Question

To find the mean of grouped data which of the following is true?

• A. Sum the products of midpoints and frequencies, then divide by the total frequency.
• B. None of the above
• C. Sum the midpoints of classes, then divide by the total number of classes.
• D. Sum the frequencies and divide by the number of classes.

Answer 1

Answer: (A)

Sum the products of midpoints and frequencies, then divide by the total frequency.

Answer 2

To find the mean of grouped data, we use the formula:

Mean ($\bar{x}$) = $\frac{\sum (f_i \cdot x_i)}{\sum f_i}$

where:

• $f_i$ is the frequency of the i-th class.
• $x_i$ is the midpoint (class mark) of the i-th class.
• $\sum (f_i \cdot x_i)$ represents the sum of the products of the midpoints and their corresponding frequencies.
• $\sum f_i$ represents the total frequency (total number of observations).

The correct option matches the formula for the mean of grouped data.