If you're seeing this message, it means we're having trouble loading external resources on our website.

If you're behind a web filter, please make sure that the domains *.kastatic.org and *.kasandbox.org are unblocked.

Main content

Data representations | Lesson

A guide to data representations on the digital SAT

What are data representations problems?

Data representations problems ask us to interpret data representations or create data representations based on given information.
Aside from tables, the two most common data representation types on the SAT are bar graphs and line graphs.
In this lesson, we'll learn to:
  1. Read types of graphs that commonly appear on the SAT
  2. Create line graphs based on verbal descriptions
You can learn anything. Let's do this!

How do I read bar graphs, dot plots, and histograms?

Note: Bar graphs appear more frequently than dot plots and histograms do on the SAT.

Reading bar graphs

Khan Academy video wrapper
Reading bar graphsSee video transcript

What are bar graphs, dot plots, and histograms?

Bar graphs

On a bar graph, the sizes of the bars are related to the size of the quantities: the larger a quantity is, the taller or longer the bar representing it is.

Dot plots

Dot plots use dots to represent the frequency with which particular values occur. Dot plots are usually used for low, easily countable frequencies because it's impractical to draw or count many dots.


Histograms use bars to represent the frequency at which a range of values occurs. Histograms are useful because it's often impractical to list every possible value independently.

Try it!

Try: interpret a bar graph
A bar graph represents the number of sunny days in 2019 for four different towns, as follows: Duskville, 100; Lumi, 225; Rayton, 175; Sunnydale, 275.
The bar graph above shows the number of sunny days in 2019 for four towns.
How many sunny days did Duskville have in 2019 ?
  • Your answer should be
  • an integer, like 6
  • a simplified proper fraction, like 3/5
  • a simplified improper fraction, like 7/4
  • a mixed number, like 1 3/4
  • an exact decimal, like 0.75
  • a multiple of pi, like 12 pi or 2/3 pi
Arrange the four towns in order from most number of sunny days to least number of sunny days in 2019.

How do I read line graphs?

Reading line graphs

Khan Academy video wrapper
Reading line graphsSee video transcript

What are line graphs?

Line graphs usually show how quantities change over time.
The SAT will most often ask us to do the following:
  • Identify values on the graph and use them in calculations
  • Determine whether the graph is increasing or decreasing. We may be asked about a specific interval or the whole graph.
  • Determine when the rate of change is the highest/lowest. Higher rates of change correspond to steeper sections of the graph, and lower rates of change correspond to shallower sections of the graph.

Try it!

try: interpret a line graph
A line graph plots the number of students versus year, for the period from 2014 to 2018. The enrollment numbers are as follows: 2014, 2200 students; 2015, 2350 students; 2016, 2600 students; 2017, 2800 students; 2018, 2900 students.
The graph above shows Musutafu school district's enrollment from 2014 to 2018.
From 2014 to 2018, the number of students enrolled in the Musutafu school district generally
The school district saw the smallest change in the number of students enrolled between

How do I draw line graphs based on verbal descriptions?

Translating a sequence of events to a line graph

On the SAT, in addition to reading line graphs, we may be asked to select a line graph that represents a given scenario.
These questions tend to be about the correct order of events and the general direction of change. The axes of the graphs are often presented without exact values.

What are some key phrases to look out for?

The table below lists some common key phrases in line graph translation problems and how to interpret them.
PhraseShape of graph
"Increases", "rises", "grows"Upward trend
"Decreases", "drops", "declines"Downward trend
"Remains constant", "stops", "stays the same"Flat trend
"Slowly", "gradually"Shallow slope
"Rapidly", "quickly"Steep slope

Let's look at an example!

Francisco drives from home to a drive-in movie theater. He parks his car to watch a movie, then drives straight home. Draw a graph that represents Francisco's distance from home as time elapses.

Try it!

Try: describe a graph based on a scenario
Marcus wants to surprise his mother with a birthday present. He gradually saves money over the course of several months until he has enough. Then, he holds onto the money for several more months. Right before his mother's birthday, he spends the money he saved all at once on the present.
Before Marcus had enough money for the present, as time elapses, the amount of money he saves
After Marcus saves enough money, but before he buys the present, the amount of money he has
When Marcus spends the money on the present, the amount of money he has

Your turn!

Practice: identify the greatest change
A vertical bar graph shows the number of women in the following US Congresses: 101st, 31; 101nd, 33; 103rd, 55; 104th, 59; 105th, 66.
The bar graph above shows the number of women in the 101st (1989 to 1991) to 105th (1997 to 1999) US Congresses. The number of women in Congress saw the greatest increase between which of the following Congresses?
Choose 1 answer:

Practice: calculate a fraction based on data
A line graph titled "Paulina's Video Game Collection" plots number of video games versus years since 2014. The graph contains the following connected points: (0, 1), (1, 5), (2, 9), (3, 12), (4, 14), (5, 15), and (6, 20).
Paulina bought her first video game in 2014. The line graph above shows the total number of video games Paulina owned since then. According to the graph, the number of video games she owned in 2015 is what fraction of the number she owned in 2019 ?
  • Your answer should be
  • an integer, like 6
  • a proper fraction, like 1/2 or 6/10
  • an improper fraction, like 10/7 or 14/8
  • an exact decimal, like 0.75

Practice: select a graph that represents a scenario
population in a national park declined two years in a row before increasing slightly. Which of the following graphs represents the situation?
Choose 1 answer:

Want to join the conversation?