| I. Average = [Sum of observations / Number of observations] | |
| II. Suppose a man covers a certain distance at x kmph and an equal distance at y kmph. Then, the average speed during the whole journey is [2xy / x + y] kmph. |
| 1. | Find the average of all prime numbers between 30 and 50. |
|---|---|
| Sol. There are five prime numbers between 30 and 50. They are 31, 37, 41, 43 and 47. ∴ Required average = [(31 + 37 + 41 + 43 + 47) / 5] = 199/5 = 39.8. |
|
| 2. | Find the average of first 40 natural numbers. |
| Sol. Sum of first n natural numbers = 40 * 41 / 2 = 820. ∴ Required average = 820 / 40 = 20.5. |
|
| 3. | Find the average of first 20 multiples of 7. |
| Sol. Required average = 7(1+2+3 ... + 20) / 20 = [7 * 20 * 21 / 20 * 2] = [147 / 2] = 73.5. | |
| 4. | The average weight of 10 oarsmen in a boat is increased by 1.8 kg when one of the crew, who weighs 53kg is replaced by a new man. find the weight of the new man. |
| Sol. Total weight increased = (1.8 * 10)kg = 18kg. ∴ Weight of the new man = (53 + 18)kg = 71kg. |
|
| 5. | A batsman makes a score of 87 runs in the 17th inning and thus increases his average by 3. find his average after 17th inning. |
| Sol. Let the average after 17th inning = x. Then, average after 16th inning = (x - 3) ∴ 16(x - 3) + 87 = 17x or x = (87 - 48) = 39. |
| 10. | The average salary of all the workers in a workshop is Rs. 8000. The average salary of 7 technicians is Rs. 12000 and the average salary of the rest is Rs. 6000. The total number of workers in the workshop is |
|---|---|
|
| 11. | Kamal obtained 76, 65, 82, 67 and 85 marks(out of 100) in English, Mathematics, Physics, Chemistry and Biology. What are his average marks? |
|---|---|
|
| 12. | In the first 10 overs of a cricket game, the run rate was only 3.2. What should be the run rate in the remaining 40 0vers to reach the target of 282 runs? |
|---|---|
|