What is the value of the first quartile for observations 15, 18, 10, 20, 23, 28, 12, 16?

To find the first quartile, we need to arrange the observations in ascending order: 10, 12, 15, 16, 18, 20, 23, 28.

Step 1: Calculate the position of the first quartile. The first quartile is the median of the lower half of the data set. Since we have 8 observations, the position of the first quartile is (8 + 1) / 4 = 2.25.

Step 2: Determine the values at the positions surrounding the first quartile. The values at positions 2 and 3 are 12 and 15, respectively.

Step 3: Calculate the first quartile. To calculate the first quartile, we take the average of the values at positions 2 and 3. (12 + 15) / 2 = 13.5

Therefore, the value of the first quartile for the given observations is 13.5.