For the following data, perform histogram analysis for variables X1 ,X2, X3 and X4. Calculate mean, variance and standard deviation of all the variables. Comment on the results. X1X2X3X4487.24.9495407.45524417.75.3461527.14.8552417.75.3524457.55.2569317.95.2547557.34.8530517.54.8530327.35.2524357.45.2501327.55.3416547.25456317.45.2399317.24.95695275.24734975552437.45.2467487.75.3524316.94.9456367.15.2399417.35501357.35450527.14.7512477.15416557.55438397.95.2569507.65490307.65.2399497.65.4427347.85.3490487.75.3512417.35.2404437.95.2541517.25.2433377.95.3558327.14.9535527.84.9421527.85.3456307.25473497.54.85304274.7473407.15.2444497.85.2558507.95.2501497.65478487.34.7410327.65.35643884.9507527.14.9569507.55.3404 2.For the same data construct covariance and correlation matrices. Comment on the results. 3.Select a system and construct a P-diagram by including inputs, outputs, control factors and noise factors

The mean, variance and standard deviation can be obtained as given below: Using EXCEL software:

Answered: For the following data, perform…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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For the following data, perform histogram analysis for variables X1 ,X2, X3 and X4. Calculate mean, variance and standard deviation of all the variables. Comment on the results.

X1	X2	X3	X4
48	7.2	4.9	495
40	7.4	5	524
41	7.7	5.3	461
52	7.1	4.8	552
41	7.7	5.3	524
45	7.5	5.2	569
31	7.9	5.2	547
55	7.3	4.8	530
51	7.5	4.8	530
32	7.3	5.2	524
35	7.4	5.2	501
32	7.5	5.3	416
54	7.2	5	456
31	7.4	5.2	399
31	7.2	4.9	569
52	7	5.2	473
49	7	5	552
43	7.4	5.2	467
48	7.7	5.3	524
31	6.9	4.9	456
36	7.1	5.2	399
41	7.3	5	501
35	7.3	5	450
52	7.1	4.7	512
47	7.1	5	416
55	7.5	5	438
39	7.9	5.2	569
50	7.6	5	490
30	7.6	5.2	399
49	7.6	5.4	427
34	7.8	5.3	490
48	7.7	5.3	512
41	7.3	5.2	404
43	7.9	5.2	541
51	7.2	5.2	433
37	7.9	5.3	558
32	7.1	4.9	535
52	7.8	4.9	421
52	7.8	5.3	456
30	7.2	5	473
49	7.5	4.8	530
42	7	4.7	473
40	7.1	5.2	444
49	7.8	5.2	558
50	7.9	5.2	501
49	7.6	5	478
48	7.3	4.7	410
32	7.6	5.3	564
38	8	4.9	507
52	7.1	4.9	569
50	7.5	5.3	404

2.For the same data construct covariance and correlation matrices. Comment on the results.

3.Select a system and construct a P-diagram by including inputs, outputs, control factors and noise factors

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

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X1	X2	X3	X4
48	7.2	4.9	495
40	7.4	5	524
41	7.7	5.3	461
52	7.1	4.8	552
41	7.7	5.3	524
45	7.5	5.2	569
31	7.9	5.2	547
55	7.3	4.8	530
51	7.5	4.8	530
32	7.3	5.2	524
35	7.4	5.2	501
32	7.5	5.3	416
54	7.2	5	456
31	7.4	5.2	399
31	7.2	4.9	569
52	7	5.2	473
49	7	5	552
43	7.4	5.2	467
48	7.7	5.3	524
31	6.9	4.9	456
36	7.1	5.2	399
41	7.3	5	501
35	7.3	5	450
52	7.1	4.7	512
47	7.1	5	416
55	7.5	5	438
39	7.9	5.2	569
50	7.6	5	490
30	7.6	5.2	399
49	7.6	5.4	427
34	7.8	5.3	490
48	7.7	5.3	512
41	7.3	5.2	404
43	7.9	5.2	541
51	7.2	5.2	433
37	7.9	5.3	558
32	7.1	4.9	535
52	7.8	4.9	421
52	7.8	5.3	456
30	7.2	5	473
49	7.5	4.8	530
42	7	4.7	473
40	7.1	5.2	444
49	7.8	5.2	558
50	7.9	5.2	501
49	7.6	5	478
48	7.3	4.7	410
32	7.6	5.3	564
38	8	4.9	507
52	7.1	4.9	569
50	7.5	5.3	404

X1	X2	X3	X4
48	7.2	4.9	495
40	7.4	5	524
41	7.7	5.3	461
52	7.1	4.8	552
41	7.7	5.3	524
45	7.5	5.2	569
31	7.9	5.2	547
55	7.3	4.8	530
51	7.5	4.8	530
32	7.3	5.2	524
35	7.4	5.2	501
32	7.5	5.3	416
54	7.2	5	456
31	7.4	5.2	399
31	7.2	4.9	569
52	7	5.2	473
49	7	5	552
43	7.4	5.2	467
48	7.7	5.3	524
31	6.9	4.9	456
36	7.1	5.2	399
41	7.3	5	501
35	7.3	5	450
52	7.1	4.7	512
47	7.1	5	416
55	7.5	5	438
39	7.9	5.2	569
50	7.6	5	490
30	7.6	5.2	399
49	7.6	5.4	427
34	7.8	5.3	490
48	7.7	5.3	512
41	7.3	5.2	404
43	7.9	5.2	541
51	7.2	5.2	433
37	7.9	5.3	558
32	7.1	4.9	535
52	7.8	4.9	421
52	7.8	5.3	456
30	7.2	5	473
49	7.5	4.8	530
42	7	4.7	473
40	7.1	5.2	444
49	7.8	5.2	558
50	7.9	5.2	501
49	7.6	5	478
48	7.3	4.7	410
32	7.6	5.3	564
38	8	4.9	507
52	7.1	4.9	569
50	7.5	5.3	404

X1	X2	X3	X4
48	7.2	4.9	495
40	7.4	5	524
41	7.7	5.3	461
52	7.1	4.8	552
41	7.7	5.3	524
45	7.5	5.2	569
31	7.9	5.2	547
55	7.3	4.8	530
51	7.5	4.8	530
32	7.3	5.2	524
35	7.4	5.2	501
32	7.5	5.3	416
54	7.2	5	456
31	7.4	5.2	399
31	7.2	4.9	569
52	7	5.2	473
49	7	5	552
43	7.4	5.2	467
48	7.7	5.3	524
31	6.9	4.9	456
36	7.1	5.2	399
41	7.3	5	501
35	7.3	5	450
52	7.1	4.7	512
47	7.1	5	416
55	7.5	5	438
39	7.9	5.2	569
50	7.6	5	490
30	7.6	5.2	399
49	7.6	5.4	427
34	7.8	5.3	490
48	7.7	5.3	512
41	7.3	5.2	404
43	7.9	5.2	541
51	7.2	5.2	433
37	7.9	5.3	558
32	7.1	4.9	535
52	7.8	4.9	421
52	7.8	5.3	456
30	7.2	5	473
49	7.5	4.8	530
42	7	4.7	473
40	7.1	5.2	444
49	7.8	5.2	558
50	7.9	5.2	501
49	7.6	5	478
48	7.3	4.7	410
32	7.6	5.3	564
38	8	4.9	507
52	7.1	4.9	569
50	7.5	5.3	404