The weights of 30 students of a class are given in the following distribution table: Weight (in kg) Number of students --- --- 40–45 2 45–50 5 50–55 8 55–60 6 60–65 6 65–70 3 Find the median weight of the students.

MathsCBSE Class 10 · Basic · Board exam 2025, set 430/3/1 · 5 marks · Long answer

CBSE Class 10 Mathematics Basic 2025: question 35

Set in the CBSE Class 10 board exam of 2025, paper 430/3/1, section D, question 35, for 5 marks. Try it first; the hints and our step-by-step solution are below.

Q35 · 5 marks · Long answerStatistics

The weights of 30 students of a class are given in the following distribution table:

Weight (in kg)	Number of students
40–45	2
45–50	5
50–55	8
55–60	6
60–65	6
65–70	3

Find the median weight of the students.

Source: official question paper from cbse.gov.in (PDF). See it in the full 2025 board paper, set 430/3/1.

Hints

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

Hint 1

Start by adding a cumulative frequency column to the table.

Hint 2

Find $N /2$ and locate the class whose cumulative frequency first reaches or exceeds it. That class is the median class.

Hint 3

Use Median $= l + \frac{N /2 - c f}{f} \times h$ , where $c f$ is the cumulative frequency of the class before the median class.

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.

Cumulative frequency table:
Weight (kg) $f$ $c f$
40–45 2 2
45–50 5 7
50–55 8 15
55–60 6 21
60–65 6 27
65–70 3 30
$N = \sum f = 30$
2 marks
$\frac{N}{2} = 15$ . The first $c f$ that is greater than or equal to 15 is 15, so the median class is 50–55.
For this class: $l = 50$ , $c f = 7$ (of the preceding class), $f = 8$ , $h = 5$ .
Median $= l + \frac{\frac{N}{2} - c f}{f} \times h = 50 + \frac{15 - 7}{8} \times 5$
2 marks
$= 50 + \frac{8}{8} \times 5 = 50 + 5 = 55$
The median weight of the students is 55 kg.
1 mark

Weight (kg)	$f$	$c f$
40–45	2	2
45–50	5	7
50–55	8	15
55–60	6	21
60–65	6	27
65–70	3	30

Answer: Median weight = 55 kg

Where the marks are

Correct cumulative frequency table with $N = 30$ (2 marks)
Identifies median class 50–55, writes the median formula and substitutes $l = 50$ , $c f = 7$ , $f = 8$ , $h = 5$ (2 marks)
Gets median = 55 kg (1 mark)

Revise the chapter

Chapter: Statistics (notes, formulas, where marks are lost and every past question)
Topic: Median 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 paper2025 board paper, set 430/3/1 (Basic): every question, by section.

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CBSE Class 10 Mathematics Basic 2025: question 35

Hints

Step-by-step solution

Revise the chapter

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