333333
Midmean - Weighted Average at X(n+1)p-8.94444444444444
Midmean - Empirical Distribution Function-9.33333333333333
Midmean - Empirical Distribution Function - Averaging-8.94444444444444
Midmean - Empirical Distribution Function - Interpolation-8.94444444444444
Midmean - Closest Observation-9.33333333333333
Midmean - True Basic - Statistics Graphics Toolkit-8.94444444444444
Midmean - MS Excel (old versions)-8.62222222222222
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')