A meteorologist is analyzing temperature data collected from weather stations across a region. To interpolate missing temperature values between stations, the meteorologist needs to use polynomial approximation techniques.

$($a$)$ Implement the Lagrange Interpolation method in Python to approximate the temperature at a specific location using temperature data from neighboring stations. $[10$ marks$]$

$($b$)$ Apply the Lagrange Interpolation method to interpolate the temperature at a location $x=3$ using the following data points $(1,10),(2,15),(4,25)and(5,30).$ marks