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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

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?

A trial has just resulted in a hung jury because eight members of the jury were in favour of a guilty verdict and the other four were for acquittal. If the jurors leave the jury room in random order and each of the first four leaving the room is accosted by a reporter in quest of an interview, what is the\({\rm{pmf}}\)of\({\rm{X = }}\)the number of jurors favouring acquittal among those interviewed? How many of those favouring acquittal do you expect to be interviewed?

The accompanying summary data on CeO2 particlesizes (nm) under certain experimental conditions wasread from a graph in the article 鈥淣anoceria鈥擡nergetics of Surfaces, Interfaces and WaterAdsorption鈥� (J. of the Amer. Ceramic Soc., 2011:3992鈥�3999):

3.0鈭�<3.5 3.5鈭�<4.0 4.0鈭�<4.5 4.5鈭�<5.0 5.0鈭�<5.5

5 15 27 34 22

5.5鈭�<6.0 6.0鈭�<6.5 6.5鈭�<7.0 7.0鈭�<7.5 7.5鈭�<8.0

14 7 2 4 1

a. What proportion of the observations are less than 5?

b. What proportion of the observations are at least 6?

c. Construct a histogram with relative frequency on the vertical axis and comment on interesting features. In particular, does the distribution of particle sizes appear to be reasonably symmetric or somewhat skewed? (Note:The investigators fit lognormaldistribution to the data; this is discussed in Chapter 4.)

d. Construct a histogram with density on the vertical axis and compare to the histogram in (c).

The amount of flow through a solenoid valve in an automobile鈥檚

pollution-control system is an important characteristic. An experiment was carried out to study how flow rate depended on three factors: armature length, spring load, and bobbin depth. Two different levels (low and high) of each factor were chosen, and a single observation on flow was made for each combination oflevels.

a. The resulting data set consisted of how manyobservations?

b. Is this an enumerative or analytic study? Explainyour reasoning.

A sample of 26 offshore oil workers took part in a simulated escape exercise, resulting in the accompanying data on time (sec) to complete the escape (鈥淥xygen Consumption and Ventilation During Escape from an Offshore Platform,鈥� Ergonomics, 1997: 281鈥�292):

389 356 359 363 375 424 325 394 402

373 373 370 364 366 364 325 339 393

392 369 374 359 356 403 334 397

a. Construct a stem-and-leaf display of the data. How does it suggest that the sample mean and median will compare?

b. Calculate the values of the sample mean and median.(Hint:\(\sum {{x_i} = } \)9638.)

c. By how much could the largest time, currently 424, be increased without affecting the value of the sample median? By how much could this value be decreased without affecting the value of the sample median?

d. What are the values of \(\bar x\)and \(\tilde x\), when the observations are re expressed in minutes?
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