Auto pistons at Wenming$$ Chung's plant in Shanghai are produced in a forging$$ process, and the diameter is a critical factor that must be controlled. From sample sizes of $10$ pistons produced each$$ day, the mean and the range of this diameter have been as$$ follows:

$$

Day

Mean x

$($mm$)$

Range R

$($mm$)$

$1$

$156\mathrm{.}9$

$4\mathrm{.}0$

$2$

$151\mathrm{.}2$

$4\mathrm{.}6$

$3$

$153\mathrm{.}6$

$4\mathrm{.}1$

$4$

$157\mathrm{.}5$

$5\mathrm{.}2$

$5$

$156\mathrm{.}6$

$4\mathrm{.}5$

Part $2$

$$a$)$ What is the value of x$?$

x$=$enter your response here mm $($round your response to two decimal$$ places$).$