Final answer:
The quartiles for the provided data set, once arranged in ascending order, are Q1 = 20, Q2 = 22, and Q3 = 23. Q1 is the median of the lower half, Q2 is the overall median, and Q3 is the median of the upper half of the data.
Step-by-step explanation:
To find the quartiles of the given data set, we need to first arrange the data in ascending order, then identify the median (second quartile), and subsequently find the medians of the lower and upper halves of the data set to determine the first and third quartiles.
Step 1: Arrange the data in ascending order.
19, 19, 19, 20, 20, 20, 20, 20, 21, 21, 21, 22, 22, 22, 22, 23, 23, 23, 24, 24, 25, 25, 25, 29
Step 2: Identify the median. Since there are 24 values, the median is the average of the 12th and 13th values, which are both 22. Therefore, the median (or the second quartile Q2) is 22.
Step 3: Find the first quartile (Q1), which is the median of the lower half of the data. Here, the lower half is 19, 19, 19, 20, 20, 20, 20, 20, 21, 21, 21, 22. The median of this set is the average of the 6th and 7th values, which are both 20. So, Q1 is 20.
Step 4: Find the third quartile (Q3), which is the median of the upper half of the data. The upper half is 22, 22, 23, 23, 23, 24, 24, 25, 25, 25, 29. The median of this set is the 6th value, which is 23. So, Q3 is 23.
Therefore, the quartiles for the given data set are Q1 = 20, Q2 = 22, and Q3 = 23.