Skip to content

ACT Statistics and Probability

Review statistics and probability for the ACT.

Written and reviewed by the Study Mondo Education TeamLast updated

📂 Subtopics in ACT Statistics and Probability

Select a subtopic below to start studying

1

Statistics & Probability

Averages, data displays, counting, probability, two-way tables and expected value.

→
🎯⭐ INTERACTIVE LESSON

Try the Interactive Version!

Learn step-by-step with practice exercises built right in.

Start Interactive Lesson →

ACT: Statistics and Probability

Mean, Median, Mode

Mean (Average)

xˉ=sum of valuesnumber of values\bar{x} = \frac{\text{sum of values}}{\text{number of values}}

Median

Middle value in ordered data.

Mode

Most frequent value.

Probability

P(E)=favorable outcomestotal outcomesP(E) = \frac{\text{favorable outcomes}}{\text{total outcomes}}

Independent Events

P(A and B)=P(A)×P(B)P(A \text{ and } B) = P(A) \times P(B)

Complement

P(not A)=1−P(A)P(\text{not } A) = 1 - P(A)

Counting Principles

Permutations (order matters)

P(n,r)=n!(n−r)!P(n,r) = \frac{n!}{(n-r)!}

Combinations (order does not matter)

C(n,r)=n!r!(n−r)!C(n,r) = \frac{n!}{r!(n-r)!}

ACT Tip: Statistics problems are usually straightforward. Read carefully and look at the data provided.

📚 Practice Problems

1Problem 1easy

❓ Question:

The test scores for 5 students are: 72, 85, 90, 78, and 85. What is the mean score?

A) 78 B) 82 C) 85 D) 90 E) 410

💡 Show Solution

The mean (average) is the sum of all values divided by the number of values.

Step 1: Add all scores 72 + 85 + 90 + 78 + 85 = 410

Step 2: Divide by number of students Mean = 410 ÷ 5 = 82

Answer: B) 82

Note: E) 410 is the sum, not the mean. This is a common trap answer!

Mean vs. Median vs. Mode: • Mean: Average (sum ÷ count) • Median: Middle value when arranged in order • Mode: Most frequent value

For this data: • Mean = 82 • Median = 85 (middle of 72, 78, 85, 85, 90) • Mode = 85 (appears twice)

2Problem 2medium

❓ Question:

A bag contains 3 red marbles, 5 blue marbles, and 2 green marbles. If one marble is randomly selected, what is the probability it is NOT blue?

F) 1/10 G) 1/5 H) 1/2 J) 3/5 K) 7/10

💡 Show Solution

Probability = (Number of favorable outcomes) / (Total outcomes)

Step 1: Find total marbles 3 red + 5 blue + 2 green = 10 total

Step 2: Find marbles that are NOT blue Red + Green = 3 + 2 = 5 marbles

Step 3: Calculate probability P(not blue) = 5/10 = 1/2

Answer: H) 1/2

Alternative method (complement): P(not blue) = 1 - P(blue) P(blue) = 5/10 = 1/2 P(not blue) = 1 - 1/2 = 1/2 ✓

ACT Tip: For "NOT" probability, you can:

  1. Count favorable outcomes directly, OR
  2. Use complement: P(not A) = 1 - P(A)

3Problem 3hard

❓ Question:

The heights (in inches) of 7 basketball players are: 70, 72, 73, 75, 76, 78, 80. What is the interquartile range (IQR)?

A) 3 B) 4 C) 6 D) 8 E) 10

💡 Show Solution

The interquartile range (IQR) = Q3 - Q1

Data: 70, 72, 73, 75, 76, 78, 80 (already ordered, n = 7)

Step 1: Find the median (Q2) Middle value = 75 (4th value)

Step 2: Find Q1 (median of lower half) Lower half: 70, 72, 73 Q1 = 72 (middle of lower half)

Step 3: Find Q3 (median of upper half) Upper half: 76, 78, 80 Q3 = 78 (middle of upper half)

Step 4: Calculate IQR IQR = Q3 - Q1 = 78 - 72 = 6

Answer: C) 6

Why IQR matters: • Measures spread of middle 50% of data • Not affected by outliers (unlike range) • Used in box plots

Quartile Review: • Q1 = 25th percentile (1st quartile) • Q2 = 50th percentile (median) • Q3 = 75th percentile (3rd quartile) • IQR = Q3 - Q1 (middle 50%) • Range = Max - Min (entire spread)

Explain using:
← Previous Topic
Intermediate Algebra and Coordinate Geometry
Next Topic →
Plane Geometry and Trigonometry
🎴

Practice with Flashcards

Rate this topic's cards with spaced repetition. Cards join your deck when you finish a topic's lesson and take its exit quiz.

📖

Browse All Topics

Explore more ACT Prep topics

📌 Related Topics in ACT Math

Pre-Algebra and Elementary AlgebraACT Algebra and FunctionsACT Geometry and TrigonometryIntermediate Algebra and Coordinate GeometryPlane Geometry and TrigonometryPre-Algebra Basics

❓ Frequently Asked Questions

What is ACT Statistics and Probability?▾
Review statistics and probability for the ACT.
How can I study ACT Statistics and Probability effectively?▾
Start by reading the study notes and working through the examples on this page. Then use the flashcards to test your recall. Practice with the 3 problems provided, checking solutions as you go. Regular review and active practice are key to retention.
Is this ACT Statistics and Probability study guide free?▾
Yes — all study notes, flashcards, and practice problems for ACT Statistics and Probability on Study Mondo are free to access. No account is needed.
What course covers ACT Statistics and Probability?▾
ACT Statistics and Probability is part of the ACT Prep course on Study Mondo, specifically in the ACT Math section. You can explore the full course for more related topics and practice resources.
Are there practice problems for ACT Statistics and Probability?▾
Yes, this page includes 3 practice problems with detailed solutions. Each problem includes a step-by-step explanation to help you understand the approach.