Expected Frequency (SQA National 5 Applications of Mathematics): Revision Note

Expected frequency

What is expected frequency?

• Expected frequency refers to the number of times you would expect a particular outcome to occur 

• It is found by multiplying the probability by the number of trials

  • e.g. if you flip a fair coin 100 times, you would expect 0.5 × 100 = 50 heads

• If the probability is given as a fraction, then find the fraction of the number of trials

What is relative frequency?

• Relative frequency is an estimate of a probability using results from an experiment

  • The relative frequency of an event is found using the fraction

• For example, consider flipping an unfair coin 50 times and it landing on heads 20 times

  • An estimate for the probability of the coin landing on heads is 

    • That is the best estimate you can make, given the data you have

    • You do not know the actual probability

• The more trials that are carried out, the more accurate relative frequency becomes

  • It gets closer and closer to the actual probability 

How can I determine if a result is more or less than expected?

• You might be given:

  • the probability of an event occurring

  • the number of trials

  • the actual number of times that the event occurred

• There are two methods to determine if the actual number is more or less than expected

  • finding the expected frequency

  • finding the relative frequency

Finding the expected frequency

• Find the expected frequency

  • Multiply the probability by the number of trials

• Compare the expected frequency with the actual number of times that the event occurred

  • If the actual number is higher, then the result is more than expected

  • If the actual number is lower, then the result is less than expected

Finding the relative frequency

• Find the relative frequency

  • Divide the actual number of times that the event occurred by the number of trials

• Compare the relative frequency with the probability

  • If the relative frequency is higher, then the result is more than expected

  • If the relative frequency is lower, then the result is less than expected