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### Course: Digital SAT Math>Unit 7

Lesson 5: Data representations: medium

# 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

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
The bar graph above shows the number of sunny days in $2019$ for four towns.
How many sunny days did Duskville have in $2019$ ?
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
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
"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
.

Practice: identify the greatest change
The bar graph above shows the number of women in the $101$st ($1989$ to $1991$) to $105$th ($1997$ to $1999$) US Congresses. The number of women in Congress saw the greatest increase between which of the following Congresses?

Practice: calculate a fraction based on data
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 $2019$ ?

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

## Want to join the conversation?

• Hello! Just wondering, will we be given a sheet of paper for our rough-work during the Math section of the Digital SAT? Or will there be a digital pen on the screen (Like in the exercises on khan academy)?
• Yes, Sheet of paper will be used.
• How many lessons do u all do per day?
• i do 3! sometimes 2 if the topic tough. just practise a lot, understand concepts, then it wont be intimidating. good luck!
• We got this guys
• this lesson was actually the first easy one I had in Unit 3.
• haha, same
(1 vote)
• will you be able to use your own calculator on test day or must it be the one provided on bluebook?
• You can use any of the two. Better use the one you are familiar with.
If bringing you own, read the guidelines for the calculator that are allowed on collegeboard's website.
• the easiest lesson since unit 3! THANKS YOU 💏
• I too feel the same
(1 vote)
• Is it enough to just prepare until medium level?