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NDA 1 2025 Maths, question 102

Topic: Statistics

Passage · Q101 to Q104

The frequency distribution of height of students of a class is given below:

Height (in cm) Number of Students
160–162 12
162–164 15
164–166 24
166–168 13
Q102

What is the median height of the class?

  1. (a) 162.41 cm
  2. (b) 163.41 cm
  3. (c) 164.41 cmCorrect answer
  4. (d) 165.41 cm

Solution.

Answer: (c) 164.41 cm

  1. Total frequency is N=12+15+24+13=64N = 12 + 15 + 24 + 13 = 64, so N/2=32N/2 = 32.
  2. The cumulative frequency before 164–166 is 27, making this the median class.
  3. Using the grouped-data formula, median =L+N/2−Cfh=164+32−2724×2=164.4166…= L + \frac{N/2 - C}{f}h = 164 + \frac{32 - 27}{24} \times 2 = 164.4166\ldots cm.
  4. This is 164.42 cm when rounded to two decimals.
  5. Option (c), 164.41 cm, is the matching listed value, apparently truncated.