Graphs: Statistics SAT

Line Graphs:

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.

Phrase

Shape 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

Line of Best Fit:

Use direction and intercepts to determine the best fit

On the SAT, questions that ask you to fit a function to a scatterplot are always multiple choice, and all four choices are usually functions of the same type, e.g., four linear functions or four quadratic functions.

For linear functions in the form \[f(x)=mx+b\]:

  • Sketch a line that fits the data and approximate its slope.

  • The value of \[m\] should match the slope. Make sure to pay attention to the signs!

  • Approximate the \[y\]-intercept of the function that best fits the data. Make sure the constant term \[b\] matches the \[y\]-intercept.

For quadratic functions in the form \[f(x)=ax^2+bx+c\]:

  • Sketch a parabola and approximately fits the data.

  • If the parabola opens upward, \[a\] should be positive. If the parabola opens downward, \[a\] should be negative.

  • Approximate the \[y\]-intercept of the function that best fits the data. Make sure the constant term \[c\] matches the \[y\]-intercept.