Relative Frequency
Experimental probability based on actual data and real-world trials
What is Relative Frequency?
Relative frequency, also known as experimental probability, provides a tangible measure of the likelihood of an event based on actual experimental results. Unlike theoretical probability, which predicts outcomes based on ideal conditions, relative frequency reflects what has actually occurred during a series of trials.
The Formula
Where:
• Relative Frequency: The experimental probability of the event
• Number of Positive Outcomes: How many times the event actually occurred
• Total Number of Trials: The total number of attempts made
Law of Large Numbers
As the number of trials increases, the relative frequency tends to converge towards the theoretical probability. With small samples, relative frequency can differ significantly (e.g., 5 heads in 5 flips = 1.0 vs theoretical 0.5). With large samples, it approaches the expected value.
Worked Example: Coin Tossing
Problem: You toss a coin 30 times, and it lands on heads 13 times. Calculate the relative frequency of landing on heads.
- Count the Positive Outcomes: Number of heads = 13
- Count the Total Trials: Total coin tosses = 30
- Apply the Formula: Relative Frequency = 13/30
- Calculate: Relative Frequency ≈ 0.4333 or 43.33%
Real-World Applications: Relative frequency is particularly useful where theoretical probabilities are difficult to calculate — predicting soccer match outcomes, estimating rain chances, quality control in factories.
Marble Bag Experiment
Draw marbles from a bag containing 4 Red, 3 Blue, and 3 Green marbles. Track the relative frequency of drawing a Red marble!
Click a marble to draw it from the bag!
Custom Spinner
Spin the wheel! Each section (Red, Blue, Green, Yellow) has a theoretical probability of 25%. See how relative frequency converges as you spin more.
Card Drawer
Draw cards from a standard 52-card deck. Track the relative frequency of drawing a Heart!
Test Your Understanding
Question 1: You flip a coin 50 times and get tails 22 times. What is the relative frequency of tails?
Question 2: According to the Law of Large Numbers, as the number of trials increases, the relative frequency...
Question 3: A die is rolled 120 times and a 4 appears 25 times. What is the relative frequency of rolling a 4?
