Answered: Roll two dice 48 times and record 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

Roll two dice 48 times and record the sum of the spots on the top faces as you roll. Then construct a probability distribution for your 48 sums. Using the probability distribution you constructed, find the mean number of spots.

(If you don't have two dice, then cut out 6 pieces of paper with each being the same size and with #1,2,3,4,5,6 written on them. Place the pieces of paper in a hat or bowl. Pull out a number, then replace, pull out a number again and record the sum of the 2 numbers.)

(c) Is the mean in (b) close to the mean in (a)? Explain why there is a difference in the two means or why they are the same.

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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