A frequency is the number that tells how many times a data or an event is repeating in an experiment. It is generally represented graphically in form of histograms.

There are two different types of frequencies:

Relative frequency is used in probability when it is not easy to evaluate the probability of certain events by looking at their situations. For example the result of any match for win, lose or tie cannot be determined as all outcomes are equally likely, but one can estimate the probability by looking at the previous win or lose of matches and also the way the game is proceeding so far.

Relative frequency = $\frac{(number\ of\ trials\ that\ are\ successful)}{(total\ number\ of\ trials )}$

With increase in number of trials the estimate of the probability that is made using the relative frequency technique can be more accurate.

Relative frequency tells how often anything is happening after
dividing by the total number of outcomes. It is more an experimental
concept than a theoretical one. In general we use the relative frequency
concept in case of big number of trials. This can only be done
practically and not theoretically. Since the concept is experimental so
it is quite possible to get distinct relative frequency each time the
experiment is repeated.

**For Example:** I have
scored an ‘A’ 7 times out of the 10 tests. Then 7 is my frequency of
scoring an ‘A’ and $\frac{7}{10}$ * 100% = 70% is the relative frequency
of my scoring an ‘A’ in exams.

When we add up all the relative frequencies, the sum is equal to 1 always, neglecting the rounding off if any.

4 | 10 | 6 | 12 | 5 | 10 | 5 | 6 | 12 | 11 | 1 | 6 | 3 |

1 | 6 | 1 2 | 1 | 5 | 4 | 4 | 12 | 6 | 6 | 1 | 12 | 4 |

10 | 12 | 3 | 8 | 6 | 12 | 9 | 8 | 4 | 3 | 8 | 12 | 3 |

12 | 5 | 4 | 11 | 12 | 5 | 5 | 5 | 8 | 5 | 12 |

Find the probability of occurrence of 12.

Here we see that occurrence of 12 is 11 times in all 50 trials.

So in this case the probability of occurrence of 12 is simply the relative frequency of 12.

P (occurrence of 12) = $\frac{11}{50}$ = 0.22

Relative frequency = 0.22 = 22%

So in an experiment of 50 trials 12 has occurred 22%.

**Example 2:** In a class of 42 students, 20 students go to school by school bus, 15 by car and 7 by walk. Find the relative frequencies.

**Solution:** Total number of students = 42

Number of students used school bus = 20

Number of students used car = 15

Number of students go by walk = 7

The relative frequencies are:

School bus = $\frac{20}{42}$ = 0.48

Car = $\frac{15}{42}$ = 0.36

Walk = $\frac{7}{42}$ = 0.17

Number of students used school bus = 20

Number of students used car = 15

Number of students go by walk = 7

The relative frequencies are:

School bus = $\frac{20}{42}$ = 0.48

Car = $\frac{15}{42}$ = 0.36

Walk = $\frac{7}{42}$ = 0.17