# Video: Pack 1 • Paper 3 • Question 4

Pack 1 • Paper 3 • Question 4

02:43

### Video Transcript

The time-series graph shows data collected from a small library. The library recorded the number of books borrowed over a period of seven weeks. The head librarian would like to achieve a mean value of 137 books borrowed per week. Did the library achieve the head librarian’s target over the period of seven weeks shown on the graph? You must show your working out.

So in order to actually solve this problem and find out the mean books borrowed, what we can actually say is that the mean books borrowed is equal to the total number of books borrowed divided by the number of weeks that they were borrowed over.

Okay, so let’s try and find out what these are. Well, I can start with the easiest. And that’s the number of weeks, cause we know that actually the books were borrowed over a period of seven weeks. It tells us that in the question.

Okay, so we know that’s going to be seven. So now let’s work out the total books borrowed. So before we can actually read off the graph and see how many books were borrowed each week, we need to actually look at the scale just to make sure we get this right. So we can see that five squares is equal to 10. So therefore, one square is gonna be equal to two books.

Okay, brilliant! We can just use this now to actually find out what the values of each week are. So we can see that week one, there gonna be 98 books. Week two is gonna be 142 books. Okay, that’s because we can see that it’s just one square above 140. Week three is 122 books, week four 190 books, week five 94 books, week six 132, and finally week seven 146 books.

Okay, great! So now let’s use this to find the total number of books borrowed. So therefore, the total books gonna be equal to 98 plus 142 plus 122 plus 190 plus 94 plus 132 plus 146, which gives us a total number of books of 924.

Okay, fab! We now have both bits of information we need to find out the mean. So let’s actually substitute these in and find out the mean number of books borrowed. So therefore, we could say that the mean number of books borrowed is equal to 924, which was our total number of books borrowed divided by seven, because that was our number of weeks, which is equal to 132 books.

So now as we found the mean to be 132, we look back at the question. And we can see, well, what was the head librarian’s target? And that target was a mean value of 137 books. So therefore, we can say no, the library did not meet the target, as 132 is less than 137.