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

In the assumed mean method for calculating the mean \( \bar{x} \) of a grouped data: Let A be the assumed mean. The deviation of each observation \( x_i \) from the assumed mean A is \( d_i = x_i - A \). The mean of these deviations is \( \bar{d} = \frac{\sum f_i d_i}{\sum f_i} \), where \( f_i \) is the frequency of \( x_i \). The formula for the actual mean \( \bar{x} \) is given by: \[ \bar{x} = A + \bar{d} \] The question uses \( d = (x - A) \), which corresponds to \( d_i \). So, \( \bar{x} = A + \bar{d} \). The term \(h\) is used in the step-deviation method where \( u_i = \frac{x_i - A}{h} \), and then \( \bar{x} = A + h\bar{u} \). Since \(d\) is used directly as \(x-A\), option (A) is correct. \[ \boxed{A + \bar{d}} \]