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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, 23 Oct 2009 07:03:38 -0600
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2009/Oct/23/t1256303054ztbz7o6kw4m0ylk.htm/, Retrieved Thu, 02 May 2024 04:25:03 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=49966, Retrieved Thu, 02 May 2024 04:25:03 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsKDGP1W52
Estimated Impact100
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [Descriptive Stati...] [2009-10-23 13:03:38] [99dd5e7f67b5ad84b7cfa9edf27cffe4] [Current]
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Dataseries X:
6
5
2
3
-2
-4
0
1
4
-3
-3
0
6
-1
0
-1
1
-4
-1
-1
0
3
0
8
8
8
8
11
13
5
12
13
9
11
7
12
11
10
13
14
10
13
12
13
17
15
6
9
6
11
12
13
11
16
16
19
14
15
12
14
16
13
13
15
12
13
12
15
10
8
11
8




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 2 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=49966&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]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=49966&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=49966&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'Gwilym Jenkins' @ 72.249.127.135







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean8.111111111111110.71468925680006511.3491437487498
Geometric MeanNaN
Harmonic Mean0
Quadratic Mean10.1022549737945
Winsorized Mean ( 1 / 24 )8.083333333333330.70924754590844511.3970550620372
Winsorized Mean ( 2 / 24 )8.083333333333330.69812794608723511.5785843821861
Winsorized Mean ( 3 / 24 )8.083333333333330.69812794608723511.5785843821861
Winsorized Mean ( 4 / 24 )8.138888888888890.68613178138194511.8619908153741
Winsorized Mean ( 5 / 24 )8.138888888888890.66145425794258412.3045377532294
Winsorized Mean ( 6 / 24 )8.138888888888890.66145425794258412.3045377532294
Winsorized Mean ( 7 / 24 )8.138888888888890.66145425794258412.3045377532294
Winsorized Mean ( 8 / 24 )8.138888888888890.66145425794258412.3045377532294
Winsorized Mean ( 9 / 24 )8.138888888888890.62024578510613313.1220382053805
Winsorized Mean ( 10 / 24 )8.138888888888890.62024578510613313.1220382053805
Winsorized Mean ( 11 / 24 )8.138888888888890.62024578510613313.1220382053805
Winsorized Mean ( 12 / 24 )7.972222222222220.59928629377141413.3028609282078
Winsorized Mean ( 13 / 24 )7.972222222222220.59928629377141413.3028609282078
Winsorized Mean ( 14 / 24 )8.166666666666670.56363452792049814.4892945022321
Winsorized Mean ( 15 / 24 )8.166666666666670.56363452792049814.4892945022321
Winsorized Mean ( 16 / 24 )8.388888888888890.52464890844679315.9895289093881
Winsorized Mean ( 17 / 24 )8.6250.48508162841781817.7805125874010
Winsorized Mean ( 18 / 24 )8.6250.48508162841781817.7805125874010
Winsorized Mean ( 19 / 24 )8.888888888888890.44297487871785720.0663498449773
Winsorized Mean ( 20 / 24 )9.166666666666670.4009964115372222.8597224387277
Winsorized Mean ( 21 / 24 )8.8750.36361163265951924.4079099865059
Winsorized Mean ( 22 / 24 )9.180555555555560.31913811263002628.7667163282328
Winsorized Mean ( 23 / 24 )9.180555555555560.31913811263002628.7667163282328
Winsorized Mean ( 24 / 24 )9.180555555555560.31913811263002628.7667163282328
Trimmed Mean ( 1 / 24 )8.128571428571430.69690871063666111.6637535225318
Trimmed Mean ( 2 / 24 )8.17647058823530.68212508683961811.9867612934719
Trimmed Mean ( 3 / 24 )8.227272727272730.67135720121972512.2546875379088
Trimmed Mean ( 4 / 24 )8.281250.65823113658248212.5810669531618
Trimmed Mean ( 5 / 24 )8.322580645161290.64666667311498512.8699699415025
Trimmed Mean ( 6 / 24 )8.366666666666670.63998881816973813.0731450755561
Trimmed Mean ( 7 / 24 )8.413793103448280.63141899498066713.3252137967530
Trimmed Mean ( 8 / 24 )8.464285714285710.62051731963766813.6406921231920
Trimmed Mean ( 9 / 24 )8.518518518518520.60670648655269514.0405924566931
Trimmed Mean ( 10 / 24 )8.576923076923080.59873304763259614.3251205371683
Trimmed Mean ( 11 / 24 )8.640.5881551926254214.6900003746164
Trimmed Mean ( 12 / 24 )8.708333333333330.57423888366103715.1650011538991
Trimmed Mean ( 13 / 24 )8.804347826086960.56003758087960515.7209946737123
Trimmed Mean ( 14 / 24 )8.90909090909090.54094328955439916.4695469582953
Trimmed Mean ( 15 / 24 )90.5246535276178117.1541779979342
Trimmed Mean ( 16 / 24 )9.10.50230239130198518.1165771009222
Trimmed Mean ( 17 / 24 )9.184210526315790.48278362952934619.0234505989137
Trimmed Mean ( 18 / 24 )9.250.4669641908707319.8087994343889
Trimmed Mean ( 19 / 24 )9.32352941176470.44425544721500420.9868657102868
Trimmed Mean ( 20 / 24 )9.3750.42537933735098322.0391522972933
Trimmed Mean ( 21 / 24 )9.40.41133368728910422.8524924908308
Trimmed Mean ( 22 / 24 )9.464285714285710.40000708610503423.6602951373731
Trimmed Mean ( 23 / 24 )9.50.39710490766585623.9231493154796
Trimmed Mean ( 24 / 24 )9.541666666666670.38999798711235824.4659382406446
Median10
Midrange7.5
Midmean - Weighted Average at Xnp9.62790697674419
Midmean - Weighted Average at X(n+1)p9.62790697674419
Midmean - Empirical Distribution Function9.62790697674419
Midmean - Empirical Distribution Function - Averaging9.62790697674419
Midmean - Empirical Distribution Function - Interpolation9.62790697674419
Midmean - Closest Observation9.62790697674419
Midmean - True Basic - Statistics Graphics Toolkit9.62790697674419
Midmean - MS Excel (old versions)9.62790697674419
Number of observations72

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 8.11111111111111 & 0.714689256800065 & 11.3491437487498 \tabularnewline
Geometric Mean & NaN &  &  \tabularnewline
Harmonic Mean & 0 &  &  \tabularnewline
Quadratic Mean & 10.1022549737945 &  &  \tabularnewline
Winsorized Mean ( 1 / 24 ) & 8.08333333333333 & 0.709247545908445 & 11.3970550620372 \tabularnewline
Winsorized Mean ( 2 / 24 ) & 8.08333333333333 & 0.698127946087235 & 11.5785843821861 \tabularnewline
Winsorized Mean ( 3 / 24 ) & 8.08333333333333 & 0.698127946087235 & 11.5785843821861 \tabularnewline
Winsorized Mean ( 4 / 24 ) & 8.13888888888889 & 0.686131781381945 & 11.8619908153741 \tabularnewline
Winsorized Mean ( 5 / 24 ) & 8.13888888888889 & 0.661454257942584 & 12.3045377532294 \tabularnewline
Winsorized Mean ( 6 / 24 ) & 8.13888888888889 & 0.661454257942584 & 12.3045377532294 \tabularnewline
Winsorized Mean ( 7 / 24 ) & 8.13888888888889 & 0.661454257942584 & 12.3045377532294 \tabularnewline
Winsorized Mean ( 8 / 24 ) & 8.13888888888889 & 0.661454257942584 & 12.3045377532294 \tabularnewline
Winsorized Mean ( 9 / 24 ) & 8.13888888888889 & 0.620245785106133 & 13.1220382053805 \tabularnewline
Winsorized Mean ( 10 / 24 ) & 8.13888888888889 & 0.620245785106133 & 13.1220382053805 \tabularnewline
Winsorized Mean ( 11 / 24 ) & 8.13888888888889 & 0.620245785106133 & 13.1220382053805 \tabularnewline
Winsorized Mean ( 12 / 24 ) & 7.97222222222222 & 0.599286293771414 & 13.3028609282078 \tabularnewline
Winsorized Mean ( 13 / 24 ) & 7.97222222222222 & 0.599286293771414 & 13.3028609282078 \tabularnewline
Winsorized Mean ( 14 / 24 ) & 8.16666666666667 & 0.563634527920498 & 14.4892945022321 \tabularnewline
Winsorized Mean ( 15 / 24 ) & 8.16666666666667 & 0.563634527920498 & 14.4892945022321 \tabularnewline
Winsorized Mean ( 16 / 24 ) & 8.38888888888889 & 0.524648908446793 & 15.9895289093881 \tabularnewline
Winsorized Mean ( 17 / 24 ) & 8.625 & 0.485081628417818 & 17.7805125874010 \tabularnewline
Winsorized Mean ( 18 / 24 ) & 8.625 & 0.485081628417818 & 17.7805125874010 \tabularnewline
Winsorized Mean ( 19 / 24 ) & 8.88888888888889 & 0.442974878717857 & 20.0663498449773 \tabularnewline
Winsorized Mean ( 20 / 24 ) & 9.16666666666667 & 0.40099641153722 & 22.8597224387277 \tabularnewline
Winsorized Mean ( 21 / 24 ) & 8.875 & 0.363611632659519 & 24.4079099865059 \tabularnewline
Winsorized Mean ( 22 / 24 ) & 9.18055555555556 & 0.319138112630026 & 28.7667163282328 \tabularnewline
Winsorized Mean ( 23 / 24 ) & 9.18055555555556 & 0.319138112630026 & 28.7667163282328 \tabularnewline
Winsorized Mean ( 24 / 24 ) & 9.18055555555556 & 0.319138112630026 & 28.7667163282328 \tabularnewline
Trimmed Mean ( 1 / 24 ) & 8.12857142857143 & 0.696908710636661 & 11.6637535225318 \tabularnewline
Trimmed Mean ( 2 / 24 ) & 8.1764705882353 & 0.682125086839618 & 11.9867612934719 \tabularnewline
Trimmed Mean ( 3 / 24 ) & 8.22727272727273 & 0.671357201219725 & 12.2546875379088 \tabularnewline
Trimmed Mean ( 4 / 24 ) & 8.28125 & 0.658231136582482 & 12.5810669531618 \tabularnewline
Trimmed Mean ( 5 / 24 ) & 8.32258064516129 & 0.646666673114985 & 12.8699699415025 \tabularnewline
Trimmed Mean ( 6 / 24 ) & 8.36666666666667 & 0.639988818169738 & 13.0731450755561 \tabularnewline
Trimmed Mean ( 7 / 24 ) & 8.41379310344828 & 0.631418994980667 & 13.3252137967530 \tabularnewline
Trimmed Mean ( 8 / 24 ) & 8.46428571428571 & 0.620517319637668 & 13.6406921231920 \tabularnewline
Trimmed Mean ( 9 / 24 ) & 8.51851851851852 & 0.606706486552695 & 14.0405924566931 \tabularnewline
Trimmed Mean ( 10 / 24 ) & 8.57692307692308 & 0.598733047632596 & 14.3251205371683 \tabularnewline
Trimmed Mean ( 11 / 24 ) & 8.64 & 0.58815519262542 & 14.6900003746164 \tabularnewline
Trimmed Mean ( 12 / 24 ) & 8.70833333333333 & 0.574238883661037 & 15.1650011538991 \tabularnewline
Trimmed Mean ( 13 / 24 ) & 8.80434782608696 & 0.560037580879605 & 15.7209946737123 \tabularnewline
Trimmed Mean ( 14 / 24 ) & 8.9090909090909 & 0.540943289554399 & 16.4695469582953 \tabularnewline
Trimmed Mean ( 15 / 24 ) & 9 & 0.52465352761781 & 17.1541779979342 \tabularnewline
Trimmed Mean ( 16 / 24 ) & 9.1 & 0.502302391301985 & 18.1165771009222 \tabularnewline
Trimmed Mean ( 17 / 24 ) & 9.18421052631579 & 0.482783629529346 & 19.0234505989137 \tabularnewline
Trimmed Mean ( 18 / 24 ) & 9.25 & 0.46696419087073 & 19.8087994343889 \tabularnewline
Trimmed Mean ( 19 / 24 ) & 9.3235294117647 & 0.444255447215004 & 20.9868657102868 \tabularnewline
Trimmed Mean ( 20 / 24 ) & 9.375 & 0.425379337350983 & 22.0391522972933 \tabularnewline
Trimmed Mean ( 21 / 24 ) & 9.4 & 0.411333687289104 & 22.8524924908308 \tabularnewline
Trimmed Mean ( 22 / 24 ) & 9.46428571428571 & 0.400007086105034 & 23.6602951373731 \tabularnewline
Trimmed Mean ( 23 / 24 ) & 9.5 & 0.397104907665856 & 23.9231493154796 \tabularnewline
Trimmed Mean ( 24 / 24 ) & 9.54166666666667 & 0.389997987112358 & 24.4659382406446 \tabularnewline
Median & 10 &  &  \tabularnewline
Midrange & 7.5 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 9.62790697674419 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 9.62790697674419 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 9.62790697674419 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 9.62790697674419 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 9.62790697674419 &  &  \tabularnewline
Midmean - Closest Observation & 9.62790697674419 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 9.62790697674419 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 9.62790697674419 &  &  \tabularnewline
Number of observations & 72 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=49966&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]8.11111111111111[/C][C]0.714689256800065[/C][C]11.3491437487498[/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]10.1022549737945[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 24 )[/C][C]8.08333333333333[/C][C]0.709247545908445[/C][C]11.3970550620372[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 24 )[/C][C]8.08333333333333[/C][C]0.698127946087235[/C][C]11.5785843821861[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 24 )[/C][C]8.08333333333333[/C][C]0.698127946087235[/C][C]11.5785843821861[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 24 )[/C][C]8.13888888888889[/C][C]0.686131781381945[/C][C]11.8619908153741[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 24 )[/C][C]8.13888888888889[/C][C]0.661454257942584[/C][C]12.3045377532294[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 24 )[/C][C]8.13888888888889[/C][C]0.661454257942584[/C][C]12.3045377532294[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 24 )[/C][C]8.13888888888889[/C][C]0.661454257942584[/C][C]12.3045377532294[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 24 )[/C][C]8.13888888888889[/C][C]0.661454257942584[/C][C]12.3045377532294[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 24 )[/C][C]8.13888888888889[/C][C]0.620245785106133[/C][C]13.1220382053805[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 24 )[/C][C]8.13888888888889[/C][C]0.620245785106133[/C][C]13.1220382053805[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 24 )[/C][C]8.13888888888889[/C][C]0.620245785106133[/C][C]13.1220382053805[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 24 )[/C][C]7.97222222222222[/C][C]0.599286293771414[/C][C]13.3028609282078[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 24 )[/C][C]7.97222222222222[/C][C]0.599286293771414[/C][C]13.3028609282078[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 24 )[/C][C]8.16666666666667[/C][C]0.563634527920498[/C][C]14.4892945022321[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 24 )[/C][C]8.16666666666667[/C][C]0.563634527920498[/C][C]14.4892945022321[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 24 )[/C][C]8.38888888888889[/C][C]0.524648908446793[/C][C]15.9895289093881[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 24 )[/C][C]8.625[/C][C]0.485081628417818[/C][C]17.7805125874010[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 24 )[/C][C]8.625[/C][C]0.485081628417818[/C][C]17.7805125874010[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 24 )[/C][C]8.88888888888889[/C][C]0.442974878717857[/C][C]20.0663498449773[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 24 )[/C][C]9.16666666666667[/C][C]0.40099641153722[/C][C]22.8597224387277[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 24 )[/C][C]8.875[/C][C]0.363611632659519[/C][C]24.4079099865059[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 24 )[/C][C]9.18055555555556[/C][C]0.319138112630026[/C][C]28.7667163282328[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 24 )[/C][C]9.18055555555556[/C][C]0.319138112630026[/C][C]28.7667163282328[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 24 )[/C][C]9.18055555555556[/C][C]0.319138112630026[/C][C]28.7667163282328[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 24 )[/C][C]8.12857142857143[/C][C]0.696908710636661[/C][C]11.6637535225318[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 24 )[/C][C]8.1764705882353[/C][C]0.682125086839618[/C][C]11.9867612934719[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 24 )[/C][C]8.22727272727273[/C][C]0.671357201219725[/C][C]12.2546875379088[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 24 )[/C][C]8.28125[/C][C]0.658231136582482[/C][C]12.5810669531618[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 24 )[/C][C]8.32258064516129[/C][C]0.646666673114985[/C][C]12.8699699415025[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 24 )[/C][C]8.36666666666667[/C][C]0.639988818169738[/C][C]13.0731450755561[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 24 )[/C][C]8.41379310344828[/C][C]0.631418994980667[/C][C]13.3252137967530[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 24 )[/C][C]8.46428571428571[/C][C]0.620517319637668[/C][C]13.6406921231920[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 24 )[/C][C]8.51851851851852[/C][C]0.606706486552695[/C][C]14.0405924566931[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 24 )[/C][C]8.57692307692308[/C][C]0.598733047632596[/C][C]14.3251205371683[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 24 )[/C][C]8.64[/C][C]0.58815519262542[/C][C]14.6900003746164[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 24 )[/C][C]8.70833333333333[/C][C]0.574238883661037[/C][C]15.1650011538991[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 24 )[/C][C]8.80434782608696[/C][C]0.560037580879605[/C][C]15.7209946737123[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 24 )[/C][C]8.9090909090909[/C][C]0.540943289554399[/C][C]16.4695469582953[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 24 )[/C][C]9[/C][C]0.52465352761781[/C][C]17.1541779979342[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 24 )[/C][C]9.1[/C][C]0.502302391301985[/C][C]18.1165771009222[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 24 )[/C][C]9.18421052631579[/C][C]0.482783629529346[/C][C]19.0234505989137[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 24 )[/C][C]9.25[/C][C]0.46696419087073[/C][C]19.8087994343889[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 24 )[/C][C]9.3235294117647[/C][C]0.444255447215004[/C][C]20.9868657102868[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 24 )[/C][C]9.375[/C][C]0.425379337350983[/C][C]22.0391522972933[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 24 )[/C][C]9.4[/C][C]0.411333687289104[/C][C]22.8524924908308[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 24 )[/C][C]9.46428571428571[/C][C]0.400007086105034[/C][C]23.6602951373731[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 24 )[/C][C]9.5[/C][C]0.397104907665856[/C][C]23.9231493154796[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 24 )[/C][C]9.54166666666667[/C][C]0.389997987112358[/C][C]24.4659382406446[/C][/ROW]
[ROW][C]Median[/C][C]10[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]7.5[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]9.62790697674419[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]9.62790697674419[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]9.62790697674419[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]9.62790697674419[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]9.62790697674419[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]9.62790697674419[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]9.62790697674419[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]9.62790697674419[/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=49966&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=49966&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 Mean8.111111111111110.71468925680006511.3491437487498
Geometric MeanNaN
Harmonic Mean0
Quadratic Mean10.1022549737945
Winsorized Mean ( 1 / 24 )8.083333333333330.70924754590844511.3970550620372
Winsorized Mean ( 2 / 24 )8.083333333333330.69812794608723511.5785843821861
Winsorized Mean ( 3 / 24 )8.083333333333330.69812794608723511.5785843821861
Winsorized Mean ( 4 / 24 )8.138888888888890.68613178138194511.8619908153741
Winsorized Mean ( 5 / 24 )8.138888888888890.66145425794258412.3045377532294
Winsorized Mean ( 6 / 24 )8.138888888888890.66145425794258412.3045377532294
Winsorized Mean ( 7 / 24 )8.138888888888890.66145425794258412.3045377532294
Winsorized Mean ( 8 / 24 )8.138888888888890.66145425794258412.3045377532294
Winsorized Mean ( 9 / 24 )8.138888888888890.62024578510613313.1220382053805
Winsorized Mean ( 10 / 24 )8.138888888888890.62024578510613313.1220382053805
Winsorized Mean ( 11 / 24 )8.138888888888890.62024578510613313.1220382053805
Winsorized Mean ( 12 / 24 )7.972222222222220.59928629377141413.3028609282078
Winsorized Mean ( 13 / 24 )7.972222222222220.59928629377141413.3028609282078
Winsorized Mean ( 14 / 24 )8.166666666666670.56363452792049814.4892945022321
Winsorized Mean ( 15 / 24 )8.166666666666670.56363452792049814.4892945022321
Winsorized Mean ( 16 / 24 )8.388888888888890.52464890844679315.9895289093881
Winsorized Mean ( 17 / 24 )8.6250.48508162841781817.7805125874010
Winsorized Mean ( 18 / 24 )8.6250.48508162841781817.7805125874010
Winsorized Mean ( 19 / 24 )8.888888888888890.44297487871785720.0663498449773
Winsorized Mean ( 20 / 24 )9.166666666666670.4009964115372222.8597224387277
Winsorized Mean ( 21 / 24 )8.8750.36361163265951924.4079099865059
Winsorized Mean ( 22 / 24 )9.180555555555560.31913811263002628.7667163282328
Winsorized Mean ( 23 / 24 )9.180555555555560.31913811263002628.7667163282328
Winsorized Mean ( 24 / 24 )9.180555555555560.31913811263002628.7667163282328
Trimmed Mean ( 1 / 24 )8.128571428571430.69690871063666111.6637535225318
Trimmed Mean ( 2 / 24 )8.17647058823530.68212508683961811.9867612934719
Trimmed Mean ( 3 / 24 )8.227272727272730.67135720121972512.2546875379088
Trimmed Mean ( 4 / 24 )8.281250.65823113658248212.5810669531618
Trimmed Mean ( 5 / 24 )8.322580645161290.64666667311498512.8699699415025
Trimmed Mean ( 6 / 24 )8.366666666666670.63998881816973813.0731450755561
Trimmed Mean ( 7 / 24 )8.413793103448280.63141899498066713.3252137967530
Trimmed Mean ( 8 / 24 )8.464285714285710.62051731963766813.6406921231920
Trimmed Mean ( 9 / 24 )8.518518518518520.60670648655269514.0405924566931
Trimmed Mean ( 10 / 24 )8.576923076923080.59873304763259614.3251205371683
Trimmed Mean ( 11 / 24 )8.640.5881551926254214.6900003746164
Trimmed Mean ( 12 / 24 )8.708333333333330.57423888366103715.1650011538991
Trimmed Mean ( 13 / 24 )8.804347826086960.56003758087960515.7209946737123
Trimmed Mean ( 14 / 24 )8.90909090909090.54094328955439916.4695469582953
Trimmed Mean ( 15 / 24 )90.5246535276178117.1541779979342
Trimmed Mean ( 16 / 24 )9.10.50230239130198518.1165771009222
Trimmed Mean ( 17 / 24 )9.184210526315790.48278362952934619.0234505989137
Trimmed Mean ( 18 / 24 )9.250.4669641908707319.8087994343889
Trimmed Mean ( 19 / 24 )9.32352941176470.44425544721500420.9868657102868
Trimmed Mean ( 20 / 24 )9.3750.42537933735098322.0391522972933
Trimmed Mean ( 21 / 24 )9.40.41133368728910422.8524924908308
Trimmed Mean ( 22 / 24 )9.464285714285710.40000708610503423.6602951373731
Trimmed Mean ( 23 / 24 )9.50.39710490766585623.9231493154796
Trimmed Mean ( 24 / 24 )9.541666666666670.38999798711235824.4659382406446
Median10
Midrange7.5
Midmean - Weighted Average at Xnp9.62790697674419
Midmean - Weighted Average at X(n+1)p9.62790697674419
Midmean - Empirical Distribution Function9.62790697674419
Midmean - Empirical Distribution Function - Averaging9.62790697674419
Midmean - Empirical Distribution Function - Interpolation9.62790697674419
Midmean - Closest Observation9.62790697674419
Midmean - True Basic - Statistics Graphics Toolkit9.62790697674419
Midmean - MS Excel (old versions)9.62790697674419
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')