### stem-and-leaf

Question Sample Titled 'stem-and-leaf'

The following stem-and-leaf diagram shows the ages of programmers in the IT department of a company.

Stem (tens)Leaf (units)
 ${1}$ ${2}$ ${3}$
 ${9}$ ${9}$ ${1}$ ${2}$ ${3}$ ${3}$ ${4}$ ${5}$ ${6}$ ${6}$ ${7}$ ${9}$ ${2}$ ${4}$

 (a) Write down the mean, range and inter-quartile range of the ages of the programmers. (3 marks) (b) The three oldest programmers leave the department and two new programmers join the department. The mean age of the programmers is then decreased by ${1}$, while the inter-quartile range of the ages of programmers remain unchanged. (i) Find the mean age of the two new programmers. (ii) Write down a possible set of ages of the two new programmers.  (4 marks)

 (a) Mean $={25}$ 1A Range $={15}$ 1A Inter-quartile range $={5}$ 1A  (bi) Let the ages of the new programmers be ${a}$ and ${b}$ respectively. $\dfrac{{{19}+{19}+\ldots+{27}+{a}+{b}}}{{13}}$ $={25}-{1}$ 1M ${a}+{b}$ $={57}$ $\dfrac{{{a}+{b}}}{{2}}$ $={28.5}$ $\therefore$Required mean age $={28.5}$ 1A  (bii) ${27}$ and ${30}$ 1M+A

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