Find mean of the following data: Class 0–15 15–30 30–45 45–60 60–75 75–90 --- --- --- --- --- --- --- Frequency 12 15 11 20 16 6

MathsCBSE Class 10 · Basic · Board exam 2023, set 430/5/1 · 3 marks · Short answer

CBSE Class 10 Mathematics Basic 2023: question 28

Set in the CBSE Class 10 board exam of 2023, paper 430/5/1, section C, question 28, for 3 marks. Try it first; the hints and our step-by-step solution are below.

Q28 · 3 marks · Short answerStatistics

Find mean of the following data:

Class	0–15	15–30	30–45	45–60	60–75	75–90
Frequency	12	15	11	20	16	6

Source: official question paper from cbse.gov.in (PDF). See it in the full 2023 board paper, set 430/5/1.

Hints

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

Hint 1

Find the class marks (mid-points) of each class first.

Hint 2

Choose a middle class mark as assumed mean and use $u = \frac{x - a}{h}$ with h = 15.

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 $a = 37.5$ , class size $h = 15$ , $u_{i} = \frac{x _{i} - 37.5}{15}$ .
Class $x_{i}$ $f_{i}$ $u_{i}$ $f_{i} u_{i}$
0–15 7.5 12 −2 −24
15–30 22.5 15 −1 −15
30–45 37.5 11 0 0
45–60 52.5 20 1 20
60–75 67.5 16 2 32
75–90 82.5 6 3 18
Total 80 31
2 marks
Mean $= a + \frac{\sum f _{i} u _{i}}{\sum f _{i}} \times h = 37.5 + \frac{31}{80} \times 15 = 37.5 + 5.8125 = 43.31$ (approx. 43.3)
1 mark

Class	$x_{i}$	$f_{i}$	$u_{i}$	$f_{i} u_{i}$
0–15	7.5	12	−2	−24
15–30	22.5	15	−1	−15
30–45	37.5	11	0	0
45–60	52.5	20	1	20
60–75	67.5	16	2	32
75–90	82.5	6	3	18
Total		80		31

Answer: Mean ≈ 43.31

Where the marks are

Correct table with class marks, $u_{i}$ , $\sum f_{i} = 80$ and $\sum f_{i} u_{i} = 31$ (2 marks)
Applies step-deviation formula to get mean ≈ 43.3 (1 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 paper2023 board paper, set 430/5/1 (Basic): every question, by section.

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CBSE Class 10 Mathematics Basic 2023: question 28

Hints

Step-by-step solution

Revise the chapter

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