### stem-leaf-diagram

Question Sample Titled 'stem-leaf-diagram'

The ages of the members of Secret Police team ${A}$ are shown as follows:

${17},{27},{30},{31},{34},{34},{44},{48},{49}$

${49},{52},{56},{57},{59},{60},{65},{66},{68}$

 (a) Write down the median and the mode of the ages of the members of Secret Police team ${A}$. (2 marks) (b) The stem-and-leaf diagram below shows the distribution of the ages of the members of Secret Police team ${B}$. It is given that the range of this distribution is ${47}$.

Stem (tens)Leaf (units)
 ${2}$ ${3}$ ${4}$ ${5}$ ${6}$
 ${h}$ ${2}$ ${4}$ ${5}$ ${5}$ ${8}$ ${0}$ ${3}$ ${9}$ ${0}$ ${4}$ ${8}$ ${9}$ ${9}$ ${k}$

 (i) Find ${h}$ and ${k}$. (ii) From each team, a member is randomly selected. The two selected members can join a special mission when the difference of their ages exceed ${37}$ . Find the probability that these two members can join the special mission.  (4 marks)

 (a) Median$={49}$ 1A Mode$={34},{49}$ 1A  (bi) Note that ${0}\le{h}\le{2}$ and ${9}\le{k}\le{9}$. 1M ∵   Range $={47}$ ∴  ${k}-{h}={7}$ ∴  ${\left\lbrace{h}={2},{k}={9}\right\rbrace}$ 1A (bii) By counting, there are ${35}$ favourable combinations. 1M Required prob.$=\dfrac{{35}}{{{18}\times{15}}}=\dfrac{{7}}{{54}}$ 1A

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