SHSAT MATH • DATA ANALYSIS AND STATISTICS

Interpreting Tables and Graphs — Interpret information in tables and graphs.

Learn to read, analyze, and draw conclusions from data presented in tables, bar graphs, line graphs, and circle graphs.

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.

~3000 BCE
Early Record Keeping
Ancient Egyptians and Babylonians used clay tablets to record crop harvests and trade records in simple table form.
1786
First Bar Graph
William Playfair, a Scottish engineer, published the first bar graph comparing Scotland's imports and exports.
1801
First Pie Chart
Playfair also created the first circle graph (pie chart) to show how much land the Turkish Empire controlled in different continents.
Today
Data Is Everywhere
Graphs and tables are used in every field — from medicine to sports analytics — and appear on standardized tests like 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.

1

Title Tells the Topic

Every table or graph has a title at the top. Read it first — it tells you what the data is about.
2

Labels & Axes Name the Data

Column headers in tables and axis labels on graphs tell you the categories (like "Month") and units (like "dollars" or "students").
3

Scale Sets the Numbers

The scale is the set of numbers along an axis. Pay attention to whether it counts by 1s, 5s, 10s, or some other interval.
4

Data Points Hold the Answers

The actual bars, dots, slices, or cell values are your data points. Line up the data point with both axes (or read the cell) to get exact values.
5

Legends Decode Colors & Symbols

A legend (or key) explains what each color, pattern, or symbol stands for. Don't skip it!
KEY TAKEAWAY
Think of a graph like a menu at a restaurant. The title is the restaurant's name, the labels are the sections (appetizers, main courses), the scale is the price range, and each data point is a specific dish. You wouldn't order without reading the menu — don't answer questions without reading the graph!

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.

This bar graph shows four students on the horizontal axis and the number of books on the vertical axis. Bella read the most (12 books) and Chris read the fewest (6 books). The scale counts by 3s.

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.

FINDING THE TOTAL
Total = Value₁ + Value₂ + Value₃ + …
Add up all the data values. Example: 9 + 12 + 6 + 10 = 37 total books
FINDING THE DIFFERENCE
Difference = Larger Value − Smaller Value
Subtract to compare two data points. Example: Bella − Chris = 12 − 6 = 6 more books
FINDING THE AVERAGE (MEAN)
Average = Total ÷ Number of Items
Divide the total by how many items there are. Example: 37 ÷ 4 = 9.25 books
FINDING A PERCENT OF THE WHOLE
Percent = (Part ÷ Whole) × 100
Used especially with circle graphs. If a slice represents 15 out of 60 total, then 15 ÷ 60 × 100 = 25%
💡 SHSAT Tip
Always double-check what the question is asking. Words like "how many more," "total," and "average" each tell you which formula to use. Underline key words in the question before looking at the graph!

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.

The four main data displays: bar graphs compare categories, line graphs show trends over time, circle graphs show parts of a whole, and tables give exact values.
Summary of graph types and reading tips
Graph TypeBest ForWatch Out For
Bar GraphComparing amounts across different categoriesRead the scale carefully — bars may not land exactly on a gridline
Line GraphShowing how something changes over timeA flat line means no change; a steep line means rapid change
Circle GraphShowing parts of a whole (percentages)All slices must add up to 100% (or the whole total)
TableDisplaying exact numbers in an organized wayRead 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.

T-Shirt Sales for the Week
DayT-Shirts SoldRevenue ($)
Monday15225
Tuesday22330
Wednesday18270
Thursday30450
Friday25375

Question: How many more T-shirts were sold on Thursday than on Monday? What was the average number of T-shirts sold per day?

Worked Example: T-Shirt Sales
1
Step 1 — Read the question carefullyThe question asks two things: (1) the difference between Thursday and Monday, and (2) the average for the whole week.
2
Step 2 — Find the relevant valuesLook at the "T-Shirts Sold" column. Thursday = 30 and Monday = 15.
Thursday = 30, Monday = 15
3
Step 3 — Calculate the differenceSubtract: 30 − 15 = 15. So Thursday had 15 more T-shirts sold than Monday.
Difference = 15 T-shirts
4
Step 4 — Find the total for the averageAdd all five values: 15 + 22 + 18 + 30 + 25 = 110.
Total = 110 T-shirts
5
Step 5 — Divide to find the averageThere are 5 days. Average = 110 ÷ 5 = 22.
Average = 22 T-shirts 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.

Avoiding common data interpretation errors
Common MistakeWhy It HappensHow to Fix It
Misreading the scaleYou 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 columnTables 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 unitsYou write 15 instead of 15 students or $15.Look at the axis label or column header. Include the unit in your answer.
KEY TAKEAWAY
Think of reading a graph like reading a map. You wouldn't just stare at a map — you'd check the key (legend), the scale, and the labels before trying to find your destination. Same idea with data displays!

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.

How today's skills grow into advanced topics
What You Learn NowWhat Comes Next
Reading values from a bar graphCreating histograms (grouped bar graphs) and analyzing distributions in statistics
Finding trends on a line graphUsing scatter plots and lines of best fit to make predictions (Algebra and Statistics)
Calculating percentages from circle graphsWorking with probability, relative frequency, and sector angles in geometry
Finding averages from a tableComputing 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.

After-School Club Membership
ClubBoysGirlsTotal
Art121830
Science201535
Drama82230
Sports252045
Music101020
PROBLEM 1CONCEPTUAL
Which club has the most total members? Which club has the fewest?
PROBLEM 2BASIC CALCULATION
How many more girls are in the Drama club than boys?
PROBLEM 3INTERMEDIATE
What is the total number of boys across all five clubs? What percentage of all club members (boys and girls combined) are boys? Round to the nearest whole percent.
PROBLEM 4APPLIED
The school wants to make a circle graph showing total membership for each club. What percentage of the circle should the Art club slice represent? What angle (in degrees) would that slice be?
PROBLEM 5CRITICAL THINKING
A student claims: "Since Sports has the most members and Music has the fewest, Sports must be at least twice as popular as Music." Is this claim correct? Use the data to explain.

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!

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