# How to calculate a relative frequency: 9 steps (with pictures)

In statistical matters, the absolute frequency of a value is easy to find: it consists of counting the number of occurrences of this value in a sample (of people, objects, etc.). Relative frequency is a bit more complex in that it measures the frequency of a value, expressed as a proportion of a whole. It is calculated by dividing the absolute frequency by the size of the sample, the latter called the population. In order to make it easier to calculate the relative frequency, you need to classify the data, do some simple calculations, and then draw up a frequency table.

## Steps

### Part 1 of 3: prepare the data for the calculation of relative frequency #### Step 1. Recover data

Unless you are given them at the outset, in an exercise for example, you will have to experience, collect your data. Whether it is weight, size, years …, it will be up to you to determine from the start the degree of precision of your measurements.

• To better understand, let's take the example of people who went to see a given film. You will record the ages of each spectator. If it's an all-audience movie, you'll have people between 10 and 70 (or 80) years old, or 60 to 70 different ages. You can group your viewers into six classes: under 20, 20 to 29, 30 to 39, 40 to 49, 50 to 59, and over 60. This grouping into classes is more practical.
• As another example, we can take the hypothesis of a doctor who takes the temperature of all his patients over a day. If he decides to take whole temperatures (37 ° C, 38 ° C…), it will not be relevant: it is then necessary to note the temperatures in tenth (37, 2 ° C, 37, 3 ° C…). #### Step 2. Sort your data

If you are the one doing the observation and the surveys, you will get a series of data, a "population" which looks like this, for example: 1, 2, 5, 4, 6, 4, 3, 7, 1, 5, 6, 5, 3, 4, 5, 1. Enough to lose your Latin! There is no logic, no ranking, this is raw data. They must be sorted in ascending order, which gives: 1, 1, 1, 2, 3, 3, 4, 4, 4, 5, 5, 5, 5, 6, 6, 7.

### If the series are made up of values ​​that are close to each other, be careful not to forget any of them when sorting or rewriting them. Recount your values ​​to check that you haven't forgotten any #### Step 3. Put your data in tabular form

You can group all of your data and calculations together by making a frequency table. You will make a table with three columns in which you will put the relative frequencies. Label your columns as follows.

• i { displaystyle i}

: dans cette colonne, vous mettrez toutes les valeurs différentes de votre série. Il n'est plus question de les mettre toutes. Ainsi, même si le 4 apparait plusieurs fois dans votre série, vous ne mettrez qu'une seule fois cette valeur dans la première colonne.

• n(i){displaystyle n(i)}
• : en statistiques, cette appellation correspond à l'effectif de la valeur i{displaystyle i}

, c'est-à-dire le nombre de fois où la valeur apparait, N{displaystyle N}

étant l'effectif total. L'expression n(i){displaystyle n(i)}

se prononce « n de i ». Cependant le plus souvent, cette colonne est intitulée « Effectifs ». C'est dans cette colonne que vous consignerez le nombre de fois où la valeur de la colonne précédente apparait. Ainsi, si la valeur 4 apparait trois fois dans la série, vous mettrez un 3 sur la même ligne que le 4, mais à droite.

• f(i){displaystyle f(i)}
• : en statistiques, cette appellation correspond à la fréquence relative et se lit « fréquence de i ». Chacune des valeurs de cette colonne s'obtient en utilisant les valeurs de la colonne précédente et celle de l'effectif total. Ces valeurs peuvent être données sous forme des chiffres décimaux ou de pourcentages, comme on va le voir à présent.

### Partie 2 sur 3: Calculer des fréquences relatives #### Step 1. Find the total strength of your series

Relative frequency measures the proportion of the presence of a value in a data series. To calculate a relative frequency, you must know the size (or the number) of your series, that is to say the number of values ​​that compose it. This size will be the denominator of the fraction used to calculate the frequency.

### If we go back to the previous example, we see that the series has a total number of 16 data #### Step 2. Calculate the counts of each value

We also speak of the "size" of the value. You must record the number of times a value appears in the sample. From there, you can calculate the relative frequency of a particular value or the frequencies of all values ​​in the sample.

### Let's take the previous example and look at the value 4: we see that it appears 3 times in the series, this is its number #### Step 3. Divide the size of the value by the size of the series

The term "effective" may be replaced by that of "size". These are the first and last calculations to be made to fill in the last column, that of the relative frequencies. You can do this by leaving the frequencies as fractions, calculating them with a calculator or, if you are using a spreadsheet, program the cells in this last column.

• Let's go back to the previous example. The value 4 { displaystyle 4}

apparait donc trois fois et l'effectif de la série est de 16: vous pouvez en déduire que la fréquence relative de cette valeur est de 3/16, ce qui, après calcul au dix-millième, donne 0, 1875, comme on le voit sur le tableau.

### Partie 3 sur 3: Bien présenter des fréquences relatives #### Step 1. Present your results in a frequency table

If you do your calculations separately, it is a good idea to present your results in the frequency table which is already partially filled. You will gain in readability. After each calculation, write on the correct line and in the third column, the frequency found. Usually the result is given as a number with two decimal places, but you may be given another instruction. Once the calculations are done, verify that the sum of the frequencies is 1 or something close (due to rounding).

• After calculations and rounding, you will obtain the following table of relative frequencies:
• i: n (i): f (i)
• 1: 3: 0, 19
• 2: 1: 0, 06
• 3: 2: 0, 13
• 4: 3: 0, 19
• 5: 4: 0, 25
• 6: 2: 0, 13
• 7: 1: 0, 06
• Total: 16: 1, 01 #### Step 2. Indicate the values ​​not present in the series

In some samples there may be values ​​not present. If you roll two dice, the 3 may not come out on 25 rolls. If so, this value 3 is output 0 times, you can indicate it in your table by putting a 0 as n (i) and therefore 0, 00 in f (i).

### In the example we took, all the values ​​from 1 to 7 were present in the series, but let's admit that the 3 was absent, on the line of 3 you would then put in effect the value 0 and the relative frequency would then be also 0 (0/16) #### Step 3. Present your results as percentages

You may be asked to present the frequencies in the form of percentages, which is often how it is done. It is easier to visualize a percentage than a decimal number between 0 and 1. To convert a decimal value into a percentage, simply multiply it by 100, without forgetting to add to the right the symbol of the percentage (%).

• Converted to a percentage, 0.13 becomes 13% (13/100).
• Converted to a percentage, 0.06 becomes 6% (be careful with leading zeros).