In the formula \(\bar{x}=a+\dfrac{\sum f_i d_i}{\sum f_i}\), for finding the mean of grouped data, \(d_i\)'s are deviations from \(a\) of
lower limits of the classes
upper limits of the classes
mid-points (class marks) of the classes
frequencies of the class marks
Step 1: In grouped data, we do not take every value separately. Instead, we take the mid-point of each class. These mid-points are also called class marks.
Step 2: In the assumed-mean method, we choose any one mid-point (class mark) as the assumed mean and call it \(a\).
Step 3: We calculate the deviation for each class mark using the formula: \(d_i = x_i - a\), where \(x_i\) is the mid-point of the \(i\)-th class.
Step 4: These deviations \(d_i\) are then multiplied with the corresponding frequencies \(f_i\), and we apply the formula: \(\bar{x} = a + \dfrac{\sum f_i d_i}{\sum f_i}\).
Conclusion: Since \(d_i\) is calculated from the class mark \(x_i\), the correct answer is mid-points (class marks) of the classes.