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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 computationMon, 29 Feb 2016 17:52:11 +0000
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2016/Feb/29/t1456768354u8w0tvgiogdp3cl.htm/, Retrieved Tue, 30 Apr 2024 08:42:52 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=293027, Retrieved Tue, 30 Apr 2024 08:42:52 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact86
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [] [2016-02-29 17:52:11] [b94c13d84d922b33c8d74b1e5b1d38c1] [Current]
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Dataseries X:
83,8
86,62
83,98
82,59
82,3
81,64
81,66
81,63
85,54
85,62
85,89
86,38
87,59
87,68
88,07
87,66
88,36
88,08
94,35
99,07
100,39
102,1
102,89
103,05
102,78
102,53
101,6
100,78
100,54
100,19
100,07
100,18
100,08
99,66
99,92
99,51
101,77
102,49
101,91
100,57
100,23
99,99
99,2
99,07
98,79
99,31
98,98
97,69
98,9
98,75
99,7
100,18
100,14
100,13
99,85
99,38
98,87
97,79
97,32
97,29
96,73
97,22
96,66
96,58
96,47
96,7
97,91
97,97
98,26
97,8
97,33
97,56




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gertrude Mary Cox' @ cox.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 & 'Gertrude Mary Cox' @ cox.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=293027&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]'Gertrude Mary Cox' @ cox.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=293027&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=293027&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'Gertrude Mary Cox' @ cox.wessa.net







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean95.83708333333330.762275453416838125.725002561412
Geometric Mean95.6105221420753
Harmonic Mean95.3725388107119
Quadratic Mean96.0520800211473
Winsorized Mean ( 1 / 24 )95.8350.761946019800092125.776626571452
Winsorized Mean ( 2 / 24 )95.83250.76140472658648125.862759520334
Winsorized Mean ( 3 / 24 )95.848750.75321039384642127.253621010896
Winsorized Mean ( 4 / 24 )95.86263888888890.748881246790194128.007797364094
Winsorized Mean ( 5 / 24 )95.91958333333330.725180039096547132.270026975416
Winsorized Mean ( 6 / 24 )95.918750.719783998026181133.260464615818
Winsorized Mean ( 7 / 24 )96.05680555555560.684015170717056140.430811578139
Winsorized Mean ( 8 / 24 )96.04680555555560.679895129835403141.26708861528
Winsorized Mean ( 9 / 24 )95.97805555555560.661480373689621145.095847697199
Winsorized Mean ( 10 / 24 )96.01694444444440.644054566614166149.082002398044
Winsorized Mean ( 11 / 24 )96.04902777777780.635905794876752151.042856586004
Winsorized Mean ( 12 / 24 )96.18569444444440.600226835915853160.248907061411
Winsorized Mean ( 13 / 24 )96.16944444444440.594865086718223161.665975347446
Winsorized Mean ( 14 / 24 )96.16555555555560.593336263935135162.075978497867
Winsorized Mean ( 15 / 24 )96.24472222222220.576843916021981166.847078644676
Winsorized Mean ( 16 / 24 )96.24694444444440.576400405262328166.979314319949
Winsorized Mean ( 17 / 24 )96.30361111111110.56231904777171.261513357985
Winsorized Mean ( 18 / 24 )97.79861111111110.275147087250936355.441200880015
Winsorized Mean ( 19 / 24 )98.34486111111110.181669788603872541.33855643742
Winsorized Mean ( 20 / 24 )98.37263888888890.176893400551485556.112543386024
Winsorized Mean ( 21 / 24 )98.37263888888890.17044048992149577.167074174701
Winsorized Mean ( 22 / 24 )98.36347222222220.165869355764169593.017750440136
Winsorized Mean ( 23 / 24 )98.35069444444440.161576414281749608.6946221801
Winsorized Mean ( 24 / 24 )98.46402777777780.132629105572059742.401355668352
Trimmed Mean ( 1 / 24 )95.9370.749856062102345127.940553992489
Trimmed Mean ( 2 / 24 )96.0450.735153119931753130.646252319403
Trimmed Mean ( 3 / 24 )96.16090909090910.71759692626906134.004070489641
Trimmed Mean ( 4 / 24 )96.277968750.699976692486387137.544535101606
Trimmed Mean ( 5 / 24 )96.39854838709680.679980629595255141.766609505445
Trimmed Mean ( 6 / 24 )96.51350.663127831708518145.542828071833
Trimmed Mean ( 7 / 24 )96.63655172413790.643640139098275150.140654464968
Trimmed Mean ( 8 / 24 )96.74303571428570.629229735245458153.748353415859
Trimmed Mean ( 9 / 24 )96.85907407407410.611851691636908158.30482353484
Trimmed Mean ( 10 / 24 )96.99461538461540.593699922015399163.373131421937
Trimmed Mean ( 11 / 24 )97.13540.574396379529264169.108656429216
Trimmed Mean ( 12 / 24 )97.28354166666670.551076114369249176.533765717673
Trimmed Mean ( 13 / 24 )97.42673913043480.529586025030875183.967730501867
Trimmed Mean ( 14 / 24 )97.5850.50169137814062194.51201326535
Trimmed Mean ( 15 / 24 )97.75880952380950.463562957795197210.885723028369
Trimmed Mean ( 16 / 24 )97.94050.415243201830767235.862982387646
Trimmed Mean ( 17 / 24 )98.14105263157890.34279077832706286.300154019726
Trimmed Mean ( 18 / 24 )98.35722222222220.225137915795514436.875423114236
Trimmed Mean ( 19 / 24 )98.42294117647060.199192455871829494.109783152638
Trimmed Mean ( 20 / 24 )98.43218750.195606343475519503.215722716677
Trimmed Mean ( 21 / 24 )98.43933333333330.191308821370316514.557209794233
Trimmed Mean ( 22 / 24 )98.44750.186405447186344528.136390250362
Trimmed Mean ( 23 / 24 )98.45807692307690.179930772354916547.199768191218
Trimmed Mean ( 24 / 24 )98.47208333333330.170864149747927576.317989927128
Median98.77
Midrange92.34
Midmean - Weighted Average at Xnp98.087027027027
Midmean - Weighted Average at X(n+1)p98.3572222222222
Midmean - Empirical Distribution Function98.087027027027
Midmean - Empirical Distribution Function - Averaging98.3572222222222
Midmean - Empirical Distribution Function - Interpolation98.3572222222222
Midmean - Closest Observation98.087027027027
Midmean - True Basic - Statistics Graphics Toolkit98.3572222222222
Midmean - MS Excel (old versions)98.1410526315789
Number of observations72

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 95.8370833333333 & 0.762275453416838 & 125.725002561412 \tabularnewline
Geometric Mean & 95.6105221420753 &  &  \tabularnewline
Harmonic Mean & 95.3725388107119 &  &  \tabularnewline
Quadratic Mean & 96.0520800211473 &  &  \tabularnewline
Winsorized Mean ( 1 / 24 ) & 95.835 & 0.761946019800092 & 125.776626571452 \tabularnewline
Winsorized Mean ( 2 / 24 ) & 95.8325 & 0.76140472658648 & 125.862759520334 \tabularnewline
Winsorized Mean ( 3 / 24 ) & 95.84875 & 0.75321039384642 & 127.253621010896 \tabularnewline
Winsorized Mean ( 4 / 24 ) & 95.8626388888889 & 0.748881246790194 & 128.007797364094 \tabularnewline
Winsorized Mean ( 5 / 24 ) & 95.9195833333333 & 0.725180039096547 & 132.270026975416 \tabularnewline
Winsorized Mean ( 6 / 24 ) & 95.91875 & 0.719783998026181 & 133.260464615818 \tabularnewline
Winsorized Mean ( 7 / 24 ) & 96.0568055555556 & 0.684015170717056 & 140.430811578139 \tabularnewline
Winsorized Mean ( 8 / 24 ) & 96.0468055555556 & 0.679895129835403 & 141.26708861528 \tabularnewline
Winsorized Mean ( 9 / 24 ) & 95.9780555555556 & 0.661480373689621 & 145.095847697199 \tabularnewline
Winsorized Mean ( 10 / 24 ) & 96.0169444444444 & 0.644054566614166 & 149.082002398044 \tabularnewline
Winsorized Mean ( 11 / 24 ) & 96.0490277777778 & 0.635905794876752 & 151.042856586004 \tabularnewline
Winsorized Mean ( 12 / 24 ) & 96.1856944444444 & 0.600226835915853 & 160.248907061411 \tabularnewline
Winsorized Mean ( 13 / 24 ) & 96.1694444444444 & 0.594865086718223 & 161.665975347446 \tabularnewline
Winsorized Mean ( 14 / 24 ) & 96.1655555555556 & 0.593336263935135 & 162.075978497867 \tabularnewline
Winsorized Mean ( 15 / 24 ) & 96.2447222222222 & 0.576843916021981 & 166.847078644676 \tabularnewline
Winsorized Mean ( 16 / 24 ) & 96.2469444444444 & 0.576400405262328 & 166.979314319949 \tabularnewline
Winsorized Mean ( 17 / 24 ) & 96.3036111111111 & 0.56231904777 & 171.261513357985 \tabularnewline
Winsorized Mean ( 18 / 24 ) & 97.7986111111111 & 0.275147087250936 & 355.441200880015 \tabularnewline
Winsorized Mean ( 19 / 24 ) & 98.3448611111111 & 0.181669788603872 & 541.33855643742 \tabularnewline
Winsorized Mean ( 20 / 24 ) & 98.3726388888889 & 0.176893400551485 & 556.112543386024 \tabularnewline
Winsorized Mean ( 21 / 24 ) & 98.3726388888889 & 0.17044048992149 & 577.167074174701 \tabularnewline
Winsorized Mean ( 22 / 24 ) & 98.3634722222222 & 0.165869355764169 & 593.017750440136 \tabularnewline
Winsorized Mean ( 23 / 24 ) & 98.3506944444444 & 0.161576414281749 & 608.6946221801 \tabularnewline
Winsorized Mean ( 24 / 24 ) & 98.4640277777778 & 0.132629105572059 & 742.401355668352 \tabularnewline
Trimmed Mean ( 1 / 24 ) & 95.937 & 0.749856062102345 & 127.940553992489 \tabularnewline
Trimmed Mean ( 2 / 24 ) & 96.045 & 0.735153119931753 & 130.646252319403 \tabularnewline
Trimmed Mean ( 3 / 24 ) & 96.1609090909091 & 0.71759692626906 & 134.004070489641 \tabularnewline
Trimmed Mean ( 4 / 24 ) & 96.27796875 & 0.699976692486387 & 137.544535101606 \tabularnewline
Trimmed Mean ( 5 / 24 ) & 96.3985483870968 & 0.679980629595255 & 141.766609505445 \tabularnewline
Trimmed Mean ( 6 / 24 ) & 96.5135 & 0.663127831708518 & 145.542828071833 \tabularnewline
Trimmed Mean ( 7 / 24 ) & 96.6365517241379 & 0.643640139098275 & 150.140654464968 \tabularnewline
Trimmed Mean ( 8 / 24 ) & 96.7430357142857 & 0.629229735245458 & 153.748353415859 \tabularnewline
Trimmed Mean ( 9 / 24 ) & 96.8590740740741 & 0.611851691636908 & 158.30482353484 \tabularnewline
Trimmed Mean ( 10 / 24 ) & 96.9946153846154 & 0.593699922015399 & 163.373131421937 \tabularnewline
Trimmed Mean ( 11 / 24 ) & 97.1354 & 0.574396379529264 & 169.108656429216 \tabularnewline
Trimmed Mean ( 12 / 24 ) & 97.2835416666667 & 0.551076114369249 & 176.533765717673 \tabularnewline
Trimmed Mean ( 13 / 24 ) & 97.4267391304348 & 0.529586025030875 & 183.967730501867 \tabularnewline
Trimmed Mean ( 14 / 24 ) & 97.585 & 0.50169137814062 & 194.51201326535 \tabularnewline
Trimmed Mean ( 15 / 24 ) & 97.7588095238095 & 0.463562957795197 & 210.885723028369 \tabularnewline
Trimmed Mean ( 16 / 24 ) & 97.9405 & 0.415243201830767 & 235.862982387646 \tabularnewline
Trimmed Mean ( 17 / 24 ) & 98.1410526315789 & 0.34279077832706 & 286.300154019726 \tabularnewline
Trimmed Mean ( 18 / 24 ) & 98.3572222222222 & 0.225137915795514 & 436.875423114236 \tabularnewline
Trimmed Mean ( 19 / 24 ) & 98.4229411764706 & 0.199192455871829 & 494.109783152638 \tabularnewline
Trimmed Mean ( 20 / 24 ) & 98.4321875 & 0.195606343475519 & 503.215722716677 \tabularnewline
Trimmed Mean ( 21 / 24 ) & 98.4393333333333 & 0.191308821370316 & 514.557209794233 \tabularnewline
Trimmed Mean ( 22 / 24 ) & 98.4475 & 0.186405447186344 & 528.136390250362 \tabularnewline
Trimmed Mean ( 23 / 24 ) & 98.4580769230769 & 0.179930772354916 & 547.199768191218 \tabularnewline
Trimmed Mean ( 24 / 24 ) & 98.4720833333333 & 0.170864149747927 & 576.317989927128 \tabularnewline
Median & 98.77 &  &  \tabularnewline
Midrange & 92.34 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 98.087027027027 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 98.3572222222222 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 98.087027027027 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 98.3572222222222 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 98.3572222222222 &  &  \tabularnewline
Midmean - Closest Observation & 98.087027027027 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 98.3572222222222 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 98.1410526315789 &  &  \tabularnewline
Number of observations & 72 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=293027&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]95.8370833333333[/C][C]0.762275453416838[/C][C]125.725002561412[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]95.6105221420753[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]95.3725388107119[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]96.0520800211473[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 24 )[/C][C]95.835[/C][C]0.761946019800092[/C][C]125.776626571452[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 24 )[/C][C]95.8325[/C][C]0.76140472658648[/C][C]125.862759520334[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 24 )[/C][C]95.84875[/C][C]0.75321039384642[/C][C]127.253621010896[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 24 )[/C][C]95.8626388888889[/C][C]0.748881246790194[/C][C]128.007797364094[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 24 )[/C][C]95.9195833333333[/C][C]0.725180039096547[/C][C]132.270026975416[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 24 )[/C][C]95.91875[/C][C]0.719783998026181[/C][C]133.260464615818[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 24 )[/C][C]96.0568055555556[/C][C]0.684015170717056[/C][C]140.430811578139[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 24 )[/C][C]96.0468055555556[/C][C]0.679895129835403[/C][C]141.26708861528[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 24 )[/C][C]95.9780555555556[/C][C]0.661480373689621[/C][C]145.095847697199[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 24 )[/C][C]96.0169444444444[/C][C]0.644054566614166[/C][C]149.082002398044[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 24 )[/C][C]96.0490277777778[/C][C]0.635905794876752[/C][C]151.042856586004[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 24 )[/C][C]96.1856944444444[/C][C]0.600226835915853[/C][C]160.248907061411[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 24 )[/C][C]96.1694444444444[/C][C]0.594865086718223[/C][C]161.665975347446[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 24 )[/C][C]96.1655555555556[/C][C]0.593336263935135[/C][C]162.075978497867[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 24 )[/C][C]96.2447222222222[/C][C]0.576843916021981[/C][C]166.847078644676[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 24 )[/C][C]96.2469444444444[/C][C]0.576400405262328[/C][C]166.979314319949[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 24 )[/C][C]96.3036111111111[/C][C]0.56231904777[/C][C]171.261513357985[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 24 )[/C][C]97.7986111111111[/C][C]0.275147087250936[/C][C]355.441200880015[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 24 )[/C][C]98.3448611111111[/C][C]0.181669788603872[/C][C]541.33855643742[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 24 )[/C][C]98.3726388888889[/C][C]0.176893400551485[/C][C]556.112543386024[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 24 )[/C][C]98.3726388888889[/C][C]0.17044048992149[/C][C]577.167074174701[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 24 )[/C][C]98.3634722222222[/C][C]0.165869355764169[/C][C]593.017750440136[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 24 )[/C][C]98.3506944444444[/C][C]0.161576414281749[/C][C]608.6946221801[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 24 )[/C][C]98.4640277777778[/C][C]0.132629105572059[/C][C]742.401355668352[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 24 )[/C][C]95.937[/C][C]0.749856062102345[/C][C]127.940553992489[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 24 )[/C][C]96.045[/C][C]0.735153119931753[/C][C]130.646252319403[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 24 )[/C][C]96.1609090909091[/C][C]0.71759692626906[/C][C]134.004070489641[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 24 )[/C][C]96.27796875[/C][C]0.699976692486387[/C][C]137.544535101606[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 24 )[/C][C]96.3985483870968[/C][C]0.679980629595255[/C][C]141.766609505445[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 24 )[/C][C]96.5135[/C][C]0.663127831708518[/C][C]145.542828071833[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 24 )[/C][C]96.6365517241379[/C][C]0.643640139098275[/C][C]150.140654464968[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 24 )[/C][C]96.7430357142857[/C][C]0.629229735245458[/C][C]153.748353415859[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 24 )[/C][C]96.8590740740741[/C][C]0.611851691636908[/C][C]158.30482353484[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 24 )[/C][C]96.9946153846154[/C][C]0.593699922015399[/C][C]163.373131421937[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 24 )[/C][C]97.1354[/C][C]0.574396379529264[/C][C]169.108656429216[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 24 )[/C][C]97.2835416666667[/C][C]0.551076114369249[/C][C]176.533765717673[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 24 )[/C][C]97.4267391304348[/C][C]0.529586025030875[/C][C]183.967730501867[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 24 )[/C][C]97.585[/C][C]0.50169137814062[/C][C]194.51201326535[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 24 )[/C][C]97.7588095238095[/C][C]0.463562957795197[/C][C]210.885723028369[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 24 )[/C][C]97.9405[/C][C]0.415243201830767[/C][C]235.862982387646[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 24 )[/C][C]98.1410526315789[/C][C]0.34279077832706[/C][C]286.300154019726[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 24 )[/C][C]98.3572222222222[/C][C]0.225137915795514[/C][C]436.875423114236[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 24 )[/C][C]98.4229411764706[/C][C]0.199192455871829[/C][C]494.109783152638[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 24 )[/C][C]98.4321875[/C][C]0.195606343475519[/C][C]503.215722716677[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 24 )[/C][C]98.4393333333333[/C][C]0.191308821370316[/C][C]514.557209794233[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 24 )[/C][C]98.4475[/C][C]0.186405447186344[/C][C]528.136390250362[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 24 )[/C][C]98.4580769230769[/C][C]0.179930772354916[/C][C]547.199768191218[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 24 )[/C][C]98.4720833333333[/C][C]0.170864149747927[/C][C]576.317989927128[/C][/ROW]
[ROW][C]Median[/C][C]98.77[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]92.34[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]98.087027027027[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]98.3572222222222[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]98.087027027027[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]98.3572222222222[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]98.3572222222222[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]98.087027027027[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]98.3572222222222[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]98.1410526315789[/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=293027&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=293027&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 Mean95.83708333333330.762275453416838125.725002561412
Geometric Mean95.6105221420753
Harmonic Mean95.3725388107119
Quadratic Mean96.0520800211473
Winsorized Mean ( 1 / 24 )95.8350.761946019800092125.776626571452
Winsorized Mean ( 2 / 24 )95.83250.76140472658648125.862759520334
Winsorized Mean ( 3 / 24 )95.848750.75321039384642127.253621010896
Winsorized Mean ( 4 / 24 )95.86263888888890.748881246790194128.007797364094
Winsorized Mean ( 5 / 24 )95.91958333333330.725180039096547132.270026975416
Winsorized Mean ( 6 / 24 )95.918750.719783998026181133.260464615818
Winsorized Mean ( 7 / 24 )96.05680555555560.684015170717056140.430811578139
Winsorized Mean ( 8 / 24 )96.04680555555560.679895129835403141.26708861528
Winsorized Mean ( 9 / 24 )95.97805555555560.661480373689621145.095847697199
Winsorized Mean ( 10 / 24 )96.01694444444440.644054566614166149.082002398044
Winsorized Mean ( 11 / 24 )96.04902777777780.635905794876752151.042856586004
Winsorized Mean ( 12 / 24 )96.18569444444440.600226835915853160.248907061411
Winsorized Mean ( 13 / 24 )96.16944444444440.594865086718223161.665975347446
Winsorized Mean ( 14 / 24 )96.16555555555560.593336263935135162.075978497867
Winsorized Mean ( 15 / 24 )96.24472222222220.576843916021981166.847078644676
Winsorized Mean ( 16 / 24 )96.24694444444440.576400405262328166.979314319949
Winsorized Mean ( 17 / 24 )96.30361111111110.56231904777171.261513357985
Winsorized Mean ( 18 / 24 )97.79861111111110.275147087250936355.441200880015
Winsorized Mean ( 19 / 24 )98.34486111111110.181669788603872541.33855643742
Winsorized Mean ( 20 / 24 )98.37263888888890.176893400551485556.112543386024
Winsorized Mean ( 21 / 24 )98.37263888888890.17044048992149577.167074174701
Winsorized Mean ( 22 / 24 )98.36347222222220.165869355764169593.017750440136
Winsorized Mean ( 23 / 24 )98.35069444444440.161576414281749608.6946221801
Winsorized Mean ( 24 / 24 )98.46402777777780.132629105572059742.401355668352
Trimmed Mean ( 1 / 24 )95.9370.749856062102345127.940553992489
Trimmed Mean ( 2 / 24 )96.0450.735153119931753130.646252319403
Trimmed Mean ( 3 / 24 )96.16090909090910.71759692626906134.004070489641
Trimmed Mean ( 4 / 24 )96.277968750.699976692486387137.544535101606
Trimmed Mean ( 5 / 24 )96.39854838709680.679980629595255141.766609505445
Trimmed Mean ( 6 / 24 )96.51350.663127831708518145.542828071833
Trimmed Mean ( 7 / 24 )96.63655172413790.643640139098275150.140654464968
Trimmed Mean ( 8 / 24 )96.74303571428570.629229735245458153.748353415859
Trimmed Mean ( 9 / 24 )96.85907407407410.611851691636908158.30482353484
Trimmed Mean ( 10 / 24 )96.99461538461540.593699922015399163.373131421937
Trimmed Mean ( 11 / 24 )97.13540.574396379529264169.108656429216
Trimmed Mean ( 12 / 24 )97.28354166666670.551076114369249176.533765717673
Trimmed Mean ( 13 / 24 )97.42673913043480.529586025030875183.967730501867
Trimmed Mean ( 14 / 24 )97.5850.50169137814062194.51201326535
Trimmed Mean ( 15 / 24 )97.75880952380950.463562957795197210.885723028369
Trimmed Mean ( 16 / 24 )97.94050.415243201830767235.862982387646
Trimmed Mean ( 17 / 24 )98.14105263157890.34279077832706286.300154019726
Trimmed Mean ( 18 / 24 )98.35722222222220.225137915795514436.875423114236
Trimmed Mean ( 19 / 24 )98.42294117647060.199192455871829494.109783152638
Trimmed Mean ( 20 / 24 )98.43218750.195606343475519503.215722716677
Trimmed Mean ( 21 / 24 )98.43933333333330.191308821370316514.557209794233
Trimmed Mean ( 22 / 24 )98.44750.186405447186344528.136390250362
Trimmed Mean ( 23 / 24 )98.45807692307690.179930772354916547.199768191218
Trimmed Mean ( 24 / 24 )98.47208333333330.170864149747927576.317989927128
Median98.77
Midrange92.34
Midmean - Weighted Average at Xnp98.087027027027
Midmean - Weighted Average at X(n+1)p98.3572222222222
Midmean - Empirical Distribution Function98.087027027027
Midmean - Empirical Distribution Function - Averaging98.3572222222222
Midmean - Empirical Distribution Function - Interpolation98.3572222222222
Midmean - Closest Observation98.087027027027
Midmean - True Basic - Statistics Graphics Toolkit98.3572222222222
Midmean - MS Excel (old versions)98.1410526315789
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')