Exercises


  1. For each situation described, state whether the data collected will be categorical or numerical. Give examples of what the data might look like.
    Situation Categorical or Numerical Examples of Data
    Ice cream flavour    
    Mosquito count    
    Types of homes for sale    
    Carbon dioxide level    
  2. For each situation described, state whether the data collected will be discrete or continuous. Give examples of what the data might look like.
    Situation Discrete or Continuous Examples of Data
    Shoe size    
    Snow fall    
    Book sales    
    Tax rate    
    Cholesterol level    
  3. The following racing times (in seconds) were collected:\[15.6,~14.9,~15.6,~15.9,~14.1,~16.5,~13.7,~13.7,~14.5,~14.3,~13.8,~13.5,~13.4,~16.0,~17.0\]
    1. Order the data set from fastest time to slowest time.
    2. Explain why a frequency table may not be a helpful way to organize the data.
    3. Explain why neither a circle graph nor a line graph is an appropriate way to display this data set. 
  4. Martha thinks that discrete data consists of only whole numbers and continuous data must consist of numbers with fractional parts. To convince Martha that this is not true, try the following:
    1. Give an example of discrete data that might consist of some decimal numbers.
    2. Give an example of continuous data that might not have any numbers with fractional parts.
  5. Inflation is the rise of prices for goods and services. It also signals that the purchasing power of a country's currency is falling. The following graphs show the inflation rate of a country for \(8\) years.

    A line graph with Year along the horizontal axis and inflation rate (%) along the vertical. Year 1 has a rate of 0.15, year 2 0.22, year 3 0.45, year 4 0.73, year 5 1.5, year 6 2.6, year 7 2.7, and year 8 4.1.

    A bar graph with Year along the horizontal axis and inflation rate (%) along the vertical. Year 1 has a rate of 0.15, year 2 0.22, year 3 0.45, year 4 0.73, year 5 1.5, year 6 2.6, year 7 2.7, and year 8 4.1.

    1. During which year did the inflation rate of the country grow the most? Explain how you can determine this information from each of the graphs.
    2. Is the inflation rate continuous data or discrete data? Which graph do you think is a more appropriate choice for displaying the data?
  6. The following table lists postage costs based on the weight of the mail. If someone collected data of postage costs over a wide range of mail sent, would this data collected be continuous or discrete? Explain.
    Postage Rate (\($\)) Weight (g)
    \($1.00\) \(0\) – \(30\)
    \($1.20\) \(30\) – \(50\)
    \($1.80\) \(50\) – \(100\)
  7. In this question, we will create a graph that plots pairs of the form \((x,y)\) that satisfy the equation \(x+y = 7\). 
    1. Two examples of pairs that satisfy the equation \(x+y=7\) are \((1,6)\) and \((1.5, 5.5)\). Find at least eight more pairs that satisfy this equation. Are you collecting continuous data or discrete data?
    2. Graph the ten pairs from part a) in the coordinate plane. Would a line graph be an appropriate graph to display the relationship between the values of \(x\) and \(y\)?
    3. Explain why the line graph of the data from part a) has the shape that it does. 
  8. When a positive number is rounded to the nearest integer, one rule says the following: If the digit in the tenths place is \(5\) or higher, round to the nearest integer to the right on the number line. Otherwise, round to the nearest integer to the left on the number line.
    1. Fill in the following table with appropriate rounding of the given value of \(x\).
      \(x\) \(y\)
      (rounded value)
      \(1.4\)  
      \(1.8\)  
      \(1.9\)  
      \(2\)  
      \(2.2\)  
      \(2.5\)  
      \(2.8\)  
      \(3.1\)  
      \(3.5\)  
      Which variable quantity in the table is continuous and which is discrete? Explain.
    2. Graph the pairs from the table above. Does it make sense to create a line graph from this set of points? Explain.
    3. What would this graph look like if you plotted a point for every positive number \(x\) on the number line? 
    4. Describe a similar rounding rule for rounding negative numbers. What would the graph look like if you plotted a point for every number \(x\) on the number line?