Question

ProCycle & Co. uses X bar and R-charts to track the thickness of bicycle brake pads in millimeters. Below are the observations for 5 samples. What are the UCL_R , LCL_R (for range) and X bar (double bar)?

Sample	Observation 1	Observation 2	Observation 3
1	22	14	12
2	24	17	18
3	19	20	21
4	16	13	15
5	10	10	13

Group of answer choices

7.722: 0: 81.34

9.575: 0: 81.34

7.222: 0: 81.34

12.87; 0: 16.266

10.666: 0: 16.266

Answer 1

Sample	Observation 1	Observation 2	Observation 3	average	range
1	22	14	12	16.00	10.00
2	24	17	18	19.67	7.00
3	19	20	21	20.00	2.00
4	16	13	15	14.67	3.00
5	10	10	13	11.00	3.00
			average	16.27	5.00

Range chart
average range R̅ =			5
sample size n   =			3
for sample size n=3, criitcal value of constant D3=					0
for sample size n=3, criitcal value of constant D4=					2.575
control line (CL) = R̅=			5
upper control limit (UCL)=D4R̅ =			12.8750
lower control limit(LCL) =D3R̅ =			0.00000

from above UCLR =12.875

LCLR =0

and Xbar =16.266

therefore corerct option is: 12.87; 0: 16.266