SAT Math Lesson Plan 11: Data Interpretation

Lesson Summary

This 45-minute SAT Math lesson focuses on developing students’ skills in interpreting data presented in tables, charts, and graphs. These types of questions typically account for 15–20% of the SAT Math section and are especially common in the Problem Solving and Data Analysis domain. Students will learn how to read data representations, recognize trends, calculate statistical measures (such as mean and median), and identify outliers. The lesson includes a Warm-Up activity, six worked-out examples, a Review with summaries and self-study tips, and a 10-question SAT-style quiz with a detailed answer key. This is Lesson 11 in a 35-lesson SAT Math prep series.

Lesson Objectives

• Interpret data from various representations, including tables, bar graphs, histograms, and scatterplots.
• Calculate and analyze statistical measures like mean and median.
• Identify trends, patterns, and outliers in data sets.
• Apply data interpretation skills to solve real-world problems.

Common Core Standards

• CCSS.MATH.CONTENT.HSS.ID.A.1 – Represent data with plots on the real number line (dot plots, histograms, and box plots).
• CCSS.MATH.CONTENT.HSS.ID.A.2 – Use statistics appropriate to the shape of the data distribution to compare center (median, mean) and spread (interquartile range, standard deviation) of two or more different data sets.
• CCSS.MATH.CONTENT.HSS.ID.B.6 – Represent data on two quantitative variables on a scatter plot, and describe how the variables are related.

Prerequisite Skills

• Basic understanding of arithmetic operations
• Familiarity with fractions, decimals, and percentages
• Ability to read and interpret simple graphs and charts

Key Vocabulary

• Mean: The average of a data set, calculated by dividing the sum of all values by the number of values.
• Median: The middle value in a data set when the numbers are arranged in ascending order.
• Mode: The value that appears most frequently in a data set.
• Range: The difference between the highest and lowest values in a data set.
• Outlier: A value significantly higher or lower than most of the values in a data set.
• Frequency: The number of times a particular value appears in a data set.

Warm Up

Start by practicing your data interpretation skills with a simple bar graph.

Problem: The bar graph below shows the number of books five students read during the summer. The table shows the data in the graph.

Question: What is the mean number of books read?

Step 1:

Add the total number of books: \[ 7 + 5 + 8 + 4 + 6 = 30 \]

Step 2:

Divide by the number of students: \[ \frac{30}{5} = 6 \]

Answer: The mean number of books read is 6.

Try this follow-up question: What is the median number of books read?

Step 1:

Arrange in order: 4, 5, 6, 7, 8

Step 2:

The middle value is 6, so the median is also 6.

Teach

Data interpretation questions on the SAT often present information in visual formats such as bar graphs, line graphs, scatterplots, histograms, and tables. These questions test your ability to analyze and draw conclusions from numerical data and graphical representations.

Common data interpretation tasks:

• Read values directly from a graph or table
• Compare values, trends, or categories
• Calculate statistical measures such as mean, median, and range
• Identify outliers or unusual data points
• Make predictions or inferences based on trends

When working through SAT data problems, always read axis labels, units, and titles carefully. Look for keywords such as “increase,” “total,” “average,” or “approximate.” The SAT will often mix numerical and conceptual reasoning in these items.

In the examples that follow, we’ll interpret different types of graphs and data representations and practice calculating important statistics. Pay close attention to how each visual element conveys meaning—and always double-check your math!

Example 1: Reading a Bar Graph

This problem tests your ability to extract exact values from a bar graph.

Problem: The bar graph shows the number of students enrolled in different math classes:

Question: What percent of the total students are enrolled in Geometry?

Step 1:

Find the total number of students: \[ 25 + 30 + 20 + 15 = 90 \]

Step 2:

Geometry students = 30 \[ \frac{30}{90} \times 100 = 33.3\% \]

Answer: Approximately 33.3% of students are in Geometry.

Example 2: Interpreting a Line Graph

This problem involves identifying trends in a line graph.

Problem: The line graph below shows a company’s monthly revenue (in thousands of dollars) from January to June:

Question: During which month did the company experience the greatest increase in revenue compared to the previous month?

Step 1:

Calculate the month-to-month changes:

• Feb - Jan: \(45 - 40 = 5\)
• Mar - Feb: \(50 - 45 = 5\)
• Apr - Mar: \(48 - 50 = -2\)
• May - Apr: \(53 - 48 = 5\)
• June - May: \(58 - 53 = 5\)

Answer: February, March, May, and June each had a \$5,000 increase. So, the greatest increase was shared across these months.

Example 3: Identifying an Outlier

This problem focuses on recognizing values that don't fit the pattern of the data.

Problem: A teacher records the following test scores out of 100:

82, 85, 87, 84, 83, 92, 88, 46, 89

Question: Which score is most likely an outlier?

Step 1:

Look at the typical score range: Most scores are in the 80s or low 90s.

Step 2:

The score 46 is far lower than the rest.

Answer: 46 is the outlier.

Here is a box and whisker plot from the data, which shows the outlier.

Example 4: Interpreting a Scatterplot

This problem involves identifying patterns in a scatterplot and determining the relationship between two variables.

Problem: The following table shows the number of hours students studied for a test and the scores they received:

Question: What kind of relationship does this data represent?

Step 1:

Observe the pattern in the table and the graph: As study time increases, test scores consistently increase.

Step 2:

This is a classic case of a positive linear correlation between the two variables.

Answer: There is a positive linear relationship between hours studied and test scores.

Example 5: Mean and Median Comparison

This problem asks you to compare measures of central tendency to evaluate data spread.

Problem: The following data set shows the number of hours students reported studying in a week:

3, 4, 5, 6, 7, 9, 16

Step 1: Use the formula for the mean

The general formula for the mean is:

\[ \text{Mean} = \frac{\text{Sum of all values}}{\text{Number of values}} \]

Apply the formula:

\[ \text{Mean} = \frac{3 + 4 + 5 + 6 + 7 + 9 + 16}{7} = \frac{50}{7} \approx 7.14 \]

Step 2: Find the median

Arrange the numbers in ascending order: 3, 4, 5, 6, 7, 9, 16

The middle value is 6 (the fourth number in the list).

Conclusion:

Mean: approximately 7.14
Median: 6

Since the mean is greater than the median, this indicates the data is slightly skewed to the right due to the outlier (16).

Example 6: Real-World Interpretation

This problem models a real-world scenario based on interpreting a circle graph (also known as a sector graph).

Problem: A company allocates its \$40,000 monthly budget across four departments. The table below shows how the budget is distributed:

Question: What fraction of the budget is spent on marketing?

Step 1:

\[ \frac{10,000}{40,000} = 0.25 = 25\% \]

Answer: 25% of the budget is allocated to marketing.

Below is a circle graph showing the full budget distribution:

Example 7: Interpreting a Histogram

This problem asks you to analyze grouped frequency data presented in a histogram.

Problem: The histogram below shows the number of students who scored within each range on a recent math test:

Question: How many students scored below 80?

Step 1:

Add frequencies from 60–69 and 70–79:
\( 4 + 8 = 12 \)

Answer: 12 students scored below 80.

Review

This lesson explored how to interpret and analyze data presented in various formats, including tables, bar graphs, line graphs, scatterplots, and pie charts. You practiced reading values directly, comparing trends, identifying outliers, and calculating statistical measures such as mean and median. Data interpretation questions are essential on the SAT, especially within the Problem Solving and Data Analysis domain. Success with these problems requires careful attention to units, labels, and relationships between variables.

Here's what you covered in this lesson:

• Reading values from charts and graphs
• Identifying trends and outliers in data
• Comparing measures of central tendency (mean, median)
• Interpreting real-world data in visual formats
• Making predictions based on numerical and graphical information

Example 1: Reading a Table

Problem: The table shows the number of items sold each day at a store:

Question: What is the average number of items sold per day?

Step 1:

\[ \frac{24 + 30 + 28 + 26 + 32}{5} = \frac{140}{5} = 28 \]

Answer: 28 items per day

Example 2: Comparing Mean and Median

Problem: A set of quiz scores is: 60, 65, 70, 75, 90

Step 1:

Mean: \[ \frac{60 + 65 + 70 + 75 + 90}{5} = \frac{360}{5} = 72 \]

Step 2:

Median: The middle value is 70.

Answer: The mean is 72 and the median is 70. The higher value (90) pulls the mean slightly above the median.

Example 3: Trend Identification

Problem: A line graph shows the population of a town over five years, increasing steadily by 200 people each year. If the population in Year 1 is 4,000, what is the population in Year 5?

Step 1:

Use the formula: \[ \text{Population} = 4,000 + 200 \times (5 - 1) = 4,000 + 800 = 4,800 \]

Answer: 4,800 people

Self-Study Tip: When interpreting graphs, look for consistent patterns and trends. Always verify the scale and axis labels before jumping to conclusions.

 Example 4: Histogram Interpretation

This problem asks you to analyze frequency data from a histogram and make inferences based on grouped scores.

Problem: The histogram below shows the distribution of test scores for a group of students:

Question: How many students scored below 80?

Step 1:

Add the number of students from the ranges 50–59, 60–69, and 70–79:
\[ 2 + 6 + 9 = 17 \]

Answer: 17 students scored below 80.

Multimedia Resources

For additional practice and support on interpreting data in charts, tables, and graphs, explore this curated set of videos, tutorials, and worksheets from Media4Math:

https://www.media4math.com/LessonPlans/SupportResourcesSATMathLesson11

Quiz

Directions: Solve each problem and choose the best answer from the choices provided. Use scratch paper to show your work if needed.

1. The table shows the number of pets owned by five households:
    

   Household	Pets
   A	3
   B	2
   C	5
   D	4
   E	6

    

   What is the median number of pets?
   a) 3
   b) 4
   c) 5
   d) 6

2. The mean of five test scores is 84. If four of the scores are 80, 85, 86, and 87, what is the fifth score?
   a) 80
   b) 82
   c) 85
   d) 82
3. In a bar graph showing monthly sales, April’s sales are twice as high as March’s. If March’s sales are \$8,000, what are April’s?
   a) \$12,000
   b) \$14,000
   c) \$16,000
   d) \$18,000
4. Which of the following data sets has an outlier?
   a) 21, 23, 24, 25, 26
   b) 50, 55, 60, 65, 120
   c) 10, 12, 14, 16, 18
   d) 30, 32, 34, 36, 38
5. A pie chart shows that 40% of a company’s budget goes to salaries. If the total budget is \$200,000, how much goes to salaries?
   a) \$75,000
   b) \$80,000
   c) \$85,000
   d) \$90,000
6. A line graph shows population increasing by 1,500 people per year. If the current population is 25,000, what will it be in 3 years?
   a) 28,000
   b) 28,500
   c) 29,000
   d) 29,500
7. Which of the following correctly describes a positive correlation?
   a) One variable increases as the other decreases
   b) Both variables remain unchanged
   c) One variable decreases while the other increases
   d) Both variables increase together
8. In a data set, the mean is 70 and the median is 72. What does this suggest about the data?
   a) It is normally distributed
   b) It has no outliers
   c) It is skewed to the left
   d) It is skewed to the right
9. The histogram below shows the number of students who scored in each range on a test:
   60–69: 4 students
   70–79: 8 students
   80–89: 10 students
   90–100: 3 students
   How many students took the test?
   a) 24
   b) 25
   c) 26
   d) 27
10. Which type of graph is most appropriate to display how a total amount is divided into categories?
    a) Line graph
    b) Scatterplot
    c) Bar graph
    d) Pie chart

Answer Key

1. Answer: b) 4
   Ordered data: 2, 3, 4, 5, 6 → Median is the middle value, which is 4.
2. Answer: b) 84
   Mean = 84 → Total = 84 × 5 = 420 Sum of four scores = 80 + 85 + 86 + 87 = 338 Fifth score = 420 – 338 = 82
3. Answer: c) \$16,000
   If March = \$8,000 and April is double: \( 8,000 \times 2 = 16,000 \)
4. Answer: b) 50, 55, 60, 65, 120
   120 is much higher than the rest of the values — it's an outlier.
5. Answer: b) \$80,000
   40% of \$200,000 = \( 0.40 \times 200,000 = 80,000 \)
6. Answer: b) 28,500
   Increase = \( 1,500 \times 3 = 4,500 \) \( 25,000 + 4,500 = 28,500 \)
7. Answer: d) Both variables increase together
   This is the definition of a positive correlation.
8. Answer: c) It is skewed to the left
   Mean < Median → Left skewed data (tail on the lower end)
9. Answer: c) 25
   Total = 4 + 8 + 10 + 3 = 25 students
10. Answer: d) Pie chart
    Pie charts show how a total is divided into parts.