Ten samples of n = 5 were collected to construct an chart.The sample mean and range for each sample are shown in the table below. Calculate the empirical centerline for the R chart.
A) 20.8
B) 17.2
C) 18.1
D) 19.4

Question

Ten samples of n = 5 were collected to construct an  chart.The sample mean and range for each sample are shown in the table below.  Calculate the empirical centerline for the R chart.
A) 20.8 
B) 17.2 
C) 18.1 
D) 19.4

Quizplus · Accepted Answer

To find the empirical centerline for the R chart, we need to calculate the average range across all samples. 
$$\bar{R} = \frac{\sum_{i=1}^{n}(R_i)}{n} = \frac{25 + 25 + 18 + 20 + 12 + 15 + 15 + 10 + 17 + 23}{10} = 18.1$$
Therefore, the empirical centerline for the R chart is 18.1, which is answer choice C.

Ten Samples of N = 5 Were Collected to Construct