Math 143 C/E, Spring 2001
IPS Reading Discussion Questions
Chapter 1, Section 1 (pp. 5-23)



  1. List by name all of the types of graphical displays of data that are discussed in the section. Which ones seem best for categorical data? Which for quantitative? Are there any that could not be used for categorical data? for quantitative data?

    Bar graphs and pie charts seem particularly associated with categorical data. They could, however, be used in conjunction with certain discrete quantitative variables (such as a variable whose values were `1', `2', `3' and `7'). Stemplots, histograms and time plots are used only for quantitative data.

  2. Why is it helpful to see a graphical display of data? Why not just look at the raw data itself (like in Table 1.1, for instance)?

    Visual displays help us in discerning the overall pattern to the data and deviations from that pattern. In other words, such displays are instrumental in our being able to make sense of data.

  3. How are stemplots and histograms similar? How are they different? Are there advantages of one over the other?

    Stemplots can give the impression of shape in much the same way as a histogram. When the divisions between data (called bins) of a histogram are the same as the breaks in the stemplot, the two types of displays are equivalent.

    A histogram provides greater flexibility in determining bin sizes, and hence makes it more appropriate than a stemplot for large data sets.

  4. What is the difference between an histogram and a bar graph? Would they be used for the same types of data (categorical and/or quantitative)?

    We have already said above that histograms are used exclusively with quantitative data, whereas bar graphs generally are employed for categorical data. The key difference is that a bar graph has a bar for every value of the variable, while a histogram has bars for ranges of values. Generally the bars of a bar graph are separated by space while those of a histogram are butted up together (suggesting a continuum of possible values).

  5. What is the difference between frequency and relative frequency?

    Frequency is the same as count. You count the number of times a certain value (or range of values) occurs in your data set. Relative frequency basically means percentage - you find what percentage of the overall set of values observed were such-and-such value. For example, in a class of 12 men and 18 women, the frequency of women is 18 while the relative frequency is 0.6 (or 60 axis is always one of these two things (frequency or relative frequency).

  6. Table 1.1 gives Newcomb's measurements of the speed of light, and a time plot of these measurements appears on p. 19. Use Minitab to produce a dotplot of these same measurements. For what purposes might you prefer having the dotplot? the time plot? Which of the two is more rightly called a distribution?

    The dot plot, which is an example of a distribution (whereas a time plot is not), gives a sense of the center (the median, mean or mode) as well as the spread (variability) of the data set. A time plot does not give a sense of center nor spread, but would be valuable if we wanted to see if there were any trend to the measurements over time - if the values seem bigger for later trials (perhaps indicating that the instrument of measurement is changing with time, perhaps as it warms up), etc.