The distribution below gives the weight of 50 students of class X. Find the Modal weight of the students. Weight (in kg) 35-45 45-55 55-65 65-75 75-85 --- --- --- --- --- --- Number of students 5 10 20 12 3

MathsCBSE Class 10 · Basic · Sample paper, session 2026-27 · 3 marks · Short answer

CBSE Class 10 Mathematics Basic sample paper 2026-27: question 30(B)

From the official CBSE sample question paper for 2026-27, section C, question 30(B), for 3 marks. Try it first; the hints and our step-by-step solution are below.

Q30(B) · 3 marks · Short answerStatistics

The distribution below gives the weight of 50 students of class X. Find the Modal weight of the students.

Weight (in kg)	35-45	45-55	55-65	65-75	75-85
Number of students	5	10	20	12	3

Source: official sample paper from cbseacademic.nic.in (PDF). See it in the full Sample paper 2026-27.

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 frequencies of the neighbouring classes.

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.

The maximum frequency is 20, so the modal class is 55-65.
$f_{1} = 20$ , $f_{0} = 10$ (class 45-55), $f_{2} = 12$ (class 65-75)
1 mark
$l = 55$ , $h = 10$
½ mark
Mode $= l + (\frac{f _{1} - f _{0}}{2 f _{1} - f _{0} - f _{2}}) h = 55 + \frac{20 - 10}{40 - 10 - 12} \times 10 = 55 + \frac{100}{18} = 60.555 \dots$
1 mark
Modal weight $\approx 60.56$ kg
½ mark

Answer: Modal weight ≈ 60.56 kg

Where the marks are

Identifies the modal class 55-65 with $f_{0}$ , $f_{1}$ , $f_{2}$ (1 mark)
Writes l = 55 and h = 10 (½ mark)
Substitutes correctly in the mode formula (1 mark)
Mode ≈ 60.56 kg (½ mark)

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 2026-27 (Basic): every question, by section.

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CBSE Class 10 Mathematics Basic sample paper 2026-27: question 30(B)

Hints

Step-by-step solution

Revise the chapter

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