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Class 8 Maths: Tales by Dots and Lines, 8 practice questions with answers

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These are 8 practice questions on Chapter 5, Tales by Dots and Lines, of the new NCERT Class 8 Maths textbook, Ganita Prakash, Part 2. Each has a worked answer and the textbook page it comes from. They cover who gives marbles when they are shared equally, whether two more tests can lift a mean, two lists with the same mean and median but different spreads, mean against median with one big score, three teams and two classes put together, when a median shoe size changes as children join, and a seedling's line graph. Try each one on paper before you open the answer.

These questions are our own, drafted with AI help. Every answer was re-worked by a test script and each question was compared with the chapter's examples, activities and exercises, but no practising teacher has reviewed them yet. If you find a mistake, please tell us.

What the chapter says you need

Facts from the NCERT textbook (Ganita Prakash, Grade 8, Part 2, Chapter 5, printed pages 103 to 133):

The mean and changing data

Question 1. Five friends have 3, 5, 6, 10 and 16 marbles, 40 in all, and they share them out so that each ends up with 8. Who must give marbles away, and what is the smallest number of marbles that must change hands?

Answer: the friends with 10 and 16 give marbles; 10 marbles must move. Only the friends who have more than 8 need to give any away: the one with 10 gives 2 and the one with 16 gives 8, so 10 marbles change hands. They exactly fill the shortfalls of the friends with 3, 5 and 6, who need 5, 3 and 2 more (also 10). The amount above the share always equals the amount below it, which is why the share, the mean, works as a balance point. (The mean as a balance point, pages 103 and 104.)

Question 2. Meena's mean mark in 4 tests is 72, and every test is out of 100. Can 2 more tests lift her mean over all 6 tests to 85? Explain.

Answer: no; the best she can reach is about 81.3. Her 4 marks add up to 4 × 72 = 288. Even with 100 in both new tests, the 6 marks add up to 288 + 200 = 488, and 488 ÷ 6 is about 81.3. A mean of 85 over 6 tests needs a total of 6 × 85 = 510, which is 22 more than is possible. (The mean and the total, page 109.)

Question 3. List A is 8, 9, 10, 11, 12 and list B is 0, 5, 10, 15, 20. Both have mean 10 and median 10. Which two numbers would you quote to show how differently the two lists are spread out, and why do the mean and median not show it?

Answer: the smallest and the largest value of each list: 8 and 12 for A, 0 and 20 for B. The mean and the median describe the centre of the data, and here both centres are 10. How far the values reach on either side is shown by the minimum and maximum: list A stays between 8 and 12, while list B stretches from 0 to 20. (The gap between them, 4 against 20, is called the range; that word is from outside this chapter.) (Describing data with its minimum, maximum, mean and median, page 116.)

Groups and the median

Question 4. A batter's scores in seven innings were 45, 12, 150, 34, 28, 51 and 40, so the mean is about 51.4 and the median is 40. Which of the two better describes a typical innings for this batter, and why?

Answer: the median. The total is 360, so the mean is 360 ÷ 7, about 51.4; in order the scores are 12, 28, 34, 40, 45, 51, 150, so the median is 40. Six of the seven innings are 51 or less, but the single score of 150 pulls the mean up to about 51. The median depends only on the middle value, so the one big score does not move it, and 40 is closer to most of the innings. (The mean and the median, pages 103 to 109.)

Question 5. Three teams go on a trip: 10 children with a mean weight of 30 kg, 15 children with a mean of 34 kg and 25 children with a mean of 38 kg. What is the mean weight of all 50 children?

Answer: 35.2 kg. Turn each mean back into a total: 10 × 30 = 300 kg, 15 × 34 = 510 kg and 25 × 38 = 950 kg, so all 50 children weigh 300 + 510 + 950 = 1,760 kg, and 1,760 ÷ 50 = 35.2 kg. The plain average of 30, 34 and 38 is 34, but the biggest team has the highest mean, so it counts more and pulls the overall mean up. (Counting each value as often as it occurs, page 110.)

Question 6. Class A has 20 students with a mean mark of 60. Class B has 30 students with a mean mark of 70. What is the mean mark of all 50 students together? Why is it not (60 + 70) ÷ 2 = 65?

Answer: 66. First turn each mean back into a total. Class A's marks add up to 20 × 60 = 1,200 and class B's to 30 × 70 = 2,100, so all 50 marks add up to 3,300, and 3,300 ÷ 50 = 66. The plain average of 60 and 70 would be right only if both classes had the same number of students (25 and 25 would give 65). Class B has more students, so its mean of 70 counts more, and the overall mean is pulled closer to 70. (Counting each value as often as it occurs, page 110.)

Question 7. In a class of 20 children, 4 wear shoe size 3, 7 wear size 4, 6 wear size 5 and 3 wear size 6. How many more children who wear size 6 must join before the median shoe size becomes size 5?

Answer: 3. In order, sizes 3 fill places 1 to 4, sizes 4 places 5 to 11 and sizes 5 places 12 to 17. With 20 children the median is the average of the 10th and 11th, both size 4. With 1 more (21 children) the median is the 11th: size 4. With 2 more (22) it is the average of the 11th and 12th, (4 + 5) ÷ 2 = 4.5. With 3 more (23) it is the 12th, size 5. (Mean and median with frequencies, page 110.)

Line graphs

Question 8. A seedling's height was measured at the end of each week for six weeks: 5, 7, 12, 15, 21 and 23 cm. (a) Between which two weeks does a line graph of this data have its steepest segment? (b) In which weeks did it grow the least?

Answer: (a) weeks 4 and 5; (b) weeks 1 to 2 and weeks 5 to 6. (a) The week-to-week changes are +2, +5, +3, +6 and +2 cm. The biggest rise, 6 cm from week 4 to week 5, gives the steepest segment: the steeper the line, the greater the increase. (b) The smallest rises, 2 cm, are from week 1 to 2 and from week 5 to 6, where the line is flattest. (Reading a line graph, pages 116 to 120.)

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Sources

All opened and read on 30 October 2026. Page numbers are the printed page numbers of the textbook; printed page = PDF page + 102.

The rules are from the textbook pages above. The questions, worked answers and checks are our own, and every number was re-computed by script. This guide is general information; follow your teacher and the textbook.