ACT · Domain 5

Statistics & Probability

8–12% of the ACT math section

Centre and spread, distributions, probability, and whether a sample can be trusted. The mean questions are totals in disguise, and the probability questions turn on one word: replacement.

Statistics & Probability · Topic 1 of 3

Centre, Spread & Distributions

The mean is the total divided by the count, which means every mean question can be turned into a question about the total. Add a value, and the total goes up by that value while the count goes up by one; the new mean follows.

The problem

Five test scores have a mean of 82. After a sixth test, the mean of all six is 84. What was the sixth score?

A $94$
B $84$
C $96$
D $92$

Working1 / 3

The old total $5 \times 82 = 410$

Statistics & Probability · Topic 2 of 3

Probability & Data Collection

A probability is favourable outcomes over total outcomes. Two events in a row multiply — and if the first draw is not put back, the second draw is from a smaller bag with one fewer of whatever left.

The problem

A jar holds 3 green and 5 yellow candies. Two are taken at random without replacement. What is the probability that both are yellow?

F $\dfrac{5}{14}$
G $\dfrac{25}{64}$
H $\dfrac{5}{8}$
J $\dfrac{1}{4}$

Working1 / 3

First draw: 5 yellow of 8 $\frac{5}{8}$

Statistics & Probability · Topic 3 of 3

Counting & Expected Value

Independent choices multiply. When the order of what is chosen matters it is a permutation; when it does not it is a combination, and the difference is dividing by the number of ways to arrange the chosen ones. Expected value is each outcome times its probability, added up.

The problem

A club with 8 members chooses a committee of 3 members. How many different committees are possible?

A $56$
B $336$
C $24$
D $512$

Working1 / 3

Pick three in order $8 \cdot 7 \cdot 6 = 336$