Answer :
The first quartile (Q1) of the data set 104, 108, 111, 114, 114, 120, 122, 126, 127, 134 is 110.25. This value represents the median of the lower half of the dataset.
Step-by-Step Explanation
- Arrange the data in ascending order: The data is already arranged.
- Determine the position of the first quartile (Q1): The first quartile is the median of the lower half of the data. There are 10 data points in total, so the position of Q1 can be found using the formula Q1 position = (N+1)/4, where N is the number of data points. Therefore, Q1 position = (10+1)/4 = 2.75.
- Interpolate to find Q1: Since 2.75 is 3/4 of the way between the 2nd (108) and 3rd (111) data points, we calculate: Q1 = 108 + 0.75 * (111 - 108) = 108 + 0.75 * 3 = 108 + 2.25 = 110.25.
Therefore, the first quartile (Q1) of the data set is 110.25.
