The table gives the relationship between the height, in metres, 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 2 cm to represent 0.5 units on the y- axis and 2cm to 10 units on the x- axis, draw a scatter diagram for the information.
(b) Find (bar{x}), the mean of x, and (bar{y}), the mean of y, and plot ((bar{x}, bar{y})) on the diagram.
(c) Draw the line of best fit to pass through ((bar{x}, bar{y})) and ((10, 1)).
(d) From graph, find the :
(i) equation of the line of best fit ; (ii) height of plant in 75 days.
Explanation
(a & c)
(b) (bar{x} = frac{10 + 20 + 30 + 40 + 50 + 60 + 70 + 80}{8} = frac{360}{8} = 45)
(bar{y} = frac{1.0 + 1.1 +1.2 + 1.4 + 1.6 + 1.8 + 2.0 + 2.3}{8} = frac{12.4}{8} = 1.55)
(therefore (bar{x}, bar{y}) = 45, 1.55).
(d)(i) Equation of line of best fit :
(frac{y – 1.8}{x – 60} = frac{1.8 – 1.55}{60 – 45})
(frac{y – 1.8}{x – 60} = frac{0.25}{15} = 0.017)
(y – 1.8 = 0.017(x – 60) implies y – 1.8 = 0.017x – 1.02)
(y = 0.017x – 1.02 + 1.8 = 0.017x + 0.78)
(ii) When x = 75 days, (y = 0.017(75) + 0.78)
= (2.055)