Question

To calculate mean of a grouped data, Rahul used assumed mean method. He used \( d = (x - A) \), where A is assumed mean. Then \( \bar{x} \) is equal to

• A. \( A + \bar{d} \)
• B. \( A + h\bar{d} \)
• C. \( h (A + \bar{d}) \)
• D. \( A - h\bar{d} \)

Answer 1

The Correct Option is A

Given:
Rahul calculated the mean of grouped data using the assumed mean method.
- He defined \( d = (x - A) \), where \(A\) is the assumed mean.

Step 1: Assumed Mean Method Explained
- \(x\) is the class mark.
- \(d\) is the difference between each class mark and the assumed mean \(A\).
- \(\bar{d}\) is the average of these differences, weighted by their frequencies.

Step 2: Formula for Mean
The mean \(\bar{x}\) is calculated as:
\[\bar{x} = A + \bar{d}\]
where \(\bar{d} = \frac{\sum f d}{\sum f}\), representing the weighted average of deviations.

Final Answer:
\[\boxed{\bar{x} = A + \bar{d}}\]