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The median of the following… (Class 10 Maths 2026, Q32a)

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MathsCBSE Class 10 · Standard · Board exam 2026, set 30/3/1 · 5 marks · Long answer

CBSE Class 10 Mathematics Standard 2026: question 32(a)

Set in the CBSE Class 10 board exam of 2026, paper 30/3/1, section D, question 32(a), for 5 marks. Try it first; the hints and our step-by-step solution are below.

Q32(a) · 5 marks · Long answerStatistics

The median of the following data is 137. Find the values of x and y, given that total of frequencies is 68.

Source: official question paper from cbse.gov.in (PDF). See it in the full 2026 board paper, set 30/3/1.

Hints

Open one hint at a time and try again before the next.

Hint 1

Make a cumulative frequency column in terms of x and y. The median 137 tells you which class is the median class.

Hint 2

Put l = 125, h = 20, f = 20, cf = 9 + x and n/2 = 34 into the median formula, then use the total 68 for y.

Step-by-step solution

Each step shows the marks it earns, as an examiner would award them. Checked by an independent re-solve from the question paper.

  1. Cumulative frequency table:

    Classfcf
    65–8544
    85–10559
    105–125x9 + x
    125–1452029 + x
    145–1651443 + x
    165–185y43 + x + y
    185–205447 + x + y

    1½ marks

  2. The median is 137, which lies in the class 125–145. So the median class is 125–145, with:

    ½ mark

  3. Median :

    1 mark

  4. 1 mark

  5. Total frequency:

    1 mark

Answer: x = 13, y = 8

Where the marks are

  • Correct cumulative frequency table (1½ marks)
  • Identifies the median class 125–145 (½ mark)
  • Substitutes correctly in the median formula (1 mark)
  • Gets x = 13 (1 mark)
  • Uses total 68 to get y = 8 (1 mark)

Revise the chapter

Practise this chapterBoard-style questions from Statistics, one at a time, marked against the answer key and marking points.Back to the full paper2026 board paper, set 30/3/1 (Standard): every question, by section.

The question is transcribed from the official paper; figures are described in words. The solution, hints and chapter tag are ours. Spotted an error? Write tosupport@questionbuddy.in.