WAEC 2022 · Paper 2 · Q13

$X$	14	16	17	18	22	24	27	28	31	33
$Y$	22	19	15	13	10	12	3	5	3	2

The table shows the corresponding values of two variables $X$ and $Y$ .

(a)
Plot a scatter diagram to represent the data.
Model answer
Plot the ten points and don't join them. They show a clear downward trend: as $X$ increases, $Y$ decreases (negative correlation).
(b)
Calculate: (i) $\bar x$ , the mean of $X$ , and $\bar y$ , the mean of $Y$ ; (ii) $\bar x_1$ , the mean of $X$ values below $\bar x$ , and $\bar y_1$ , the mean of the corresponding $Y$ values.
Separate values with commas, e.g. 3, −2
(c)
Draw the line of best fit through $(\bar x, \bar y)$ and $(\bar x_1, \bar y_1)$ .
Model answer
Rule a straight line through $(\bar x_1, \bar y_1) = (17.4, 15.8)$ and $(\bar x, \bar y) = (23, 10.4)$ , extended across the points. Its gradient is $-\frac{27}{28}$ . At $X = 20$ the line gives $Y \approx 13.3$ .
(d)
From the graph in (c), determine the: (i) relationship between $X$ and $Y$ ; (ii) value of $Y$ when $X$ is 20.

Try it on a graph

Scatter points, the two means (purple) and the line of best fit.

Worked solution (try it first)

(a)

(b)(i)

(ii)

The $X$ values below 23 are $14, 16, 17, 18, 22$ : $\bar x_1 = 17.4$ , with $\bar y_1 = \dfrac{22 + 19 + 15 + 13 + 10}{5}$
$= 15.8$ .

(c)

(d)(i)

Gradient $= \dfrac{15.8 - 10.4}{17.4 - 23}$
$= -\dfrac{27}{28}$ , so $y - 10.4 = -\dfrac{27}{28}(x - 23)$ , which gives $140y + 135x - 4561 = 0$ .

(ii)