The first quartile of a frequency distribution is a measure of central tendency that divides the data into four equal parts. It represents the value below which 25% of the observations lie. To find the first quartile, we need to calculate the cumulative frequencies and determine the observation that corresponds to the 25th percentile.

Let's calculate the cumulative frequencies for the given frequency distribution:

Observation Frequency Cumulative Frequency
----------------------------------------------
1 10 10
2 8 18
3 12 30
4 23 53
5 30 83
6 18 101
7 19 120
8 15 135

The cumulative frequency column represents the total frequency up to that observation. Now, we need to find the observation that corresponds to the 25th percentile. This can be done by multiplying the total number of observations by 0.25:

25% of 135 = 0.25 * 135 = 33.75

Since 33.75 falls between the cumulative frequencies of 30 and 53, the first quartile lies within the observation 4.

To find the exact value of the first quartile, we can use interpolation. Interpolation involves determining the position of the desired value within a range. In this case, we know that the desired value lies between the observation 4 and observation 5.

Let's calculate the position of the first quartile within this range:

Position = (Desired value - Lower value) / (Upper value - Lower value)
= (33.75 - 30) / (53 - 30)
≈ 0.5625

Using this position, we can interpolate the first quartile:

First quartile = Lower value + (Position * (Upper value - Lower value))
= 4 + (0.5625 * (5 - 4))
≈ 4.5625

Therefore, the first quartile of the given frequency distribution is approximately 4.5625.

In conclusion, the first quartile of the frequency distribution with the given observations and frequencies is approximately 4.5625.