In a data set, what does it mean to say that a value is the exact first quartile (Q1)?

• A. Exactly 25% of the observations are less than or equal to that value.
• B. Exactly 20% of the observations are less than or equal to that value.
• C. Exactly 25% of the observations are greater than or equal to that value.
• D. Exactly 10% of the observations are less than or equal to that value.

Answer: (A)

Verified step by step guidance

1. Understand that quartiles divide a data set into four equal parts when the data is ordered from smallest to largest.
2. The first quartile (Q1) is the value below which 25% of the data falls, meaning it marks the 25th percentile of the data set.
3. This implies that exactly 25% of the observations are less than or equal to the Q1 value.
4. Recognize that the other options (20%, 10%, or 25% greater than or equal) do not correctly describe the position of Q1 in the data distribution.
5. Therefore, the correct interpretation of Q1 is that exactly 25% of the observations are less than or equal to that value.