Answers and Solutions


  1. Temperature Vs. Drink Sales Scatter Plot
    Temperature in celsius is along the horizontal axis and Drink Sales in dollars along the vertical. 5 points are plotted at (12,200), (14,220), (18,300), (20,350), and (26,450).
  2. Below are the two graphs. Interchanging the roles of the variables means reversing the roles of the \(x\)- and \(y\)-coordinates. The second graph can be obtained from the first graph by reflecting each point in the diagonal line through the points \((0,0)\) and \((6,6)\).
    Scatter Plot 1
    Variable 1 is along the horizontal axis and Variable 2 along the vertical. 5 points are plotted at (1,1), (3.5,4.5), (3,6), (5,1), and (2,4).
    Scatter Plot 2
    Variable 2 is along the horizontal axis and Variable 1 along the vertical. 5 points are plotted at (1,1), (4.5,3.5), (6,3), (1,5), and (4,2).
    1. The two variables are the condition of the vehicle (perhaps given as an "overall score") and the age of a vehicle (perhaps given as number of years on the road). One might expect the condition of a vehicle to be at least somewhat dependent on the age of the vehicle.
    2. The two variables are the brand name of the car and the value at which the car was resold. One might expect that the sale price of a car will be at least somewhat dependent on the brand of car.
    3. The two variables are the popularity of a vehicle (but it is not exactly clear how we might measure that) and the colour of the vehicle. It may not be obvious whether or not the popularity of a vehicle will be dependent on its colour. 
       
  4. The table shows the scores for \(18\) students.
    1. The mean score on the practice test was \(\dfrac{906}{18} \approx 50\) and the mean score on the final test was \(\dfrac{1241}{18} \approx 69\). Therefore, the mean score on the final test was about \(19\) points higher than the mean score on the practice test.
    2. From the table, exactly \(2\) students did worse on the final test than the practice test and exactly \(1\) student got the same score. The remaining \(15\) students improved from the practice test to the final test which represents \(\dfrac{15}{18}\) or  \(83 \dfrac{1}{3} \%\).
      The largest improvement was \(22\) points on the practice test to \(85\) points on the final test which is a change of \(63\) points.
    3. A scatter plot of practice test scores along the horizontal axis and test scores along the vertical from the test score table.
      The scatter plot does not appear to give an easier way to calculate the means of the two tests than the numbers in the table. Can you use the shape of the scatter plot to estimate the means?
      We can use the scatter plot to find the students that improved from one test to the other, and some people might find this easier than looking through the data table. If a student has improved, then their data point will lie above the diagonal line as shown:
    4. Answers may vary.
      All data points lie above (or on) the horizontal line representing a score of \(50\) on the final test. This shows that every student got at least \(50\) on the final test.
      Most of the data points lie above the diagonal line shown in the graph in part c). This indicates that most students improved from the practice test to the final test.
    1. Answers may vary depending on the interval choices for the histogram.
      Age in years is along the horizontal axis ranging from 0 to 50 and split into 5 equal intervals or bins. From left to right the bins have the following frequencies: 1, 7, 4, 1, and 1.
    2. Answers may vary depending on the interval choices for the histogram.
      Height in cm is along the horizontal axis ranging from 120 to 180 and split into 4 equal intervals or bins. From left to right the bins have the following frequencies: 2, 4, 5, and 3.
    3. Answers may vary. Since the data points correspond to individual people and are not related, it does not make sense to plot this data using a line graph.
    4. We would expect a person's height to be dependent on their age, so we put the variable of age on the horizontal axis.
      A scatter plot of age in years along the horizontal axis and height in cm along the vertical from the data table.
  6. Yes, it is possible. This would indicate that there is a linear relationship between the variables.
    1. Age is numerical data (which could be continuous, but is likely entered as only integers). Vision score is likely categorical data, but might be measured using a numerical scale. Reaction time will be continuous data. Since no pair of these three variables are measured on similar scales, it seems unlikely that we can plot all three variables on the same scatter plot. We could use a scatter plot to compare any of the pairs of variables.
    2. Arm length and leg length are both continuous data and could be measured using the same units. We could create a scatter plot of "Arm Length Vs. Age" and a separate plot of "Leg Length Vs. Age". If we choose our scale carefully, we can actually plot all of the data on one scatter plot. We could use different shapes when making the points. In this case, we have (Age, Arm Length) as circular points and (Age, Leg Length) as triangular points.
      This idea is shown using the data in the following table to create the scatter plot:
      Age Arm Length (cm) Leg Length (cm)
      \(24\) \(63.5\) \(73.5\)
      \(20\) \(62.0\) \(70.2\)
      \(15\) \(56.2\) \(67.0\)
      A scatter plot of the data from the table provided.
  8. Solutions will vary. A few ideas are given below (without displaying the associated graphs):
    • The categorical data of "Car Owner" could be displayed in a circle graph.
    • The discrete data of "Number of Pets" could be displayed in a bar graph.
    • It does not seem as though any data pairs in the table would be appropriate for a line graph.
    • The numerical "Salary" data could be displayed in a histogram.
    • The numerical paired data of "Age" and "Height" could be displayed in a Scatter Plot.