The _third quartile_ is the median between the median and the highest value in the data. The _median_ is the middle value of the data when there are an odd number of values and the average of the two middle values when there are an even number of data.
Since there are $19$ data points and they are listed in increasing order, the median is the tenth value, which is $65$. Thus, the third quartile is the median of the data $$65, 69, 71, 76, 78, 81, 85, 91, 92, 99$$ Since there are ten values in this set and they are listed in increasing order, the third quartile is the average of the fifth and sixth values, which is $$\frac{78 + 81}{2} = \frac{159}{2} = 79.5$$