Find 'mean' and 'mode' of the following data: Class 10-25 25-40 40-55 55-70 70-85 85-100 --- --- --- --- --- --- --- Number of Students 12 10 15 13 8 12

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

CBSE Class 10 Mathematics Basic 2025: question 35(a)

Set in the CBSE Class 10 board exam of 2025, paper 430/5/1, 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

Find 'mean' and 'mode' of the following data:

Class	10-25	25-40	40-55	55-70	70-85	85-100
Number of Students	12	10	15	13	8	12

Source: official question paper from cbse.gov.in (PDF). See it in the full 2025 board paper, set 430/5/1.

Hints

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

Hint 1

Find class marks and use the step-deviation method with assumed mean 47.5 and $h = 15$ .

Hint 2

For the mode, locate the class with the highest frequency and note the frequencies of the classes just before and after it.

Hint 3

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

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.

Take assumed mean $a = 47.5$ , class size $h = 15$ , $u_{i} = \frac{x _{i} - 47.5}{15}$ .
Class $x_{i}$ $f_{i}$ $u_{i}$ $f_{i} u_{i}$
10–25 17.5 12 −2 −24
25–40 32.5 10 −1 −10
40–55 47.5 15 0 0
55–70 62.5 13 1 13
70–85 77.5 8 2 16
85–100 92.5 12 3 36
Total 70 31
1½ marks
Mean $= a + h \times \frac{\sum f _{i} u _{i}}{\sum f _{i}} = 47.5 + 15 \times \frac{31}{70} = 47.5 + 6.64 = 54.14$
1½ marks
Highest frequency is 15, so modal class is 40–55: $l = 40$ , $f_{1} = 15$ , $f_{0} = 10$ , $f_{2} = 13$ , $h = 15$ .
Mode $= l + \frac{f _{1} - f _{0}}{2 f _{1} - f _{0} - f _{2}} \times h = 40 + \frac{15 - 10}{30 - 10 - 13} \times 15$
1½ marks
$= 40 + \frac{5}{7} \times 15 = 40 + 10.71 = 50.71$
½ mark

Class	$x_{i}$	$f_{i}$	$u_{i}$	$f_{i} u_{i}$
10–25	17.5	12	−2	−24
25–40	32.5	10	−1	−10
40–55	47.5	15	0	0
55–70	62.5	13	1	13
70–85	77.5	8	2	16
85–100	92.5	12	3	36
Total		70		31

Answer: Mean ≈ 54.14; Mode ≈ 50.71

Where the marks are

Correct table with $x_{i}$ , $u_{i}$ , $f_{i} u_{i}$ and totals 70, 31 (1½ marks)
Mean $= 47.5 + 15 \times \frac{31}{70} = 54.14$ (1½ marks)
Identifies modal class 40–55 and substitutes in mode formula (1½ marks)
Mode = 50.71 (½ mark)

Revise the chapter

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

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 430/5/1 (Basic): every question, by section.

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CBSE Class 10 Mathematics Basic 2025: question 35(a)

Hints

Step-by-step solution

Revise the chapter

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