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rwasp_centraltendency.wasp

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Central Tendency

Date of computation

Sat, 05 Mar 2016 15:48:29 +0000

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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/Mar/05/t1457193226f9p1oyvas4asmc0.htm/, Retrieved Sat, 27 Apr 2024 10:24:08 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=293495, Retrieved Sat, 27 Apr 2024 10:24:08 +0000

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

-       [Central Tendency] [] [2016-03-05 15:48:29] [ed8c98a61958118f8b1101b2c94f1953] [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	2 seconds
R Server	'Sir Ronald Aylmer Fisher' @ fisher.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 & 2 seconds \tabularnewline
R Server & 'Sir Ronald Aylmer Fisher' @ fisher.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=293495&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]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Sir Ronald Aylmer Fisher' @ fisher.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=293495&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=293495&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	2 seconds
R Server	'Sir Ronald Aylmer Fisher' @ fisher.wessa.net

Central Tendency - Ungrouped Data
Measure	Value	S.E.	Value/S.E.
Arithmetic Mean	100.705	0.819801232636829	122.840752112668
Geometric Mean	100.501897478671
Harmonic Mean	100.327015483379
Quadratic Mean	100.941638005995
Winsorized Mean ( 1 / 24 )	100.705	0.819801232636829	122.840752112668
Winsorized Mean ( 2 / 24 )	100.705	0.819801232636829	122.840752112668
Winsorized Mean ( 3 / 24 )	99.4741666666667	0.273261881620529	364.025037362524
Winsorized Mean ( 4 / 24 )	99.4741666666667	0.273261881620529	364.025037362524
Winsorized Mean ( 5 / 24 )	99.4741666666667	0.273261881620529	364.025037362524
Winsorized Mean ( 6 / 24 )	99.4741666666667	0.273261881620529	364.025037362524
Winsorized Mean ( 7 / 24 )	99.4741666666667	0.273261881620529	364.025037362524
Winsorized Mean ( 8 / 24 )	99.4741666666667	0.273261881620529	364.025037362524
Winsorized Mean ( 9 / 24 )	99.4741666666667	0.273261881620529	364.025037362524
Winsorized Mean ( 10 / 24 )	99.4741666666667	0.273261881620529	364.025037362524
Winsorized Mean ( 11 / 24 )	99.4741666666667	0.273261881620529	364.025037362524
Winsorized Mean ( 12 / 24 )	99.5541666666667	0.26023416609855	382.556096146752
Winsorized Mean ( 13 / 24 )	99.5541666666667	0.26023416609855	382.556096146752
Winsorized Mean ( 14 / 24 )	99.5541666666667	0.26023416609855	382.556096146752
Winsorized Mean ( 15 / 24 )	99.2875	0.221413314039158	448.426059791692
Winsorized Mean ( 16 / 24 )	99.2875	0.221413314039158	448.426059791692
Winsorized Mean ( 17 / 24 )	99.2875	0.221413314039158	448.426059791692
Winsorized Mean ( 18 / 24 )	99.2825	0.220784253559257	449.68107280963
Winsorized Mean ( 19 / 24 )	99.2825	0.220784253559257	449.68107280963
Winsorized Mean ( 20 / 24 )	99.2825	0.220784253559257	449.68107280963
Winsorized Mean ( 21 / 24 )	100	0.116416566267042	858.984276950889
Winsorized Mean ( 22 / 24 )	100	0.116416566267042	858.984276950889
Winsorized Mean ( 23 / 24 )	100	0.116416566267042	858.984276950889
Winsorized Mean ( 24 / 24 )	100	0.116416566267042	858.984276950889
Trimmed Mean ( 1 / 24 )	100.321142857143	0.707827415269958	141.731078357401
Trimmed Mean ( 2 / 24 )	99.9147058823529	0.550832495926306	181.388546647619
Trimmed Mean ( 3 / 24 )	99.4836363636364	0.273532587249397	363.699394518324
Trimmed Mean ( 4 / 24 )	99.4871875	0.273102532924144	364.285114586005
Trimmed Mean ( 5 / 24 )	99.4909677419355	0.272323542067364	365.341046119783
Trimmed Mean ( 6 / 24 )	99.495	0.271123681827054	366.972738528486
Trimmed Mean ( 7 / 24 )	99.4993103448276	0.269413431776059	369.318298976026
Trimmed Mean ( 8 / 24 )	99.5039285714286	0.267080132750141	372.562075459639
Trimmed Mean ( 9 / 24 )	99.5088888888889	0.263980134285633	376.95597495688
Trimmed Mean ( 10 / 24 )	99.5142307692308	0.259927380819503	382.853974273433
Trimmed Mean ( 11 / 24 )	99.52	0.254676265089623	390.770612114081
Trimmed Mean ( 12 / 24 )	99.52625	0.247894793122903	401.485843031226
Trimmed Mean ( 13 / 24 )	99.5226086956522	0.24210578491665	411.070758717785
Trimmed Mean ( 14 / 24 )	99.5186363636364	0.234487338539679	424.409424335704
Trimmed Mean ( 15 / 24 )	99.5142857142857	0.224417724527566	443.433271252432
Trimmed Mean ( 16 / 24 )	99.5415	0.220028421823764	452.402917654563
Trimmed Mean ( 17 / 24 )	99.5715789473684	0.213778419975441	465.770019999245
Trimmed Mean ( 18 / 24 )	99.605	0.204923330610674	486.059833710374
Trimmed Mean ( 19 / 24 )	99.6429411764706	0.192420333035199	517.839978783547
Trimmed Mean ( 20 / 24 )	99.685625	0.174085709273872	572.623826595521
Trimmed Mean ( 21 / 24 )	99.734	0.145633455800087	684.828904540356
Trimmed Mean ( 22 / 24 )	99.7014285714286	0.144379455116415	690.551356431136
Trimmed Mean ( 23 / 24 )	99.6638461538462	0.141409472996877	704.7890359937
Trimmed Mean ( 24 / 24 )	99.62	0.13560652799472	734.625400953257
Median	99.58
Midrange	114.14
Midmean - Weighted Average at Xnp	99.1857142857143
Midmean - Weighted Average at X(n+1)p	99.1857142857143
Midmean - Empirical Distribution Function	99.1857142857143
Midmean - Empirical Distribution Function - Averaging	99.1857142857143
Midmean - Empirical Distribution Function - Interpolation	99.1857142857143
Midmean - Closest Observation	99.1857142857143
Midmean - True Basic - Statistics Graphics Toolkit	99.1857142857143
Midmean - MS Excel (old versions)	99.3246666666667
Number of observations	72

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 100.705 & 0.819801232636829 & 122.840752112668 \tabularnewline
Geometric Mean & 100.501897478671 &  &  \tabularnewline
Harmonic Mean & 100.327015483379 &  &  \tabularnewline
Quadratic Mean & 100.941638005995 &  &  \tabularnewline
Winsorized Mean ( 1 / 24 ) & 100.705 & 0.819801232636829 & 122.840752112668 \tabularnewline
Winsorized Mean ( 2 / 24 ) & 100.705 & 0.819801232636829 & 122.840752112668 \tabularnewline
Winsorized Mean ( 3 / 24 ) & 99.4741666666667 & 0.273261881620529 & 364.025037362524 \tabularnewline
Winsorized Mean ( 4 / 24 ) & 99.4741666666667 & 0.273261881620529 & 364.025037362524 \tabularnewline
Winsorized Mean ( 5 / 24 ) & 99.4741666666667 & 0.273261881620529 & 364.025037362524 \tabularnewline
Winsorized Mean ( 6 / 24 ) & 99.4741666666667 & 0.273261881620529 & 364.025037362524 \tabularnewline
Winsorized Mean ( 7 / 24 ) & 99.4741666666667 & 0.273261881620529 & 364.025037362524 \tabularnewline
Winsorized Mean ( 8 / 24 ) & 99.4741666666667 & 0.273261881620529 & 364.025037362524 \tabularnewline
Winsorized Mean ( 9 / 24 ) & 99.4741666666667 & 0.273261881620529 & 364.025037362524 \tabularnewline
Winsorized Mean ( 10 / 24 ) & 99.4741666666667 & 0.273261881620529 & 364.025037362524 \tabularnewline
Winsorized Mean ( 11 / 24 ) & 99.4741666666667 & 0.273261881620529 & 364.025037362524 \tabularnewline
Winsorized Mean ( 12 / 24 ) & 99.5541666666667 & 0.26023416609855 & 382.556096146752 \tabularnewline
Winsorized Mean ( 13 / 24 ) & 99.5541666666667 & 0.26023416609855 & 382.556096146752 \tabularnewline
Winsorized Mean ( 14 / 24 ) & 99.5541666666667 & 0.26023416609855 & 382.556096146752 \tabularnewline
Winsorized Mean ( 15 / 24 ) & 99.2875 & 0.221413314039158 & 448.426059791692 \tabularnewline
Winsorized Mean ( 16 / 24 ) & 99.2875 & 0.221413314039158 & 448.426059791692 \tabularnewline
Winsorized Mean ( 17 / 24 ) & 99.2875 & 0.221413314039158 & 448.426059791692 \tabularnewline
Winsorized Mean ( 18 / 24 ) & 99.2825 & 0.220784253559257 & 449.68107280963 \tabularnewline
Winsorized Mean ( 19 / 24 ) & 99.2825 & 0.220784253559257 & 449.68107280963 \tabularnewline
Winsorized Mean ( 20 / 24 ) & 99.2825 & 0.220784253559257 & 449.68107280963 \tabularnewline
Winsorized Mean ( 21 / 24 ) & 100 & 0.116416566267042 & 858.984276950889 \tabularnewline
Winsorized Mean ( 22 / 24 ) & 100 & 0.116416566267042 & 858.984276950889 \tabularnewline
Winsorized Mean ( 23 / 24 ) & 100 & 0.116416566267042 & 858.984276950889 \tabularnewline
Winsorized Mean ( 24 / 24 ) & 100 & 0.116416566267042 & 858.984276950889 \tabularnewline
Trimmed Mean ( 1 / 24 ) & 100.321142857143 & 0.707827415269958 & 141.731078357401 \tabularnewline
Trimmed Mean ( 2 / 24 ) & 99.9147058823529 & 0.550832495926306 & 181.388546647619 \tabularnewline
Trimmed Mean ( 3 / 24 ) & 99.4836363636364 & 0.273532587249397 & 363.699394518324 \tabularnewline
Trimmed Mean ( 4 / 24 ) & 99.4871875 & 0.273102532924144 & 364.285114586005 \tabularnewline
Trimmed Mean ( 5 / 24 ) & 99.4909677419355 & 0.272323542067364 & 365.341046119783 \tabularnewline
Trimmed Mean ( 6 / 24 ) & 99.495 & 0.271123681827054 & 366.972738528486 \tabularnewline
Trimmed Mean ( 7 / 24 ) & 99.4993103448276 & 0.269413431776059 & 369.318298976026 \tabularnewline
Trimmed Mean ( 8 / 24 ) & 99.5039285714286 & 0.267080132750141 & 372.562075459639 \tabularnewline
Trimmed Mean ( 9 / 24 ) & 99.5088888888889 & 0.263980134285633 & 376.95597495688 \tabularnewline
Trimmed Mean ( 10 / 24 ) & 99.5142307692308 & 0.259927380819503 & 382.853974273433 \tabularnewline
Trimmed Mean ( 11 / 24 ) & 99.52 & 0.254676265089623 & 390.770612114081 \tabularnewline
Trimmed Mean ( 12 / 24 ) & 99.52625 & 0.247894793122903 & 401.485843031226 \tabularnewline
Trimmed Mean ( 13 / 24 ) & 99.5226086956522 & 0.24210578491665 & 411.070758717785 \tabularnewline
Trimmed Mean ( 14 / 24 ) & 99.5186363636364 & 0.234487338539679 & 424.409424335704 \tabularnewline
Trimmed Mean ( 15 / 24 ) & 99.5142857142857 & 0.224417724527566 & 443.433271252432 \tabularnewline
Trimmed Mean ( 16 / 24 ) & 99.5415 & 0.220028421823764 & 452.402917654563 \tabularnewline
Trimmed Mean ( 17 / 24 ) & 99.5715789473684 & 0.213778419975441 & 465.770019999245 \tabularnewline
Trimmed Mean ( 18 / 24 ) & 99.605 & 0.204923330610674 & 486.059833710374 \tabularnewline
Trimmed Mean ( 19 / 24 ) & 99.6429411764706 & 0.192420333035199 & 517.839978783547 \tabularnewline
Trimmed Mean ( 20 / 24 ) & 99.685625 & 0.174085709273872 & 572.623826595521 \tabularnewline
Trimmed Mean ( 21 / 24 ) & 99.734 & 0.145633455800087 & 684.828904540356 \tabularnewline
Trimmed Mean ( 22 / 24 ) & 99.7014285714286 & 0.144379455116415 & 690.551356431136 \tabularnewline
Trimmed Mean ( 23 / 24 ) & 99.6638461538462 & 0.141409472996877 & 704.7890359937 \tabularnewline
Trimmed Mean ( 24 / 24 ) & 99.62 & 0.13560652799472 & 734.625400953257 \tabularnewline
Median & 99.58 &  &  \tabularnewline
Midrange & 114.14 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 99.1857142857143 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 99.1857142857143 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 99.1857142857143 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 99.1857142857143 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 99.1857142857143 &  &  \tabularnewline
Midmean - Closest Observation & 99.1857142857143 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 99.1857142857143 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 99.3246666666667 &  &  \tabularnewline
Number of observations & 72 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=293495&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]100.705[/C][C]0.819801232636829[/C][C]122.840752112668[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]100.501897478671[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]100.327015483379[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]100.941638005995[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 24 )[/C][C]100.705[/C][C]0.819801232636829[/C][C]122.840752112668[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 24 )[/C][C]100.705[/C][C]0.819801232636829[/C][C]122.840752112668[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 24 )[/C][C]99.4741666666667[/C][C]0.273261881620529[/C][C]364.025037362524[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 24 )[/C][C]99.4741666666667[/C][C]0.273261881620529[/C][C]364.025037362524[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 24 )[/C][C]99.4741666666667[/C][C]0.273261881620529[/C][C]364.025037362524[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 24 )[/C][C]99.4741666666667[/C][C]0.273261881620529[/C][C]364.025037362524[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 24 )[/C][C]99.4741666666667[/C][C]0.273261881620529[/C][C]364.025037362524[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 24 )[/C][C]99.4741666666667[/C][C]0.273261881620529[/C][C]364.025037362524[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 24 )[/C][C]99.4741666666667[/C][C]0.273261881620529[/C][C]364.025037362524[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 24 )[/C][C]99.4741666666667[/C][C]0.273261881620529[/C][C]364.025037362524[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 24 )[/C][C]99.4741666666667[/C][C]0.273261881620529[/C][C]364.025037362524[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 24 )[/C][C]99.5541666666667[/C][C]0.26023416609855[/C][C]382.556096146752[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 24 )[/C][C]99.5541666666667[/C][C]0.26023416609855[/C][C]382.556096146752[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 24 )[/C][C]99.5541666666667[/C][C]0.26023416609855[/C][C]382.556096146752[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 24 )[/C][C]99.2875[/C][C]0.221413314039158[/C][C]448.426059791692[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 24 )[/C][C]99.2875[/C][C]0.221413314039158[/C][C]448.426059791692[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 24 )[/C][C]99.2875[/C][C]0.221413314039158[/C][C]448.426059791692[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 24 )[/C][C]99.2825[/C][C]0.220784253559257[/C][C]449.68107280963[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 24 )[/C][C]99.2825[/C][C]0.220784253559257[/C][C]449.68107280963[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 24 )[/C][C]99.2825[/C][C]0.220784253559257[/C][C]449.68107280963[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 24 )[/C][C]100[/C][C]0.116416566267042[/C][C]858.984276950889[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 24 )[/C][C]100[/C][C]0.116416566267042[/C][C]858.984276950889[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 24 )[/C][C]100[/C][C]0.116416566267042[/C][C]858.984276950889[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 24 )[/C][C]100[/C][C]0.116416566267042[/C][C]858.984276950889[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 24 )[/C][C]100.321142857143[/C][C]0.707827415269958[/C][C]141.731078357401[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 24 )[/C][C]99.9147058823529[/C][C]0.550832495926306[/C][C]181.388546647619[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 24 )[/C][C]99.4836363636364[/C][C]0.273532587249397[/C][C]363.699394518324[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 24 )[/C][C]99.4871875[/C][C]0.273102532924144[/C][C]364.285114586005[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 24 )[/C][C]99.4909677419355[/C][C]0.272323542067364[/C][C]365.341046119783[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 24 )[/C][C]99.495[/C][C]0.271123681827054[/C][C]366.972738528486[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 24 )[/C][C]99.4993103448276[/C][C]0.269413431776059[/C][C]369.318298976026[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 24 )[/C][C]99.5039285714286[/C][C]0.267080132750141[/C][C]372.562075459639[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 24 )[/C][C]99.5088888888889[/C][C]0.263980134285633[/C][C]376.95597495688[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 24 )[/C][C]99.5142307692308[/C][C]0.259927380819503[/C][C]382.853974273433[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 24 )[/C][C]99.52[/C][C]0.254676265089623[/C][C]390.770612114081[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 24 )[/C][C]99.52625[/C][C]0.247894793122903[/C][C]401.485843031226[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 24 )[/C][C]99.5226086956522[/C][C]0.24210578491665[/C][C]411.070758717785[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 24 )[/C][C]99.5186363636364[/C][C]0.234487338539679[/C][C]424.409424335704[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 24 )[/C][C]99.5142857142857[/C][C]0.224417724527566[/C][C]443.433271252432[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 24 )[/C][C]99.5415[/C][C]0.220028421823764[/C][C]452.402917654563[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 24 )[/C][C]99.5715789473684[/C][C]0.213778419975441[/C][C]465.770019999245[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 24 )[/C][C]99.605[/C][C]0.204923330610674[/C][C]486.059833710374[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 24 )[/C][C]99.6429411764706[/C][C]0.192420333035199[/C][C]517.839978783547[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 24 )[/C][C]99.685625[/C][C]0.174085709273872[/C][C]572.623826595521[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 24 )[/C][C]99.734[/C][C]0.145633455800087[/C][C]684.828904540356[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 24 )[/C][C]99.7014285714286[/C][C]0.144379455116415[/C][C]690.551356431136[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 24 )[/C][C]99.6638461538462[/C][C]0.141409472996877[/C][C]704.7890359937[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 24 )[/C][C]99.62[/C][C]0.13560652799472[/C][C]734.625400953257[/C][/ROW]
[ROW][C]Median[/C][C]99.58[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]114.14[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]99.1857142857143[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]99.1857142857143[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]99.1857142857143[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]99.1857142857143[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]99.1857142857143[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]99.1857142857143[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]99.1857142857143[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]99.3246666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]72[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=293495&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=293495&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	100.705	0.819801232636829	122.840752112668
Geometric Mean	100.501897478671
Harmonic Mean	100.327015483379
Quadratic Mean	100.941638005995
Winsorized Mean ( 1 / 24 )	100.705	0.819801232636829	122.840752112668
Winsorized Mean ( 2 / 24 )	100.705	0.819801232636829	122.840752112668
Winsorized Mean ( 3 / 24 )	99.4741666666667	0.273261881620529	364.025037362524
Winsorized Mean ( 4 / 24 )	99.4741666666667	0.273261881620529	364.025037362524
Winsorized Mean ( 5 / 24 )	99.4741666666667	0.273261881620529	364.025037362524
Winsorized Mean ( 6 / 24 )	99.4741666666667	0.273261881620529	364.025037362524
Winsorized Mean ( 7 / 24 )	99.4741666666667	0.273261881620529	364.025037362524
Winsorized Mean ( 8 / 24 )	99.4741666666667	0.273261881620529	364.025037362524
Winsorized Mean ( 9 / 24 )	99.4741666666667	0.273261881620529	364.025037362524
Winsorized Mean ( 10 / 24 )	99.4741666666667	0.273261881620529	364.025037362524
Winsorized Mean ( 11 / 24 )	99.4741666666667	0.273261881620529	364.025037362524
Winsorized Mean ( 12 / 24 )	99.5541666666667	0.26023416609855	382.556096146752
Winsorized Mean ( 13 / 24 )	99.5541666666667	0.26023416609855	382.556096146752
Winsorized Mean ( 14 / 24 )	99.5541666666667	0.26023416609855	382.556096146752
Winsorized Mean ( 15 / 24 )	99.2875	0.221413314039158	448.426059791692
Winsorized Mean ( 16 / 24 )	99.2875	0.221413314039158	448.426059791692
Winsorized Mean ( 17 / 24 )	99.2875	0.221413314039158	448.426059791692
Winsorized Mean ( 18 / 24 )	99.2825	0.220784253559257	449.68107280963
Winsorized Mean ( 19 / 24 )	99.2825	0.220784253559257	449.68107280963
Winsorized Mean ( 20 / 24 )	99.2825	0.220784253559257	449.68107280963
Winsorized Mean ( 21 / 24 )	100	0.116416566267042	858.984276950889
Winsorized Mean ( 22 / 24 )	100	0.116416566267042	858.984276950889
Winsorized Mean ( 23 / 24 )	100	0.116416566267042	858.984276950889
Winsorized Mean ( 24 / 24 )	100	0.116416566267042	858.984276950889
Trimmed Mean ( 1 / 24 )	100.321142857143	0.707827415269958	141.731078357401
Trimmed Mean ( 2 / 24 )	99.9147058823529	0.550832495926306	181.388546647619
Trimmed Mean ( 3 / 24 )	99.4836363636364	0.273532587249397	363.699394518324
Trimmed Mean ( 4 / 24 )	99.4871875	0.273102532924144	364.285114586005
Trimmed Mean ( 5 / 24 )	99.4909677419355	0.272323542067364	365.341046119783
Trimmed Mean ( 6 / 24 )	99.495	0.271123681827054	366.972738528486
Trimmed Mean ( 7 / 24 )	99.4993103448276	0.269413431776059	369.318298976026
Trimmed Mean ( 8 / 24 )	99.5039285714286	0.267080132750141	372.562075459639
Trimmed Mean ( 9 / 24 )	99.5088888888889	0.263980134285633	376.95597495688
Trimmed Mean ( 10 / 24 )	99.5142307692308	0.259927380819503	382.853974273433
Trimmed Mean ( 11 / 24 )	99.52	0.254676265089623	390.770612114081
Trimmed Mean ( 12 / 24 )	99.52625	0.247894793122903	401.485843031226
Trimmed Mean ( 13 / 24 )	99.5226086956522	0.24210578491665	411.070758717785
Trimmed Mean ( 14 / 24 )	99.5186363636364	0.234487338539679	424.409424335704
Trimmed Mean ( 15 / 24 )	99.5142857142857	0.224417724527566	443.433271252432
Trimmed Mean ( 16 / 24 )	99.5415	0.220028421823764	452.402917654563
Trimmed Mean ( 17 / 24 )	99.5715789473684	0.213778419975441	465.770019999245
Trimmed Mean ( 18 / 24 )	99.605	0.204923330610674	486.059833710374
Trimmed Mean ( 19 / 24 )	99.6429411764706	0.192420333035199	517.839978783547
Trimmed Mean ( 20 / 24 )	99.685625	0.174085709273872	572.623826595521
Trimmed Mean ( 21 / 24 )	99.734	0.145633455800087	684.828904540356
Trimmed Mean ( 22 / 24 )	99.7014285714286	0.144379455116415	690.551356431136
Trimmed Mean ( 23 / 24 )	99.6638461538462	0.141409472996877	704.7890359937
Trimmed Mean ( 24 / 24 )	99.62	0.13560652799472	734.625400953257
Median	99.58
Midrange	114.14
Midmean - Weighted Average at Xnp	99.1857142857143
Midmean - Weighted Average at X(n+1)p	99.1857142857143
Midmean - Empirical Distribution Function	99.1857142857143
Midmean - Empirical Distribution Function - Averaging	99.1857142857143
Midmean - Empirical Distribution Function - Interpolation	99.1857142857143
Midmean - Closest Observation	99.1857142857143
Midmean - True Basic - Statistics Graphics Toolkit	99.1857142857143
Midmean - MS Excel (old versions)	99.3246666666667
Number of observations	72

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,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')

Free Statistics

Description of Statistical Computation

Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code