IB MYP 4-5 Maths- Relative frequency- Study Notes - New Syllabus
IB MYP 4-5 Maths- Relative frequency – Study Notes
Standard
- Relative frequency
IB MYP 4-5 Maths- Relative frequency – Study Notes – All topics
Relative and Expected Frequency
Relative Frequency
Relative frequency is the ratio of the number of times an event occurs to the total number of trials. It estimates the probability of an event based on experimental data.
\( \text{Relative Frequency} = \dfrac{\text{Number of successful outcomes}}{\text{Total number of trials}} \)
Key Points:
- The more trials conducted, the closer the relative frequency comes to the theoretical probability (Law of Large Numbers).
- Used when theoretical probability is hard to calculate.
Example:
A coin was flipped 100 times and landed on heads 58 times. Find the relative frequency of getting heads.
▶️Answer/Explanation
Step 1: Number of successful outcomes = 58, Total trials = 100.
Step 2: Relative frequency = \( \dfrac{58}{100} = 0.58 \).
Interpretation: The experimental probability of getting heads is approximately 0.58 (or 58%).
Example:
A spinner with 4 equal sectors (A, B, C, D) was spun 50 times. Results were: A = 14, B = 12, C = 10, D = 14. Find the relative frequency for landing on C.
▶️Answer/Explanation
Step 1: Frequency for C = 10, Total spins = 50.
Step 2: Relative frequency for C = \( \dfrac{10}{50} = 0.2 \).
Interpretation: The spinner landed on C 20% of the time.
Expected Frequency
Expected frequency is the number of times an event is likely to occur based on its theoretical probability in a given number of trials.
\( \text{Expected Frequency} = \text{Total Trials} \times \text{Theoretical Probability} \)
Key Points:
- Expected frequency is a prediction based on probability, not actual results.
- It is useful in probability experiments and statistical tests (e.g., Chi-square test).
Example:
A fair coin is tossed 200 times. What is the expected frequency of getting heads?
▶️Answer/Explanation
Step 1: Theoretical probability of heads = \( \dfrac{1}{2} = 0.5 \).
Step 2: Total trials = 200.
Step 3: Expected frequency = \( 200 \times 0.5 = 100 \).
Answer: We expect 100 heads in 200 tosses.
Example:
A die is rolled 600 times. What is the expected frequency of getting an even number (2, 4, or 6)?
▶️Answer/Explanation
Step 1: Theoretical probability of an even number = \( \dfrac{3}{6} = 0.5 \).
Step 2: Total trials = 600.
Step 3: Expected frequency = \( 600 \times 0.5 = 300 \).
Answer: We expect 300 even numbers in 600 rolls.