Find the first and third quartiles of the data set.

1, 5, 1, 2.5, 3, 2, 3.5, 2, 3, 1.5, 4, 2, 4, 1, 3, 4.5

sort the values, then divide them into four equal parts. Pick the 1st and 3rd portions.

To find the first and third quartiles of a data set, you need to arrange the data in ascending order.

First, let's arrange the data in ascending order:
1, 1, 1.5, 2, 2, 2, 2.5, 3, 3, 3, 3.5, 4, 4, 4.5

Next, calculate the position of the quartiles.
The first quartile (Q1) is the median of the lower half of the data set, and the third quartile (Q3) is the median of the upper half of the data set.

Since we have 14 data points, the median (Q2) is the average of the 7th and 8th data points.

Q2 = (2 + 2.5) / 2 = 2.25

Now, we can determine Q1 and Q3. For both, we split the data set into two halves and find the median of each half.

Q1 is the median of the lower half:
1, 1, 1.5, 2, 2, 2

Q1 = (1 + 1.5) / 2 = 1.25

Q3 is the median of the upper half:
3, 3, 3, 3.5, 4, 4, 4.5

Q3 = (3.5 + 4) / 2 = 3.75

Therefore, the first quartile (Q1) is 1.25 and the third quartile (Q3) is 3.75.