The frequency distribution table of agriculture holdings in a village is given below: Area of land (in hectares) 1 – 3 3 – 5 5 – 7 7 – 9 9 – 11 11 – 13 --- --- --- --- --- --- --- No. of families 20 45 80 55 40 12 Find the modal agriculture holdings of the village.

MathsCBSE Class 10 · Basic · Sample paper, session 2025-26 · 3 marks · Short answer

CBSE Class 10 Mathematics Basic sample paper 2025-26: question 27(A)

From the official CBSE sample question paper for 2025-26, section C, question 27(A), for 3 marks. Try it first; the hints and our step-by-step solution are below.

Q27(A) · 3 marks · Short answerStatistics

The frequency distribution table of agriculture holdings in a village is given below:

Area of land (in hectares)	1 – 3	3 – 5	5 – 7	7 – 9	9 – 11	11 – 13
No. of families	20	45	80	55	40	12

Find the modal agriculture holdings of the village.

Source: official sample paper from cbseacademic.nic.in (PDF). See it in the full Sample paper 2025-26.

Hints

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

Hint 1

The modal class is the class with the highest frequency.

Hint 2

Use Mode $= l + \frac{f _{1} - f _{0}}{2 f _{1} - f _{0} - f _{2}} \times h$ with the neighbouring frequencies.

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.

Maximum frequency is 80, so modal class = 5 – 7. Here $l = 5$ , $h = 2$ , $f_{1} = 80$ , $f_{0} = 45$ , $f_{2} = 55$ .
1 mark
Mode $= l + (\frac{f _{1} - f _{0}}{2 f _{1} - f _{0} - f _{2}}) h = 5 + \frac{80 - 45}{160 - 45 - 55} \times 2 = 5 + \frac{35}{60} \times 2 = 5 + 1.17 \approx 6.17$
2 marks
Hence, the modal agriculture holding of the village is about 6.17 hectares.

Answer: Mode ≈ 6.17 hectares

Where the marks are

Identifies modal class 5–7 with correct $l, h, f_{0}, f_{1}, f_{2}$ (1 mark)
Substitutes in mode formula and gets ≈ 6.17 hectares (2 marks)

Revise the chapter

Chapter: Statistics (notes, formulas, where marks are lost and every past question)
Topic: Mode of Grouped Data

Practise this chapterBoard-style questions from Statistics, one at a time, marked against the answer key and marking points.Back to the full paperSample paper 2025-26 (Basic): every question, by section.

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CBSE Class 10 Mathematics Basic sample paper 2025-26: question 27(A)

Hints

Step-by-step solution

Revise the chapter

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