Video: AQA GCSE Mathematics Higher Tier Pack 5 • Paper 2 • Question 13

Here is some information about the time spent in a week reading fiction books by students in a school. Shortest time: 15 minutes, longest time: 8 hours, lower quartile: 1 hour 15 minutes, interquartile range: 3 hours 30 minutes, median time: 3 hours. Draw a box plot to show this information.

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Video Transcript

Here is some information about the time spent in a week reading fiction books by students in a school. Shortest time: 15 minutes, longest time: eight hours, lower quartile: one hour 15 minutes, interquartile range: three hours 30 minutes, median time: three hours. Draw a box plot to show this information.

A box plot — sometimes called a box and whisker plot — is a diagram that can be used to display information about the range, the median, and the quartiles of a dataset. We can read several pieces of information from the box plot. The smallest and largest values are represented by the end of each whisker. The box itself represents the middle 50 percent of the data. The left-hand side of the box tells us the lower quartile. Remember that’s just one-quarter of the way through the dataset. And the right-hand side of the box tells us the upper quartile. That’s three-quarters of the way through the dataset. The line inside the box is the median average of the data.

Let’s use this information to draw a box plot representing our dataset. Before we do though, let’s double-check the scale. We can see that four small squares represent one hour. We can work out the value of one small square by dividing by four. When we do though, it’s sensible to work out the time represented by one small square in minutes. There are 60 minutes in one hour. And when we divide this by four, we can halve it and halve it again to do that quickly, we get 15 minutes. One small square on our scale represents 15 minutes.

We can now plot the shortest and longest time. The shortest time is 15 minutes. That’s one small square above zero. The longest time is eight hours. That’s here. The lower quartile is the left-hand side of the box and it’s one hour 15 minutes. That’s one small square above one. We don’t actually know the value of the upper quartile. Instead, we’re told that the interquartile range is three hours and 30 minutes. Remember the interquartile range — I’ve written IQR — is the difference between the upper quartile and the lower quartile.

If we rearrange this formula by adding the lower quartile to both sides, we can see that to work out the upper quartile, we need to add the interquartile range to the lower quartile. That’s three hours 30 minutes plus one hour 15 minutes. Three hours plus one hour is four hours. And 30 minutes plus 15 minutes is 45 minutes. So the upper quartile is four hours 45 minutes. That’s one square below the number five.

At this point, it is important to remember that we can’t easily use our calculator to work this out. We don’t want to add 3.3 and 1.15. Time is a tricky one and we’re best to avoid using the calculator for this type of problem wherever possible. Finally, let’s add the median in at three. Remember we need to join the edges of our box together as shown. And finally, it wouldn’t be complete without adding in the whiskers.

And we’re done. This is the box plot representing the data about the time spent in a week reading fiction books by students in a school.

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