Interpreting Tables and Graphs — Interpret information in tables and graphs. - SHSAT Math

SECTION 1

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!

SECTION 2

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

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

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").

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.

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.

Legends Decode Colors & Symbols

A legend (or key) explains what each color, pattern, or symbol stands for. Don't skip it!

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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!

SECTION 3

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.

SECTION 4

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%

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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!

SECTION 5

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.

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

Summary of graph types and reading tips

SECTION 6

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

T-Shirt Sales for the Week

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 carefully

The question asks two things: (1) the difference between Thursday and Monday, and (2) the average for the whole week.
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Step 2 — Find the relevant values

Look at the "T-Shirts Sold" column. Thursday = 30 and Monday = 15.

Thursday = 30, Monday = 15
3
Step 3 — Calculate the difference

Subtract: 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 average

Add all five values: 15 + 22 + 18 + 30 + 25 = 110.

Total = 110 T-shirts
5
Step 5 — Divide to find the average

There are 5 days. Average = 110 ÷ 5 = 22.

Average = 22 T-shirts per day

SECTION 7

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.

Avoiding common data interpretation errors

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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!

SECTION 8

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

How today's skills grow into advanced topics

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.

SECTION 9

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

After-School Club Membership

Question 1: CONCEPTUAL

Which club has the most total members? Which club has the fewest?

Show answer

Look at the "Total" column. Sports has the highest total with 45 members. Music has the lowest total with 20 members. You find this by scanning down the Total column and comparing the numbers. Always read the correct column — don't accidentally look at Boys or Girls only.

Question 2: BASIC CALCULATION

How many more girls are in the Drama club than boys?

Show answer

Find the Drama row. Girls = 22 and Boys = 8. The word "more" tells you to subtract: 22 − 8 = 14. There are 14 more girls than boys in the Drama club. Remember, "how many more" always means you subtract the smaller value from the larger value.

Question 3: INTERMEDIATE

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.

Show answer

Add the Boys column: 12 + 20 + 8 + 25 + 10 = 75 boys. Next, find the grand total of all members by adding the Total column: 30 + 35 + 30 + 45 + 20 = 160. Now use the percent formula: (75 ÷ 160) × 100 = 46.875%, which rounds to 47%. So about 47% of all club members are boys.

Question 4: APPLIED

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?

Show answer

The grand total is 160 members (from the previous problem). Art has 30 members. Percentage = (30 ÷ 160) × 100 = 18.75%. A full circle has 360 degrees, so the Art slice angle = 0.1875 × 360 = 67.5 degrees. On the SHSAT, you might round to the nearest degree, which gives 68°. Always remember that a circle graph's slices must add up to 100% or 360°.

Question 5: CRITICAL 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.

Show answer

Sports has 45 members and Music has 20 members. To check if Sports is "at least twice" as popular, multiply Music's total by 2: 20 × 2 = 40. Since 45 > 40, yes, Sports has more than double Music's membership — the claim is correct. In fact, 45 ÷ 20 = 2.25, which means Sports is 2.25 times as popular. This problem teaches you to verify claims by doing the math, not just eyeballing. Critical thinking on the SHSAT means checking whether a statement is supported by the actual numbers.

SUMMARY

Lesson Summary

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!