Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationFri, 10 Mar 2017 15:28:00 +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/2017/Mar/10/t1489160183elxqhkkz9q6f7s9.htm/, Retrieved Wed, 15 May 2024 10:40:43 +0200
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=, Retrieved Wed, 15 May 2024 10:40:43 +0200
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact0
Dataseries X:
89,78
90,31
90,69
90,71
90,77
90,98
91,02
91,16
91,45
92,86
93,48
94,07
94,09
94,19
94,3
94,34
94,4
94,47
94,54
95,1
95,36
95,54
95,87
95,96
96
96,11
96,22
96,42
97,45
97,95
98,06
98,09
98,14
98,17
98,26
98,32
98,35
98,39
98,41
98,43
98,46
98,48
98,64
98,67
98,69
98,7
98,72
98,72
98,75
98,8
98,82
98,83
98,84
98,85
98,89
98,89
99,05
99,13
99,18
99,22
99,25
99,33
99,39
99,4
99,61
100,28
100,31
100,45
100,55
100,68
100,78
101,69




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Herman Ole Andreas Wold' @ wold.wessa.net

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 1 seconds \tabularnewline
R Server & 'Herman Ole Andreas Wold' @ wold.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Herman Ole Andreas Wold' @ wold.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&T=0

As an alternative you can also use a QR Code:  

The GUIDs for individual cells are displayed in the table below:

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Herman Ole Andreas Wold' @ wold.wessa.net







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean96.89250.359741133997529269.339507893656
Geometric Mean96.8441848433645
Harmonic Mean96.7949653240046
Quadratic Mean96.939903691812
Winsorized Mean ( 1 / 24 )96.88722222222220.355594414200905272.465534758042
Winsorized Mean ( 2 / 24 )96.8950.352486417456606274.89002469699
Winsorized Mean ( 3 / 24 )96.89041666666670.351473114832304275.669496692216
Winsorized Mean ( 4 / 24 )96.88819444444440.349844103799923276.94676969561
Winsorized Mean ( 5 / 24 )96.89305555555560.344911684897837280.921348269936
Winsorized Mean ( 6 / 24 )96.89388888888890.343760306748632281.864680088677
Winsorized Mean ( 7 / 24 )96.84236111111110.332129486519859291.580136788971
Winsorized Mean ( 8 / 24 )96.851250.321764983971245300.999968376469
Winsorized Mean ( 9 / 24 )97.026250.282304638883898343.693431264881
Winsorized Mean ( 10 / 24 )97.10402777777780.26402444370719367.784233968384
Winsorized Mean ( 11 / 24 )97.18194444444450.245800697196188395.368872232604
Winsorized Mean ( 12 / 24 )97.18027777777780.244617085411154397.275102899851
Winsorized Mean ( 13 / 24 )97.19111111111110.240579841701259403.986927681989
Winsorized Mean ( 14 / 24 )97.20277777777780.235719872856317412.365646561449
Winsorized Mean ( 15 / 24 )97.19444444444440.232379328141409418.25770485617
Winsorized Mean ( 16 / 24 )97.17222222222220.226172585491919429.637491258613
Winsorized Mean ( 17 / 24 )97.188750.223328948305435.182052025202
Winsorized Mean ( 18 / 24 )97.196250.219268009513671443.276017397968
Winsorized Mean ( 19 / 24 )97.34138888888890.194338521898575500.885711890364
Winsorized Mean ( 20 / 24 )97.41083333333330.182447791962145533.910727478381
Winsorized Mean ( 21 / 24 )97.46041666666670.173886625672122560.482534467236
Winsorized Mean ( 22 / 24 )97.55513888888890.15777142608691618.332110626607
Winsorized Mean ( 23 / 24 )97.56791666666670.151698384123551643.170441335764
Winsorized Mean ( 24 / 24 )97.571250.14861724918949656.527089097138
Trimmed Mean ( 1 / 24 )96.92557142857140.348876495241896277.822016531574
Trimmed Mean ( 2 / 24 )96.96617647058820.340797754218813284.527040657463
Trimmed Mean ( 3 / 24 )97.0050.333053139813144291.259827348944
Trimmed Mean ( 4 / 24 )97.047968750.324111053780817299.428136183314
Trimmed Mean ( 5 / 24 )97.09435483870970.313807633982724309.407242922762
Trimmed Mean ( 6 / 24 )97.14266666666670.302796557409274320.818266554346
Trimmed Mean ( 7 / 24 )97.19413793103450.289503824285671335.726611456182
Trimmed Mean ( 8 / 24 )97.258750.275988784651201352.401095294207
Trimmed Mean ( 9 / 24 )97.32666666666670.261711963123981371.884668568092
Trimmed Mean ( 10 / 24 )97.37288461538460.254453446233363382.674654467374
Trimmed Mean ( 11 / 24 )97.41160.249610367393272390.254623705288
Trimmed Mean ( 12 / 24 )97.44291666666670.247375399958703393.907060616917
Trimmed Mean ( 13 / 24 )97.47717391304350.244357515667388398.912117136296
Trimmed Mean ( 14 / 24 )97.51318181818180.240944620221024404.712011119943
Trimmed Mean ( 15 / 24 )97.55119047619050.237142591853911411.360901951707
Trimmed Mean ( 16 / 24 )97.5940.232334804836601420.057597778503
Trimmed Mean ( 17 / 24 )97.64394736842110.226658433428664430.79776865727
Trimmed Mean ( 18 / 24 )97.69750.219129002738729445.844679521891
Trimmed Mean ( 19 / 24 )97.75647058823530.209161334566238467.373526713072
Trimmed Mean ( 20 / 24 )97.8056250.202747229357387482.40178329439
Trimmed Mean ( 21 / 24 )97.8530.196754792256407497.334773287147
Trimmed Mean ( 22 / 24 )97.90107142857140.190133856556162514.906041469018
Trimmed Mean ( 23 / 24 )97.94461538461540.185420296598114528.230281051182
Trimmed Mean ( 24 / 24 )97.993750.179078572039672547.210919117062
Median98.335
Midrange95.735
Midmean - Weighted Average at Xnp97.6102702702703
Midmean - Weighted Average at X(n+1)p97.6975
Midmean - Empirical Distribution Function97.6102702702703
Midmean - Empirical Distribution Function - Averaging97.6975
Midmean - Empirical Distribution Function - Interpolation97.6975
Midmean - Closest Observation97.6102702702703
Midmean - True Basic - Statistics Graphics Toolkit97.6975
Midmean - MS Excel (old versions)97.6758974358974
Number of observations72

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 96.8925 & 0.359741133997529 & 269.339507893656 \tabularnewline
Geometric Mean & 96.8441848433645 &  &  \tabularnewline
Harmonic Mean & 96.7949653240046 &  &  \tabularnewline
Quadratic Mean & 96.939903691812 &  &  \tabularnewline
Winsorized Mean ( 1 / 24 ) & 96.8872222222222 & 0.355594414200905 & 272.465534758042 \tabularnewline
Winsorized Mean ( 2 / 24 ) & 96.895 & 0.352486417456606 & 274.89002469699 \tabularnewline
Winsorized Mean ( 3 / 24 ) & 96.8904166666667 & 0.351473114832304 & 275.669496692216 \tabularnewline
Winsorized Mean ( 4 / 24 ) & 96.8881944444444 & 0.349844103799923 & 276.94676969561 \tabularnewline
Winsorized Mean ( 5 / 24 ) & 96.8930555555556 & 0.344911684897837 & 280.921348269936 \tabularnewline
Winsorized Mean ( 6 / 24 ) & 96.8938888888889 & 0.343760306748632 & 281.864680088677 \tabularnewline
Winsorized Mean ( 7 / 24 ) & 96.8423611111111 & 0.332129486519859 & 291.580136788971 \tabularnewline
Winsorized Mean ( 8 / 24 ) & 96.85125 & 0.321764983971245 & 300.999968376469 \tabularnewline
Winsorized Mean ( 9 / 24 ) & 97.02625 & 0.282304638883898 & 343.693431264881 \tabularnewline
Winsorized Mean ( 10 / 24 ) & 97.1040277777778 & 0.26402444370719 & 367.784233968384 \tabularnewline
Winsorized Mean ( 11 / 24 ) & 97.1819444444445 & 0.245800697196188 & 395.368872232604 \tabularnewline
Winsorized Mean ( 12 / 24 ) & 97.1802777777778 & 0.244617085411154 & 397.275102899851 \tabularnewline
Winsorized Mean ( 13 / 24 ) & 97.1911111111111 & 0.240579841701259 & 403.986927681989 \tabularnewline
Winsorized Mean ( 14 / 24 ) & 97.2027777777778 & 0.235719872856317 & 412.365646561449 \tabularnewline
Winsorized Mean ( 15 / 24 ) & 97.1944444444444 & 0.232379328141409 & 418.25770485617 \tabularnewline
Winsorized Mean ( 16 / 24 ) & 97.1722222222222 & 0.226172585491919 & 429.637491258613 \tabularnewline
Winsorized Mean ( 17 / 24 ) & 97.18875 & 0.223328948305 & 435.182052025202 \tabularnewline
Winsorized Mean ( 18 / 24 ) & 97.19625 & 0.219268009513671 & 443.276017397968 \tabularnewline
Winsorized Mean ( 19 / 24 ) & 97.3413888888889 & 0.194338521898575 & 500.885711890364 \tabularnewline
Winsorized Mean ( 20 / 24 ) & 97.4108333333333 & 0.182447791962145 & 533.910727478381 \tabularnewline
Winsorized Mean ( 21 / 24 ) & 97.4604166666667 & 0.173886625672122 & 560.482534467236 \tabularnewline
Winsorized Mean ( 22 / 24 ) & 97.5551388888889 & 0.15777142608691 & 618.332110626607 \tabularnewline
Winsorized Mean ( 23 / 24 ) & 97.5679166666667 & 0.151698384123551 & 643.170441335764 \tabularnewline
Winsorized Mean ( 24 / 24 ) & 97.57125 & 0.14861724918949 & 656.527089097138 \tabularnewline
Trimmed Mean ( 1 / 24 ) & 96.9255714285714 & 0.348876495241896 & 277.822016531574 \tabularnewline
Trimmed Mean ( 2 / 24 ) & 96.9661764705882 & 0.340797754218813 & 284.527040657463 \tabularnewline
Trimmed Mean ( 3 / 24 ) & 97.005 & 0.333053139813144 & 291.259827348944 \tabularnewline
Trimmed Mean ( 4 / 24 ) & 97.04796875 & 0.324111053780817 & 299.428136183314 \tabularnewline
Trimmed Mean ( 5 / 24 ) & 97.0943548387097 & 0.313807633982724 & 309.407242922762 \tabularnewline
Trimmed Mean ( 6 / 24 ) & 97.1426666666667 & 0.302796557409274 & 320.818266554346 \tabularnewline
Trimmed Mean ( 7 / 24 ) & 97.1941379310345 & 0.289503824285671 & 335.726611456182 \tabularnewline
Trimmed Mean ( 8 / 24 ) & 97.25875 & 0.275988784651201 & 352.401095294207 \tabularnewline
Trimmed Mean ( 9 / 24 ) & 97.3266666666667 & 0.261711963123981 & 371.884668568092 \tabularnewline
Trimmed Mean ( 10 / 24 ) & 97.3728846153846 & 0.254453446233363 & 382.674654467374 \tabularnewline
Trimmed Mean ( 11 / 24 ) & 97.4116 & 0.249610367393272 & 390.254623705288 \tabularnewline
Trimmed Mean ( 12 / 24 ) & 97.4429166666667 & 0.247375399958703 & 393.907060616917 \tabularnewline
Trimmed Mean ( 13 / 24 ) & 97.4771739130435 & 0.244357515667388 & 398.912117136296 \tabularnewline
Trimmed Mean ( 14 / 24 ) & 97.5131818181818 & 0.240944620221024 & 404.712011119943 \tabularnewline
Trimmed Mean ( 15 / 24 ) & 97.5511904761905 & 0.237142591853911 & 411.360901951707 \tabularnewline
Trimmed Mean ( 16 / 24 ) & 97.594 & 0.232334804836601 & 420.057597778503 \tabularnewline
Trimmed Mean ( 17 / 24 ) & 97.6439473684211 & 0.226658433428664 & 430.79776865727 \tabularnewline
Trimmed Mean ( 18 / 24 ) & 97.6975 & 0.219129002738729 & 445.844679521891 \tabularnewline
Trimmed Mean ( 19 / 24 ) & 97.7564705882353 & 0.209161334566238 & 467.373526713072 \tabularnewline
Trimmed Mean ( 20 / 24 ) & 97.805625 & 0.202747229357387 & 482.40178329439 \tabularnewline
Trimmed Mean ( 21 / 24 ) & 97.853 & 0.196754792256407 & 497.334773287147 \tabularnewline
Trimmed Mean ( 22 / 24 ) & 97.9010714285714 & 0.190133856556162 & 514.906041469018 \tabularnewline
Trimmed Mean ( 23 / 24 ) & 97.9446153846154 & 0.185420296598114 & 528.230281051182 \tabularnewline
Trimmed Mean ( 24 / 24 ) & 97.99375 & 0.179078572039672 & 547.210919117062 \tabularnewline
Median & 98.335 &  &  \tabularnewline
Midrange & 95.735 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 97.6102702702703 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 97.6975 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 97.6102702702703 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 97.6975 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 97.6975 &  &  \tabularnewline
Midmean - Closest Observation & 97.6102702702703 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 97.6975 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 97.6758974358974 &  &  \tabularnewline
Number of observations & 72 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&T=1

[TABLE]
[ROW][C]Central Tendency - Ungrouped Data[/C][/ROW]
[ROW][C]Measure[/C][C]Value[/C][C]S.E.[/C][C]Value/S.E.[/C][/ROW]
[ROW][C]Arithmetic Mean[/C][C]96.8925[/C][C]0.359741133997529[/C][C]269.339507893656[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]96.8441848433645[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]96.7949653240046[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]96.939903691812[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 24 )[/C][C]96.8872222222222[/C][C]0.355594414200905[/C][C]272.465534758042[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 24 )[/C][C]96.895[/C][C]0.352486417456606[/C][C]274.89002469699[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 24 )[/C][C]96.8904166666667[/C][C]0.351473114832304[/C][C]275.669496692216[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 24 )[/C][C]96.8881944444444[/C][C]0.349844103799923[/C][C]276.94676969561[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 24 )[/C][C]96.8930555555556[/C][C]0.344911684897837[/C][C]280.921348269936[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 24 )[/C][C]96.8938888888889[/C][C]0.343760306748632[/C][C]281.864680088677[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 24 )[/C][C]96.8423611111111[/C][C]0.332129486519859[/C][C]291.580136788971[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 24 )[/C][C]96.85125[/C][C]0.321764983971245[/C][C]300.999968376469[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 24 )[/C][C]97.02625[/C][C]0.282304638883898[/C][C]343.693431264881[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 24 )[/C][C]97.1040277777778[/C][C]0.26402444370719[/C][C]367.784233968384[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 24 )[/C][C]97.1819444444445[/C][C]0.245800697196188[/C][C]395.368872232604[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 24 )[/C][C]97.1802777777778[/C][C]0.244617085411154[/C][C]397.275102899851[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 24 )[/C][C]97.1911111111111[/C][C]0.240579841701259[/C][C]403.986927681989[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 24 )[/C][C]97.2027777777778[/C][C]0.235719872856317[/C][C]412.365646561449[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 24 )[/C][C]97.1944444444444[/C][C]0.232379328141409[/C][C]418.25770485617[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 24 )[/C][C]97.1722222222222[/C][C]0.226172585491919[/C][C]429.637491258613[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 24 )[/C][C]97.18875[/C][C]0.223328948305[/C][C]435.182052025202[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 24 )[/C][C]97.19625[/C][C]0.219268009513671[/C][C]443.276017397968[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 24 )[/C][C]97.3413888888889[/C][C]0.194338521898575[/C][C]500.885711890364[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 24 )[/C][C]97.4108333333333[/C][C]0.182447791962145[/C][C]533.910727478381[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 24 )[/C][C]97.4604166666667[/C][C]0.173886625672122[/C][C]560.482534467236[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 24 )[/C][C]97.5551388888889[/C][C]0.15777142608691[/C][C]618.332110626607[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 24 )[/C][C]97.5679166666667[/C][C]0.151698384123551[/C][C]643.170441335764[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 24 )[/C][C]97.57125[/C][C]0.14861724918949[/C][C]656.527089097138[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 24 )[/C][C]96.9255714285714[/C][C]0.348876495241896[/C][C]277.822016531574[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 24 )[/C][C]96.9661764705882[/C][C]0.340797754218813[/C][C]284.527040657463[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 24 )[/C][C]97.005[/C][C]0.333053139813144[/C][C]291.259827348944[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 24 )[/C][C]97.04796875[/C][C]0.324111053780817[/C][C]299.428136183314[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 24 )[/C][C]97.0943548387097[/C][C]0.313807633982724[/C][C]309.407242922762[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 24 )[/C][C]97.1426666666667[/C][C]0.302796557409274[/C][C]320.818266554346[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 24 )[/C][C]97.1941379310345[/C][C]0.289503824285671[/C][C]335.726611456182[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 24 )[/C][C]97.25875[/C][C]0.275988784651201[/C][C]352.401095294207[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 24 )[/C][C]97.3266666666667[/C][C]0.261711963123981[/C][C]371.884668568092[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 24 )[/C][C]97.3728846153846[/C][C]0.254453446233363[/C][C]382.674654467374[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 24 )[/C][C]97.4116[/C][C]0.249610367393272[/C][C]390.254623705288[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 24 )[/C][C]97.4429166666667[/C][C]0.247375399958703[/C][C]393.907060616917[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 24 )[/C][C]97.4771739130435[/C][C]0.244357515667388[/C][C]398.912117136296[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 24 )[/C][C]97.5131818181818[/C][C]0.240944620221024[/C][C]404.712011119943[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 24 )[/C][C]97.5511904761905[/C][C]0.237142591853911[/C][C]411.360901951707[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 24 )[/C][C]97.594[/C][C]0.232334804836601[/C][C]420.057597778503[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 24 )[/C][C]97.6439473684211[/C][C]0.226658433428664[/C][C]430.79776865727[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 24 )[/C][C]97.6975[/C][C]0.219129002738729[/C][C]445.844679521891[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 24 )[/C][C]97.7564705882353[/C][C]0.209161334566238[/C][C]467.373526713072[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 24 )[/C][C]97.805625[/C][C]0.202747229357387[/C][C]482.40178329439[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 24 )[/C][C]97.853[/C][C]0.196754792256407[/C][C]497.334773287147[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 24 )[/C][C]97.9010714285714[/C][C]0.190133856556162[/C][C]514.906041469018[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 24 )[/C][C]97.9446153846154[/C][C]0.185420296598114[/C][C]528.230281051182[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 24 )[/C][C]97.99375[/C][C]0.179078572039672[/C][C]547.210919117062[/C][/ROW]
[ROW][C]Median[/C][C]98.335[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]95.735[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]97.6102702702703[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]97.6975[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]97.6102702702703[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]97.6975[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]97.6975[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]97.6102702702703[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]97.6975[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]97.6758974358974[/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=&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&T=1

As an alternative you can also use a QR Code:  

The GUIDs for individual cells are displayed in the table below:

Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean96.89250.359741133997529269.339507893656
Geometric Mean96.8441848433645
Harmonic Mean96.7949653240046
Quadratic Mean96.939903691812
Winsorized Mean ( 1 / 24 )96.88722222222220.355594414200905272.465534758042
Winsorized Mean ( 2 / 24 )96.8950.352486417456606274.89002469699
Winsorized Mean ( 3 / 24 )96.89041666666670.351473114832304275.669496692216
Winsorized Mean ( 4 / 24 )96.88819444444440.349844103799923276.94676969561
Winsorized Mean ( 5 / 24 )96.89305555555560.344911684897837280.921348269936
Winsorized Mean ( 6 / 24 )96.89388888888890.343760306748632281.864680088677
Winsorized Mean ( 7 / 24 )96.84236111111110.332129486519859291.580136788971
Winsorized Mean ( 8 / 24 )96.851250.321764983971245300.999968376469
Winsorized Mean ( 9 / 24 )97.026250.282304638883898343.693431264881
Winsorized Mean ( 10 / 24 )97.10402777777780.26402444370719367.784233968384
Winsorized Mean ( 11 / 24 )97.18194444444450.245800697196188395.368872232604
Winsorized Mean ( 12 / 24 )97.18027777777780.244617085411154397.275102899851
Winsorized Mean ( 13 / 24 )97.19111111111110.240579841701259403.986927681989
Winsorized Mean ( 14 / 24 )97.20277777777780.235719872856317412.365646561449
Winsorized Mean ( 15 / 24 )97.19444444444440.232379328141409418.25770485617
Winsorized Mean ( 16 / 24 )97.17222222222220.226172585491919429.637491258613
Winsorized Mean ( 17 / 24 )97.188750.223328948305435.182052025202
Winsorized Mean ( 18 / 24 )97.196250.219268009513671443.276017397968
Winsorized Mean ( 19 / 24 )97.34138888888890.194338521898575500.885711890364
Winsorized Mean ( 20 / 24 )97.41083333333330.182447791962145533.910727478381
Winsorized Mean ( 21 / 24 )97.46041666666670.173886625672122560.482534467236
Winsorized Mean ( 22 / 24 )97.55513888888890.15777142608691618.332110626607
Winsorized Mean ( 23 / 24 )97.56791666666670.151698384123551643.170441335764
Winsorized Mean ( 24 / 24 )97.571250.14861724918949656.527089097138
Trimmed Mean ( 1 / 24 )96.92557142857140.348876495241896277.822016531574
Trimmed Mean ( 2 / 24 )96.96617647058820.340797754218813284.527040657463
Trimmed Mean ( 3 / 24 )97.0050.333053139813144291.259827348944
Trimmed Mean ( 4 / 24 )97.047968750.324111053780817299.428136183314
Trimmed Mean ( 5 / 24 )97.09435483870970.313807633982724309.407242922762
Trimmed Mean ( 6 / 24 )97.14266666666670.302796557409274320.818266554346
Trimmed Mean ( 7 / 24 )97.19413793103450.289503824285671335.726611456182
Trimmed Mean ( 8 / 24 )97.258750.275988784651201352.401095294207
Trimmed Mean ( 9 / 24 )97.32666666666670.261711963123981371.884668568092
Trimmed Mean ( 10 / 24 )97.37288461538460.254453446233363382.674654467374
Trimmed Mean ( 11 / 24 )97.41160.249610367393272390.254623705288
Trimmed Mean ( 12 / 24 )97.44291666666670.247375399958703393.907060616917
Trimmed Mean ( 13 / 24 )97.47717391304350.244357515667388398.912117136296
Trimmed Mean ( 14 / 24 )97.51318181818180.240944620221024404.712011119943
Trimmed Mean ( 15 / 24 )97.55119047619050.237142591853911411.360901951707
Trimmed Mean ( 16 / 24 )97.5940.232334804836601420.057597778503
Trimmed Mean ( 17 / 24 )97.64394736842110.226658433428664430.79776865727
Trimmed Mean ( 18 / 24 )97.69750.219129002738729445.844679521891
Trimmed Mean ( 19 / 24 )97.75647058823530.209161334566238467.373526713072
Trimmed Mean ( 20 / 24 )97.8056250.202747229357387482.40178329439
Trimmed Mean ( 21 / 24 )97.8530.196754792256407497.334773287147
Trimmed Mean ( 22 / 24 )97.90107142857140.190133856556162514.906041469018
Trimmed Mean ( 23 / 24 )97.94461538461540.185420296598114528.230281051182
Trimmed Mean ( 24 / 24 )97.993750.179078572039672547.210919117062
Median98.335
Midrange95.735
Midmean - Weighted Average at Xnp97.6102702702703
Midmean - Weighted Average at X(n+1)p97.6975
Midmean - Empirical Distribution Function97.6102702702703
Midmean - Empirical Distribution Function - Averaging97.6975
Midmean - Empirical Distribution Function - Interpolation97.6975
Midmean - Closest Observation97.6102702702703
Midmean - True Basic - Statistics Graphics Toolkit97.6975
Midmean - MS Excel (old versions)97.6758974358974
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')