Log out Go to App
Go to App

Learning Materials

Features

Discover

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∑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 “average” 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¯=n∑1xforx observations.

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

x¯=2138+156=20.0442=45.2766

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

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

In Exercises 29–32, find the mean of the data summarized in the frequency distribution. Also, compare the computed means to the actual means obtained by using the original list of data values, which are as follows: (Exercise 29) 36.2 years; (Exercise 30) 44.1 years; (Exercise 31) 224.3; (Exercise 32) 255.1..

Blood Platelet Count of Males (1000 cells /μL )

Frequency(f)

100-199

25

200-299

92

300-399

28

400-499

0

500-599

2

Quadratic Mean The quadratic mean (or root mean square, or R.M.S.) is used in physical applications, such as power distribution systems. The quadratic mean of a set of values is obtained by squaring each value, adding those squares, dividing the sum by the number of values n, and then taking the square root of that result, as indicated below:

Quadraticmean=∑x2n

Find the R.M.S. of these voltages measured from household current: 0, 60, 110, -110, -60, 0.

How does the result compare to the mean?

In Exercises 9 –12, consider a value to be significantly low if its z score is less than or equal to -2 or consider the value to be significantly high if its z score is greater than or equal to 2.

ACT The ACT test is used to assess readiness for college. In a recent year, the mean ACT score was 21.1 and the standard deviation was 5.1. Identify the ACT scores that are significantly low or significantly high

Weighted Mean A student of the author earned grades of A, C, B, A, and D. Those courses had these corresponding numbers of credit hours: 3, 3, 3, 4, and 1. The grading system assigns quality points to letter grades as follows: A = 4; B = 3; C = 2; D = 1; F = 0. Compute the grade-point average (GPA) and round the result with two decimal places. If the dean’s list requires a GPA of 3.00 or greater, did this student make the dean’s list?

In Exercises 5–20, find the range, variance, and standard deviation for the given sample data. Include appropriate units (such as “minutes”) in your results. (The same data were used in Section 3-1, where we found measures of center. Here we find measures of variation.) Then answer the given questions.

Fireighter Fatalities Listed below are the numbers of heroic firefighters who lost their lives in the United States each year while fighting forest fires. The numbers are listed in order by year, starting with the year 2000. What important feature of the data is not revealed by any of the measures of variation?

20 18 23 30 20 12 24 9 25 15 8 11 15 34
See all solutions

Recommended explanations on Math Textbooks

Geometry

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Calculus

Read Explanation

Discrete Mathematics

Read Explanation

Logic and Functions

Read Explanation

Applied Mathematics

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.

Sign-up for free