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Harmonic Mean The harmonic mean is often used as a measure
Chapter 3, Problem 36BB(choose chapter or problem)
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
\(n \Sigma 1 x\)
(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?
Equation Transcription:
Text Transcription:
n \Sigma 1 x
Questions & Answers
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
\(n \Sigma 1 x\)
(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?
Equation Transcription:
Text Transcription:
n \Sigma 1 x
ANSWER:
Answer:
Step 1 of 1
Given, the onward trip mean speed is 38 mi/h and return trip mean speed is 56 mi/h.
Actual Mean speed =
=
= 47 mi/h