The stem lengths of a sample of 120 tulips are recorded in the grouped frequency table below. A histogram is drawn to represent these data. The area of the bar representing the $$\(40 \leqslant x< 42\)$$ class is $$\(16.5 \mathrm{~cm}^{2}\)$$ (a) Calculate the exact area of the bar representing the $$\(42 \leqslant x< 45\)$$ class. (2) The height of the tallest bar in the histogram is $$\(10 \mathrm{~cm}\)$$. (b) Find the exact height of the second tallest bar. (3) $$\(Q_{1}\)$$ for these data is $$\(45 \mathrm{~cm}\)$$. (c) Use linear interpolation to find an estimate for (i) $$\(Q_{2}\)$$ (ii) the interquartile range. (4) One measure of skewness is given by $$\[ \frac{Q_{3}-2 Q_{2}+Q_{1}}{Q_{3}-Q_{1}} \]$$ (d) By calculating this measure, describe the skewness of these data. (2)

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