A company manufactures refills of pens. Five observations of refills are taken on each day. These observations were taken 6 times during a working day. Calculate the control limits for mean and range, and plot the control charts using any statistical software. Make suitable assumptions, if any.

The data is given in the following table:

(Please take the suitable values of d2 , d3, d4 , A2 and other variables.)

To calculate the control limits for the mean and range, we need to determine the appropriate constants based on the sample size. Here are the steps to calculate the control limits:

Step 1: Calculate the sample means and ranges.

For each row of data in the table, calculate the mean and range using the following formulas:

Mean (x̄) = (x1 + x2 + x3 + x4 + x5) / 5
Range (R) = xmax - xmin

Here is the calculation for each row:

Sample No. Point size of pen in mm Mean (x̄) Range (R)
1 2.04, 2.01, 1.87, 1.85, 1.90 1.954 0.19
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