Question: A college's provost (chief academic officer) selects a random sample of 5 students' overall grade point averages (GPAs) in each of 8 consecutive semesters. These

A college's provost (chief academic officer) selects a random sample of 5 students' overall grade point averages (GPAs) in each of 8 consecutive semesters. These sample GPAs along with their sample means (x), sample ranges (R), and sample proportions (p^) are given in the table below.

(FYI: Any GPA that is less than 2.0 was considered "defective" in the calculation of the p^ statistics for each subgroup.)

Subgroup

x

R

p^

1 3.5 3.1 2.4 2.9 3.4 3.06 1.1 0
2 3.0 3.8 2.8 2.9 2.1 2.92 1.7 0
3 1.3 3.0 1.2 1.4 1.9 1.76 1.8 0.8
4 2.2 1.6 3.3 3.0 1.5 2.32 1.8 0.4
5 1.1 3.6 3.3 1.9 1.8 2.34 2.5 0.6
6 3.7 3.3 4.0 3.8 1.5 3.26 2.5 0.2
7 2.2 2.1 3.8 3.8 1.7 2.72 2.1 0.2
8 3.0 2.6 1.1 2.5 1.7 2.18 1.9 0.4
Averages 2.57 1.9 0.4

Find the values of the UCL and LCL on the following control charts for this data. Round all answers to 4 places after the decimal point (if necessary).

  1. x chart
  2. R chart
  3. p chart

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