Several students compared how many emails they had sent during the previous week.
| Number of Emails Sent | Number of Students |
|---|---|
| \(0\) | \(12\) |
| \(1\) | \(19\) |
| \(2\) | \(11\) |
| \(3\) | \(8\) |
| \(4\) | \(14\) |
| \(5\) | \(2\) |
| \(6\) | \(15\) |
How many students sent fewer than \(2\) emails?
How many students sent more than \(4\) emails?
Separate the students into two groups so that all the students in one group sent more emails than all the students in the other group, and the number of students in each group are as close as possible.
We can use the table information to determine the answers.
The numbers \(0\) and \(1\) are less than \(2\). So the total number of students who sent fewer than \(2\) emails is \(12 + 19 = 31\).
The numbers \(5\) and \(6\) are more than \(4\). So the total number of students who sent more than \(4\) emails is \(2 + 15 = 17\).
The total number of students is \(12+19+11+8+14+2+15=81\). If the number of students in each group are as close as possible, then one group would have \(40\) students and the other would have \(41\). This is our target.
We notice that the number of students who sent fewer than \(3\) emails is \(12+19+11=42\). This is quite close to \(41\). In fact, it is as close as we can get to \(41\) because the number of students who sent \(3\) emails is \(8\) and the number of students who sent \(2\) emails is \(11\), so adding \(8\) or subtracting \(11\) from \(42\) would take us further away from \(41\). Thus, one group contains the \(42\) students who sent fewer than \(3\) emails and the other group contains the \(81-42=39\) students who sent \(3\) or more emails.