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.