To find the quartiles and interquartile range, we first need to arrange the data in ascending order: 7, 8, 10, 12, 12, 14, 15, 15, 16, 19, 21, 23, 24.
Q1 represents the first quartile, which is the median of the lower half of the data. To find Q1, we need to find the median of the numbers below the median.
Lower half: 7, 8, 10, 12, 12, 14
The median of the lower half is (10 + 12) / 2 = 11.
Q1 = 11.
Q2 represents the second quartile, which is the median of the entire data set. In this case, the median is 15.
Q2 = 15.
Q3 represents the third quartile, which is the median of the upper half of the data. To find Q3, we need to find the median of the numbers above the median.
Upper half: 16, 19, 21, 23, 24
The median of the upper half is (21 + 23) / 2 = 22.
Q3 = 22.
To find the interquartile range, we subtract Q1 from Q3:
Interquartile Range = Q3 - Q1
= 22 - 11
= 11.
So, the quartiles are Q1 = 11, Q2 = 15, Q3 = 22, and the interquartile range is 11.
Let me know if there's anything else I can help with!
