Okay, let's tackle this question step by step. The question is about understanding the distribution of FEV in a sample of smokers and determining how many people fall between the first and third quartiles.

First, I need to recall what quartiles mean. The median divides the data into two halves. The first quartile (Q1) is the 25th percentile, meaning 25% of the data is below it, and the third quartile (Q3) is the 75th percentile, so 75% of the data is below it. The interquartile range (IQR) is between Q1 and Q3, which should contain the middle 50% of the data.

The question states the median is 2.5 liters, Q1 is 1.5 liters, and Q3 is 4.5 liters. The sample size is 300. So, the number of people between Q1 and Q3 would be 50% of 300, which is 150. That seems straightforward.

Now, checking the options. The correct answer is 150. The options aren't given here, but the user's correct answer is likely option C or D, but since the user hasn't provided the options, I need to focus on the explanation.

Wait, the user provided the correct answer as . So maybe they filled it in later. Regardless, the key point is that the IQR covers 50% of the data. So 300 * 0.5 = 150.

The distractors might try to trick someone into thinking it's 75% (which would be from Q1 to the max) or 25% (from min to Q1). Alternatively, someone might miscalculate by subtracting Q1 from Q3 and multiplying by sample size, but that's not the case here. The quartiles directly indicate the percentage.

So the core concept here is understanding quartiles and percentiles. The FEV distribution's quartiles tell us about the spread. The median is the middle value, and the quartiles split the data into quarters. The IQR is the range between Q1 and Q3, which contains the middle 50% of the data. Therefore, 50% of 300 is 150.

The clinical pearl here is to remember that the interquartile range always captures 50% of the data, regardless of the distribution's shape. This is a fundamental concept in descriptive statistics that's crucial for interpreting medical data.

**Core Concept**
Quartiles divide a dataset into four equal parts. The first quartile (Q1) marks the 25th percentile, the third quartile (Q3) the 75th percentile. The interquartile range (IQR) between Q1 and Q3 contains the **middle 50% of data values**, a key principle in descriptive statistics.

**Why the Correct Answer is Right**
The question provides Q1 (1.5 L) and Q3 (4.5 L), defining the IQR. By definition, **50% of data lies between Q1 and Q3**. For 300 smokers, this equals **300 × 0.5 = 1

✓ Correct Answer: B. 150