MathsCBSE Class 10 · Standard · Board exam 2023, set 30/2/1 · 5 marks · Long answer

CBSE Class 10 Mathematics Standard 2023: question 34

Set in the CBSE Class 10 board exam of 2023, paper 30/2/1, section D, question 34, for 5 marks. Try it first; the hints and our step-by-step solution are below.

Q34 · 5 marks · Long answerCompetency-basedStatistics

A student noted the number of cars passing through a spot on a road for $100$ periods each of $3$ minutes and summarised it in the table given below. Find the mean and median of the following data.

Source: official question paper from cbse.gov.in (PDF). See it in the full 2023 board paper, set 30/2/1.

Hints

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

Hint 1

Find the class marks and $f_{i} x_{i}$ for the mean, and a cumulative frequency column for the median.

Hint 2

The median class is the one whose cumulative frequency first exceeds $\frac{n}{2} = 50$ .

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.

Class $x_{i}$ $f_{i}$ $f_{i} x_{i}$ c.f.
0–10 5 7 35 7
10–20 15 14 210 21
20–30 25 13 325 34
30–40 35 12 420 46
40–50 45 20 900 66
50–60 55 11 605 77
60–70 65 15 975 92
70–80 75 8 600 100
Total 100 4070
2 marks
Mean $= \frac{\sum f _{i} x _{i}}{\sum f _{i}} = \frac{4070}{100} = 40.7$
1 mark
$\frac{n}{2} = 50$ . The c.f. just greater than 50 is 66, so the median class is 40–50.
Here $l = 40$ , $c f = 46$ , $f = 20$ , $h = 10$ .
½ mark
Median $= l + \frac{\frac{n}{2} - c f}{f} \times h = 40 + \frac{50 - 46}{20} \times 10 = 40 + 2 = 42$
1½ marks

Class	$x_{i}$	$f_{i}$	$f_{i} x_{i}$	c.f.
0–10	5	7	35	7
10–20	15	14	210	21
20–30	25	13	325	34
30–40	35	12	420	46
40–50	45	20	900	66
50–60	55	11	605	77
60–70	65	15	975	92
70–80	75	8	600	100
Total		100	4070

Answer: Mean = 40.7 cars; Median = 42 cars

Where the marks are

Correct table with class marks, $f_{i} x_{i}$ and cumulative frequencies (2 marks)
Mean = 40.7 (1 mark)
Identifies median class 40–50 (½ mark)
Median = 42 using the formula (1½ marks)

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 30/2/1 (Standard): every question, by section.

The question is transcribed from the official paper; figures are described in words. The solution, hints and chapter tag are ours. Spotted an error? Write tosupport@questionbuddy.in.

CBSE Class 10 Mathematics Standard 2023: question 34

Hints

Step-by-step solution

Revise the chapter

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