The monthly expenditure on milk in 200 families of a Housing Society is given below. Monthly Expenditure (in Rs.) 1000-1500 1500-2000 2000-2500 2500-3000 3000-3500 3500-4000 4000-4500 4500-5000 --- --- --- --- --- --- --- --- --- Number of families 24 40 33 x 30 22 16 7 Find the value of x and also find the mean expenditure.

MathsCBSE Class 10 · Standard · Sample paper, session 2024-25 · 5 marks · Long answer

CBSE Class 10 Mathematics Standard sample paper 2024-25: question 35(B)

From the official CBSE sample question paper for 2024-25, section D, question 35(B), for 5 marks. Try it first; the hints and our step-by-step solution are below.

Q35(B) · 5 marks · Long answerCompetency-basedStatistics

The monthly expenditure on milk in $200$ families of a Housing Society is given below.

Monthly Expenditure (in Rs.)	1000-1500	1500-2000	2000-2500	2500-3000	3000-3500	3500-4000	4000-4500	4500-5000
Number of families	24	40	33	$x$	30	22	16	7

Find the value of $x$ and also find the mean expenditure.

Source: official sample paper from cbseacademic.nic.in (PDF). See it in the full Sample paper 2024-25.

Hints

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

Hint 1

The frequencies must add up to 200 families.

Hint 2

After finding $x$ , use the direct method: mean $= \sum f_{i} x_{i} / \sum f_{i}$ with class marks $x_{i}$ .

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.

Expenditure (Rs.)	$f_{i}$	$x_{i}$	$f_{i} x_{i}$
1000-1500	24	1250	30000
1500-2000	40	1750	70000
2000-2500	33	2250	74250
2500-3000	$x = 28$	2750	77000
3000-3500	30	3250	97500
3500-4000	22	3750	82500
4000-4500	16	4250	68000
4500-5000	7	4750	33250
Total	200		532500

2 marks

Total number of families $= 200$ :
$24 + 40 + 33 + x + 30 + 22 + 16 + 7 = 200$
$172 + x = 200$ , so $x = 28$ .
1 mark
$\sum f_{i} x_{i} = 532500$ and $\sum f_{i} = 200$ .
Mean $= \frac{\sum f _{i} x _{i}}{\sum f _{i}} = \frac{532500}{200}$
1 mark
Mean $= 2662.5$
The mean monthly expenditure on milk is Rs. 2662.50.
1 mark

Answer: x = 28; mean expenditure = Rs. 2662.50

Where the marks are

Draws a correct table with class marks and $f_{i} x_{i}$ (2 marks)
Forms $172 + x = 200$ and gets $x = 28$ (1 mark)
Writes mean $= 532500/200$ (1 mark)
Gets mean $=$ Rs. 2662.5 (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 paperSample paper 2024-25 (Standard): every question, by section.

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CBSE Class 10 Mathematics Standard sample paper 2024-25: question 35(B)

Hints

Step-by-step solution

Revise the chapter

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