Introduction
Data Displays Extended is an important Grade 7 math skill because students are moving from simple answers toward explaining how the math works.
In this lesson, students use models, real questions, worked examples, practice problems, and two online quizzes to build confidence with data displays extended.
What Is Data Displays Extended?
Data Displays Extended means reading, creating, and explaining displays so data can answer real questions.
The goal is not only to get the answer. Students should be able to show the idea, explain the strategy, and check whether the answer makes sense.
Understanding Data Displays Extended
Before solving, students should slow down and decide what each number, shape, unit, or label represents.
- Read the title, labels, and scale before answering.
- Use the scale value instead of counting marks as ones when the graph is scaled.
- Compare categories by subtracting or adding values from the display.
- Explain what the data shows in a complete sentence.
Visual Models
Visual Model 1
Question: A line plot shows the number of goals scored by 15 soccer players this season:
Which statement best describes the data?
| Goals | 2 | 2 | 3 | 3 | 3 | 4 | 4 | 4 | 4 | 5 | 5 | 6 | 6 | 7 | 9 |
|---|
- A. The data shows a uniform distribution with all scores equally common
- B. Most players scored between 3 and 5 goals, with one outlier at 9
- C. All players scored at least 2 goals, with the median at 4
- D. The mode is 4 goals, appearing 4 times
Why it works: Counting occurrences: 2 (twice), 3 (three times), 4 (four times), 5 (twice), 6 (twice), 7 (once), 9 (once). The value 4 appears most frequently, making it the mode.
Answer: The mode is 4 goals, appearing 4 times
Worked Examples
Example 1
Question: A histogram shows the same data displayed in two different ways: Version A uses intervals of width 5 (0--5, 5--10, 10--15, etc.), while Version B uses intervals of width 10 (0--10, 10--20, 20--30, etc.). How would the two histograms appear different?
- A. Version A would show more detail and variation; Version B would show a smoother pattern
- B. Both histograms would look identical regardless of interval width
- C. Version B would be more accurate because larger intervals are always better
- D. Version A would have fewer bars but higher frequencies
- Smaller intervals reveal more variability and detail in the distribution; larger intervals group data together, creating a smoother appearance.
- Both are valid depending on the purpose.
Answer: Version A would show more detail and variation; Version B would show a smoother pattern
Example 2
Question: A histogram shows the frequency of ages in a fitness class: 10--20 (6), 20--30 (18), 30--40 (24), 40--50 (12). A promotional flyer claims "Our class serves ALL age groups equally." Is this supported by the histogram?
- A. Yes, because four different age intervals are shown
- B. No, because frequencies vary significantly (6 to 24)
- C. Yes, because the highest bar represents the most popular age group
- D. No, because the bar widths are all equal
- Equal representation would show nearly equal frequencies.
- The 30--40 interval (24) has 4 times as many people as the 10--20 interval (6), contradicting the "equal" claim.
Answer: No, because frequencies vary significantly (6 to 24)
Example 3
Question: A dot plot shows the number of text messages sent by 12 students in one day: 5, 8, 10, 10, 12, 12, 12, 15, 18, 20, 22, 25. Which measure BEST represents the "typical" number of messages sent?
- A. The mean (approximately 14.3)
- B. The median (12.5)
- C. The mode (12)
- D. The range (20)
- The mode (12 messages, appearing 3 times) best represents what students "typically" sent because it identifies the most common value.
- The mean is inflated by 25 outliers, and the median (12.5) is between two values.
Answer: The mode (12)
Real-World Word Problems
Problem 1
Question: Two classes have test-score distributions displayed as histograms with identical means (both 75). Class A has most scores clustered near 75 (narrow, bell-shaped); Class B has scores spread across the range (flat). What does this comparison reveal?
- A. Class A has higher variability than Class B
- B. Class B has lower variability than Class A
- C. Class A's shape shows less variability despite the same mean
- D. The mean tells you everything about variability
Why it works: Two distributions can share a mean but differ in spread (variability). Shape reveals this: a narrow cluster indicates low variability; a flat spread indicates high variability.
Answer: Class A's shape shows less variability despite the same mean
Problem 2
Question: The test scores of 24 students are: 72, 78, 81, 75, 89, 92, 74, 80, 85, 88, 76, 91, 84, 79, 86, 83, 77, 90, 73, 87, 82, 94, 68, 95. Which display would BEST show the spread and identify outliers?
- A. Circle graph
- B. Box plot
- C. Pictograph
- D. Scatter plot
Why it works: A box plot displays the quartiles, median, and extreme values (min/max), making outliers visually apparent as points beyond the whiskers.
Answer: Box plot
Common Mistakes
- Ignoring the graph scale.
- Reading the wrong category or axis label.
- Answering a comparison question without subtracting.
- Writing a number without explaining what it represents.
Strategy Tips
- Circle the scale before using the graph.
- Write down the value for each category you compare.
- Use addition for totals and subtraction for differences.
- Answer in words so the data result has meaning.
Practice Questions
Question 1
A histogram shows the ages of people visiting a museum. The x-axis shows age intervals (10--20, 20--30, 30--40, etc.), and the heights of the bars show the number of people. What does the height of each bar represent?
- A. The width of each age interval
- B. The frequency (count) in each age interval
- C. The average age in each interval
- D. The age of the oldest person
Question 2
A dot plot shows the number of hours 10 students studied for a math test. The data is: 1, 1, 1, 2, 2, 2, 2, 3, 4, 5. What is the median?
- A. 1 hour
- B. 2 hours
- C. 3 hours
- D. 5 hours
Question 3
A researcher collects data on the relationship between hours of sleep and performance on a math test for 20 students. Some data points show students who slept 7 hours and scored 60, while others slept 7 hours and scored 95. What does this variation BEST indicate?
- A. Sleep has no effect on test performance
- B. Sleep alone does not determine test scores; other factors matter
- C. The data is incorrect because the same sleep results in different scores
- D. Students who sleep 7 hours have inconsistent abilities
Question 4
A pictograph uses one star symbol = 50 votes. Candidate A has 7.5 stars, Candidate B has 6 stars. Which statement correctly interprets this pictograph?
- A. Candidate A received 7.5 votes and Candidate B received 6 votes
- B. Candidate A received 375 votes and Candidate B received 300 votes
- C. The difference is 75 votes
- D. Candidate B has fewer than half the votes of Candidate A
Question 5
A histogram shows the weights (in pounds) of 50 dogs. The intervals are 10--20 lbs, 20--30 lbs, 30--40 lbs, and 40--50 lbs, with frequencies 8, 15, 20, and 7. Which interval contains the mode?
- A. 10--20 lbs
- B. 20--30 lbs
- C. 30--40 lbs
- D. 40--50 lbs
Question 6
A line plot shows the number of rainy days per month for 12 months. There are 2 months with 8 rainy days, 4 months with 10 rainy days, 3 months with 12 rainy days, 2 months with 14 rainy days, and 1 month with 16 rainy days. What is the median number of rainy days?
- A. 8 days
- B. 10 days
- C. 11 days
- D. 12 days
Full Answer Explanations Click to show all answers and explanations
Question 1
Answer: Frequency
In a histogram, the height of each bar represents the frequency (count or number of data points) in that interval.
Question 2
Answer: 2 hours
With 10 data points, the median is the average of the 5th and 6th values. Ordered: 1, 1, 1, 2, 2, 2, 2, 3, 4, 5. The 5th and 6th values are both 2, so median = 2 hours.
Question 3
Answer: Sleep alone does not determine test scores; other factors matter
A scatter plot reveals association, not causation. Variation in scores at the same sleep duration indicates that other variables (studying, prior knowledge, test anxiety) also influence performance.
Question 4
Answer: Candidate A received 375 votes and Candidate B received 300 votes
Pictograph: 7.5 stars × 50 votes/star = 375 votes for A; 6 stars × 50 votes/star = 300 votes for B. Symbol counts must be multiplied by the legend value.
Question 5
Answer: 30--40 lbs
The mode is in the interval with the highest frequency. The 30--40 lbs interval has a frequency of 20, which is the highest among all intervals.
Question 6
Answer: 11 days
With 12 data points, the median is the average of the 6th and 7th values. Counting: positions 1--2 are 8, positions 3--6 are 10, position 7--9 are 12. The 6th and 7th values average to 11.
Connection to Standards
This lesson supports Grade 7 math expectations for reasoning, modeling, problem solving, and explaining answers clearly. It connects classroom skills to the kind of questions students see on state math assessments.
Summary
Data Displays Extended becomes easier when students connect the question to a model, use clear steps, and explain why the answer fits.
GOLDEN RULE
Read the scale before reading the answer.
