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Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationWed, 19 Oct 2011 06:29:30 -0400
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2011/Oct/19/t13190203641tr3sa4ifm1g1gf.htm/, Retrieved Wed, 15 May 2024 02:26:26 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=132743, Retrieved Wed, 15 May 2024 02:26:26 +0000
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Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact122
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [centrummaten inde...] [2011-10-19 10:29:30] [280688e1dcdd2fd70f339c81d6605b50] [Current]
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Dataseries X:
92,9
93,3
93,6
93,6
94
94
94,2
93,3
93
93
94,7
95,6
95,8
96
95,4
95,3
94,4
94,4
94,3
93,9
94,5
93,6
93,9
93,9
93,7
94,6
94,4
94
91,1
91,1
90,7
90,8
89,8
90,7
90,3
89,7
89
88,4
89,3
89,3
89,3
89,3
88,4
89,4
91,3
90,9
91
89,3
88,1
89
90,1
90,6
90,6
90,2
89,5
90,5
90,4
89,7
90
90,2
89,3
89,6
89,8
89,4
89,3
89,4
89,5
89,2
90
88
88,3
89,1




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=132743&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=132743&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=132743&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 Mean91.4750.27516355927075332.438642102285
Geometric Mean91.4457908417766
Harmonic Mean91.4167640415319
Quadratic Mean91.504379069468
Winsorized Mean ( 1 / 24 )91.47361111111110.274289472300432333.492971290269
Winsorized Mean ( 2 / 24 )91.47361111111110.272141517770923336.125159660899
Winsorized Mean ( 3 / 24 )91.46944444444440.269720185448795339.1271746764
Winsorized Mean ( 4 / 24 )91.46388888888890.268591247143461340.531904377494
Winsorized Mean ( 5 / 24 )91.46388888888890.254454105576814359.451417305892
Winsorized Mean ( 6 / 24 )91.45555555555550.252978260622856361.5154730307
Winsorized Mean ( 7 / 24 )91.45555555555560.249983480587934365.846396491728
Winsorized Mean ( 8 / 24 )91.45555555555560.246643261870917370.800948956876
Winsorized Mean ( 9 / 24 )91.46805555555560.245059368017717373.248557259572
Winsorized Mean ( 10 / 24 )91.46805555555560.245059368017717373.248557259572
Winsorized Mean ( 11 / 24 )91.45277777777780.242508830665589377.111124270308
Winsorized Mean ( 12 / 24 )91.43611111111110.239777752758958381.336925794902
Winsorized Mean ( 13 / 24 )91.40.234019781676598390.565273350736
Winsorized Mean ( 14 / 24 )91.40.234019781676598390.565273350736
Winsorized Mean ( 15 / 24 )91.40.234019781676598390.565273350736
Winsorized Mean ( 16 / 24 )91.40.227784457324101401.256525900503
Winsorized Mean ( 17 / 24 )91.40.227784457324101401.256525900503
Winsorized Mean ( 18 / 24 )91.40.227784457324101401.256525900503
Winsorized Mean ( 19 / 24 )91.37361111111110.216467885118731422.111626678449
Winsorized Mean ( 20 / 24 )91.34583333333330.212288166531845430.29168712346
Winsorized Mean ( 21 / 24 )91.3750.208755440925035437.713142206497
Winsorized Mean ( 22 / 24 )91.40555555555560.205136399609606445.584283089246
Winsorized Mean ( 23 / 24 )91.30972222222220.190873124807953478.37914485915
Winsorized Mean ( 24 / 24 )91.34305555555560.186955535926309488.581710634981
Trimmed Mean ( 1 / 24 )91.460.270911352037019337.601209075588
Trimmed Mean ( 2 / 24 )91.44558823529410.266817436537472342.727182383568
Trimmed Mean ( 3 / 24 )91.4303030303030.263196857883712347.383717896434
Trimmed Mean ( 4 / 24 )91.4156250.259838345941906351.817298823318
Trimmed Mean ( 5 / 24 )91.40161290322580.256089164464092356.913237990754
Trimmed Mean ( 6 / 24 )91.38666666666670.255653219690717357.463390358331
Trimmed Mean ( 7 / 24 )91.37241379310340.255215329691751358.020867725552
Trimmed Mean ( 8 / 24 )91.35714285714290.255063744806385358.173769174802
Trimmed Mean ( 9 / 24 )91.34074074074070.255238868383603357.863758443965
Trimmed Mean ( 10 / 24 )91.32115384615380.255340197440239357.645034983288
Trimmed Mean ( 11 / 24 )91.30.255007002704968358.02938363081
Trimmed Mean ( 12 / 24 )91.27916666666670.254654513792313358.443152282432
Trimmed Mean ( 13 / 24 )91.25869565217390.254269363181489358.905589373095
Trimmed Mean ( 14 / 24 )91.24090909090910.254418006451066358.62598863834
Trimmed Mean ( 15 / 24 )91.22142857142860.253970461904843359.181252367873
Trimmed Mean ( 16 / 24 )91.20.252728698156333360.861274027477
Trimmed Mean ( 17 / 24 )91.17631578947370.251720515231527362.212494701163
Trimmed Mean ( 18 / 24 )91.150.249586960383853365.203373845396
Trimmed Mean ( 19 / 24 )91.12058823529410.245885188769905370.581850379622
Trimmed Mean ( 20 / 24 )91.0906250.242897470031247375.016771431509
Trimmed Mean ( 21 / 24 )91.060.238944037116567381.093418772268
Trimmed Mean ( 22 / 24 )91.02142857142860.233013223893942390.627737989917
Trimmed Mean ( 23 / 24 )90.97307692307690.223920156945261406.274621115578
Trimmed Mean ( 24 / 24 )90.92916666666670.214972122111273422.98120227701
Median90.65
Midrange92
Midmean - Weighted Average at Xnp91.2
Midmean - Weighted Average at X(n+1)p91.2
Midmean - Empirical Distribution Function91.2
Midmean - Empirical Distribution Function - Averaging91.2
Midmean - Empirical Distribution Function - Interpolation91.2
Midmean - Closest Observation91.2
Midmean - True Basic - Statistics Graphics Toolkit91.2
Midmean - MS Excel (old versions)91.2
Number of observations72

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 91.475 & 0.27516355927075 & 332.438642102285 \tabularnewline
Geometric Mean & 91.4457908417766 &  &  \tabularnewline
Harmonic Mean & 91.4167640415319 &  &  \tabularnewline
Quadratic Mean & 91.504379069468 &  &  \tabularnewline
Winsorized Mean ( 1 / 24 ) & 91.4736111111111 & 0.274289472300432 & 333.492971290269 \tabularnewline
Winsorized Mean ( 2 / 24 ) & 91.4736111111111 & 0.272141517770923 & 336.125159660899 \tabularnewline
Winsorized Mean ( 3 / 24 ) & 91.4694444444444 & 0.269720185448795 & 339.1271746764 \tabularnewline
Winsorized Mean ( 4 / 24 ) & 91.4638888888889 & 0.268591247143461 & 340.531904377494 \tabularnewline
Winsorized Mean ( 5 / 24 ) & 91.4638888888889 & 0.254454105576814 & 359.451417305892 \tabularnewline
Winsorized Mean ( 6 / 24 ) & 91.4555555555555 & 0.252978260622856 & 361.5154730307 \tabularnewline
Winsorized Mean ( 7 / 24 ) & 91.4555555555556 & 0.249983480587934 & 365.846396491728 \tabularnewline
Winsorized Mean ( 8 / 24 ) & 91.4555555555556 & 0.246643261870917 & 370.800948956876 \tabularnewline
Winsorized Mean ( 9 / 24 ) & 91.4680555555556 & 0.245059368017717 & 373.248557259572 \tabularnewline
Winsorized Mean ( 10 / 24 ) & 91.4680555555556 & 0.245059368017717 & 373.248557259572 \tabularnewline
Winsorized Mean ( 11 / 24 ) & 91.4527777777778 & 0.242508830665589 & 377.111124270308 \tabularnewline
Winsorized Mean ( 12 / 24 ) & 91.4361111111111 & 0.239777752758958 & 381.336925794902 \tabularnewline
Winsorized Mean ( 13 / 24 ) & 91.4 & 0.234019781676598 & 390.565273350736 \tabularnewline
Winsorized Mean ( 14 / 24 ) & 91.4 & 0.234019781676598 & 390.565273350736 \tabularnewline
Winsorized Mean ( 15 / 24 ) & 91.4 & 0.234019781676598 & 390.565273350736 \tabularnewline
Winsorized Mean ( 16 / 24 ) & 91.4 & 0.227784457324101 & 401.256525900503 \tabularnewline
Winsorized Mean ( 17 / 24 ) & 91.4 & 0.227784457324101 & 401.256525900503 \tabularnewline
Winsorized Mean ( 18 / 24 ) & 91.4 & 0.227784457324101 & 401.256525900503 \tabularnewline
Winsorized Mean ( 19 / 24 ) & 91.3736111111111 & 0.216467885118731 & 422.111626678449 \tabularnewline
Winsorized Mean ( 20 / 24 ) & 91.3458333333333 & 0.212288166531845 & 430.29168712346 \tabularnewline
Winsorized Mean ( 21 / 24 ) & 91.375 & 0.208755440925035 & 437.713142206497 \tabularnewline
Winsorized Mean ( 22 / 24 ) & 91.4055555555556 & 0.205136399609606 & 445.584283089246 \tabularnewline
Winsorized Mean ( 23 / 24 ) & 91.3097222222222 & 0.190873124807953 & 478.37914485915 \tabularnewline
Winsorized Mean ( 24 / 24 ) & 91.3430555555556 & 0.186955535926309 & 488.581710634981 \tabularnewline
Trimmed Mean ( 1 / 24 ) & 91.46 & 0.270911352037019 & 337.601209075588 \tabularnewline
Trimmed Mean ( 2 / 24 ) & 91.4455882352941 & 0.266817436537472 & 342.727182383568 \tabularnewline
Trimmed Mean ( 3 / 24 ) & 91.430303030303 & 0.263196857883712 & 347.383717896434 \tabularnewline
Trimmed Mean ( 4 / 24 ) & 91.415625 & 0.259838345941906 & 351.817298823318 \tabularnewline
Trimmed Mean ( 5 / 24 ) & 91.4016129032258 & 0.256089164464092 & 356.913237990754 \tabularnewline
Trimmed Mean ( 6 / 24 ) & 91.3866666666667 & 0.255653219690717 & 357.463390358331 \tabularnewline
Trimmed Mean ( 7 / 24 ) & 91.3724137931034 & 0.255215329691751 & 358.020867725552 \tabularnewline
Trimmed Mean ( 8 / 24 ) & 91.3571428571429 & 0.255063744806385 & 358.173769174802 \tabularnewline
Trimmed Mean ( 9 / 24 ) & 91.3407407407407 & 0.255238868383603 & 357.863758443965 \tabularnewline
Trimmed Mean ( 10 / 24 ) & 91.3211538461538 & 0.255340197440239 & 357.645034983288 \tabularnewline
Trimmed Mean ( 11 / 24 ) & 91.3 & 0.255007002704968 & 358.02938363081 \tabularnewline
Trimmed Mean ( 12 / 24 ) & 91.2791666666667 & 0.254654513792313 & 358.443152282432 \tabularnewline
Trimmed Mean ( 13 / 24 ) & 91.2586956521739 & 0.254269363181489 & 358.905589373095 \tabularnewline
Trimmed Mean ( 14 / 24 ) & 91.2409090909091 & 0.254418006451066 & 358.62598863834 \tabularnewline
Trimmed Mean ( 15 / 24 ) & 91.2214285714286 & 0.253970461904843 & 359.181252367873 \tabularnewline
Trimmed Mean ( 16 / 24 ) & 91.2 & 0.252728698156333 & 360.861274027477 \tabularnewline
Trimmed Mean ( 17 / 24 ) & 91.1763157894737 & 0.251720515231527 & 362.212494701163 \tabularnewline
Trimmed Mean ( 18 / 24 ) & 91.15 & 0.249586960383853 & 365.203373845396 \tabularnewline
Trimmed Mean ( 19 / 24 ) & 91.1205882352941 & 0.245885188769905 & 370.581850379622 \tabularnewline
Trimmed Mean ( 20 / 24 ) & 91.090625 & 0.242897470031247 & 375.016771431509 \tabularnewline
Trimmed Mean ( 21 / 24 ) & 91.06 & 0.238944037116567 & 381.093418772268 \tabularnewline
Trimmed Mean ( 22 / 24 ) & 91.0214285714286 & 0.233013223893942 & 390.627737989917 \tabularnewline
Trimmed Mean ( 23 / 24 ) & 90.9730769230769 & 0.223920156945261 & 406.274621115578 \tabularnewline
Trimmed Mean ( 24 / 24 ) & 90.9291666666667 & 0.214972122111273 & 422.98120227701 \tabularnewline
Median & 90.65 &  &  \tabularnewline
Midrange & 92 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 91.2 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 91.2 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 91.2 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 91.2 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 91.2 &  &  \tabularnewline
Midmean - Closest Observation & 91.2 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 91.2 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 91.2 &  &  \tabularnewline
Number of observations & 72 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=132743&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]91.475[/C][C]0.27516355927075[/C][C]332.438642102285[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]91.4457908417766[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]91.4167640415319[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]91.504379069468[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 24 )[/C][C]91.4736111111111[/C][C]0.274289472300432[/C][C]333.492971290269[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 24 )[/C][C]91.4736111111111[/C][C]0.272141517770923[/C][C]336.125159660899[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 24 )[/C][C]91.4694444444444[/C][C]0.269720185448795[/C][C]339.1271746764[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 24 )[/C][C]91.4638888888889[/C][C]0.268591247143461[/C][C]340.531904377494[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 24 )[/C][C]91.4638888888889[/C][C]0.254454105576814[/C][C]359.451417305892[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 24 )[/C][C]91.4555555555555[/C][C]0.252978260622856[/C][C]361.5154730307[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 24 )[/C][C]91.4555555555556[/C][C]0.249983480587934[/C][C]365.846396491728[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 24 )[/C][C]91.4555555555556[/C][C]0.246643261870917[/C][C]370.800948956876[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 24 )[/C][C]91.4680555555556[/C][C]0.245059368017717[/C][C]373.248557259572[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 24 )[/C][C]91.4680555555556[/C][C]0.245059368017717[/C][C]373.248557259572[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 24 )[/C][C]91.4527777777778[/C][C]0.242508830665589[/C][C]377.111124270308[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 24 )[/C][C]91.4361111111111[/C][C]0.239777752758958[/C][C]381.336925794902[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 24 )[/C][C]91.4[/C][C]0.234019781676598[/C][C]390.565273350736[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 24 )[/C][C]91.4[/C][C]0.234019781676598[/C][C]390.565273350736[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 24 )[/C][C]91.4[/C][C]0.234019781676598[/C][C]390.565273350736[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 24 )[/C][C]91.4[/C][C]0.227784457324101[/C][C]401.256525900503[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 24 )[/C][C]91.4[/C][C]0.227784457324101[/C][C]401.256525900503[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 24 )[/C][C]91.4[/C][C]0.227784457324101[/C][C]401.256525900503[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 24 )[/C][C]91.3736111111111[/C][C]0.216467885118731[/C][C]422.111626678449[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 24 )[/C][C]91.3458333333333[/C][C]0.212288166531845[/C][C]430.29168712346[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 24 )[/C][C]91.375[/C][C]0.208755440925035[/C][C]437.713142206497[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 24 )[/C][C]91.4055555555556[/C][C]0.205136399609606[/C][C]445.584283089246[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 24 )[/C][C]91.3097222222222[/C][C]0.190873124807953[/C][C]478.37914485915[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 24 )[/C][C]91.3430555555556[/C][C]0.186955535926309[/C][C]488.581710634981[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 24 )[/C][C]91.46[/C][C]0.270911352037019[/C][C]337.601209075588[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 24 )[/C][C]91.4455882352941[/C][C]0.266817436537472[/C][C]342.727182383568[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 24 )[/C][C]91.430303030303[/C][C]0.263196857883712[/C][C]347.383717896434[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 24 )[/C][C]91.415625[/C][C]0.259838345941906[/C][C]351.817298823318[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 24 )[/C][C]91.4016129032258[/C][C]0.256089164464092[/C][C]356.913237990754[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 24 )[/C][C]91.3866666666667[/C][C]0.255653219690717[/C][C]357.463390358331[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 24 )[/C][C]91.3724137931034[/C][C]0.255215329691751[/C][C]358.020867725552[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 24 )[/C][C]91.3571428571429[/C][C]0.255063744806385[/C][C]358.173769174802[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 24 )[/C][C]91.3407407407407[/C][C]0.255238868383603[/C][C]357.863758443965[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 24 )[/C][C]91.3211538461538[/C][C]0.255340197440239[/C][C]357.645034983288[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 24 )[/C][C]91.3[/C][C]0.255007002704968[/C][C]358.02938363081[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 24 )[/C][C]91.2791666666667[/C][C]0.254654513792313[/C][C]358.443152282432[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 24 )[/C][C]91.2586956521739[/C][C]0.254269363181489[/C][C]358.905589373095[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 24 )[/C][C]91.2409090909091[/C][C]0.254418006451066[/C][C]358.62598863834[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 24 )[/C][C]91.2214285714286[/C][C]0.253970461904843[/C][C]359.181252367873[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 24 )[/C][C]91.2[/C][C]0.252728698156333[/C][C]360.861274027477[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 24 )[/C][C]91.1763157894737[/C][C]0.251720515231527[/C][C]362.212494701163[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 24 )[/C][C]91.15[/C][C]0.249586960383853[/C][C]365.203373845396[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 24 )[/C][C]91.1205882352941[/C][C]0.245885188769905[/C][C]370.581850379622[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 24 )[/C][C]91.090625[/C][C]0.242897470031247[/C][C]375.016771431509[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 24 )[/C][C]91.06[/C][C]0.238944037116567[/C][C]381.093418772268[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 24 )[/C][C]91.0214285714286[/C][C]0.233013223893942[/C][C]390.627737989917[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 24 )[/C][C]90.9730769230769[/C][C]0.223920156945261[/C][C]406.274621115578[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 24 )[/C][C]90.9291666666667[/C][C]0.214972122111273[/C][C]422.98120227701[/C][/ROW]
[ROW][C]Median[/C][C]90.65[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]92[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]91.2[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]91.2[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]91.2[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]91.2[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]91.2[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]91.2[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]91.2[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]91.2[/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=132743&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=132743&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 Mean91.4750.27516355927075332.438642102285
Geometric Mean91.4457908417766
Harmonic Mean91.4167640415319
Quadratic Mean91.504379069468
Winsorized Mean ( 1 / 24 )91.47361111111110.274289472300432333.492971290269
Winsorized Mean ( 2 / 24 )91.47361111111110.272141517770923336.125159660899
Winsorized Mean ( 3 / 24 )91.46944444444440.269720185448795339.1271746764
Winsorized Mean ( 4 / 24 )91.46388888888890.268591247143461340.531904377494
Winsorized Mean ( 5 / 24 )91.46388888888890.254454105576814359.451417305892
Winsorized Mean ( 6 / 24 )91.45555555555550.252978260622856361.5154730307
Winsorized Mean ( 7 / 24 )91.45555555555560.249983480587934365.846396491728
Winsorized Mean ( 8 / 24 )91.45555555555560.246643261870917370.800948956876
Winsorized Mean ( 9 / 24 )91.46805555555560.245059368017717373.248557259572
Winsorized Mean ( 10 / 24 )91.46805555555560.245059368017717373.248557259572
Winsorized Mean ( 11 / 24 )91.45277777777780.242508830665589377.111124270308
Winsorized Mean ( 12 / 24 )91.43611111111110.239777752758958381.336925794902
Winsorized Mean ( 13 / 24 )91.40.234019781676598390.565273350736
Winsorized Mean ( 14 / 24 )91.40.234019781676598390.565273350736
Winsorized Mean ( 15 / 24 )91.40.234019781676598390.565273350736
Winsorized Mean ( 16 / 24 )91.40.227784457324101401.256525900503
Winsorized Mean ( 17 / 24 )91.40.227784457324101401.256525900503
Winsorized Mean ( 18 / 24 )91.40.227784457324101401.256525900503
Winsorized Mean ( 19 / 24 )91.37361111111110.216467885118731422.111626678449
Winsorized Mean ( 20 / 24 )91.34583333333330.212288166531845430.29168712346
Winsorized Mean ( 21 / 24 )91.3750.208755440925035437.713142206497
Winsorized Mean ( 22 / 24 )91.40555555555560.205136399609606445.584283089246
Winsorized Mean ( 23 / 24 )91.30972222222220.190873124807953478.37914485915
Winsorized Mean ( 24 / 24 )91.34305555555560.186955535926309488.581710634981
Trimmed Mean ( 1 / 24 )91.460.270911352037019337.601209075588
Trimmed Mean ( 2 / 24 )91.44558823529410.266817436537472342.727182383568
Trimmed Mean ( 3 / 24 )91.4303030303030.263196857883712347.383717896434
Trimmed Mean ( 4 / 24 )91.4156250.259838345941906351.817298823318
Trimmed Mean ( 5 / 24 )91.40161290322580.256089164464092356.913237990754
Trimmed Mean ( 6 / 24 )91.38666666666670.255653219690717357.463390358331
Trimmed Mean ( 7 / 24 )91.37241379310340.255215329691751358.020867725552
Trimmed Mean ( 8 / 24 )91.35714285714290.255063744806385358.173769174802
Trimmed Mean ( 9 / 24 )91.34074074074070.255238868383603357.863758443965
Trimmed Mean ( 10 / 24 )91.32115384615380.255340197440239357.645034983288
Trimmed Mean ( 11 / 24 )91.30.255007002704968358.02938363081
Trimmed Mean ( 12 / 24 )91.27916666666670.254654513792313358.443152282432
Trimmed Mean ( 13 / 24 )91.25869565217390.254269363181489358.905589373095
Trimmed Mean ( 14 / 24 )91.24090909090910.254418006451066358.62598863834
Trimmed Mean ( 15 / 24 )91.22142857142860.253970461904843359.181252367873
Trimmed Mean ( 16 / 24 )91.20.252728698156333360.861274027477
Trimmed Mean ( 17 / 24 )91.17631578947370.251720515231527362.212494701163
Trimmed Mean ( 18 / 24 )91.150.249586960383853365.203373845396
Trimmed Mean ( 19 / 24 )91.12058823529410.245885188769905370.581850379622
Trimmed Mean ( 20 / 24 )91.0906250.242897470031247375.016771431509
Trimmed Mean ( 21 / 24 )91.060.238944037116567381.093418772268
Trimmed Mean ( 22 / 24 )91.02142857142860.233013223893942390.627737989917
Trimmed Mean ( 23 / 24 )90.97307692307690.223920156945261406.274621115578
Trimmed Mean ( 24 / 24 )90.92916666666670.214972122111273422.98120227701
Median90.65
Midrange92
Midmean - Weighted Average at Xnp91.2
Midmean - Weighted Average at X(n+1)p91.2
Midmean - Empirical Distribution Function91.2
Midmean - Empirical Distribution Function - Averaging91.2
Midmean - Empirical Distribution Function - Interpolation91.2
Midmean - Closest Observation91.2
Midmean - True Basic - Statistics Graphics Toolkit91.2
Midmean - MS Excel (old versions)91.2
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')