6.2 Mode and Mean of Grouped Data
(A) Modal Class
(B) Class Midpoint
The class midpoint is the value of data that lies at the centre of a class.
Class midpoint=Lower limit + Upper limit2
Class midpoint=Lower limit + Upper limit2
(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.
Mean of grouped data, ˉx=Sum of (frequency × midpoint)Sum of frequencies=∑fx∑fWhere Σ is the notation of summation,x is the midpoint of a class and f is its frequency.
Mean of grouped data, ˉx=Sum of (frequency × midpoint)Sum of frequencies=∑fx∑fWhere Σ is the notation of summation,x is the midpoint of a class and f is its frequency.