Exam 3 Review
How can graphics be misleading when the scales do not go all the way to zero? Why are such graphics sometimes useful?
How can the graphics sometimes be misleading? The variation can seem to be larger than it really is. How can the graphics sometimes be useful? It can make it easier to show small scale trends in the data.
The accompanying figure shows the highway fuel consumption (mi/gal) for two different models of car. How is the graph misleading? How could it be drawn so that it is not misleading?
How is the graph misleading? The graph is misleading because the vertical axis scale does not start at zero. How could the graph be drawn so that it is not misleading? By starting the vertical scale at 0, the graph will not be misleading.
The given figure depicts the amounts of daily oil consumption (in millions of barrels) for two countries. Does the illustration accurately depict the data? Why or why not?
No. The height of the barrels represents oil consumption, but the eye is drawn to the volume of the barrels.
What is a pictograph? How can a pictograph enhance a graph? How can it make a graph misleading?
Pictographs are graphs embellished with additional artwork. The artwork may make the graph more appealing, but it can also distract or mislead.
For the following pair of variables, state whether you believe the two variables are correlated. If you believe they are correlated, state whether the correlation is positive or negative. Explain your reasoning. The time it takes to run 100 meters and the order of finish in the 100 meter dash
Positive correlation because running it in less time will result in a lower finish order
The pie charts in the figure represent the percentages of Americans in three age categories in 1990 and 2050 (projected). Briefly explain how the three-dimensional effects create a perceptual distortion in this case. Why would flat pies (without the three-dimensional effects) give a more accurate representation of the data?
The pieces that are 'farther' will look smaller and the pieces that are 'closer' will look larger. The actual values for the 1990 data and 2050 data are not reflected accurately in the tilted pie charts for this reason.
Decide whether the following statement makes sense (or is clearly true) or does not make sense (or is clearly false). Explain your reasoning. I had originally suspected that an increase in variable E would cause a decrease in variable F, but I no longer believe this because I found no correlation between the two variables.
The statement make sense. Originally, a negative correlation was suspected. Since no correlation was found, there is apparently no relationship between the variables.
Decide whether the following statement makes sense (or is clearly true) or does not make sense (or is clearly false). Explain your reasoning. My bar chart contains more information than yours, because I made my bars three-dimensional.
The statement does not make sense because making the bars three-dimensional does not necessarily mean that information was added. It could mean that only the appearance of the graph was changed.
Decide whether the following statement makes sense (or is clearly true) or does not make sense (or is clearly false). Explain your reasoning. The cumulative frequency of C grades in our class of 31 students was 50.
The statement does not make sense because the frequency cannot be greater than the total.
Decide whether the following statements makes sense (or is clearly true) or does not make sense (or is clearly false). Explain your reasoning. I made a frequency table with two columns, one labeled "State" and one labeled "State Capitol."
The statement does not make sense. In a frequency table, one of the columns lists the frequency of each category, which is the number of data values in the category. The table described in the given statement does not have this column.
Decide whether the following statements makes sense (or is clearly true) or does not make sense (or is clearly false). Explain your reasoning. The relative frequency of B grades in our class was 0.3.
The statement makes sense. Suppose there were 20 people in the class. If 6 received Bs, then the relative frequency of B grades was 620=0.3.
Determine whether the following variable is qualitative or quantitative, and explain why. The flavors of ice cream sold at a delicatessen
The variable is qualitative because flavors are nonnumerical categories.
Determine whether the following variable is qualitative or quantitative, and explain why. The gold medal count of each team in the most recent Olympics
The variable is quantitative because the count is a measurement.
Consider the following statement about a correlation. State the correlation clearly (for example, there is a positive correlation between variable A and variable B). Then state whether the correlation is most likely due to coincidence, a common underlying cause, or a direct cause. Explain your answer. In a large resort city, the number of burglaries increased as the number of hotel rooms increased.
There is a positive correlation between the burglaries and the number of hotel rooms. Part 2 Determine the possible explanation for the correlation. Choose the correct answer below. This correlation is due to a common underlying cause because it is possible that, with an increase in tourism, both the rate of burglaries and the number of hotel rooms increase.
Consider the following statement about a correlation. State the correlation clearly. Then state whether the correlation is most likely due to a coincidence, a common underlying cause, or a direct cause. Explain your answer. Over the past three decades, the number of miles of freeways in Los Angeles has grown, and traffic congestion has worsened.
There is a positive correlation between the number of miles of freeways and the traffic congestion in Los Angeles. The correlation is most likely due to the common underlying cause of Los Angeles having a very large population.
For the following pair of variables, state the units that might be used to measure each variable. Then state whether you believe that they are correlated. If you believe they are correlated, state whether the correlation is positive or negative. Explain your reasoning. Wind speed and air temperature along the route
To measure wind speed, the unit meters per second might be used. To measure air temperature, the unit degrees Celsius might be used. What correlation, if any, is there between the variables? There is a negative correlation because air temperature tends to increase when wind speed decreases.
Consider the scatterplot. a. State whether the diagram shows a positive correlation, a negative correlation, or no correlation. If there is a positive or negative correlation, is it strong or weak? b. Summarize any conclusions that can be drawn from the diagram.
a. Select the correct answer below. There is a weak negative correlation. b. Select the correct answer below. Players who get more points per game may be likely to have a lower three-point percentage.