Important Questions Class 8 Maths Ganita Prakash – II Chapter 5 Tales by Dots and Lines

Short Questions

Q1. Find the mean of 5, 10, 15.

Step 1: Add all numbers
5 + 10 + 15 = 30

Step 2: Count numbers = 3

Step 3: Mean = Total ÷ Number
= 30 ÷ 3 = 10

Q2. Find the median of 2, 4, 6, 8, 10.

Step 1: Arrange numbers (already arranged)
2, 4, 6, 8, 10

Step 2: Count numbers = 5 (odd)

Step 3: Middle number = 6

Q3. Find mean of first 4 natural numbers.

Step 1: Numbers = 1, 2, 3, 4

Step 2: Add → 1 + 2 + 3 + 4 = 10

Step 3: Mean = 10 ÷ 4 = 2.5

Q4. Mean of 2 numbers is 7. Find sum.

Step 1: Formula → Mean = Sum ÷ Number

Step 2: Sum = Mean × Number
= 7 × 2 = 14

Q5. Find median of 3, 5, 7, 9.

Step 1: Arrange → 3, 5, 7, 9

Step 2: Count = 4 (even)

Step 3: Median = (middle two numbers ÷ 2)
= (5 + 7) ÷ 2 = 12 ÷ 2 = 6

Q6. Find mean of 8, 12, 16, 20.

Step 1: Add → 8 + 12 + 16 + 20 = 56

Step 2: Count = 4

Step 3: Mean = 56 ÷ 4 = 14

Q7. What happens if a number greater than mean is added?

Step 1: Mean is the balance point

Step 2: Larger value increases total

Step 3: So meanincreases

Q8. Find x if mean of 4, 6, x is 8.

Step 1: Formula → Mean = (Sum ÷ Number)

Step 2: (4 + 6 + x) ÷ 3 = 8

Step 3: Multiply both sides by 3
10 + x = 24

Step 4: x = 24 − 10 = 14

Q9. Find mean of 3, 3, 3, 3.

Step 1: Add → 3 + 3 + 3 + 3 = 12

Step 2: Count = 4

Step 3: Mean = 12 ÷ 4 = 3

Q10. Find median of 1, 3, 5, 7, 9, 11.

Step 1: Arrange → 1, 3, 5, 7, 9, 11

Step 2: Count = 6 (even)

Step 3: Median = (5 + 7) ÷ 2 = 12 ÷ 2 = 6

Long Questions

Q1. Find mean of first 10 natural numbers.

Step 1: Numbers = 1 to 10

Step 2: Use formula → Sum = n(n + 1) ÷ 2
= 10 × 11 ÷ 2 = 55

Step 3: Mean = 55 ÷ 10 = 5.5

Q2. Mean of 5 numbers is 20. One removed, new mean = 18. Find removed number.

Step 1: Total sum = 20 × 5 = 100

Step 2: New sum = 18 × 4 = 72

Step 3: Removed number = 100 − 72 = 28

Q3. Find median of 12, 15, 18, 20, 22, 25, 30.

Step 1: Arrange (already sorted)

Step 2: Count = 7 (odd)

Step 3: Middle value = 4th value = 20

Q4. Mean of 8 numbers is 15. Each increases by 5. Find new mean.

Step 1: When all values increase equally

Step 2: Mean also increases by same number

Step 3: New mean = 15 + 5 = 20

Q5. Mean of 6 numbers is 12. One number is 18. Find mean of remaining.

Step 1: Total sum = 12 × 6 = 72

Step 2: Remaining sum = 72 − 18 = 54

Step 3: Remaining numbers = 5

Step 4: New mean = 54 ÷ 5 = 10.8