The frequencies of the classes 5-15, 15-25, 25-35, 35-45, 45-55 are 7, $x$, 18, 13, 8. The median of the distribution is 30. Find $x$. (The total frequency is not given.)

Here $n=46+x$, so $\frac{n}{2}=23+\frac{x}{2}$, and the cumulative frequency before 25-35 is $7+x$. The median 30 lies in 25-35, so $l=25,f=18,h=10$ and $30=25+\left(\frac{23+x/2-7-x}{18}\right)\times 10$. That gives $5=\frac{10(16-x/2)}{18}$, so $16-\frac{x}{2}=9$ and $x=14$. Check: 7, 14, 18, 13, 8 has $n=60$, cumulative 7, 21, 39, 52, 60, and $25+\frac{30-21}{18}\times 10=30.x=15$ comes from using $\frac{n+1}{2}$ instead of $\frac{n}{2}$; $x=7$ comes from forgetting that the unknown frequency is itself part of $n$; $x=19$ comes from using $f=13$, the frequency of the class AFTER the median class.