Answered: The α angle of a triangle ABC was…

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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Question

The α angle of a triangle ABC was measured 50 times with a theodolite to obtain the following values (In the table, after the first value, only the last two digits of the measured angle are written).

a) Calculate the mean value and standard deviation of the angle α using the relevant formulas (write the standard deviation in cc)

b) For the angle α, create the frequency table of the sample set given in the question and draw the frequency histogram.

c) Find the confidence intervals of 0.95 of the mean value of the angle α and its variance.

71,6075
62
59
56
66
65
80
86
57
90
85
87
73
41
67
61
74
64
45
71
53
78
67
69
61
60
77
79
71
68
76
89
68
58
89
93
66
49
40
65
72
94
48
81
69
83
63
55
54
70

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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