Introduction To Statistics And Data Analysis

6th Edition

ISBN: 9781337793612

Author: PECK, Roxy.

Publisher: Cengage Learning,

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Textbook Question

Chapter 4.4, Problem 53E

Suppose that the manufacturer of a scale claims that its scale weighs items up to 110 pounds and provides accuracy to within 0.25 ounce. Suppose that a 50-ounce weight was repeatedly weighed on this scale and the weight readings recorded. The mean value was 49.5 ounces, and the standard deviation was 0.1. What can be said about the percentage of the time that the scale actually showed a weight that was within 0.25 ounce of the true value of 50 ounces? (Hint: Use Chebyshev’s Rule.)

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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Chapter 4 Solutions

Introduction To Statistics And Data Analysis

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Solution Summary: The author calculates the percentage of time that the weight on the scale falls within 0.25 ounce of the true value of 50-ounce. The standardized z-score is also known as the standard score.

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