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 i. Calculate:x̄, the mean of X and ȳ, the mean of Y;
ii. Caculate:
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 relationship between X and Y;
ii. From the graph, determine the value of Y when X is 20.
Explanation
a.
b i. x̄ = \(\frac{14+16+17+18+22+24+27+28+31+33}{10}\)
x̄ = \(\frac{230}{10}\)
y = \(\frac{22+19+15+13+10+12+3+5+3+2}{10}\)
= \(\frac{104}{10}\)
ii.
x̄\(_1\) = \(\frac{14+16+17+18+22}{5}\) → \(\frac{79}{5}\) = 15.8
c.
d i. There is a negative correlation between X and Y. X increases as Y decreases
ii. The point labelled Y1 is the corresponding value on Y-axis when X = 20, Y1 = 12.6