Relative frequencies

I did an experiment of rolling a pair of dice 144 \times and recorded the sum of the numbers that the two dice land on. Let x represent the number that has been landed on. The results are below.

We can see these results in a plot

We can see in the plot above that the shape is different to the expected frequency plot but also that it is similar, with a higher frequency at the centre that gets lower as we move towards 2 and 12.

Now we are going to calculate the relative frequencies.

Relative means compared to something else. For relative frequencies, we compare the frequency of each outcome to the number of trials by dividing the frequency of each outcome by the number of trials.

So, in my experiment, the relative frequency of 2 is 3/144 and the relative frequency is of 7 is 27/144.

The relative frequencies of all of the outcomes are shown below

This can be simplified to

and can be shown in decimals rather than fractions as

Relative frequencies are probabilities based on experiments. If we were to add up all of the relative frequencies in the table above, we would get 144/144 which is 1. Each relative frequency is between 0 and 1. The relative frequency is an estimate of the probability of achieving each outcome based on an experiment.

We can plot the actual probability against the relative frequencies that we have just looked at.

We can see that the relative frequency is quite a good estimate of the probability of each outcome from the experiment of 144 trials with two dice.

If I did the experiment again but this time with 1000 trials. Do you think the relative frequencies would be closer to the probabilities?