Question

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

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

Hint:

Mean using assumed mean method: \(\bar{x} = A + h\bar{d}\), where \(h\) is class width.

Answer 1

The Correct Option is B

Given:
Rahul uses the assumed mean method to calculate mean of grouped data.
He defines \(d = (x - A)\), where \(A\) is the assumed mean.

Step 1: Recall formula for mean using assumed mean method
If \(h\) is the class width and \(\bar{d}\) is the mean of deviations \(d\), then
\[ \bar{x} = A + h \bar{d} \]

Explanation:
- \(A\) is the assumed mean.
- \(d\) represents deviation of class mid-point \(x\) from \(A\), scaled by class width \(h\).
- \(\bar{d} = \frac{\sum f d}{\sum f}\) is the mean deviation.

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