Answered: Consider the accompanying data on…

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter10: Statistics

Section10.3: Measures Of Spread

Problem 1GP

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Question

Consider the accompanying data on flexural strength (MPa) for concrete beams of a certain type.

8.3	7.4	7.0	6.8	7.8	9.7	5.0
6.3	6.8	9.0	7.7	7.3	7.4	11.8
6.3	7.7	11.6	7.2	11.3	9.7	10.7
7.0	7.9	8.7	7.9	8.1	6.5

(a) Calculate a point estimate of the mean value of strength for the conceptual population of all beams manufactured in this fashion. [Hint: Σx_i = 218.9.] (Round your answer to three decimal places.)
MPa

(b) Calculate a point estimate of the strength value that separates the weakest 50% of all such beams from the strongest 50%.
MPa

(c) Calculate a point estimate of the population standard deviation ?. [Hint: Σx_i² = 1851.35.] (Round your answer to three decimal places.)
MPa

(d) Calculate a point estimate of the proportion of all such beams whose flexural strength exceeds 10 MPa. [Hint: Think of an observation as a "success" if it exceeds 10.] (Round your answer to three decimal places.)

(e) Calculate a point estimate of the population coefficient of variation ?/?. (Round your answer to four decimal places.)

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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