WAEC 2013 · Paper 2 · Q13

Number of days ( $x$ )	10	20	30	40	50	60	70	80
Height ( $y$ m)	1.0	1.1	1.2	1.4	1.6	1.8	2.0	2.3

The table gives the relationship between the height, in metres, of a plant and the number of days it is left to grow.

(a)
Using a scale of 2 cm to 0.5 units on the $y$ -axis and 2 cm to 10 units on the $x$ -axis, draw the scatter diagram for the information.
Model answer
Plot the eight points, using 2 cm to 10 days across and 2 cm to 0.5 m up; don't join them. The points rise steadily, curving up slightly at the end.
(b)
Find $\bar x$ , the mean of $x$ , and $\bar y$ , the mean of $y$ , and plot $(\bar x, \bar y)$ on the diagram.
Separate values with commas, e.g. 3, −2
(c)
Draw the line of best fit to pass through $(\bar x, \bar y)$ and $(10, 1)$ .
Model answer
Rule a straight line through $(10, 1)$ and the mean point $(45, 1.55)$ , extending it across the graph. Its gradient is $\frac{0.55}{35} \approx 0.016$ , so the line is $y - 1 = 0.016(x - 10)$ . At 75 days it gives a height of about 2.02 m.
(d)
From the graph, find the: (i) equation of the line of best fit; (ii) height of the plant in 75 days.

Scatter points, the mean point (purple) and the line of best fit.

Worked solution (try it first)

Gradient $= \dfrac{1.55 - 1}{45 - 10}$
$= \dfrac{11}{700}$ , so $y = 1 + \dfrac{11}{700}(x - 10)$ , about $y = 0.016x + 0.84$ .