What is the value of the first quartile for observations 15, 18, 10, 20, 23, 28, 12, 16?(a) 17 (b) 16 (c) 12.75 (d) 12

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

Since we have 8 observations, the first quartile is the median of the lower half of the data set. In this case, the lower half consists of the first 4 observations: 10, 12, 15, 16.

To find the median of this lower half, we take the average of the middle two values. In this case, the middle two values are 12 and 15.

Therefore, the first quartile is (12 + 15) / 2 = 27 / 2 = 13.5.

Since none of the answer choices match 13.5 exactly, we can round it to the nearest whole number, which is 14.

So, the correct answer is not provided in the options given.