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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

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4772

5133

5095

4618

4848

5089

5518

5333

5164

5342

5069

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4925

5001

4803

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5256

5207

5621

4918

5138

4786

4500

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4173

5296

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5173

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5555

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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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