A sample of $120$ continuous observations is plotted in a histogram. The frequencies are: $[100, 120)$ with frequency $20$; $[120, 140)$ with frequency $30$; $[140, 160)$ with frequency $50$; and $[160, 180)$ with frequency $20$. Using linear interpolation, what is the estimated 80th percentile ($P_{80}$) of this dataset?