Q1 X and R chart

A quality engineer collected process data for 10 subgroups with each subgroup consisting of four samples (n=4). The averages and ranges of samples in each subgroup are summarized in Table 1 below.

Table 1. Subgroup Data

Subgroup	1	2	3	4	5	6	7	8	9	10
Average X	13.01	12.99	13.01	12.99	12.98	12.93	12.93	13.00	13.01	13.01
Range R	0.06	0.04	0.03	0.05	0.04	0.06	0.07	0.03	0.04	0.06

(1-1) Calculate center line X of X chart.

	Answer
Center line of X chart	12.986

(1-2) Calculate average range R , which is also the center line of R chart.

	Answer
Average range R	0.048

(1-3) Calculate upper control limit (UCL) and lower control limit (LCL) of X chart.

	Answer
UCL of X chart	13.021
LCL of X chart	12.951

please show work for the questions