The marks scored by students in a class test are out of 50. Find the median of the following data:

Question

The marks scored by students in a class test are out of 50. Find the median of the following data:

1. A. 38.9
2. B. 23.3 (Correct answer)
3. C. 18.8
4. D. 14.1

Correct Answer

Option B — 23.3

Detailed Solution & Explanation

The correct answer is 23.3.

Key Points

• Build the cumulative frequencies: 5, 13, 19, 25, 30. Total n = 30, so n/2 = 15.
• The median class is the first whose cumulative frequency reaches 15 — that is 20-30 (cf 13 before it, 19 after).
• Apply the median formula l + h × (n/2 − cf) / f:
  • l = 20, h = 10, cf = 13, f = 6
  • median = 20 + 10 × (15 − 13)/6 = 20 + 20/6 = 23.33

Additional Information

• In the formula, cf is the cumulative frequency of the class *before* the median class, and f is the frequency of the median class itself — mixing those two is the commonest error.
• For grouped data the median is an estimate, since the exact values inside each class are unknown; it assumes an even spread within the class.
• The companion formulae: mode = l + h(f₁ − f₀)/(2f₁ − f₀ − f₂), and mean by the direct or step-deviation method.
• The median is unaffected by extreme values, which is why it is preferred to the mean for skewed data such as incomes.