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R Software Module

rwasp_centraltendency.wasp

Title produced by software

Central Tendency

Date of computation

Thu, 01 Feb 2018 11:18:08 +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/2018/Feb/01/t1517480310evx4yfftj9b18mp.htm/, Retrieved Sun, 28 Apr 2024 23:19:14 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=314572, Retrieved Sun, 28 Apr 2024 23:19:14 +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] [] [2018-02-01 10:18:08] [30069f3559c38bd35521ff63d790353e] [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	4 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 time4 seconds \tabularnewline
R ServerBig Analytics Cloud Computing Center \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=314572&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]

4 seconds[/C][/ROW] [ROW]

R Server[/C]

Big Analytics Cloud Computing Center[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=314572&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=314572&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	4 seconds
R Server	Big Analytics Cloud Computing Center

Central Tendency - Ungrouped Data
Measure	Value	S.E.	Value/S.E.
Arithmetic Mean	10.5084	0.170914	61.4835
Geometric Mean	10.2328
Harmonic Mean	9.90915
Quadratic Mean	10.7529
Winsorized Mean ( 1 / 59 )	10.5251	0.167566	62.8118
Winsorized Mean ( 2 / 59 )	10.5251	0.167566	62.8118
Winsorized Mean ( 3 / 59 )	10.5251	0.167566	62.8118
Winsorized Mean ( 4 / 59 )	10.5251	0.167566	62.8118
Winsorized Mean ( 5 / 59 )	10.5251	0.167566	62.8118
Winsorized Mean ( 6 / 59 )	10.5251	0.167566	62.8118
Winsorized Mean ( 7 / 59 )	10.5251	0.167566	62.8118
Winsorized Mean ( 8 / 59 )	10.5251	0.167566	62.8118
Winsorized Mean ( 9 / 59 )	10.5251	0.167566	62.8118
Winsorized Mean ( 10 / 59 )	10.5251	0.167566	62.8118
Winsorized Mean ( 11 / 59 )	10.4637	0.1591	65.7681
Winsorized Mean ( 12 / 59 )	10.5307	0.149338	70.5161
Winsorized Mean ( 13 / 59 )	10.5307	0.149338	70.5161
Winsorized Mean ( 14 / 59 )	10.5307	0.149338	70.5161
Winsorized Mean ( 15 / 59 )	10.5307	0.149338	70.5161
Winsorized Mean ( 16 / 59 )	10.5307	0.149338	70.5161
Winsorized Mean ( 17 / 59 )	10.6257	0.137902	77.0523
Winsorized Mean ( 18 / 59 )	10.5251	0.12535	83.9659
Winsorized Mean ( 19 / 59 )	10.5251	0.12535	83.9659
Winsorized Mean ( 20 / 59 )	10.5251	0.12535	83.9659
Winsorized Mean ( 21 / 59 )	10.5251	0.12535	83.9659
Winsorized Mean ( 22 / 59 )	10.5251	0.12535	83.9659
Winsorized Mean ( 23 / 59 )	10.5251	0.12535	83.9659
Winsorized Mean ( 24 / 59 )	10.5251	0.12535	83.9659
Winsorized Mean ( 25 / 59 )	10.3855	0.111821	92.8757
Winsorized Mean ( 26 / 59 )	10.5307	0.0964795	109.15
Winsorized Mean ( 27 / 59 )	10.5307	0.0964795	109.15
Winsorized Mean ( 28 / 59 )	10.5307	0.0964795	109.15
Winsorized Mean ( 29 / 59 )	10.5307	0.0964795	109.15
Winsorized Mean ( 30 / 59 )	10.5307	0.0964795	109.15
Winsorized Mean ( 31 / 59 )	10.5307	0.0964795	109.15
Winsorized Mean ( 32 / 59 )	10.5307	0.0964795	109.15
Winsorized Mean ( 33 / 59 )	10.5307	0.0964795	109.15
Winsorized Mean ( 34 / 59 )	10.5307	0.0964795	109.15
Winsorized Mean ( 35 / 59 )	10.5307	0.0964795	109.15
Winsorized Mean ( 36 / 59 )	10.5307	0.0964795	109.15
Winsorized Mean ( 37 / 59 )	10.5307	0.0964795	109.15
Winsorized Mean ( 38 / 59 )	10.5307	0.0964795	109.15
Winsorized Mean ( 39 / 59 )	10.5307	0.0964795	109.15
Winsorized Mean ( 40 / 59 )	10.5307	0.0964795	109.15
Winsorized Mean ( 41 / 59 )	10.5307	0.0964795	109.15
Winsorized Mean ( 42 / 59 )	10.5307	0.0964795	109.15
Winsorized Mean ( 43 / 59 )	10.5307	0.0964795	109.15
Winsorized Mean ( 44 / 59 )	10.5307	0.0964795	109.15
Winsorized Mean ( 45 / 59 )	10.5307	0.0964795	109.15
Winsorized Mean ( 46 / 59 )	10.5307	0.0964795	109.15
Winsorized Mean ( 47 / 59 )	10.5307	0.0964795	109.15
Winsorized Mean ( 48 / 59 )	10.5307	0.0964795	109.15
Winsorized Mean ( 49 / 59 )	10.5307	0.0964795	109.15
Winsorized Mean ( 50 / 59 )	10.5307	0.0964795	109.15
Winsorized Mean ( 51 / 59 )	10.5307	0.0964795	109.15
Winsorized Mean ( 52 / 59 )	10.5307	0.0964795	109.15
Winsorized Mean ( 53 / 59 )	10.5307	0.0964795	109.15
Winsorized Mean ( 54 / 59 )	10.5307	0.0964795	109.15
Winsorized Mean ( 55 / 59 )	10.5307	0.0964795	109.15
Winsorized Mean ( 56 / 59 )	10.5307	0.0964795	109.15
Winsorized Mean ( 57 / 59 )	10.5307	0.0964795	109.15
Winsorized Mean ( 58 / 59 )	10.5307	0.0964795	109.15
Winsorized Mean ( 59 / 59 )	10.5307	0.0964795	109.15
Trimmed Mean ( 1 / 59 )	10.5254	0.165585	63.5652
Trimmed Mean ( 2 / 59 )	10.5257	0.163464	64.3918
Trimmed Mean ( 3 / 59 )	10.526	0.161191	65.3016
Trimmed Mean ( 4 / 59 )	10.5263	0.158752	66.3065
Trimmed Mean ( 5 / 59 )	10.5266	0.156133	67.4207
Trimmed Mean ( 6 / 59 )	10.5269	0.153316	68.6617
Trimmed Mean ( 7 / 59 )	10.5273	0.15028	70.0509
Trimmed Mean ( 8 / 59 )	10.5276	0.147002	71.6152
Trimmed Mean ( 9 / 59 )	10.528	0.143455	73.3885
Trimmed Mean ( 10 / 59 )	10.5283	0.139606	75.4145
Trimmed Mean ( 11 / 59 )	10.5287	0.135416	77.7506
Trimmed Mean ( 12 / 59 )	10.5355	0.132102	79.7526
Trimmed Mean ( 13 / 59 )	10.5359	0.129839	81.1464
Trimmed Mean ( 14 / 59 )	10.5364	0.127387	82.7122
Trimmed Mean ( 15 / 59 )	10.5364	0.124725	84.4774
Trimmed Mean ( 16 / 59 )	10.5374	0.121829	86.4937
Trimmed Mean ( 17 / 59 )	10.5379	0.118669	88.8007
Trimmed Mean ( 18 / 59 )	10.5315	0.116502	90.3972
Trimmed Mean ( 19 / 59 )	10.5319	0.11545	91.2253
Trimmed Mean ( 20 / 59 )	10.5324	0.1143	92.1465
Trimmed Mean ( 21 / 59 )	10.5328	0.113045	93.1738
Trimmed Mean ( 22 / 59 )	10.5333	0.111674	94.3226
Trimmed Mean ( 23 / 59 )	10.5338	0.110173	95.6114
Trimmed Mean ( 24 / 59 )	10.5344	0.108531	97.0632
Trimmed Mean ( 25 / 59 )	10.5349	0.10673	98.7059
Trimmed Mean ( 26 / 59 )	10.5433	0.105915	99.5445
Trimmed Mean ( 27 / 59 )	10.544	0.106258	99.2298
Trimmed Mean ( 28 / 59 )	10.5447	0.106595	98.9236
Trimmed Mean ( 29 / 59 )	10.5455	0.106923	98.6267
Trimmed Mean ( 30 / 59 )	10.5455	0.107242	98.333
Trimmed Mean ( 31 / 59 )	10.547	0.107551	98.0648
Trimmed Mean ( 32 / 59 )	10.5478	0.107849	97.8021
Trimmed Mean ( 33 / 59 )	10.5487	0.108133	97.5531
Trimmed Mean ( 34 / 59 )	10.5495	0.108401	97.3195
Trimmed Mean ( 35 / 59 )	10.5505	0.108652	97.1029
Trimmed Mean ( 36 / 59 )	10.5514	0.108884	96.9051
Trimmed Mean ( 37 / 59 )	10.5524	0.109093	96.7283
Trimmed Mean ( 38 / 59 )	10.5534	0.109277	96.575
Trimmed Mean ( 39 / 59 )	10.5545	0.109432	96.4479
Trimmed Mean ( 40 / 59 )	10.5556	0.109554	96.3501
Trimmed Mean ( 41 / 59 )	10.5567	0.10964	96.2854
Trimmed Mean ( 42 / 59 )	10.5579	0.109683	96.2581
Trimmed Mean ( 43 / 59 )	10.5591	0.109679	96.2729
Trimmed Mean ( 44 / 59 )	10.5604	0.109621	96.3358
Trimmed Mean ( 45 / 59 )	10.5618	0.109501	96.4535
Trimmed Mean ( 46 / 59 )	10.5632	0.109311	96.6342
Trimmed Mean ( 47 / 59 )	10.5647	0.109041	96.8875
Trimmed Mean ( 48 / 59 )	10.5663	0.108678	97.2251
Trimmed Mean ( 49 / 59 )	10.5679	0.10821	97.6613
Trimmed Mean ( 50 / 59 )	10.5696	0.107619	98.2135
Trimmed Mean ( 51 / 59 )	10.5696	0.106886	98.8866
Trimmed Mean ( 52 / 59 )	10.5733	0.105989	99.7589
Trimmed Mean ( 53 / 59 )	10.5753	0.104899	100.815
Trimmed Mean ( 54 / 59 )	10.5775	0.103582	102.117
Trimmed Mean ( 55 / 59 )	10.5797	0.101996	103.727
Trimmed Mean ( 56 / 59 )	10.5821	0.100089	105.727
Trimmed Mean ( 57 / 59 )	10.5846	0.0977937	108.234
Trimmed Mean ( 58 / 59 )	10.5873	0.0950245	111.417
Trimmed Mean ( 59 / 59 )	10.5902	0.0916666	115.529
Median	11
Midrange	9
Midmean - Weighted Average at Xnp	10.5547
Midmean - Weighted Average at X(n+1)p	10.5547
Midmean - Empirical Distribution Function	10.5547
Midmean - Empirical Distribution Function - Averaging	10.5547
Midmean - Empirical Distribution Function - Interpolation	10.5547
Midmean - Closest Observation	10.5547
Midmean - True Basic - Statistics Graphics Toolkit	10.5547
Midmean - MS Excel (old versions)	10.5547
Number of observations	179

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 10.5084 & 0.170914 & 61.4835 \tabularnewline
Geometric Mean & 10.2328 &  &  \tabularnewline
Harmonic Mean & 9.90915 &  &  \tabularnewline
Quadratic Mean & 10.7529 &  &  \tabularnewline
Winsorized Mean ( 1 / 59 ) & 10.5251 & 0.167566 & 62.8118 \tabularnewline
Winsorized Mean ( 2 / 59 ) & 10.5251 & 0.167566 & 62.8118 \tabularnewline
Winsorized Mean ( 3 / 59 ) & 10.5251 & 0.167566 & 62.8118 \tabularnewline
Winsorized Mean ( 4 / 59 ) & 10.5251 & 0.167566 & 62.8118 \tabularnewline
Winsorized Mean ( 5 / 59 ) & 10.5251 & 0.167566 & 62.8118 \tabularnewline
Winsorized Mean ( 6 / 59 ) & 10.5251 & 0.167566 & 62.8118 \tabularnewline
Winsorized Mean ( 7 / 59 ) & 10.5251 & 0.167566 & 62.8118 \tabularnewline
Winsorized Mean ( 8 / 59 ) & 10.5251 & 0.167566 & 62.8118 \tabularnewline
Winsorized Mean ( 9 / 59 ) & 10.5251 & 0.167566 & 62.8118 \tabularnewline
Winsorized Mean ( 10 / 59 ) & 10.5251 & 0.167566 & 62.8118 \tabularnewline
Winsorized Mean ( 11 / 59 ) & 10.4637 & 0.1591 & 65.7681 \tabularnewline
Winsorized Mean ( 12 / 59 ) & 10.5307 & 0.149338 & 70.5161 \tabularnewline
Winsorized Mean ( 13 / 59 ) & 10.5307 & 0.149338 & 70.5161 \tabularnewline
Winsorized Mean ( 14 / 59 ) & 10.5307 & 0.149338 & 70.5161 \tabularnewline
Winsorized Mean ( 15 / 59 ) & 10.5307 & 0.149338 & 70.5161 \tabularnewline
Winsorized Mean ( 16 / 59 ) & 10.5307 & 0.149338 & 70.5161 \tabularnewline
Winsorized Mean ( 17 / 59 ) & 10.6257 & 0.137902 & 77.0523 \tabularnewline
Winsorized Mean ( 18 / 59 ) & 10.5251 & 0.12535 & 83.9659 \tabularnewline
Winsorized Mean ( 19 / 59 ) & 10.5251 & 0.12535 & 83.9659 \tabularnewline
Winsorized Mean ( 20 / 59 ) & 10.5251 & 0.12535 & 83.9659 \tabularnewline
Winsorized Mean ( 21 / 59 ) & 10.5251 & 0.12535 & 83.9659 \tabularnewline
Winsorized Mean ( 22 / 59 ) & 10.5251 & 0.12535 & 83.9659 \tabularnewline
Winsorized Mean ( 23 / 59 ) & 10.5251 & 0.12535 & 83.9659 \tabularnewline
Winsorized Mean ( 24 / 59 ) & 10.5251 & 0.12535 & 83.9659 \tabularnewline
Winsorized Mean ( 25 / 59 ) & 10.3855 & 0.111821 & 92.8757 \tabularnewline
Winsorized Mean ( 26 / 59 ) & 10.5307 & 0.0964795 & 109.15 \tabularnewline
Winsorized Mean ( 27 / 59 ) & 10.5307 & 0.0964795 & 109.15 \tabularnewline
Winsorized Mean ( 28 / 59 ) & 10.5307 & 0.0964795 & 109.15 \tabularnewline
Winsorized Mean ( 29 / 59 ) & 10.5307 & 0.0964795 & 109.15 \tabularnewline
Winsorized Mean ( 30 / 59 ) & 10.5307 & 0.0964795 & 109.15 \tabularnewline
Winsorized Mean ( 31 / 59 ) & 10.5307 & 0.0964795 & 109.15 \tabularnewline
Winsorized Mean ( 32 / 59 ) & 10.5307 & 0.0964795 & 109.15 \tabularnewline
Winsorized Mean ( 33 / 59 ) & 10.5307 & 0.0964795 & 109.15 \tabularnewline
Winsorized Mean ( 34 / 59 ) & 10.5307 & 0.0964795 & 109.15 \tabularnewline
Winsorized Mean ( 35 / 59 ) & 10.5307 & 0.0964795 & 109.15 \tabularnewline
Winsorized Mean ( 36 / 59 ) & 10.5307 & 0.0964795 & 109.15 \tabularnewline
Winsorized Mean ( 37 / 59 ) & 10.5307 & 0.0964795 & 109.15 \tabularnewline
Winsorized Mean ( 38 / 59 ) & 10.5307 & 0.0964795 & 109.15 \tabularnewline
Winsorized Mean ( 39 / 59 ) & 10.5307 & 0.0964795 & 109.15 \tabularnewline
Winsorized Mean ( 40 / 59 ) & 10.5307 & 0.0964795 & 109.15 \tabularnewline
Winsorized Mean ( 41 / 59 ) & 10.5307 & 0.0964795 & 109.15 \tabularnewline
Winsorized Mean ( 42 / 59 ) & 10.5307 & 0.0964795 & 109.15 \tabularnewline
Winsorized Mean ( 43 / 59 ) & 10.5307 & 0.0964795 & 109.15 \tabularnewline
Winsorized Mean ( 44 / 59 ) & 10.5307 & 0.0964795 & 109.15 \tabularnewline
Winsorized Mean ( 45 / 59 ) & 10.5307 & 0.0964795 & 109.15 \tabularnewline
Winsorized Mean ( 46 / 59 ) & 10.5307 & 0.0964795 & 109.15 \tabularnewline
Winsorized Mean ( 47 / 59 ) & 10.5307 & 0.0964795 & 109.15 \tabularnewline
Winsorized Mean ( 48 / 59 ) & 10.5307 & 0.0964795 & 109.15 \tabularnewline
Winsorized Mean ( 49 / 59 ) & 10.5307 & 0.0964795 & 109.15 \tabularnewline
Winsorized Mean ( 50 / 59 ) & 10.5307 & 0.0964795 & 109.15 \tabularnewline
Winsorized Mean ( 51 / 59 ) & 10.5307 & 0.0964795 & 109.15 \tabularnewline
Winsorized Mean ( 52 / 59 ) & 10.5307 & 0.0964795 & 109.15 \tabularnewline
Winsorized Mean ( 53 / 59 ) & 10.5307 & 0.0964795 & 109.15 \tabularnewline
Winsorized Mean ( 54 / 59 ) & 10.5307 & 0.0964795 & 109.15 \tabularnewline
Winsorized Mean ( 55 / 59 ) & 10.5307 & 0.0964795 & 109.15 \tabularnewline
Winsorized Mean ( 56 / 59 ) & 10.5307 & 0.0964795 & 109.15 \tabularnewline
Winsorized Mean ( 57 / 59 ) & 10.5307 & 0.0964795 & 109.15 \tabularnewline
Winsorized Mean ( 58 / 59 ) & 10.5307 & 0.0964795 & 109.15 \tabularnewline
Winsorized Mean ( 59 / 59 ) & 10.5307 & 0.0964795 & 109.15 \tabularnewline
Trimmed Mean ( 1 / 59 ) & 10.5254 & 0.165585 & 63.5652 \tabularnewline
Trimmed Mean ( 2 / 59 ) & 10.5257 & 0.163464 & 64.3918 \tabularnewline
Trimmed Mean ( 3 / 59 ) & 10.526 & 0.161191 & 65.3016 \tabularnewline
Trimmed Mean ( 4 / 59 ) & 10.5263 & 0.158752 & 66.3065 \tabularnewline
Trimmed Mean ( 5 / 59 ) & 10.5266 & 0.156133 & 67.4207 \tabularnewline
Trimmed Mean ( 6 / 59 ) & 10.5269 & 0.153316 & 68.6617 \tabularnewline
Trimmed Mean ( 7 / 59 ) & 10.5273 & 0.15028 & 70.0509 \tabularnewline
Trimmed Mean ( 8 / 59 ) & 10.5276 & 0.147002 & 71.6152 \tabularnewline
Trimmed Mean ( 9 / 59 ) & 10.528 & 0.143455 & 73.3885 \tabularnewline
Trimmed Mean ( 10 / 59 ) & 10.5283 & 0.139606 & 75.4145 \tabularnewline
Trimmed Mean ( 11 / 59 ) & 10.5287 & 0.135416 & 77.7506 \tabularnewline
Trimmed Mean ( 12 / 59 ) & 10.5355 & 0.132102 & 79.7526 \tabularnewline
Trimmed Mean ( 13 / 59 ) & 10.5359 & 0.129839 & 81.1464 \tabularnewline
Trimmed Mean ( 14 / 59 ) & 10.5364 & 0.127387 & 82.7122 \tabularnewline
Trimmed Mean ( 15 / 59 ) & 10.5364 & 0.124725 & 84.4774 \tabularnewline
Trimmed Mean ( 16 / 59 ) & 10.5374 & 0.121829 & 86.4937 \tabularnewline
Trimmed Mean ( 17 / 59 ) & 10.5379 & 0.118669 & 88.8007 \tabularnewline
Trimmed Mean ( 18 / 59 ) & 10.5315 & 0.116502 & 90.3972 \tabularnewline
Trimmed Mean ( 19 / 59 ) & 10.5319 & 0.11545 & 91.2253 \tabularnewline
Trimmed Mean ( 20 / 59 ) & 10.5324 & 0.1143 & 92.1465 \tabularnewline
Trimmed Mean ( 21 / 59 ) & 10.5328 & 0.113045 & 93.1738 \tabularnewline
Trimmed Mean ( 22 / 59 ) & 10.5333 & 0.111674 & 94.3226 \tabularnewline
Trimmed Mean ( 23 / 59 ) & 10.5338 & 0.110173 & 95.6114 \tabularnewline
Trimmed Mean ( 24 / 59 ) & 10.5344 & 0.108531 & 97.0632 \tabularnewline
Trimmed Mean ( 25 / 59 ) & 10.5349 & 0.10673 & 98.7059 \tabularnewline
Trimmed Mean ( 26 / 59 ) & 10.5433 & 0.105915 & 99.5445 \tabularnewline
Trimmed Mean ( 27 / 59 ) & 10.544 & 0.106258 & 99.2298 \tabularnewline
Trimmed Mean ( 28 / 59 ) & 10.5447 & 0.106595 & 98.9236 \tabularnewline
Trimmed Mean ( 29 / 59 ) & 10.5455 & 0.106923 & 98.6267 \tabularnewline
Trimmed Mean ( 30 / 59 ) & 10.5455 & 0.107242 & 98.333 \tabularnewline
Trimmed Mean ( 31 / 59 ) & 10.547 & 0.107551 & 98.0648 \tabularnewline
Trimmed Mean ( 32 / 59 ) & 10.5478 & 0.107849 & 97.8021 \tabularnewline
Trimmed Mean ( 33 / 59 ) & 10.5487 & 0.108133 & 97.5531 \tabularnewline
Trimmed Mean ( 34 / 59 ) & 10.5495 & 0.108401 & 97.3195 \tabularnewline
Trimmed Mean ( 35 / 59 ) & 10.5505 & 0.108652 & 97.1029 \tabularnewline
Trimmed Mean ( 36 / 59 ) & 10.5514 & 0.108884 & 96.9051 \tabularnewline
Trimmed Mean ( 37 / 59 ) & 10.5524 & 0.109093 & 96.7283 \tabularnewline
Trimmed Mean ( 38 / 59 ) & 10.5534 & 0.109277 & 96.575 \tabularnewline
Trimmed Mean ( 39 / 59 ) & 10.5545 & 0.109432 & 96.4479 \tabularnewline
Trimmed Mean ( 40 / 59 ) & 10.5556 & 0.109554 & 96.3501 \tabularnewline
Trimmed Mean ( 41 / 59 ) & 10.5567 & 0.10964 & 96.2854 \tabularnewline
Trimmed Mean ( 42 / 59 ) & 10.5579 & 0.109683 & 96.2581 \tabularnewline
Trimmed Mean ( 43 / 59 ) & 10.5591 & 0.109679 & 96.2729 \tabularnewline
Trimmed Mean ( 44 / 59 ) & 10.5604 & 0.109621 & 96.3358 \tabularnewline
Trimmed Mean ( 45 / 59 ) & 10.5618 & 0.109501 & 96.4535 \tabularnewline
Trimmed Mean ( 46 / 59 ) & 10.5632 & 0.109311 & 96.6342 \tabularnewline
Trimmed Mean ( 47 / 59 ) & 10.5647 & 0.109041 & 96.8875 \tabularnewline
Trimmed Mean ( 48 / 59 ) & 10.5663 & 0.108678 & 97.2251 \tabularnewline
Trimmed Mean ( 49 / 59 ) & 10.5679 & 0.10821 & 97.6613 \tabularnewline
Trimmed Mean ( 50 / 59 ) & 10.5696 & 0.107619 & 98.2135 \tabularnewline
Trimmed Mean ( 51 / 59 ) & 10.5696 & 0.106886 & 98.8866 \tabularnewline
Trimmed Mean ( 52 / 59 ) & 10.5733 & 0.105989 & 99.7589 \tabularnewline
Trimmed Mean ( 53 / 59 ) & 10.5753 & 0.104899 & 100.815 \tabularnewline
Trimmed Mean ( 54 / 59 ) & 10.5775 & 0.103582 & 102.117 \tabularnewline
Trimmed Mean ( 55 / 59 ) & 10.5797 & 0.101996 & 103.727 \tabularnewline
Trimmed Mean ( 56 / 59 ) & 10.5821 & 0.100089 & 105.727 \tabularnewline
Trimmed Mean ( 57 / 59 ) & 10.5846 & 0.0977937 & 108.234 \tabularnewline
Trimmed Mean ( 58 / 59 ) & 10.5873 & 0.0950245 & 111.417 \tabularnewline
Trimmed Mean ( 59 / 59 ) & 10.5902 & 0.0916666 & 115.529 \tabularnewline
Median & 11 &  &  \tabularnewline
Midrange & 9 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 10.5547 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 10.5547 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 10.5547 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 10.5547 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 10.5547 &  &  \tabularnewline
Midmean - Closest Observation & 10.5547 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 10.5547 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 10.5547 &  &  \tabularnewline
Number of observations & 179 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=314572&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]10.5084[/C][C]0.170914[/C][C]61.4835[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]10.2328[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]9.90915[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]10.7529[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 59 )[/C][C]10.5251[/C][C]0.167566[/C][C]62.8118[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 59 )[/C][C]10.5251[/C][C]0.167566[/C][C]62.8118[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 59 )[/C][C]10.5251[/C][C]0.167566[/C][C]62.8118[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 59 )[/C][C]10.5251[/C][C]0.167566[/C][C]62.8118[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 59 )[/C][C]10.5251[/C][C]0.167566[/C][C]62.8118[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 59 )[/C][C]10.5251[/C][C]0.167566[/C][C]62.8118[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 59 )[/C][C]10.5251[/C][C]0.167566[/C][C]62.8118[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 59 )[/C][C]10.5251[/C][C]0.167566[/C][C]62.8118[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 59 )[/C][C]10.5251[/C][C]0.167566[/C][C]62.8118[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 59 )[/C][C]10.5251[/C][C]0.167566[/C][C]62.8118[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 59 )[/C][C]10.4637[/C][C]0.1591[/C][C]65.7681[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 59 )[/C][C]10.5307[/C][C]0.149338[/C][C]70.5161[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 59 )[/C][C]10.5307[/C][C]0.149338[/C][C]70.5161[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 59 )[/C][C]10.5307[/C][C]0.149338[/C][C]70.5161[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 59 )[/C][C]10.5307[/C][C]0.149338[/C][C]70.5161[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 59 )[/C][C]10.5307[/C][C]0.149338[/C][C]70.5161[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 59 )[/C][C]10.6257[/C][C]0.137902[/C][C]77.0523[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 59 )[/C][C]10.5251[/C][C]0.12535[/C][C]83.9659[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 59 )[/C][C]10.5251[/C][C]0.12535[/C][C]83.9659[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 59 )[/C][C]10.5251[/C][C]0.12535[/C][C]83.9659[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 59 )[/C][C]10.5251[/C][C]0.12535[/C][C]83.9659[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 59 )[/C][C]10.5251[/C][C]0.12535[/C][C]83.9659[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 59 )[/C][C]10.5251[/C][C]0.12535[/C][C]83.9659[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 59 )[/C][C]10.5251[/C][C]0.12535[/C][C]83.9659[/C][/ROW]
[ROW][C]Winsorized Mean ( 25 / 59 )[/C][C]10.3855[/C][C]0.111821[/C][C]92.8757[/C][/ROW]
[ROW][C]Winsorized Mean ( 26 / 59 )[/C][C]10.5307[/C][C]0.0964795[/C][C]109.15[/C][/ROW]
[ROW][C]Winsorized Mean ( 27 / 59 )[/C][C]10.5307[/C][C]0.0964795[/C][C]109.15[/C][/ROW]
[ROW][C]Winsorized Mean ( 28 / 59 )[/C][C]10.5307[/C][C]0.0964795[/C][C]109.15[/C][/ROW]
[ROW][C]Winsorized Mean ( 29 / 59 )[/C][C]10.5307[/C][C]0.0964795[/C][C]109.15[/C][/ROW]
[ROW][C]Winsorized Mean ( 30 / 59 )[/C][C]10.5307[/C][C]0.0964795[/C][C]109.15[/C][/ROW]
[ROW][C]Winsorized Mean ( 31 / 59 )[/C][C]10.5307[/C][C]0.0964795[/C][C]109.15[/C][/ROW]
[ROW][C]Winsorized Mean ( 32 / 59 )[/C][C]10.5307[/C][C]0.0964795[/C][C]109.15[/C][/ROW]
[ROW][C]Winsorized Mean ( 33 / 59 )[/C][C]10.5307[/C][C]0.0964795[/C][C]109.15[/C][/ROW]
[ROW][C]Winsorized Mean ( 34 / 59 )[/C][C]10.5307[/C][C]0.0964795[/C][C]109.15[/C][/ROW]
[ROW][C]Winsorized Mean ( 35 / 59 )[/C][C]10.5307[/C][C]0.0964795[/C][C]109.15[/C][/ROW]
[ROW][C]Winsorized Mean ( 36 / 59 )[/C][C]10.5307[/C][C]0.0964795[/C][C]109.15[/C][/ROW]
[ROW][C]Winsorized Mean ( 37 / 59 )[/C][C]10.5307[/C][C]0.0964795[/C][C]109.15[/C][/ROW]
[ROW][C]Winsorized Mean ( 38 / 59 )[/C][C]10.5307[/C][C]0.0964795[/C][C]109.15[/C][/ROW]
[ROW][C]Winsorized Mean ( 39 / 59 )[/C][C]10.5307[/C][C]0.0964795[/C][C]109.15[/C][/ROW]
[ROW][C]Winsorized Mean ( 40 / 59 )[/C][C]10.5307[/C][C]0.0964795[/C][C]109.15[/C][/ROW]
[ROW][C]Winsorized Mean ( 41 / 59 )[/C][C]10.5307[/C][C]0.0964795[/C][C]109.15[/C][/ROW]
[ROW][C]Winsorized Mean ( 42 / 59 )[/C][C]10.5307[/C][C]0.0964795[/C][C]109.15[/C][/ROW]
[ROW][C]Winsorized Mean ( 43 / 59 )[/C][C]10.5307[/C][C]0.0964795[/C][C]109.15[/C][/ROW]
[ROW][C]Winsorized Mean ( 44 / 59 )[/C][C]10.5307[/C][C]0.0964795[/C][C]109.15[/C][/ROW]
[ROW][C]Winsorized Mean ( 45 / 59 )[/C][C]10.5307[/C][C]0.0964795[/C][C]109.15[/C][/ROW]
[ROW][C]Winsorized Mean ( 46 / 59 )[/C][C]10.5307[/C][C]0.0964795[/C][C]109.15[/C][/ROW]
[ROW][C]Winsorized Mean ( 47 / 59 )[/C][C]10.5307[/C][C]0.0964795[/C][C]109.15[/C][/ROW]
[ROW][C]Winsorized Mean ( 48 / 59 )[/C][C]10.5307[/C][C]0.0964795[/C][C]109.15[/C][/ROW]
[ROW][C]Winsorized Mean ( 49 / 59 )[/C][C]10.5307[/C][C]0.0964795[/C][C]109.15[/C][/ROW]
[ROW][C]Winsorized Mean ( 50 / 59 )[/C][C]10.5307[/C][C]0.0964795[/C][C]109.15[/C][/ROW]
[ROW][C]Winsorized Mean ( 51 / 59 )[/C][C]10.5307[/C][C]0.0964795[/C][C]109.15[/C][/ROW]
[ROW][C]Winsorized Mean ( 52 / 59 )[/C][C]10.5307[/C][C]0.0964795[/C][C]109.15[/C][/ROW]
[ROW][C]Winsorized Mean ( 53 / 59 )[/C][C]10.5307[/C][C]0.0964795[/C][C]109.15[/C][/ROW]
[ROW][C]Winsorized Mean ( 54 / 59 )[/C][C]10.5307[/C][C]0.0964795[/C][C]109.15[/C][/ROW]
[ROW][C]Winsorized Mean ( 55 / 59 )[/C][C]10.5307[/C][C]0.0964795[/C][C]109.15[/C][/ROW]
[ROW][C]Winsorized Mean ( 56 / 59 )[/C][C]10.5307[/C][C]0.0964795[/C][C]109.15[/C][/ROW]
[ROW][C]Winsorized Mean ( 57 / 59 )[/C][C]10.5307[/C][C]0.0964795[/C][C]109.15[/C][/ROW]
[ROW][C]Winsorized Mean ( 58 / 59 )[/C][C]10.5307[/C][C]0.0964795[/C][C]109.15[/C][/ROW]
[ROW][C]Winsorized Mean ( 59 / 59 )[/C][C]10.5307[/C][C]0.0964795[/C][C]109.15[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 59 )[/C][C]10.5254[/C][C]0.165585[/C][C]63.5652[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 59 )[/C][C]10.5257[/C][C]0.163464[/C][C]64.3918[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 59 )[/C][C]10.526[/C][C]0.161191[/C][C]65.3016[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 59 )[/C][C]10.5263[/C][C]0.158752[/C][C]66.3065[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 59 )[/C][C]10.5266[/C][C]0.156133[/C][C]67.4207[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 59 )[/C][C]10.5269[/C][C]0.153316[/C][C]68.6617[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 59 )[/C][C]10.5273[/C][C]0.15028[/C][C]70.0509[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 59 )[/C][C]10.5276[/C][C]0.147002[/C][C]71.6152[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 59 )[/C][C]10.528[/C][C]0.143455[/C][C]73.3885[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 59 )[/C][C]10.5283[/C][C]0.139606[/C][C]75.4145[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 59 )[/C][C]10.5287[/C][C]0.135416[/C][C]77.7506[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 59 )[/C][C]10.5355[/C][C]0.132102[/C][C]79.7526[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 59 )[/C][C]10.5359[/C][C]0.129839[/C][C]81.1464[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 59 )[/C][C]10.5364[/C][C]0.127387[/C][C]82.7122[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 59 )[/C][C]10.5364[/C][C]0.124725[/C][C]84.4774[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 59 )[/C][C]10.5374[/C][C]0.121829[/C][C]86.4937[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 59 )[/C][C]10.5379[/C][C]0.118669[/C][C]88.8007[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 59 )[/C][C]10.5315[/C][C]0.116502[/C][C]90.3972[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 59 )[/C][C]10.5319[/C][C]0.11545[/C][C]91.2253[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 59 )[/C][C]10.5324[/C][C]0.1143[/C][C]92.1465[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 59 )[/C][C]10.5328[/C][C]0.113045[/C][C]93.1738[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 59 )[/C][C]10.5333[/C][C]0.111674[/C][C]94.3226[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 59 )[/C][C]10.5338[/C][C]0.110173[/C][C]95.6114[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 59 )[/C][C]10.5344[/C][C]0.108531[/C][C]97.0632[/C][/ROW]
[ROW][C]Trimmed Mean ( 25 / 59 )[/C][C]10.5349[/C][C]0.10673[/C][C]98.7059[/C][/ROW]
[ROW][C]Trimmed Mean ( 26 / 59 )[/C][C]10.5433[/C][C]0.105915[/C][C]99.5445[/C][/ROW]
[ROW][C]Trimmed Mean ( 27 / 59 )[/C][C]10.544[/C][C]0.106258[/C][C]99.2298[/C][/ROW]
[ROW][C]Trimmed Mean ( 28 / 59 )[/C][C]10.5447[/C][C]0.106595[/C][C]98.9236[/C][/ROW]
[ROW][C]Trimmed Mean ( 29 / 59 )[/C][C]10.5455[/C][C]0.106923[/C][C]98.6267[/C][/ROW]
[ROW][C]Trimmed Mean ( 30 / 59 )[/C][C]10.5455[/C][C]0.107242[/C][C]98.333[/C][/ROW]
[ROW][C]Trimmed Mean ( 31 / 59 )[/C][C]10.547[/C][C]0.107551[/C][C]98.0648[/C][/ROW]
[ROW][C]Trimmed Mean ( 32 / 59 )[/C][C]10.5478[/C][C]0.107849[/C][C]97.8021[/C][/ROW]
[ROW][C]Trimmed Mean ( 33 / 59 )[/C][C]10.5487[/C][C]0.108133[/C][C]97.5531[/C][/ROW]
[ROW][C]Trimmed Mean ( 34 / 59 )[/C][C]10.5495[/C][C]0.108401[/C][C]97.3195[/C][/ROW]
[ROW][C]Trimmed Mean ( 35 / 59 )[/C][C]10.5505[/C][C]0.108652[/C][C]97.1029[/C][/ROW]
[ROW][C]Trimmed Mean ( 36 / 59 )[/C][C]10.5514[/C][C]0.108884[/C][C]96.9051[/C][/ROW]
[ROW][C]Trimmed Mean ( 37 / 59 )[/C][C]10.5524[/C][C]0.109093[/C][C]96.7283[/C][/ROW]
[ROW][C]Trimmed Mean ( 38 / 59 )[/C][C]10.5534[/C][C]0.109277[/C][C]96.575[/C][/ROW]
[ROW][C]Trimmed Mean ( 39 / 59 )[/C][C]10.5545[/C][C]0.109432[/C][C]96.4479[/C][/ROW]
[ROW][C]Trimmed Mean ( 40 / 59 )[/C][C]10.5556[/C][C]0.109554[/C][C]96.3501[/C][/ROW]
[ROW][C]Trimmed Mean ( 41 / 59 )[/C][C]10.5567[/C][C]0.10964[/C][C]96.2854[/C][/ROW]
[ROW][C]Trimmed Mean ( 42 / 59 )[/C][C]10.5579[/C][C]0.109683[/C][C]96.2581[/C][/ROW]
[ROW][C]Trimmed Mean ( 43 / 59 )[/C][C]10.5591[/C][C]0.109679[/C][C]96.2729[/C][/ROW]
[ROW][C]Trimmed Mean ( 44 / 59 )[/C][C]10.5604[/C][C]0.109621[/C][C]96.3358[/C][/ROW]
[ROW][C]Trimmed Mean ( 45 / 59 )[/C][C]10.5618[/C][C]0.109501[/C][C]96.4535[/C][/ROW]
[ROW][C]Trimmed Mean ( 46 / 59 )[/C][C]10.5632[/C][C]0.109311[/C][C]96.6342[/C][/ROW]
[ROW][C]Trimmed Mean ( 47 / 59 )[/C][C]10.5647[/C][C]0.109041[/C][C]96.8875[/C][/ROW]
[ROW][C]Trimmed Mean ( 48 / 59 )[/C][C]10.5663[/C][C]0.108678[/C][C]97.2251[/C][/ROW]
[ROW][C]Trimmed Mean ( 49 / 59 )[/C][C]10.5679[/C][C]0.10821[/C][C]97.6613[/C][/ROW]
[ROW][C]Trimmed Mean ( 50 / 59 )[/C][C]10.5696[/C][C]0.107619[/C][C]98.2135[/C][/ROW]
[ROW][C]Trimmed Mean ( 51 / 59 )[/C][C]10.5696[/C][C]0.106886[/C][C]98.8866[/C][/ROW]
[ROW][C]Trimmed Mean ( 52 / 59 )[/C][C]10.5733[/C][C]0.105989[/C][C]99.7589[/C][/ROW]
[ROW][C]Trimmed Mean ( 53 / 59 )[/C][C]10.5753[/C][C]0.104899[/C][C]100.815[/C][/ROW]
[ROW][C]Trimmed Mean ( 54 / 59 )[/C][C]10.5775[/C][C]0.103582[/C][C]102.117[/C][/ROW]
[ROW][C]Trimmed Mean ( 55 / 59 )[/C][C]10.5797[/C][C]0.101996[/C][C]103.727[/C][/ROW]
[ROW][C]Trimmed Mean ( 56 / 59 )[/C][C]10.5821[/C][C]0.100089[/C][C]105.727[/C][/ROW]
[ROW][C]Trimmed Mean ( 57 / 59 )[/C][C]10.5846[/C][C]0.0977937[/C][C]108.234[/C][/ROW]
[ROW][C]Trimmed Mean ( 58 / 59 )[/C][C]10.5873[/C][C]0.0950245[/C][C]111.417[/C][/ROW]
[ROW][C]Trimmed Mean ( 59 / 59 )[/C][C]10.5902[/C][C]0.0916666[/C][C]115.529[/C][/ROW]
[ROW][C]Median[/C][C]11[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]9[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]10.5547[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]10.5547[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]10.5547[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]10.5547[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]10.5547[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]10.5547[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]10.5547[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]10.5547[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]179[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=314572&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=314572&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	10.5084	0.170914	61.4835
Geometric Mean	10.2328
Harmonic Mean	9.90915
Quadratic Mean	10.7529
Winsorized Mean ( 1 / 59 )	10.5251	0.167566	62.8118
Winsorized Mean ( 2 / 59 )	10.5251	0.167566	62.8118
Winsorized Mean ( 3 / 59 )	10.5251	0.167566	62.8118
Winsorized Mean ( 4 / 59 )	10.5251	0.167566	62.8118
Winsorized Mean ( 5 / 59 )	10.5251	0.167566	62.8118
Winsorized Mean ( 6 / 59 )	10.5251	0.167566	62.8118
Winsorized Mean ( 7 / 59 )	10.5251	0.167566	62.8118
Winsorized Mean ( 8 / 59 )	10.5251	0.167566	62.8118
Winsorized Mean ( 9 / 59 )	10.5251	0.167566	62.8118
Winsorized Mean ( 10 / 59 )	10.5251	0.167566	62.8118
Winsorized Mean ( 11 / 59 )	10.4637	0.1591	65.7681
Winsorized Mean ( 12 / 59 )	10.5307	0.149338	70.5161
Winsorized Mean ( 13 / 59 )	10.5307	0.149338	70.5161
Winsorized Mean ( 14 / 59 )	10.5307	0.149338	70.5161
Winsorized Mean ( 15 / 59 )	10.5307	0.149338	70.5161
Winsorized Mean ( 16 / 59 )	10.5307	0.149338	70.5161
Winsorized Mean ( 17 / 59 )	10.6257	0.137902	77.0523
Winsorized Mean ( 18 / 59 )	10.5251	0.12535	83.9659
Winsorized Mean ( 19 / 59 )	10.5251	0.12535	83.9659
Winsorized Mean ( 20 / 59 )	10.5251	0.12535	83.9659
Winsorized Mean ( 21 / 59 )	10.5251	0.12535	83.9659
Winsorized Mean ( 22 / 59 )	10.5251	0.12535	83.9659
Winsorized Mean ( 23 / 59 )	10.5251	0.12535	83.9659
Winsorized Mean ( 24 / 59 )	10.5251	0.12535	83.9659
Winsorized Mean ( 25 / 59 )	10.3855	0.111821	92.8757
Winsorized Mean ( 26 / 59 )	10.5307	0.0964795	109.15
Winsorized Mean ( 27 / 59 )	10.5307	0.0964795	109.15
Winsorized Mean ( 28 / 59 )	10.5307	0.0964795	109.15
Winsorized Mean ( 29 / 59 )	10.5307	0.0964795	109.15
Winsorized Mean ( 30 / 59 )	10.5307	0.0964795	109.15
Winsorized Mean ( 31 / 59 )	10.5307	0.0964795	109.15
Winsorized Mean ( 32 / 59 )	10.5307	0.0964795	109.15
Winsorized Mean ( 33 / 59 )	10.5307	0.0964795	109.15
Winsorized Mean ( 34 / 59 )	10.5307	0.0964795	109.15
Winsorized Mean ( 35 / 59 )	10.5307	0.0964795	109.15
Winsorized Mean ( 36 / 59 )	10.5307	0.0964795	109.15
Winsorized Mean ( 37 / 59 )	10.5307	0.0964795	109.15
Winsorized Mean ( 38 / 59 )	10.5307	0.0964795	109.15
Winsorized Mean ( 39 / 59 )	10.5307	0.0964795	109.15
Winsorized Mean ( 40 / 59 )	10.5307	0.0964795	109.15
Winsorized Mean ( 41 / 59 )	10.5307	0.0964795	109.15
Winsorized Mean ( 42 / 59 )	10.5307	0.0964795	109.15
Winsorized Mean ( 43 / 59 )	10.5307	0.0964795	109.15
Winsorized Mean ( 44 / 59 )	10.5307	0.0964795	109.15
Winsorized Mean ( 45 / 59 )	10.5307	0.0964795	109.15
Winsorized Mean ( 46 / 59 )	10.5307	0.0964795	109.15
Winsorized Mean ( 47 / 59 )	10.5307	0.0964795	109.15
Winsorized Mean ( 48 / 59 )	10.5307	0.0964795	109.15
Winsorized Mean ( 49 / 59 )	10.5307	0.0964795	109.15
Winsorized Mean ( 50 / 59 )	10.5307	0.0964795	109.15
Winsorized Mean ( 51 / 59 )	10.5307	0.0964795	109.15
Winsorized Mean ( 52 / 59 )	10.5307	0.0964795	109.15
Winsorized Mean ( 53 / 59 )	10.5307	0.0964795	109.15
Winsorized Mean ( 54 / 59 )	10.5307	0.0964795	109.15
Winsorized Mean ( 55 / 59 )	10.5307	0.0964795	109.15
Winsorized Mean ( 56 / 59 )	10.5307	0.0964795	109.15
Winsorized Mean ( 57 / 59 )	10.5307	0.0964795	109.15
Winsorized Mean ( 58 / 59 )	10.5307	0.0964795	109.15
Winsorized Mean ( 59 / 59 )	10.5307	0.0964795	109.15
Trimmed Mean ( 1 / 59 )	10.5254	0.165585	63.5652
Trimmed Mean ( 2 / 59 )	10.5257	0.163464	64.3918
Trimmed Mean ( 3 / 59 )	10.526	0.161191	65.3016
Trimmed Mean ( 4 / 59 )	10.5263	0.158752	66.3065
Trimmed Mean ( 5 / 59 )	10.5266	0.156133	67.4207
Trimmed Mean ( 6 / 59 )	10.5269	0.153316	68.6617
Trimmed Mean ( 7 / 59 )	10.5273	0.15028	70.0509
Trimmed Mean ( 8 / 59 )	10.5276	0.147002	71.6152
Trimmed Mean ( 9 / 59 )	10.528	0.143455	73.3885
Trimmed Mean ( 10 / 59 )	10.5283	0.139606	75.4145
Trimmed Mean ( 11 / 59 )	10.5287	0.135416	77.7506
Trimmed Mean ( 12 / 59 )	10.5355	0.132102	79.7526
Trimmed Mean ( 13 / 59 )	10.5359	0.129839	81.1464
Trimmed Mean ( 14 / 59 )	10.5364	0.127387	82.7122
Trimmed Mean ( 15 / 59 )	10.5364	0.124725	84.4774
Trimmed Mean ( 16 / 59 )	10.5374	0.121829	86.4937
Trimmed Mean ( 17 / 59 )	10.5379	0.118669	88.8007
Trimmed Mean ( 18 / 59 )	10.5315	0.116502	90.3972
Trimmed Mean ( 19 / 59 )	10.5319	0.11545	91.2253
Trimmed Mean ( 20 / 59 )	10.5324	0.1143	92.1465
Trimmed Mean ( 21 / 59 )	10.5328	0.113045	93.1738
Trimmed Mean ( 22 / 59 )	10.5333	0.111674	94.3226
Trimmed Mean ( 23 / 59 )	10.5338	0.110173	95.6114
Trimmed Mean ( 24 / 59 )	10.5344	0.108531	97.0632
Trimmed Mean ( 25 / 59 )	10.5349	0.10673	98.7059
Trimmed Mean ( 26 / 59 )	10.5433	0.105915	99.5445
Trimmed Mean ( 27 / 59 )	10.544	0.106258	99.2298
Trimmed Mean ( 28 / 59 )	10.5447	0.106595	98.9236
Trimmed Mean ( 29 / 59 )	10.5455	0.106923	98.6267
Trimmed Mean ( 30 / 59 )	10.5455	0.107242	98.333
Trimmed Mean ( 31 / 59 )	10.547	0.107551	98.0648
Trimmed Mean ( 32 / 59 )	10.5478	0.107849	97.8021
Trimmed Mean ( 33 / 59 )	10.5487	0.108133	97.5531
Trimmed Mean ( 34 / 59 )	10.5495	0.108401	97.3195
Trimmed Mean ( 35 / 59 )	10.5505	0.108652	97.1029
Trimmed Mean ( 36 / 59 )	10.5514	0.108884	96.9051
Trimmed Mean ( 37 / 59 )	10.5524	0.109093	96.7283
Trimmed Mean ( 38 / 59 )	10.5534	0.109277	96.575
Trimmed Mean ( 39 / 59 )	10.5545	0.109432	96.4479
Trimmed Mean ( 40 / 59 )	10.5556	0.109554	96.3501
Trimmed Mean ( 41 / 59 )	10.5567	0.10964	96.2854
Trimmed Mean ( 42 / 59 )	10.5579	0.109683	96.2581
Trimmed Mean ( 43 / 59 )	10.5591	0.109679	96.2729
Trimmed Mean ( 44 / 59 )	10.5604	0.109621	96.3358
Trimmed Mean ( 45 / 59 )	10.5618	0.109501	96.4535
Trimmed Mean ( 46 / 59 )	10.5632	0.109311	96.6342
Trimmed Mean ( 47 / 59 )	10.5647	0.109041	96.8875
Trimmed Mean ( 48 / 59 )	10.5663	0.108678	97.2251
Trimmed Mean ( 49 / 59 )	10.5679	0.10821	97.6613
Trimmed Mean ( 50 / 59 )	10.5696	0.107619	98.2135
Trimmed Mean ( 51 / 59 )	10.5696	0.106886	98.8866
Trimmed Mean ( 52 / 59 )	10.5733	0.105989	99.7589
Trimmed Mean ( 53 / 59 )	10.5753	0.104899	100.815
Trimmed Mean ( 54 / 59 )	10.5775	0.103582	102.117
Trimmed Mean ( 55 / 59 )	10.5797	0.101996	103.727
Trimmed Mean ( 56 / 59 )	10.5821	0.100089	105.727
Trimmed Mean ( 57 / 59 )	10.5846	0.0977937	108.234
Trimmed Mean ( 58 / 59 )	10.5873	0.0950245	111.417
Trimmed Mean ( 59 / 59 )	10.5902	0.0916666	115.529
Median	11
Midrange	9
Midmean - Weighted Average at Xnp	10.5547
Midmean - Weighted Average at X(n+1)p	10.5547
Midmean - Empirical Distribution Function	10.5547
Midmean - Empirical Distribution Function - Averaging	10.5547
Midmean - Empirical Distribution Function - Interpolation	10.5547
Midmean - Closest Observation	10.5547
Midmean - True Basic - Statistics Graphics Toolkit	10.5547
Midmean - MS Excel (old versions)	10.5547
Number of observations	179

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