Part of step 12 of 20·Problem-Solving and Data Analysis·Two-Variable Data: Models and Scatterplots Prev Next

Math

Data Interpretation

4 min readEasy10-question checkpoint

Data-interpretation questions are mostly about reading carefully — bar charts, line graphs, scatter plots, frequency tables. The questions are easy once you learn to slow down and check the units, axes, and labels.

Where this lesson fits

Before

Statistics→

Data Interpretation

You are here

→Probability

These questions show you a chart, table, or graph and ask you to extract or compute information from it. The math itself is usually basic. The errors come from misreading.

Common chart types — what each is for

Chart	Best for	What to look at
Line graph	Trends over time	Slope (rate of change), peaks/troughs
Bar chart	Comparing categories	Bar heights
Scatter plot	Relationship between two variables	Direction, strength, outliers
Pie chart	Parts of a whole	Slice sizes (fractions)
Histogram	Distribution of one variable	Shape (bell, skewed, bimodal)
Box plot	Five-number summary	Median, IQR, outliers

The four-step protocol before answering anything:

1. Read the title. What's the data about? Population growth vs birth rate are different things.

2. Read the axis labels. Especially the units. Is it dollars or thousands of dollars? Years or decades? Per capita or total?

3. Read the legend / colors. If multiple series are plotted, you need to know which is which.

4. Read the question carefully. "What was the value in 2020?" is different from "By how much did the value change from 2018 to 2020?"

Common chart types and what they emphasize:

Line graph: trends over time. Look at slope to compare rates of change.
Bar chart: comparing discrete categories. Look at heights.
Stacked bar: parts of a whole that add up. Each segment shows a category's contribution.
Scatter plot: relationship between two variables. Look for clustering, correlation direction, outliers.
Pie chart: parts of a whole as fractions. Slice size = proportion.
Histogram: distribution of one variable in bins. Look at the shape (bell, skewed, bimodal).
Box plot: five-number summary (min, Q1, median, Q3, max). The box is the middle 50%.

Computing from a line of best fit. When a scatter plot has a regression line:

Predict the value at $x = a$ : read off the line at $x = a$ , not the data points.
Slope: the rate of change. If the line is $y = 3x + 7$ , $y$ goes up by 3 for every 1 unit $x$ goes up.
Intercept: the value when $x = 0$ .

Loading…

Reading a regression equation $y = mx + b$

Symbol	Meaning	Example: $y = 5x + 60$
$m$ (slope)	Rate of change — how much $y$ changes per unit $x$	Score goes up 5 points per study hour
$b$ (intercept)	Predicted $y$ when $x = 0$	60 — predicted score for someone who studied 0 hours
At $x = 7$	Plug in: $y = 5(7) + 60 = 95$	Predicted score: 95
At $x = 0$	Just $b$	Predicted score: 60

Watch for percent vs absolute change. Increased by 50 is different from increased by 50%. Read the problem.

Frequency tables:

Score	Frequency
60-70	5
70-80	12
80-90	8
90-100	3

Total = 5 + 12 + 8 + 3 = 28.

Mean: estimate using midpoints. $\frac{5(65) + 12(75) + 8(85) + 3(95)}{28} \approx 76.6$ .
Median: locate the middle value (the 14th and 15th of 28). Both fall in the 70-80 bin.
Mode bin: the bin with the highest frequency (70-80, with 12).

Loading…

Quick check

Read the title, axes, and units carefully before computing. Check whether the question wants absolute or percent change.

A scatterplot shows the relationship between the age of a car (in years) and its resale value (in thousands of dollars). The line of best fit is y = -2.3x + 28. In the context of this situation, what does the slope of the line represent?

The car loses approximately $2,300 in resale value for each additional year of age.

The car gains approximately $2,300 in resale value for each additional year of age.

The initial resale value of the car is $2,300.

The car will be worth $0 after 2.3 years.

Worked examples

Example 1

A line graph shows a company's annual revenue (in thousands of dollars) from 2018 to 2024. The values are: 2018: 240, 2019: 260, 2020: 250, 2021: 290, 2022: 310, 2023: 340, 2024: 380.

By what amount did revenue change from 2020 to 2024?

Example 2

A scatter plot of study hours (x) vs test score (y) shows a line of best fit: $y = 5x + 60$ . According to the line, what is the predicted score for a student who studied 7 hours?

Loading…

Common pitfalls

Misreading axis units

Thousands of dollars, millions of people, per 100,000 — the SAT loves to bury units in the axis label. Always check before computing differences or rates.

Confusing percent change with absolute change

Revenue went from 100 to 130 is an increase of 30 (absolute) or 30% (relative). Always read whether the question asks the amount (subtraction) or the percent (divide by old value).

Reading the wrong axis

On a graph, $x$ and $y$ axes are different. Make sure you read the right one for each data point. Especially on dual-axis charts where left and right axes show different scales.

Loading…

Using actual data points when the question asks for predictions

According to the line of best fit means use the regression line equation, not the closest scatter point. The line is the model; the points are observations.

Key takeaways

Read titles, axis labels, units, and legend BEFORE computing anything.
Check whether the question asks for absolute change or percent change.
On line-of-best-fit questions, use the regression equation — not nearby data points.
On two-way / frequency tables, identify the right denominator for the question.
Slope of a regression line = rate of change. Intercept = value at $x = 0$ .
Loading…

Tracks your progress across lessons.

Checkpoint

10 questions on Two-Variable Data: Models and Scatterplots, from our question bank. Score 70% or better across 10 answers to reach Silver and pass this step.

Start checkpoint · 10 questions

Where this lesson fits

Before

Statistics→

Data Interpretation

You are here

→Probability