An inspector took $7$ samples to check product quality. Each sample has $4$ measures, as shown in the table

below.

The coefficients for constructing charts are given in the table below.

a$)$ Calculate and plot the $x-$bar chart. Based on $x-$bar chart, is the process under control?

b$)$ Calculate and plot the R chart. Based on $R$ chart, is the process under control?