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NDA 1 2025 Maths, question 103

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
Q103

The height which occurs most frequently in the class is

  1. (a) 163.5 cm
  2. (b) 163.9 cm
  3. (c) 164.5 cm
  4. (d) 164.9 cmCorrect answer

Solution.

Answer: (d) 164.9 cm

  1. The modal class is 164–166, with frequency 24.
  2. Its preceding and succeeding frequencies are 15 and 13.
  3. The grouped mode is L+f1−f02f1−f0−f2h=164+24−1548−15−13×2=164.9L + \frac{f_{1} - f_{0}}{2f_{1} - f_{0} - f_{2}}h = 164 + \frac{24 - 15}{48 - 15 - 13} \times 2 = 164.9 cm.