Answered: For questions (1) – (8) use the…

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

For questions (1) – (8) use the following information. You have measured the length of a
table to be 205.0 cm, 205.8 cm, 205.4 cm, 204.6 cm, and 204.9 cm five independent
times. You measured the width of the same table to be 60.1 cm, 60.4 cm, 60.2 cm, 60.0
cm, and 60.5 cm five independent times.

1) Calculate the mean length L of the table.

2) Calculate the standard deviation of the mean length σL of the table.

3) Calculate the mean width W of the table.

4) Calculate the standard deviation of the mean width σW of the table.

5) Calculate the area A = L x W of the table.

6) Using the correct equation for propagation of error, calculate the uncertainty of
the area σA of the table.

7) Calculate the perimeter P = 2L + 2W of the table.

8) Using the correct equation for propagation of error, calculate the uncertainty of
the perimeter σP of the table.

9) Report the mean length, mean width, area, and perimeter including their
uncertainties in the correct format discussed above.

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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