SAT Math · Lesson 3 of 4
Problem-solving and data analysis
Interpret ratios, percentages, units, and statistical displays, and avoid treating a model as a cause.
Units and models
A model is useful only if you know what each variable measures. If d = 40t + 10, and t is hours after noon, then 40 has units of distance per hour and 10 is the distance already completed at noon. Predicting a value outside the described interval may not be justified by the model.
Percent change compares a change with the starting amount. A rise from 50 to 65 is a change of 15, and 15/50 = 0.30, so the increase is 30%. Percentage points are different: moving from 50% to 65% is an increase of 15 percentage points.
What a graph or sample supports
In a scatterplot, a line of best fit summarizes a trend. A point far from the line can strongly influence the slope. Association does not by itself show that one variable causes the other.
A sample estimate describes the people or objects that were measured. “Students in this survey” is not automatically “all students.” Read the axis scale before you estimate a coordinate, because a grid may count by 2 or by 10.
Worked example
A price rises from $25 to $30. What is the percent increase?
- The change is 30 − 25 = 5.
- Compare that change with the original price: 5/25 = 0.20.
- The percent increase is 20%. It is not 5%, and it is not 30/25 without subtracting first if the question asks for the increase.
Why this works. Percent increase uses the change divided by the starting value, then converted to a percent.
Check your understanding
- State the units of a rate before you use it.
- Use the original amount as the base of a percent change.
- Separate what a graph shows from a cause you were not given.