Answered: For a data set of the pulse rates for a…

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 14PPS

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Question

For a data set of the pulse rates for a sample of adult females, the lowest pulse rate is

beats per minute, the mean of the listed pulse rates is `x=79.0 beats per minute, and their standard deviation is s=14.7 beats per minute.

a. What is the difference between the pulse rate of 31 beats per minute and the mean pulse rate of the females?

b. How many standard deviations is that [the difference found in part (a)]?

c. Convert the pulse rate of 31 beats per minutes to a z score.

d. If we consider pulse rates that convert to z scores between −2 and 2 to be neither significantly low nor significantly high, is the pulse rate of 31 beats per minute significant?

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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