ACT Statistics and Probability - Complete Interactive Lesson

Part 1: Mean, Median, Mode

ACT Statistics and Probability

Part 1 of 7 — Mean, median, and weighted averages

ACT math statistics questions are usually short and computation-based. Core scoring rule: compute exactly what is asked, then test units and constraints.

Common formulas used in this unit:

Mean = sum of values / number of values
Range = max - min
P(A or B) = P(A) + P(B) - P(A and B)

Core Concepts

Worked Table Example

A class survey result:

40 students total
18 take art
15 take music
7 take both

Probability a random student takes art or music: (P(A cup M) = (18 + 15 - 7)/40 = 26/40 = 0.65)

Subtracting overlap once is the key move. ACT often tests this exact trap.

Numeric Practice

Dataset: 4, 7, 9, 10. Enter the median.
If P(A)=0.4 and P(B)=0.5 and P(A and B)=0.2, enter P(A or B).
How many 2-letter arrangements can be made from letters A, B, C with no repetition?

ACT Pitfalls for Mean, median, and weighted averages

Do not confuse mean with median when outliers are present.
For conditional probability tables, confirm row/column denominator before dividing.
In counting problems, decide first: does order matter?
Translate wording to symbols before computing to avoid arithmetic slips.

Formula Selection

ACT-Style Review

Part 2: Data Displays

ACT Statistics and Probability

Part 2 of 7 — Spread: range and IQR

ACT math statistics questions are usually short and computation-based. Core scoring rule: compute exactly what is asked, then test units and constraints.

Common formulas used in this unit:

Mean = sum of values / number of values
Range = max - min
P(A or B) = P(A) + P(B) - P(A and B)

Core Concepts

Worked Table Example

A class survey result:

40 students total
18 take art
15 take music
7 take both

Probability a random student takes art or music: (P(A cup M) = (18 + 15 - 7)/40 = 26/40 = 0.65)

Subtracting overlap once is the key move. ACT often tests this exact trap.

Numeric Practice

Dataset: 4, 7, 9, 10. Enter the median.
If P(A)=0.4 and P(B)=0.5 and P(A and B)=0.2, enter P(A or B).
How many 2-letter arrangements can be made from letters A, B, C with no repetition?

ACT Pitfalls for Spread: range and IQR

Do not confuse mean with median when outliers are present.
For conditional probability tables, confirm row/column denominator before dividing.
In counting problems, decide first: does order matter?
Translate wording to symbols before computing to avoid arithmetic slips.

Formula Selection

ACT-Style Review

Part 3: Counting Principles

ACT Statistics and Probability

Part 3 of 7 — Probability rules and complements

ACT math statistics questions are usually short and computation-based. Core scoring rule: compute exactly what is asked, then test units and constraints.

Common formulas used in this unit:

Mean = sum of values / number of values
Range = max - min
P(A or B) = P(A) + P(B) - P(A and B)

Core Concepts

Worked Table Example

A class survey result:

40 students total
18 take art
15 take music
7 take both

Probability a random student takes art or music: (P(A cup M) = (18 + 15 - 7)/40 = 26/40 = 0.65)

Subtracting overlap once is the key move. ACT often tests this exact trap.

Numeric Practice

Dataset: 4, 7, 9, 10. Enter the median.
If P(A)=0.4 and P(B)=0.5 and P(A and B)=0.2, enter P(A or B).
How many 2-letter arrangements can be made from letters A, B, C with no repetition?

ACT Pitfalls for Probability rules and complements

Do not confuse mean with median when outliers are present.
For conditional probability tables, confirm row/column denominator before dividing.
In counting problems, decide first: does order matter?
Translate wording to symbols before computing to avoid arithmetic slips.

Formula Selection

ACT-Style Review

Part 4: Basic Probability

ACT Statistics and Probability

Part 4 of 7 — Conditional probability tables

ACT math statistics questions are usually short and computation-based. Core scoring rule: compute exactly what is asked, then test units and constraints.

Common formulas used in this unit:

Mean = sum of values / number of values
Range = max - min
P(A or B) = P(A) + P(B) - P(A and B)

Core Concepts

Worked Table Example

A class survey result:

40 students total
18 take art
15 take music
7 take both

Probability a random student takes art or music: (P(A cup M) = (18 + 15 - 7)/40 = 26/40 = 0.65)

Subtracting overlap once is the key move. ACT often tests this exact trap.

Numeric Practice

Dataset: 4, 7, 9, 10. Enter the median.
If P(A)=0.4 and P(B)=0.5 and P(A and B)=0.2, enter P(A or B).
How many 2-letter arrangements can be made from letters A, B, C with no repetition?

ACT Pitfalls for Conditional probability tables

Do not confuse mean with median when outliers are present.
For conditional probability tables, confirm row/column denominator before dividing.
In counting problems, decide first: does order matter?
Translate wording to symbols before computing to avoid arithmetic slips.

Formula Selection

ACT-Style Review

Part 5: Combinations & Permutations

ACT Statistics and Probability

Part 5 of 7 — Combinatorics basics

ACT math statistics questions are usually short and computation-based. Core scoring rule: compute exactly what is asked, then test units and constraints.

Common formulas used in this unit:

Mean = sum of values / number of values
Range = max - min
P(A or B) = P(A) + P(B) - P(A and B)

Core Concepts

Worked Table Example

A class survey result:

40 students total
18 take art
15 take music
7 take both

Probability a random student takes art or music: (P(A cup M) = (18 + 15 - 7)/40 = 26/40 = 0.65)

Subtracting overlap once is the key move. ACT often tests this exact trap.

Numeric Practice

Dataset: 4, 7, 9, 10. Enter the median.
If P(A)=0.4 and P(B)=0.5 and P(A and B)=0.2, enter P(A or B).
How many 2-letter arrangements can be made from letters A, B, C with no repetition?

ACT Pitfalls for Combinatorics basics

Do not confuse mean with median when outliers are present.
For conditional probability tables, confirm row/column denominator before dividing.
In counting problems, decide first: does order matter?
Translate wording to symbols before computing to avoid arithmetic slips.

Formula Selection

ACT-Style Review

Part 6: Problem-Solving Workshop

ACT Statistics and Probability

Part 6 of 7 — ACT statistics traps

ACT math statistics questions are usually short and computation-based. Core scoring rule: compute exactly what is asked, then test units and constraints.

Common formulas used in this unit:

Mean = sum of values / number of values
Range = max - min
P(A or B) = P(A) + P(B) - P(A and B)

Core Concepts

Worked Table Example

A class survey result:

40 students total
18 take art
15 take music
7 take both

Probability a random student takes art or music: (P(A cup M) = (18 + 15 - 7)/40 = 26/40 = 0.65)

Subtracting overlap once is the key move. ACT often tests this exact trap.

Numeric Practice

Dataset: 4, 7, 9, 10. Enter the median.
If P(A)=0.4 and P(B)=0.5 and P(A and B)=0.2, enter P(A or B).
How many 2-letter arrangements can be made from letters A, B, C with no repetition?

ACT Pitfalls for ACT statistics traps

Do not confuse mean with median when outliers are present.
For conditional probability tables, confirm row/column denominator before dividing.
In counting problems, decide first: does order matter?
Translate wording to symbols before computing to avoid arithmetic slips.

Formula Selection

ACT-Style Review

Part 7: Review & Applications

ACT Statistics and Probability

Part 7 of 7 — Mixed review and test execution

ACT math statistics questions are usually short and computation-based. Core scoring rule: compute exactly what is asked, then test units and constraints.

Common formulas used in this unit:

Mean = sum of values / number of values
Range = max - min
P(A or B) = P(A) + P(B) - P(A and B)

Core Concepts

Worked Table Example

A class survey result:

40 students total
18 take art
15 take music
7 take both

Probability a random student takes art or music: (P(A cup M) = (18 + 15 - 7)/40 = 26/40 = 0.65)

Subtracting overlap once is the key move. ACT often tests this exact trap.

Numeric Practice

Dataset: 4, 7, 9, 10. Enter the median.
If P(A)=0.4 and P(B)=0.5 and P(A and B)=0.2, enter P(A or B).
How many 2-letter arrangements can be made from letters A, B, C with no repetition?

ACT Pitfalls for Mixed review and test execution

Do not confuse mean with median when outliers are present.
For conditional probability tables, confirm row/column denominator before dividing.
In counting problems, decide first: does order matter?
Translate wording to symbols before computing to avoid arithmetic slips.

Formula Selection

ACT-Style Review