Find 'mean' and 'mode' of the following data: Class 15–20 20–25 25–30 30–35 35–40 40–45 --- --- --- --- --- --- --- Frequency 12 10 15 11 7 5

MathsCBSE Class 10 · Basic · Board exam 2025, set 430/6/1 · 5 marks · Long answer

CBSE Class 10 Mathematics Basic 2025: question 35

Set in the CBSE Class 10 board exam of 2025, paper 430/6/1, 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

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

Class	15–20	20–25	25–30	30–35	35–40	40–45
Frequency	12	10	15	11	7	5

Source: official question paper from cbse.gov.in (PDF). See it in the full 2025 board paper, set 430/6/1.

Hints

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

Hint 1

Find class marks, then use the step-deviation method with a = 27.5 and h = 5.

Hint 2

For the mode, the modal class has the highest frequency; use $l + \frac{f _{1} - f _{0}}{2 f _{1} - f _{0} - f _{2}} \times h$ .

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 $a = 27.5$ , class size $h = 5$ , $u_{i} = \frac{x _{i} - 27.5}{5}$ .
Class $x_{i}$ $f_{i}$ $u_{i}$ $f_{i} u_{i}$
15–20 17.5 12 −2 −24
20–25 22.5 10 −1 −10
25–30 27.5 15 0 0
30–35 32.5 11 1 11
35–40 37.5 7 2 14
40–45 42.5 5 3 15
Total 60 6
1½ marks
Mean $\overset{x}{ˉ} = a + h \times \frac{\sum f _{i} u _{i}}{\sum f _{i}} = 27.5 + 5 \times \frac{6}{60} = 27.5 + 0.5 = 28$ .
1½ marks
Highest frequency is 15, so the modal class is 25–30: $l = 25$ , $f_{1} = 15$ , $f_{0} = 10$ , $f_{2} = 11$ , $h = 5$ .
Mode $= l + (\frac{f _{1} - f _{0}}{2 f _{1} - f _{0} - f _{2}}) \times h = 25 + \frac{15 - 10}{30 - 10 - 11} \times 5 = 25 + \frac{25}{9}$
1½ marks
$= 25 + 2.78 = 27.78$ (approx.)
½ mark

Class	$x_{i}$	$f_{i}$	$u_{i}$	$f_{i} u_{i}$
15–20	17.5	12	−2	−24
20–25	22.5	10	−1	−10
25–30	27.5	15	0	0
30–35	32.5	11	1	11
35–40	37.5	7	2	14
40–45	42.5	5	3	15
Total		60		6

Answer: Mean = 28; Mode ≈ 27.78

Where the marks are

Correct table with $x_{i}$ , $u_{i}$ , $f_{i} u_{i}$ , $\sum f_{i} = 60$ , $\sum f_{i} u_{i} = 6$ (1½ marks)
Mean $= 27.5 + 5 \times \frac{6}{60} = 28$ (1½ marks)
Identifies modal class 25–30 and substitutes in mode formula (1½ marks)
Mode ≈ 27.78 (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 430/6/1 (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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