6.2 Mode and Mean of Grouped Data

6.2 Mode and Mean of Grouped Data

(A) Modal Class

The modal class of grouped data is the class interval in the frequency table with the highest frequency.

(B) Class Midpoint

The class midpoint is the value of data that lies at the centre of a class.

Class midpoint = \frac{Lower limit + Upper limit}{2}

(C) Calculating the Mean of Grouped Data

The steps to calculate the mean of grouped data are as follows.

Step 1: Calculate the midpoint value of each class.

Step 2: Calculate the value of (frequency × midpoint value) of each class.

Step 3: Calculate the sum of the values of (frequency × midpoint value) of all the classes.

Step 4: Calculate the sum of all the frequencies of all the classes.

Step 5: Calculate the value of the mean using the formula below.

\begin{array}{l} \begin{array}{l} Mean of grouped data, \bar{x} \\ = \frac{Sum of (frequency \times midpoint)}{Sum of frequencies} \\ = \frac{\sum f x}{\sum f} \\ Where Σ is the notation of summation, \\ x is the midpoint of a class and f is its frequency . \end{array} \end{array}