The following table gives the monthly consumption of electricity of 100 families: Monthly Consumption (in units) 130-140 140-150 150-160 160-170 170-180 180-190 190-200 --- --- --- --- --- --- --- --- Number of families 5 9 17 28 24 10 7 Find the median of the above data.

MathsCBSE Class 10 · Basic · Board exam 2023, set 430/4/1 · 5 marks · Long answer

CBSE Class 10 Mathematics Basic 2023: question 34

Set in the CBSE Class 10 board exam of 2023, paper 430/4/1, section D, question 34, for 5 marks. Try it first; the hints and our step-by-step solution are below.

Q34 · 5 marks · Long answerStatistics

The following table gives the monthly consumption of electricity of $100$ families:

Monthly Consumption (in units)	130-140	140-150	150-160	160-170	170-180	180-190	190-200
Number of families	5	9	17	28	24	10	7

Find the median of the above data.

Source: official question paper from cbse.gov.in (PDF). See it in the full 2023 board paper, set 430/4/1.

Hints

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

Hint 1

The median of grouped data needs a cumulative frequency column first.

Hint 2

The median class is the class whose cumulative frequency first goes past $N /2$ .

Hint 3

Use Median $= l + \frac{N /2 - c f}{f} \times h$ , where $c f$ belongs to 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 Families ( $f$ ) $c f$
130–140 5 5
140–150 9 14
150–160 17 31
160–170 28 59
170–180 24 83
180–190 10 93
190–200 7 100
$N = 100$
1 mark
$\frac{N}{2} = \frac{100}{2} = 50$ . The first $c f$ greater than 50 is 59, so the median class is $160$ – $170$ .
1 mark
For the median class: $l = 160$ , $h = 10$ , $f = 28$ . The $c f$ of the class before it is $31$ .
1 mark
Median $= l + (\frac{\frac{N}{2} - c f}{f}) \times h = 160 + \frac{50 - 31}{28} \times 10 = 160 + \frac{190}{28}$
1½ marks
$= 160 + 6.79 \approx 166.8$ units
½ mark

Monthly consumption	Families ( $f$ )	$c f$
130–140	5	5
140–150	9	14
150–160	17	31
160–170	28	59
170–180	24	83
180–190	10	93
190–200	7	100

Answer: Median ≈ 166.8 units

Where the marks are

Correct cumulative frequency table (1 mark)
Finds $N /2 = 50$ and identifies median class 160–170 (1 mark)
Writes $l = 160$ , $h = 10$ , $c f = 31$ , $f = 28$ (1 mark)
Substitutes correctly in the median formula (1½ marks)
Final answer 166.8 (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 paper2023 board paper, set 430/4/1 (Basic): every question, by section.

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CBSE Class 10 Mathematics Basic 2023: question 34

Hints

Step-by-step solution

Revise the chapter

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