MathStat474 - HW 2

Posted: Mon Jan 12. Due: Thu 1/29.

Problem 1

Solve Exercise 2.9.14: in the textbook. The problem asks to:

  • Find the sample mean and sample standard deviation of these 100-meter swim times.
  • Construct a dot diagram of the data.
  • Comment on anything unusual that you see.

Problem 2.

Solve Exercise 2.9.28. The problem asks to:

  • Construct a frequency distribution and histogram.

(Note that problem 2.9.30 has an online solution for you to see, if you are stuck and need some ideas.)

Problem 3.

Solve Exercise 2.9.39. The problem asks to:

  • Calculate the sample mean, sample variance, and sample standard deviation.
  • Construct a box plot of the data.

Problem 4.

Solve Exercise 2.9.44. The problem asks to compare two boxplots from added data.

Problem 5.

This problem is about visualization of distributions & interpretation of histograms.

In the workplace, depression is a leading cause of absenteeism and loss of productivity (Greenberg, et al. 1993). To assess the degree to which people suffer from depression, prior to receiving treatment, data were collected on the number of days that 105 patients were depressed prior to starting a new treatment. These data are displayed in the following table and histogram:

Days Count
[20–60] 5
[60–100] 10
[100–140] 20
[140–180] 30
[180–220] 16
[220–260] 10
[260–300] 6
[300–340] 4
[340–380] 2
[380–420] 0
[420–460] 0
[460–500] 0
[500–540] 2

  • Which of the following is a possible value of the median number of days that patients were depressed? Explain your answer.
  1. 53
  2. 170
  3. 220
  4. 290

  • Using this same histogram of 105 patients, which of the following is most likely to be true? Explain your answer.

    1. The mean will be larger than the median.
    2. The median will be larger than the mean.
    3. The mean and median will be about the same.

  • Using this same histogram of 105 patients, what percentage of patients had 220 or more days of depression? Explain your answer.

    1. 13
    2. 23
    3. 24