Jenny sits nine exams over the course of a year, which are all out of 30 marks. After she received the results of her eighth exam, her average score was 27. After the final exam, her average mark decreased by two. Work out what score Jenny got on her last exam. You must show how you got to your answer.
We’re told that Jenny’s average score was 27 after the first eight exams. And as we haven’t been told what type of average this is, we, therefore, assume that
this is the mean average. To find the mean average of a set of numbers, we add all the numbers up and then we
divide by how many there are.
In this question, we know what the mean average is — it’s 27 — and we know how many
data points they are — they’re eight. But we don’t know what the total of all the scores was. We can, however, work this out and we’ll do so by forming an equation. We’ll introduce the letter 𝑥 to represent the sum of all of Jenny’s marks for the
first eight exams. As the average was 27 and the number of results was eight, we therefore have the
equation 27 is equal to 𝑥 over eight.
To solve this equation for 𝑥, we can multiply both sides by eight to give 27
multiplied by eight is equal to 𝑥. We can work out 27 multiplied by eight using a column method. Seven multiplied by eight is 56. Two multiplied by eight is 16. And adding the five that we’ve carried, we see that 27 multiplied by eight is
216. So we know that Jenny’s total score after eight exams was 216.
We’ve been told that after the final exam, Jenny’s average mark has decreased by
two. So her new average is 25. If we now let 𝑦 equal Jenny’s score on just the ninth exam, we can form another
equation: the total across all nine papers — so that’s 𝑦 — plus the total across
the previous eight papers 216 divided by how many papers there are which is nine is
equal to the new average of 25. We can now solve this equation to find the value of 𝑦.
We begin by multiplying both sides by nine giving 𝑦 plus 216 is equal to 225. 25 multiplied by 10 is 250. So to find 25 multiplied by nine, we just subtract 25. Next, we subtract 216 from each side of the equation, giving 𝑦 is equal to nine. Remember that 𝑦 represents Jenny’s score on the ninth exam. So our answer to the question is nine marks.
Now, remember all of these papers are out of 30. And you may find it a little odd that Jenny scored a very low mark on the ninth paper
— only nine out of 30 — and her average only decreased by two. The reason for this is that Jenny’s previous high average of 27 was across a much
larger number of papers. It was across eight papers. Therefore, this one low result of nine does affect the mean by bringing it down by
two, but it doesn’t affect a huge amount.