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Unit 4: Data, Statistics, and Probability

Topic 1

Reading Tables, Graphs, and Scatterplots

The SAT often presents data in tables, bar graphs, line graphs, or scatterplots and asks you to interpret or compare values. Your task is to read carefully, identify patterns, and connect the question to what’s shown.
Common Data Displays
  • Tables: Show exact numerical values, often for multiple categories.
  • Bar graphs: Compare quantities across categories.
  • Line graphs: Show trends or change over time.
  • Scatterplots: Show relationships between two variables. Look for positive, negative, or no correlation.

Positive Correlation

Negative Correlation

No Correlation

Core Skills

  • Identify which variable is on each axis.
  • Read exact values (e.g., from a table or bar height).
  • Estimate trends and slopes for graphs.
  • Distinguish between correlation and causation.
  • Recognize outliers and general patterns in scatterplots.

Example 1: Reading a Table

A table lists the number of books sold by a store each month:
MonthJanFebMarAprMayJunBooks Sold120150180210240270\begin{array}{c|cccccc} \text{Month} & \text{Jan} & \text{Feb} & \text{Mar} & \text{Apr} & \text{May} & \text{Jun}\\ \hline \text{Books Sold} & 120 & 150 & 180 & 210 & 240 & 270 \end{array}
The number of books increases by 30 each month. Question: How many books were sold in March? Answer: 180.

Example 2: Interpreting a Bar Graph

MathScienceEnglishHistoryArtSubject015304560Students
A bar graph shows the number of students choosing each subject. The tallest bar is at Science with 50 students, and the shortest is at Art with 20 students. Question: Which subject is most popular? Answer: Science.

Example 3: Interpreting a Line Graph

JanFebMarAprMayJunJulAugMonth0255075100Temperature (°F)
A line graph shows monthly temperatures. Temperature shows a steady rise from January to July, peaking at 85°F, then declining in August. Question: During which months does temperature increase the fastest? Answer: Between March and June.

Example 4: Reading a Scatterplot

05101520Hours studied0200400600800SAT Math score
A scatterplot shows points roughly following an upward trend. Interpretation: As hours studied increase, SAT scores tend to increase — this is a positive correlation.

Example 5: Identifying Outliers

In the same scatterplot, one point shows a student who studied 20 hours but scored very low. This point is an outlier, meaning it does not fit the general pattern.

Example 6: Misinterpretation Warning

  • Ice cream sales
  • Drowning incidents
JunJulAugMonth0255075100Index (illustrative, not real data)
Correlation does not imply causation. Even if two variables move together, one does not necessarily cause the other (for example, ice cream sales and drowning incidents both increase in summer, but one does not cause the other).

Key Takeaways

  • Identify variable types and axes before answering.
  • Use the graph or table for exact or approximate values as needed.
  • Check for overall trends, correlations, and anomalies.
  • Be cautious when interpreting correlations — do not assume cause and effect.