Question

If assumed mean of a data is 47.5, \( \sum f_i d_i = 435 \) and \( \sum f_i = 30 \), then mean of that data is:

• A. 42
• B. 52
• C. 62
• D. 72

Hint:

To calculate the mean using the assumed mean method, use the formula \( \bar{x} = A + \frac{\sum f_i d_i}{\sum f_i} \), where \( A \) is the assumed mean.

Answer 1

The Correct Option is B

Step 1: Formula for Mean.
The formula for calculating the mean \( \bar{x} \) is: \[ \bar{x} = A + \frac{\sum f_i d_i}{\sum f_i} \] where:
\( A \) is the assumed mean,
\( \sum f_i d_i \) is the sum of the products of the frequency and the deviation from the assumed mean,
\( \sum f_i \) is the total frequency.
Step 2: Substituting the Given Values.
Here, \( A = 47.5 \), \( \sum f_i d_i = 435 \), and \( \sum f_i = 30 \). Substitute these values into the formula: \[ \bar{x} = 47.5 + \frac{435}{30} \] \[ \bar{x} = 47.5 + 14.5 \] Step 3: Conclusion.
Thus, the mean of the data is: \[ \bar{x} = 52 \]