Historical Context & Motivation
Humans have been organizing information for thousands of years. Before computers, scientists and merchants needed ways to make sense of large amounts of data. Tables (rows and columns of numbers) and graphs (pictures that show data) were invented to help people spot patterns quickly. Today, you see tables and graphs everywhere — in news articles, science class, sports stats, and yes, on the SHSAT.
The big question this lesson answers is: How do you pull the right numbers from a table or graph and use them to answer questions? Let's find out!
Core Principles & Definitions
Before we dive in, let's nail down the key ideas you'll need. Every table and graph is built on the same simple parts. Once you know what to look for, reading data becomes almost automatic.
Title Tells the Topic
Labels & Axes Name the Data
Scale Sets the Numbers
Data Points Hold the Answers
Legends Decode Colors & Symbols
Visual Explanation — Reading a Bar Graph
A bar graph uses bars of different heights to compare amounts. The diagram below shows the number of books read by four students during a reading challenge. Study each labeled part before answering questions.
Notice how the bar heights match the numbers on the vertical axis. To find how many books Alex read, you look at Alex's bar and trace a horizontal line to the left until you hit the scale. The bar reaches up to 9, so Alex read 9 books. This "read across" strategy works for every bar graph you'll see on the SHSAT.
Mathematical Framework — Calculating from Data
SHSAT questions don't just ask you to read a number. They often ask you to calculate something using the data. Here are the most common calculations.
Types of Graphs You'll See
The SHSAT can show you several types of data displays. Each type works best for certain kinds of information. The diagram below shows the four main types you should know.
| Graph Type | Best For | Watch Out For |
|---|---|---|
| Bar Graph | Comparing amounts across different categories | Read the scale carefully — bars may not land exactly on a gridline |
| Line Graph | Showing how something changes over time | A flat line means no change; a steep line means rapid change |
| Circle Graph | Showing parts of a whole (percentages) | All slices must add up to 100% (or the whole total) |
| Table | Displaying exact numbers in an organized way | Read column headers to match the right row with the right column |
Worked Example — Solving a Table & Graph Problem
Let's work through a full SHSAT-style problem step by step. Use the table below.
| Day | T-Shirts Sold | Revenue ($) |
|---|---|---|
| Monday | 15 | 225 |
| Tuesday | 22 | 330 |
| Wednesday | 18 | 270 |
| Thursday | 30 | 450 |
| Friday | 25 | 375 |
Question: How many more T-shirts were sold on Thursday than on Monday? What was the average number of T-shirts sold per day?
Common Mistakes & How to Avoid Them
Even strong math students lose points on data questions because of small, avoidable errors. Here are the biggest traps and how to dodge them.
| Common Mistake | Why It Happens | How to Fix It |
|---|---|---|
| Misreading the scale | You assume the axis counts by 1s when it really counts by 5s or 10s. | Check two consecutive numbers on the axis and find the interval before reading any bars or points. |
| Reading the wrong row or column | Tables have lots of numbers. It's easy to slip into the wrong row. | Use your finger or pencil to trace across the row. Double-check the column header. |
| Confusing "how many more" with "how many" | "How many more" means subtract. "How many" means read the value directly. | Underline the key phrase in the question. If you see "more," "fewer," or "difference," you need to subtract. |
| Forgetting units | You write 15 instead of 15 students or $15. | Look at the axis label or column header. Include the unit in your answer. |
Connection to More Advanced Data Skills
The skills you're building now are the foundation for more complex data work in high school and beyond. Here's how what you learn today connects to what comes next.
| What You Learn Now | What Comes Next |
|---|---|
| Reading values from a bar graph | Creating histograms (grouped bar graphs) and analyzing distributions in statistics |
| Finding trends on a line graph | Using scatter plots and lines of best fit to make predictions (Algebra and Statistics) |
| Calculating percentages from circle graphs | Working with probability, relative frequency, and sector angles in geometry |
| Finding averages from a table | Computing mean, median, mode, range, and standard deviation |
On the SHSAT specifically, you might also see double bar graphs (two bars per category) or double line graphs (two lines on the same axes). These work the same way — just use the legend to figure out which bar or line belongs to which group.
Practice Problems
Use the data below to answer all five questions. A school tracked the number of students who joined after-school clubs.
| Club | Boys | Girls | Total |
|---|---|---|---|
| Art | 12 | 18 | 30 |
| Science | 20 | 15 | 35 |
| Drama | 8 | 22 | 30 |
| Sports | 25 | 20 | 45 |
| Music | 10 | 10 | 20 |
Lesson Summary
To interpret data on the SHSAT, always start by reading the title, labels, scale, and legend before jumping to the data. Bar graphs compare categories, line graphs show change over time, circle graphs show parts of a whole, and tables provide exact values in rows and columns.
The key calculations are totals (add), differences (subtract), averages (total ÷ count), and percentages (part ÷ whole × 100). Underline key words in the question, trace carefully across rows and columns, and always double-check the scale before reading a graph. These habits will help you earn every point on data questions!