ACT Statistics & Probability: Complete Guide + Practice

ACT says Statistics & Probability make up roughly 12–15% of Math.

This category includes:

• center and spread;
• probability;
• data displays;
• two-way tables;
• sampling;
• simple statistical reasoning.

Mean

[ \text{mean}=\frac{\text{sum of values}}{\text{number of values}} ]

For:

4, 7, 9, 10

mean:

[ \frac{30}{4}=7.5 ]

Median

Order the values.

For:

2, 5, 9, 12, 20

median = 9.

For an even number of values, average the two middle values.

Effect of an outlier

Dataset:

10, 11, 12, 13, 14

Mean = 12.

Add 50.

The mean rises substantially.

The median changes much less.

That is why the median is more resistant to extreme values.

Probability

[ P(A)=\frac{\text{favorable outcomes}}{\text{total outcomes}} ]

Bag:

• 4 red
• 3 blue
• 1 green

Probability of blue:

[ 3/8 ]

Complement probability

If:

[ P(A)=0.72 ]

then:

[ P(\text{not }A)=1-0.72=0.28 ]

Two-way tables

Probability a randomly selected Grade 11 student walks:

[ 12/30=0.4 ]

The phrase “Grade 11 student” changes the denominator.

Weighted averages

Suppose:

• quizzes = 40% of grade, average 80
• exams = 60%, average 90

Overall:

[ 0.4(80)+0.6(90)=86 ]

Samples and populations

If a school wants to know how all students feel about lunch but surveys only students eating in the cafeteria, the sample may be biased.

Good sampling tries to represent the population. For the full breakdown of every ACT Math category, see our enhanced ACT guide.

Standard deviation

You usually need the idea more than long manual calculations.

Larger standard deviation: more spread.

Smaller standard deviation: values cluster more tightly.

If geometry and trigonometry problems are still shaky, the ACT geometry and trigonometry guide covers those separately. See our other ACT guides for the rest of the Math and Reading skill breakdowns.

Original practice

1

Find the mean of:

6, 8, 10, 16

2

A fair die is rolled. Probability of rolling a number greater than 4?

3

If 35% of students take Art, what percent do not?

4

Dataset A and Dataset B have equal means. Dataset B is much more spread out. Which has the larger standard deviation?

5

A survey about school parking is sent only to students who drive to school. What is the main concern?

A. random assignment
B. selection bias
C. too much data
D. arithmetic error

Answers

1. 10
2. 2/6 = 1/3
3. 65%
4. Dataset B
5. B

Common traps

• using the wrong denominator;
• confusing mean and median;
• treating correlation as causation;
• forgetting complement probability;
• assuming a large sample automatically removes bias.

Once you're comfortable with this material, how many ACT practice tests you should take is the next logical question to answer.

Official source

• ACT Math Test Description: https://www.act.org/content/act/en/products-and-services/the-act/test-preparation/description-of-math-test.html

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