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Chapter 3: Q38 (page 96)

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鈭�1x

(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. Find the harmonic mean of 38 mi/h and 56 mi/h to find the true 鈥渁verage鈥� speed for the round trip.

Short Answer

Expert verified

The harmonic mean is 45.3 mi/h.

Step by step solution

01

Given information

The distance driven by the author is 1163 miles.

The speed measures are 38 mi/h and 56 mi/h.

02

Harmonic mean formula

If there are n counts of observations, the formula for harmonic mean is x炉=n鈭�1xforx observations.

Substitute the values to obtainthe harmonic mean for the speed of the round trip.

x炉=2138+156=20.0442=45.2766

Thus, the actual average value of the speed for the round trip is 45.3 mil/h.

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P25

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13.0 Mbps
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