The breaking strength of 80 “test pieces” of a certain alloy is given in the following table, the unit being given to the nearest thousand grams per square inch.Breaking strengthNumber of pieces44 – 463 46 – 482448 – 502750 – 522152 – 545 Calculate the average breaking strength. Calculate the standard deviation of the breaking strength. Calculate the percentage of observations lying between two standard deviations of the mean.

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

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter10: Statistics

Section10.5: Comparing Sets Of Data

Problem 13PPS

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The breaking strength of 80 “test pieces” of a certain alloy is given in the following table, the unit being given to the nearest thousand grams per square inch.

Breaking strength	Number of pieces
44 – 46	3
46 – 48	24
48 – 50	27
50 – 52	21
52 – 54	5

Calculate the average breaking strength.
Calculate the standard deviation of the breaking strength.
Calculate the percentage of observations lying between two standard deviations of the mean.

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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