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Chapter 1: Q11E (page 24)

The accompanying specific gravity values for various wood types used in construction appeared in the article 鈥淏olted Connection Design Values Based on European Yield Model鈥� (J. of Structural Engr., 1993: 2169鈥�2186):

.31

.35

.36

.36

.37

.38

.40

.40

.40

.41

.41

.42

.42

.42

.42

.42

.43

.44

.45

.46

.46

.47

.48

.48

.48

.51

.54

.54

.55

.58

.62

.66

.66

.67

.68

.75

Construct a stem-and-leaf display using repeated stems, and comment on any interesting features of the display.

Short Answer

Expert verified

The stem and leaf display for the provided scenario is,

Unit: 3L|1=0.31 and 3R|5=0.35.

Step by step solution

01

Given information

The gravity values for various wood types used in construction is provided as,

.31

.35

.36

.36

.37

.38

.40

.40

.40

.41

.41

.42

.42

.42

.42

.42

.43

.44

.45

.46

.46

.47

.48

.48

.48

.51

.54

.54

.55

.58

.62

.66

.66

.67

.68

.75

02

Construct a stem and leaf diagram and comment

a.

A stem-and-leaf display providesa visual representation of the dataset.

The steps to construct a stem-and-leaf display are as follows,

1) Select the leading digit for the stem and trailing digits for the leaves.

2) Represent the stem digits vertically and similarly the trailing digits corresponding to the stem digits.

3) Mention the units for the display.

The stem and leaf display for the provided scenario is,

Unit: 3L|1=0.31 and 3R|5=0.35.

From the above display, the features are,

1)It can be observed that a good representative strength value is 0.45.

2) The display appears to be right or positively skewed and not symmetric.

3) The range of the data is 0.44 (0.75-0.31).

4)There is a reasonably large amount of variation in the data.

5)A possible outlier can be observed as 0.75.

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Most popular questions from this chapter

Zinfandel is a popular red wine varietal produced almostexclusively in California. It is rather controversialamong wine connoisseurs because its alcohol contentvaries quite substantially from one producer to another.In May 2013, the author went to the website klwines.com, randomly selected 10 zinfandels from among the 325 available, and obtained the following values of alcoholcontent (%):

14.8 14.5 16.1 14.2 15.9

13.7 16.2 14.6 13.8 15.0

  1. Calculate and interpret several measures of center.
  2. Calculate the sample variance using the defining formula.
  3. Calculate the sample variance using the short cut formula after subtracting 13 from each observation

The three measures of center introduced in this chapter are the mean, median, and trimmed mean. Two additional measures of center that are occasionally used are the midrange,which is the average of the smallest and largest observations, and the midfourth,which is the average of the two fourths. Which of these five measures of center are resistant to the effects of outliers and which are not? Explain your reasoning.

The weekly demand for propane gas (in \({\rm{1000s}}\) of gallons) from a particular facility is an \({\rm{rv}}\) \({\rm{X}}\) with pdf

\({\rm{f(x) = }}\left\{ {\begin{array}{*{20}{c}}{{\rm{2}}\left( {{\rm{1 - }}\frac{{\rm{1}}}{{{{\rm{x}}^{\rm{2}}}}}} \right)}&{{\rm{1}} \le {\rm{x}} \le {\rm{2}}}\\{\rm{0}}&{{\rm{ otherwise }}}\end{array}} \right.\)

a. Compute the cdf of \({\rm{X}}\).

b. Obtain an expression for the \({\rm{(100p)th}}\) percentile. What is the value of \({\rm{\tilde \mu }}\)?

c. Compute \({\rm{E(X)}}\) and \({\rm{V(X)}}\).

d. If \({\rm{1}}{\rm{.5}}\) thousand gallons are in stock at the beginning of the week and no new supply is due in during the week, how much of the \({\rm{1}}{\rm{.5}}\) thousand gallons is expected to be left at the end of the week? (Hint: Let \({\rm{h(x) = }}\) amount left when demand \({\rm{ = x}}\).)

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.

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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