### Analyze data from stem-and-leaf diagram

Question Sample Titled 'Analyze data from stem-and-leaf diagram'

The stem-and-leaf diagram below shows the distribution of the marks of the students in a test and the marks can only be integers.

Stem (tens)Leaf (units)
 ${5}$ ${6}$ ${7}$ ${8}$ ${9}$
 ${h}$ ${3}$ ${3}$ ${2}$ ${4}$ ${8}$ ${9}$ ${1}$ ${2}$ ${2}$ ${2}$ ${2}$ ${6}$ ${3}$ ${4}$ ${5}$ ${5}$ ${8}$ ${3}$ ${k}$ ${5}$

If the range of the above distribution is at most ${44}$ , which of the following must be true?

 I. ${0}<{h}<{4}$ II. ${2}<{k}<{6}$ III. ${0}\le{k}-{h}\le{4}$

A
I, II and III
B
I and II only
C
I and III only
D
II and III only

 Note that the range is at most ${44}$,  ${95}-{\left({50}+{h}\right)}$ $\le{44}$ ${h}$ $\ge{1}$ And from the stem-and-leaf diagram, ${h}$ $\le{3}$ $\therefore{1}$ $\le{h}\le{3}$ i.e. ${0}$ $<{h}<{4}$ the marks can only be integers  From the stem-and-leaf diagram, ${3}$ $\le{k}\le{5}$ i.e. ${2}$ $<{k}<{6}$ the marks can only be integers  From (I), possible values of ${h}$ are ${1}$ , ${2}$ and ${3}$ . From (II), possible values of ${k}$ are ${3}$ , ${4}$ and ${5}$ . ∴  ${0}\le{k}-{h}\le{4}$

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