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AP Statistics Practice Quiz: Representing a Quantitative Variable with Graphs

Written by AP Content Team, Verified for 2026 AP Exams, Last updated: May 2026

Test your understanding with short quizzes. This quiz has 16 questions to check your progress.

Question 1 of 16

According to the provided content, which of the following best describes a discrete variable?

All Questions (16)

According to the provided content, which of the following best describes a discrete variable?

A) A variable that can take on infinitely many values within an interval.

B) A variable that can take a countable number of values.

C) A variable represented by the height of a bar in a histogram.

D) A variable that is split into a 'stem' and a 'leaf'.

Correct Answer: B

The content explicitly states, 'A discrete variable can take a countable number of values.'

A variable that can take on infinitely many values within a given interval is known as what type of variable?

A) A discrete variable

B) A cumulative variable

C) A continuous variable

D) A stem variable

Correct Answer: C

The content defines a continuous variable as one that 'can take on infinitely many values within an interval.'

Which of the following is an example of a discrete variable?

A) The exact weight of a student.

B) The precise time it takes to run a mile.

C) The number of students in a classroom.

D) The height of a tree.

Correct Answer: C

The number of students in a classroom is countable (e.g., 25, 26, 27 students, but not 25.5). The other options represent measurements that can take on infinitely many values within an interval, making them continuous. This aligns with the definition of a discrete variable having a 'countable number of values.'

Which of the following is an example of a continuous variable?

A) The number of cars in a parking lot.

B) The number of questions answered correctly on a test.

C) The volume of water in a bottle.

D) The number of leaves on a stem-and-leaf plot.

Correct Answer: C

The volume of water can take on any value within an interval (e.g., 1.25 liters, 1.251 liters), making it continuous. The other options are countable and therefore discrete. This aligns with the definition of a continuous variable taking 'infinitely many values within an interval.'

In a histogram, what does the height of each bar represent?

A) A single data value.

B) The cumulative count of all observations up to that point.

C) The number or proportion of observations falling within a specific interval.

D) The 'leaf' portion of a data value.

Correct Answer: C

The content states, 'A histogram's bar height shows the number or proportion of observations in an interval.'

Which graphical representation for quantitative data involves splitting each data value into two parts, a 'stem' and a 'leaf'?

A) Dotplot

B) Histogram

C) Cumulative graph

D) Stem and leaf plot

Correct Answer: D

The definition provided is 'A stem and leaf plot splits each data value into a 'stem' and a 'leaf'.'

A data analyst creates a graph where each individual observation is shown as a single mark above a horizontal axis. Which type of graph was created?

A) A histogram

B) A dotplot

C) A cumulative graph

D) A stem and leaf plot

Correct Answer: B

The content describes a dotplot as a graph that 'represents each observation with a dot on a horizontal axis.'

What information is conveyed by a cumulative graph?

A) The frequency of data within distinct, non-overlapping intervals.

B) The individual value of every observation in the dataset.

C) The number or proportion of data less than or equal to a specific value.

D) The separation of data values into two components for display.

Correct Answer: C

The content defines a cumulative graph as one that 'shows the number or proportion of data less than or equal to a given value.'

A researcher wants to create a graph for a quantitative variable that groups data into intervals and displays the frequency of each interval using bars. Which graphical representation should be used?

A) A dotplot, because it shows each observation.

B) A histogram, because its bars represent the number of observations in an interval.

C) A stem and leaf plot, because it splits data values.

D) A cumulative graph, because it shows proportions.

Correct Answer: B

The key features described—grouping data into intervals and using bar height for frequency—are the defining characteristics of a histogram as per the provided content.

The number of goals scored by a soccer team in a season is a quantitative variable. How would this variable be classified?

A) Continuous, because the number of goals can vary.

B) Discrete, because the number of goals is a countable value.

C) Cumulative, because the total number of goals can be summed.

D) Graphical, because it can be represented by a graph.

Correct Answer: B

The number of goals is countable (0, 1, 2, 3, etc.) and cannot take on values in between (e.g., 2.5 goals). Therefore, it is a discrete variable, which can take a 'countable number of values.'

On a cumulative graph of student test scores, the point (85, 0.75) is plotted. What does this point signify?

A) 75% of students scored exactly 85.

B) The average score of 75% of the students was 85.

C) 75% of students scored 85 or less.

D) 85% of students scored 75 or less.

Correct Answer: C

A cumulative graph 'shows the number or proportion of data less than or equal to a given value.' Therefore, a point (x, y) means that a proportion y of the data is less than or equal to the value x. In this case, 75% (0.75) of students scored less than or equal to 85.

Which statement is directly supported by the provided content?

A) Histograms are the only valid way to represent quantitative data.

B) Dotplots and stem-and-leaf plots are identical in their construction.

C) There are multiple types of graphical representations for quantitative data distributions.

D) Continuous variables cannot be represented graphically.

Correct Answer: C

The content explicitly states, 'Many other graphical representations exist for quantitative data distributions.' This confirms that the listed methods are not exhaustive.

A primary difference between a dotplot and a histogram, based on the provided descriptions, is that:

A) A dotplot is used for discrete variables, while a histogram is used for continuous variables.

B) A dotplot shows each individual data point, while a histogram groups data into intervals.

C) A dotplot uses a vertical axis for frequency, while a histogram uses a horizontal axis.

D) A dotplot cannot be used for quantitative data, while a histogram can.

Correct Answer: B

Based on the definitions, a dotplot 'represents each observation with a dot,' preserving individual data. A histogram's 'bar height shows the number or proportion of observations in an interval,' meaning individual values are grouped and not distinguishable.

A scientist measures the exact length, in centimeters, of several plant leaves. What type of quantitative variable is being measured?

A) A discrete variable, because each leaf has one length.

B) A continuous variable, because length can be any value within an interval.

C) A cumulative variable, because the lengths can be ordered.

D) A stem variable, because the data could be put in a stem-and-leaf plot.

Correct Answer: B

The exact length is a measurement that can take on any value within a range (e.g., 10.1 cm, 10.11 cm, 10.112 cm). This fits the definition of a continuous variable, which 'can take on infinitely many values within an interval.'

What is the fundamental principle behind the construction of a stem-and-leaf plot?

A) To show the cumulative proportion of data.

B) To display the frequency of data within specified class intervals.

C) To represent each data point as a dot on a number line.

D) To split each data value into two parts for a compact display of the distribution.

Correct Answer: D

The content directly states that 'A stem and leaf plot splits each data value into a 'stem' and a 'leaf'.' This is its fundamental construction principle.

How does the information presented on the vertical axis of a cumulative graph differ from that of a standard frequency histogram?

A) The cumulative graph's vertical axis shows intervals, while the histogram's shows individual values.

B) The cumulative graph's vertical axis shows a running total, while the histogram's shows the count within a specific interval.

C) There is no difference; both show the frequency of observations.

D) The cumulative graph's vertical axis represents the 'stem', while the histogram's represents the bar height.

Correct Answer: B

A cumulative graph's vertical axis represents the 'number or proportion of data less than or equal to a given value,' which is a running total. A histogram's vertical axis (bar height) represents the 'number or proportion of observations in an interval,' which is a count for just that specific bin, not a cumulative one.