$$P_{1}$$ is the average of all prime numbers below 12 and $$P_{2}$$ is the average of all prime numbers between 12 and 30. What is the value of $$5P_{1} - P_{2}$$?

$$P_{1}$$ is the average of all prime numbers below 12.

prime numbers below 12 ==> 2, 3, 5, 7, 11

Average = $$P_{1}$$ = $$\frac{2+3+5+7+11}{5}$$

= $$\frac{28}{5}$$

= 5.6

$$P_{2}$$ is the average of all prime numbers between 12 and 30.

prime numbers between 12 and 30 ==> 13, 17, 19, 23, 29

Average = $$P_{2}$$ = $$\frac{13+17+19+23+29}{5}$$

= $$\frac{101}{5}$$

= 20.2

Value of $$5P_{1} - P_{2}$$ = $$5\times5.6 - 20.2$$

=  28 - 20.2

= 7.8