Final answer:
To find the interquartile range of the given data, you need to first find the first quartile (Q1) and the third quartile (Q3). The IQR is the difference between Q3 and Q1.
Step-by-step explanation:
To find the interquartile range of the given data, we need to first find the first quartile (Q1) and the third quartile (Q3). The first quartile is the median of the lower half of the data, and the third quartile is the median of the upper half of the data.
1. Arrange the data in ascending order: {3, 12, 14, 22, 28, 38, 42, 56, 65, 70}
2. Find the median (Q2) of the entire data set. In this case, the median is the average of the two middle values, which are 28 and 38. So, Q2 = (28 + 38) / 2 = 33.
3. Find Q1, which is the median of the lower half of the data. The lower half is {3, 12, 14, 22, 28}. Since there are an even number of values, the median is the average of the two middle values, which are 12 and 14. So, Q1 = (12 + 14) / 2 = 13.
4. Find Q3, which is the median of the upper half of the data. The upper half is {38, 42, 56, 65, 70}. Since there are an odd number of values, the median is the middle value, which is 56.
5. The interquartile range (IQR) is the difference between Q3 and Q1. So, IQR = Q3 - Q1 = 56 - 13 = 43.