Solutions to tutorial 1

Identifying the type of data

a.quantitative (ratio)b.qualitative (ordinal)

c.qualitative (nominal)d.quantitative (ratio)

Age Data

Determining appropriate classes for the frequency distribution for the age data

  • With 200 data points, approximately 9 - 10 classes is appropriate.
  • The range of the data = 79 - 18 = 61
  • Approximate class width = 61/9 = 6.78
  • Use a class width of 10 with upper limits of 20 through 80

I have chosen a class width of 10 as it is convenient and easy to use. Note that a class width of 10 gives us 7 classes. Table 2.4 in the text book indicates that with 200 observations we should use approximately 9-10 classes. A class width of 7 would give us 9 classes. However a class width of 7 is not as convenient as a class width of 10. There is no fixed rule about the number of class intervals. Table 2.4 is only a guide. You just need to make sure that the chosen number of classes is not too different from the suggested number of classes, i.e.7 classes is not too far from the suggested 9-10, and not too much information about the distribution of the ages is lost by only using 7 classes.

Frequency Distribution and Histogram

The frequency distribution and histogram which follow, represent one possible solution based on the class intervals determined above. Many others are possible.

Age (years) / Midpoint / Frequency
20 / 15 / 7
30 / 25 / 63
40 / 35 / 48
50 / 45 / 39
60 / 55 / 16
70 / 65 / 23
80 / 75 / 4
More / 0

  1. The population of interest would be the ages of all adults who live in Wagga Wagga.
  2. The data represents a sample as the question clearly states that "A random sample of 200 adults who live in Wagga Wagga was taken."
  3. The distribution of age appears to be positively skewed.

Annual Income Data

Determining appropriate classes for the frequency distribution for the salaries

  • With 200 data points, approximately 9 - 10 classes is appropriate.
  • The range of the data = 180 - 8 = 172
  • Approximate class width = 172/9 = 19.11
  • Use a class width of 20 with upper limits 20 through 180

Frequency distribution and histogram

The frequency distribution and histogram which follow, represent one possible solution based on the class intervals determined above. Many others are possible.

Annual Income ($000's) / Midpoint / Frequency
20 / 10 / 45
40 / 30 / 86
60 / 50 / 51
80 / 70 / 13
100 / 90 / 3
120 / 110 / 1
140 / 130 / 0
160 / 150 / 0
180 / 170 / 1
More / 0

  1. The population of interest would be the annual incomes of all adults who live in Wagga Wagga.
  2. The data represents a sample as the question clearly states that "A random sample of 200 adults who live in Wagga Wagga was taken."
  3. The distribution of annual income appears to positively skewed with an outlier to the right (an annual income of $180 000).