I was wondering if these xbar, rbar, lcl, cl, and ucl, values were correct given

Question

I was wondering if these xbar, rbar, lcl, cl, and ucl, values were correct given the 15 sample sizes with 6 observations. Should I have a mean and xbar? Or is the mean the xbar?

Values to be easily copied to excel!

1 2 3 4 5 6 1.62 1.54 1.38 1.75 2.5 1.32 1.25 1.963 1.55 1.66 1.38 2.01 1.85 1.01 0.95 1.79 1.66 1.94 3.1 1.18 1.25 1.45 1.09 2.11 1.95 0.76 1.34 2.12 1.45 1.03 0.88 2.5 1.07 1.5 1.33 1.62 1.55 1.41 1.95 1.14 1.86 1.02 2.78 1.56 1.87 2.03 0.79 1.14 1.31 1.05 0.94 1.53 1.71 1.15 1.67 1.85 2.03 1.12 1.5 1.36 0.95 1.73 1.12 1.67 2.05 1.42 3.21 4.16 1.67 1.75 2.87 3.76 1.65 1.78 2.63 1.05 1.21 2.09 2.36 3.55 1.92 1.45 3.64 2.3 1.07 0.96 1.13 2.05 0.91 1.66 1 2 3 4 5 6 mean Xbar rbar LCL CL UCL LCL CL days UCL 1 1.62 154 1.38 1.75 2.5 1.32 1.685 1.672 1.18 0.965 1.718 2.472 0 1.306 2.761 2 1.25 1.963 1.55 1.66 1.38 2.01 0.327 1.631 0.76 0.965 1.718 2.472 1.306 2.761 3 1.85 1.01 0.95 1.79 1.66 1.94 1.533 1482 0.99 0.965 1.718 2.472 1.306 2.761 4 3.1 1.18 1.25 1.45 1.09 2.11 1.697 1.746 2.01 0.965 1.718 2.472 0 1.306 2.761 5 1.95 0.76 1.34 2.12 145 1.03 1.442 1.306 1-19 0.965 1.718 2.472 1.306 2.761 6 0.88 25 1.07 1.5 1.33 1.62 1.483 1.48 1.62 0.965 1.718 2.472 0 1.306 2.761 7 1.55 141 1.95 1.14 1.86 1.02 1.488 1.558 0.93 0.965 1.718 2.472 1.306 2.761 8 2.78 1.36 1.87 2.03 0.79 1.14 1.695 1.628 1.99 0.965 1.718 2.472 0 1.306 2.761 9 1.31 1.05 0.94 1.53 1.71 1.15 1.282 1.232 0.77 0.965 1.718 2.472 0 1.306 2.761 10 1.67 1.85 2.03 1.12 15 1.36 1.588 1.682 0.67 0.965 1.718 2.472 1.306 2.761 12 3.21 4.16 1.67 1.75 2.87 3.76 2.903 3.134 249 0.965 1.718 2.472 0 1.306 2.761 14 2.36 3.35 1.92 1.45 364 2.3 2.537 2.754 1.72 0.965 1.718 2.472 0 1.306 2.761 15 1.07 0.96 1.13 2.05 0.91 1.66 1.297 1.146 0.75 0.965 1.718 2.472 0 1.306 2.761

Explanation / Answer

No, you don't have to calculate and mean and X bar. Here the mean of a subgroup is x bar.

And, average of all x bar is called xbar-bar

I will solve this question for you.

subgroup size = 6

CLX - bar = 1.6994

UCLX = (Xbar-bar) + 3(Rbar)/d2n = 1.6994 + 3 * 0.441925/(2.534 *6) = 1.9130

LCLX = (Xbar-bar) - 3*(Rbar)/d2n = 1.6994 - 3 * 0.441925/(2.534 *6) = 1.4858

value of d2 can be taken from control chart table for subgroup size =6.

CLR-bar = 1.4013

UCLR =  D4 *Rbar  = 2.004 * 1.4013 = 2.8082

LCLR = D3 * Rbar = 0 * 1.4013 = 0

So here i have calculated all value you desired and you can see that X bar and mean are not different for sub group and there is a value, namely, x bar-bar, which is the mean of all means of samples. Here, the mean is the xbar.

The Table

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