Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 2: Q 29. (page 108)

Biking accidents What is the mean μ of the density curve pictured in Exercise 27? (That is, where would the curve balance?) What is the median? (That is, where is the point with an area 0.5 on either side?)

Short Answer

Expert verified

The mean and median are equal to 1.5

Step by step solution

01

Step 1. Given

The points with an area of0.5are on either side.

02

Step 2. Concept

The value with p%of the observations less than it is called the p% percentile of a distribution.

03

Step 3. Calculation

The rectangle's balancing point is the distribution's mean point. As a result, the mean is calculated as follows: μ=3+0/2=1.5

The median of the asymmetric distribution is the point where the area of the curve is equal on both sides. As a result, the median is calculated as follows:

Md=arealiestotheleft=arealiestotherightMd=1.5

The uniform distribution's mean and median are presented below.

Therefore, both the mean and median are equal to 1.5

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

Questions T2.9 and T2.10 refer to the following setting. Until the scale was changed in 1995, SAT scores were based on a scale set many years ago. For Math scores, the mean under the old scale in the 1990swas 470and the standard deviation was 110. In 2009, the mean was 515 and the standard deviation was 116 .
T2.9. What is the standardized score ( z-score) for a student who scored 500 on the old SAT scale?
(a) -30
(b) -0.27
(c) -0.13
(d) 0.13
(e) 0.27

Gas it up! (1.3) Interested in a sporty car? Worried that it might use too much gas? The Environmental Protection Agency lists most such vehicles in its “two-seater” or “minicompact” categories. The figure shows boxplots for both city and highway gas mileages for our two groups of cars. Write a few sentences comparing these distributions.

T2.4. The figure shows a cumulative relative frequency graph of the number of ounces of alcohol consumed per week in a sample of 150adults. About what percent of these adults consume between 4and 8ounces per week?

(a)20%(b)40%(c)50%(d)60%(e)80%

Which of the following is least likely to have a nearly Normal distribution?

(a) Heights of all female students taking STAT 001 at State Tech.

(b) IQ scores of all students taking STAT 001 at State Tech.

(c) SAT Math scores of all students taking STAT 001 at State Tech.

(d) Family incomes of all students taking STAT 001 at State Tech.

(e) All of (a)–(d) will be approximately Normal.

R2.4 Aussie, Aussie, Aussie A group of Australian students were asked to estimate the width of their classroom in feet. Use the dot plot and summary statistics below to answer the following questions.

(a) Suppose we converted each student's guess from feet to meters (3.28ft=1m). How would the shape of the distribution be affected? Find the mean, median, standard deviation, and IQR for the transformed data.

(b) The actual width of the room was 42.6feet. Suppose we calculated the error in each student's guess as follows: guess -42.6. Find the mean and standard deviation of the errors. How good were the students' guesses? Justify your answer.

Approximately locate the median (equal-areas point) and the mean (balance point) on a density curve.
See all solutions

Recommended explanations on Math Textbooks

Logic and Functions

Read Explanation

Applied Mathematics

Read Explanation

Discrete Mathematics

Read Explanation

Mechanics Maths

Read Explanation

Calculus

Read Explanation

Geometry

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