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R Software Module

rwasp_centraltendency.wasp

Title produced by software

Central Tendency

Date of computation

Thu, 15 Dec 2016 11:38:29 +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/15/t1481798366ro4mfc5mlacxb1w.htm/, Retrieved Fri, 03 May 2024 10:37:00 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=299835, Retrieved Fri, 03 May 2024 10:37:00 +0000

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Estimated Impact

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

-       [Central Tendency] [CT Mannen] [2016-12-15 10:38:29] [ada7696de20b35d9f514c719a1db97fd] [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

\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
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=299835&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] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=299835&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=299835&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

Central Tendency - Ungrouped Data
Measure	Value	S.E.	Value/S.E.
Arithmetic Mean	4.31707	0.099499	43.3881
Geometric Mean	4.18514
Harmonic Mean	3.98058
Quadratic Mean	4.40897
Winsorized Mean ( 1 / 27 )	4.32927	0.0951312	45.5084
Winsorized Mean ( 2 / 27 )	4.32927	0.0951312	45.5084
Winsorized Mean ( 3 / 27 )	4.32927	0.0951312	45.5084
Winsorized Mean ( 4 / 27 )	4.32927	0.0951312	45.5084
Winsorized Mean ( 5 / 27 )	4.39024	0.0790567	55.5329
Winsorized Mean ( 6 / 27 )	4.39024	0.0790567	55.5329
Winsorized Mean ( 7 / 27 )	4.39024	0.0790567	55.5329
Winsorized Mean ( 8 / 27 )	4.39024	0.0790567	55.5329
Winsorized Mean ( 9 / 27 )	4.39024	0.0790567	55.5329
Winsorized Mean ( 10 / 27 )	4.39024	0.0790567	55.5329
Winsorized Mean ( 11 / 27 )	4.52439	0.0554894	81.5361
Winsorized Mean ( 12 / 27 )	4.52439	0.0554894	81.5361
Winsorized Mean ( 13 / 27 )	4.52439	0.0554894	81.5361
Winsorized Mean ( 14 / 27 )	4.52439	0.0554894	81.5361
Winsorized Mean ( 15 / 27 )	4.52439	0.0554894	81.5361
Winsorized Mean ( 16 / 27 )	4.52439	0.0554894	81.5361
Winsorized Mean ( 17 / 27 )	4.52439	0.0554894	81.5361
Winsorized Mean ( 18 / 27 )	4.52439	0.0554894	81.5361
Winsorized Mean ( 19 / 27 )	4.52439	0.0554894	81.5361
Winsorized Mean ( 20 / 27 )	4.52439	0.0554894	81.5361
Winsorized Mean ( 21 / 27 )	4.52439	0.0554894	81.5361
Winsorized Mean ( 22 / 27 )	4.52439	0.0554894	81.5361
Winsorized Mean ( 23 / 27 )	4.52439	0.0554894	81.5361
Winsorized Mean ( 24 / 27 )	4.52439	0.0554894	81.5361
Winsorized Mean ( 25 / 27 )	4.52439	0.0554894	81.5361
Winsorized Mean ( 26 / 27 )	4.52439	0.0554894	81.5361
Winsorized Mean ( 27 / 27 )	4.52439	0.0554894	81.5361
Trimmed Mean ( 1 / 27 )	4.35	0.0926064	46.973
Trimmed Mean ( 2 / 27 )	4.37179	0.0896008	48.7919
Trimmed Mean ( 3 / 27 )	4.39474	0.0860007	51.1012
Trimmed Mean ( 4 / 27 )	4.41892	0.0816499	54.1203
Trimmed Mean ( 5 / 27 )	4.44444	0.0763222	58.2327
Trimmed Mean ( 6 / 27 )	4.45714	0.0752792	59.2081
Trimmed Mean ( 7 / 27 )	4.47059	0.0739889	60.4224
Trimmed Mean ( 8 / 27 )	4.48485	0.0723963	61.9486
Trimmed Mean ( 9 / 27 )	4.5	0.0704295	63.8937
Trimmed Mean ( 10 / 27 )	4.51613	0.067992	66.4214
Trimmed Mean ( 11 / 27 )	4.53333	0.0649496	69.7977
Trimmed Mean ( 12 / 27 )	4.53448	0.0660689	68.6326
Trimmed Mean ( 13 / 27 )	4.53571	0.0672478	67.4478
Trimmed Mean ( 14 / 27 )	4.53704	0.0684916	66.2422
Trimmed Mean ( 15 / 27 )	4.53846	0.0698066	65.0148
Trimmed Mean ( 16 / 27 )	4.54	0.0711996	63.7644
Trimmed Mean ( 17 / 27 )	4.54167	0.0726788	62.4896
Trimmed Mean ( 18 / 27 )	4.54348	0.0742533	61.1889
Trimmed Mean ( 19 / 27 )	4.54545	0.0759336	59.8609
Trimmed Mean ( 20 / 27 )	4.54762	0.0777319	58.5039
Trimmed Mean ( 21 / 27 )	4.55	0.0796628	57.1158
Trimmed Mean ( 22 / 27 )	4.55263	0.0817428	55.6946
Trimmed Mean ( 23 / 27 )	4.55556	0.0839921	54.2379
Trimmed Mean ( 24 / 27 )	4.55882	0.0864344	52.7432
Trimmed Mean ( 25 / 27 )	4.5625	0.0890983	51.2075
Trimmed Mean ( 26 / 27 )	4.56667	0.0920187	49.6276
Trimmed Mean ( 27 / 27 )	4.57143	0.0952381	48
Median	5
Midrange	3
Midmean - Weighted Average at Xnp	4.60563
Midmean - Weighted Average at X(n+1)p	4.60563
Midmean - Empirical Distribution Function	4.60563
Midmean - Empirical Distribution Function - Averaging	4.60563
Midmean - Empirical Distribution Function - Interpolation	4.60563
Midmean - Closest Observation	4.60563
Midmean - True Basic - Statistics Graphics Toolkit	4.60563
Midmean - MS Excel (old versions)	4.60563
Number of observations	82

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 4.31707 & 0.099499 & 43.3881 \tabularnewline
Geometric Mean & 4.18514 &  &  \tabularnewline
Harmonic Mean & 3.98058 &  &  \tabularnewline
Quadratic Mean & 4.40897 &  &  \tabularnewline
Winsorized Mean ( 1 / 27 ) & 4.32927 & 0.0951312 & 45.5084 \tabularnewline
Winsorized Mean ( 2 / 27 ) & 4.32927 & 0.0951312 & 45.5084 \tabularnewline
Winsorized Mean ( 3 / 27 ) & 4.32927 & 0.0951312 & 45.5084 \tabularnewline
Winsorized Mean ( 4 / 27 ) & 4.32927 & 0.0951312 & 45.5084 \tabularnewline
Winsorized Mean ( 5 / 27 ) & 4.39024 & 0.0790567 & 55.5329 \tabularnewline
Winsorized Mean ( 6 / 27 ) & 4.39024 & 0.0790567 & 55.5329 \tabularnewline
Winsorized Mean ( 7 / 27 ) & 4.39024 & 0.0790567 & 55.5329 \tabularnewline
Winsorized Mean ( 8 / 27 ) & 4.39024 & 0.0790567 & 55.5329 \tabularnewline
Winsorized Mean ( 9 / 27 ) & 4.39024 & 0.0790567 & 55.5329 \tabularnewline
Winsorized Mean ( 10 / 27 ) & 4.39024 & 0.0790567 & 55.5329 \tabularnewline
Winsorized Mean ( 11 / 27 ) & 4.52439 & 0.0554894 & 81.5361 \tabularnewline
Winsorized Mean ( 12 / 27 ) & 4.52439 & 0.0554894 & 81.5361 \tabularnewline
Winsorized Mean ( 13 / 27 ) & 4.52439 & 0.0554894 & 81.5361 \tabularnewline
Winsorized Mean ( 14 / 27 ) & 4.52439 & 0.0554894 & 81.5361 \tabularnewline
Winsorized Mean ( 15 / 27 ) & 4.52439 & 0.0554894 & 81.5361 \tabularnewline
Winsorized Mean ( 16 / 27 ) & 4.52439 & 0.0554894 & 81.5361 \tabularnewline
Winsorized Mean ( 17 / 27 ) & 4.52439 & 0.0554894 & 81.5361 \tabularnewline
Winsorized Mean ( 18 / 27 ) & 4.52439 & 0.0554894 & 81.5361 \tabularnewline
Winsorized Mean ( 19 / 27 ) & 4.52439 & 0.0554894 & 81.5361 \tabularnewline
Winsorized Mean ( 20 / 27 ) & 4.52439 & 0.0554894 & 81.5361 \tabularnewline
Winsorized Mean ( 21 / 27 ) & 4.52439 & 0.0554894 & 81.5361 \tabularnewline
Winsorized Mean ( 22 / 27 ) & 4.52439 & 0.0554894 & 81.5361 \tabularnewline
Winsorized Mean ( 23 / 27 ) & 4.52439 & 0.0554894 & 81.5361 \tabularnewline
Winsorized Mean ( 24 / 27 ) & 4.52439 & 0.0554894 & 81.5361 \tabularnewline
Winsorized Mean ( 25 / 27 ) & 4.52439 & 0.0554894 & 81.5361 \tabularnewline
Winsorized Mean ( 26 / 27 ) & 4.52439 & 0.0554894 & 81.5361 \tabularnewline
Winsorized Mean ( 27 / 27 ) & 4.52439 & 0.0554894 & 81.5361 \tabularnewline
Trimmed Mean ( 1 / 27 ) & 4.35 & 0.0926064 & 46.973 \tabularnewline
Trimmed Mean ( 2 / 27 ) & 4.37179 & 0.0896008 & 48.7919 \tabularnewline
Trimmed Mean ( 3 / 27 ) & 4.39474 & 0.0860007 & 51.1012 \tabularnewline
Trimmed Mean ( 4 / 27 ) & 4.41892 & 0.0816499 & 54.1203 \tabularnewline
Trimmed Mean ( 5 / 27 ) & 4.44444 & 0.0763222 & 58.2327 \tabularnewline
Trimmed Mean ( 6 / 27 ) & 4.45714 & 0.0752792 & 59.2081 \tabularnewline
Trimmed Mean ( 7 / 27 ) & 4.47059 & 0.0739889 & 60.4224 \tabularnewline
Trimmed Mean ( 8 / 27 ) & 4.48485 & 0.0723963 & 61.9486 \tabularnewline
Trimmed Mean ( 9 / 27 ) & 4.5 & 0.0704295 & 63.8937 \tabularnewline
Trimmed Mean ( 10 / 27 ) & 4.51613 & 0.067992 & 66.4214 \tabularnewline
Trimmed Mean ( 11 / 27 ) & 4.53333 & 0.0649496 & 69.7977 \tabularnewline
Trimmed Mean ( 12 / 27 ) & 4.53448 & 0.0660689 & 68.6326 \tabularnewline
Trimmed Mean ( 13 / 27 ) & 4.53571 & 0.0672478 & 67.4478 \tabularnewline
Trimmed Mean ( 14 / 27 ) & 4.53704 & 0.0684916 & 66.2422 \tabularnewline
Trimmed Mean ( 15 / 27 ) & 4.53846 & 0.0698066 & 65.0148 \tabularnewline
Trimmed Mean ( 16 / 27 ) & 4.54 & 0.0711996 & 63.7644 \tabularnewline
Trimmed Mean ( 17 / 27 ) & 4.54167 & 0.0726788 & 62.4896 \tabularnewline
Trimmed Mean ( 18 / 27 ) & 4.54348 & 0.0742533 & 61.1889 \tabularnewline
Trimmed Mean ( 19 / 27 ) & 4.54545 & 0.0759336 & 59.8609 \tabularnewline
Trimmed Mean ( 20 / 27 ) & 4.54762 & 0.0777319 & 58.5039 \tabularnewline
Trimmed Mean ( 21 / 27 ) & 4.55 & 0.0796628 & 57.1158 \tabularnewline
Trimmed Mean ( 22 / 27 ) & 4.55263 & 0.0817428 & 55.6946 \tabularnewline
Trimmed Mean ( 23 / 27 ) & 4.55556 & 0.0839921 & 54.2379 \tabularnewline
Trimmed Mean ( 24 / 27 ) & 4.55882 & 0.0864344 & 52.7432 \tabularnewline
Trimmed Mean ( 25 / 27 ) & 4.5625 & 0.0890983 & 51.2075 \tabularnewline
Trimmed Mean ( 26 / 27 ) & 4.56667 & 0.0920187 & 49.6276 \tabularnewline
Trimmed Mean ( 27 / 27 ) & 4.57143 & 0.0952381 & 48 \tabularnewline
Median & 5 &  &  \tabularnewline
Midrange & 3 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 4.60563 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 4.60563 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 4.60563 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 4.60563 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 4.60563 &  &  \tabularnewline
Midmean - Closest Observation & 4.60563 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 4.60563 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 4.60563 &  &  \tabularnewline
Number of observations & 82 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=299835&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]4.31707[/C][C]0.099499[/C][C]43.3881[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]4.18514[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]3.98058[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]4.40897[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 27 )[/C][C]4.32927[/C][C]0.0951312[/C][C]45.5084[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 27 )[/C][C]4.32927[/C][C]0.0951312[/C][C]45.5084[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 27 )[/C][C]4.32927[/C][C]0.0951312[/C][C]45.5084[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 27 )[/C][C]4.32927[/C][C]0.0951312[/C][C]45.5084[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 27 )[/C][C]4.39024[/C][C]0.0790567[/C][C]55.5329[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 27 )[/C][C]4.39024[/C][C]0.0790567[/C][C]55.5329[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 27 )[/C][C]4.39024[/C][C]0.0790567[/C][C]55.5329[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 27 )[/C][C]4.39024[/C][C]0.0790567[/C][C]55.5329[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 27 )[/C][C]4.39024[/C][C]0.0790567[/C][C]55.5329[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 27 )[/C][C]4.39024[/C][C]0.0790567[/C][C]55.5329[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 27 )[/C][C]4.52439[/C][C]0.0554894[/C][C]81.5361[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 27 )[/C][C]4.52439[/C][C]0.0554894[/C][C]81.5361[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 27 )[/C][C]4.52439[/C][C]0.0554894[/C][C]81.5361[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 27 )[/C][C]4.52439[/C][C]0.0554894[/C][C]81.5361[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 27 )[/C][C]4.52439[/C][C]0.0554894[/C][C]81.5361[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 27 )[/C][C]4.52439[/C][C]0.0554894[/C][C]81.5361[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 27 )[/C][C]4.52439[/C][C]0.0554894[/C][C]81.5361[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 27 )[/C][C]4.52439[/C][C]0.0554894[/C][C]81.5361[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 27 )[/C][C]4.52439[/C][C]0.0554894[/C][C]81.5361[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 27 )[/C][C]4.52439[/C][C]0.0554894[/C][C]81.5361[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 27 )[/C][C]4.52439[/C][C]0.0554894[/C][C]81.5361[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 27 )[/C][C]4.52439[/C][C]0.0554894[/C][C]81.5361[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 27 )[/C][C]4.52439[/C][C]0.0554894[/C][C]81.5361[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 27 )[/C][C]4.52439[/C][C]0.0554894[/C][C]81.5361[/C][/ROW]
[ROW][C]Winsorized Mean ( 25 / 27 )[/C][C]4.52439[/C][C]0.0554894[/C][C]81.5361[/C][/ROW]
[ROW][C]Winsorized Mean ( 26 / 27 )[/C][C]4.52439[/C][C]0.0554894[/C][C]81.5361[/C][/ROW]
[ROW][C]Winsorized Mean ( 27 / 27 )[/C][C]4.52439[/C][C]0.0554894[/C][C]81.5361[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 27 )[/C][C]4.35[/C][C]0.0926064[/C][C]46.973[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 27 )[/C][C]4.37179[/C][C]0.0896008[/C][C]48.7919[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 27 )[/C][C]4.39474[/C][C]0.0860007[/C][C]51.1012[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 27 )[/C][C]4.41892[/C][C]0.0816499[/C][C]54.1203[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 27 )[/C][C]4.44444[/C][C]0.0763222[/C][C]58.2327[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 27 )[/C][C]4.45714[/C][C]0.0752792[/C][C]59.2081[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 27 )[/C][C]4.47059[/C][C]0.0739889[/C][C]60.4224[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 27 )[/C][C]4.48485[/C][C]0.0723963[/C][C]61.9486[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 27 )[/C][C]4.5[/C][C]0.0704295[/C][C]63.8937[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 27 )[/C][C]4.51613[/C][C]0.067992[/C][C]66.4214[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 27 )[/C][C]4.53333[/C][C]0.0649496[/C][C]69.7977[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 27 )[/C][C]4.53448[/C][C]0.0660689[/C][C]68.6326[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 27 )[/C][C]4.53571[/C][C]0.0672478[/C][C]67.4478[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 27 )[/C][C]4.53704[/C][C]0.0684916[/C][C]66.2422[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 27 )[/C][C]4.53846[/C][C]0.0698066[/C][C]65.0148[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 27 )[/C][C]4.54[/C][C]0.0711996[/C][C]63.7644[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 27 )[/C][C]4.54167[/C][C]0.0726788[/C][C]62.4896[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 27 )[/C][C]4.54348[/C][C]0.0742533[/C][C]61.1889[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 27 )[/C][C]4.54545[/C][C]0.0759336[/C][C]59.8609[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 27 )[/C][C]4.54762[/C][C]0.0777319[/C][C]58.5039[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 27 )[/C][C]4.55[/C][C]0.0796628[/C][C]57.1158[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 27 )[/C][C]4.55263[/C][C]0.0817428[/C][C]55.6946[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 27 )[/C][C]4.55556[/C][C]0.0839921[/C][C]54.2379[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 27 )[/C][C]4.55882[/C][C]0.0864344[/C][C]52.7432[/C][/ROW]
[ROW][C]Trimmed Mean ( 25 / 27 )[/C][C]4.5625[/C][C]0.0890983[/C][C]51.2075[/C][/ROW]
[ROW][C]Trimmed Mean ( 26 / 27 )[/C][C]4.56667[/C][C]0.0920187[/C][C]49.6276[/C][/ROW]
[ROW][C]Trimmed Mean ( 27 / 27 )[/C][C]4.57143[/C][C]0.0952381[/C][C]48[/C][/ROW]
[ROW][C]Median[/C][C]5[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]3[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]4.60563[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]4.60563[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]4.60563[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]4.60563[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]4.60563[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]4.60563[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]4.60563[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]4.60563[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]82[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=299835&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=299835&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	4.31707	0.099499	43.3881
Geometric Mean	4.18514
Harmonic Mean	3.98058
Quadratic Mean	4.40897
Winsorized Mean ( 1 / 27 )	4.32927	0.0951312	45.5084
Winsorized Mean ( 2 / 27 )	4.32927	0.0951312	45.5084
Winsorized Mean ( 3 / 27 )	4.32927	0.0951312	45.5084
Winsorized Mean ( 4 / 27 )	4.32927	0.0951312	45.5084
Winsorized Mean ( 5 / 27 )	4.39024	0.0790567	55.5329
Winsorized Mean ( 6 / 27 )	4.39024	0.0790567	55.5329
Winsorized Mean ( 7 / 27 )	4.39024	0.0790567	55.5329
Winsorized Mean ( 8 / 27 )	4.39024	0.0790567	55.5329
Winsorized Mean ( 9 / 27 )	4.39024	0.0790567	55.5329
Winsorized Mean ( 10 / 27 )	4.39024	0.0790567	55.5329
Winsorized Mean ( 11 / 27 )	4.52439	0.0554894	81.5361
Winsorized Mean ( 12 / 27 )	4.52439	0.0554894	81.5361
Winsorized Mean ( 13 / 27 )	4.52439	0.0554894	81.5361
Winsorized Mean ( 14 / 27 )	4.52439	0.0554894	81.5361
Winsorized Mean ( 15 / 27 )	4.52439	0.0554894	81.5361
Winsorized Mean ( 16 / 27 )	4.52439	0.0554894	81.5361
Winsorized Mean ( 17 / 27 )	4.52439	0.0554894	81.5361
Winsorized Mean ( 18 / 27 )	4.52439	0.0554894	81.5361
Winsorized Mean ( 19 / 27 )	4.52439	0.0554894	81.5361
Winsorized Mean ( 20 / 27 )	4.52439	0.0554894	81.5361
Winsorized Mean ( 21 / 27 )	4.52439	0.0554894	81.5361
Winsorized Mean ( 22 / 27 )	4.52439	0.0554894	81.5361
Winsorized Mean ( 23 / 27 )	4.52439	0.0554894	81.5361
Winsorized Mean ( 24 / 27 )	4.52439	0.0554894	81.5361
Winsorized Mean ( 25 / 27 )	4.52439	0.0554894	81.5361
Winsorized Mean ( 26 / 27 )	4.52439	0.0554894	81.5361
Winsorized Mean ( 27 / 27 )	4.52439	0.0554894	81.5361
Trimmed Mean ( 1 / 27 )	4.35	0.0926064	46.973
Trimmed Mean ( 2 / 27 )	4.37179	0.0896008	48.7919
Trimmed Mean ( 3 / 27 )	4.39474	0.0860007	51.1012
Trimmed Mean ( 4 / 27 )	4.41892	0.0816499	54.1203
Trimmed Mean ( 5 / 27 )	4.44444	0.0763222	58.2327
Trimmed Mean ( 6 / 27 )	4.45714	0.0752792	59.2081
Trimmed Mean ( 7 / 27 )	4.47059	0.0739889	60.4224
Trimmed Mean ( 8 / 27 )	4.48485	0.0723963	61.9486
Trimmed Mean ( 9 / 27 )	4.5	0.0704295	63.8937
Trimmed Mean ( 10 / 27 )	4.51613	0.067992	66.4214
Trimmed Mean ( 11 / 27 )	4.53333	0.0649496	69.7977
Trimmed Mean ( 12 / 27 )	4.53448	0.0660689	68.6326
Trimmed Mean ( 13 / 27 )	4.53571	0.0672478	67.4478
Trimmed Mean ( 14 / 27 )	4.53704	0.0684916	66.2422
Trimmed Mean ( 15 / 27 )	4.53846	0.0698066	65.0148
Trimmed Mean ( 16 / 27 )	4.54	0.0711996	63.7644
Trimmed Mean ( 17 / 27 )	4.54167	0.0726788	62.4896
Trimmed Mean ( 18 / 27 )	4.54348	0.0742533	61.1889
Trimmed Mean ( 19 / 27 )	4.54545	0.0759336	59.8609
Trimmed Mean ( 20 / 27 )	4.54762	0.0777319	58.5039
Trimmed Mean ( 21 / 27 )	4.55	0.0796628	57.1158
Trimmed Mean ( 22 / 27 )	4.55263	0.0817428	55.6946
Trimmed Mean ( 23 / 27 )	4.55556	0.0839921	54.2379
Trimmed Mean ( 24 / 27 )	4.55882	0.0864344	52.7432
Trimmed Mean ( 25 / 27 )	4.5625	0.0890983	51.2075
Trimmed Mean ( 26 / 27 )	4.56667	0.0920187	49.6276
Trimmed Mean ( 27 / 27 )	4.57143	0.0952381	48
Median	5
Midrange	3
Midmean - Weighted Average at Xnp	4.60563
Midmean - Weighted Average at X(n+1)p	4.60563
Midmean - Empirical Distribution Function	4.60563
Midmean - Empirical Distribution Function - Averaging	4.60563
Midmean - Empirical Distribution Function - Interpolation	4.60563
Midmean - Closest Observation	4.60563
Midmean - True Basic - Statistics Graphics Toolkit	4.60563
Midmean - MS Excel (old versions)	4.60563
Number of observations	82

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

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,'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