Q1.
In a cricket match, can a team's median runs scored by a player be 0 but the team's total score be 407/10?
Answer
Yes, it can. The median only depends on the middle value of the sorted scores, so it says nothing about the total.
A team has 11 players, so the median is the 6th score in sorted order.
If 6 or more players score 0, that 6th score is 0 → median = 0.
Example: 0, 0, 0, 0, 0, 0, 12, 41, 96, 108, 131
Median = 6th value = 0
Runs off the bat = 0×6 + 12 + 41 + 96 + 108 + 131 = 388
Extras = 19
Team total = 388 + 19 = 407
If 6 or more players score 0, that 6th score is 0 → median = 0.
Example: 0, 0, 0, 0, 0, 0, 12, 41, 96, 108, 131
Median = 6th value = 0
Runs off the bat = 0×6 + 12 + 41 + 96 + 108 + 131 = 388
Extras = 19
Team total = 388 + 19 = 407
The book's own figure follows from this:
Average runs scored by a player = (407 − 19) ÷ 11
= 388 ÷ 11 = 35.27 runs
= 388 ÷ 11 = 35.27 runs
Why it happens: the extras (19 runs) are not credited to any batter, so they are subtracted before dividing by 11. And the median ignores how big the big scores are — six ducks are enough to fix the median at 0 no matter whether the other five players score 5 runs or 150 runs each.
Zero vs no value: a 0 is a real score and must be counted. A match a player did not play is not a value at all. So for a player with scores 57, 13, 0, 84, —, 51, 27 the average is (57 + 13 + 0 + 84 + 51 + 27) ÷ 6 = 232 ÷ 6 ≈ 38.67, dividing by 6 and not by 7. In the same way, Sita's mango tree gave 0, 0, 8, 24, 41, 16, 5, 0, 0, 0, 0, 0 mangoes — but only the summer months when mangoes are expected should be used to find a meaningful mean.