The table shows the ages of a group of 80 children who are members of a club. The club organised a trip which was attended by all children aged 13 or above. The parent of each child who attended the trip had to pay 70 pounds.
Part a) Estimate the total amount that was paid for the trip.
To begin, we’ll need to estimate how many children are actually aged 13 or above. Notice how we’re quite clearly not interested in the first two categories since those
are children aged four to six and six to 10. The third category is a little trickier. The age group is 10 to 15. So some of these students will be 13 or above. But how do we work out an estimate for how many children are aged 13 or above?
Well, we can see in this age group that there are children aged 11, 12, 13, 14, and
15. That’s five discrete ages. Notice how the strict inequality “𝑎 is greater than 10” tells us that there are no
children in this group aged 10. We do know though that there are 25 children aged 11, 12, 13, 14, or 15.
If we assume that the ages of the children is evenly spread within the group, we can
divide 25 by five to get an estimate for the number of children aged 11, the number
aged 12, the number aged 13, and so on. 25 divided by five is five. So we assume that there are five children for each age. There are five children aged 11, five aged 12, and so on.
And we can use this to find an estimate for the number of children aged 13 or above
in this group. We estimated that there are five children aged 13, five aged 14, and five aged
15. There are three individual ages here that we’re interested in. So if we multiply five by three, that tells us that there’s 15 children within this
group who are aged 13 or above.
There are also 23 children who are aged over 15 years old. So we add 15 and 23, and that gives us a total of 38 children who are aged 13 or
above, 38 children who will be attending the trip.
Finally, we know that each child needed to pay 70 pounds. So we’re going to multiply 38 by 70 pounds. And that gives us 2660. The total amount of money that was paid for the trip is 2660 pounds.
Part b) Give a reason why your estimate may not be very accurate.
Remember, we made an assumption, and that was that the ages of the children in the
group 10 to 15 was evenly distributed. What this means is we don’t know the exact number of children who are aged 13 and
above. It could be more or it could be less. We can only make an estimate based on the assumption that the ages are evenly