Definition: Absolute frequency is the number of times a specific event occurs in a dataset.
For example, the table shows how students in Class A get to school. These exact counts represent absolute frequencies:
The Total Absolute Frequency is the sum of all individual counts:
$$5+12+3+5=25$$
This means there are 25 students in Class A.
Definition: Relative frequency shows the proportion of each category compared to the total count. It is calculated using the formula:
$$ \text{Relative Frequency} = \frac{\text{Absolute Frequency}}{\text{Total Count}} $$
For example, in class A, the total frequency is 25, we can calculate the relative frequency of each method:
$$
\begin{alignat}{3}
\bullet \quad & \text{Walking} &\quad & \tfrac{5}{25} = \tfrac{1}{5} = 20\% \\[1.2ex]
\bullet \quad & \text{By bus} &\quad & \tfrac{12}{25} = 48\% \\[1.2ex]
\bullet \quad & \text{By car} &\quad & \tfrac{3}{25} = 12\% \\[1.2ex]
\bullet \quad & \text{Cycling} &\quad & \tfrac{5}{25} = 20\%
\end{alignat}
$$
Note: The sum of all relative frequencies is always 1 or 100%. (If not, uh-oh! Time for a quick double-check!)
$$ 20\% + 48\% + 12\% + 20\% = 100\% $$
Finding missing values in the frequency table:
$$ \text{Absolute Frequency} = \text{Relative Frequency} \times \text{Total Count} $$
$$ a = 10\% \times 40 = 4 $$So, 4 students go to school on foot.
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