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Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationSun, 21 Dec 2008 12:03:14 -0700
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/Dec/21/t1229886234wx8ht5fcwlzp5ut.htm/, Retrieved Sat, 18 May 2024 21:27:14 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=35761, Retrieved Sat, 18 May 2024 21:27:14 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact166
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Central Tendency] [Paper central ten...] [2007-11-09 08:56:17] [74be16979710d4c4e7c6647856088456]
-   PD    [Central Tendency] [CT Frankrijk] [2008-12-21 19:03:14] [4ef5c191fa12c0a7497d8cf4a02b2cfe] [Current]
-   PD      [Central Tendency] [CT Nederland] [2008-12-22 08:00:21] [74be16979710d4c4e7c6647856088456]
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Dataseries X:
3755.3
3001.4
3815.7
4034.4
3590.4
4176.4
3943.5
3934.2
3859.2
3300.5
3800.0
3958.7
3451.4
2678.6
3279.3
3550.3
3294.4
3202.2
3486.4
3139.7
3283.2
2933.6
3391.6
3301.3
3257.6
2537.0
2970.5
3481.9
3361.1
3123.2
3843.3
3153.0
3365.1
3528.5
3506.7
3146.6
3195.1
2424.0
2676.3
3174.6
3067.4
3121.2
3517.7
3014.7
2949.6
2990.3
3084.1
3077.9
3023.6
2226.2
2628.3
3088.7
2551.4
2856.7
3176.2
2663.1
2630.4
2584.4
2472.2
2895.6




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=35761&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=35761&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=35761&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 Mean3208.76557.18892359593956.1081551852789
Geometric Mean3178.30390462362
Harmonic Mean3147.41776865984
Quadratic Mean3238.69366121075
Winsorized Mean ( 1 / 20 )3209.69555.676512835280757.6489948193398
Winsorized Mean ( 2 / 20 )3208.7783333333354.69072939606758.6713391605286
Winsorized Mean ( 3 / 20 )3211.2583333333353.800624105954459.6881241936731
Winsorized Mean ( 4 / 20 )3211.5983333333353.455643077125960.0796875401842
Winsorized Mean ( 5 / 20 )3208.0983333333351.49896809298462.2944197161572
Winsorized Mean ( 6 / 20 )3210.8983333333350.277208924532163.8638938401096
Winsorized Mean ( 7 / 20 )3207.9233333333349.550943218297864.7399045301873
Winsorized Mean ( 8 / 20 )3210.1948.266948412340666.5090730944001
Winsorized Mean ( 9 / 20 )3205.46546.519523076444968.90580100601
Winsorized Mean ( 10 / 20 )3178.36541.343964084772376.8761552105414
Winsorized Mean ( 11 / 20 )3203.66533.8554864846694.627646288633
Winsorized Mean ( 12 / 20 )3207.08531.7804984818845100.913615367868
Winsorized Mean ( 13 / 20 )3212.9783333333330.0451835909695106.938216024050
Winsorized Mean ( 14 / 20 )3214.14529.0226133755541110.746229445598
Winsorized Mean ( 15 / 20 )3214.29527.3628125541894117.469466767511
Winsorized Mean ( 16 / 20 )3218.37526.3742483358765122.027174348779
Winsorized Mean ( 17 / 20 )3212.8783333333324.4670454132156131.314520371059
Winsorized Mean ( 18 / 20 )3198.9283333333320.9943755034004152.370730570920
Winsorized Mean ( 19 / 20 )3193.35519.2878982616117165.562621530189
Winsorized Mean ( 20 / 20 )3206.6216666666716.9762218371027188.889005895197
Trimmed Mean ( 1 / 20 )3209.0224137931054.100109532610359.3163755400306
Trimmed Mean ( 2 / 20 )3208.3017857142952.156531416712761.5129437976053
Trimmed Mean ( 3 / 20 )3208.0370370370450.412652545385463.635553279981
Trimmed Mean ( 4 / 20 )3206.7980769230848.671305783950565.8868305518223
Trimmed Mean ( 5 / 20 )3205.35846.614127322527668.7636599484491
Trimmed Mean ( 6 / 20 )3204.6729166666744.713566306835171.6711544472977
Trimmed Mean ( 7 / 20 )3203.3195652173942.677835112044775.0581550541991
Trimmed Mean ( 8 / 20 )3202.4227272727340.262163062322579.5392617708006
Trimmed Mean ( 9 / 20 )3201.0357142857137.479864020367485.406812376539
Trimmed Mean ( 10 / 20 )3200.297534.309903348573693.2762027186838
Trimmed Mean ( 11 / 20 )3203.7605263157931.6854698200382101.111346762790
Trimmed Mean ( 12 / 20 )3203.77530.4860075566813105.090015281383
Trimmed Mean ( 13 / 20 )3203.2882352941229.4121486427704108.910378299802
Trimmed Mean ( 14 / 20 )3201.89062528.3797080644976112.823240384403
Trimmed Mean ( 15 / 20 )3200.1427.171513819042117.775550575225
Trimmed Mean ( 16 / 20 )3198.1178571428625.9098840476819123.432349263214
Trimmed Mean ( 17 / 20 )3195.1961538461524.2923536439376131.530941821421
Trimmed Mean ( 18 / 20 )3192.5958333333322.5308705126270141.698734256366
Trimmed Mean ( 19 / 20 )3191.6363636363621.2665779952974150.077570747025
Trimmed Mean ( 20 / 20 )3191.36519.9090157770425160.297477069662
Median3175.4
Midrange3201.3
Midmean - Weighted Average at Xnp3192.05806451613
Midmean - Weighted Average at X(n+1)p3200.14
Midmean - Empirical Distribution Function3192.05806451613
Midmean - Empirical Distribution Function - Averaging3200.14
Midmean - Empirical Distribution Function - Interpolation3200.14
Midmean - Closest Observation3192.05806451613
Midmean - True Basic - Statistics Graphics Toolkit3200.14
Midmean - MS Excel (old versions)3201.890625
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 3208.765 & 57.188923595939 & 56.1081551852789 \tabularnewline
Geometric Mean & 3178.30390462362 &  &  \tabularnewline
Harmonic Mean & 3147.41776865984 &  &  \tabularnewline
Quadratic Mean & 3238.69366121075 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 3209.695 & 55.6765128352807 & 57.6489948193398 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 3208.77833333333 & 54.690729396067 & 58.6713391605286 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 3211.25833333333 & 53.8006241059544 & 59.6881241936731 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 3211.59833333333 & 53.4556430771259 & 60.0796875401842 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 3208.09833333333 & 51.498968092984 & 62.2944197161572 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 3210.89833333333 & 50.2772089245321 & 63.8638938401096 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 3207.92333333333 & 49.5509432182978 & 64.7399045301873 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 3210.19 & 48.2669484123406 & 66.5090730944001 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 3205.465 & 46.5195230764449 & 68.90580100601 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 3178.365 & 41.3439640847723 & 76.8761552105414 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 3203.665 & 33.85548648466 & 94.627646288633 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 3207.085 & 31.7804984818845 & 100.913615367868 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 3212.97833333333 & 30.0451835909695 & 106.938216024050 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 3214.145 & 29.0226133755541 & 110.746229445598 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 3214.295 & 27.3628125541894 & 117.469466767511 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 3218.375 & 26.3742483358765 & 122.027174348779 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 3212.87833333333 & 24.4670454132156 & 131.314520371059 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 3198.92833333333 & 20.9943755034004 & 152.370730570920 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 3193.355 & 19.2878982616117 & 165.562621530189 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 3206.62166666667 & 16.9762218371027 & 188.889005895197 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 3209.02241379310 & 54.1001095326103 & 59.3163755400306 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 3208.30178571429 & 52.1565314167127 & 61.5129437976053 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 3208.03703703704 & 50.4126525453854 & 63.635553279981 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 3206.79807692308 & 48.6713057839505 & 65.8868305518223 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 3205.358 & 46.6141273225276 & 68.7636599484491 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 3204.67291666667 & 44.7135663068351 & 71.6711544472977 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 3203.31956521739 & 42.6778351120447 & 75.0581550541991 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 3202.42272727273 & 40.2621630623225 & 79.5392617708006 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 3201.03571428571 & 37.4798640203674 & 85.406812376539 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 3200.2975 & 34.3099033485736 & 93.2762027186838 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 3203.76052631579 & 31.6854698200382 & 101.111346762790 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 3203.775 & 30.4860075566813 & 105.090015281383 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 3203.28823529412 & 29.4121486427704 & 108.910378299802 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 3201.890625 & 28.3797080644976 & 112.823240384403 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 3200.14 & 27.171513819042 & 117.775550575225 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 3198.11785714286 & 25.9098840476819 & 123.432349263214 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 3195.19615384615 & 24.2923536439376 & 131.530941821421 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 3192.59583333333 & 22.5308705126270 & 141.698734256366 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 3191.63636363636 & 21.2665779952974 & 150.077570747025 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 3191.365 & 19.9090157770425 & 160.297477069662 \tabularnewline
Median & 3175.4 &  &  \tabularnewline
Midrange & 3201.3 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 3192.05806451613 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 3200.14 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 3192.05806451613 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 3200.14 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 3200.14 &  &  \tabularnewline
Midmean - Closest Observation & 3192.05806451613 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 3200.14 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 3201.890625 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=35761&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]3208.765[/C][C]57.188923595939[/C][C]56.1081551852789[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]3178.30390462362[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]3147.41776865984[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]3238.69366121075[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]3209.695[/C][C]55.6765128352807[/C][C]57.6489948193398[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]3208.77833333333[/C][C]54.690729396067[/C][C]58.6713391605286[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]3211.25833333333[/C][C]53.8006241059544[/C][C]59.6881241936731[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]3211.59833333333[/C][C]53.4556430771259[/C][C]60.0796875401842[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]3208.09833333333[/C][C]51.498968092984[/C][C]62.2944197161572[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]3210.89833333333[/C][C]50.2772089245321[/C][C]63.8638938401096[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]3207.92333333333[/C][C]49.5509432182978[/C][C]64.7399045301873[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]3210.19[/C][C]48.2669484123406[/C][C]66.5090730944001[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]3205.465[/C][C]46.5195230764449[/C][C]68.90580100601[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]3178.365[/C][C]41.3439640847723[/C][C]76.8761552105414[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]3203.665[/C][C]33.85548648466[/C][C]94.627646288633[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]3207.085[/C][C]31.7804984818845[/C][C]100.913615367868[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]3212.97833333333[/C][C]30.0451835909695[/C][C]106.938216024050[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]3214.145[/C][C]29.0226133755541[/C][C]110.746229445598[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]3214.295[/C][C]27.3628125541894[/C][C]117.469466767511[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]3218.375[/C][C]26.3742483358765[/C][C]122.027174348779[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]3212.87833333333[/C][C]24.4670454132156[/C][C]131.314520371059[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]3198.92833333333[/C][C]20.9943755034004[/C][C]152.370730570920[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]3193.355[/C][C]19.2878982616117[/C][C]165.562621530189[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]3206.62166666667[/C][C]16.9762218371027[/C][C]188.889005895197[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]3209.02241379310[/C][C]54.1001095326103[/C][C]59.3163755400306[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]3208.30178571429[/C][C]52.1565314167127[/C][C]61.5129437976053[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]3208.03703703704[/C][C]50.4126525453854[/C][C]63.635553279981[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]3206.79807692308[/C][C]48.6713057839505[/C][C]65.8868305518223[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]3205.358[/C][C]46.6141273225276[/C][C]68.7636599484491[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]3204.67291666667[/C][C]44.7135663068351[/C][C]71.6711544472977[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]3203.31956521739[/C][C]42.6778351120447[/C][C]75.0581550541991[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]3202.42272727273[/C][C]40.2621630623225[/C][C]79.5392617708006[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]3201.03571428571[/C][C]37.4798640203674[/C][C]85.406812376539[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]3200.2975[/C][C]34.3099033485736[/C][C]93.2762027186838[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]3203.76052631579[/C][C]31.6854698200382[/C][C]101.111346762790[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]3203.775[/C][C]30.4860075566813[/C][C]105.090015281383[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]3203.28823529412[/C][C]29.4121486427704[/C][C]108.910378299802[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]3201.890625[/C][C]28.3797080644976[/C][C]112.823240384403[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]3200.14[/C][C]27.171513819042[/C][C]117.775550575225[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]3198.11785714286[/C][C]25.9098840476819[/C][C]123.432349263214[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]3195.19615384615[/C][C]24.2923536439376[/C][C]131.530941821421[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]3192.59583333333[/C][C]22.5308705126270[/C][C]141.698734256366[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]3191.63636363636[/C][C]21.2665779952974[/C][C]150.077570747025[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]3191.365[/C][C]19.9090157770425[/C][C]160.297477069662[/C][/ROW]
[ROW][C]Median[/C][C]3175.4[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]3201.3[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]3192.05806451613[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]3200.14[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]3192.05806451613[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]3200.14[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]3200.14[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]3192.05806451613[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]3200.14[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]3201.890625[/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=35761&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=35761&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 Mean3208.76557.18892359593956.1081551852789
Geometric Mean3178.30390462362
Harmonic Mean3147.41776865984
Quadratic Mean3238.69366121075
Winsorized Mean ( 1 / 20 )3209.69555.676512835280757.6489948193398
Winsorized Mean ( 2 / 20 )3208.7783333333354.69072939606758.6713391605286
Winsorized Mean ( 3 / 20 )3211.2583333333353.800624105954459.6881241936731
Winsorized Mean ( 4 / 20 )3211.5983333333353.455643077125960.0796875401842
Winsorized Mean ( 5 / 20 )3208.0983333333351.49896809298462.2944197161572
Winsorized Mean ( 6 / 20 )3210.8983333333350.277208924532163.8638938401096
Winsorized Mean ( 7 / 20 )3207.9233333333349.550943218297864.7399045301873
Winsorized Mean ( 8 / 20 )3210.1948.266948412340666.5090730944001
Winsorized Mean ( 9 / 20 )3205.46546.519523076444968.90580100601
Winsorized Mean ( 10 / 20 )3178.36541.343964084772376.8761552105414
Winsorized Mean ( 11 / 20 )3203.66533.8554864846694.627646288633
Winsorized Mean ( 12 / 20 )3207.08531.7804984818845100.913615367868
Winsorized Mean ( 13 / 20 )3212.9783333333330.0451835909695106.938216024050
Winsorized Mean ( 14 / 20 )3214.14529.0226133755541110.746229445598
Winsorized Mean ( 15 / 20 )3214.29527.3628125541894117.469466767511
Winsorized Mean ( 16 / 20 )3218.37526.3742483358765122.027174348779
Winsorized Mean ( 17 / 20 )3212.8783333333324.4670454132156131.314520371059
Winsorized Mean ( 18 / 20 )3198.9283333333320.9943755034004152.370730570920
Winsorized Mean ( 19 / 20 )3193.35519.2878982616117165.562621530189
Winsorized Mean ( 20 / 20 )3206.6216666666716.9762218371027188.889005895197
Trimmed Mean ( 1 / 20 )3209.0224137931054.100109532610359.3163755400306
Trimmed Mean ( 2 / 20 )3208.3017857142952.156531416712761.5129437976053
Trimmed Mean ( 3 / 20 )3208.0370370370450.412652545385463.635553279981
Trimmed Mean ( 4 / 20 )3206.7980769230848.671305783950565.8868305518223
Trimmed Mean ( 5 / 20 )3205.35846.614127322527668.7636599484491
Trimmed Mean ( 6 / 20 )3204.6729166666744.713566306835171.6711544472977
Trimmed Mean ( 7 / 20 )3203.3195652173942.677835112044775.0581550541991
Trimmed Mean ( 8 / 20 )3202.4227272727340.262163062322579.5392617708006
Trimmed Mean ( 9 / 20 )3201.0357142857137.479864020367485.406812376539
Trimmed Mean ( 10 / 20 )3200.297534.309903348573693.2762027186838
Trimmed Mean ( 11 / 20 )3203.7605263157931.6854698200382101.111346762790
Trimmed Mean ( 12 / 20 )3203.77530.4860075566813105.090015281383
Trimmed Mean ( 13 / 20 )3203.2882352941229.4121486427704108.910378299802
Trimmed Mean ( 14 / 20 )3201.89062528.3797080644976112.823240384403
Trimmed Mean ( 15 / 20 )3200.1427.171513819042117.775550575225
Trimmed Mean ( 16 / 20 )3198.1178571428625.9098840476819123.432349263214
Trimmed Mean ( 17 / 20 )3195.1961538461524.2923536439376131.530941821421
Trimmed Mean ( 18 / 20 )3192.5958333333322.5308705126270141.698734256366
Trimmed Mean ( 19 / 20 )3191.6363636363621.2665779952974150.077570747025
Trimmed Mean ( 20 / 20 )3191.36519.9090157770425160.297477069662
Median3175.4
Midrange3201.3
Midmean - Weighted Average at Xnp3192.05806451613
Midmean - Weighted Average at X(n+1)p3200.14
Midmean - Empirical Distribution Function3192.05806451613
Midmean - Empirical Distribution Function - Averaging3200.14
Midmean - Empirical Distribution Function - Interpolation3200.14
Midmean - Closest Observation3192.05806451613
Midmean - True Basic - Statistics Graphics Toolkit3200.14
Midmean - MS Excel (old versions)3201.890625
Number of observations60



Parameters (Session):
par1 = grey ; par2 = grey ; par3 = TRUE ; par4 = Uitvoer naar Frankrijk ; par5 = Uitvoer naar Italië ;
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')