### Stem-and-leaf; two new data

Question Sample Titled 'Stem-and-leaf; two new data'

The stem-and-leaf diagram below shows the distribution of the weights (in $\text{kg}$) of the students in a class.

Stem (tens)Leaf (units)
 ${4}$ ${5}$ ${6}$ ${7}$
 ${1}$ ${2}$ ${4}$ ${4}$ ${5}$ ${6}$ ${0}$ ${3}$ ${5}$ ${6}$ ${8}$ ${1}$ ${1}$ ${2}$ ${1}$ ${2}$ ${2}$ ${4}$ ${6}$

 (a) Find the mean and the range of the above distribution. (2 marks) (b) Two more students now join the class. It is found that both the mean and the range of the distribution of the weights are increased by ${2}$ $\text{kg}$ . Find the weights of each of these two students. (4 marks)

 (a) Mean $=\dfrac{{{41}+{42}+\ldots+{74}+{76}}}{{19}}$  $={57}$ $\text{kg}$ 1A Range $={35}$ $\text{kg}$ 1A  (b) Let ${x}$ $\text{kg}$ and ${y}$ $\text{kg}$ be the weights of the new students. ∵ New mean $={57}+{2}={59}$ ∴ $\dfrac{{{x}+{y}+{57}\times{19}}}{{{21}}}$ $={59}$ 1M ${x}+{y}$ $={156}$ 1M Since the range is increased by ${2}$ , ${39}$ $\le{x}\le{78}$ ${39}$ $\le{y}\le{78}$ Note that ${78}\times{2}={156}$ , 1M ∴  ${x}$ and ${y}$ must be ${78}$ . The weights of the new students are both ${78}$ $\text{kg}$ . 1A

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