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Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationFri, 09 Oct 2015 13:14:04 +0100
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2015/Oct/09/t14443928992vidogxzo7xq56s.htm/, Retrieved Sat, 18 May 2024 21:54:13 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=281874, Retrieved Sat, 18 May 2024 21:54:13 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact50
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [] [2015-10-09 12:14:04] [b3d63f0d56915497ce660fdd9ec1cd3f] [Current]
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Dataseries X:
92.3
97.1
117.61
104.42
101.88
117.54
105.34
96.77
116.43
113.33
110.76
100.95
105.91
110.2
125.05
108.98
119.11
113.7
107.45
97.48
110.56
108.74
107.71
101.05
104.0
110.56
120.88
106.09
109.18
111.06
106.16
98.24
103.53
113.3
107.86
95.34
103.23
103.12
113.77
111.83
112.12
108.57
114.31
93.22
112.42
119.31
109.95
103.21
109.16
108.58
114.71
116.04
110.69
113.46
113.98
93.73
118.97
117.69
104.42
101.11




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gwilym Jenkins' @ jenkins.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 & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=281874&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' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=281874&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=281874&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' @ jenkins.wessa.net







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean108.4028333333330.953569241829988113.681134602557
Geometric Mean108.151497394052
Harmonic Mean107.896195885664
Quadratic Mean108.650000636601
Winsorized Mean ( 1 / 20 )108.3486666666670.931024357387584116.375759459923
Winsorized Mean ( 2 / 20 )108.3133333333330.915082400867074118.364568295382
Winsorized Mean ( 3 / 20 )108.3838333333330.892187912222325121.480947957884
Winsorized Mean ( 4 / 20 )108.4698333333330.867559877341114125.028642018082
Winsorized Mean ( 5 / 20 )108.3906666666670.840326438677547128.986381574814
Winsorized Mean ( 6 / 20 )108.4206666666670.830254840281992130.587214197802
Winsorized Mean ( 7 / 20 )108.5011666666670.809281996470746134.070901292549
Winsorized Mean ( 8 / 20 )108.71450.708882960903905153.360294993375
Winsorized Mean ( 9 / 20 )108.6710.695447208067615156.260602874452
Winsorized Mean ( 10 / 20 )108.4593333333330.65569775086517165.410561787386
Winsorized Mean ( 11 / 20 )108.5271666666670.617651881715597175.709278769167
Winsorized Mean ( 12 / 20 )108.7091666666670.56364408029066192.868461619623
Winsorized Mean ( 13 / 20 )108.6831666666670.553218548352326196.456114839899
Winsorized Mean ( 14 / 20 )108.67150.549897413391113197.621406017976
Winsorized Mean ( 15 / 20 )108.68650.528154329493484205.785494751569
Winsorized Mean ( 16 / 20 )108.7771666666670.502359522577875216.532506656733
Winsorized Mean ( 17 / 20 )108.8876666666670.4821069791651225.857893314955
Winsorized Mean ( 18 / 20 )108.6236666666670.442376349136064245.545827390643
Winsorized Mean ( 19 / 20 )108.820.382530675259023284.473918140851
Winsorized Mean ( 20 / 20 )108.9133333333330.33950800783236320.797538852491
Trimmed Mean ( 1 / 20 )108.3934482758620.900773901039522120.333691008113
Trimmed Mean ( 2 / 20 )108.4414285714290.863432986013279125.593335357888
Trimmed Mean ( 3 / 20 )108.5125925925930.827836258617683131.079777507917
Trimmed Mean ( 4 / 20 )108.5621153846150.79483050435864136.585240235861
Trimmed Mean ( 5 / 20 )108.58980.763450624681473142.235524458842
Trimmed Mean ( 6 / 20 )108.6395833333330.733280298594028148.155600991375
Trimmed Mean ( 7 / 20 )108.6871739130430.697802739386991155.756301571019
Trimmed Mean ( 8 / 20 )108.7234090909090.658482057300472165.112181699581
Trimmed Mean ( 9 / 20 )108.7250.637827618442359170.46141756219
Trimmed Mean ( 10 / 20 )108.7340.61401002246894177.088314556788
Trimmed Mean ( 11 / 20 )108.7773684210530.592883073757391183.47187368949
Trimmed Mean ( 12 / 20 )108.8152777777780.574586184579563189.380254343219
Trimmed Mean ( 13 / 20 )108.8308823529410.563972788506632192.971867740497
Trimmed Mean ( 14 / 20 )108.85218750.55071942214747197.654528099886
Trimmed Mean ( 15 / 20 )108.8780.531464340127902204.864168259713
Trimmed Mean ( 16 / 20 )108.9053571428570.509328970869411213.821249863244
Trimmed Mean ( 17 / 20 )108.9238461538460.484322866539723224.899243209514
Trimmed Mean ( 18 / 20 )108.9291666666670.452516280701056240.718779218085
Trimmed Mean ( 19 / 20 )108.9754545454550.417340439101468261.118847672845
Trimmed Mean ( 20 / 20 )1090.388489653049236280.573753108904
Median109.07
Midrange108.675
Midmean - Weighted Average at Xnp108.695806451613
Midmean - Weighted Average at X(n+1)p108.878
Midmean - Empirical Distribution Function108.695806451613
Midmean - Empirical Distribution Function - Averaging108.878
Midmean - Empirical Distribution Function - Interpolation108.878
Midmean - Closest Observation108.695806451613
Midmean - True Basic - Statistics Graphics Toolkit108.878
Midmean - MS Excel (old versions)108.8521875
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 108.402833333333 & 0.953569241829988 & 113.681134602557 \tabularnewline
Geometric Mean & 108.151497394052 &  &  \tabularnewline
Harmonic Mean & 107.896195885664 &  &  \tabularnewline
Quadratic Mean & 108.650000636601 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 108.348666666667 & 0.931024357387584 & 116.375759459923 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 108.313333333333 & 0.915082400867074 & 118.364568295382 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 108.383833333333 & 0.892187912222325 & 121.480947957884 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 108.469833333333 & 0.867559877341114 & 125.028642018082 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 108.390666666667 & 0.840326438677547 & 128.986381574814 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 108.420666666667 & 0.830254840281992 & 130.587214197802 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 108.501166666667 & 0.809281996470746 & 134.070901292549 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 108.7145 & 0.708882960903905 & 153.360294993375 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 108.671 & 0.695447208067615 & 156.260602874452 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 108.459333333333 & 0.65569775086517 & 165.410561787386 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 108.527166666667 & 0.617651881715597 & 175.709278769167 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 108.709166666667 & 0.56364408029066 & 192.868461619623 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 108.683166666667 & 0.553218548352326 & 196.456114839899 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 108.6715 & 0.549897413391113 & 197.621406017976 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 108.6865 & 0.528154329493484 & 205.785494751569 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 108.777166666667 & 0.502359522577875 & 216.532506656733 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 108.887666666667 & 0.4821069791651 & 225.857893314955 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 108.623666666667 & 0.442376349136064 & 245.545827390643 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 108.82 & 0.382530675259023 & 284.473918140851 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 108.913333333333 & 0.33950800783236 & 320.797538852491 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 108.393448275862 & 0.900773901039522 & 120.333691008113 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 108.441428571429 & 0.863432986013279 & 125.593335357888 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 108.512592592593 & 0.827836258617683 & 131.079777507917 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 108.562115384615 & 0.79483050435864 & 136.585240235861 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 108.5898 & 0.763450624681473 & 142.235524458842 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 108.639583333333 & 0.733280298594028 & 148.155600991375 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 108.687173913043 & 0.697802739386991 & 155.756301571019 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 108.723409090909 & 0.658482057300472 & 165.112181699581 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 108.725 & 0.637827618442359 & 170.46141756219 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 108.734 & 0.61401002246894 & 177.088314556788 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 108.777368421053 & 0.592883073757391 & 183.47187368949 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 108.815277777778 & 0.574586184579563 & 189.380254343219 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 108.830882352941 & 0.563972788506632 & 192.971867740497 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 108.8521875 & 0.55071942214747 & 197.654528099886 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 108.878 & 0.531464340127902 & 204.864168259713 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 108.905357142857 & 0.509328970869411 & 213.821249863244 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 108.923846153846 & 0.484322866539723 & 224.899243209514 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 108.929166666667 & 0.452516280701056 & 240.718779218085 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 108.975454545455 & 0.417340439101468 & 261.118847672845 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 109 & 0.388489653049236 & 280.573753108904 \tabularnewline
Median & 109.07 &  &  \tabularnewline
Midrange & 108.675 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 108.695806451613 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 108.878 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 108.695806451613 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 108.878 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 108.878 &  &  \tabularnewline
Midmean - Closest Observation & 108.695806451613 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 108.878 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 108.8521875 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=281874&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]108.402833333333[/C][C]0.953569241829988[/C][C]113.681134602557[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]108.151497394052[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]107.896195885664[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]108.650000636601[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]108.348666666667[/C][C]0.931024357387584[/C][C]116.375759459923[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]108.313333333333[/C][C]0.915082400867074[/C][C]118.364568295382[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]108.383833333333[/C][C]0.892187912222325[/C][C]121.480947957884[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]108.469833333333[/C][C]0.867559877341114[/C][C]125.028642018082[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]108.390666666667[/C][C]0.840326438677547[/C][C]128.986381574814[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]108.420666666667[/C][C]0.830254840281992[/C][C]130.587214197802[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]108.501166666667[/C][C]0.809281996470746[/C][C]134.070901292549[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]108.7145[/C][C]0.708882960903905[/C][C]153.360294993375[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]108.671[/C][C]0.695447208067615[/C][C]156.260602874452[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]108.459333333333[/C][C]0.65569775086517[/C][C]165.410561787386[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]108.527166666667[/C][C]0.617651881715597[/C][C]175.709278769167[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]108.709166666667[/C][C]0.56364408029066[/C][C]192.868461619623[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]108.683166666667[/C][C]0.553218548352326[/C][C]196.456114839899[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]108.6715[/C][C]0.549897413391113[/C][C]197.621406017976[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]108.6865[/C][C]0.528154329493484[/C][C]205.785494751569[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]108.777166666667[/C][C]0.502359522577875[/C][C]216.532506656733[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]108.887666666667[/C][C]0.4821069791651[/C][C]225.857893314955[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]108.623666666667[/C][C]0.442376349136064[/C][C]245.545827390643[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]108.82[/C][C]0.382530675259023[/C][C]284.473918140851[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]108.913333333333[/C][C]0.33950800783236[/C][C]320.797538852491[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]108.393448275862[/C][C]0.900773901039522[/C][C]120.333691008113[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]108.441428571429[/C][C]0.863432986013279[/C][C]125.593335357888[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]108.512592592593[/C][C]0.827836258617683[/C][C]131.079777507917[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]108.562115384615[/C][C]0.79483050435864[/C][C]136.585240235861[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]108.5898[/C][C]0.763450624681473[/C][C]142.235524458842[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]108.639583333333[/C][C]0.733280298594028[/C][C]148.155600991375[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]108.687173913043[/C][C]0.697802739386991[/C][C]155.756301571019[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]108.723409090909[/C][C]0.658482057300472[/C][C]165.112181699581[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]108.725[/C][C]0.637827618442359[/C][C]170.46141756219[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]108.734[/C][C]0.61401002246894[/C][C]177.088314556788[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]108.777368421053[/C][C]0.592883073757391[/C][C]183.47187368949[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]108.815277777778[/C][C]0.574586184579563[/C][C]189.380254343219[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]108.830882352941[/C][C]0.563972788506632[/C][C]192.971867740497[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]108.8521875[/C][C]0.55071942214747[/C][C]197.654528099886[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]108.878[/C][C]0.531464340127902[/C][C]204.864168259713[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]108.905357142857[/C][C]0.509328970869411[/C][C]213.821249863244[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]108.923846153846[/C][C]0.484322866539723[/C][C]224.899243209514[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]108.929166666667[/C][C]0.452516280701056[/C][C]240.718779218085[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]108.975454545455[/C][C]0.417340439101468[/C][C]261.118847672845[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]109[/C][C]0.388489653049236[/C][C]280.573753108904[/C][/ROW]
[ROW][C]Median[/C][C]109.07[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]108.675[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]108.695806451613[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]108.878[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]108.695806451613[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]108.878[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]108.878[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]108.695806451613[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]108.878[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]108.8521875[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]60[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=281874&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=281874&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 Mean108.4028333333330.953569241829988113.681134602557
Geometric Mean108.151497394052
Harmonic Mean107.896195885664
Quadratic Mean108.650000636601
Winsorized Mean ( 1 / 20 )108.3486666666670.931024357387584116.375759459923
Winsorized Mean ( 2 / 20 )108.3133333333330.915082400867074118.364568295382
Winsorized Mean ( 3 / 20 )108.3838333333330.892187912222325121.480947957884
Winsorized Mean ( 4 / 20 )108.4698333333330.867559877341114125.028642018082
Winsorized Mean ( 5 / 20 )108.3906666666670.840326438677547128.986381574814
Winsorized Mean ( 6 / 20 )108.4206666666670.830254840281992130.587214197802
Winsorized Mean ( 7 / 20 )108.5011666666670.809281996470746134.070901292549
Winsorized Mean ( 8 / 20 )108.71450.708882960903905153.360294993375
Winsorized Mean ( 9 / 20 )108.6710.695447208067615156.260602874452
Winsorized Mean ( 10 / 20 )108.4593333333330.65569775086517165.410561787386
Winsorized Mean ( 11 / 20 )108.5271666666670.617651881715597175.709278769167
Winsorized Mean ( 12 / 20 )108.7091666666670.56364408029066192.868461619623
Winsorized Mean ( 13 / 20 )108.6831666666670.553218548352326196.456114839899
Winsorized Mean ( 14 / 20 )108.67150.549897413391113197.621406017976
Winsorized Mean ( 15 / 20 )108.68650.528154329493484205.785494751569
Winsorized Mean ( 16 / 20 )108.7771666666670.502359522577875216.532506656733
Winsorized Mean ( 17 / 20 )108.8876666666670.4821069791651225.857893314955
Winsorized Mean ( 18 / 20 )108.6236666666670.442376349136064245.545827390643
Winsorized Mean ( 19 / 20 )108.820.382530675259023284.473918140851
Winsorized Mean ( 20 / 20 )108.9133333333330.33950800783236320.797538852491
Trimmed Mean ( 1 / 20 )108.3934482758620.900773901039522120.333691008113
Trimmed Mean ( 2 / 20 )108.4414285714290.863432986013279125.593335357888
Trimmed Mean ( 3 / 20 )108.5125925925930.827836258617683131.079777507917
Trimmed Mean ( 4 / 20 )108.5621153846150.79483050435864136.585240235861
Trimmed Mean ( 5 / 20 )108.58980.763450624681473142.235524458842
Trimmed Mean ( 6 / 20 )108.6395833333330.733280298594028148.155600991375
Trimmed Mean ( 7 / 20 )108.6871739130430.697802739386991155.756301571019
Trimmed Mean ( 8 / 20 )108.7234090909090.658482057300472165.112181699581
Trimmed Mean ( 9 / 20 )108.7250.637827618442359170.46141756219
Trimmed Mean ( 10 / 20 )108.7340.61401002246894177.088314556788
Trimmed Mean ( 11 / 20 )108.7773684210530.592883073757391183.47187368949
Trimmed Mean ( 12 / 20 )108.8152777777780.574586184579563189.380254343219
Trimmed Mean ( 13 / 20 )108.8308823529410.563972788506632192.971867740497
Trimmed Mean ( 14 / 20 )108.85218750.55071942214747197.654528099886
Trimmed Mean ( 15 / 20 )108.8780.531464340127902204.864168259713
Trimmed Mean ( 16 / 20 )108.9053571428570.509328970869411213.821249863244
Trimmed Mean ( 17 / 20 )108.9238461538460.484322866539723224.899243209514
Trimmed Mean ( 18 / 20 )108.9291666666670.452516280701056240.718779218085
Trimmed Mean ( 19 / 20 )108.9754545454550.417340439101468261.118847672845
Trimmed Mean ( 20 / 20 )1090.388489653049236280.573753108904
Median109.07
Midrange108.675
Midmean - Weighted Average at Xnp108.695806451613
Midmean - Weighted Average at X(n+1)p108.878
Midmean - Empirical Distribution Function108.695806451613
Midmean - Empirical Distribution Function - Averaging108.878
Midmean - Empirical Distribution Function - Interpolation108.878
Midmean - Closest Observation108.695806451613
Midmean - True Basic - Statistics Graphics Toolkit108.878
Midmean - MS Excel (old versions)108.8521875
Number of observations60



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')