MathsCBSE Class 10 · Standard · Board exam 2025, set 30/6/1 · 5 marks · Long answer

CBSE Class 10 Mathematics Standard 2025: question 35

Set in the CBSE Class 10 board exam of 2025, paper 30/6/1, 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

Following distribution shows the marks of 230 students in a particular subject. If the median marks are 46, then find the values of x and y.

Marks	Number of Students
10 – 20	12
20 – 30	30
30 – 40	$x$
40 – 50	65
50 – 60	$y$
60 – 70	25
70 – 80	18

Source: official question paper from cbse.gov.in (PDF). See it in the full 2025 board paper, set 30/6/1.

Hints

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

Hint 1

Make a cumulative frequency column and use the total of 230 students to get one equation in $x$ and $y$ .

Hint 2

The median 46 tells you the median class. Use $l + \frac{n /2 - c f}{f} \times h$ with $c f = 42 + x$ .

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:
Marks $f$ cf
10 – 20 12 12
20 – 30 30 42
30 – 40 $x$ $42 + x$
40 – 50 65 $107 + x$
50 – 60 $y$ $107 + x + y$
60 – 70 25 $132 + x + y$
70 – 80 18 $150 + x + y$
1 mark
Total frequency is 230, so $150 + x + y = 230 \Rightarrow x + y = 80$ .
1 mark
The median is 46, which lies in 40 – 50, so the median class is 40 – 50. Here $l = 40$ , $\frac{n}{2} = 115$ , $c f = 42 + x$ , $f = 65$ , $h = 10$ .
½ mark
Median $= l + (\frac{\frac{n}{2} - c f}{f}) \times h$ , so $46 = 40 + \frac{115 - ( 42 + x )}{65} \times 10$ .
1 mark
$6 = \frac{( 73 - x ) \times 10}{65} \Rightarrow 73 - x = 39 \Rightarrow x = 34$ .
1 mark
From $x + y = 80$ : $y = 80 - 34 = 46$ .
½ mark

Marks	$f$	cf
10 – 20	12	12
20 – 30	30	42
30 – 40	$x$	$42 + x$
40 – 50	65	$107 + x$
50 – 60	$y$	$107 + x + y$
60 – 70	25	$132 + x + y$
70 – 80	18	$150 + x + y$

Answer: x = 34, y = 46

Where the marks are

Correct cumulative frequency table (1 mark)
Uses total 230 to get $x + y = 80$ (1 mark)
Identifies median class 40 – 50 (½ mark)
Substitutes correctly in the median formula (1 mark)
Obtains $x = 34$ (1 mark)
Obtains $y = 46$ (½ 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 30/6/1 (Standard): every question, by section.

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CBSE Class 10 Mathematics Standard 2025: question 35

Hints

Step-by-step solution

Revise the chapter

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