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A survey conducted on 20… (Class 10 Maths Basic 2023, Q27)

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MathsCBSE Class 10 · Basic · Board exam 2023, set 430/6/1 · 3 marks · Short answer

CBSE Class 10 Mathematics Basic 2023: question 27

Set in the CBSE Class 10 board exam of 2023, paper 430/6/1, section C, question 27, for 3 marks. Try it first; the hints and our step-by-step solution are below.

Q27 · 3 marks · Short answerStatistics

A survey conducted on 20 households in a locality by a group of students resulted in the following frequency table for the number of family members in a household:

Family size1-33-55-77-99-11
Number of Families78221

Find the median of this data.

Source: official question paper from cbse.gov.in (PDF). See it in the full 2023 board paper, set 430/6/1.

Hints

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

Hint 1

Make a cumulative frequency column and find N/2.

Hint 2

The median class is the one whose cf first exceeds N/2 = 10; then use .

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: 1–3: f = 7, cf = 7; 3–5: f = 8, cf = 15; 5–7: f = 2, cf = 17; 7–9: f = 2, cf = 19; 9–11: f = 1, cf = 20.

    1 mark

  2. , . The cf just greater than 10 is 15, so the median class is 3–5.

    ½ mark

  3. Here , , , . Median

    1 mark

  4. ½ mark

Answer: Median = 3.75

Where the marks are

  • Correct cumulative frequencies (1 mark)
  • Identifies median class 3–5 (½ mark)
  • Substitutes correctly in median formula (1 mark)
  • Median = 3.75 (½ 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 paper2023 board paper, set 430/6/1 (Basic): 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.