/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Q31E The cumulative frequency and cum... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 1: Q31E (page 29)

The cumulative frequency and cumulative relativefrequency for a particular class interval are the sum offrequencies and relativefrequencies, respectively, forthat interval and all intervals lying below it. If, forexample, there are four intervals with frequencies 9,16, 13, and 12, then the cumulative frequencies are 9,25, 38, and 50, and the cumulative relative frequenciesare .18, .50, .76, and 1.00. Compute the cumulativefrequencies and cumulative relative frequencies for thedata of Exercise 24.

Short Answer

Expert verified

The cumulative frequency and the cumulative relative frequency is,

x

Cumulative frequency

Cumulative Relative Frequency

4000-4200

1

0.01

4200-4400

3

0.03

4400-4600

12

0.12

4600-4800

24

0.24

4800-5000

43

0.43

5000-5200

65

0.65

5200-5400

85

0.85

5400-5600

92

0.92

5600-5800

99

0.99

5800-6000

100

1

Step by step solution

01

Given information

The cumulative frequency and cumulative relative frequency for a particular class interval are the sum of frequencies and relative frequencies, respectively, for that interval and all intervals lying below it.

02

Compute the cumulative frequencies and cumulative relative frequencies

Referring to the exercise 24, we have,

x representing the shear strength (lb) of ultrasonic spot welds.

The table representing the frequency and relative frequency as,

x

Frequency

Relative Frequency

4000-4200

1

0.01

4200-4400

2

0.02

4400-4600

9

0.09

4600-4800

12

0.12

4800-5000

19

0.19

5000-5200

22

0.22

5200-5400

20

0.2

5400-5600

7

0.07

5600-5800

7

0.07

5800-6000

1

0.01

Using the given information, the cumulative frequency and the cumulative relative frequency is represented as,

x

Cumulative frequency

Cumulative Relative Frequency

4000-4200

1

0.01

4200-4400

3

0.03

4400-4600

12

0.12

4600-4800

24

0.24

4800-5000

43

0.43

5000-5200

65

0.65

5200-5400

85

0.85

5400-5600

92

0.92

5600-5800

99

0.99

5800-6000

100

1

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.

Over 30 million students worldwide already upgrade their learning with 91影视!

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

Anxiety disorders and symptoms can often be effectively treated with benzodiazepine medications. It isknown that animals exposed to stress exhibit a decrease in benzodiazepine receptor binding in the frontal cortex. Thearticle 鈥淒ecreased Benzodiazepine Receptor Binding in Prefrontal Cortex in Combat-Related Posttraumatic Stress Disorder鈥� (Amer. J. of Psychiatry, 2000: 1120鈥�1126) described the first study of benzodiazepine receptor binding in individuals suffering from PTSD. The accompanying data on a receptor binding measure (adjusted distribution volume) was read from a graph in the article.
PTSD: 10, 20, 25, 28, 31, 35, 37, 38, 38, 39, 39,
42, 46
Healthy: 23, 39, 40, 41, 43, 47, 51, 58, 63, 66, 67,
69, 72
Use various methods from this chapter to describe and summarize the data.

How does the speed of a runner vary over the course of a marathon (a distance of 42.195 km)? Consider determining both the time to run the first 5 km and the time to run between the 35-km and 40-km points, and then subtracting the former time from the latter time. A positive value of this difference corresponds to a runner slowing down toward the end of the race. The accompanying histogram is based on times of runners who participated in several different Japanese marathons (鈥淔actors Affecting Runners鈥� Marathon Performance,鈥� Chance, Fall, 1993: 24鈥�30).What are some interesting features of this histogram? What is a typical difference value? Roughly what proportion of the runners ran the late distance more quickly than the early distance?

The sample data \({x_1},{x_2}, \ldots ,{x_n}\) sometimes represents a time series, where \({x_t} = {\rm{the observed value of a response variable x at time t}}\). Often the observed series shows a great deal of random variation, which makes it difficult to study longer-term behavior. In such situations, it is desirable to produce a smoothed version of the series. One technique for doing so involves exponential smoothing. The value of a smoothing constant \(\alpha \) is chosen \(\left( {0 < \alpha < 1} \right)\).Then with \({{\bf{x}}_t} = {\bf{smoothed}}{\rm{ }}{\bf{value}}{\rm{ }}{\bf{at}}{\rm{ }}{\bf{time}}{\rm{ }}{\bf{t}}\), we set \({\bar x_1} = {x_1}\), and for \(t = 2,{\rm{ }}3,...,n,\)\({x_t} = a{x_t} + \left( {1 - \alpha } \right){\bar x_{t - 1}}\).

a. Consider the following time series in which \({x_t} = {\rm{temperature}}\left( {8F} \right)\)of effluent at a sewage treatment plant on dayt:

47, 54, 53, 50, 46, 46, 47, 50, 51, 50, 46, 52, 50, 50

Plot each \({x_t}\)against t on a two-dimensional coordinate system (a time-series plot). Does there appear to be any pattern?

b. Calculate the \({\bar x_t}s\) using\(\;\alpha = 0.1\). Repeat using \(\;\alpha = 0.5\). Which value of a gives a smoother \({x_t}\)series?

c. Substitute \({x_{t - 1}} = a{x_{t - 1}} + \left( {1 - \alpha } \right){\bar x_{t - 2}}\)on the right-hand side of the expression for \({x_t}\), then substitute \({\bar x_{t - 2}}\)in terms of \({x_{t - 2}}\) and \({\bar x_{t - 3}}\), and so on. On how many of the values \({x_t},{x_{t - 1}}{\rm{,}} \ldots ,{x_1}\)does \({\bar x_t}\)depend? What happens to the coefficient on \({x_{t - k}}\) ask increases?

d. Refer to part (c). If t is large, how sensitive is x t to the initialization \({\bar x_1} = {x_1}\)? Explain.(Note: A relevant reference is the article 鈥淪imple Statistics for Interpreting Environmental Data,鈥漌ater Pollution Control Fed. J., 1981: 167鈥�175.)

The actual tracking weight of a stereo cartridge that is set to track at \({\rm{3 g}}\) on a particular changer can be regarded as a continuous rv \({\rm{X}}\) with pdf

\({\rm{f(x) = \{ }}\begin{array}{*{20}{c}}{{\rm{k(1 - (x - 3}}{{\rm{)}}^2})}&{{\rm{2}} \le {\rm{x}} \le {\rm{4}}}\\{\rm{0}}&{{\rm{otherwise}}}\end{array}\)

a. Sketch the graph of \({\rm{f(x)}}\).

b. Find the value of \({\rm{k}}\).

c. What is the probability that the actual tracking weight is greater than the prescribed weight?

d. What is the probability that the actual weight is within \({\rm{.25 g}}\) of the prescribed weight?

e. What is the probability that the actual weight differs from the prescribed weight by more than \({\rm{.5 g}}\)?

In a famous experiment carried out in 1882, Michelson,and Newcomb obtained 66 observations on the time it took for light to travel between two locations in Washington, D.C. A few of the measurements(coded in a certain manner) were 31, 23, 32, 36, 22, 26, 27, and 31.

a. Why are these measurements not identical?

b. Is this an enumerative study? Why or why not?
See all solutions

Recommended explanations on Math Textbooks

Applied Mathematics

Read Explanation

Logic and Functions

Read Explanation

Calculus

Read Explanation

Discrete Mathematics

Read Explanation

Pure Maths

Read Explanation

Probability and Statistics

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.