The average of $33$ numbers is $70$. The average of the first $17$ numbers is $65$ and the average of the last $17$ numbers is $74$. If the $17$ th number is excluded, what is the average of the remaining numbers (approximate to one decimal place)?

* Sum of all $33$ numbers:
$${\text{Sum}}_{33}=33\times 70=2310$$
Sum of the first $17$ numbers:
$${\text{Sum}}_{\text{first }17}=17\times 65=1105$$
Sum of the last $17$ numbers:
$${\text{Sum}}_{\text{last }17}=17\times 74=1258$$
Since the first 17 numbers and the last 17 numbers overlap at the 17th number, adding their sums includes the 17th number twice:
$${\text{Sum}}_{\text{first }17}+{\text{Sum}}_{\text{last }17}={\text{Sum}}_{33}+\text{17th number}$$
$$1105+1258=2310+\text{17th number}$$
$$2363=2310+\text{17th number}⟹\text{17th number}=2363-2310=53$$
If the 17th number is excluded, the sum of the remaining 32 numbers is:
$${\text{Sum}}_{32}=2310-53=2257$$
The average of the remaining 32 numbers is:
$${\text{Average}}_{32}=\frac{2257}{32}\approx 70.531$$
Approximating to one decimal place, we get $70.5$.