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Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationSun, 12 Oct 2014 20:56:02 +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/2014/Oct/12/t1413143963etvdsykxeltoeod.htm/, Retrieved Thu, 16 May 2024 02:11:37 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=240682, Retrieved Thu, 16 May 2024 02:11:37 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact73
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [] [2014-10-12 19:56:02] [18123dc03e4972c6afb0cd442b9891ee] [Current]
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Dataseries X:
7,3
7,1
6,8
6,4
6,1
6,5
7,7
7,9
7,5
6,9
6,6
6,9
7,7
8
8
7,7
7,3
7,4
8,1
8,3
8,1
7,9
7,9
8,3
8,6
8,7
8,5
8,3
8
8
8,8
8,7
8,5
8,1
7,8
7,7
7,5
7,2
6,9
6,6
6,5
6,6
7,7
8
7,7
7,3
7
7
7,3
7,3
7,1
7,1
7
7
7,5
7,8
7,9
8,1
8,3
8,4
8,6
8,5
8,4
8,3
8
8
8,7
8,7
8,6
8,5
8,5
8,6




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 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 & 2 seconds \tabularnewline
R Server & 'Sir Maurice George Kendall' @ kendall.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=240682&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]'Sir Maurice George Kendall' @ kendall.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=240682&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=240682&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'Sir Maurice George Kendall' @ kendall.wessa.net







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean7.726388888888890.081096579132112495.2739187222931
Geometric Mean7.69533029345589
Harmonic Mean7.66346068014674
Quadratic Mean7.75654741349383
Winsorized Mean ( 1 / 24 )7.729166666666670.079769756212864296.8934472614097
Winsorized Mean ( 2 / 24 )7.731944444444440.079139206724836197.7005553180247
Winsorized Mean ( 3 / 24 )7.731944444444450.079139206724836197.7005553180247
Winsorized Mean ( 4 / 24 )7.73750.07795903733594699.2508407544475
Winsorized Mean ( 5 / 24 )7.730555555555560.0768012415765723100.656648211189
Winsorized Mean ( 6 / 24 )7.730555555555560.0768012415765723100.656648211189
Winsorized Mean ( 7 / 24 )7.750.0729975239145314106.167984671289
Winsorized Mean ( 8 / 24 )7.761111111111110.0710296383827033109.265811959998
Winsorized Mean ( 9 / 24 )7.748611111111110.0690306529505152112.248845692735
Winsorized Mean ( 10 / 24 )7.748611111111110.0690306529505152112.248845692735
Winsorized Mean ( 11 / 24 )7.763888888888890.0664699431867063116.803001727879
Winsorized Mean ( 12 / 24 )7.763888888888890.0664699431867063116.803001727879
Winsorized Mean ( 13 / 24 )7.763888888888890.0664699431867063116.803001727879
Winsorized Mean ( 14 / 24 )7.744444444444440.063538366192707121.886112415232
Winsorized Mean ( 15 / 24 )7.765277777777780.0601952912746192129.001415448785
Winsorized Mean ( 16 / 24 )7.743055555555560.0570131079596702135.811848058394
Winsorized Mean ( 17 / 24 )7.743055555555560.0570131079596702135.811848058394
Winsorized Mean ( 18 / 24 )7.768055555555550.0531417623426821146.176099796307
Winsorized Mean ( 19 / 24 )7.794444444444450.0492863343918094158.146158374881
Winsorized Mean ( 20 / 24 )7.794444444444450.0492863343918094158.146158374881
Winsorized Mean ( 21 / 24 )7.736111111111110.0414102700757281186.816243819803
Winsorized Mean ( 22 / 24 )7.736111111111110.0414102700757281186.816243819803
Winsorized Mean ( 23 / 24 )7.736111111111110.0414102700757281186.816243819803
Winsorized Mean ( 24 / 24 )7.769444444444440.0365597506999129212.513605692146
Trimmed Mean ( 1 / 24 )7.734285714285710.078571240353623698.4365994411722
Trimmed Mean ( 2 / 24 )7.739705882352940.0771285515140682100.348129589096
Trimmed Mean ( 3 / 24 )7.743939393939390.0757904357638948102.175681085455
Trimmed Mean ( 4 / 24 )7.74843750.0741684118140055104.470856399501
Trimmed Mean ( 5 / 24 )7.751612903225810.0726379114820432106.715800951161
Trimmed Mean ( 6 / 24 )7.756666666666670.0711236158967593109.058947142479
Trimmed Mean ( 7 / 24 )7.762068965517240.0692552895984689112.079077432503
Trimmed Mean ( 8 / 24 )7.764285714285710.0679681252370365114.234219160938
Trimmed Mean ( 9 / 24 )7.764814814814820.0668319443598202116.184182417459
Trimmed Mean ( 10 / 24 )7.767307692307690.0658349983854669117.981436664276
Trimmed Mean ( 11 / 24 )7.770.0645391828461515120.391979838389
Trimmed Mean ( 12 / 24 )7.770833333333330.0634385790327359122.493811365532
Trimmed Mean ( 13 / 24 )7.771739130434780.0619851192581881125.380724009951
Trimmed Mean ( 14 / 24 )7.772727272727270.0600707507775736129.392877100998
Trimmed Mean ( 15 / 24 )7.776190476190480.0582167765820492133.573016795784
Trimmed Mean ( 16 / 24 )7.77750.0565557927387434137.519069636735
Trimmed Mean ( 17 / 24 )7.781578947368420.0550255679815415141.417512491262
Trimmed Mean ( 18 / 24 )7.786111111111110.0528779333724618147.246887586685
Trimmed Mean ( 19 / 24 )7.788235294117650.0509735358065988152.789779458646
Trimmed Mean ( 20 / 24 )7.78750.0493404074410783157.832097541954
Trimmed Mean ( 21 / 24 )7.786666666666670.0469123254968767165.98338675803
Trimmed Mean ( 22 / 24 )7.792857142857140.0456952672078882170.539699601798
Trimmed Mean ( 23 / 24 )7.80.0436771371279335178.583133256954
Trimmed Mean ( 24 / 24 )7.808333333333330.0403412376971406193.557108781687
Median7.85
Midrange7.45
Midmean - Weighted Average at Xnp7.7609756097561
Midmean - Weighted Average at X(n+1)p7.81315789473684
Midmean - Empirical Distribution Function7.7609756097561
Midmean - Empirical Distribution Function - Averaging7.81315789473684
Midmean - Empirical Distribution Function - Interpolation7.81315789473684
Midmean - Closest Observation7.7609756097561
Midmean - True Basic - Statistics Graphics Toolkit7.81315789473684
Midmean - MS Excel (old versions)7.7609756097561
Number of observations72

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 7.72638888888889 & 0.0810965791321124 & 95.2739187222931 \tabularnewline
Geometric Mean & 7.69533029345589 &  &  \tabularnewline
Harmonic Mean & 7.66346068014674 &  &  \tabularnewline
Quadratic Mean & 7.75654741349383 &  &  \tabularnewline
Winsorized Mean ( 1 / 24 ) & 7.72916666666667 & 0.0797697562128642 & 96.8934472614097 \tabularnewline
Winsorized Mean ( 2 / 24 ) & 7.73194444444444 & 0.0791392067248361 & 97.7005553180247 \tabularnewline
Winsorized Mean ( 3 / 24 ) & 7.73194444444445 & 0.0791392067248361 & 97.7005553180247 \tabularnewline
Winsorized Mean ( 4 / 24 ) & 7.7375 & 0.077959037335946 & 99.2508407544475 \tabularnewline
Winsorized Mean ( 5 / 24 ) & 7.73055555555556 & 0.0768012415765723 & 100.656648211189 \tabularnewline
Winsorized Mean ( 6 / 24 ) & 7.73055555555556 & 0.0768012415765723 & 100.656648211189 \tabularnewline
Winsorized Mean ( 7 / 24 ) & 7.75 & 0.0729975239145314 & 106.167984671289 \tabularnewline
Winsorized Mean ( 8 / 24 ) & 7.76111111111111 & 0.0710296383827033 & 109.265811959998 \tabularnewline
Winsorized Mean ( 9 / 24 ) & 7.74861111111111 & 0.0690306529505152 & 112.248845692735 \tabularnewline
Winsorized Mean ( 10 / 24 ) & 7.74861111111111 & 0.0690306529505152 & 112.248845692735 \tabularnewline
Winsorized Mean ( 11 / 24 ) & 7.76388888888889 & 0.0664699431867063 & 116.803001727879 \tabularnewline
Winsorized Mean ( 12 / 24 ) & 7.76388888888889 & 0.0664699431867063 & 116.803001727879 \tabularnewline
Winsorized Mean ( 13 / 24 ) & 7.76388888888889 & 0.0664699431867063 & 116.803001727879 \tabularnewline
Winsorized Mean ( 14 / 24 ) & 7.74444444444444 & 0.063538366192707 & 121.886112415232 \tabularnewline
Winsorized Mean ( 15 / 24 ) & 7.76527777777778 & 0.0601952912746192 & 129.001415448785 \tabularnewline
Winsorized Mean ( 16 / 24 ) & 7.74305555555556 & 0.0570131079596702 & 135.811848058394 \tabularnewline
Winsorized Mean ( 17 / 24 ) & 7.74305555555556 & 0.0570131079596702 & 135.811848058394 \tabularnewline
Winsorized Mean ( 18 / 24 ) & 7.76805555555555 & 0.0531417623426821 & 146.176099796307 \tabularnewline
Winsorized Mean ( 19 / 24 ) & 7.79444444444445 & 0.0492863343918094 & 158.146158374881 \tabularnewline
Winsorized Mean ( 20 / 24 ) & 7.79444444444445 & 0.0492863343918094 & 158.146158374881 \tabularnewline
Winsorized Mean ( 21 / 24 ) & 7.73611111111111 & 0.0414102700757281 & 186.816243819803 \tabularnewline
Winsorized Mean ( 22 / 24 ) & 7.73611111111111 & 0.0414102700757281 & 186.816243819803 \tabularnewline
Winsorized Mean ( 23 / 24 ) & 7.73611111111111 & 0.0414102700757281 & 186.816243819803 \tabularnewline
Winsorized Mean ( 24 / 24 ) & 7.76944444444444 & 0.0365597506999129 & 212.513605692146 \tabularnewline
Trimmed Mean ( 1 / 24 ) & 7.73428571428571 & 0.0785712403536236 & 98.4365994411722 \tabularnewline
Trimmed Mean ( 2 / 24 ) & 7.73970588235294 & 0.0771285515140682 & 100.348129589096 \tabularnewline
Trimmed Mean ( 3 / 24 ) & 7.74393939393939 & 0.0757904357638948 & 102.175681085455 \tabularnewline
Trimmed Mean ( 4 / 24 ) & 7.7484375 & 0.0741684118140055 & 104.470856399501 \tabularnewline
Trimmed Mean ( 5 / 24 ) & 7.75161290322581 & 0.0726379114820432 & 106.715800951161 \tabularnewline
Trimmed Mean ( 6 / 24 ) & 7.75666666666667 & 0.0711236158967593 & 109.058947142479 \tabularnewline
Trimmed Mean ( 7 / 24 ) & 7.76206896551724 & 0.0692552895984689 & 112.079077432503 \tabularnewline
Trimmed Mean ( 8 / 24 ) & 7.76428571428571 & 0.0679681252370365 & 114.234219160938 \tabularnewline
Trimmed Mean ( 9 / 24 ) & 7.76481481481482 & 0.0668319443598202 & 116.184182417459 \tabularnewline
Trimmed Mean ( 10 / 24 ) & 7.76730769230769 & 0.0658349983854669 & 117.981436664276 \tabularnewline
Trimmed Mean ( 11 / 24 ) & 7.77 & 0.0645391828461515 & 120.391979838389 \tabularnewline
Trimmed Mean ( 12 / 24 ) & 7.77083333333333 & 0.0634385790327359 & 122.493811365532 \tabularnewline
Trimmed Mean ( 13 / 24 ) & 7.77173913043478 & 0.0619851192581881 & 125.380724009951 \tabularnewline
Trimmed Mean ( 14 / 24 ) & 7.77272727272727 & 0.0600707507775736 & 129.392877100998 \tabularnewline
Trimmed Mean ( 15 / 24 ) & 7.77619047619048 & 0.0582167765820492 & 133.573016795784 \tabularnewline
Trimmed Mean ( 16 / 24 ) & 7.7775 & 0.0565557927387434 & 137.519069636735 \tabularnewline
Trimmed Mean ( 17 / 24 ) & 7.78157894736842 & 0.0550255679815415 & 141.417512491262 \tabularnewline
Trimmed Mean ( 18 / 24 ) & 7.78611111111111 & 0.0528779333724618 & 147.246887586685 \tabularnewline
Trimmed Mean ( 19 / 24 ) & 7.78823529411765 & 0.0509735358065988 & 152.789779458646 \tabularnewline
Trimmed Mean ( 20 / 24 ) & 7.7875 & 0.0493404074410783 & 157.832097541954 \tabularnewline
Trimmed Mean ( 21 / 24 ) & 7.78666666666667 & 0.0469123254968767 & 165.98338675803 \tabularnewline
Trimmed Mean ( 22 / 24 ) & 7.79285714285714 & 0.0456952672078882 & 170.539699601798 \tabularnewline
Trimmed Mean ( 23 / 24 ) & 7.8 & 0.0436771371279335 & 178.583133256954 \tabularnewline
Trimmed Mean ( 24 / 24 ) & 7.80833333333333 & 0.0403412376971406 & 193.557108781687 \tabularnewline
Median & 7.85 &  &  \tabularnewline
Midrange & 7.45 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 7.7609756097561 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 7.81315789473684 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 7.7609756097561 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 7.81315789473684 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 7.81315789473684 &  &  \tabularnewline
Midmean - Closest Observation & 7.7609756097561 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 7.81315789473684 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 7.7609756097561 &  &  \tabularnewline
Number of observations & 72 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=240682&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]7.72638888888889[/C][C]0.0810965791321124[/C][C]95.2739187222931[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]7.69533029345589[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]7.66346068014674[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]7.75654741349383[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 24 )[/C][C]7.72916666666667[/C][C]0.0797697562128642[/C][C]96.8934472614097[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 24 )[/C][C]7.73194444444444[/C][C]0.0791392067248361[/C][C]97.7005553180247[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 24 )[/C][C]7.73194444444445[/C][C]0.0791392067248361[/C][C]97.7005553180247[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 24 )[/C][C]7.7375[/C][C]0.077959037335946[/C][C]99.2508407544475[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 24 )[/C][C]7.73055555555556[/C][C]0.0768012415765723[/C][C]100.656648211189[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 24 )[/C][C]7.73055555555556[/C][C]0.0768012415765723[/C][C]100.656648211189[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 24 )[/C][C]7.75[/C][C]0.0729975239145314[/C][C]106.167984671289[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 24 )[/C][C]7.76111111111111[/C][C]0.0710296383827033[/C][C]109.265811959998[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 24 )[/C][C]7.74861111111111[/C][C]0.0690306529505152[/C][C]112.248845692735[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 24 )[/C][C]7.74861111111111[/C][C]0.0690306529505152[/C][C]112.248845692735[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 24 )[/C][C]7.76388888888889[/C][C]0.0664699431867063[/C][C]116.803001727879[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 24 )[/C][C]7.76388888888889[/C][C]0.0664699431867063[/C][C]116.803001727879[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 24 )[/C][C]7.76388888888889[/C][C]0.0664699431867063[/C][C]116.803001727879[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 24 )[/C][C]7.74444444444444[/C][C]0.063538366192707[/C][C]121.886112415232[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 24 )[/C][C]7.76527777777778[/C][C]0.0601952912746192[/C][C]129.001415448785[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 24 )[/C][C]7.74305555555556[/C][C]0.0570131079596702[/C][C]135.811848058394[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 24 )[/C][C]7.74305555555556[/C][C]0.0570131079596702[/C][C]135.811848058394[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 24 )[/C][C]7.76805555555555[/C][C]0.0531417623426821[/C][C]146.176099796307[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 24 )[/C][C]7.79444444444445[/C][C]0.0492863343918094[/C][C]158.146158374881[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 24 )[/C][C]7.79444444444445[/C][C]0.0492863343918094[/C][C]158.146158374881[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 24 )[/C][C]7.73611111111111[/C][C]0.0414102700757281[/C][C]186.816243819803[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 24 )[/C][C]7.73611111111111[/C][C]0.0414102700757281[/C][C]186.816243819803[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 24 )[/C][C]7.73611111111111[/C][C]0.0414102700757281[/C][C]186.816243819803[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 24 )[/C][C]7.76944444444444[/C][C]0.0365597506999129[/C][C]212.513605692146[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 24 )[/C][C]7.73428571428571[/C][C]0.0785712403536236[/C][C]98.4365994411722[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 24 )[/C][C]7.73970588235294[/C][C]0.0771285515140682[/C][C]100.348129589096[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 24 )[/C][C]7.74393939393939[/C][C]0.0757904357638948[/C][C]102.175681085455[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 24 )[/C][C]7.7484375[/C][C]0.0741684118140055[/C][C]104.470856399501[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 24 )[/C][C]7.75161290322581[/C][C]0.0726379114820432[/C][C]106.715800951161[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 24 )[/C][C]7.75666666666667[/C][C]0.0711236158967593[/C][C]109.058947142479[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 24 )[/C][C]7.76206896551724[/C][C]0.0692552895984689[/C][C]112.079077432503[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 24 )[/C][C]7.76428571428571[/C][C]0.0679681252370365[/C][C]114.234219160938[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 24 )[/C][C]7.76481481481482[/C][C]0.0668319443598202[/C][C]116.184182417459[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 24 )[/C][C]7.76730769230769[/C][C]0.0658349983854669[/C][C]117.981436664276[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 24 )[/C][C]7.77[/C][C]0.0645391828461515[/C][C]120.391979838389[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 24 )[/C][C]7.77083333333333[/C][C]0.0634385790327359[/C][C]122.493811365532[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 24 )[/C][C]7.77173913043478[/C][C]0.0619851192581881[/C][C]125.380724009951[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 24 )[/C][C]7.77272727272727[/C][C]0.0600707507775736[/C][C]129.392877100998[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 24 )[/C][C]7.77619047619048[/C][C]0.0582167765820492[/C][C]133.573016795784[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 24 )[/C][C]7.7775[/C][C]0.0565557927387434[/C][C]137.519069636735[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 24 )[/C][C]7.78157894736842[/C][C]0.0550255679815415[/C][C]141.417512491262[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 24 )[/C][C]7.78611111111111[/C][C]0.0528779333724618[/C][C]147.246887586685[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 24 )[/C][C]7.78823529411765[/C][C]0.0509735358065988[/C][C]152.789779458646[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 24 )[/C][C]7.7875[/C][C]0.0493404074410783[/C][C]157.832097541954[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 24 )[/C][C]7.78666666666667[/C][C]0.0469123254968767[/C][C]165.98338675803[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 24 )[/C][C]7.79285714285714[/C][C]0.0456952672078882[/C][C]170.539699601798[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 24 )[/C][C]7.8[/C][C]0.0436771371279335[/C][C]178.583133256954[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 24 )[/C][C]7.80833333333333[/C][C]0.0403412376971406[/C][C]193.557108781687[/C][/ROW]
[ROW][C]Median[/C][C]7.85[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]7.45[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]7.7609756097561[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]7.81315789473684[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]7.7609756097561[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]7.81315789473684[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]7.81315789473684[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]7.7609756097561[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]7.81315789473684[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]7.7609756097561[/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=240682&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=240682&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 Mean7.726388888888890.081096579132112495.2739187222931
Geometric Mean7.69533029345589
Harmonic Mean7.66346068014674
Quadratic Mean7.75654741349383
Winsorized Mean ( 1 / 24 )7.729166666666670.079769756212864296.8934472614097
Winsorized Mean ( 2 / 24 )7.731944444444440.079139206724836197.7005553180247
Winsorized Mean ( 3 / 24 )7.731944444444450.079139206724836197.7005553180247
Winsorized Mean ( 4 / 24 )7.73750.07795903733594699.2508407544475
Winsorized Mean ( 5 / 24 )7.730555555555560.0768012415765723100.656648211189
Winsorized Mean ( 6 / 24 )7.730555555555560.0768012415765723100.656648211189
Winsorized Mean ( 7 / 24 )7.750.0729975239145314106.167984671289
Winsorized Mean ( 8 / 24 )7.761111111111110.0710296383827033109.265811959998
Winsorized Mean ( 9 / 24 )7.748611111111110.0690306529505152112.248845692735
Winsorized Mean ( 10 / 24 )7.748611111111110.0690306529505152112.248845692735
Winsorized Mean ( 11 / 24 )7.763888888888890.0664699431867063116.803001727879
Winsorized Mean ( 12 / 24 )7.763888888888890.0664699431867063116.803001727879
Winsorized Mean ( 13 / 24 )7.763888888888890.0664699431867063116.803001727879
Winsorized Mean ( 14 / 24 )7.744444444444440.063538366192707121.886112415232
Winsorized Mean ( 15 / 24 )7.765277777777780.0601952912746192129.001415448785
Winsorized Mean ( 16 / 24 )7.743055555555560.0570131079596702135.811848058394
Winsorized Mean ( 17 / 24 )7.743055555555560.0570131079596702135.811848058394
Winsorized Mean ( 18 / 24 )7.768055555555550.0531417623426821146.176099796307
Winsorized Mean ( 19 / 24 )7.794444444444450.0492863343918094158.146158374881
Winsorized Mean ( 20 / 24 )7.794444444444450.0492863343918094158.146158374881
Winsorized Mean ( 21 / 24 )7.736111111111110.0414102700757281186.816243819803
Winsorized Mean ( 22 / 24 )7.736111111111110.0414102700757281186.816243819803
Winsorized Mean ( 23 / 24 )7.736111111111110.0414102700757281186.816243819803
Winsorized Mean ( 24 / 24 )7.769444444444440.0365597506999129212.513605692146
Trimmed Mean ( 1 / 24 )7.734285714285710.078571240353623698.4365994411722
Trimmed Mean ( 2 / 24 )7.739705882352940.0771285515140682100.348129589096
Trimmed Mean ( 3 / 24 )7.743939393939390.0757904357638948102.175681085455
Trimmed Mean ( 4 / 24 )7.74843750.0741684118140055104.470856399501
Trimmed Mean ( 5 / 24 )7.751612903225810.0726379114820432106.715800951161
Trimmed Mean ( 6 / 24 )7.756666666666670.0711236158967593109.058947142479
Trimmed Mean ( 7 / 24 )7.762068965517240.0692552895984689112.079077432503
Trimmed Mean ( 8 / 24 )7.764285714285710.0679681252370365114.234219160938
Trimmed Mean ( 9 / 24 )7.764814814814820.0668319443598202116.184182417459
Trimmed Mean ( 10 / 24 )7.767307692307690.0658349983854669117.981436664276
Trimmed Mean ( 11 / 24 )7.770.0645391828461515120.391979838389
Trimmed Mean ( 12 / 24 )7.770833333333330.0634385790327359122.493811365532
Trimmed Mean ( 13 / 24 )7.771739130434780.0619851192581881125.380724009951
Trimmed Mean ( 14 / 24 )7.772727272727270.0600707507775736129.392877100998
Trimmed Mean ( 15 / 24 )7.776190476190480.0582167765820492133.573016795784
Trimmed Mean ( 16 / 24 )7.77750.0565557927387434137.519069636735
Trimmed Mean ( 17 / 24 )7.781578947368420.0550255679815415141.417512491262
Trimmed Mean ( 18 / 24 )7.786111111111110.0528779333724618147.246887586685
Trimmed Mean ( 19 / 24 )7.788235294117650.0509735358065988152.789779458646
Trimmed Mean ( 20 / 24 )7.78750.0493404074410783157.832097541954
Trimmed Mean ( 21 / 24 )7.786666666666670.0469123254968767165.98338675803
Trimmed Mean ( 22 / 24 )7.792857142857140.0456952672078882170.539699601798
Trimmed Mean ( 23 / 24 )7.80.0436771371279335178.583133256954
Trimmed Mean ( 24 / 24 )7.808333333333330.0403412376971406193.557108781687
Median7.85
Midrange7.45
Midmean - Weighted Average at Xnp7.7609756097561
Midmean - Weighted Average at X(n+1)p7.81315789473684
Midmean - Empirical Distribution Function7.7609756097561
Midmean - Empirical Distribution Function - Averaging7.81315789473684
Midmean - Empirical Distribution Function - Interpolation7.81315789473684
Midmean - Closest Observation7.7609756097561
Midmean - True Basic - Statistics Graphics Toolkit7.81315789473684
Midmean - MS Excel (old versions)7.7609756097561
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')