The first quartile (Q1) is defined as what?

The first quartile (Q1) is defined as what?

• A. Median of upper half
• B. Median of lower half
• C. Mean of all values
• D. Range

Answer: (B)

The first quartile is the value that marks the cutoff for the lowest 25% of the data. To find it, arrange the data from smallest to largest, split the data into a lower half and an upper half, and take the median of the lower half. For example, with eight numbers 1, 2, 3, 4, 5, 6, 7, 8, the lower half is 1, 2, 3, 4, and its median is the average of 2 and 3, giving Q1 = 2.5. This means 25% of the data are at or below Q1. So Q1 is not the overall median, nor the mean, nor the range.

The first quartile is the value that marks the cutoff for the lowest 25% of the data. To find it, arrange the data from smallest to largest, split the data into a lower half and an upper half, and take the median of the lower half.

For example, with eight numbers 1, 2, 3, 4, 5, 6, 7, 8, the lower half is 1, 2, 3, 4, and its median is the average of 2 and 3, giving Q1 = 2.5. This means 25% of the data are at or below Q1.

So Q1 is not the overall median, nor the mean, nor the range.