Video: Pack 2 • Paper 2 • Question 3

Pack 2 • Paper 2 • Question 3

02:55

Video Transcript

Gabriela graphed the heights of 10 girls in her class as a function of their ages. Her graph is the shown scatter graph. a) What piece of advice could you give to Gabriella for her to improve her graph?

Well, if we look at all the points on the graph, we can see that all their 𝑦-coordinates are between about 120 and 150. They’re all rather squashed up on this scale. Her 𝑦-axis runs from 50 up to 150. But if she’d have chosen from 100 to 150, then all of those points would have been a bit more spread out and she’d been able to get more precision when analyzing the graph.

You could say something like rescale the 𝑦-axis so that it runs from 100 to 150 centimeters rather than 50 to 150 centimeters. This would make it easier to carry out more precise analysis of the points. For example, our line of best fit might go here or here or even here.

Now, there’s a difference of about five squares in where those lines of best fit cut the 𝑦-axis. And on this scale, five squares equates to 12 and a half centimeters. But if we’d used a much larger scale, then a difference of five squares would represent a much smaller difference in height in our final answer. The point representing the height and age of one of the girls is an outlier.

Part b) Describe how this girl is different from the other girls.

Now, most of the points are pretty close to this line of best fit. But this point — the outlier — lies a long way away from that trend line. Now, the equation of that line of best fit gives us a pretty good way to make predictions about the height of a girl based on their age.

If we know a girl’s age, we can use that line to make a pretty good prediction of what that height will be. And likewise, if we know the height, then we can make a pretty good prediction of what her age will be. But if we take the age of this girl and feed that into our relationship, it makes a very bad prediction about how tall she will be.

There’s a large difference between the prediction that a line makes and her actual height. We can say something like this girl is much taller for her age than the other girls in the class.

Now to get your mark for this, you do need to draw those two things together. The girl isn’t just much taller than the other girls. She’s tall for her age. If she’d have been that height and about nine and a quarter years old, then she would have followed the same pattern as the rest of the girls and wouldn’t be an outlier.

The reason that point is so far away from the line is the fact that she’s that height, but she’s only just under eight and a quarter years old.

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