Answered: A line’s length has been measured…

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

A line’s length has been measured repeatedly on different occasions. The following are the results obtained:

1st measurement record = 352.33 ± 0.03cm

2nd measurement record = 351.79 ± 0.07cm

3rd measurement record = 352.16 ± 0.08cm

4th measurement record = 352.84 ± 0.01cm

5th measurement record = 351.55 ± 0.04cm

Determine the weighted mean of the 5 sets of measurements. Given the computed weighted mean of the measurements, what is the relative precision if the true length of the line is 352.39cm.

Bearing or Azimuth of Line AB:
Sta
Sta Obs
Distance(m)
Mean
Observed Interior Angle 0
Corr
Adjusted
Осс
List
Direct
Reversed
Mean
Interior
Angle
A
E
11.55
103°22'
102°57
В
13.20
A
13.20
88°14'
88°14'
C
17.42
В
17.42
113°36'
112°48'
D
10.00
10.00
156°06'
154°31
E
13.90
13.90
81°42'
81°42
A
11.55
B.

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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