Q5. Find the range of 36, 72, 46, 42, 60, 45, 53, 46, 51, 49 (NCERT Exercise 13.1, Q4 data).
72 − 36 = 36.
Q6. Find the range of: xi = 5, 7, 9, 10, 12, 15 with frequencies 8, 6, 2, 2, 2, 6 (NCERT Exercise 13.1, Q7 data).
15 − 5 = 10.
Q7. Find the range of the daily incomes grouped as ₹0–100, 100–200, …, 700–800 (NCERT Exercise 13.1, Q9 data).
₹800 − ₹0 = ₹800.
Q8. Find the coefficient of range for batsman A (scores from 0 to 117), and compare it with batsman B’s.
(117 − 0)/(117 + 0) = 1 for A, against 14/106 ≈ 0.13 for B: A’s scores are much more spread out relative to their size. For data that are never negative, 1 is the largest possible value, reached when the minimum is 0 and the maximum is positive.
Q9. The range of the marks in a test is 40. Each mark is converted to a percentage of the maximum 80 by multiplying by 5/4. Find the new range.
5/4 × 40 = 50.
Q10. Two data sets have the same range 20. Must they have the same spread? Give an example.
No. 0, 10, 10, 10, 20 and 0, 0, 0, 20, 20 both have range 20, but the first is bunched in the middle and the second sits at the ends.
Q11. The values 2, 5, a, 9 have range 10, and a is the smallest value. Find a.
The largest value is 9, so 9 − a = 10 and a = −1.
Q12. Find the range of the first 10 multiples of 3 (NCERT Exercise 13.2, Q3 data).
30 − 3 = 27.