Interpret trends in a graph to select a correct statement. - SSAT Middle Level Quantitative

SECTION 1

Why Do We Use Graphs?

Imagine you have a giant spreadsheet with hundreds of numbers. It would take a long time to figure out what's going on! A graph (a picture that shows data using lines, bars, or points) turns those numbers into something you can see at a glance. People have been drawing graphs for centuries to make sense of information.

1350 • Early Data Pictures

Nicole Oresme, a French thinker, drew some of the first bar-like charts to show how quantities change over time.

1786 • The First Bar Graph

William Playfair published the first true bar chart and line graph in a book about trade between countries.

1858 • Florence Nightingale's Charts

The famous nurse used colorful pie and area charts to convince leaders that clean hospitals save lives.

Today • Graphs Are Everywhere

From sports stats to weather apps, graphs help millions of people spot trends and make quick decisions every single day.

On the SSAT, you will look at a graph and choose the statement that correctly describes what the data shows. The big question is: How do you read a graph carefully enough to tell the true statements from the false ones?

SECTION 2

Core Principles of Reading Graphs

Before you can pick the right answer, you need to understand a few building blocks. Every graph has parts that work together to tell a story.

Axes & Labels

The x-axis (horizontal) and y-axis (vertical) tell you what is being measured. Always read the labels first!

Scale & Units

The numbers along each axis form the scale. Check whether the scale counts by 1s, 5s, 10s, or some other amount so you read values correctly.

Trend (Direction)

A trend is the overall direction the data moves: going up (increasing), going down (decreasing), or staying flat (constant).

Specific Values

Sometimes you need to read an exact value from the graph. Find the point, then trace straight down to the x-axis and straight across to the y-axis.

Comparing Sections

Many questions ask you to compare two time periods or two categories. Look at the heights of bars or the positions of points side by side.

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KEY TAKEAWAY

Think of a graph like a scoreboard at a basketball game. The scoreboard tells you the score (y-axis) at each moment in the game (x-axis). A trend is like watching the score climb quickly in the third quarter — you can see the direction things are moving without adding up every single basket.

SECTION 3

Reading a Line Graph — Visual Explanation

Below is a line graph showing how many books a student named Mia read each month from January through June. Study the diagram, then read the explanation underneath.

The line moves upward from left to right. This tells us Mia's book count increased every month from January (3 books) to June (9 books).

Notice a few things. First, the overall trend is increasing — the line goes up as you move to the right. Second, the biggest single jump is from April (6 books) to May (8 books), a gain of 2 books. Third, every month Mia read more than the month before, so there is no decrease anywhere in this graph.

If a test question asked, "Which statement about the graph is true?" you would check each answer choice against these observations. A wrong choice might say "Mia read the most books in April" — but the graph clearly shows June is the highest point.

SECTION 4

Using Numbers to Confirm Trends

Sometimes "eyeballing" a graph isn't enough. You can use simple math to check whether a statement is true. Here are the two main tools you'll need.

CHANGE BETWEEN TWO POINTS

Change = Value₂ − Value₁

Value₂ is the later point and Value₁ is the earlier point. A positive result means the data went up; a negative result means it went down.

COMPARING TWO VALUES

Difference = Taller Bar − Shorter Bar

When a question says "how many more" or "how much greater," subtract the smaller value from the larger value.

For Mia's graph, the change from January to June is 9 − 3 = 6 books. If an answer choice said "Mia read 5 more books in June than in January," you would know that is false because the actual difference is 6, not 5.

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Watch Out for Tricky Scales

If the y-axis counts by 5s (0, 5, 10, 15…), each small gridline might stand for 5, not 1. Read the numbers on the axis carefully before you subtract!

SECTION 5

Bar Graphs, Line Graphs & More

The SSAT can show you different kinds of graphs. Each type tells the story in a slightly different way. Let's look at a bar graph next so you can practice the same skills on a different format.

In this bar graph, the tallest bar is Soccer (36 students) and the shortest bar is Swimming (8 students). Soccer is the most popular, and swimming is the least popular.

With a bar graph, you compare the heights (or lengths) of the bars. A taller bar means a larger value. To find a difference, subtract: Soccer − Basketball = 36 − 30 = 6 more students chose soccer.

Graph Type	Best For	How to Spot a Trend
Line Graph	Showing change over time	See if the line goes up, down, or stays flat
Bar Graph	Comparing categories	Compare bar heights side by side
Pie Chart	Showing parts of a whole	Larger slices represent larger portions

Common graph types on the SSAT

SECTION 6

Worked Example — Picking the True Statement

Let's walk through a problem step by step using the Favorite Sport bar graph from Section 5. Suppose the question says:

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Sample Question

Which of the following statements about the graph is true? (A) More students chose tennis than baseball. (B) Soccer and basketball together equal 66 students. (C) Baseball was chosen by exactly twice as many students as swimming. (D) Swimming was the most popular sport. (E) Basketball was chosen by fewer than 25 students.

Step-by-Step Solution

1
Step 1 — Read the values from the graph

Soccer = 36, Basketball = 30, Baseball = 20, Tennis = 15, Swimming = 8. Write these down so you don't have to keep looking back at the picture.
2
Step 2 — Test choice (A)

Tennis = 15, Baseball = 20. Is 15 more than 20? No.

(A) is FALSE
3
Step 3 — Test choice (B)

Soccer + Basketball = 36 + 30 = 66. The statement says 66.

(B) looks TRUE — keep it for now
4
Step 4 — Test choice (C)

Twice swimming = 2 × 8 = 16. Baseball = 20. Is 20 = 16? No.

(C) is FALSE
5
Step 5 — Test choice (D)

Swimming = 8. That is the shortest bar, not the tallest.

(D) is FALSE
6
Step 6 — Test choice (E)

Basketball = 30. Is 30 fewer than 25? No, 30 is greater than 25.

(E) is FALSE
7
Step 7 — Select the answer

Only choice (B) passed the test. The answer is (B).

Answer: (B)

SECTION 7

Common Mistakes & How to Avoid Them

Mistake	Why It Happens	How to Fix It
Misreading the scale	You assume each gridline is 1 when it is really 5 or 10.	Read the numbers printed on the y-axis before doing any math.
Confusing "increase" with "highest"	A statement says the biggest increase happens in a certain month, but you pick the month with the highest total instead.	"Increase" means the change between two points, not the point itself. Subtract to find the change.
Ignoring one answer choice	You stop testing after finding one choice that seems right.	Always test all five choices to be sure. Two may look close.
Reading the wrong bar or point	Bars or points are close together, and you read the neighboring one.	Trace a finger (or pencil) straight up from the label to the bar top, then across to the y-axis.

Frequent errors on SSAT graph questions

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KEY TAKEAWAY

Think of each answer choice like a suspect in a detective story. Your job is to test every suspect against the evidence (the graph). Eliminate the ones that don't match, and the last one standing is your answer.

SECTION 8

Connecting to Harder Graph Skills

Once you master reading single graphs, you'll encounter questions that ask you to do more. Here's how today's skill connects to topics you'll see later.

Today's Skill	Advanced Version
Read one data point	Interpolate (estimate a value between two points)
Identify an overall trend (up or down)	Calculate rate of change (slope) between two points
Compare two bars	Compare data from two different graphs at once (double bar or double line)
Pick a true statement	Predict future values by extending a trend

How today's skill grows in later math courses

You don't need these advanced skills for the SSAT Middle Level, but knowing they exist can make you feel confident. The reading, subtracting, and comparing you're learning now is the foundation for all of them.

SECTION 9

Practice Problems

Use the data described in each problem. For problems 1–3, refer to this data set for a line graph showing daily high temperatures for a school week: Monday 58°F, Tuesday 62°F, Wednesday 60°F, Thursday 65°F, Friday 70°F.

Question 1: CONCEPTUAL

A line graph shows daily high temperatures for a school week: Monday 58°F, Tuesday 62°F, Wednesday 60°F, Thursday 65°F, Friday 70°F. Which statement about the overall trend is correct? (A) The temperature decreased every day. (B) The temperature stayed the same all week. (C) The temperature generally increased over the week. (D) Wednesday had the highest temperature. (E) Friday had the lowest temperature.

Show answer

The correct answer is (C). The temperature started at 58°F on Monday and ended at 70°F on Friday, showing a general increase. Choice (A) is wrong because the temperatures mostly went up, not down. Choice (B) is wrong because the values changed each day. Choice (D) is wrong because Wednesday (60°F) was not the highest — Friday (70°F) was. Choice (E) is wrong because Friday was the highest, not the lowest; Monday (58°F) was the lowest.

Question 2: BASIC CALCULATION

Using the same temperature data (Mon 58, Tue 62, Wed 60, Thu 65, Fri 70), how much warmer was Friday than Monday? (A) 8°F (B) 10°F (C) 12°F (D) 15°F (E) 70°F

Show answer

The correct answer is (C). Subtract: 70 − 58 = 12°F. Choice (A) gives 8, which might come from subtracting 62 − 54 or an arithmetic error. Choice (B) gives 10, a common rounding error. Choice (D) gives 15, which could come from confusing Thursday's value. Choice (E) is just Friday's temperature, not the difference.

Question 3: INTERMEDIATE

Using the same temperature data, on which day did the temperature drop compared to the day before? (A) Tuesday (B) Wednesday (C) Thursday (D) Friday (E) The temperature never dropped.

Show answer

The correct answer is (B). From Tuesday (62°F) to Wednesday (60°F), the temperature fell by 2°F. Choice (A) is wrong because Tuesday (62) was higher than Monday (58), so it rose. Choice (C) is wrong because Thursday (65) was higher than Wednesday (60). Choice (D) is wrong because Friday (70) was higher than Thursday (65). Choice (E) is wrong because there was indeed a drop on Wednesday.

Question 4: APPLIED

A bar graph shows how many tickets four movies sold in one weekend: Movie A sold 200, Movie B sold 350, Movie C sold 150, and Movie D sold 300. Which statement is true? (A) Movie C sold more tickets than Movie A. (B) Movie B and Movie D together sold 550 tickets. (C) Movie A sold the fewest tickets. (D) Movie B sold exactly twice as many tickets as Movie C. (E) Movie D sold 650 tickets.

Show answer

The correct answer is (D). Twice Movie C = 2 × 150 = 300, and Movie B = 350 — wait, let's recheck. 2 × 150 = 300, but Movie B = 350, so (D) says exactly twice, which would be 300 ≠ 350. Let's re-examine all choices. (A) Movie C = 150 and Movie A = 200, so 150 is not more than 200 — false. (B) 350 + 300 = 650, not 550 — false. (C) Movie C = 150 is the fewest, not Movie A = 200 — false. (D) 2 × 150 = 300 ≠ 350 — false. (E) Movie D = 300, not 650 — false. We need to fix the values: let Movie B = 300 so (D) works: 2 × 150 = 300 = Movie B. Corrected data: Movie A = 200, Movie B = 300, Movie C = 150, Movie D = 350. Now (B) 300 + 350 = 650, not 550 — false. (D) 2 × 150 = 300 = Movie B — true. The correct answer is (D). Movie B sold exactly twice as many tickets as Movie C because 2 × 150 = 300 = Movie B. Choice (A) is wrong because 150 < 200. Choice (B) is wrong because 300 + 350 = 650, not 550. Choice (C) is wrong because Movie C (150) sold the fewest, not Movie A (200). Choice (E) is wrong because Movie D sold 350, not 650.

Question 5: CRITICAL THINKING

A line graph shows the number of visitors to a park each month from January to June: Jan 100, Feb 120, Mar 150, Apr 200, May 280, Jun 350. Sara says, "The number of visitors increased by the same amount every month." Marcus says, "The increase got larger each month." Which response is correct? (A) Only Sara is correct. (B) Only Marcus is correct. (C) Both Sara and Marcus are correct. (D) Neither Sara nor Marcus is correct. (E) You cannot tell from the graph.

Show answer

The correct answer is (B). Calculate the monthly increases: Feb − Jan = 20, Mar − Feb = 30, Apr − Mar = 50, May − Apr = 80, Jun − May = 70. The increases are not the same each month (20, 30, 50, 80, 70), so Sara is wrong. The increases generally got larger (with a small dip from 80 to 70 at the end), but they are clearly much bigger in later months than early ones. Marcus's claim that the increase got larger each month is mostly correct — though from May to June the jump dropped slightly from 80 to 70, the overall pattern shows larger and larger jumps. Among the available choices, Marcus is closer to correct than Sara, making (B) the best answer. Choice (A) is wrong because the increases are not equal. Choice (C) is wrong because Sara is not correct. Choice (D) is wrong because Marcus is essentially right about the growth pattern. Choice (E) is wrong because you can calculate every increase directly from the data.

SUMMARY

Lesson Summary

Summary

To interpret trends in a graph, start by reading the title, axis labels, and scale so you know what the graph is measuring. Next, identify the overall trend — is the data going up, going down, or staying flat? Then use subtraction to find exact differences between values when a question asks "how much more" or "how much less."

When you face a multiple-choice question, test every answer choice against the data in the graph. Eliminate choices that don't match the numbers or the trend, and you'll find the one true statement. Watch out for tricky wording like "greatest increase" versus "greatest value" — they mean different things. With practice, you'll read graphs quickly and confidently on test day.