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R Software Module

rwasp_centraltendency.wasp

Title produced by software

Central Tendency

Date of computation

Tue, 08 Dec 2015 14:36:39 +0000

Cite this page as follows

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2015/Dec/08/t14495856144h3ed4qkskxb26o.htm/, Retrieved Thu, 16 May 2024 08:26:07 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=285503, Retrieved Thu, 16 May 2024 08:26:07 +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] [Central tendency ...] [2015-12-08 14:36:39] [c64ec7a2d0db7c519901da97df98e10d] [Current]

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1.9
2
2
1.8
1.6
1.4
0.2
0.3
0.4
0.7
1
1.1
0.8
0.8
1
1.1
1
0.8
1.6
1.5
1.6
1.6
1.6
1.9
2
1.9
2
2.1
2.3
2.3
2.6
2.6
2.7
2.6
2.6
2.4
2.5
2.5
2.5
2.4
2.1
2.1
2.3
2.3
2.3
2.9
2.8
2.9
3
3
2.9
2.6
2.8
2.9
3.1
2.8
2.4
1.6
1.5
1.7
1.4
1.1
0.8
1.2
0.8
0.9
0.9
1
0.9
1.1
1
0.7

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	'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 & 1 seconds \tabularnewline
R Server & 'Sir Ronald Aylmer Fisher' @ fisher.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=285503&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]'Sir Ronald Aylmer Fisher' @ fisher.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=285503&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=285503&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	'Sir Ronald Aylmer Fisher' @ fisher.wessa.net

Central Tendency - Ungrouped Data
Measure	Value	S.E.	Value/S.E.
Arithmetic Mean	1.79861111111111	0.092320397382751	19.4822721966225
Geometric Mean	1.58191817201876
Harmonic Mean	1.29115402212179
Quadratic Mean	1.95962723212577
Winsorized Mean ( 1 / 24 )	1.79861111111111	0.0917251852384331	19.6086942363294
Winsorized Mean ( 2 / 24 )	1.80138888888889	0.091104616118358	19.7727509937436
Winsorized Mean ( 3 / 24 )	1.80972222222222	0.087884182798493	20.5921266443551
Winsorized Mean ( 4 / 24 )	1.80972222222222	0.087884182798493	20.5921266443551
Winsorized Mean ( 5 / 24 )	1.81666666666667	0.0866928454502975	20.9552086706877
Winsorized Mean ( 6 / 24 )	1.81666666666667	0.0866928454502975	20.9552086706877
Winsorized Mean ( 7 / 24 )	1.80694444444444	0.0850371912764719	21.2488726088063
Winsorized Mean ( 8 / 24 )	1.80694444444444	0.0850371912764719	21.2488726088063
Winsorized Mean ( 9 / 24 )	1.80694444444444	0.0850371912764719	21.2488726088063
Winsorized Mean ( 10 / 24 )	1.80694444444444	0.0805479665628231	22.4331478689176
Winsorized Mean ( 11 / 24 )	1.79166666666667	0.078242380520701	22.8989283652053
Winsorized Mean ( 12 / 24 )	1.79166666666667	0.078242380520701	22.8989283652053
Winsorized Mean ( 13 / 24 )	1.80972222222222	0.0754267909377481	23.9930958181137
Winsorized Mean ( 14 / 24 )	1.80972222222222	0.0754267909377481	23.9930958181137
Winsorized Mean ( 15 / 24 )	1.80972222222222	0.0754267909377481	23.9930958181137
Winsorized Mean ( 16 / 24 )	1.7875	0.0722415933453622	24.7433634451358
Winsorized Mean ( 17 / 24 )	1.7875	0.0722415933453622	24.7433634451358
Winsorized Mean ( 18 / 24 )	1.8125	0.0684885303900746	26.4642851828905
Winsorized Mean ( 19 / 24 )	1.78611111111111	0.0648612807583242	27.537401208068
Winsorized Mean ( 20 / 24 )	1.78611111111111	0.0648612807583242	27.537401208068
Winsorized Mean ( 21 / 24 )	1.78611111111111	0.0648612807583242	27.537401208068
Winsorized Mean ( 22 / 24 )	1.78611111111111	0.0563393458592208	31.7027307270162
Winsorized Mean ( 23 / 24 )	1.85	0.0473474818502387	39.0728276923279
Winsorized Mean ( 24 / 24 )	1.85	0.0473474818502387	39.0728276923279
Trimmed Mean ( 1 / 24 )	1.80285714285714	0.090225652900323	19.9816469585302
Trimmed Mean ( 2 / 24 )	1.80735294117647	0.0884287825847621	20.4385143428166
Trimmed Mean ( 3 / 24 )	1.81060606060606	0.0866665444112134	20.8916378621852
Trimmed Mean ( 4 / 24 )	1.8109375	0.0859735674674222	21.0638868822818
Trimmed Mean ( 5 / 24 )	1.81129032258065	0.0850888371022697	21.28704991471
Trimmed Mean ( 6 / 24 )	1.81	0.0843285208872316	21.4636754084709
Trimmed Mean ( 7 / 24 )	1.80862068965517	0.0833466831203647	21.6999719958053
Trimmed Mean ( 8 / 24 )	1.80892857142857	0.082504497544242	21.9252116584136
Trimmed Mean ( 9 / 24 )	1.80925925925926	0.081404019465717	22.2256747410516
Trimmed Mean ( 10 / 24 )	1.80961538461538	0.0799820688513507	22.6252635197348
Trimmed Mean ( 11 / 24 )	1.81	0.0791407941969402	22.8706322493536
Trimmed Mean ( 12 / 24 )	1.8125	0.0784730721307978	23.0970949751904
Trimmed Mean ( 13 / 24 )	1.81521739130435	0.0775199766246573	23.4161240797765
Trimmed Mean ( 14 / 24 )	1.81590909090909	0.0767979131847787	23.6452921128201
Trimmed Mean ( 15 / 24 )	1.81666666666667	0.0757399937363398	23.9855666345934
Trimmed Mean ( 16 / 24 )	1.8175	0.0742386570805817	24.481854487578
Trimmed Mean ( 17 / 24 )	1.82105263157895	0.0728565588074523	24.9950404107293
Trimmed Mean ( 18 / 24 )	1.825	0.0708648389317678	25.7532512245911
Trimmed Mean ( 19 / 24 )	1.82647058823529	0.0690279882693762	26.4598554010822
Trimmed Mean ( 20 / 24 )	1.83125	0.0672677455900983	27.2232997246389
Trimmed Mean ( 21 / 24 )	1.83666666666667	0.0645912583198454	28.4352204066345
Trimmed Mean ( 22 / 24 )	1.84285714285714	0.0605155477482802	30.4526226966113
Trimmed Mean ( 23 / 24 )	1.85	0.0574456264653803	32.2043663518041
Trimmed Mean ( 24 / 24 )	1.85	0.0561442242180216	32.9508515927837
Median	1.9
Midrange	1.65
Midmean - Weighted Average at Xnp	1.76046511627907
Midmean - Weighted Average at X(n+1)p	1.86052631578947
Midmean - Empirical Distribution Function	1.76046511627907
Midmean - Empirical Distribution Function - Averaging	1.86052631578947
Midmean - Empirical Distribution Function - Interpolation	1.86052631578947
Midmean - Closest Observation	1.76046511627907
Midmean - True Basic - Statistics Graphics Toolkit	1.86052631578947
Midmean - MS Excel (old versions)	1.76046511627907
Number of observations	72

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 1.79861111111111 & 0.092320397382751 & 19.4822721966225 \tabularnewline
Geometric Mean & 1.58191817201876 &  &  \tabularnewline
Harmonic Mean & 1.29115402212179 &  &  \tabularnewline
Quadratic Mean & 1.95962723212577 &  &  \tabularnewline
Winsorized Mean ( 1 / 24 ) & 1.79861111111111 & 0.0917251852384331 & 19.6086942363294 \tabularnewline
Winsorized Mean ( 2 / 24 ) & 1.80138888888889 & 0.091104616118358 & 19.7727509937436 \tabularnewline
Winsorized Mean ( 3 / 24 ) & 1.80972222222222 & 0.087884182798493 & 20.5921266443551 \tabularnewline
Winsorized Mean ( 4 / 24 ) & 1.80972222222222 & 0.087884182798493 & 20.5921266443551 \tabularnewline
Winsorized Mean ( 5 / 24 ) & 1.81666666666667 & 0.0866928454502975 & 20.9552086706877 \tabularnewline
Winsorized Mean ( 6 / 24 ) & 1.81666666666667 & 0.0866928454502975 & 20.9552086706877 \tabularnewline
Winsorized Mean ( 7 / 24 ) & 1.80694444444444 & 0.0850371912764719 & 21.2488726088063 \tabularnewline
Winsorized Mean ( 8 / 24 ) & 1.80694444444444 & 0.0850371912764719 & 21.2488726088063 \tabularnewline
Winsorized Mean ( 9 / 24 ) & 1.80694444444444 & 0.0850371912764719 & 21.2488726088063 \tabularnewline
Winsorized Mean ( 10 / 24 ) & 1.80694444444444 & 0.0805479665628231 & 22.4331478689176 \tabularnewline
Winsorized Mean ( 11 / 24 ) & 1.79166666666667 & 0.078242380520701 & 22.8989283652053 \tabularnewline
Winsorized Mean ( 12 / 24 ) & 1.79166666666667 & 0.078242380520701 & 22.8989283652053 \tabularnewline
Winsorized Mean ( 13 / 24 ) & 1.80972222222222 & 0.0754267909377481 & 23.9930958181137 \tabularnewline
Winsorized Mean ( 14 / 24 ) & 1.80972222222222 & 0.0754267909377481 & 23.9930958181137 \tabularnewline
Winsorized Mean ( 15 / 24 ) & 1.80972222222222 & 0.0754267909377481 & 23.9930958181137 \tabularnewline
Winsorized Mean ( 16 / 24 ) & 1.7875 & 0.0722415933453622 & 24.7433634451358 \tabularnewline
Winsorized Mean ( 17 / 24 ) & 1.7875 & 0.0722415933453622 & 24.7433634451358 \tabularnewline
Winsorized Mean ( 18 / 24 ) & 1.8125 & 0.0684885303900746 & 26.4642851828905 \tabularnewline
Winsorized Mean ( 19 / 24 ) & 1.78611111111111 & 0.0648612807583242 & 27.537401208068 \tabularnewline
Winsorized Mean ( 20 / 24 ) & 1.78611111111111 & 0.0648612807583242 & 27.537401208068 \tabularnewline
Winsorized Mean ( 21 / 24 ) & 1.78611111111111 & 0.0648612807583242 & 27.537401208068 \tabularnewline
Winsorized Mean ( 22 / 24 ) & 1.78611111111111 & 0.0563393458592208 & 31.7027307270162 \tabularnewline
Winsorized Mean ( 23 / 24 ) & 1.85 & 0.0473474818502387 & 39.0728276923279 \tabularnewline
Winsorized Mean ( 24 / 24 ) & 1.85 & 0.0473474818502387 & 39.0728276923279 \tabularnewline
Trimmed Mean ( 1 / 24 ) & 1.80285714285714 & 0.090225652900323 & 19.9816469585302 \tabularnewline
Trimmed Mean ( 2 / 24 ) & 1.80735294117647 & 0.0884287825847621 & 20.4385143428166 \tabularnewline
Trimmed Mean ( 3 / 24 ) & 1.81060606060606 & 0.0866665444112134 & 20.8916378621852 \tabularnewline
Trimmed Mean ( 4 / 24 ) & 1.8109375 & 0.0859735674674222 & 21.0638868822818 \tabularnewline
Trimmed Mean ( 5 / 24 ) & 1.81129032258065 & 0.0850888371022697 & 21.28704991471 \tabularnewline
Trimmed Mean ( 6 / 24 ) & 1.81 & 0.0843285208872316 & 21.4636754084709 \tabularnewline
Trimmed Mean ( 7 / 24 ) & 1.80862068965517 & 0.0833466831203647 & 21.6999719958053 \tabularnewline
Trimmed Mean ( 8 / 24 ) & 1.80892857142857 & 0.082504497544242 & 21.9252116584136 \tabularnewline
Trimmed Mean ( 9 / 24 ) & 1.80925925925926 & 0.081404019465717 & 22.2256747410516 \tabularnewline
Trimmed Mean ( 10 / 24 ) & 1.80961538461538 & 0.0799820688513507 & 22.6252635197348 \tabularnewline
Trimmed Mean ( 11 / 24 ) & 1.81 & 0.0791407941969402 & 22.8706322493536 \tabularnewline
Trimmed Mean ( 12 / 24 ) & 1.8125 & 0.0784730721307978 & 23.0970949751904 \tabularnewline
Trimmed Mean ( 13 / 24 ) & 1.81521739130435 & 0.0775199766246573 & 23.4161240797765 \tabularnewline
Trimmed Mean ( 14 / 24 ) & 1.81590909090909 & 0.0767979131847787 & 23.6452921128201 \tabularnewline
Trimmed Mean ( 15 / 24 ) & 1.81666666666667 & 0.0757399937363398 & 23.9855666345934 \tabularnewline
Trimmed Mean ( 16 / 24 ) & 1.8175 & 0.0742386570805817 & 24.481854487578 \tabularnewline
Trimmed Mean ( 17 / 24 ) & 1.82105263157895 & 0.0728565588074523 & 24.9950404107293 \tabularnewline
Trimmed Mean ( 18 / 24 ) & 1.825 & 0.0708648389317678 & 25.7532512245911 \tabularnewline
Trimmed Mean ( 19 / 24 ) & 1.82647058823529 & 0.0690279882693762 & 26.4598554010822 \tabularnewline
Trimmed Mean ( 20 / 24 ) & 1.83125 & 0.0672677455900983 & 27.2232997246389 \tabularnewline
Trimmed Mean ( 21 / 24 ) & 1.83666666666667 & 0.0645912583198454 & 28.4352204066345 \tabularnewline
Trimmed Mean ( 22 / 24 ) & 1.84285714285714 & 0.0605155477482802 & 30.4526226966113 \tabularnewline
Trimmed Mean ( 23 / 24 ) & 1.85 & 0.0574456264653803 & 32.2043663518041 \tabularnewline
Trimmed Mean ( 24 / 24 ) & 1.85 & 0.0561442242180216 & 32.9508515927837 \tabularnewline
Median & 1.9 &  &  \tabularnewline
Midrange & 1.65 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 1.76046511627907 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 1.86052631578947 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 1.76046511627907 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 1.86052631578947 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 1.86052631578947 &  &  \tabularnewline
Midmean - Closest Observation & 1.76046511627907 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 1.86052631578947 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 1.76046511627907 &  &  \tabularnewline
Number of observations & 72 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=285503&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]1.79861111111111[/C][C]0.092320397382751[/C][C]19.4822721966225[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]1.58191817201876[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]1.29115402212179[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]1.95962723212577[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 24 )[/C][C]1.79861111111111[/C][C]0.0917251852384331[/C][C]19.6086942363294[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 24 )[/C][C]1.80138888888889[/C][C]0.091104616118358[/C][C]19.7727509937436[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 24 )[/C][C]1.80972222222222[/C][C]0.087884182798493[/C][C]20.5921266443551[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 24 )[/C][C]1.80972222222222[/C][C]0.087884182798493[/C][C]20.5921266443551[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 24 )[/C][C]1.81666666666667[/C][C]0.0866928454502975[/C][C]20.9552086706877[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 24 )[/C][C]1.81666666666667[/C][C]0.0866928454502975[/C][C]20.9552086706877[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 24 )[/C][C]1.80694444444444[/C][C]0.0850371912764719[/C][C]21.2488726088063[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 24 )[/C][C]1.80694444444444[/C][C]0.0850371912764719[/C][C]21.2488726088063[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 24 )[/C][C]1.80694444444444[/C][C]0.0850371912764719[/C][C]21.2488726088063[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 24 )[/C][C]1.80694444444444[/C][C]0.0805479665628231[/C][C]22.4331478689176[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 24 )[/C][C]1.79166666666667[/C][C]0.078242380520701[/C][C]22.8989283652053[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 24 )[/C][C]1.79166666666667[/C][C]0.078242380520701[/C][C]22.8989283652053[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 24 )[/C][C]1.80972222222222[/C][C]0.0754267909377481[/C][C]23.9930958181137[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 24 )[/C][C]1.80972222222222[/C][C]0.0754267909377481[/C][C]23.9930958181137[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 24 )[/C][C]1.80972222222222[/C][C]0.0754267909377481[/C][C]23.9930958181137[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 24 )[/C][C]1.7875[/C][C]0.0722415933453622[/C][C]24.7433634451358[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 24 )[/C][C]1.7875[/C][C]0.0722415933453622[/C][C]24.7433634451358[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 24 )[/C][C]1.8125[/C][C]0.0684885303900746[/C][C]26.4642851828905[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 24 )[/C][C]1.78611111111111[/C][C]0.0648612807583242[/C][C]27.537401208068[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 24 )[/C][C]1.78611111111111[/C][C]0.0648612807583242[/C][C]27.537401208068[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 24 )[/C][C]1.78611111111111[/C][C]0.0648612807583242[/C][C]27.537401208068[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 24 )[/C][C]1.78611111111111[/C][C]0.0563393458592208[/C][C]31.7027307270162[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 24 )[/C][C]1.85[/C][C]0.0473474818502387[/C][C]39.0728276923279[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 24 )[/C][C]1.85[/C][C]0.0473474818502387[/C][C]39.0728276923279[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 24 )[/C][C]1.80285714285714[/C][C]0.090225652900323[/C][C]19.9816469585302[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 24 )[/C][C]1.80735294117647[/C][C]0.0884287825847621[/C][C]20.4385143428166[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 24 )[/C][C]1.81060606060606[/C][C]0.0866665444112134[/C][C]20.8916378621852[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 24 )[/C][C]1.8109375[/C][C]0.0859735674674222[/C][C]21.0638868822818[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 24 )[/C][C]1.81129032258065[/C][C]0.0850888371022697[/C][C]21.28704991471[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 24 )[/C][C]1.81[/C][C]0.0843285208872316[/C][C]21.4636754084709[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 24 )[/C][C]1.80862068965517[/C][C]0.0833466831203647[/C][C]21.6999719958053[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 24 )[/C][C]1.80892857142857[/C][C]0.082504497544242[/C][C]21.9252116584136[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 24 )[/C][C]1.80925925925926[/C][C]0.081404019465717[/C][C]22.2256747410516[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 24 )[/C][C]1.80961538461538[/C][C]0.0799820688513507[/C][C]22.6252635197348[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 24 )[/C][C]1.81[/C][C]0.0791407941969402[/C][C]22.8706322493536[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 24 )[/C][C]1.8125[/C][C]0.0784730721307978[/C][C]23.0970949751904[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 24 )[/C][C]1.81521739130435[/C][C]0.0775199766246573[/C][C]23.4161240797765[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 24 )[/C][C]1.81590909090909[/C][C]0.0767979131847787[/C][C]23.6452921128201[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 24 )[/C][C]1.81666666666667[/C][C]0.0757399937363398[/C][C]23.9855666345934[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 24 )[/C][C]1.8175[/C][C]0.0742386570805817[/C][C]24.481854487578[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 24 )[/C][C]1.82105263157895[/C][C]0.0728565588074523[/C][C]24.9950404107293[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 24 )[/C][C]1.825[/C][C]0.0708648389317678[/C][C]25.7532512245911[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 24 )[/C][C]1.82647058823529[/C][C]0.0690279882693762[/C][C]26.4598554010822[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 24 )[/C][C]1.83125[/C][C]0.0672677455900983[/C][C]27.2232997246389[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 24 )[/C][C]1.83666666666667[/C][C]0.0645912583198454[/C][C]28.4352204066345[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 24 )[/C][C]1.84285714285714[/C][C]0.0605155477482802[/C][C]30.4526226966113[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 24 )[/C][C]1.85[/C][C]0.0574456264653803[/C][C]32.2043663518041[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 24 )[/C][C]1.85[/C][C]0.0561442242180216[/C][C]32.9508515927837[/C][/ROW]
[ROW][C]Median[/C][C]1.9[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]1.65[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]1.76046511627907[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]1.86052631578947[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]1.76046511627907[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]1.86052631578947[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]1.86052631578947[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]1.76046511627907[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]1.86052631578947[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]1.76046511627907[/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=285503&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=285503&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	1.79861111111111	0.092320397382751	19.4822721966225
Geometric Mean	1.58191817201876
Harmonic Mean	1.29115402212179
Quadratic Mean	1.95962723212577
Winsorized Mean ( 1 / 24 )	1.79861111111111	0.0917251852384331	19.6086942363294
Winsorized Mean ( 2 / 24 )	1.80138888888889	0.091104616118358	19.7727509937436
Winsorized Mean ( 3 / 24 )	1.80972222222222	0.087884182798493	20.5921266443551
Winsorized Mean ( 4 / 24 )	1.80972222222222	0.087884182798493	20.5921266443551
Winsorized Mean ( 5 / 24 )	1.81666666666667	0.0866928454502975	20.9552086706877
Winsorized Mean ( 6 / 24 )	1.81666666666667	0.0866928454502975	20.9552086706877
Winsorized Mean ( 7 / 24 )	1.80694444444444	0.0850371912764719	21.2488726088063
Winsorized Mean ( 8 / 24 )	1.80694444444444	0.0850371912764719	21.2488726088063
Winsorized Mean ( 9 / 24 )	1.80694444444444	0.0850371912764719	21.2488726088063
Winsorized Mean ( 10 / 24 )	1.80694444444444	0.0805479665628231	22.4331478689176
Winsorized Mean ( 11 / 24 )	1.79166666666667	0.078242380520701	22.8989283652053
Winsorized Mean ( 12 / 24 )	1.79166666666667	0.078242380520701	22.8989283652053
Winsorized Mean ( 13 / 24 )	1.80972222222222	0.0754267909377481	23.9930958181137
Winsorized Mean ( 14 / 24 )	1.80972222222222	0.0754267909377481	23.9930958181137
Winsorized Mean ( 15 / 24 )	1.80972222222222	0.0754267909377481	23.9930958181137
Winsorized Mean ( 16 / 24 )	1.7875	0.0722415933453622	24.7433634451358
Winsorized Mean ( 17 / 24 )	1.7875	0.0722415933453622	24.7433634451358
Winsorized Mean ( 18 / 24 )	1.8125	0.0684885303900746	26.4642851828905
Winsorized Mean ( 19 / 24 )	1.78611111111111	0.0648612807583242	27.537401208068
Winsorized Mean ( 20 / 24 )	1.78611111111111	0.0648612807583242	27.537401208068
Winsorized Mean ( 21 / 24 )	1.78611111111111	0.0648612807583242	27.537401208068
Winsorized Mean ( 22 / 24 )	1.78611111111111	0.0563393458592208	31.7027307270162
Winsorized Mean ( 23 / 24 )	1.85	0.0473474818502387	39.0728276923279
Winsorized Mean ( 24 / 24 )	1.85	0.0473474818502387	39.0728276923279
Trimmed Mean ( 1 / 24 )	1.80285714285714	0.090225652900323	19.9816469585302
Trimmed Mean ( 2 / 24 )	1.80735294117647	0.0884287825847621	20.4385143428166
Trimmed Mean ( 3 / 24 )	1.81060606060606	0.0866665444112134	20.8916378621852
Trimmed Mean ( 4 / 24 )	1.8109375	0.0859735674674222	21.0638868822818
Trimmed Mean ( 5 / 24 )	1.81129032258065	0.0850888371022697	21.28704991471
Trimmed Mean ( 6 / 24 )	1.81	0.0843285208872316	21.4636754084709
Trimmed Mean ( 7 / 24 )	1.80862068965517	0.0833466831203647	21.6999719958053
Trimmed Mean ( 8 / 24 )	1.80892857142857	0.082504497544242	21.9252116584136
Trimmed Mean ( 9 / 24 )	1.80925925925926	0.081404019465717	22.2256747410516
Trimmed Mean ( 10 / 24 )	1.80961538461538	0.0799820688513507	22.6252635197348
Trimmed Mean ( 11 / 24 )	1.81	0.0791407941969402	22.8706322493536
Trimmed Mean ( 12 / 24 )	1.8125	0.0784730721307978	23.0970949751904
Trimmed Mean ( 13 / 24 )	1.81521739130435	0.0775199766246573	23.4161240797765
Trimmed Mean ( 14 / 24 )	1.81590909090909	0.0767979131847787	23.6452921128201
Trimmed Mean ( 15 / 24 )	1.81666666666667	0.0757399937363398	23.9855666345934
Trimmed Mean ( 16 / 24 )	1.8175	0.0742386570805817	24.481854487578
Trimmed Mean ( 17 / 24 )	1.82105263157895	0.0728565588074523	24.9950404107293
Trimmed Mean ( 18 / 24 )	1.825	0.0708648389317678	25.7532512245911
Trimmed Mean ( 19 / 24 )	1.82647058823529	0.0690279882693762	26.4598554010822
Trimmed Mean ( 20 / 24 )	1.83125	0.0672677455900983	27.2232997246389
Trimmed Mean ( 21 / 24 )	1.83666666666667	0.0645912583198454	28.4352204066345
Trimmed Mean ( 22 / 24 )	1.84285714285714	0.0605155477482802	30.4526226966113
Trimmed Mean ( 23 / 24 )	1.85	0.0574456264653803	32.2043663518041
Trimmed Mean ( 24 / 24 )	1.85	0.0561442242180216	32.9508515927837
Median	1.9
Midrange	1.65
Midmean - Weighted Average at Xnp	1.76046511627907
Midmean - Weighted Average at X(n+1)p	1.86052631578947
Midmean - Empirical Distribution Function	1.76046511627907
Midmean - Empirical Distribution Function - Averaging	1.86052631578947
Midmean - Empirical Distribution Function - Interpolation	1.86052631578947
Midmean - Closest Observation	1.76046511627907
Midmean - True Basic - Statistics Graphics Toolkit	1.86052631578947
Midmean - MS Excel (old versions)	1.76046511627907
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