Question 1

Some variables that were recorded while studying diets of sharks are given below. Which of these variables is not quantitative?

Accepted Answer

Type of shark being observed is a categorical variable and not quantitative, as it does not represent a numerical value or quantity. The other variables listed are quantitative, as they involve numerical measurements.

Question 2

A survey is conducted among students taking a statistics class. Several variables are measured in the survey. Which of the variables listed below is qualitative?

Accepted Answer

Gender is a categorical variable that can take on values such as male or female. It is qualitative in nature. Number of credit hours taken during the quarter, parents' annual income and high school GPA are all quantitative variables that involve numerical measurements.

Question 3

Stream quality is based on the levels of many variables, including those listed below. Which of these variables is quantitative?

Accepted Answer

All the options listed (amount of phosphorus, number of distinct species present, and amount of dissolved oxygen) are quantitative variables because they can be measured and expressed numerically.

Question 4

During winter, red foxes hunt small rodents by jumping into thick snow cover. Researchers report that a hunting trip lasts, on average, 19 minutes and involves, on average, 7 jumps. In a surprising finding, they report that 79% of successful jumps are made in the northeast direction. Which of the following statements about these results is TRUE?

Accepted Answer

The variables "duration of hunting trip" and "number of jumps" are both quantitative variables because they involve numerical measurements. The variable "direction of successful jumps" is categorical because it involves the direction categories (northeast, southeast, southwest, northwest). Therefore, two variables are quantitative, and one variable is categorical.

Question 5

A survey records many variables of interest to the researchers conducting the survey. The following variables are some of the variables collected in a survey conducted by the USDA. Which of these variables is categorical?

Accepted Answer

Type of grain grown is a categorical variable because it describes a quality or characteristic of the data, not a numerical value.

Question 6

The EPA sends out a survey to learn about people's water-usage habits. Some of the variables to be analyzed are responses to the following questions. Which of these questions leads to categorical responses?

Accepted Answer

This question can only be answered with a yes or no response, making it a categorical variable. A and C both ask for numerical responses, and therefore are not categorical. Option D is incorrect as one of the options is categorical.

Question 7

Which of the following is a discrete variable?

Accepted Answer

A discrete variable is a variable that can only take on a finite or countable number of values. In this case, the number of different toxins present in a fish can only be a finite number, making it a discrete variable. Length and weight of a fish are continuous variables, as they can take on any value within a certain range.

Question 8

Some variables were recorded while surveying plants in a wildlife area. Which of the following variables is continuous?

Accepted Answer

Continuous variables are those that can take on any value within a certain range, such as height or weight. Count variables (A and B) are discrete and can only take on integer values. Plant species (D) is a categorical variable.

Question 9

Some variables were recorded while surveying plants in a wildlife area. Which of the following variables is discrete?

Accepted Answer

A discrete variable is a variable that can only take on a finite number of values or whole numbers. The count of petals per flower is always a whole number and cannot take on decimal values or be broken down into smaller units. Therefore, it is a discrete variable.

Question 10

Here are records of eye color for a random sample of 103 individuals:
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$$\begin{array} { | l | l | } 
\hline \text { Eye color } & \text { Number of individuals } \
\hline \text { Blue } & 21 \
\hline \text { Green } & 7 \
\hline \text { Hazel } & 23 \
\hline \text { Brown } & 47 \
\hline \text { Other } & 5 \
\hline
\end{array}$$ This data set is best represented graphically in a

Accepted Answer

A pie chart is best for representing parts of a whole, which is suitable for the given data set showing the distribution of eye colors among a group of individuals.

Question 11

During winter, red foxes hunt small rodents by jumping into thick snow cover. Researchers report that a hunting trip lasts, on average, 19 minutes and involves, on average, 7 jumps. In a surprising finding, they report that 79% of all successful jumps are made in the northeast direction. Three variables are mentioned in this report. What is the best description of the first variable mentioned?

Accepted Answer

The first variable mentioned (duration of hunting trip) is quantitative and continuous as it can take on any value within a range (e.g. 18.5 minutes, 19.2 minutes, etc.).

Answer: C
 The second variable mentioned (number of jumps) is categorical as it represents a count of discrete events rather than a continuous measurement.

Answer: C
 The third variable mentioned (direction of successful jumps) is also categorical as it represents a specific category or label (northeast) rather than a numerical measurement.

Question 12

During winter, red foxes hunt small rodents by jumping into thick snow cover. Researchers report that a hunting trip lasts, on average, 19 minutes and involves, on average, 7 jumps. In a surprising finding, they report that 79% of all successful jumps are made in the northeast direction. Three variables are mentioned in this report. What is the best description of the second variable mentioned?

Accepted Answer

The second variable mentioned is the average number of jumps (7 jumps), which is quantitative because it involves numbers and measurements, and discrete because it can only take specific values (you can't have a fraction of a jump).

Question 13

During winter, red foxes hunt small rodents by jumping into thick snow cover. Researchers report that a hunting trip lasts, on average, 19 minutes and involves, on average, 7 jumps. In a surprising finding, they report that 79% of all successful jumps are made in the northeast direction. Three variables are mentioned in this report. What is the best description of the third variable mentioned?

Accepted Answer

The third variable mentioned is the direction of the jump, which is categorical as it represents different categories or groups (north, northeast, east, etc.) rather than a numerical measurement.

Question 14

What is important to do when drawing a histogram?

Accepted Answer

Labeling the vertical axis is important because it provides information about the counts or percentages in each class interval, allowing the reader to interpret the histogram. Options A and B are not essential requirements for drawing a histogram, and option D is not always necessary as the type of skewness can often be identified by examining the shape of the distribution.

Question 15

For a biology lab course containing 10 students, the maximum point total for the quarter was 200. The point totals for the 10 students are given in the following stemplot:
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$$\begin{array} { l | l l } 
11 & 68 \
12 & 148 \
13 & 37 \
14 & 26 \
15 & \
16 & \
17 & 9
\end{array}$$ To which type of graph is this stemplot most similar?

Accepted Answer

A stemplot is most similar to a histogram because both display the distribution of data across different intervals. In this stemplot, the stems (11, 12, 13, etc.) act like the bins or intervals in a histogram (110-119, 120-129, etc.), and the leaves represent the frequency of data points within those intervals.

Question 16

For a biology lab course containing 10 students, the maximum point total for the quarter was 200. The point totals for the 10 students are given in the following stemplot:
$$\begin{array} { l | l } 
11 & 68 \
12 & 148 \
13 & 37 \
14 & 26 \
15 & \
16 & \
17 & 9
\end{array}$$ Suppose this stemplot was drawn as a histogram. What would be the best description of the shape of this histogram?

Accepted Answer

The stemplot shows that most of the data points are concentrated on the lower end (110-170 range) with fewer points extending towards the higher end (up to 179). This distribution suggests that the histogram would have a longer tail extending to the right, indicating a right-skewed (or positively skewed) distribution.

Question 17

A sample of 55 streams in severe distress was obtained during 2007. The following bar graph illustrates the number of streams that are from the Northeast, Northwest, Southeast, or Southwest. In the bar graph, the bar for the Northeast has been omitted.
What percent of streams are not from the Northeast?

Accepted Answer

Since the bar for the Northeast has been omitted, we have to subtract the number of streams from the other three regions from the total number of streams (55). We can estimate that the number of streams from the Northeast is around 15-20, which gives us:
55 - (10 + 12 + 18) = 15
Therefore, the percentage of streams that are not from the Northeast is:
100 x (55-15)/55 = 72.7%
Rounding to the nearest percent gives us choice C, which is 73%.

Question 18

A sample of 55 streams in severe distress was obtained during 2007. The following bar graph illustrates the number of streams that are from the Northeast, Northwest, Southeast, or Southwest. In the bar graph, the bar for the Northeast has been omitted.
How many streams are from the Northeast?

Accepted Answer

The total number of streams is 55, and the bars for the Northwest, Southeast, and Southwest add up to 40. Therefore, the remaining 15 streams must be from the Northeast.

Question 19

A sample of 55 streams in severe distress was obtained during 2007. The following bar graph illustrates the number of streams that are from the Northeast, Northwest, Southeast, or Southwest. In the bar graph, the bar for the Northeast has been omitted.
Which of the following statements is correct about these data?

Accepted Answer

The answer of A sample of 55 streams in severe...

Question 20

The following table shows the percent of current smokers in 2006 among various groups, according to the Centers for Disease Control and Prevention.
$$\begin{array} { l c } 
\hline \text { Group } & \text { Percent who are smoking } \
\hline \text { Men 18-24 years } & 28.5 \% \
\text { Women 18-24 years } & 19.3 \% \
\text { Men 25-29 years } & 28.9 \% \
\text { Women 25-29 years } & 23.3 \% \
\hline
\end{array}$$ Would it be correct to display these data in a single pie chart?

Accepted Answer

The data represent smokers within four different groups, making it inappropriate to combine them into a single pie chart, which is typically used for showing the proportions of a whole.

Quiz 1: Picturing Distributions With Graphs