Multiple choice

The median of $100$ observations grouped in classes of equal width is $25$. If the median class interval is $20-30$ and the number of observations less than $20$ is $45$, then the frequency of median class is :

  1. $20$
  2. $12$
  3. $10$
  4. $15$
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C Correct answer
Explanation

Median = L + [(N/2 - cf) / f] * h. 25 = 20 + [(50 - 45) / f] * 10. 5 = (5 / f) * 10 => 5 = 50 / f => f = 10.

AI explanation

Using the median formula for grouped data, Median = L + ((N/2 - CF) / f) * w, where L is 20, N/2 is 50, CF is 45, and w is 10. Substituting the values gives 25 = 20 + ((50 - 45) / f) * 10. Solving 5 = 50/f yields a frequency of 10.

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