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Elementary Statistics | 12th Edition | ISBN: 9780321836960 | Authors: Mario F. Triola
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Harmonic Mean The harmonic mean is often used as a measure of center for data sets

Chapter 3, Problem 36

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QUESTION:

Harmonic Mean The harmonic mean is often used as a measure of center for data sets consisting of rates of change, such as speeds. It is found by dividing the number of values n by the sum of the reciprocals of all values, expressed as n 1 x (No value can be zero.) The author drove 1163 miles to a conference in Orlando, Florida. For the trip to the conference, the author stopped overnight, and the mean speed from start to finish was 38 mi/h. For the return trip, the author stopped only for food and fuel, and the mean speed from start to finish was 56 mi/h. Is the actual average speed for the roundtrip the mean of 38 mi/h and 56 mi/h? Why or why not? What is the harmonic mean of 38 mi/h and 56 mi/h, and does this represent the true average speed?

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QUESTION:

Harmonic Mean The harmonic mean is often used as a measure of center for data sets consisting of rates of change, such as speeds. It is found by dividing the number of values n by the sum of the reciprocals of all values, expressed as n 1 x (No value can be zero.) The author drove 1163 miles to a conference in Orlando, Florida. For the trip to the conference, the author stopped overnight, and the mean speed from start to finish was 38 mi/h. For the return trip, the author stopped only for food and fuel, and the mean speed from start to finish was 56 mi/h. Is the actual average speed for the roundtrip the mean of 38 mi/h and 56 mi/h? Why or why not? What is the harmonic mean of 38 mi/h and 56 mi/h, and does this represent the true average speed?

ANSWER:

Step 1 of 3

Given that, the author drove 1163 miles to a conference in Orlando, Florida.

For the trip to the conference, the mean speed was 38 mi/h and for the return trip the mean speed from start to finish was 56 mi/h.

The harmonic mean is calculated using the formula:

Substituting the given value, we get,

Therefore, the harmonic mean of 38 mi/h and 56 mi/h is 45.3514 mi/h.

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