Final answer:
The first quartile (Q₁) is 1, the median (second quartile, Q₂) is 4, and the third quartile (Q₃) is 6 for the given data set after arranging it in ascending order and splitting it into two halves to find the median of each half.
Step-by-step explanation:
The quartiles of a data set are values that divide the set into four equal parts. To find the quartiles of the given data set 0,2,4,6,8,0,2,4,6,8, we first organize the data in ascending order: 0, 0, 2, 2, 4, 4, 6, 6, 8, 8. With 10 data points, the median (or second quartile Q₂) will be the average of the 5th and 6th values, which are both 4, so Q₂ is 4.
To find the first quartile (Q₁), we take the median of the lower half of the data set. In this case, the lower half is 0, 0, 2, 2, 4, and since we have an even number of values, Q₁ will be the average of the 2nd and 3rd values, yielding 1 (since (0+2)/2=1). Similarly, the third quartile (Q₃) is the median of the upper half of the data set, which is 4, 6, 6, 8, 8. Thus, Q₃ is 6 (since (6+6)/2=6).
Therefore, the first quartile (Q₁) is 1, the second quartile (Q₂) is 4, and the third quartile (Q₃) is 6.