Question

The formula for median in a grouped data is (with usual notation)

• A. \(L+\frac{\frac{N}{2}-F}{f}\times C\)
• B. \(L-\frac{\frac{N}{2}-F}{f}\)
• C. \(\frac{\frac{N}{2}-F}{f}\times F\)
• D. \(L+\frac{\frac{N}{2}+F}{f}\times C\)

Answer 1

The Correct Option is A

Correct answer: \(L + \frac{\frac{N}{2} - F}{f} \times C\) 

Explanation:
The formula for the median of a grouped data set is: \[ \text{Median} = L + \frac{\frac{N}{2} - F}{f} \times C \] Where: - \( L \) is the lower boundary of the median class, - \( N \) is the total number of frequencies, - \( F \) is the cumulative frequency of the class before the median class, - \( f \) is the frequency of the median class, - \( C \) is the class width.

Hence, the correct formula for median in a grouped data set is \(L + \frac{\frac{N}{2} - F}{f} \times C\).