### Stem

Question Sample Titled 'Stem'

Dexter conducts a survey about the amount of apples eaten by his classmates every month. The stem-and-leaf diagram below shows the result.

Stem (tens)Leaf (units)
 ${0}$ ${1}$ ${2}$
 ${0}$ ${0}$ ${5}$ ${5}$ ${6}$ ${6}$ ${9}$ ${2}$ ${4}$ ${8}$ ${8}$ ${8}$ ${1}$ ${2}$ ${6}$

 (a) Write down the mean, mode and median of the amount of apples eaten by the ${15}$ students every month. (3 marks) (b) Dexter asked five more classmates. The mean of the amount of apples eaten by them every month is ${14}$. (i) Find the mean of the amount of apples eaten by the ${20}$ students every month. (ii) After that, Dexter found that the mode and median of the amount of apples eaten by ${20}$ students every month are ${14}$ and ${16}$ respectively. Hugo claimed that there are something wrong in Dexter's calculation. Do you agree? Explain your answer. (4 marks)

 (a) Mean $={12}$ 1A Mode $={18}$ 1A Median $={12}$ 1A  (bi) Required mean $=\dfrac{{{12}\times{15}+{14}\times{5}}}{{20}}$  $={12.5}$ 1A (bii) Assume mode  $={14}$ Then, at least ${3}$ data are ${14}$ , 1M such that the median become ${14}$ . Since the mean of the ${5}$ new data is ${14}$ , the remaining ${2}$ data cannot be both smaller than ${14}$ or both greater than ${14}$. Thus, it is not possible that the median is ${16}$ . 1M Thus, she's correct. 1A

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