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Chapter 1: Q24E (page 27)

The accompanying data set consists of observations on shear strength (lb) of ultrasonic spot welds made on a certain type of alclad sheet. Construct a relative frequency histogram based on ten equal-width classes with boundaries 4000, 4200, 鈥�. [The histogram will agree with the one in 鈥淐omparison of Properties of Joints Prepared by Ultrasonic Welding and Other Means鈥� (J. of Aircraft, 1983: 552鈥�556).] Comment on its features.

5434

4948

4521

4570

4990

5702

5241

5112

5015

4659

4806

4637

5670

4381

4820

5043

4886

4599

5288

5299

4848

5378

5260

5055

5828

5218

4859

4780

5027

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4772

5133

5095

4618

4848

5089

5518

5333

5164

5342

5069

4755

4925

5001

4803

4951

5679

5256

5207

5621

4918

5138

4786

4500

5461

5049

4974

4592

4173

5296

4965

5170

4740

5173

4568

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5078

4900

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5248

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4723

5275

5419

5205

4452

5227

5555

5388

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4681

5076

4774

4931

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5582

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4823

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5188

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5042

5189

4986

Short Answer

Expert verified

The histogram is represented as,

Step by step solution

01

Given information

The data for the shear strength (lb) of ultrasonic spot welds made on a certain type of alclad sheet is provided.

02

Construct a histogram and state its features

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

The total number of observations is 100.

The relative frequency is computed as,

\({\rm{relative frequency }} = \frac{{frequency}}{{Total\;number\;of\;observations}}\)

The table representing the relative frequency is as follows,

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

Steps to construct a histogram are,

1) Determine the frequency or the relative frequency.

2) Mark the class boundaries on the horizontal axis.

3) Draw a rectangle on the horizontal axis corresponding to the frequency or relative frequency.

The histogram is represented as,

From the above-diagram, it can be concluded that the distribution is approximately negatively-skewed. There are no outliers present in the data. The typical or representative value of x is 5049.

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Most popular questions from this chapter

a. Give three different examples of concrete populations and three different examples of hypothetical populations.

b. For one each of your concrete and your hypothetical populations, give an example of a probability question and an example of an inferential statistics question.

a. Give three different examples of concrete populations and three different examples of hypothetical populations.

b. For one each of your concrete and your hypothetical populations, give an example of a probability question and an example of an inferential statistics question.

Consider the strength data for beams given in Example

1.2.

a. Construct a stem-and-leaf display of the data. What appears to be a representative strength value? Do the observations appear to be highly

concentrated about the representative value or rather spread out?

b. Does the display appear to be reasonably symmetric about a representative value, or would you describe its shape in some other way?

c. Do there appear to be any outlying strength values?

d. What proportion of strength observations in this sample exceeds 10 MPa?

The propagation of fatigue cracks in various aircraft parts has been the subject of extensive study in recent years. The accompanying data consists of propagation lives(flight hours/\({\bf{1}}{{\bf{0}}^{\bf{4}}}\)) to reach a given crack size in fastener holes intended for use in military aircraft (鈥淪tatistical Crack Propagation in Fastener Holes Under Spectrum Loading,鈥� J. Aircraft,1983: 1028鈥�1032):

.736 .863 .865 .913 .915 .937 .983 1.007

1.011 1.064 1.109 1.132 1.140 1.153 1.253 1.394

  1. Compute and compare the values of the sample mean and median.
  2. By how much could the largest sample observation be decreased without affecting the value of the median?

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 \({\rm{.5 g}}\)?
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