Relative Frequency

Understanding Relative Frequency

You surely know what frequency is, right? Frequency is simply how many times a value or data point appears in a dataset.

For example, if we ask 30 students about their phone brands, and 10 students answer "Apple", then the frequency for the "Apple" brand is 10.

Now, we will get acquainted with Relative Frequency. What is it?

Relative Frequency is how we look at the frequency of a data point compared to the total number of all data points. So, it's not just about how many times it appears, but we look at the "part" or "proportion" of that data relative to the whole.

Why Do We Need Relative Frequency?

Relative frequency is very important, you know. With relative frequency, we can:

1. Compare Proportions: We can compare how large the proportion of one data group is compared to another group within the same dataset. For example, how large the proportion of Apple users is compared to Samsung users in your class.
2. Compare Between Different Groups: We can compare the proportion of data from two groups with different total numbers! For example, comparing the percentage of students who like Math in class A (total 30 students) with class B (total 40 students). It would be difficult with just regular frequency, but with relative frequency (percentage), the comparison becomes fair.

Relative Frequency Formula

Calculating it is super easy!

Where:

• Class Frequency: This is how many times the data or value in that class/group appears (the regular frequency we already know).
• Total Frequency: This is the total number of all data points we observed.

Relative Frequency is usually expressed in the form of:

• Fraction: The most basic form of division.
• Decimal: The result of the fraction division.
• Percentage: The decimal form multiplied by 100%. This is the most commonly used because it's easy to understand.

Example of Calculating Relative Frequency

Let's use the phone brand data example from the 30 students earlier:

Total Frequency = 12 + 10 + 8 = 30 students.

Now let's calculate the relative frequency for each brand:

1. Apple:

   $$\text{Relative Frequency Apple} = \frac{12}{30}$$

   Relative Frequency Apple = $0.4$

   In percent: $0.4 \times 100\% = 40\%$

2. Samsung:

   $$\text{Relative Frequency Samsung} = \frac{10}{30}$$

   Relative Frequency Samsung = $0.333...$ (we round it to $0.33$)

   In percent: $0.33 \times 100\% = 33\%$

3. Xiaomi:

   $$\text{Relative Frequency Xiaomi} = \frac{8}{30}$$

   Relative Frequency Xiaomi = $0.266...$ (we round it to $0.27$)

   In percent: $0.27 \times 100\% = 27\%$

Relative Frequency Table:

The sum of relative frequencies (in decimal form) should always be 1, and in percent should be $100\%$. There might be slight differences due to rounding, but it should be very close to 1 or $100\%$.

Interpreting Relative Frequency

From the relative frequency table above, we can say:

• $40\%$ of the students in that class use Apple brand phones.
• About $33\%$ students use Samsung.
• The rest, about $27\%$, use Xiaomi.

With relative frequency, we get a clearer picture of the proportion of each phone brand among the 30 students.

So, relative frequency helps us understand how large the "portion" of a data point is within the entire dataset. Easy, right?