Family height statistics

The average height of a member of a family of five is 1.5 m, the mode of their height is 1.2 m and the median is 1.6 m.
Find out the heights of individual members of this family if you know that they are integers in dm.

Final Answer:

a =  12 dm
b =  12 dm
c =  16 dm
d =  17 dm
e =  18 dm

Step-by-step explanation:

$$\begin{gathered} m=1.5\text{m}\to \text{dm}=1.5\cdot 10\text{dm}=15\text{dm} \\ {m}_2=1.2\text{m}\to \text{dm}=1.2\cdot 10\text{dm}=12\text{dm} \\ {m}_3=1.6\text{m}\to \text{dm}=1.6\cdot 10\text{dm}=16\text{dm} \\ 1212161718 \\ a=12\text{dm} \\ b=a=12\text{dm} \\ c=16\text{dm} \\ d=c+1=16+1=17\text{dm} \\ e=d+1=17+1=18\text{dm} \\ \text{ Verifying Solution: } \\ M=\frac{a+b+c+d+e}{5}=\frac{12+12+16+17+18}{5}=15\text{dm} \end{gathered}$$

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