Question

13. The table shows the corresponding values of two variables X and Y:
x: 14,16,17,18,22,24,27,28,31,33
y: 22,19,15,13,10,12,3,5,3,2
(a) Plot a scatter diagram to represent the data.
(b) Calculate: (i) x̄, the mean of x, and ȳ, the mean of y; (ii) x̄₁, the mean of x values below x̄, and ȳ₁, the mean of the corresponding y values below x̄.
(c) Draw the line of best fit through (x̄,ȳ) and (x̄₁,ȳ₁).
(d) From the graph, determine the: (i) relationship between X and Y; (ii) value of y when x is 20.

Accepted Answer

(a)/(c) See scatter diagram with line of best fit in the Diagram column.
(b)(i) x̄ = 230/10 = 23. ȳ = 104/10 = 10.4.
(ii) Values of x below x̄(23): 14,16,17,18,22 → x̄₁ = 87/5 = 17.4. Corresponding y-values: 22,19,15,13,10 → ȳ₁ = 79/5 = 15.8.
(d)(i) As X increases, Y decreases — the variables show a negative (inverse) correlation.
(ii) Using the line through (17.4,15.8) and (23,10.4), the value of y when x=20 is approximately 13.

WAEC Further Mathematics 2022 Theory — Question 13

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