Section 1.2 Exercises

Complete the following exercises from Section 1.2:

• Problem 11
• Problem 15
• Problem 17
• Problem 20
• Problem 24

See the Vignettes document for examples in R.

See the companion website to download datasets in SPSS or MINITAB format.

Problems:

• 11 Construct a stem-and-leaf display where stem 6 is repeated twice, stem 7 is repeated twice, and so on to produce a stem-and-leaf plot with eight rows. Use dataset ex01.11.
• 15 Construct a comparative stem-and-leaf plot by listing stems in the middle of the page and leaves out to the right and left. Describe the similarities and differences for the two types. Use dataset ex01.15.
• 17 Transducers are produced in batches of 50. Testing of 60 batches resulted in the numbers of nonconforming transducers recorded in dataset ex01.17.
  • a) Determine the frequencies and relative frequencies for the observed numbers of nonconforming transducers in a batch.
  • b) What proportion of batches in the sample have at most five nonconforming transducers? What proportion have fewer than five? What proportion have at least five nonconforming units.
  • c) Draw a histogram of the data using relative frequency on the vertical scale, and comment on its features.
• 20 The data in ex01.20 represents the total length of streets in a subdivision.
  • a) Construct a stem-and-leaf display using the thousands digit as the stem. Comment on the various features of the display.
  • b) Construct a histogram using the class boundaries 0,1000,2000,3000,4000,5000, and 6000. What proportion have total length less than 2000? Between 2000 and 4000? How would you describe the shape of the histogram?
• 24 Dataset ex01.24 represents the shear strength of ultrasonic spot welds. Construct a relative frequency histogram based on ten equal-width classes with boundaries 4000,4300,.... . Comment on its features.