PSAT/NMSQT Math · Lesson 3 of 4
Data, probability, and conditional statements
Read the group a statistic refers to, and change the denominator when the problem says “given that.”
Reference groups
A percentage is meaningless until you know “percent of what.” In a two-way table, a row percent and a column percent answer different questions. “Of the students who prefer bus” uses only that column or row as the whole.
Measures of center summarize differently. The mean uses the sum of all values. The median uses position in an ordered list. A large outlier moves the mean more than the median.
Conditional probability
The word “given” restricts the outcomes you are allowed to count. If 9 of 24 bus riders are in a music club, then among bus riders the probability of being in the club is 9/24. Dividing 9 by every student in the school answers a different question.
Write the restricted group in words before you form the fraction. That sentence is the denominator.
Worked example
Of 60 students, 24 ride the bus, and 9 of those 24 are in a club. A student is chosen among bus riders. What is the probability the student is in the club?
- The condition “rides the bus” leaves 24 possible students.
- Nine of those 24 are in the club.
- The probability is 9/24 = 3/8.
Why this works. Do not use 60 in the denominator after the group has already been restricted.
Check your understanding
- Underline the group that follows “of” or “given that.”
- Say whether a display asks for a count, a rate, or a conditional probability.
- Explain how an outlier would affect the mean and the median differently.