Final answer:
The first quartile (Q₁) of the ordered data is 58, which is the median of the lower half of the data.
Step-by-step explanation:
To find the first quartile (Q₁) of the accompanying data set, you must first arrange the data in ascending order and then determine the median of the lower half of the data. The given data set in order is: 54, 55, 55, 58, 58, 59, 62, 62, 62, 63, 63, 63, 63, 63, 75. With 15 numbers, the 8th number (62) is the median. The first quartile will be the median of the lower half, i.e., the middle number from the first seven numbers. The first seven numbers are: 54, 55, 55, 58, 58, 59, 62. Here, the fourth number, 58, is the median of the lower half, making it the first quartile (Q₁).