the first picture is the question. the 2nd and third picture are the answers and the 4th picture is the tabls my teacher provided us with. for the moving range chart section in a, how did they find that D4 is 3.27 and D3 is 0? thank you.

Q2 (Ref: Q. 10-5. p 352-353): In a refinery, the octane rating of gasoline produced is measured by taking one observation from each batch. Twenty observations follow. a) Construct Three Sigma control charts for the individual unit and moving range. Is the process in control? b) A new batch has octane rating of 94.0. Using the control charts in part a, is the process still in control? Observation number Observation number 11 12 13 Octane Rating 89.2 86.5 88.4 91.8 90.3 87.5 92.6 87 89.8 92.2 Octane Rating 85.4 91.6 87.7 85 91.5 90.3 85.6 90.9 82.1 85.8 PROBLEM NO. 10 - 5 Moving Range obs # Octane rating 89.20 86.50 88.4o 91.80 90.30 87.50 92.60 87.00 89.80 92.20 85.4o 91.60 87.70 85- 91.50 90.30 85.60 90.90 82. 10 85.80 88.56 2.91 2.70 1.90 3.4o 1.50 2.80 5.10 5.60 2.80 2.4o 6.80 6.20 3-90 2.70 6.50 1.20 4.70 5.30 8.80 3.70 4.11 14 16 avg std dev For the individual unit or x chart: UCL = X + 20 = 88.56 + 3(2.91)= 97.29 LCL = X - zo = 88.56 - 3(2.91) = 79.83 For the moving range chart: UCL MR= D. R = 3.27(4.11) = 13.42 LCL R=D, R=0(4.11) = 0 Yes, the process is in control bec. all observations and moving ranges fall in their respective control limits. The new moving range = 94.0 - 85.8 = 8.2. Yes, the process is still in control because 79.83