In a test, the marks obtained by 100 students (out of 50) are given below: Marks obtained 0 – 10 10 – 20 20 – 30 30 – 40 40 – 50 --- --- --- --- --- --- Number of students 12 23 34 25 6 Find the mean marks of the students.

MathsCBSE Class 10 · Standard · Board exam 2024, set 30/2/1 · 3 marks · Short answer

CBSE Class 10 Mathematics Standard 2024: question 30

Set in the CBSE Class 10 board exam of 2024, paper 30/2/1, section C, question 30, for 3 marks. Try it first; the hints and our step-by-step solution are below.

Q30 · 3 marks · Short answerStatistics

In a test, the marks obtained by 100 students (out of 50) are given below:

Marks obtained	0 – 10	10 – 20	20 – 30	30 – 40	40 – 50
Number of students	12	23	34	25	6

Find the mean marks of the students.

Source: official question paper from cbse.gov.in (PDF). See it in the full 2024 board paper, set 30/2/1.

Hints

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

Hint 1

Find the class mark (mid-point) of each class.

Hint 2

Multiply each class mark by its frequency and add; divide by the total frequency.

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.

Table with class marks $x_{i}$ and $f_{i} x_{i}$ :
Marks $f_{i}$ $x_{i}$ $f_{i} x_{i}$
0–10 12 5 60
10–20 23 15 345
20–30 34 25 850
30–40 25 35 875
40–50 6 45 270
Total 100 2400
1½ marks
Mean $\overset{x}{ˉ} = \frac{\sum f _{i} x _{i}}{\sum f _{i}} = \frac{2400}{100}$
1 mark
$= 24$ marks
½ mark

Marks	$f_{i}$	$x_{i}$	$f_{i} x_{i}$
0–10	12	5	60
10–20	23	15	345
20–30	34	25	850
30–40	25	35	875
40–50	6	45	270
Total	100		2400

Answer: Mean marks = 24

Where the marks are

Correct table with $x_{i}$ , $f_{i} x_{i}$ , $\sum f_{i} = 100$ , $\sum f_{i} x_{i} = 2400$ (1½ marks)
Uses mean formula $\sum f_{i} x_{i} / \sum f_{i}$ (1 mark)
Mean = 24 (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 paper2024 board paper, set 30/2/1 (Standard): every question, by section.

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CBSE Class 10 Mathematics Standard 2024: question 30

Hints

Step-by-step solution

Revise the chapter

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