The first quartile (Q1) is a measure of central tendency that divides the data set into four equal parts. To find the first quartile of the data set 10, 11, 12, 15, 17, 19, 22, 24, 29, 33, 38, follow these steps:
- Arrange the data in ascending order: The given data set is already arranged in ascending order: 10, 11, 12, 15, 17, 19, 22, 24, 29, 33, 38.
- Determine the position of Q1: The first quartile is the median of the first half of the data. Since there are 11 data points, the first half includes the first 5 data points: 10, 11, 12, 15, 17.
- Find the median of the first half: The median of 10, 11, 12, 15, 17 is 12.
Therefore, the first quartile (Q1) of the data set is 12.