The median of the following data is 50 and sum of all frequencies is 90 : Class : 20 – 30 30 – 40 40 – 50 50 – 60 60 – 70 70 – 80 80 – 90 --- --- --- --- --- --- --- --- Frequency : p 15 25 20 q 8 10 Find the values of p and q.

MathsCBSE Class 10 · Standard · Board exam 2026, set 30/4/1 · 5 marks · Long answer

CBSE Class 10 Mathematics Standard 2026: question 35(a)

Set in the CBSE Class 10 board exam of 2026, paper 30/4/1, section D, question 35(a), for 5 marks. Try it first; the hints and our step-by-step solution are below.

Q35(a) · 5 marks · Long answerStatistics

The median of the following data is 50 and sum of all frequencies is 90 :

Class :	20 – 30	30 – 40	40 – 50	50 – 60	60 – 70	70 – 80	80 – 90
Frequency :	p	15	25	20	q	8	10

Find the values of p and q.

Source: official question paper from cbse.gov.in (PDF). See it in the full 2026 board paper, set 30/4/1.

Hints

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

Hint 1

Make a cumulative frequency column; the entries will contain p and q.

Hint 2

Since the median is 50, the median class must start at 50. Use Median = l + ((N/2 − cf)/f) × h.

Hint 3

For q, add all the frequencies and set the total equal to 90.

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:
Class $f$ c.f.
20–30 $p$ $p$
30–40 15 $p + 15$
40–50 25 $p + 40$
50–60 20 $p + 60$
60–70 $q$ $p + q + 60$
70–80 8 $p + q + 68$
80–90 10 $p + q + 78$
1½ marks
Median = 50, which lies in the class 50–60. So the median class is 50–60, with $l = 50$ , $h = 10$ , $f = 20$ , $c f = p + 40$ and $\frac{N}{2} = \frac{90}{2} = 45$ .
½ mark
Median $= l + (\frac{\frac{N}{2} - c f}{f}) \times h$
$\Rightarrow 50 = 50 + \frac{45 - ( p + 40 )}{20} \times 10$
1 mark
$\Rightarrow \frac{5 - p}{2} = 0 \Rightarrow p = 5$
½ mark
The sum of all frequencies is 90, so $p + q + 78 = 90$ .
$\Rightarrow 5 + q = 12$
1 mark
$∴ q = 7$
Hence $p = 5$ and $q = 7$ .
½ mark

Class	$f$	c.f.
20–30	$p$	$p$
30–40	15	$p + 15$
40–50	25	$p + 40$
50–60	20	$p + 60$
60–70	$q$	$p + q + 60$
70–80	8	$p + q + 68$
80–90	10	$p + q + 78$

Answer: p = 5, q = 7

Where the marks are

Correct cumulative frequency table in terms of p and q (1½ marks)
Identifies median class 50–60 (½ mark)
Substitutes correctly in the median formula (1 mark)
Gets p = 5 (½ mark)
Uses total frequency: p + q + 78 = 90 (1 mark)
Gets q = 7 (½ mark)

Revise the chapter

Chapter: Statistics (notes, formulas, where marks are lost and every past question)

Practise this chapterBoard-style questions from Statistics, one at a time, marked against the answer key and marking points.Back to the full paper2026 board paper, set 30/4/1 (Standard): every question, by section.

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CBSE Class 10 Mathematics Standard 2026: question 35(a)

Hints

Step-by-step solution

Revise the chapter

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