Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationTue, 14 Oct 2008 11:52:05 -0600
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2008/Oct/14/t1224006886nj72an0abthqtmh.htm/, Retrieved Sat, 18 May 2024 08:08:04 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=16261, Retrieved Sat, 18 May 2024 08:08:04 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact132
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [Kledij] [2008-10-14 17:52:05] [701cc898ddafddb72d72f8df86ee2872] [Current]
Feedback Forum

Post a new message
Dataseries X:
109.20
88.60
94.30
98.30
86.40
8060
104.10
108.20
93.40
71.90
94.10
94.90
96.40
91.10
84.40
86.40
88.00
75.10
109.70
103.00
82.10
68.00
96.40
94.30
90.00
88.00
76.10
82.50
81.40
66.50
97.20
94.10
80.70
70.50
87.80
89.50
99.60
84.20
75.10
92.00
80.80
73.10
99.80
90.00
83.10
72.40
78.80
87.30
91.00
80.10
73.60
86.40
74.50
71.20
92.40
81.50
85.30
69.90
84.20
90.70
100.30




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 1 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=16261&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]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=16261&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=16261&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'Gwilym Jenkins' @ 72.249.127.135







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean217.703278688525130.7119094328451.66551984155944
Geometric Mean93.0217105312874
Harmonic Mean87.1208480615763
Quadratic Mean1035.63068398274
Winsorized Mean ( 1 / 20 )87.39508196721311.3937456436835762.7051875378309
Winsorized Mean ( 2 / 20 )87.44098360655741.3755503162007263.5680008042673
Winsorized Mean ( 3 / 20 )87.42131147540991.3565850623691764.4421893624094
Winsorized Mean ( 4 / 20 )87.19836065573771.2830813572867667.960118164393
Winsorized Mean ( 5 / 20 )87.16557377049181.2518813934241769.6276613969592
Winsorized Mean ( 6 / 20 )86.94918032786881.1889441128818473.131427613629
Winsorized Mean ( 7 / 20 )86.9721311475411.1621116335764274.8397388294636
Winsorized Mean ( 8 / 20 )87.0114754098361.1443663346943376.0346339907648
Winsorized Mean ( 9 / 20 )86.95245901639341.0843511987227580.1884658022367
Winsorized Mean ( 10 / 20 )86.87049180327871.0348710863521883.9432978164353
Winsorized Mean ( 11 / 20 )86.72622950819671.0113668229125585.7515073101185
Winsorized Mean ( 12 / 20 )86.92295081967210.97429922537215589.2158677294134
Winsorized Mean ( 13 / 20 )87.17868852459020.820659187110287106.230076862436
Winsorized Mean ( 14 / 20 )87.3393442622950.749747785236707116.491633562773
Winsorized Mean ( 15 / 20 )87.48688524590160.726382139901927120.441955329069
Winsorized Mean ( 16 / 20 )87.4606557377050.714136257255129122.470543750111
Winsorized Mean ( 17 / 20 )87.6278688524590.688528688512392127.268290071957
Winsorized Mean ( 18 / 20 )87.45081967213110.652165886867406134.092907085634
Winsorized Mean ( 19 / 20 )87.32622950819670.577307210690758151.264747592031
Winsorized Mean ( 20 / 20 )87.32622950819670.538521055290276162.159359695093
Trimmed Mean ( 1 / 20 )87.34576271186441.3499168146198264.704551988608
Trimmed Mean ( 2 / 20 )87.29298245614041.2960438638601967.3534167247578
Trimmed Mean ( 3 / 20 )87.2109090909091.2416581525768070.2374553816777
Trimmed Mean ( 4 / 20 )87.13018867924531.1832698812178273.6350937873705
Trimmed Mean ( 5 / 20 )87.10980392156861.1405167556065576.3774872165219
Trimmed Mean ( 6 / 20 )87.0959183673471.0975272112585779.3565002069256
Trimmed Mean ( 7 / 20 )87.12765957446811.0629523671176281.9676048238451
Trimmed Mean ( 8 / 20 )87.15777777777781.0262636403399184.9272782858312
Trimmed Mean ( 9 / 20 )87.18372093023260.98345071412644688.650828839627
Trimmed Mean ( 10 / 20 )87.22195121951220.9442412891499992.3725240801848
Trimmed Mean ( 11 / 20 )87.27692307692310.90566861946979796.3673922234573
Trimmed Mean ( 12 / 20 )87.35945945945950.859424518148212101.648786617924
Trimmed Mean ( 13 / 20 )87.42285714285710.80710173168078108.317023382914
Trimmed Mean ( 14 / 20 )87.45757575757580.7814617022624111.915370266231
Trimmed Mean ( 15 / 20 )87.47419354838710.764761087746981114.381072664261
Trimmed Mean ( 16 / 20 )87.47241379310340.745625940499601117.314070020811
Trimmed Mean ( 17 / 20 )87.4740740740740.719084424838539121.646459097922
Trimmed Mean ( 18 / 20 )87.4520.685787138987018127.520618320688
Trimmed Mean ( 19 / 20 )87.45217391304350.646329544464833135.305858539168
Trimmed Mean ( 20 / 20 )87.47142857142860.613814880467224142.504574839970
Median87.8
Midrange4063.25
Midmean - Weighted Average at Xnp87.2466666666667
Midmean - Weighted Average at X(n+1)p87.6875
Midmean - Empirical Distribution Function87.6875
Midmean - Empirical Distribution Function - Averaging87.6875
Midmean - Empirical Distribution Function - Interpolation87.6875
Midmean - Closest Observation87.4575757575758
Midmean - True Basic - Statistics Graphics Toolkit87.6875
Midmean - MS Excel (old versions)87.6875
Number of observations61

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 217.703278688525 & 130.711909432845 & 1.66551984155944 \tabularnewline
Geometric Mean & 93.0217105312874 &  &  \tabularnewline
Harmonic Mean & 87.1208480615763 &  &  \tabularnewline
Quadratic Mean & 1035.63068398274 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 87.3950819672131 & 1.39374564368357 & 62.7051875378309 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 87.4409836065574 & 1.37555031620072 & 63.5680008042673 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 87.4213114754099 & 1.35658506236917 & 64.4421893624094 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 87.1983606557377 & 1.28308135728676 & 67.960118164393 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 87.1655737704918 & 1.25188139342417 & 69.6276613969592 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 86.9491803278688 & 1.18894411288184 & 73.131427613629 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 86.972131147541 & 1.16211163357642 & 74.8397388294636 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 87.011475409836 & 1.14436633469433 & 76.0346339907648 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 86.9524590163934 & 1.08435119872275 & 80.1884658022367 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 86.8704918032787 & 1.03487108635218 & 83.9432978164353 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 86.7262295081967 & 1.01136682291255 & 85.7515073101185 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 86.9229508196721 & 0.974299225372155 & 89.2158677294134 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 87.1786885245902 & 0.820659187110287 & 106.230076862436 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 87.339344262295 & 0.749747785236707 & 116.491633562773 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 87.4868852459016 & 0.726382139901927 & 120.441955329069 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 87.460655737705 & 0.714136257255129 & 122.470543750111 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 87.627868852459 & 0.688528688512392 & 127.268290071957 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 87.4508196721311 & 0.652165886867406 & 134.092907085634 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 87.3262295081967 & 0.577307210690758 & 151.264747592031 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 87.3262295081967 & 0.538521055290276 & 162.159359695093 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 87.3457627118644 & 1.34991681461982 & 64.704551988608 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 87.2929824561404 & 1.29604386386019 & 67.3534167247578 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 87.210909090909 & 1.24165815257680 & 70.2374553816777 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 87.1301886792453 & 1.18326988121782 & 73.6350937873705 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 87.1098039215686 & 1.14051675560655 & 76.3774872165219 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 87.095918367347 & 1.09752721125857 & 79.3565002069256 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 87.1276595744681 & 1.06295236711762 & 81.9676048238451 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 87.1577777777778 & 1.02626364033991 & 84.9272782858312 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 87.1837209302326 & 0.983450714126446 & 88.650828839627 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 87.2219512195122 & 0.94424128914999 & 92.3725240801848 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 87.2769230769231 & 0.905668619469797 & 96.3673922234573 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 87.3594594594595 & 0.859424518148212 & 101.648786617924 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 87.4228571428571 & 0.80710173168078 & 108.317023382914 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 87.4575757575758 & 0.7814617022624 & 111.915370266231 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 87.4741935483871 & 0.764761087746981 & 114.381072664261 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 87.4724137931034 & 0.745625940499601 & 117.314070020811 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 87.474074074074 & 0.719084424838539 & 121.646459097922 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 87.452 & 0.685787138987018 & 127.520618320688 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 87.4521739130435 & 0.646329544464833 & 135.305858539168 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 87.4714285714286 & 0.613814880467224 & 142.504574839970 \tabularnewline
Median & 87.8 &  &  \tabularnewline
Midrange & 4063.25 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 87.2466666666667 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 87.6875 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 87.6875 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 87.6875 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 87.6875 &  &  \tabularnewline
Midmean - Closest Observation & 87.4575757575758 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 87.6875 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 87.6875 &  &  \tabularnewline
Number of observations & 61 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=16261&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]217.703278688525[/C][C]130.711909432845[/C][C]1.66551984155944[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]93.0217105312874[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]87.1208480615763[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]1035.63068398274[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]87.3950819672131[/C][C]1.39374564368357[/C][C]62.7051875378309[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]87.4409836065574[/C][C]1.37555031620072[/C][C]63.5680008042673[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]87.4213114754099[/C][C]1.35658506236917[/C][C]64.4421893624094[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]87.1983606557377[/C][C]1.28308135728676[/C][C]67.960118164393[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]87.1655737704918[/C][C]1.25188139342417[/C][C]69.6276613969592[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]86.9491803278688[/C][C]1.18894411288184[/C][C]73.131427613629[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]86.972131147541[/C][C]1.16211163357642[/C][C]74.8397388294636[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]87.011475409836[/C][C]1.14436633469433[/C][C]76.0346339907648[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]86.9524590163934[/C][C]1.08435119872275[/C][C]80.1884658022367[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]86.8704918032787[/C][C]1.03487108635218[/C][C]83.9432978164353[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]86.7262295081967[/C][C]1.01136682291255[/C][C]85.7515073101185[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]86.9229508196721[/C][C]0.974299225372155[/C][C]89.2158677294134[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]87.1786885245902[/C][C]0.820659187110287[/C][C]106.230076862436[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]87.339344262295[/C][C]0.749747785236707[/C][C]116.491633562773[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]87.4868852459016[/C][C]0.726382139901927[/C][C]120.441955329069[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]87.460655737705[/C][C]0.714136257255129[/C][C]122.470543750111[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]87.627868852459[/C][C]0.688528688512392[/C][C]127.268290071957[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]87.4508196721311[/C][C]0.652165886867406[/C][C]134.092907085634[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]87.3262295081967[/C][C]0.577307210690758[/C][C]151.264747592031[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]87.3262295081967[/C][C]0.538521055290276[/C][C]162.159359695093[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]87.3457627118644[/C][C]1.34991681461982[/C][C]64.704551988608[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]87.2929824561404[/C][C]1.29604386386019[/C][C]67.3534167247578[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]87.210909090909[/C][C]1.24165815257680[/C][C]70.2374553816777[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]87.1301886792453[/C][C]1.18326988121782[/C][C]73.6350937873705[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]87.1098039215686[/C][C]1.14051675560655[/C][C]76.3774872165219[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]87.095918367347[/C][C]1.09752721125857[/C][C]79.3565002069256[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]87.1276595744681[/C][C]1.06295236711762[/C][C]81.9676048238451[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]87.1577777777778[/C][C]1.02626364033991[/C][C]84.9272782858312[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]87.1837209302326[/C][C]0.983450714126446[/C][C]88.650828839627[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]87.2219512195122[/C][C]0.94424128914999[/C][C]92.3725240801848[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]87.2769230769231[/C][C]0.905668619469797[/C][C]96.3673922234573[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]87.3594594594595[/C][C]0.859424518148212[/C][C]101.648786617924[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]87.4228571428571[/C][C]0.80710173168078[/C][C]108.317023382914[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]87.4575757575758[/C][C]0.7814617022624[/C][C]111.915370266231[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]87.4741935483871[/C][C]0.764761087746981[/C][C]114.381072664261[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]87.4724137931034[/C][C]0.745625940499601[/C][C]117.314070020811[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]87.474074074074[/C][C]0.719084424838539[/C][C]121.646459097922[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]87.452[/C][C]0.685787138987018[/C][C]127.520618320688[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]87.4521739130435[/C][C]0.646329544464833[/C][C]135.305858539168[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]87.4714285714286[/C][C]0.613814880467224[/C][C]142.504574839970[/C][/ROW]
[ROW][C]Median[/C][C]87.8[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]4063.25[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]87.2466666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]87.6875[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]87.6875[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]87.6875[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]87.6875[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]87.4575757575758[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]87.6875[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]87.6875[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]61[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=16261&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=16261&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 Mean217.703278688525130.7119094328451.66551984155944
Geometric Mean93.0217105312874
Harmonic Mean87.1208480615763
Quadratic Mean1035.63068398274
Winsorized Mean ( 1 / 20 )87.39508196721311.3937456436835762.7051875378309
Winsorized Mean ( 2 / 20 )87.44098360655741.3755503162007263.5680008042673
Winsorized Mean ( 3 / 20 )87.42131147540991.3565850623691764.4421893624094
Winsorized Mean ( 4 / 20 )87.19836065573771.2830813572867667.960118164393
Winsorized Mean ( 5 / 20 )87.16557377049181.2518813934241769.6276613969592
Winsorized Mean ( 6 / 20 )86.94918032786881.1889441128818473.131427613629
Winsorized Mean ( 7 / 20 )86.9721311475411.1621116335764274.8397388294636
Winsorized Mean ( 8 / 20 )87.0114754098361.1443663346943376.0346339907648
Winsorized Mean ( 9 / 20 )86.95245901639341.0843511987227580.1884658022367
Winsorized Mean ( 10 / 20 )86.87049180327871.0348710863521883.9432978164353
Winsorized Mean ( 11 / 20 )86.72622950819671.0113668229125585.7515073101185
Winsorized Mean ( 12 / 20 )86.92295081967210.97429922537215589.2158677294134
Winsorized Mean ( 13 / 20 )87.17868852459020.820659187110287106.230076862436
Winsorized Mean ( 14 / 20 )87.3393442622950.749747785236707116.491633562773
Winsorized Mean ( 15 / 20 )87.48688524590160.726382139901927120.441955329069
Winsorized Mean ( 16 / 20 )87.4606557377050.714136257255129122.470543750111
Winsorized Mean ( 17 / 20 )87.6278688524590.688528688512392127.268290071957
Winsorized Mean ( 18 / 20 )87.45081967213110.652165886867406134.092907085634
Winsorized Mean ( 19 / 20 )87.32622950819670.577307210690758151.264747592031
Winsorized Mean ( 20 / 20 )87.32622950819670.538521055290276162.159359695093
Trimmed Mean ( 1 / 20 )87.34576271186441.3499168146198264.704551988608
Trimmed Mean ( 2 / 20 )87.29298245614041.2960438638601967.3534167247578
Trimmed Mean ( 3 / 20 )87.2109090909091.2416581525768070.2374553816777
Trimmed Mean ( 4 / 20 )87.13018867924531.1832698812178273.6350937873705
Trimmed Mean ( 5 / 20 )87.10980392156861.1405167556065576.3774872165219
Trimmed Mean ( 6 / 20 )87.0959183673471.0975272112585779.3565002069256
Trimmed Mean ( 7 / 20 )87.12765957446811.0629523671176281.9676048238451
Trimmed Mean ( 8 / 20 )87.15777777777781.0262636403399184.9272782858312
Trimmed Mean ( 9 / 20 )87.18372093023260.98345071412644688.650828839627
Trimmed Mean ( 10 / 20 )87.22195121951220.9442412891499992.3725240801848
Trimmed Mean ( 11 / 20 )87.27692307692310.90566861946979796.3673922234573
Trimmed Mean ( 12 / 20 )87.35945945945950.859424518148212101.648786617924
Trimmed Mean ( 13 / 20 )87.42285714285710.80710173168078108.317023382914
Trimmed Mean ( 14 / 20 )87.45757575757580.7814617022624111.915370266231
Trimmed Mean ( 15 / 20 )87.47419354838710.764761087746981114.381072664261
Trimmed Mean ( 16 / 20 )87.47241379310340.745625940499601117.314070020811
Trimmed Mean ( 17 / 20 )87.4740740740740.719084424838539121.646459097922
Trimmed Mean ( 18 / 20 )87.4520.685787138987018127.520618320688
Trimmed Mean ( 19 / 20 )87.45217391304350.646329544464833135.305858539168
Trimmed Mean ( 20 / 20 )87.47142857142860.613814880467224142.504574839970
Median87.8
Midrange4063.25
Midmean - Weighted Average at Xnp87.2466666666667
Midmean - Weighted Average at X(n+1)p87.6875
Midmean - Empirical Distribution Function87.6875
Midmean - Empirical Distribution Function - Averaging87.6875
Midmean - Empirical Distribution Function - Interpolation87.6875
Midmean - Closest Observation87.4575757575758
Midmean - True Basic - Statistics Graphics Toolkit87.6875
Midmean - MS Excel (old versions)87.6875
Number of observations61



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')