The following frequency distribution table gives the monthly consumption of electricity of 70 consumers of a locality. Find the median of the data. Monthly consumption (in units) Number of consumers --- --- 65 – 85 7 85 – 105 8 105 – 125 7 125 – 145 20 145 – 165 14 165 – 185 9 185 – 205 5

MathsCBSE Class 10 · Basic · Board exam 2024, set 430/5/1 · 5 marks · Long answer

CBSE Class 10 Mathematics Basic 2024: question 35

Set in the CBSE Class 10 board exam of 2024, paper 430/5/1, 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

The following frequency distribution table gives the monthly consumption of electricity of 70 consumers of a locality. Find the median of the data.

Monthly consumption (in units)	Number of consumers
65 – 85	7
85 – 105	8
105 – 125	7
125 – 145	20
145 – 165	14
165 – 185	9
185 – 205	5

Source: official question paper from cbse.gov.in (PDF). See it in the full 2024 board paper, set 430/5/1.

Hints

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

Hint 1

Start by adding a cumulative frequency column to the table.

Hint 2

Find $N /2$ ; the median class is the class whose cumulative frequency first exceeds it.

Hint 3

Use Median $= l + \frac{N /2 - c f}{f} \times h$ , where $c f$ is the cumulative frequency of the class just before the median class.

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.

Cumulative frequency table:
Monthly consumption (units) No. of consumers $f$ $c f$
65 – 85 7 7
85 – 105 8 15
105 – 125 7 22
125 – 145 20 42
145 – 165 14 56
165 – 185 9 65
185 – 205 5 70
2 marks
$N = 70$ , so $\frac{N}{2} = 35$ . The first $c f$ greater than 35 is 42, so the median class is 125 – 145. Hence $l = 125$ , $c f = 22$ , $f = 20$ and $h = 20$ .
1 mark
Median $= l + (\frac{\frac{N}{2} - c f}{f}) \times h = 125 + \frac{35 - 22}{20} \times 20$
1½ marks
$= 125 + 13 = 138$ . The median monthly consumption is 138 units.
½ mark

Monthly consumption (units)	No. of consumers $f$	$c f$
65 – 85	7	7
85 – 105	8	15
105 – 125	7	22
125 – 145	20	42
145 – 165	14	56
165 – 185	9	65
185 – 205	5	70

Answer: Median = 138 units

Where the marks are

Correct cumulative frequency column (2 marks)
Identifies $N /2 = 35$ , median class 125–145 and $l, c f, f, h$ (1 mark)
Correct substitution in the median formula (1½ marks)
Median = 138 (½ mark)

Revise the chapter

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

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

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CBSE Class 10 Mathematics Basic 2024: question 35

Hints

Step-by-step solution

Revise the chapter

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