The Mean (average) of grouped frequency distribution data using the standard Direct Method is calculated as:
Where $x_i = \text{class mark} = \frac{\text{Upper Limit} + \text{Lower Limit}}{2}$, and $f_i = \text{frequency}$.
The Mode represents the value that appears most frequently. For grouped data, find the Modal Class (the class interval with the highest frequency) and use:
• $l = \text{lower limit of modal class}$
• $f_1 = \text{frequency of modal class}$
• $f_0 = \text{frequency of preceding class}$
• $f_2 = \text{frequency of succeeding class}$
• $h = \text{class interval width}$
The Median represents the middle-most score. Find the Median Class where the cumulative frequency ($cf$) crosses the value of $N/2$:
Empirical Relationship Formula: If a 1-mark question gives you any two parameters out of mean, median, or mode and asks for the third, do not calculate tables! Just use this golden rule:
$$3 \times \text{Median} = \text{Mode} + 2 \times \text{Mean}$$