Final answer:
To determine the three-sigma control limits for the given data, calculate the mean and standard deviation. Add and subtract three times the standard deviation from the mean to obtain the upper and lower control limits, respectively.
Step-by-step explanation:
To determine the three-sigma control limits, we need to calculate the mean and standard deviation of the given data. The mean is calculated by summing up all the values and dividing by the number of values. In this case, the mean is (2+3+1+0+1+3+2+0+2+1+3+1+2+0) / 14 = 1.8571 (rounded to 4 decimal places).
The standard deviation is calculated using the formula: sqrt(sum((xi - mean)^2) / (n-1)). Applying the formula to the given data gives us a standard deviation of 1.3284 (rounded to 4 decimal places).
The three-sigma control limits are then calculated by adding and subtracting three times the standard deviation from the mean. The upper control limit is 1.8571 + (3 * 1.3284) = 5.8423 (rounded to 4 decimal places), and the lower control limit is 1.8571 - (3 * 1.3284) = -2.1283 (rounded to 4 decimal places).