WAEC 2008 · Paper 2 · Q13

The table shows the examination marks of 8 students in Algebra and Statistics tests.

Algebra ( $x$ )	10	24	30	35	48	59	68	70
Statistics ( $y$ )	30	47	44	71	60	89	97	74

(a)
Draw a scatter diagram for the data.
Model answer
Put Algebra ( $x$ ) on the horizontal axis and Statistics ( $y$ ) on the vertical axis, with a uniform scale on each, and plot the 8 points $(10, 30), (24, 47), \ldots, (70, 74)$ .
(b)
Find $\bar x$ , the mean of $x$ , and $\bar y$ , the mean of $y$ , and plot $(\bar x, \bar y)$ on the graph.
Separate values with commas, e.g. 3, −2
(c)
Draw a line of best fit to pass through $(\bar x, \bar y)$ .
Model answer
Draw a straight line through $(43, 64)$ that follows the trend of the points, with about as many points above it as below. A good line has a gradient near $0.94$ .
(d)(i)
From your graph, find the equation of the line.
Model answer
Read two points on your line, such as $(43, 64)$ and $(78, 97)$ , find the gradient $m$ , then use $y - 64 = m(x - 43)$ . The least-squares line is $y \approx 0.94x + 23.5$ ; a line drawn by eye will be close to this.
(d)(ii)
From your graph, estimate the Statistics mark for a student who scored 50 in Algebra.

Worked solution (try it first)

$\sum x = 10 + 24 + 30 + 35 + 48 + 59 + 68 + 70$
$= 344$ , so $\bar x = \frac{344}{8} = 43$ .
$\sum y = 30 + 47 + 44 + 71 + 60 + 89 + 97 + 74$
$= 512$ , so $\bar y = \frac{512}{8} = 64$ .
Plot $(43, 64)$ .

Draw a straight line through $(43, 64)$ that follows the trend, with the points spread evenly on both sides.

Read up from $x = 50$ to the line and across: $y \approx 0.94(50) + 23.5 \approx 71$ .
The Statistics mark is about 71.