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R Software Module

rwasp_centraltendency.wasp

Title produced by software

Central Tendency

Date of computation

Thu, 22 Dec 2016 17:07:56 +0100

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Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2016/Dec/22/t1482423056h5dvk3lojb24cz2.htm/, Retrieved Mon, 07 Apr 2025 19:14:50 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=302551, Retrieved Mon, 07 Apr 2025 19:14:50 +0000

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User-defined keywords

Estimated Impact

179

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)

-       [Central Tendency] [CT2] [2016-12-22 16:07:56] [636d0f72197ac5e1dae4a755427db02a] [Current]

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Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	1 seconds
R Server	Big Analytics Cloud Computing Center
R Framework error message	Warning: there are blank lines in the 'Data' field. Please, use NA for missing data - blank lines are simply deleted and are NOT treated as missing values.

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input view raw input (R code)  \tabularnewline
Raw Outputview raw output of R engine  \tabularnewline
Computing time1 seconds \tabularnewline
R ServerBig Analytics Cloud Computing Center \tabularnewline
R Framework error message & Warning: there are blank lines in the 'Data' field.
Please, use NA for missing data - blank lines are simply
 deleted and are NOT treated as missing values. \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=302551&T=0

[TABLE]
[ROW]

Summary of computational transaction[/C][/ROW] [ROW]

Raw Input[/C]

view raw input (R code) [/C][/ROW] [ROW]

Raw Output[/C]

view raw output of R engine [/C][/ROW] [ROW]

Computing time[/C]

1 seconds[/C][/ROW] [ROW]

R Server[/C]

Big Analytics Cloud Computing Center[/C][/ROW] [ROW]

R Framework error message[/C][C]

Warning: there are blank lines in the 'Data' field.
Please, use NA for missing data - blank lines are simply
 deleted and are NOT treated as missing values.

[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=302551&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=302551&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 Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	1 seconds
R Server	Big Analytics Cloud Computing Center
R Framework error message	Warning: there are blank lines in the 'Data' field. Please, use NA for missing data - blank lines are simply deleted and are NOT treated as missing values.

Central Tendency - Ungrouped Data
Measure	Value	S.E.	Value/S.E.
Arithmetic Mean	2919.8	97.6494	29.9009
Geometric Mean	2839.2
Harmonic Mean	2758.77
Quadratic Mean	3000.34
Winsorized Mean ( 1 / 17 )	2910.39	93.3578	31.1746
Winsorized Mean ( 2 / 17 )	2905.69	88.0001	33.0191
Winsorized Mean ( 3 / 17 )	2905.69	84.4638	34.4015
Winsorized Mean ( 4 / 17 )	2891.57	78.8219	36.6848
Winsorized Mean ( 5 / 17 )	2891.57	76.2732	37.9107
Winsorized Mean ( 6 / 17 )	2891.57	76.2732	37.9107
Winsorized Mean ( 7 / 17 )	2875.1	72.8417	39.4705
Winsorized Mean ( 8 / 17 )	2875.1	69.0202	41.6559
Winsorized Mean ( 9 / 17 )	2896.27	60.7592	47.6681
Winsorized Mean ( 10 / 17 )	2908.04	58.6622	49.5726
Winsorized Mean ( 11 / 17 )	2908.04	53.9746	53.8779
Winsorized Mean ( 12 / 17 )	2908.04	49.041	59.2981
Winsorized Mean ( 13 / 17 )	2908.04	49.041	59.2981
Winsorized Mean ( 14 / 17 )	2875.1	43.2071	66.5423
Winsorized Mean ( 15 / 17 )	2892.75	40.3874	71.6249
Winsorized Mean ( 16 / 17 )	2873.92	37.218	77.2185
Winsorized Mean ( 17 / 17 )	2873.92	30.8737	93.0865
Trimmed Mean ( 1 / 17 )	2904.29	88.3754	32.8631
Trimmed Mean ( 2 / 17 )	2897.66	81.9237	35.3702
Trimmed Mean ( 3 / 17 )	2893.11	77.4895	37.3355
Trimmed Mean ( 4 / 17 )	2888.14	73.6053	39.2382
Trimmed Mean ( 5 / 17 )	2887.07	71.0103	40.6571
Trimmed Mean ( 6 / 17 )	2885.9	68.512	42.1225
Trimmed Mean ( 7 / 17 )	2884.59	65.0878	44.3185
Trimmed Mean ( 8 / 17 )	2886.57	61.5991	46.8606
Trimmed Mean ( 9 / 17 )	2888.79	58.065	49.7509
Trimmed Mean ( 10 / 17 )	2887.42	55.9338	51.622
Trimmed Mean ( 11 / 17 )	2883.79	53.4578	53.9452
Trimmed Mean ( 12 / 17 )	2879.63	51.3756	56.0505
Trimmed Mean ( 13 / 17 )	2874.8	49.8702	57.6456
Trimmed Mean ( 14 / 17 )	2869.13	47.2606	60.7087
Trimmed Mean ( 15 / 17 )	2868.1	45.5319	62.9909
Trimmed Mean ( 16 / 17 )	2863.68	43.5636	65.7358
Trimmed Mean ( 17 / 17 )	2861.76	41.4998	68.9585
Median	2880
Midrange	3300
Midmean - Weighted Average at Xnp	2879.63
Midmean - Weighted Average at X(n+1)p	2879.63
Midmean - Empirical Distribution Function	2879.63
Midmean - Empirical Distribution Function - Averaging	2879.63
Midmean - Empirical Distribution Function - Interpolation	2879.63
Midmean - Closest Observation	2879.63
Midmean - True Basic - Statistics Graphics Toolkit	2879.63
Midmean - MS Excel (old versions)	2879.63
Number of observations	51

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 2919.8 & 97.6494 & 29.9009 \tabularnewline
Geometric Mean & 2839.2 &  &  \tabularnewline
Harmonic Mean & 2758.77 &  &  \tabularnewline
Quadratic Mean & 3000.34 &  &  \tabularnewline
Winsorized Mean ( 1 / 17 ) & 2910.39 & 93.3578 & 31.1746 \tabularnewline
Winsorized Mean ( 2 / 17 ) & 2905.69 & 88.0001 & 33.0191 \tabularnewline
Winsorized Mean ( 3 / 17 ) & 2905.69 & 84.4638 & 34.4015 \tabularnewline
Winsorized Mean ( 4 / 17 ) & 2891.57 & 78.8219 & 36.6848 \tabularnewline
Winsorized Mean ( 5 / 17 ) & 2891.57 & 76.2732 & 37.9107 \tabularnewline
Winsorized Mean ( 6 / 17 ) & 2891.57 & 76.2732 & 37.9107 \tabularnewline
Winsorized Mean ( 7 / 17 ) & 2875.1 & 72.8417 & 39.4705 \tabularnewline
Winsorized Mean ( 8 / 17 ) & 2875.1 & 69.0202 & 41.6559 \tabularnewline
Winsorized Mean ( 9 / 17 ) & 2896.27 & 60.7592 & 47.6681 \tabularnewline
Winsorized Mean ( 10 / 17 ) & 2908.04 & 58.6622 & 49.5726 \tabularnewline
Winsorized Mean ( 11 / 17 ) & 2908.04 & 53.9746 & 53.8779 \tabularnewline
Winsorized Mean ( 12 / 17 ) & 2908.04 & 49.041 & 59.2981 \tabularnewline
Winsorized Mean ( 13 / 17 ) & 2908.04 & 49.041 & 59.2981 \tabularnewline
Winsorized Mean ( 14 / 17 ) & 2875.1 & 43.2071 & 66.5423 \tabularnewline
Winsorized Mean ( 15 / 17 ) & 2892.75 & 40.3874 & 71.6249 \tabularnewline
Winsorized Mean ( 16 / 17 ) & 2873.92 & 37.218 & 77.2185 \tabularnewline
Winsorized Mean ( 17 / 17 ) & 2873.92 & 30.8737 & 93.0865 \tabularnewline
Trimmed Mean ( 1 / 17 ) & 2904.29 & 88.3754 & 32.8631 \tabularnewline
Trimmed Mean ( 2 / 17 ) & 2897.66 & 81.9237 & 35.3702 \tabularnewline
Trimmed Mean ( 3 / 17 ) & 2893.11 & 77.4895 & 37.3355 \tabularnewline
Trimmed Mean ( 4 / 17 ) & 2888.14 & 73.6053 & 39.2382 \tabularnewline
Trimmed Mean ( 5 / 17 ) & 2887.07 & 71.0103 & 40.6571 \tabularnewline
Trimmed Mean ( 6 / 17 ) & 2885.9 & 68.512 & 42.1225 \tabularnewline
Trimmed Mean ( 7 / 17 ) & 2884.59 & 65.0878 & 44.3185 \tabularnewline
Trimmed Mean ( 8 / 17 ) & 2886.57 & 61.5991 & 46.8606 \tabularnewline
Trimmed Mean ( 9 / 17 ) & 2888.79 & 58.065 & 49.7509 \tabularnewline
Trimmed Mean ( 10 / 17 ) & 2887.42 & 55.9338 & 51.622 \tabularnewline
Trimmed Mean ( 11 / 17 ) & 2883.79 & 53.4578 & 53.9452 \tabularnewline
Trimmed Mean ( 12 / 17 ) & 2879.63 & 51.3756 & 56.0505 \tabularnewline
Trimmed Mean ( 13 / 17 ) & 2874.8 & 49.8702 & 57.6456 \tabularnewline
Trimmed Mean ( 14 / 17 ) & 2869.13 & 47.2606 & 60.7087 \tabularnewline
Trimmed Mean ( 15 / 17 ) & 2868.1 & 45.5319 & 62.9909 \tabularnewline
Trimmed Mean ( 16 / 17 ) & 2863.68 & 43.5636 & 65.7358 \tabularnewline
Trimmed Mean ( 17 / 17 ) & 2861.76 & 41.4998 & 68.9585 \tabularnewline
Median & 2880 &  &  \tabularnewline
Midrange & 3300 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 2879.63 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 2879.63 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 2879.63 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 2879.63 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 2879.63 &  &  \tabularnewline
Midmean - Closest Observation & 2879.63 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 2879.63 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 2879.63 &  &  \tabularnewline
Number of observations & 51 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=302551&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]2919.8[/C][C]97.6494[/C][C]29.9009[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]2839.2[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]2758.77[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]3000.34[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 17 )[/C][C]2910.39[/C][C]93.3578[/C][C]31.1746[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 17 )[/C][C]2905.69[/C][C]88.0001[/C][C]33.0191[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 17 )[/C][C]2905.69[/C][C]84.4638[/C][C]34.4015[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 17 )[/C][C]2891.57[/C][C]78.8219[/C][C]36.6848[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 17 )[/C][C]2891.57[/C][C]76.2732[/C][C]37.9107[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 17 )[/C][C]2891.57[/C][C]76.2732[/C][C]37.9107[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 17 )[/C][C]2875.1[/C][C]72.8417[/C][C]39.4705[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 17 )[/C][C]2875.1[/C][C]69.0202[/C][C]41.6559[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 17 )[/C][C]2896.27[/C][C]60.7592[/C][C]47.6681[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 17 )[/C][C]2908.04[/C][C]58.6622[/C][C]49.5726[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 17 )[/C][C]2908.04[/C][C]53.9746[/C][C]53.8779[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 17 )[/C][C]2908.04[/C][C]49.041[/C][C]59.2981[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 17 )[/C][C]2908.04[/C][C]49.041[/C][C]59.2981[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 17 )[/C][C]2875.1[/C][C]43.2071[/C][C]66.5423[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 17 )[/C][C]2892.75[/C][C]40.3874[/C][C]71.6249[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 17 )[/C][C]2873.92[/C][C]37.218[/C][C]77.2185[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 17 )[/C][C]2873.92[/C][C]30.8737[/C][C]93.0865[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 17 )[/C][C]2904.29[/C][C]88.3754[/C][C]32.8631[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 17 )[/C][C]2897.66[/C][C]81.9237[/C][C]35.3702[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 17 )[/C][C]2893.11[/C][C]77.4895[/C][C]37.3355[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 17 )[/C][C]2888.14[/C][C]73.6053[/C][C]39.2382[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 17 )[/C][C]2887.07[/C][C]71.0103[/C][C]40.6571[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 17 )[/C][C]2885.9[/C][C]68.512[/C][C]42.1225[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 17 )[/C][C]2884.59[/C][C]65.0878[/C][C]44.3185[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 17 )[/C][C]2886.57[/C][C]61.5991[/C][C]46.8606[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 17 )[/C][C]2888.79[/C][C]58.065[/C][C]49.7509[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 17 )[/C][C]2887.42[/C][C]55.9338[/C][C]51.622[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 17 )[/C][C]2883.79[/C][C]53.4578[/C][C]53.9452[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 17 )[/C][C]2879.63[/C][C]51.3756[/C][C]56.0505[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 17 )[/C][C]2874.8[/C][C]49.8702[/C][C]57.6456[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 17 )[/C][C]2869.13[/C][C]47.2606[/C][C]60.7087[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 17 )[/C][C]2868.1[/C][C]45.5319[/C][C]62.9909[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 17 )[/C][C]2863.68[/C][C]43.5636[/C][C]65.7358[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 17 )[/C][C]2861.76[/C][C]41.4998[/C][C]68.9585[/C][/ROW]
[ROW][C]Median[/C][C]2880[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]3300[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]2879.63[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]2879.63[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]2879.63[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]2879.63[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]2879.63[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]2879.63[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]2879.63[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]2879.63[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]51[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=302551&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=302551&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
Measure	Value	S.E.	Value/S.E.
Arithmetic Mean	2919.8	97.6494	29.9009
Geometric Mean	2839.2
Harmonic Mean	2758.77
Quadratic Mean	3000.34
Winsorized Mean ( 1 / 17 )	2910.39	93.3578	31.1746
Winsorized Mean ( 2 / 17 )	2905.69	88.0001	33.0191
Winsorized Mean ( 3 / 17 )	2905.69	84.4638	34.4015
Winsorized Mean ( 4 / 17 )	2891.57	78.8219	36.6848
Winsorized Mean ( 5 / 17 )	2891.57	76.2732	37.9107
Winsorized Mean ( 6 / 17 )	2891.57	76.2732	37.9107
Winsorized Mean ( 7 / 17 )	2875.1	72.8417	39.4705
Winsorized Mean ( 8 / 17 )	2875.1	69.0202	41.6559
Winsorized Mean ( 9 / 17 )	2896.27	60.7592	47.6681
Winsorized Mean ( 10 / 17 )	2908.04	58.6622	49.5726
Winsorized Mean ( 11 / 17 )	2908.04	53.9746	53.8779
Winsorized Mean ( 12 / 17 )	2908.04	49.041	59.2981
Winsorized Mean ( 13 / 17 )	2908.04	49.041	59.2981
Winsorized Mean ( 14 / 17 )	2875.1	43.2071	66.5423
Winsorized Mean ( 15 / 17 )	2892.75	40.3874	71.6249
Winsorized Mean ( 16 / 17 )	2873.92	37.218	77.2185
Winsorized Mean ( 17 / 17 )	2873.92	30.8737	93.0865
Trimmed Mean ( 1 / 17 )	2904.29	88.3754	32.8631
Trimmed Mean ( 2 / 17 )	2897.66	81.9237	35.3702
Trimmed Mean ( 3 / 17 )	2893.11	77.4895	37.3355
Trimmed Mean ( 4 / 17 )	2888.14	73.6053	39.2382
Trimmed Mean ( 5 / 17 )	2887.07	71.0103	40.6571
Trimmed Mean ( 6 / 17 )	2885.9	68.512	42.1225
Trimmed Mean ( 7 / 17 )	2884.59	65.0878	44.3185
Trimmed Mean ( 8 / 17 )	2886.57	61.5991	46.8606
Trimmed Mean ( 9 / 17 )	2888.79	58.065	49.7509
Trimmed Mean ( 10 / 17 )	2887.42	55.9338	51.622
Trimmed Mean ( 11 / 17 )	2883.79	53.4578	53.9452
Trimmed Mean ( 12 / 17 )	2879.63	51.3756	56.0505
Trimmed Mean ( 13 / 17 )	2874.8	49.8702	57.6456
Trimmed Mean ( 14 / 17 )	2869.13	47.2606	60.7087
Trimmed Mean ( 15 / 17 )	2868.1	45.5319	62.9909
Trimmed Mean ( 16 / 17 )	2863.68	43.5636	65.7358
Trimmed Mean ( 17 / 17 )	2861.76	41.4998	68.9585
Median	2880
Midrange	3300
Midmean - Weighted Average at Xnp	2879.63
Midmean - Weighted Average at X(n+1)p	2879.63
Midmean - Empirical Distribution Function	2879.63
Midmean - Empirical Distribution Function - Averaging	2879.63
Midmean - Empirical Distribution Function - Interpolation	2879.63
Midmean - Closest Observation	2879.63
Midmean - True Basic - Statistics Graphics Toolkit	2879.63
Midmean - MS Excel (old versions)	2879.63
Number of observations	51

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Parameters (Session):

par1 = 12 ; par2 = -0.3 ; par3 = 0 ; par4 = 1 ; par5 = 12 ; par6 = 3 ; par7 = 1 ; par8 = 2 ; par9 = 0 ; par10 = FALSE ;

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,'Arithmetic Mean',header=TRUE)
a<-table.element(a,signif(arm,6))
a<-table.element(a, signif(armse,6))
a<-table.element(a,signif(armose,6))
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Geometric Mean',header=TRUE)
a<-table.element(a,signif(geo,6))
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Harmonic Mean',header=TRUE)
a<-table.element(a,signif(har,6))
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Quadratic Mean',header=TRUE)
a<-table.element(a,signif(qua,6))
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, mylabel,header=TRUE)
a<-table.element(a,signif(win[j,1],6))
a<-table.element(a,signif(win[j,2],6))
a<-table.element(a,signif(win[j,1]/win[j,2],6))
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, mylabel,header=TRUE)
a<-table.element(a,signif(tri[j,1],6))
a<-table.element(a,signif(tri[j,2],6))
a<-table.element(a,signif(tri[j,1]/tri[j,2],6))
a<-table.row.end(a)
}
a<-table.row.start(a)
a<-table.element(a, 'Median',header=TRUE)
a<-table.element(a,signif(median(x),6))
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Midrange',header=TRUE)
a<-table.element(a,signif(midr,6))
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <-  'Midmean'
mylabel <- paste(mymid,'Weighted Average at Xnp',sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,signif(midm[1],6))
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <-  'Midmean'
mylabel <- paste(mymid,'Weighted Average at X(n+1)p',sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,signif(midm[2],6))
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <-  'Midmean'
mylabel <- paste(mymid,'Empirical Distribution Function',sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,signif(midm[3],6))
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <-  'Midmean'
mylabel <- paste(mymid,'Empirical Distribution Function - Averaging',sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,signif(midm[4],6))
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <-  'Midmean'
mylabel <- paste(mymid,'Empirical Distribution Function - Interpolation',sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,signif(midm[5],6))
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <-  'Midmean'
mylabel <- paste(mymid,'Closest Observation',sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,signif(midm[6],6))
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <-  'Midmean'
mylabel <- paste(mymid,'True Basic - Statistics Graphics Toolkit',sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,signif(midm[7],6))
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <-  'Midmean'
mylabel <- paste(mymid,'MS Excel (old versions)',sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,signif(midm[8],6))
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,signif(length(x),6))
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable.tab')

Free Statistics

Description of Statistical Computation

Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code