Theory question 113
StatisticsThe table gives the relationship between the height, in meters, of a plant and the number of days it is left to grow.
Number of days (x): 10, 20, 30, 40, 50, 60, 70, 80
Height (y): 1.0, 1.1, 1.2, 1.4, 1.6, 1.8, 2.0, 2.3
(a) Using a scale of 2cm to represent 0.5 units on the y-axis and 2 cm to represent 10 units on the x-axis, draw a scatter diagram for the information. (b) Find x̄ the mean of x, and ȳ the mean of y, and plot (x̄, ȳ) on the diagram. (c) Draw the line of best fit to pass through (x̄, ȳ) and (10, 1). (d) From the graph, find the: (i) equation of the line of best fit; (ii) height of plant in 75 days.
Show the model answer
(a) Plot the eight points (10, 1.0) … (80, 2.3).
(b) x̄ = 360/8 = 45; ȳ = 12.4/8 = 1.55. Plot (45, 1.55).
(c) Straight line through (10, 1) and (45, 1.55).
(d)(i) Gradient = 0.55/35 ≈ 0.0157; y = 0.0157x + 0.843 (about y = 0.016x + 0.84).
(ii) At x = 75: y ≈ 2.02 m.
Read values from your line, or use its equation.